physics performance report for: panda strong interaction ... · fair/panda/physics book vii preface...

FAIR/PANDA/Physics Book i

Physics Performance Report for:

PANDA(AntiProton Annihilations at Darmstadt)

Strong Interaction Studies with Antiprotons

PANDA Collaboration

To study fundamental questions of hadron and nuclear physics in interactions of antiprotons with nucleonsand nuclei, the universal PANDA detector will be build. Gluonic excitations, the physics of strange andcharm quarks and nucleon structure studies will be performed with unprecedented accuracy therebyallowing high-precision tests of the strong interaction. The proposed PANDA detector is a state-of-the-art internal target detector at the HESR at FAIR allowing the detection and identification of neutral andcharged particles generated within the relevant angular and energy range.This report presents a summary of the physics accessible at PANDA and what performance can beexpected.

ii PANDA - Strong interaction studies with antiprotons

The PANDA Collaboration

Universitat Basel, SwitzerlandW. Erni, I. Keshelashvili, B. Krusche, M. Steinacher

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, ChinaY. Heng, Z. Liu, H. Liu, X. Shen, O. Wang, H. Xu

Ruhr-Universitat Bochum, Institut fur Experimentalphysik I, GermanyJ. Becker, F. Feldbauer, F.-H. Heinsius, T. Held, H. Koch, B. Kopf, C. Motzko, M. Pelizaus, B. Roth,

T. Schroder, M. Steinke, U. Wiedner, J. Zhong

Universita di Brescia, ItalyA. Bianconi

Institutul National de C&D pentru Fizica si Inginerie Nucleara ”Horia Hulubei”, Bukarest-Magurele,Romania

M. Bragadireanu, D. Pantea, A. Tudorache, V. Tudorache

Dipartimento di Fisica e Astronomia dell’Universita di Catania and INFN, Sezione di Catania, ItalyM. De Napoli, F. Giacoppo, G. Raciti, E. Rapisarda, C. Sfienti

IFJ, Institute of Nuclear Physics PAN, Cracow, PolandE. Bialkowski, A. Budzanowski, B. Czech, M. Kistryn, S. Kliczewski, A. Kozela, P. Kulessa, K. Pysz,

W. Schafer, R. Siudak, A. Szczurek

Institute of Applied Informatics, Cracow University of Technology, PolandW. Czyzycki, M. Domaga la, M. Hawryluk, E. Lisowski, F. Lisowski, L. Wojnar

Institute of Physics, Jagiellonian University, Cracow, PolandD. Gil, P. Hawranek, B. Kamys, St. Kistryn, K. Korcyl, W. Krzemien, A. Magiera, P. Moskal, Z. Rudy,

P. Salabura, J. Smyrski, A. Wronska

GSI Helmholtzzentrum fur Schwerionenforschung GmbH, Darmstadt, GermanyM. Al-Turany, I. Augustin, H. Deppe, H. Flemming, J. Gerl, K. Gotzen, R. Hohler, D. Lehmann,

B. Lewandowski, J. Luhning, F. Maas, D. Mishra, H. Orth, K. Peters, T. Saito, G. Schepers,C.J. Schmidt, L. Schmitt, C. Schwarz, B. Voss, P. Wieczorek, A. Wilms

Technische Universitat Dresden, GermanyK.-T. Brinkmann, H. Freiesleben, R. Jakel, R. Kliemt, T. Wurschig, H.-G. Zaunick

Veksler-Baldin Laboratory of High Energies (VBLHE), Joint Institute for Nuclear Research, Dubna,Russia

V.M. Abazov, G. Alexeev, A. Arefiev, V.I. Astakhov, M.Yu. Barabanov, B.V. Batyunya, Yu.I. Davydov,V.Kh. Dodokhov, A.A. Efremov, A.G. Fedunov, A.A. Feshchenko, A.S. Galoyan, S. Grigoryan,

A. Karmokov, E.K. Koshurnikov, V.Ch. Kudaev, V.I. Lobanov, Yu.Yu. Lobanov, A.F. Makarov,L.V. Malinina, V.L. Malyshev, G.A. Mustafaev, A. Olshevski, M.A.. Pasyuk, E.A. Perevalova,

A.A. Piskun, T.A. Pocheptsov, G. Pontecorvo, V.K. Rodionov, Yu.N. Rogov, R.A. Salmin,A.G. Samartsev, M.G. Sapozhnikov, A. Shabratova, G.S. Shabratova, A.N. Skachkova, N.B. Skachkov,E.A. Strokovsky, M.K. Suleimanov, R.Sh. Teshev, V.V. Tokmenin, V.V. Uzhinsky A.S. Vodopianov,

S.A. Zaporozhets, N.I. Zhuravlev, A.G. Zorin

University of Edinburgh, United KingdomD. Branford, K. Fohl, D. Glazier, D. Watts, P. Woods

Friedrich Alexander Universitat Erlangen-Nurnberg, GermanyW. Eyrich, A. Lehmann, A. Teufel

Northwestern University, Evanston, U.S.A.S. Dobbs, Z. Metreveli, K. Seth, B. Tann, A. Tomaradze

FAIR/PANDA/Physics Book iii

Universita di Ferrara and INFN, Sezione di Ferrara, ItalyD. Bettoni, V. Carassiti, A. Cecchi, P. Dalpiaz, E. Fioravanti, I. Garzia, M. Negrini, M. Savrie,

G. Stancari

INFN-Laboratori Nazionali di Frascati, ItalyB. Dulach, P. Gianotti, C. Guaraldo, V. Lucherini, E. Pace

INFN, Sezione di Genova, ItalyA. Bersani, M. Macri, M. Marinelli, R.F. Parodi

Justus Liebig-Universitat Gießen, II. Physikalisches Institut, GermanyI. Brodski, W. Doring, P. Drexler, M. Duren, Z. Gagyi-Palffy, A. Hayrapetyan, M. Kotulla, W. Kuhn,

S. Lange, M. Liu, V. Metag, M. Nanova, R. Novotny, C. Salz, J. Schneider, P. Schonmeier, R. Schubert,S. Spataro, H. Stenzel, C. Strackbein, M. Thiel, U. Thoring, S. Yang,

University of Glasgow, United KingdomT. Clarkson, E. Cowie, E. Downie, G. Hill, M. Hoek, D. Ireland, R. Kaiser, T. Keri, I. Lehmann,

K. Livingston, S. Lumsden, D. MacGregor, B. McKinnon, M. Murray, D. Protopopescu, G. Rosner,B. Seitz, G. Yang

Kernfysisch Versneller Instituut, University of Groningen, NetherlandsM. Babai, A.K. Biegun, A. Bubak, E. Guliyev, V.S. Jothi, M. Kavatsyuk, H. Lohner, J. Messchendorp,

H. Smit, J.C. van der Weele

Helsinki Institute of Physics, FinlandF. Garcia, D.-O. Riska

Forschungszentrum Julich, Julich Center for Hadron Physics, GermanyM. Buscher, R. Dosdall, R. Dzhygadlo, A. Gillitzer, D. Grunwald, V. Jha, G. Kemmerling, H. Kleines,

A. Lehrach, R. Maier, M. Mertens, H. Ohm, D. Prasuhn, T. Randriamalala, J. Ritman, M. Roder,T. Stockmanns, P. Wintz, P. Wustner

University of Silesia, Katowice, PolandJ. Kisiel

Chinese Academy of Science, Institute of Modern Physics, Lanzhou, ChinaS. Li, Z. Li, Z. Sun, H. Xu

Lunds Universitet, Department of Physics, Lund, SwedenS. Fissum, K. Hansen, L. Isaksson, M. Lundin, B. Schroder

Johannes Gutenberg-Universitat, Institut fur Kernphysik, Mainz, GermanyP. Achenbach, M.C. Mora Espi, J. Pochodzalla, S. Sanchez, A. Sanchez-Lorente

Research Institute for Nuclear Problems, Belarus State University, Minsk, BelarusV.I. Dormenev, A.A. Fedorov, M.V. Korzhik, O.V. Missevitch

Institute for Theoretical and Experimental Physics, Moscow, RussiaV. Balanutsa, V. Chernetsky, A. Demekhin, A. Dolgolenko, P. Fedorets, A. Gerasimov, V. Goryachev

Moscow Power Engineering Institute, RussiaA. Boukharov, O. Malyshev, I. Marishev, A. Semenov

Technische Universitat Munchen, GermanyC. Hoppner, B. Ketzer, I. Konorov, A. Mann, S. Neubert, S. Paul, Q. Weitzel

Westfalische Wilhelms-Universitat Munster, GermanyA. Khoukaz, T. Rausmann, A. Taschner, J. Wessels

IIT Bombay, Department of Physics, Mumbai, IndiaR. Varma

Budker Institute of Nuclear Physics, Novosibirsk, RussiaE. Baldin, K. Kotov, S. Peleganchuk, Yu. Tikhonov

Institut de Physique Nucleaire, Orsay, FranceJ. Boucher, T. Hennino, R. Kunne, D. Marchand, S. Ong, J. Pouthas, B. Ramstein, P. Rosier,

iv PANDA - Strong interaction studies with antiprotons

M. Sudol, E. Tomasi-Gustafsson, J. Van de Wiele, T. Zerguerras

Warsaw University of Technology, Institute of Atomic Energy, Otwock-Swierk, PolandK. Dmowski, R. Korzeniewski, D. Przemyslaw, B. Slowinski

Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, INFN, Sezione di Pavia, ItalyG. Boca, A. Braghieri, S. Costanza, A. Fontana, P. Genova, L. Lavezzi, P. Montagna, A. Rotondi

Institute for High Energy Physics, Protvino, RussiaN.I. Belikov, A.M. Davidenko, A.A. Derevschikov, Y.M. Goncharenko, V.N. Grishin, V.A. Kachanov,D.A. Konstantinov, V.A. Kormilitsin, V.I. Kravtsov, Y.A. Matulenko, Y.M. Melnik A.P. Meschanin,

N.G. Minaev, V.V. Mochalov, D.A. Morozov, L.V. Nogach, S.B. Nurushev, A.V. Ryazantsev,P.A. Semenov, L.F. Soloviev, A.V. Uzunian, A.N. Vasiliev, A.E. Yakutin

Kungliga Tekniska Hogskolan, Stockholm, SwedenT. Back, B. Cederwall

Stockholms Universitet, Stockholm, SwedenC. Bargholtz, L. Geren, P.E. Tegner

Petersburg Nuclear Physics Institute of Academy of Science, Gatchina, St. Petersburg, RussiaS. Belostotski, G. Gavrilov, A. Itzotov, A. Kisselev, P. Kravchenko, S. Manaenkov, O. Miklukho,

Y. Naryshkin, D. Veretennikov, V. Vikhrov, A. Zhadanov

Universita del Piemonte Orientale Alessandria and INFN, Sezione di Torino, ItalyL. Fava, D. Panzieri

Universita di Torino and INFN, Sezione di Torino, ItalyD. Alberto, A. Amoroso, E. Botta, T. Bressani, S. Bufalino, M.P. Bussa, L. Busso, F. De Mori,

M. Destefanis, L. Ferrero, A. Grasso, M. Greco, T. Kugathasan, M. Maggiora, S. Marcello, G. Serbanut,S. Sosio

INFN, Sezione di Torino, ItalyR. Bertini, D. Calvo, S. Coli, P. De Remigis, A. Feliciello, A. Filippi, G. Giraudo, G. Mazza, A. Rivetti,

K. Szymanska, F. Tosello, R. Wheadon

INAF-IFSI and INFN, Sezione di Torino, ItalyO. Morra

Politecnico di Torino and INFN, Sezione di Torino, ItalyM. Agnello, F. Iazzi, K. Szymanska

Universita di Trieste and INFN, Sezione di Trieste, ItalyR. Birsa, F. Bradamante, A. Bressan, A. Martin

Universitat Tubingen, GermanyH. Clement

The Svedberg Laboratory, Uppsala, SwedenC. Ekstrom

Uppsala University, Department of Physics and Astronomy, SwedenH. Calen, S. Grape, B. Hoistad, T. Johansson, A. Kupsc, P. Marciniewski, E. Thome, J. Zlomanczuk

Universitat de Valencia, Dpto. de Fısica Atomica, Molecular y Nuclear, SpainJ. Dıaz, A. Ortiz

Soltan Institute for Nuclear Studies, Warsaw, PolandS. Borsuk, A. Chlopik, Z. Guzik, J. Kopec, T. Kozlowski, D. Melnychuk, M. Plominski, J. Szewinski,

K. Traczyk, B. Zwieglinski

Osterreichische Akademie der Wissenschaften, Stefan Meyer Institut fur Subatomare Physik, Vienna,Austria

P. Buhler, M. Cargnelli, A. Gruber, P. Kienle, J. Marton, K. Nikolics, E. Widmann, J. Zmeskal

FAIR/PANDA/Physics Book v

AND

GSI Helmholtzzentrum fur Schwerionenforschung GmbH, Darmstadt, GermanyM.F.M. Lutz

CPhT, Ecole Polytechnique, CNRS, Palaiseau, FranceB. Pire

Kernfysisch Versneller Instituut, University of Groningen, NetherlandsO. Scholten, R. Timmermans

Editors: Diego Bettoni (chief editor) Email: [email protected] Timmermans (chief editor) Email: [email protected] Pia Bussa Email: [email protected] Dueren Email: [email protected] Feliciello Email: [email protected] Gillitzer Email: [email protected] Iazzi Email: [email protected] Johansson Email: [email protected] Kopf Email: [email protected] Lehrach Email: [email protected] F.M. Lutz Email: [email protected] Maas Email: [email protected] Maggiora Email: [email protected] Negrini Email: [email protected] Peters Email: [email protected] Pochodzalla Email: [email protected] Schmitt Email: [email protected] Scholten Email: [email protected] Stancari Email: [email protected]

Spokesperson: Ulrich Wiedner Email: [email protected]: Paola Gianotti Email: [email protected]

vi PANDA - Strong interaction studies with antiprotons

FAIR/PANDA/Physics Book vii

Preface

PANDA is one of the major projects of the FAIR-Facility in Darmstadt. FAIR is an extension of theexisting Heavy Ion Research Lab (GSI) and is expected to start its operation in 2014. PANDA studiesinteractions between antiprotons and fixed target protons and nuclei in the momentum range of 1.5-15 GeV/c using the high energy storage ring HESR. The antiproton project was initiated by a largecommunity of scientists outside GSI, who had worked very successfully with antiprotons at LEAR/CERNand the Fermilab antiproton accumulator. Many of the physics ideas of PANDA were already describedin a Letter of Intent (Construction of a GLUE/CHARM-Factory at GSI, Ruhr-University Bochum, 1999)and were extended afterwards in the FAIR Conceptual Design Report (GSI, 2001), the Technical ProgressReport (FAIR, 2005) and further PANDA specific reports. After the approval of FAIR further projectsinvolving antiprotons were proposed (experiments with low energy and polarized antiprotons) which arenow in the preparatory phase.

The PANDA scientific program includes several measurements, which address fundamental questions ofQCD, mostly in the non-perturbative regime:

• Hadron spectroscopy up to the region of charm quarks. Here the search for exotic states like glueballs,hybrids and multiquark states in the light quark domain and in the hidden and open charm regionis in the focus of interest. The recently found XYZ states will be further explored.

• Study of properties of hadrons inside nuclear matter. Mass and width modifications have beenreported and will be investigated also in the charm region.

• Study of nonperturbative dynamics, also including spin degrees of freedom.

• Antiproton induced reactions are a very effective tool to implant strange baryons in nuclei. PANDAwill particularly study double Λ hypernuclei, which are of great importance for nuclear structurestudies and the ΛΛ interaction.

• Hard exclusive antiproton-proton reactions can be used to study the structure of nucleons (time-likeform factors) and the relevance of certain models, like the Hand Bag approach. Interesting aspectsof Transverse Parton Distributions will be studied in Drell-Yan production.

• In a later stage of the project, when all systematic effects are well studied, also contributions toelectroweak physics can be expected, like direct CP violation in hyperon decays and CP violationand mixing in the charm sector.

All measurements will profit from the high yield of antiproton induced reactions and from the factthat, in contrast to e+e− reactions, all non-exotic quantum number combinations for directly formedstates are allowed, whereas states with exotic quantum numbers can be observed in production. Theachievable precision, as far mass and width measurements are concerned, is very high as was successfullydemonstrated by the Fermilab experiments. It is independent of the mass resolution of the detector andonly limited by the tiny energy spread of the primary cooled antiproton beam. It will allow a measurementof the widths of the recently discovered very narrow states. The international PANDA collaboration wasestablished in 2002. More than 400 scientists from 16 countries and 53 institutions are involved in R&Dhardware and software projects. The most recent achievement is the definition of the final setup of theelectromagnetic calorimeter. The delivery of a first tranche of PWO crystals for the calorimeter hasalready started. An overview of all studies and results achieved in the last years can be found on thePANDA Web site (http://www-panda.gsi.de/auto/ home.htm).

viii PANDA - Strong interaction studies with antiprotons

This PANDA Physics Book describes in detail the physics topics envisioned. The first chapter gives acomprehensive overview of the challenges of QCD; the PANDA detector and the high energy storage ringHESR are described in detail in chapter 2; in chapter 3 the status of the software is discussed. Chapter4 shows very detailed simulations of selected benchmark reactions. They take into account the eventgeneration, digitization, reconstruction, event selection and background estimations. A refinement ofthe analysis is achieved by using kinematical fitting and neural network tools. A summary and outlookconcludes the Physics Book. The setup used in the simulations described in this book is not final: somedetector components are still undergoing R&D and will be finalised in the coming months. At the sametime a new software framework is being developed. In the next two years we also expect advances inbackground simulations and better estimates of presently unknown cross-sections. A new version of thephysics book is planned, which will reflect the progress described above and which will feature a morecomplete list of benchmark channels.

FAIR/PANDA/Physics Book ix

The use of registered names, trademarks, etc. in this publicationdoes not imply, even in the absence of specific statement, thatsuch names are exempt from the relevant laws and regulationsand therefore free for general use.

x PANDA - Strong interaction studies with antiprotons

xi

Contents

Preface vii

1 Introduction 1

1.1 The Challenge of QCD . . . . . . . . 1

1.1.1 Quantum Chromodynamics . . . . 1

1.1.2 The QCD Coupling Constant . . 2

1.1.3 The Symmetries of QCD . . . . . 2

1.1.4 Theoretical Approaches to non-Perturbative QCD . . . . . . . . . 3

1.2 Lattice QCD: Status and Prospects . 3

1.3 EFT with Quark and Gluon Degreesof Freedom . . . . . . . . . . . . . . . 5

1.3.1 Non-Relativistic QCD . . . . . . . 6

1.4 EFT with Hadronic Degrees of Freedom 7

1.4.1 Chiral Symmetry and OpenCharm Meson Systems . . . . . . 7

1.4.2 Phenomenology of Open CharmBaryon Systems . . . . . . . . . . 9

References . . . . . . . . . . . . . . . . . . . 10

2 Experimental Setup 13

2.1 Overview . . . . . . . . . . . . . . . . 13

2.2 The PANDA Detector . . . . . . . . . 13

2.2.1 Target Spectrometer . . . . . . . 13

2.2.2 Forward Spectrometer . . . . . . . 21

2.2.3 Luminosity Monitor . . . . . . . . 23

2.2.4 Data Acquisition . . . . . . . . . . 24

2.2.5 Infrastructure . . . . . . . . . . . 25

2.3 The HESR . . . . . . . . . . . . . . . 27

2.3.1 Introduction . . . . . . . . . . . . 27

2.3.2 Beam Equilibria and LuminosityEstimates . . . . . . . . . . . . . . 27

2.4 Precision Measurements of Reso-nance Parameters . . . . . . . . . . . 31

2.4.1 Experimental Technique . . . . . 31

2.4.2 Mass Measurements . . . . . . . . 33

2.4.3 Total and Partial Widths . . . . . 34

2.4.4 Line Shapes . . . . . . . . . . . . 35

2.4.5 Achievable Precision . . . . . . . . 36

References . . . . . . . . . . . . . . . . . . . 36

3 Software 39

3.1 Event Generation . . . . . . . . . . . 39

3.1.1 EvtGen Generator . . . . . . . . . 39

3.1.2 Dual Parton Model . . . . . . . . 39

3.1.3 UrQMD . . . . . . . . . . . . . . 41

3.2 Particle Tracking and Detector Sim-ulation . . . . . . . . . . . . . . . . . 43

3.2.1 Detector Setup . . . . . . . . . . . 43

3.2.2 Digitization . . . . . . . . . . . . 43

3.3 Reconstruction . . . . . . . . . . . . . 45

3.3.1 Charged Particle Track Recon-struction . . . . . . . . . . . . . . 45

3.3.2 Photon Reconstruction . . . . . . 47

3.3.3 Charged Particle Identification . . 49

3.4 Physics Analysis . . . . . . . . . . . . 55

3.4.1 Analysis Tools . . . . . . . . . . . 56

3.5 Data Production . . . . . . . . . . . . 56

3.5.1 Bookkeeping . . . . . . . . . . . . 56

3.5.2 Event Production . . . . . . . . . 56

3.5.3 Filter on Generator Level . . . . . 57

3.6 Software Developments . . . . . . . . 58

References . . . . . . . . . . . . . . . . . . . 60

4 Physics Performance 63

4.1 Overview . . . . . . . . . . . . . . . . 63

4.2 QCD Bound States . . . . . . . . . . 64

4.2.1 The QCD Spectrum . . . . . . . . 64

4.2.2 Charmonium . . . . . . . . . . . . 64

4.2.3 Exotic Excitations . . . . . . . . . 86

4.2.4 Heavy-Light Systems . . . . . . . 103

4.2.5 Strange and Charmed Baryons . . 112

4.3 Non-perturbative QCD Dynamics . . 117

4.3.1 Previous Experiments . . . . . . . 117

4.3.2 Experimental Aims . . . . . . . . 118

4.3.3 Reconstruction of the pp → Y YReaction . . . . . . . . . . . . . . 118

4.3.4 Two-Meson Production in pp -Annihilation at Large Angle . . . 127

4.4 Hadrons in the Nuclear Medium . . . 129

xii PANDA - Strong interaction studies with antiprotons

4.4.1 In-Medium Properties ofCharmed Hadrons . . . . . . . . . 129

4.4.2 Charmonium Dissociation . . . . 130

4.4.3 J/ψ N Dissociation Cross Sectionin pA Collisions . . . . . . . . . . 131

4.4.4 Antibaryons and Antikaons Pro-duced in pA Collisions . . . . . . 135

4.4.5 Colour Transparency . . . . . . . 136

4.5 Hypernuclear Physics . . . . . . . . . 139

4.5.1 Physics Goals . . . . . . . . . . . 139

4.5.2 Experimental Integration andSimulation . . . . . . . . . . . . . 141

4.6 The Structure of the Nucleon UsingElectromagnetic Processes . . . . . . 148

4.6.1 Partonic Picture of Hard Exclu-sive pp-Annihilation Processes . . 148

4.6.2 Transverse Parton DistributionFunctions in Drell-Yan Production 153

4.6.3 Electromagnetic Form Factors inthe Time-like Region . . . . . . . 165

4.7 Electroweak Physics . . . . . . . . . . 176

4.7.1 CP-Violation and Mixing in theCharm-Sector . . . . . . . . . . . 176

4.7.2 CP-Violation in Hyperon Decays . 176

4.7.3 Rare Decays . . . . . . . . . . . . 176

References . . . . . . . . . . . . . . . . . . . 177

5 Summary and Outlook 191

Acknowledgements 193

List of Acronyms 195

List of Figures 197

List of Tables 203

1

1 Introduction

1.1 The Challenge of QCD

The modern theory of the strong interactions isQuantum Chromodynamics (QCD), the quantumfield theory of quarks and gluons based on thenon-abelian gauge group SU(3). Together with theSU(2)×U(1) electroweak theory, QCD is part of theStandard Model of particle physics. QCD is welltested at high energies, where the strong couplingconstant becomes small and perturbation theoryapplies. In the low-energy regime, however, QCDbecomes a strongly-coupled theory, many aspectsof which are not understood. The thriving ques-tions are: How can we bring order into the richphenomena of low energy QCD? Are there effectivedegrees of freedom in terms of which we can un-derstand the resonances and bound states of QCDefficiently and systematically? Does QCD generateexotic structures so far undiscovered? PANDA willbe in a unique position to provide answers to suchimportant questions about non-perturbative QCD.A major part of the physics programme of PANDAis designed to collect high-quality data that allowa clean interpretation in terms of the predictions ofnon-perturbative QCD. In this introductory chap-ter, we first summarize the basics of QCD and thenreview the theoretical approaches that can be jus-tified rigorously within QCD and provide testablepredictions for experiments like PANDA.

1.1.1 Quantum Chromodynamics

The development of QCD as the theory of strong in-teractions is a success story. Its quantitative predic-tions at high energies, in the perturbative regime,are such that it is beyond serious doubt that QCD isthe correct theory of the strong interactions. Never-theless, in the non-perturbative low-energy regime,it remains very hard to make quantitative predic-tions starting from first principles, i.e. from theQCD Lagrangian. Conceptually, QCD is simple:it is a relativistic quantum field theory of quarksand gluons interacting according to the laws of non-abelian forces between colour charges. The startingpoint of all considerations is the celebrated QCDLagrangian density:

LQCD = −14Gµνa Gaµν

+∑f

qf [i γµDµ −mf ] qf , (1.1)

where

Gµνa = ∂µAνa − ∂νAµa + g f bca Aµb A

νc , (1.2)

is the gluon field strength tensor, and

Dµ = ∂µ − i g2Aµa λ

a , (1.3)

the gauge covariant derivative involving the gluonfield Aµa ; g is the strong coupling constant, αS =g2/4π; f denotes the quark flavour, where forthe energy regime of PANDA, the relevant quarkflavours are u, d, s, c: up, down, strange, andcharm. We take ~ = 1 = c.

This deceptively simple looking QCD Lagrangianis at the basis of the rich and complex phenomenaof nuclear and hadronic physics. How this com-plexity arises in a theory with quarks and gluonsas fundamental degrees of freedom is only qualita-tively understood. The QCD field equations arenon-linear, since the gluons that mediate the in-teraction carry colour charge, and hence interactamong themselves. This makes every strongly-interacting system intrinsically a many-body prob-lem, wherein apart from the valence quarks manyquark-antiquark pairs and many gluons are alwaysinvolved. These non-abelian features of QCD arebelieved to lead to the phenomenon that the ba-sic degrees of freedom, the quarks and the gluons,cannot be observed in the QCD spectrum: the con-finement of colour charge is the reason behind thecomplex world of nuclear and hadronic physics.

The process of renormalization in quantum fieldtheory generates an intrinsic QCD scale ΛQCDthrough the mechanism of dimensional transmuta-tion; ΛQCD is, loosely speaking, the scale belowwhich the coupling constant becomes so large thatstandard perturbation theory no longer applies. Allhadron masses are in principle calculable withinQCD in terms of ΛQCD. This dynamical genera-tion of the mass scale of the strong interactions isthe famous QCD gap phenomenon: the proton massis non-zero because of the energy of the confinedquarks and gluons. Although a mathematical proofof colour confinement is lacking, qualitatively this isthought to be linked to the fact that the quark andgluon bilinears qaqa and GaµνG

µνa acquire non-zero

vacuum expectation values.

Now, some 35 years after the discovery of QCD,it is fair to say that strong interactions are under-stood in principle, but a long list of unresolved ques-tions about low-energy QCD remains. Our present

2 PANDA - Strong interaction studies with antiprotons

understanding of QCD thereby serves as the ba-sis to set priorities for theoretical and experimen-tal research. Clearly, not all phenomena in nuclearphysics need to be understood in detail from QCD.Many areas of nuclear physics will be happily de-scribed in terms of well-established phenomenologywith its own degrees of freedom, just like many com-plex phenomena in atomic physics and chemistrydo not have to be understood directly in terms ofQED. Likewise, while not all experiments in nuclearand hadronic physics should be guided by QCD,dedicated experiments that test QCD in the non-perturbative regime and to improve our limited un-derstanding of these aspects of QCD are crucial. Inits choice of topics, the PANDA physics programmeaims to achieve precisely this.

1.1.2 The QCD Coupling Constant

The qualitative understanding of QCD as outlinedabove is to a large extent based on the classicalcalculation of the renormalization scale dependenceof the QCD coupling constant αS as given by theβ-function at an energy scale µ,

β(αS) ≡ µ

2∂αS∂µ

= −β0

4πα2S −

β1

8π2α3S − . . . (1.4)

where

β0 = 11− 23nf , (1.5)

β1 = 51− 193nf , (1.6)

where nf is the number of quarks with mass lessthan µ; expressions for β2 and β3 exist. In solv-ing this differential equation for αS(µ), one intro-duces the scale Λ to provide the µ dependence ofαS . The solution then demonstrates the famousproperties of asymptotic freedom, αS → 0 whenµ → ∞, and of strong coupling at scales belowµ ∼ Λ. Based on this result for the scale de-pendence of the QCD coupling constant, one mayroughly divide the field of strong interaction physicsinto the areas of perturbative QCD (pQCD) and ofnon-perturbative QCD. QCD has been very success-ful in quantitatively describing phenomena whereperturbation theory with its standard machineryof Feynman rules applies. An important exampleis e+e− annihilation in the area of the Z0 boson,where the multi-particle hadronic final-state systemreveals the perturbative QCD physics in the formof the quark and gluon jets. In this perturbativeregime predictions can be made on the basis of themagnitude of the QCD coupling constant. Its value

Figure 1.1: The running of the strong coupling con-stant as function of the scale µ [1].

as a function of energy determines a host of phe-nomena, such as scaling violations in deep inelasticscattering, the τ lifetime, high-energy hadron col-lisions, heavy-quarkonium (in particular bottomo-nium) decay, e+e− collisions, and jet rates in epcollisions. The coupling constants derived fromthese processes are consistent and lead to an av-erage value [1]

αS(MZ) = 0.1176± 0.0002 . (1.7)

The non-perturbative regime is the area of strongnuclear forces and hadronic resonances, which isquantitatively much less well understood and whereimportant questions still have to be addressed. Inbetween are areas like deep inelastic lepton-hadronscattering where perturbation theory is used, how-ever, with non-perturbative input.

1.1.3 The Symmetries of QCD

It has been said that QCD is a most elegant the-ory in physics, since its structure is solely deter-mined by symmetry principles: QCD is the mostgeneral renormalisable quantum field theory basedon the gauge group SU(3). In addition to exactLorentz invariance and SU(3) colour gauge invari-ance, it has several other important symmetry prop-erties. The QCD Lagrangian as given above has anumber of “accidental” symmetries, i.e. symme-tries that are an automatic consequence of the as-sumed gauge invariance. The discrete symmetriesparity and charge conjugation are such accidentalsymmetries (we ignore here the mysterious θ-term

FAIR/PANDA/Physics Book 3

that results in the still unsolved strong CP-problemof QCD). Flavour conservation is another: the num-ber of quarks (minus antiquarks) of each flavour(e.g. strangeness) is conserved, corresponding to anautomatic invariance of the QCD Lagrangian underphase rotations of the quark fields of each flavourseparately.

Additional symmetries result from the considera-tion that the masses of the up, down, and strangequarks can be considered small compared to thetypical hadronic scale ΛQCD. To the extent thatthese masses can be ignored, the QCD Lagrangianis invariant under unitary transformations of thequark fields of the form q′i = Uij qj . This ac-counts for the rather accurate SU(2)-isospin andthe approximate SU(3)-flavour symmetries of nu-clear and hadronic physics. Moreover, when theu, d, and s masses can be ignored, QCD is invari-ant under separate unitary transformations amongthe left- and right-handed quarks, qL′i = ULij q

Lj

and qR′i = URij qRj , resulting in the chiral symme-

try group U(3)L×U(3)R. The diagonal subgroup(UL = UR) corresponds to the SU(3)-flavour (andbaryon number) symmetry mentioned. The remain-ing chiral SU(3) symmetry (U−1

L = UR) is believedto be spontaneously broken by the vacuum stateof QCD, resulting in the existence of an octet ofGoldstone bosons identified with the pseudoscalarmesons π, K, η.

These approximate flavour and chiral symmetriesdue to the smallness of the u, d, and s quark masses,are important, since they can be exploited to for-mulate effective field theories that are equivalent toQCD in a certain energy range. A classic exampleis chiral perturbation theory for the interaction ofbaryons with the octet of the pseudoscalar mesons,which results in an expansion of matrix elements interms of small momenta or light-quark masses [2].On similar footing is heavy-quark effective theory(HQET) for hadrons containing a quark (c, b, t)with mass mQ ΛQCD. In the limit mQ → ∞,the heavy quark becomes on-shell and the dynam-ics becomes independent of its mass. The hadronicmatrix elements can be expanded as a power seriesin 1/mQ, resulting in symmetry relations betweenvarious matrix elements [3].

Generalizing QCD to an SU(Nc) gauge theory, theinverse of the number of colours, 1/Nc, is a hid-den expansion parameter [4]. This theory, whereinthe coupling is decreased such that g2Nc is con-stant, is “large-Nc QCD”. Diagrammatic consid-erations suggest that large-Nc QCD is a weakly-coupled theory of mesons and baryons, whereinbaryons are heavy semiclassical objects. Signifi-

cant, mostly qualitative, insight into QCD can beobtained from considering the large-Nc limit, espe-cially when combined with the techniques of effec-tive field theory.

1.1.4 Theoretical Approaches tonon-Perturbative QCD

In this brief introduction, we focus on theoreti-cal frameworks that have a rigorous justification inQCD and that, with allowance for further progressin the coming years and with a reasonable extrapo-lation of available computing resources, can be ex-pected to provide a direct confrontation of the datafrom experiments like PANDA with the predictionsof non-perturbative QCD. Among these theoreticalapproaches the best established are (i) lattice QCD,which attempts a direct attack to solve QCD non-perturbatively by numerical simulation, and (ii) ef-fective field theories, which exploit the symmetriesof QCD and the existence of hierarchies of scales toprovide predictions from effective Lagrangians thatare equivalent to QCD; among the latter we distin-guish systematic effective field theories formulatedin terms of quark-gluon and in terms of hadronicdegrees of freedom.

It should be kept in mind that the theoretical ap-proaches will, in many cases, calculate quantitiesthat require an additional step to be compared withmeasured data. This is because a full computa-tion of the cross section as measured by experi-mentalists in antiproton-proton collisions demandssignificantly more effort. Such an additional stepmay involve a partial-wave analysis of the measureddata, in order to, for instance determine the quan-tum numbers of a resonance. Effective field theorywith hadronic degrees of freedom offers some ad-vantages in this respect. In the case of PANDA, anexample is the associated production of hyperon-antihyperon pairs in the reactions pp→ Y Y , wherethe spin observables in the final state can be pre-cisely measured [5]. Therefore, the possibility existsin this case to perform a full partial-wave analysisof the data to study in detail the contribution ofresonances.

1.2 Lattice QCD: Status andProspects

Lattice QCD (LQCD) is an ab initio approach todeal with QCD in the non-perturbative low-energyregime. The equations of motion of QCD are dis-


Figure 1.2: On the left the quenched calculations areshown, on the right the corresponding unquenched ones.While the former exhibit systematic deviations of some10 % from experiment, the latter are in impressive agree-ment with experiment.

cretised on a 4-dimensional space-time lattice andsolved by large-scale numerical simulations on bigcomputers. For numerical reasons the QCD actionis Wick rotated into Euclidean space-time. The lat-tice spacing, a, acts as the ultraviolet regulator ofthe theory. By letting a → 0, the regulator is re-moved and continuum results are obtained. LQCD(originally proposed by Wilson in 1974) has madeenormous progress over the last decades. In thepast, the accuracy of LQCD results were limitedby the use of the “quenched approximation” (i.e.the neglect of sea quarks), by unrealistic heavy upand down quarks, and by the use of only two in-stead of three light quark flavours. These deviationsfrom “real QCD” were partly mandated by the lim-ited availability of CPU-time. In recent years, allthese limiting aspects (finite volume effects, latticeartefacts, unrealistic quark masses, exclusion of seaquarks) are being improved upon gradually. Thus,there is every reason to expect that progress inLQCD will continue in the future, to the extent thatprecise LQCD predictions will be available when thePANDA experiment starts.

In LQCD, the SU(3) group elements Ux,µ are 3×3matrices defined on the links that connect theneighbouring sites x and x + aµ on the lattice.Traces of products of such matrices along closedpaths, so-called Wilson loops, are gauge invariant.The elementary building block is the “plaquette,”the 1×1 lattice square. The simplest discretisedaction is then the Wilson action, which is propor-tional to the (gauge-invariant) trace of the sum over

all plaquettes,

SW = − 6g2

Re∑x,µ>ν

Tr Πx,µ,ν , (1.8)

where Πx,µν = Ux,µ Ux+aµ,ν U†x+aν,µ U

†x,ν . In the

continuum limit, this action agrees with the (Yang-Mills part of the) QCD action (in 4D Euclideanspace) to order O(a2),

SYM = − 14 g2

∫d4xGµνa (x)Gaµν(x)

= SW + constant +O(a2) . (1.9)

The simplest discretised version for the fermionicquark part of the QCD action reads

Sf =∑x

(12γµ ψx

[Ux+aµ,µ ψx+aµ

−U†x−aµ,µ ψx−aµ]

+maψx ψx

),(1.10)

which again corresponds to the continuum action upto order O(a2) terms. A major part of the progressin LQCD has consisted in developing improved ver-sions of these naive discretised actions for the gluonand the quark fields, for instance to remove theorder O(a2) artefacts when taking the continuumlimit. Improved fermionic actions have been de-veloped for instance to implement an exact chiralsymmetry on the lattice that in the continuum limitcorresponds to the usual continuum chiral symme-try.

In LQCD the expectation values of n-point Greenfunctions are calculated in the path integral sense,by evaluating their averages over all possible gaugefield configurations on the lattice, weighted withthe exponent of the action. For instance, for ahadron mass a zero-momentum two-point Greenfunction with the desired quantum numbers is cal-culated that creates the hadron at Euclidean timezero and annihilates it at time t. For large t, thisquantity will decay as exp(−mt), from which themass can be extracted. In such a LQCD calcula-tion it is the production of the gauge-field config-urations that consumes the bulk of the CPU-time,especially in (“unquenched”) calculations that in-clude sea quarks.

Many impressive results have been obtained forhadron spectroscopy within LQCD. As an exam-ple of great relevance to the PANDA programme,we discuss briefly (quenched) lattice calculations forthe glueball spectrum. One first chooses an interpo-lating operator for a glueball with specific quantumnumbers, e.g. for a scalar glueball one can take

O(~x, t) =∑

i<j=x,y,z

Re TrUij(~x) , (1.11)


where Uij is the plaquette in the ij-plane. The glue-ball masses are then obtained from the asymptoticbehaviour of the time correlator

C(t) =∑x,x′,t

〈O(~x, t)O†(~x′, 0)〉

=∑i

|〈0|O|i〉|2 exp(−mi t) . (1.12)

However, because the scalar glueball has vacuumquantum numbers, it provides from the simulationpoint of view a particular “noisy” signal. The massmust be obtained from a fit to a function of thetype C(t) ' C0 +C1 exp(−mt). Special techniqueshave been developed to improve the signal-to-noisequality of the glueball signal on the lattice. Forinstance, one can use an anisotropic lattice with asmaller lattice spacing in the temporal direction.The glueball spectrum obtained in this manner [6]is shown in Fig. 1.3.

While this LQCD result for the glueball spectrumis already very impressive, further improvement isclearly needed in order to compare ultimately tospectroscopic results obtained from a partial-waveanalysis of the experimental data. The glueballsfrom a quenched calculations, for instance, decayonly to lighter glueballs and the η′ meson. More-over, significant limitations will have to be over-come for LQCD to become as predictive for dy-namical (scattering) observables as it is for spec-troscopy. Lattice QCD applications in the charmsector constitute an important test for applicationsto hadronic corrections required in B physics.

Figure 1.3: The LQCD glueball spectrum in pureSU(3) gauge theory [6].

From lattice calculation of various quantities theQCD coupling constant can be determined. For in-stance, from the bottomonium spectrum, the valueαS(MZ) = 0.1170± 0.0012 was extracted. Also therunning of αS was studied and the results are ingood agreement with the two-loop result calculatedwithin pQCD.

An area that so far has proven challenging forLQCD, but where it is foreseeable that significantprogress will be made in the coming years, is the(ground-state) structure of the nucleon. The nu-cleon electromagnetic form factors, measured withincreasing precision in electron scattering, are clas-sical observables in this respect, but recent surpris-ing results obtained at JLAB demonstrate that ourunderstanding is far from complete. The protoncharge form factor falls off more rapidly than thestandard dipole form supported by pQCD, and alsothe neutron data are not consistent with pQCD.LQCD results are becoming more accurate, but atpresent only the space-like region, in a limited q2-range, can be handled. Significant progress hasbeen achieved in recent years by applying disper-sion relation techniques to relate the space-like andthe time-like regime [7]. The latter can be ad-dressed by PANDA in a wide q2-range via the re-action pp→ e+e−.

Certain hard exclusive processes in electron scatter-ing have offered more detailed probes of the tran-sition from the non-perturbative to the perturba-tive regime in QCD. The success of the theoreti-cal framework of generalized parton distributions(GPDs) to describe the “soft” part of deeply vir-tual Compton scattering is a case in point. WithPANDA the opportunity exists to measure the time-like counterparts of such processes, viz. antiproton-proton annihilation with crossed kinematics, as inpp → γγ. A framework analogous to the GPDsfor the space-like case has been developed: the am-plitudes that encode the soft part of these anni-hilation reactions are the generalized distributionamplitudes (GDAs). The theoretical descriptionwithin QCD of such time-like dynamical processesneeds to be developed.

1.3 EFT with Quark and GluonDegrees of Freedom

Ab initio calculations from QCD, be it pQCD orLQCD, are and will remain very difficult, especiallyin situations where several dynamical scales are in-volved. Effective field theory (EFT) techniques inmany such cases can provide a solution. For in-


stance, LQCD is particularly powerful when it iscombined with EFT. A variety of EFTs with quarkand gluon degrees of freedom have been developedin recent years. Exploiting a scale separation a sim-pler theory is obtained that is equivalent to fullQCD in the energy region considered. The degreesof freedom above a chosen energy scale are inte-grated out (in a path-integral sense) and the re-sulting field theory is organized as a power seriesof operators containing the low-energy degrees offreedom over the heavy scales. The high-energyphysics is encoded in the coupling constants mul-tiplying these operators, which are calculated by“matching” selected observables in the EFT and infull QCD. In the process, the symmetries of QCDneed to be obeyed.

1.3.1 Non-Relativistic QCD

Applications of QCD to systems involving charm,beauty or top quarks, can be simplified significantlyby the use of effective field theory methods. It isnot always necessary to solve the dynamics of suchsystems based on the QCD Lagrangian (Eq. 1.1)directly. One may integrate out fast modes of theheavy quarks by a systematic non-relativistic ex-pansion [8]. The role of the four-component Diracspinor fields qf is taken over by two-componentPauli spinor fields ψf and χf describing heavyquarks and antiquarks. For the purpose of charmphysics as studied with PANDA at FAIR it is usefulto integrate out the b and t quarks and keep u, d,s, and c quarks as active degrees of freedom only.The resulting effective Lagrangian of QCD reads

LeffQCD = −1

4Gµνa Gµν

+∑

f=u,d,s

qf [i γµDµ −mf ] qf

+ψ†[iD0 +

12mc

D2

]ψ

+χ†[iD0 −

12mc

D2

]χ+

∞∑n=0

Ln,(1.13)

where the non-trivial terms Ln are expanded in in-verse powers of the charm-quark mass. The index ndenotes the number of heavy-quark and antiquarkfields involved. Terms with n ≥ 4 arise only if partof the gluon dynamics is integrated out, as will bediscussed below. For a given heavy-quark species

we illustrate the form of typical one-body terms,

L2 =c1

8m3f

(ψ†(D2)2ψ − χ†(D2)2χ

)+

c28m2

f

(ψ†(D · gE− gE ·D)ψ

+χ†(D · gE− gE ·D)χ)

+c3

8m2f

(ψ†(iD× gE− gE× iD) · σ ψ

+χ†(iD× gE− gE× iD) · σ χ)

+c4

2mf

(ψ†(gB · σ)ψ − χ†(gB · σ)χ

)+ . . . , (1.14)

where Ei = G0i and Bi = 12εijkG

jk are theelectric and magnetic components of the gluonfield strength tensor Gµν . The coefficients ci in(Eq. 1.14) are calculable in perturbation theorywith ci = 1 +O (αs). The relevance of the variousterms in (Eq. 1.14) is predicted by power-countingrules [8].

The characteristic quantity that controls the rela-tive importance of the infinite number of terms inLn is the typical velocity v of the heavy quark. Byassumption it must hold v 1, as to justify theuse of the non-relativistic fields in (Eq. 1.13). Theprecise realization of the power-counting rules de-pends on the system, whether for instance heavy-light or heavy-heavy systems are studied. We focuson heavy-quarkonium systems [9] for which the twoterms D0 and D2/(2mf ) in (Eq. 1.13) are of equalimportance. This is reflected in the counting ruleswith D0 ∼ mf v

2 and D ∼ mf v. If supplementedby the identification αS(mc) ∼ v and gE ∼ m2

f v3

and gB ∼ m2f v

4 all terms displayed in (Eq. 1.14)are of equal relevance [8].

The effective Lagrangian (Eq. 1.13) defines still aquite complicated theory, since it is not always jus-tified to treat the gluon dynamics in an expansionin powers of αS . Nevertheless, it is a powerfultool since it can be and is used for simulations onthe lattice. Depending on the typical velocity v ofthe heavy quark it is possible to integrate out thegluon dynamics at least in part. This is desirablesince it would make contact with the phenomeno-logical quark-potential model [10]. The one-gluonexchange part of such models follows by the as-sumption of perturbative gluon dynamics. A cor-responding contribution in L4 of (Eq. 1.13) wouldarise. For charmonium systems there are three rel-evant scales: the mass mc (the “hard scale”), themomentum transfer mc v (the “soft scale”, propor-tional to the inverse of the typical size of the sys-


Figure 1.4: LQCD predictions for the charmonium,the glueball and the spin-exotic cc-glue hybrids spec-trum in quenched lattice QCD.

tem), and the binding energy mc v2 (the “ultra-soft

scale”, proportional to the inverse of the typicaltime of the system). In charmonium v2 ' 0.3. Thecrucial question is how ΛQCD relates to the threescales discussed above. If ΛQCD > mc v

2 theremust be non-perturbative physics involved when in-tegrating out gluon dynamics. Since one expectsmc > mc v ∼ ΛQCD, part of the gluon dynamics isperturbative [11, 12].

One can integrate out the soft scale mc v by employ-ing a matching procedure keeping only dynamicalultra-soft degrees. This results in potential Non-relativistic QCD (pNRQCD). In lowest order theproblem reduces to solving a Schrodinger equationfor the c c states. The quark-potential model is re-covered from pNRQCD, with potentials calculatedfrom QCD following a formal non-perturbative pro-cedure. An actual evaluation of the low-energypart requires a calculation on a lattice or QCD vac-uum models. Some actual examples are shown inFig. 1.4. The charmonium ground-state hyperfinesplitting has been calculated at NLO.

1.4 EFT with Hadronic Degreesof Freedom

We discuss the concepts of EFT with hadronic de-grees of freedom at hand of open-charm systems insome detail. This is a sector most relevant for thePANDA experiment with its goal to study propertiesof the spectrum of the D mesons in free-space and innuclear matter. Analogous developments are possi-ble in the light sector of QCD with up, down and

strange quarks only. The description of baryon reso-nances with double strangeness, another importanttopic of the PANDA experiment, will profit fromsuch developments. The study of hypernuclei withPANDA is motivated in part as a mean to learn onthe interaction of hyperons. For the latter chiraleffective field theories are being developed [13]. Inthe charmonium sector, the construction of an EFTwith hadronic degrees of freedom is in its infancy,though further developments would be importantfor the charmonium programme at PANDA.

There are three important steps in the course ofconstructing an EFT. The first step is the choice ofdegrees of freedom. In most cases this can not bederived from QCD, but must be conjectured andthen falsified by explicit computations to be con-fronted with QCD lattice results or experiments.Most predictive are EFTs involving Goldstone bo-son fields, since the interaction of the latter withmatter fields is strongly constrained by the sponta-neously broken chiral SU(3) symmetry QCD. Thesecond step is of more technical nature, the con-struction of the effective Lagrangian, in a mannerconsistent with the symmetries of QCD. Though thesecond step is least controversial, it involves an infi-nite number of unknown parameters. This leads tothe third crucial step: the identification of a suitableapproximation scheme for the effective Lagrangianbased on power-counting rules. This programme isquite rewarding since the leading order Lagrangianinvolves typically a few unknown parameters only,in terms of which a lot of physics can be understood.

A quite radical approach is the hadrogenesis con-jecture [14], which postulates the spectrum of QCDto be generated by the interaction of a few “quasi-fundamental” hadronic degrees of freedom, the se-lection of which is guided by symmetry propertiesof QCD. Clearly, alternative or complementary as-sumptions may be used at this stage. It is an im-portant goal of the PANDA project to give answersto the fundamental question how QCD manifestsitself in the hadronic spectrum.

1.4.1 Chiral Symmetry and OpenCharm Meson Systems

In the open charm sector consider the flavour octetof Goldstone bosons

Φ =

π0 + 1√3η

√2π+

√2K+

√2π− −π0 + 1√

3η√

2K0

√2K−

√2 K0 − 2√

3η

,(1.15)


and the flavor anti-triplets of pseudo-scalar and vec-tor open-charm mesons

P = (D0,−D+, D+s ) ,

Pµν = (D∗0µν ,−D∗+µν , D∗+s,µν) , (1.16)

where one may represent the vector states by anti-symmetric tensor fields. In the limit of an infinitecharm-quark mass the properties of pseudo-scalarand vector D mesons are closely related, in particu-lar they are mass degenerate. In order to constructthe effective Lagrangian describing the interactionof Goldstone bosons and the D mesons it is use-ful to identify building blocks that have convenienttransformation properties under chiral transforma-tions

Uµ =12u†((∂µe

i Φf

)+ i eAµ

[Q, ei

Φf

])u† ,

u = exp(iΦ2 f

),

χ± =12uχ0 u±

12u† χ0 u

† ,

χ0 = 2B0

mu 0 00 md 00 0 ms

, (1.17)

where the parameter f ' fπ may be identified withthe pion-decay constant, fπ = 92.4 MeV, at leadingorder. A precise determination of f requires a chiralSU(3) extrapolation of some data set. The field Uµinvolves the photon field Aµ and the electromag-netic coupling constant e ' 0.303 and the quarkcharge matrix Q = diag(2,−1,−1)/3. The buildingblocks in (Eq. 1.17) illustrate two important aspectsof EFTs: first the Goldstone boson field Φ entersin a non-linear fashion and second the chiral sym-metry breaking fields χ± are proportional to thequark-mass matrix of QCD. The parameter B0 isrelated to the chiral quark condensate.

The chiral Ward identities of QCD are transportedinto the EFT by the use of a covariant derivative,Dµ,

Dµ Uν = ∂µ Uν +[Γµ, Uν

]+ i eAµ

[Q, Uν

],

Dµ P = ∂µ P − P Γµ + i e P Q′Aµ ,

Γµ =12

(u† ∂µ u+ u ∂µ u

†), (1.18)

with Q′ = (0, 1, 1). Given the building blocksEqs. (1.17, 1.18) it is straightforward to write downinteraction terms that are compatible with the chi-ral constraints of QCD. This is because a covariantderivative Dµ acting on the fields Uµ, P , Pµν orχ± does not alter their transformation propertiesunder chiral transformation [15].

We display the leading order Lagrangian con-structed in terms of the building blocks Eqs. (1.17,1.18)

L = f2 trUµ U†µ

+

12

tr (χ+)

+ (DµP ) (DµP )− P M20− P

− (DµPµα) (Dν Pνα) +

12PµαM2

1− Pµα

+ 2 gPPµν U

µ (Dν P )− (DνP )Uµ Pµν

− i gP2εµναβ

Pµν Uα (Dτ Pτβ)

+ (DτPτβ)Uα Pµν, (1.19)

where we use the notation P = P †. The decay ofthe charged D∗-mesons implies |gP | = 0.57 ± 0.07.The parameter gP in (Eq. 1.19) can not be ex-tracted from empirical data directly. In the absenceof an accurate evaluation within unquenched lat-tice QCD, the size of gP can be estimated using theheavy-quark symmetry, one expects gP = gP atleading order [16]. In that limit it holds also thatM0− = M1− .

If we admit isospin-breaking effects, i.e. mu 6=md, there is a term in Eq. 1.19) after insertion ofEq. 1.15 proportional to (mu − md)π0 η. A uni-tary transformation is required such that the trans-formed fields π0 and η decouple. The Lagrangiandensity (Eq. 1.19), when written in terms of thenew fields and a mixing angle ε, does not show aπ0 η term if and only if

sin(2 ε)cos(2 ε)

=√

3md −mu

2ms −mu −md, (1.20)

where we recalled the value for the mixing angleε = 0.010± 0.001 as determined in Ref. [17].

We give a brief discussion of the power-countingrules underlying (Eq. 1.19). Such counting rules arebased on naive dimensional counting supplementedby a naturalness assumption. Dimensional countingrules are realized in a computation of a given Feyn-man diagram if the theory is treated in dimensionalregularization. It is an important issue to deviserenormalisation schemes that are compatible witha given counting scheme. To be specific we collectsome counting rules

Uµ ∼ Q ,

Dµ Uµ ∼ Q2 ,

Dµ P ∼ Q0 ,

χ± ∼ Q2 . (1.21)

The fact that a covariant derivative acting on Uµmust be counted Q reflects the “lightness” of the


Goldstone boson fields: the squared mass of theGoldstone boson is proportional to the currentquark mass of QCD. On the other hand the massof a D meson is much larger than the masses ofthe Goldstone bosons. Thus, at a formal level onemust assign a covariant derivative acting on a D-meson field the order Q0. A systematic approacharises if one orders the interaction terms of the chi-ral Lagrangian according to inverse powers in thecharm-quark mass. The leading-order term is thenlinear in the charm quark mass, like the QCD actionis linear in that parameter.

The central guiding rule of EFTs is the derivation ofmost general approximations compatible with thesymmetries of the underlying theory but also thefundamental concepts of local quantum field the-ory like micro-causality, covariance, unitarity, andcrossing symmetry. As emphasized by Weinberg forthe case of nucleon-nucleon scattering a systematicapproximation scheme can be devised if one evalu-ates a two-body potential based on power-countingrules in a perturbative manner [18]. The lattershould then be used in a Schrodinger-type equationas to arrive at scattering amplitude compatible withthe unitarity constraint. It is important to realizethat within this type of EFT one does not applythe counting rules to the scattering amplitude di-rectly, rather to the subset or irreducible diagrams.The rationale behind this approach is the observa-tion that the “naive” counting rules are spoiled fora Feynman diagram in phase-space regions close tothe opening of thresholds: an appropriate summa-tion is required.

We illustrate the power of the effective Lagrangian(Eq. 1.19) and extract the leading order two-bodyinteraction terms of the Goldstone bosons with theD mesons

LWT =1

8 f2

(∂µP ) [Φ, (∂µΦ)] P

−P [Φ, (∂µΦ)] (∂µP ),

− 18 f2

(∂νPνα) [Φ, (∂µΦ)] Pµα

−Pνα [Φ, (∂νΦ)] (∂µPµα).(1.22)

The Weinberg-Tomozawa interaction (Eq. 1.22) isa direct consequence of the chiral SU(3) symme-try of QCD and illustrates the predictive powerof chiral EFT: the interaction is determined byone parameter f ' 90 MeV only that is knownfrom the pion-decay process. Analogous interac-tions of the Goldstone bosons with other matterfields were derived and studied in detail in the re-cent literature [19, 20, 21, 22, 23]. It was shown

that the chiral interaction (Eq. 1.22) is relevant forthe study of open-charm resonances with JP = 0+

or 1+ quantum number: it implies unambiguouslythe existence of two resonances with masses be-low the DK and D∗K thresholds and astonish-ingly close to the empirical masses of the D∗s0(2317)and D∗s1(2460) [24]. Such states manifest them-selves as poles in the S-wave scattering amplitudeof Goldstone bosons with the pseudo-scalar or vec-tor open-charm ground states. For the formationof the scalar D∗s0(2317) resonance the four isospinstates 〈KD, I|, 〈πDs, 1| and 〈η Ds, 0| are relevantwith their coupled-channel interactions determinedby (Eq. 1.22) at leading order. In the presenceof isospin mixing all channels couple. The mix-ing of the two isospin sectors is of order ε. It pre-dicts the leading isospin-violating hadronic decayD∗s0(2317) → π0Ds. Analogous statements holdfor the axial-vector state.

The detailed consequence of the EFT approach forthe properties of scalar and axial vector open-charmstates has been addressed in the recent literaturewhere chiral correction terms were considered sys-tematically [25, 26]. In particular their electromag-netic and isospin-violating decay properties havebeen computed and confronted with experimentalbounds successfully [25]. The leading order inter-action predicts sizeable attraction in channels onlythat have an interpretation as c q states. Exoticchannels, which would require tetra-quark config-urations, are sensitive to chiral correction terms.Since the latter involve further a priori unknownparameters, the predictions in exotic channel aremore uncertain. Nevertheless, it was shown that iffurther constraints of QCD, which arise in the limitof large number of colours Nc, are considered onewould expect exotic signals in the invariant massdistribution of the πD and ηD∗ channels. It wouldbe an important step towards a better understand-ing of the physics of open-charm meson systemsto measure such mass distributions with high ac-curacy [25].

Further studies of open-charm systems that involvelight vector mesons as active degrees of freedom arenecessary. Within the hadrogenesis conjecture onewould expect further resonance states, like tensorstates, to be formed.

1.4.2 Phenomenology of Open CharmBaryon Systems

While EFT is a rigorous and systematic approachto solve QCD, there are many systems for whichsuch tools are not yet available. In such cases it


is useful to develop schematic models to pave theway towards more systematic approaches. A goodexample is the interaction of D mesons with nucle-ons. The theoretical efforts to describe such sys-tems with hadronic degrees of freedom are few sofar. Since the experimental study of the open-charmbaryon spectrum and properties ofD mesons in coldnuclear matter may be feasible with PANDA, it isimportant to work out the relevance of this physicsfor the better understanding of strong QCD. Onemay model the interaction of D mesons with matterfields by a t-channel exchange of universally coupledlight vector mesons. If written down for all two-body channels that are implied by the presence ofup, down, strange and charm quarks such an inter-action is compatible with the leading order chiralinteraction in the case where the initial and finalstate involves a Goldstone boson [27]. For instance,the chiral interaction of Goldstone bosons with theopen-charm baryon ground state, that is analogousto (Eq. 1.22), is recovered. The open-charm baryonsystems are considerably more complicated than theopen-charm meson systems since the charm quarkmay be exchanged from a meson to baryon and viceversa. For instance such processes are implied bythe t-channel exchanges of D mesons. This com-plicates the construction of an EFT considerably.On the other hand, coupled-channel models basedon that simple t-channel exchange force predict asurprising rich phenomenology. Thus a dedicatedtheoretical and experimental study appears quiterewarding and should be undertaken.

References

[1] W. M. Yao et al., J. Phys. G33, 1 (2006).

[2] V. Bernard, Prog. Part. Nucl. Phys. 60, 82(2008).

[3] A. V. Manohar and M. B. Wise, Camb.Monogr. Part. Phys. Nucl. Phys. Cosmol. 10,1 (2000).

[4] G. ’t Hooft, Nucl. Phys. B72, 461 (1974).

[5] K. D. Paschke et al., Phys. Rev. C74, 015206(2006).

[6] C. J. Morningstar and M. Peardon, Phys.Rev. D 60, 034509 (1999).

[7] S. Pacetti, Eur. Phys. J. A32, 421 (2007).

[8] G. T. Bodwin, E. Braaten, and G. P. Lepage,Phys. Rev. D 51, 1125 (1995).

[9] N. Brambilla et al., hep-ph/0412158 (2004).

[10] E. S. Swanson, Phys. Rept. 429, 243 (2006).

[11] M. Luke and A. V. Manohar, Phys. Rev. D55, 4129 (1997).

[12] N. Brambilla, A. Pineda, J. Soto, andA. Vairo, Rev. Mod. Phys. 77, 1423 (2005).

[13] H. Polinder, J. Haidenbauer, and U.-G.Meissner, Nucl. Phys. A779, 244 (2006).

[14] M. F. M. Lutz and E. E. Kolomeitsev, Nucl.Phys. A700, 193 (2002).

[15] A. Krause, Helv. Phys. Acta 63, 3 (1990).

[16] T.-M. Yan et al., Phys. Rev. D 46, 1148(1992).

[17] J. Gasser and H. Leutwyler, Nucl. Phys.B250, 465 (1985).

[18] S. Weinberg, Nucl. Phys. B363, 3 (1991).

[19] N. Kaiser, T. Waas, and W. Weise, Nucl.Phys. A612, 297 (1997).

[20] J. A. Oller, E. Oset, and J. R. Pelaez, Phys.Rev. D59, 074001 (1999).

[21] C. Garcia-Recio, M. F. M. Lutz, andJ. Nieves, Phys. Lett. B582, 49 (2004).

[22] E. E. Kolomeitsev and M. F. M. Lutz, Phys.Lett. B585, 243 (2004).




[25] M. F. M. Lutz and M. Soyeur, Nucl. Phys. A,in print (2007).

[26] F.-K. Guo, C. Hanhart, S. Krewald, andU.-G. Meissner, Phys. Lett. B666, 251(2008).

[27] J. Hofmann and M. F. M. Lutz, Nucl. Phys.A763, 90 (2005).

13

2 Experimental Setup

2.1 Overview

2.2 The PANDA Detector

The main objectives of the design of the PANDAexperiment pictured in Fig. 2.1 are to achieve 4π ac-ceptance, high resolution for tracking, particle iden-tification and calorimetry, high rate capabilities anda versatile readout and event selection. To obtain agood momentum resolution the detector is split intoa target spectrometer based on a superconductingsolenoid magnet surrounding the interaction pointand measuring at high angles and a forward spec-trometer based on a dipole magnet for small angletracks. A silicon vertex detector surrounds the in-teraction point. In both spectrometer parts track-ing, charged particle identification, electromagneticcalorimetry and muon identification are available toallow to detect the complete spectrum of final statesrelevant for the PANDA physics objectives.

In the following paragraphs the components of alldetector subsystems are briefly described.

2.2.1 Target Spectrometer

The target spectrometer surrounds the interactionpoint and measures charged tracks in a solenoidalfield of 2 T. It consists of detector layers arranged inan onion shell configuration. Pipes for the injectionof target material have to cross the spectrometerperpendicular to the beam pipe.

The target spectrometer is arranged in a barrel partfor angles larger than 22 and an end-cap part forthe forward range down to 5 in the vertical and 10

in the horizontal plane. A side view of the targetspectrometer is shown in Fig. 2.2.

One of the main design requirements is compactnessto avoid a too large and a too costly magnet andcrystal calorimeter.

2.2.1.1 Target

The compact geometry of the detector layers nestedinside the solenoidal magnetic field combined withthe request of minimal distance from the interactionpoint to the vertex tracker leaves very restrictedspace for the target installations. The situation isdisplayed in Fig. 2.3, showing the intersection be-

tween the antiproton beam pipe and the target pipebeing gauged to the available space. In order toreach the design luminosity of 2 · 1032 cm−2s−1 atarget thickness of about 4 · 1015 hydrogen atomsper cm2 is required assuming 1011 stored antipro-tons in the HESR ring.

These are conditions posing a real challenge for aninternal target inside a storage ring. At present, twodifferent, complementary techniques for the internaltarget are being developed: the cluster-jet targetand the pellet target. Both techniques are capableof providing sufficient densities for hydrogen at theinteraction point, but exhibit different propertiesconcerning their effect on the beam quality and thedefinition of the interaction point. In addition, in-ternal targets also of heavier gases, like deuterium,nitrogen or argon can be made available.

For non-gaseous nuclear targets the situation is dif-ferent in particular in case of the planned hyper-nuclear experiment. In these studies the whole up-stream end cap and part of the inner detector ge-ometry will be modified.

Cluster-Jet Target The expansion of pressurizedcold hydrogen gas into vacuum through a Laval-type nozzle leads to a condensation of hydrogenmolecules forming a narrow jet of hydrogen clusters.The cluster size varies from ·103 to ·106 hydrogenmolecules tending to become larger at higher in-let pressure and lower nozzle temperatures. Sucha cluster-jet with density of ·1015 atoms/cm3 actsas a very diluted target since it may be seen as alocalized and homogeneous mono-layer of hydrogenatoms being passed by the antiprotons once per rev-olution.

Fulfilling the luminosity demand for PANDA still re-quires a density increase compared to current appli-cations. Additionally, due to detector constraints,the distance between the cluster-jet nozzle and thetarget will be larger. The size of the target re-gion will be given by the lateral spread of hydro-gen clusters. This width should stay smaller than10 mm when optimized with skimmers and colli-mators both for maximum cluster flux as well asfor minimum gas load in the adjacent beam pipes.The great advantage of cluster targets is the homo-geneous density profile and the possibility to focusthe antiproton beam at highest phase space den-sity. Hence, the interaction point is defined trans-


Figure 2.1: Artistic view of the PANDA Detector

versely but has to be reconstructed longitudinallyin beam direction. In addition the low β-functionof the antiproton beam keeps the transverse beamtarget heating effects at the minimum. The possi-bility of adjusting the target density along with thegradual consumption of antiprotons for running atconstant luminosity will be an important feature.

Pellet Target The pellet target features a streamof frozen hydrogen micro-spheres, called pellets,traversing the antiproton beam perpendicularly.Pellet targets are presently in use at the WASA atCOSY experiment [1] and were previously developedat TSL [2]. Typical parameters for pellets at the in-teraction point are the rate of 1.0 - 1.5 ·104 s−1, thepellet size of 25 - 40 µm, and the velocity of about 60m/s. At the interaction point the pellet train hasa lateral spread of σ ≈ 1 mm and an inter spacingof pellets that varies between 0.5 to 5 mm. Withproper adjustment of the β-function of the coastingantiproton beam at the target position, the designluminosity for PANDA can be reached. The presentR&D is concentrating on minimizing the luminos-ity variations such that the instantaneous interac-tion rate does not exceed the acceptance of the de-tector systems. Since a single pellet becomes thevertex for more than hundred nuclear interactionswith antiprotons during the time a pellet traversesthe beam, it will be possible to determine the posi-

tion of individual pellets with the resolution of themicro-vertex detector averaged over many events.R&D is going on to devise an optical pellet trackingsystem. Such a device could determine the vertexposition to about 50 µm precision for each individ-ual event independently of the detector. It remainsto be seen if this device can later be implementedin PANDA.

The production of deuterium pellets is also well es-tablished, the use of other gases like N2, Ar or Xeas pellet target material does not pose problems [3].

Other Targets are under consideration for the hy-pernuclear studies where a separate target stationupstream will comprise primary and secondary tar-get and detectors. Moreover, current R&D is under-taken for the development of a liquid helium targetand a polarized 3He target. A wire target may beemployed to study antiproton-nucleus interactions.

2.2.1.2 Solenoid Magnet

The magnetic field in the target spectrometer isprovided by a superconducting solenoid coil withan inner radius of 90 cm and a length of 2.8 m. Themaximum magnetic field is 2 T. The field homogene-ity is foreseen to be better than 2 % over the vol-ume of the vertex detector and central tracker. In


Figure 2.2: Side view of the target spectrometer

Figure 2.3: Schematic of the target and beam pipe setup with pumps.

addition the transverse component of the solenoidfield should be as small as possible, in order to

allow a uniform drift of charges in the time pro-jection chamber. This is expressed by a limit of


∫Br/Bzdz < 2 mm for the normalized integral of

the radial field component.

In order to minimize the amount of material infront of the electromagnetic calorimeter, the latteris placed inside the magnetic coil. The trackingdevices in the solenoid cover angles down to 5/10

where momentum resolution is still acceptable. Thedipole magnet with a gap height of 1.4 m providesa continuation of the angular coverage to smallerpolar angles.

The cryostat for the solenoid coils has two warmbores of 100 mm diameter, one above and one belowthe target position, to allow for insertion of internaltargets.

2.2.1.3 Microvertex Detector

The design of the micro-vertex detector (MVD) forthe target spectrometer is optimized for the detec-tion of secondary vertices from D and hyperon de-cays and maximum acceptance close to the interac-tion point. It will also strongly improve the trans-verse momentum resolution. The setup is depictedin Fig. 2.4.

The concept of the MVD is based on radiation hardsilicon pixel detectors with fast individual pixelreadout circuits and silicon strip detectors. Thelayout foresees a four layer barrel detector with aninner radius of 2.5 cm and an outer radius of 13 cm.The two innermost layers will consist of pixel de-tectors while the outer two layers are considered toconsist of double sided silicon strip detectors.

Eight detector wheels arranged perpendicular to thebeam will achieve the best acceptance for the for-ward part of the particle spectrum. Here again, theinner two layers are made entirely of pixel detectors,the following four are a combination of strip detec-tors on the outer radius and pixel detectors closerto the beam pipe. Finally the last two wheels, madeentirely of silicon strip detectors, are placed furtherdownstream to achieve a better acceptance of hy-peron cascades.

The present design of the pixel detectors comprisesdetector wafers which are 200 µm thick (0.25%X0).The readout via bump-bonded wafers with ASICsas it is used in ATLAS and CMS [4, 5] is foreseenas the default solution. It is highly parallelised andallows zero suppression as well as the transfer ofanalogue information at the same time. The read-out wafer has a thickness of 300 µm (0.37%X0). Apixel readout chip based on a 0.13 µm CMOS tech-nology is under development for PANDA. This chipallows smaller pixels, lower power consumption and

a continuously sampling readout without externaltrigger.

2.2.1.4 Central Tracker

The charged particle tracking devices must handlethe high particle fluxes that are anticipated for aluminosity of up to several 1032 cm−2s−1. The mo-mentum resolution δp/p has to be on the percentlevel. The detectors should have good detection ef-ficiency for secondary vertices which can occur out-side the inner vertex detector (e.g. K0

S or Λ). Thisis achieved by the combination of the silicon vertexdetectors close to the interaction point (MVD) withtwo outer systems. One system is covering a largearea and is designed as a barrel around the MVD.This will be either a stack of straw tubes (STT) ora time-projection chamber (TPC). The forward an-gles will be covered using three sets of GEM trackerssimilar to those developed for the COMPASS exper-iment [6] at CERN. The two options for the centraltracker are explained briefly in the following.

Straw Tube Tracker (STT) This detector con-sists of aluminized mylar tubes called straws, whichare self supporting by the operation at 1 bar over-pressure. The straws are arranged in planar layerswhich are mounted in a hexagonal shape aroundthe MVD as shown in Fig. 2.5. In total there are24 layers of which the 8 central ones are tilted toachieve an acceptable resolution of 3 mm also in z(parallel to the beam). The gap to the surroundingdetectors is filled with further individual straws. Intotal there are 4200 straws around the beam pipe atradial distances between 15 cm and 42 cm with anoverall length of 150 cm. All straws have a diameterof 10 mm. A thin and light space frame will holdthe straws in place, the force of the wire howeveris kept solely by the straw itself. The mylar foil is30 µm thick, the wire is made of 20 µm thick goldplated tungsten. This design results in a materialbudget of 1.3 % of a radiation length.

The gas mixture used will be Argon based with CO2

as quencher. It is foreseen to have a gas gain nogreater than 105 in order to warrant long term op-eration. With these parameters, a resolution in xand y coordinates of about 150 µm is expected.

Time Projection Chamber (TPC) A challengingbut advantageous alternative to the STT is a TPC,which would combine superior track resolution witha low material budget and additional particle iden-tification capabilities through energy loss measure-ments.


Figure 2.4: The Micro-vertex detector of PANDA

The TPC depicted in a schematic view in Fig. 2.6consists of two large gas-filled half-cylinders enclos-ing the target and beam pipe and surrounding theMVD. An electric field along the cylinder axis sepa-rates positive gas ions from electrons created by ion-izing particles traversing the gas volume. The elec-trons drift with constant velocity towards the anodeat the upstream end face and create an avalanchedetected by a pad readout plane yielding informa-tion on two coordinates. The third coordinate of thetrack comes from the measurement of the drift timeof each primary electron cluster. In common TPCsthe amplification stage typically occurs in multi-wire proportional chambers. These are gated byan external trigger to avoid a continuous backflowof ions in the drift volume which would distort theelectric drift field and jeopardize the principle ofoperation.

In PANDA the interaction rate is too high and thereis no fast external trigger to allow such an oper-ation. Therefore a novel readout scheme is em-ployed which is based on GEM foils as amplificationstage. These foils have a strong suppression of ionbackflow, since the ions produced in the avalancheswithin the holes are mostly caught on the backsideof the foil. Nevertheless about two ions per pri-mary electron are drifting back into the ionizationvolume even at moderate gains. The deformationof the drift field can be measured by a laser calibra-

tion system and the resulting drift can be correctedaccordingly. In addition a very good homogeneityof the solenoid field with a low radial component isrequired.

A further challenge is the large number of tracks ac-cumulating in the drift volume because of the highrate and slow drift. While the TPC is capable ofstoring a lot of tracks at the same time, their as-signment to specific interactions has to be done bytime correlations with other detectors in the targetspectrometer. To achieve this, first a tracklet re-construction has to take place. The tracklets arethen matched against other detector signals or arepointed to the interaction. This requires either highcomputing power close to the readout electronics ora very high bandwidth at the full interaction rate.

Forward GEM Detectors Particles emitted at an-gles below 22 which are not covered fully by theStraw Tube Tracker or TPC will be tracked by threestations of GEM detectors placed 1.1 m, 1.4 m and1.9 m downstream of the target. The chambers haveto sustain a high counting rate of particles peakedat the most forward angles due to the relativisticboost of the reaction products as well as due to thesmall angle pp elastic scattering. With the envis-aged luminosity, the expected particle flux in thefirst chamber in the vicinity of the 5 cm diameterbeam pipe is about 3·104 cm−2s−1. In addition it


Figure 2.5: Straw Tube Tracker in the Target Spectrometer.

Figure 2.6: GEM Time Projection Chamber in the Target Spectrometer.

is required that the chambers work in the 2 T mag-netic field produced by the solenoid. Drift cham-bers cannot fulfil the requirements here since theywould suffer from aging and the occupancy wouldbe too high. Therefore gaseous micropattern detec-tors based on GEM foils as amplification stages arechosen. These detectors have rate capabilities threeorders of magnitude higher than drift chambers.

In the current layout there are three double planeswith two projections per plane. The readout planeis subdivided in an outer ring with longer and aninner ring with shorter strips. The strips are ar-ranged in two orthogonal projections per readoutplane. Owing to the charge sharing between striplayers a strong correlation between the orthogonalstrips can be found giving an almost 2D informationrather than just two projections.

The readout is performed by the same front-endchips as are used for the silicon microstrips. The

first chamber has a diameter of 90 cm, the last oneof 150 cm. The readout boards carrying the ASICsare placed at the outer rim of the detectors.

2.2.1.5 Cherenkov Detectors andTime-of-Flight

Charged particle identification of hadrons and lep-tons over a large range of angles and momenta isan essential requirement for meeting the physicsobjectives of PANDA. There will be several dedi-cated systems which, complementary to the otherdetectors, will provide means to identify particles.The main part of the momentum spectrum above1 GeV/c will be covered by Cherenkov detectors. Be-low the Cherenkov threshold of kaons several otherprocesses have to be employed for particle identifi-cation: the tracking detectors are able to provideenergy loss measurements. Here in particular theTPC with its large number of measurements along


each track excels. In addition a time-of-flight barrelcan identify slow particles.

Barrel DIRC Charged particles in a medium withindex of refraction n, propagating with velocityβc < 1/n, emit radiation at an angle ΘC =arccos(1/nβ). Thus, the mass of the detected par-ticle can be determined by combining the velocityinformation determined from ΘC with the momen-tum information from the tracking detectors.

A very good choice as radiator material for thesedetectors is fused silica (i.e. artificial quartz) witha refractive index of 1.47. This provides pion-kaon-separation from rather low momenta of 800 MeV/cup to about 5 GeV/c and fits well to the compactdesign of the target spectrometer. In this way theloss of photons converting in the radiator materialcan be reduced by placing the conversion point asclose as possible to the electromagnetic calorimeter.

At polar angles between 22 and 140, particle iden-tification will be performed by the detection of in-ternally reflected Cherenkov (DIRC) light as re-alized in the BaBar detector [7]. It will consistof 1.7 cm thick quartz slabs surrounding the beamline at a radial distance of 45 - 54 cm. At BaBarthe light was imaged across a large stand-off vol-ume filled with water onto 11 000 photomultipliertubes. At PANDA, it is intended to focus the imagesby lenses onto micro-channel plate photomultipliertubes (MCP PMTs) which are insensitive to mag-netic fields. This fast light detector type allows amore compact design and the readout of two spatialcoordinates. In addition MCP PMTs provide goodtime resolution to measure the time of light prop-agation for dispersion correction and backgroundsuppression.

Forward Endcap DIRC A similar concept can beemployed in the forward direction for particles be-tween 5 and 22. The same radiator, fused silica,is to be employed however in shape of a disk. At therim around the disk focussing will be done by mir-roring quartz elements reflecting onto MCP PMTs.Once again two spatial coordinates plus the prop-agation time for corrections will be read. The diskwill be 2 cm thick and will have a radius of 110 cm.It will be placed directly upstream of the forwardend-cap calorimeter.

Barrel Time-of-Flight For slow particles at largepolar angles particle identification will be providedby a time-of-flight detector. In the target spec-trometer the flight path is only of the order of 50

- 100 cm. Therefore the detector must have a verygood time resolution between 50 and 100 ps.

Implementing an additional start detector would in-troduce too much material close to the interactionpoint deteriorating considerably the resolution ofthe electromagnetic crystal calorimeter. In the ab-sence of a start detector relative timing of a mini-mum of two particles has to be employed.

As detector candidates scintillator bars and stripsor pads of multi-gap resistive plate chambers areconsidered. In both cases a compromise betweentime resolution and material budget has to befound. The detectors will cover angles between 22

and 140 using a barrel arrangement around theSTT/TPC at 42 - 45 cm radial distance.

2.2.1.6 Electromagnetic Calorimeters

Expected high count rates and a geometrically com-pact design of the target spectrometer require a fastscintillator material with a short radiation lengthand Moliere radius for the construction of the elec-tromagnetic calorimeter (EMC). Lead tungstate(PbWO4) is a high density inorganic scintillatorwith sufficient energy and time resolution for pho-ton, electron, and hadron detection even at inter-mediate energies [8, 9, 10]. For high energy physicsPbWO4 has been chosen by the CMS and ALICEcollaborations at CERN [11, 12] and optimized forlarge scale production. Apart from a short decaytime of less than 10 ns good radiation hardness hasbeen achieved [13]. Recent developments indicatea significant increase of light yield due to crystalperfection and appropriate doping to enable pho-ton detection down to a few MeV with sufficientresolution. The light yield can be increased by afactor of about 4 compared to room temperatureby cooling the crystals down to -25C.

The crystals will be 20 cm long, i.e. approximately22X0, in order to achieve an energy resolution be-low 2 % at 1 GeV [8, 9, 10] at a tolerable energy lossdue to longitudinal leakage of the shower. Taperedcrystals with a front size of 2.1 × 2.1 cm2 will bemounted with an inner radius of 57 cm. This implies11 360 crystals for the barrel part of the calorime-ter. The forward end-cap calorimeter will have 3600tapered crystals, the backward end-cap calorimeter592. The readout of the crystals will be accom-plished by large area avalanche photo diodes in thebarrel and vacuum photo-triodes in the forward andbackward endcaps.

The barrel part and the forward endcap of the tar-get spectrometer EMC are depicted in Fig. 2.7.


Figure 2.7: The PANDA barrel and forward end-cap EMC

2.2.1.7 Muon Detectors

Muons are an important probe for, among others,J/ψ decays, semi-leptonic D-meson decays and theDrell-Yan process. The strongest background arepions and their decay daughter muons. However atthe low momenta of PANDA the signature is lessclean than in high energy physics experiments. Toallow nevertheless a proper separation of primarymuons from pions and decay muons a range track-ing system will be implemented in the yoke of thesolenoid magnet. Here a fine segmentation of theyoke as absorber with interleaved tracking detec-tors allows the distinction of energy loss processes ofmuons and pions and kinks from pion decays. Onlyin this way a high separation of primary muons fromthe background can be achieved.

In the barrel region the yoke is segmented in a firstlayer of 6 cm iron followed by 12 layers of 3 cm thick-ness. The gaps for the detectors are 3 cm wide. Thisis enough material for the absorption of pions inthe momentum range in PANDA at these angles. Inthe forward end-cap more material is needed. Since

the downstream door of the return yoke has to ful-fil constraints for space and accessibility, the muonsystem is split in several layers. Six detection lay-ers are placed around five iron layers of 6 cm eachwithin the door, and a removable muon filter withadditional five layers of 6 cm iron is located in thespace between the solenoid and the dipole. Thisfilter has to provide cut-outs for forward detectorsand pump lines and has to be built in a way that itcan be removed with few crane operations to alloweasy access to these parts.

As detector within the absorber layers rectangularaluminium drift tubes are used as they were con-structed for the COMPASS muon detection system[14]. They are essentially drift tubes with additionalcapacitively coupled strips read out on both ends toobtain the longitudinal coordinate.

2.2.1.8 Hypernuclear Detector

The hypernuclei study will make use of the mod-ular structure of PANDA. Removing the backwardend-cap calorimeter will allow to add a dedicated


nuclear target station and the required additionaldetectors for γ spectroscopy (see Fig. 2.8) close tothe entrance of PANDA. While the detection of anti-hyperons and low momentum K+ can be ensuredby the universal detector and its PID system, a spe-cific target system and a γ-detector are additionalcomponents required for the hypernuclear studies.

Figure 2.8: The beam enters from left.

Active Secondary Target The production of hy-pernuclei proceeds as a two-stage process. First hy-perons, in particular ΞΞ, are produced on a primarynuclear target. The slowing down of the Ξ proceedsthrough a sequence of nuclear elastic scattering pro-cesses inside the residual nucleus in which the an-tiproton annihilation has occurred and by energyloss during the passage through an active absorber.If decelerated to rest before decaying, the particlecan be captured in a nucleus, eventually releasingtwo Λ hyperons and forming a double hypernucleus.

The geometry of this secondary target is essentiallydetermined by the short mean life of the Ξ− ofonly 0.164 ns and its stopping time in solid material.This limits the required thickness of the active sec-ondary target to about 25–30 mm. The present lay-out shows a compact structure of 26mm thickness,consisting of 20 layers of silicon strip detectors withalternating layers of absorber material (Fig. 2.9).The active silicon layers provide also tracking infor-mation on the emitted weak decay products of theproduced hypernuclei (see Fig. 4.70 in Sec. 4.5.2).

Germanium Array An existing germanium-arraywith refurbished readout is planned to be used forthe γ-spectroscopy of the nuclear decay cascadesof hypernuclei. The main limitation will be theload due to neutral or charged particles travers-ing the germanium detectors. Therefore, readout

p

30 mm z

x

y

Figure 2.9: The active silicon layers provide alsotracking information on the emitted weak decay prod-ucts of the produced hypernuclei.

Figure 2.10: Design of the γ–ray spectroscopy setupwith 15 germanium cluster detector, each comprising 3germanium crystals.

schemes and tracking algorithms are presently be-ing developed which will enable high resolution γ-spectroscopy in an environment of high particleflux. The germanium-array crystals will be groupedasymmetrically by forming triple clusters. Eachcluster consists of three encapsulated n–type Ger-manium crystals of the Euroball type. The total γ–array set-up consists of 15 triple Germanium clus-ters positioned at backward axial angle around thetarget region as shown in Fig. 2.10.

2.2.2 Forward Spectrometer

2.2.2.1 Dipole Magnet

A dipole magnet with a window frame, a 1 m gap,and more than 2 m aperture will be used for themomentum analysis of charged particles in the for-


ward spectrometer. In the current planning, themagnet yoke will occupy about 2.5 m in beam di-rection starting from 3.5 m downstream of the tar-get. Thus, it covers the entire angular acceptanceof the forward spectrometer of ±10 and ±5 in thehorizontal and in the vertical direction, respectively.The maximum bending power of the magnet will be2 Tm and the resulting deflection of the antiprotonbeam at the maximum momentum of 15 GeV/c willbe 2.2. The design acceptance for charged parti-cles covers a dynamic range of a factor 15 with thedetectors downstream of the magnet. For particleswith lower momenta, detectors will be placed insidethe yoke opening. The beam deflection will be com-pensated by two correcting dipole magnets, placedaround the PANDA detection system.

2.2.2.2 Forward Trackers

The deflection of particle trajectories in the field ofthe dipole magnet will be measured with a set ofwire chambers (either small cell size drift chambersor straw tubes), two placed in front, two within andtwo behind the dipole magnet. This will allow totrack particles with highest momenta as well as verylow momentum particles where tracks will curl upinside the magnetic field.

The chambers will contain drift cells of 1 cm width.Each chamber will contain three pairs of detectionplanes, one pair with vertical wires and two pairswith wires inclined by +10 and -10. This configu-ration will allow to reconstruct tracks in each cham-ber separately, also in case of multi-track events.The beam pipe will pass through central holes inthe chambers. The most central wires will be sepa-rately mounted on insulating rings surrounding thebeam pipe. The expected momentum resolution ofthe system for 3 GeV/c protons is δp/p = 0.2 %and is limited by the small angle scattering on thechamber wires and gas.

2.2.2.3 Forward Particle Identification

RICH Detector To enable the π/K and K/p sep-aration also at the very highest momenta a RICHdetector is proposed. The favoured design is a dualradiator RICH detector similar to the one used atHermes [15]. Using two radiators, silica aerogel andC4F10 gas, provides π/K/p separation in a broadmomentum range from 2–15 GeV/c. The two differ-ent indices of refraction are 1.0304 and 1.00137, re-spectively. The total thickness of the detector is re-duced to the freon gas radiator (5 % X0), the aero-gel radiator (2.8 % X0), and the aluminium window

(3 % X0) by using a lightweight mirror focusing theCherenkov light on an array of photo tubes placedoutside the active volume. It has been studied toreuse components of the HERMES RICH.

Time-of-Flight Wall A wall of slabs made of plas-tic scintillator and read out on both ends by fastphoto tubes will serve as time-of-flight stop counterplaced at about 7 m from the target. In addition,similar detectors will be placed inside the dipolemagnet opening, to detect low momentum particleswhich do not exit the dipole magnet. The relativetime of flight between two charged tracks reachingany of the time-of-flight detectors in the experiment(including the barrel TOF) will be measured. Thewall in front of the forward spectrometer EMC willconsist of vertical strips varying in width from 5 to10 cm to account for the differences in count rate.With the expected time resolution of σ = 50 ps π-K and K/p separation on a 3σ level will be possibleup to momenta of 2.8 GeV/c and 4.7 GeV/c, respec-tively.

2.2.2.4 Forward Electromagnetic Calorimeter

For the detection of photons and electrons aShashlyk-type calorimeter with high resolution andefficiency will be employed. The detection is basedon lead-scintillator sandwiches read out with wave-length shifting fibres passing through the block andcoupled to photomultipliers. The technique has al-ready been successfully used in the E865 experi-ment [16]. It has been adopted for various otherexperiments [17, 18, 19, 20, 21, 22]. An energy res-olution of 4 %/

√E [20] has been achieved. To cover

the forward acceptance, 26 rows and 54 columns arerequired with a cell size of 55 mm, i.e. 1404 mod-ules in total, which will be placed at a distance of7–8 m from the target.

2.2.2.5 Forward Muon Detectors

For the very forward part of the muon spectruma further range tracking system consisting of inter-leaved absorber layers and rectangular aluminiumdrift-tubes is being designed, similar to the muonsystem of the target spectrometer, but laid out forhigher momenta. The system allows discriminationof pions from muons, detection of pion decays and,with moderate resolution, also the energy determi-nation of neutrons and antineutrons.


2.2.3 Luminosity Monitor

In order to determine the cross section for physicalprocesses, it is essential to determine the time in-tegrated luminosity L for reactions at the PANDAinteraction point that was available while collect-ing a given data sample. Typically the precisionfor a relative measurement is higher than for anabsolute measurement. For many observables con-nected to narrow resonance scans a relative mea-surement might be sufficient for PANDA, but forother observables an absolute determination of Lis required. The absolute cross section can be de-termined from the measured count rate of a spe-cific process with known cross section. In the fol-lowing we concentrate on elastic antiproton-protonscattering as the reference channel. For most otherhadronic processes that will be measured concur-rently in PANDA the precision with which the crosssection is known is poor.

The optical theorem connects the forward elasticscattering amplitude to the total cross section. Thetotal reaction rate and the differential elastic reac-tion rate as a function of the 4-momentum transfert can be used to determine the total cross section.

The differential cross section dσel/dt becomes dom-inated by Coulomb scattering at very low valuesof t. Since the electromagnetic amplitude can beprecisely calculated, Coulomb elastic scattering al-lows both the luminosity and total cross section tobe determined without measuring the inelastic rate[23].

Due to the 2 T solenoid field and the existenceof the MVD it appears most feasible to mea-sure the forward going antiproton in PANDA. TheCoulomb-nuclear interference region corresponds to4-momentum transfers of −t ≈ 0.001 GeV2 at thebeam momentum range of interest to PANDA. At abeam momentum of 6 GeV/c this momentum trans-fer corresponds to a scattering angle of the antipro-ton of about 5 mrad.

The basic concept of the luminosity monitor is to re-construct the angle (and thus t) of the scattered an-tiprotons in the polar angle range of 3-8 mrad withrespect to the beam axis. Due to the large trans-verse dimensions of the interaction region when us-ing the pellet target, there is only a weak correlationof the position of the antiproton at e.g. z =+10.0 mto the recoil angle. Therefore, it is necessary to re-construct the angle of the antiproton at the lumi-nosity monitor. As a result the luminosity monitorwill consist of a sequence of four planes of double-sided silicon strip detectors located as far down-stream and as close to the beam axis as possible.

Figure 2.11: Schematic overview of the luminositymonitor concept.

The planes are separated by 20 cm along the beamdirection. Each plane consists of 4 wafers (e.g. 2 cm× 5 cm × 200 µm, with 50 µm pitch) arranged ra-dially to the beam axis. Four planes are requiredfor sufficient redundancy and background suppres-sion. The use of 4 wafers (up, down, right, left) ineach plane allows systematic errors to be stronglysuppressed.

The silicon wafers are located inside a vacuumchamber to minimize scattering of the antiprotonsbefore traversing the 4 tracking planes. The ac-ceptance for the antiproton beam in the HESR is±3 mrad, corresponding to the 89 mm inner di-ameter of the beam pipe at the quadrupoles lo-cated at about 15 m downstream of the interac-tion point. The luminosity monitor can be lo-cated in the space between the downstream sideof the forward spectrometer hadronic calorimeterand the HESR dipole needed to redirect the an-tiproton beam out of the PANDA chicane back intothe direction of the HESR straight stretch (i.e. be-tween z =+10.0 m and z =+12.0 m downstream ofthe target). At this distance from the target theluminosity monitor needs to measure particles ata radial distance of between 3 and 8 cm from thebeam axis. A sketch of the detector concept is givenin Fig. 2.11. As pilot simulations show, at a beammomentum of 6.2 GeV/c the proposed detector mea-sures antiprotons elastically scattered in the range0.0006 GeV2 < −t < 0.0035 GeV2, which spans theCoulomb-nuclear interference region. Based uponthe granularity of the readout the resolution of tcould reach σt ≈ 0.0001 GeV2. In reality this valueis expected to degrade to σt ≈ 0.0005 GeV2 whentaking small-angle scattering into account. At thenominal PANDA interaction rate of 2 · 107/s therewill be an average of 10 kHz/cm2 in the sensors.In comparison with other experiments an absoluteprecision of about 3 % is considered feasible for thisdetector concept at PANDA, which will be verified


by more detailed simulations.

2.2.4 Data Acquisition

In many contemporary experiments the trigger anddata acquisition (DAQ) system is based on a twolayer hierarchical approach. A subset of speciallyinstrumented detectors is used to evaluate a firstlevel trigger condition. For the accepted events,the full information of all detectors is then trans-ported to the next higher trigger level or to stor-age. The available time for the first level decision isusually limited by the buffering capabilities of thefront-end electronics. Furthermore, the hard-wireddetector connectivity severely constrains both thecomplexity and the flexibility of the possible trig-ger schemes.

In PANDA, a data acquisition concept is being de-veloped which is better matched to the high datarates, to the complexity of the experiment and thediversity of physics objectives and the rate capabil-ity of at least 2 · 107 events/s.

In our approach, every sub-detector system is aself-triggering entity. Signals are detected au-tonomously by the sub-systems and are prepro-cessed. Only the physically relevant informationis extracted and transmitted. This requires hit-detection, noise-suppression and clustering at thereadout level. The data related to a particle hit,with a substantially reduced rate in the preprocess-ing step, is marked by a precise time stamp andbuffered for further processing. The trigger selec-tion finally occurs in computing nodes which accessthe buffers via a high-bandwidth network fabric.The new concept provides a high degree of flexi-bility in the choice of trigger algorithms. It makestrigger conditions available which are outside thecapabilities of the standard approach. One obviousexample is displaced vertex triggering.

In this scheme, sub-detectors can contribute to thetrigger decision on the same footing without re-strictions due to hard-wired connectivity. Differ-ent physics can be accessed either in parallel or viasoftware reconfiguration of the system.

High speed serial (10 Gb/s per link and beyond)and high-density FPGA (field programmable gatearrays) with large numbers of programmable gatesas well as more advanced embedded features arekey technologies to be exploited within the DAQframework.

The basic building blocks of the hardware infras-tructure which can be combined in a flexible way tocope with varying demands, are the following:

• Intelligent front-end modules capable of au-tonomous hit detection and data preprocessing(e.g. clustering, hit time reconstruction, andpattern recognition) are needed.

• A precise time distribution system is manda-tory to provide a clock norm from which alltime stamps can be derived. Without this,data from subsystems cannot be correlated.

• Data concentrators provide point-to-pointcommunication, typically via optical links,buffering and online data manipulation.

• Compute nodes aggregate large amounts ofcomputing power in a specialized architec-ture rather than through commodity PC hard-ware. They may employ fast FPGAs (Fast Pro-grammable Gate Arrays), DSPs (Digital Sig-nal Processors), or other computing units. Thenodes have to deal with feature extraction, as-sociation of data fragments to events, and, fi-nally, event selection.

A major component providing the link for all build-ing blocks is the network fabric. Here, special em-phasis is put on embedded switches which can becascaded and reconfigured to reroute traffic for dif-ferent physics selection topologies. Alternatively,with an even higher aggregate bandwidth of thenetwork, which according to projections of networkspeed evolution will be available by the time the ex-periment will start, a flat network topology whereall data is transferred directly to processing nodesmay be feasible as well. This requires a higher totalbandwidth but would have a simpler architectureand allow event selection in a single environment.The bandwidth required in this case would be atleast 200 GB/s. After event selection in the orderof 100-200 MB/s will be saved to mass storage.

An important requirement for this scheme is that alldetectors perform a continuous online calibrationwith data. The normal data taking is interleavedwith special calibration runs. For the monitoring ofthe quality of data, calibration constants and eventselection a small fraction of unfiltered raw data istransmitted to mass storage.

To facilitate the association of data fragments toevents the beam structure of the accelerator is ex-ploited: Every 1.8 µs there is a gap of about 400 nsneeded for the compensation of energy loss with abucket barrier cavity. This gap provides a clean di-vision between consistent data blocks which can beprocessed coherently by one processing unit.


2.2.5 Infrastructure

The target for antiproton physics is located in thestraight section at the east side of the HESR. At thislocation an experimental hall of 43 m × 29 m floorspace and 14.5 m height is planned (see Fig. 2.12).A concrete radiation shield of 2 m thickness on bothsides along the beam line is covered by concrete barsof 1 m thickness to suppress the neutron sky shine.Within the elongated concrete cave the PANDAdetector together with auxiliary equipment, beamsteering, and focusing elements will be housed. Theroof of the cave can be opened and heavy compo-nents hoisted by crane. The shielded beam line areafor the PANDA experiment including dipoles andfocusing elements is foreseen to have 37 m × 9.4 mfloor space and a height of 8.5 m with the beam lineat a height of 3.5 m. The general floor level of theHESR is 2 m higher. This level will be kept for alength of 4 m in the north of the hall (right partin Fig. 2.12), to facilitate transport of heavy equip-ment into the HESR tunnel.

The target spectrometer with electronics and sup-plies will be mounted on rails which makes it re-tractable to a parking position outside the HESRbeam line i.e. into the lower part of the hall inFig. 2.12). The experimental hall provides addi-tional space for delivery of components and assem-bly of the detector parts. In the south corner of thehall, a counting house complex with five floors isforeseen. The lowest floor will contain various sup-plies for power, high voltage, cooling water, gasesetc. . The next level is planned for readout electron-ics including data concentrators. The third levelwill house the online computing farm. The fourthfloor is at level with the surrounding ground andwill house the control room, a meeting room andsocial rooms for the shift crew. Above this floor,hall electricity supplies and ventilation is placed. Acrane (15 t) spans the whole area with a hook at aheight of about 10 m. Sufficient (300 kW) electricpower will be available.

Liquid helium coolant may come from the maincryogenic liquefier for the SIS rings. Alternatively, aseparate small liquefier (50 W cooling power at 4 K)would be mounted. The temperature of the build-ing will be moderately controlled. The more strin-gent requirements with respect to temperature andhumidity for the detectors have to be maintainedlocally. To facilitate cooling and avoid condensa-tion the target spectrometer will be kept in a tentwith dry air at a controlled temperature.


Figure 2.12: Top view of the experimental area indicating the location of PANDA in the HESR beam line. Thetarget centre is at the centre of HESR and is indicated as vertical dash-dotted line. North is to the right and thebeam comes in from the left. The roll-out position of the detector will be on the east side of the Hall.


2.3 The HESR

2.3.1 Introduction

The HESR is being realized by a consortium con-sisting of IKP at Forschungszentrum Julich, TSL atUppsala University, and GSI Darmstadt [24]. Animportant feature of this new facility is the com-bination of phase-space cooled beams and denseinternal targets, comprising challenging beam pa-rameters in two operation modes: high-luminositymode with beam intensities up to 1011, and high-resolution mode with a momentum spread downto a few times 10−5, respectively. Powerful elec-tron and stochastic cooling systems are necessaryto meet the experimental requirements.

The HESR lattice is designed as a racetrack shapedring, consisting of two 180 arc sections connectedby two long straight sections. One straight sectionwill mainly be occupied by the electron cooler. Theother section will host the experimental installationwith internal H2 pellet target, RF cavities, injectionkickers and septa (see Fig. 2.13). For stochasticcooling pickup (P) and kicker (K) tanks are alsolocated in the straight sections, opposite to eachother. Special requirements for the lattice are dis-persion free straight sections and small betatronamplitudes in the range of a few metres at the inter-nal interaction point. In addition the betatron am-plitudes at the electron cooler are adjustable withina large range.

Table 2.1 summarizes the specified injection pa-rameters, experimental requirements and operationmodes.

2.3.2 Beam Equilibria and LuminosityEstimates

The equilibrium beam parameters are most im-portant for the high-resolution mode. Cal-culations of beam equilibria for beam cooling,intra-beam scattering and beam-target interactionare being performed utilizing different simulationcodes like BETACOOL (JINR, Dubna), MOCAC(ITEP, Moscow), and PTARGET (GSI, Darm-stadt). Cooled beam equilibria calculations includ-ing special features of pellet targets have been car-ried out with a simulation code based on PTAR-GET.

2.3.2.1 Beam Equilibria with Electron Cooling

An electron beam with up to 1 A current, accel-erated in special accelerator columns to energiesin the range of 0.4 to 4.5 MeV is proposed for theHESR. Since the design is modular it facilitates fu-ture increase of the high voltage to 8 MV. The 22 mlong solenoidal field in the cooler section has a longi-tudinal field strength of 0.2 T with a magnetic fieldstraightness on the order of 10−5 [24]. This arrange-ment allows beam cooling for beam momentum be-tween 1.5 GeV/c and 8.9 GeV/c.

To simulate the dynamics of the core particles,an analytic “rms” model was applied [25]. Theempirical magnetized cooling force formula byV. V. Parkhomchuk for electron cooling [26] and ananalytical description for intra-beam scattering [27]was used. Beam heating by beam-target interactionis described by transverse and longitudinal emit-tance growth due to Coulomb scattering and energystraggling, respectively [28, 29]. In the HR mode,rms relative momentum spreads are 7.9 × 10−6 at1.5 GeV/c, 2.7× 10−5 at 8.9 GeV/c, and 1.2× 10−4

at 15 GeV/c [30].

2.3.2.2 Beam Equilibria with StochasticCooling

The main stochastic cooling parameters were de-termined for a cooling system utilizing pickups andkickers with a band-width of 2 – 4 GHz and theoption for an extension to 4 – 6 GHz. Stochasticcooling is presently specified above 3.8 GeV/c [31].Beam equilibria have been simulated based ona Fokker-Planck approach. Applying stochasticcooling, one can achieve rms relative momentumspreads of 5.1 × 10−5 at 3.8 GeV/c, 5.4 × 10−5 at8.9 GeV/c, and 3.9 × 10−5 at 15 GeV/c for the HRmode. With a combination of electron and stochas-tic cooling the beam equilibria can be further im-proved. In the HL mode, rms relative momentumspread of roughly 10−4 can be expected. Transversestochastic cooling can be adjusted independently toensure sufficient beam-target overlap.

2.3.2.3 Beam Losses and Luminosity Estimates

Beam losses are the main restriction for high lu-minosities, since the antiproton production rate islimited. Three dominating contributions of beam-target interaction have been identified: hadronicinteraction, single Coulomb scattering and energystraggling of the circulating beam in the target. Inaddition, single intra-beam scattering due to the


Figure 2.13: Tentative positions for injection, cooling devices and experimental installations are indicated.

Injection Parameters

Transverse emittance 0.25 mm ·mrad (normalized, rms) for 3.5 · 1010 particles,

scaling with number of accumulated particles: ε⊥ ∼ N4/5

Relative momentum spread 3.3 · 10−4 (normalized, rms) for 3.5 · 1010 particles,

scaling with number of accumulated particles: σp/p ∼ N2/5

Bunch length 150 m

Injection Momentum 3.8 GeV/c

Injection Kicker injection using multi-harmonic RF cavities

Experimental Requirements

Ion species Antiprotons

p production rate 2 · 107 /s (1.2 · 1010 per 10 min)

Momentum / Kinetic energy range 1.5 to 15 GeV/c / 0.83 to 14.1 GeV

Number of particles 1010 to 1011

Target thickness 4 · 1015 atoms/cm2 (H2 pellets)

Transverse emittance < 1 mm ·mrad

Betatron amplitude E-Cooler 25–200 m

Betatron amplitude at IP 1–15 m

Operation Modes

High resolution (HR) Luminosity of 2 · 1031 cm−2s−1 for 1010 p

rms momentum spread σp/p ≤ 2 · 10−5,

1.5 to 9 GeV/c, electron cooling up to 9 GeV/c

High luminosity (HL) Luminosity of 2 · 1032 cm−2s−1 for 1011 p

rms momentum spread σp/p ∼ 10−4,

1.5 to 15 GeV/c, stochastic cooling above 3.8 GeV/c

Table 2.1: Injection parameters, experimental requirements and operation modes.

Touschek effect has also to be considered for beamlifetime estimates. Beam losses due to residualgas scattering can be neglected compared to beam-target interaction, if the vacuum is better than

10−9 mbar. A detailed analysis of all beam lossprocesses can be found in [32, 33].


(τ−1loss) / s−1

Heating process 1.5 GeV/c 9 GeV/c 15 GeV/c

Hadronic Interaction 1.8 · 10−4 1.2 · 10−4 1.1 · 10−4

Single Coulomb 2.9 · 10−4 6.8 · 10−6 2.4 · 10−6

Energy Straggling 1.3 · 10−4 4.1 · 10−5 2.8 · 10−5

Touschek Effect 4.9 · 10−5 2.3 · 10−7 4.9 · 10−8

Total relative loss rate 6.5 · 10−4 1.7 · 10−4 1.4 · 10−4

1/e beam lifetime tp / s ∼ 1540 ∼ 6000 ∼ 7100

Lmax / 1032 cm−2s−1 0.82 3.22 3.93

Table 2.2: Upper limit for relative beam loss rate, 1/e beam lifetime tp, and maximum average luminosity Lmax

for a H2 pellet target.

Figure 2.14: Time dependent luminosity during the cycle L(t) versus the time in the cycle. Different measuresfor beam preparation are indicated.

0

2 1031

4 1031

6 1031

8 1031

1 1032

0 5000 10000 15000 20000

Avera

ge L

um

ino

sit

y /

cm

-2s

-1

Cycle Time / s

tprep

= 120 s

ττττ = 1540 s

nt = 4*10

15 cm

-2

f0 = 0.443 MHz

2*107 pbar / s

1*107 pbar / s

0

5 1031

1 1032

1.5 1032

2 1032

2.5 1032

3 1032

0 5000 10000 15000 20000

Avera

ge L

um

ino

sit

y /

cm

-2s

-1

Cycle Time / s

2*107 pbar / s

1*107 pbar / s

nt = 4*10

15 cm

-2

f0 = 0.521MHz

tprep

= 290 s

ττττ = 7100 s

Figure 2.15: The maximum number of particles is limited to 1011 (solid line), and unlimited (dashed lines).

2.3.2.4 Beam lifetime

The relative beam loss rate for the total cross sec-tion σtot is given by the expression

(τ−1loss) = ntσtotf0 (2.1)


0.01

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80

1.5 - 15 GeV/c

1.5 GeV/c9 GeV/c15 GeV/c

Max

imu

m L

um

ino

sity

/ 10

30cm

-2s-1

Z

Figure 2.16: Maximum average luminosity Lmaxvs.atomic charge Z for three different beam momenta.

where (τ−1loss) is the relative beam loss rate, nt the

target thickness and f0 the reference particle’s rev-olution frequency. In Table 2.2 the upper limit forbeam losses and corresponding lifetimes are listedfor a transverse beam emittance of 1 mm ·mrad, alongitudinal ring acceptance of ∆p/p = ±10−3 and1011 circulating particles in the ring.

For beam-target interaction, the beam lifetime isindependent of the beam intensity, whereas for theTouschek effect it depends on the beam equilibriaand beam intensity. Beam lifetimes are rangingfrom 1540 s to 7100 s. Beam lifetimes at low mo-menta strongly depend on the beam cooling sce-nario and the ring acceptance. Beam losses corre-sponding to beam lifetimes below half an hour ob-viously cannot be compensated by the antiprotonproduction rate.

2.3.2.5 Luminosity Considerations forHydrogen-Pellet Targets

The maximum average luminosity depends on theantiproton production rate dNp/dt = 2 · 107 /s andloss rate

Lmax =dNp/dt

σtot(2.2)

and is also given in Table 2.2 for different beammomenta. The maximum average luminosity for1.5 GeV/c is below the specified value for the HLmode.

To calculate the cycle average luminosity, machinecycles and beam preparation times have to be speci-fied. After injection, the beam is pre-cooled to equi-librium (with target off) at 3.8 GeV/c. The beam is

then accelerated or decelerated to the desired beammomentum. A maximum ramp rate of 25 mT/sis specified. After reaching the final momentum,beam steering and focusing in the target and beamcooler region takes place. The total beam prepara-tion time tprep ranges from 120 s for 1.5 GeV/c to290 s for 15 GeV/c. A typical example for the evo-lution of the luminosity during a cycle is plotted inFig. 2.14 versus the time in the cycle.

In the high-luminosity mode, particles should bere-used in the next cycle. Therefore the used beamis transferred back to the injection momentum andmerged with the newly injected beam. A bucketscheme utilizing broad-band cavities is foreseen forbeam injection and the refill procedure. During ac-celeration 1 % and during deceleration 5 % beamlosses are assumed. The cycle average luminosityreads

L = f0Ni,0ntτ[1− e−texp/τ

]texp + tprep

(2.3)

where τ is the 1/e beam lifetime, texp the experi-mental time (beam on target time), and tcycle thetotal time of the cycle, with tcycle = texp + tprep.The dependence of the cycle average luminosity onthe cycle time is shown for different antiproton pro-duction rates in Fig. 2.15.

With limited number of antiprotons of 1011, as spec-ified for the high-luminosity mode, cycle averageluminosities of up to 1.6 · 1032 cm−2s−1 can beachieved at 15 GeV/c for cycle times of less thanone beam lifetime. If one does not restrict thenumber of available particles, cycle times should belonger to reach maximum average luminosities closeto 3·1032 cm−2s−1. This is a theoretical upper limit,since the larger momentum spread of the injectedbeam would lead to higher beam losses during injec-tion due to the limited longitudinal ring acceptance.For the lowest momentum, more than 1011 particlescan not be provided in average, due to very shortbeam lifetimes. As expected, cycle average lumi-nosities are below 1032 cm−2s−1.

2.3.2.6 Luminosity Considerations for NuclearTargets

The hadronic cross section for the interaction ofantiprotons with nuclear targets can be estimatedfrom geometric considerations. Starting from theantiproton-proton hadronic cross section σ

ppH for

1.5 GeV/c

σppH ≈ 100 mbarn := πr2

p


with the proton radius of rp = 0.9 fm, theantiproton-nucleus hadronic cross section can be de-duced to be

σpAH = π(RA + rp)2. (2.4)

The radius of a spherical nucleus as a first approx-imation reads RA = r0A

1/3, with r0 = 1.2 fm andthe mass number A. The total hadronic cross sec-tion decreases with the beam momentum from 100,60 to 50 mb for hydrogen targets at 1.5, 9, and15 GeV/c, respectively. The cross sections for nu-clear targets is scaled with beam momentum ac-cordingly [34]. To evaluate beam losses also singleCoulomb scattering and energy straggling of the cir-culating beam in the target have been calculated[35]. Fig. 2.16 shows maximum average luminosi-ties for nuclear targets under the same conditionsas for hydrogen targets.

For the specified antiproton production rate max-imum average luminosities of 5 · 1031, 4 · 1029 to4 · 1028 cm−2 · s−1 (deuterium, argon to gold)are achieved at 1.5 GeV/c beam momentum. Formaximum beam momentum of 15 GeV/c the max-imum average luminosities increase by more thanone order of magnitude to 1.9 · 1032, 2.4 · 1031 to2.2 · 1030 cm−2· s−1 (deuterium, argon to gold) for1011 circulating antiprotons.

In order to reach these values an effective targetthickness of 3.6 ·1015 atoms/cm2 for a deuteriumtarget, 4.6 ·1014 atoms/cm2 for an argon target to4.1 ·1013 atoms/cm2 for gold at 1011 p is required.The optimum effective target thickness can be ad-justed by proper beam focussing and steering ontothe target.

2.4 Precision Measurements ofResonance Parameters

The study of resonances is an important part ofthe PANDA physics programme. Masses, widthsand decay fractions are measured by scanning thebeam energy across the resonance under study.In antiproton-proton annihilations, there are twomain advantages over inclusive production: (a) res-onances can be formed directly; (b) the detector isused as an event counter (y axis of the excitationcurve), while the energy determination (x axis) re-lies entirely on the precisely-calibrated and cooledantiproton beam.

This is an area where a close interplay between ma-chine and detector is needed, and this is why thisdiscussion is included here. In this section, we de-

scribe the technique of resonance scans for precisedetermination of resonance parameters. A discus-sion of the main sources of uncertainty is given, asit is an important input for the following physicschapters. The issue of determining line shapes isalso briefly addressed.

Much of the discussion is based upon E835 expe-rience with charmonium resonances [36, 37]. Weassume Breit-Wigner resonant shapes and constantbackgrounds, but the analysis can be easily ex-tended to more general cases.

2.4.1 Experimental Technique

The resonance parameters are determined froma maximum-likelihood fit to the excitation curve(Fig. 2.17). For each data-taking run (subscript i),we assume that the average number of observedevents µi in each channel depends on a Breit-Wigner cross section σBWr and on the centre-of-mass energy distribution, Bi, as follows:

µi = εiLi[∫

σBWr(w)Bi(w) dw + σbkg

], (2.5)

where w is the centre-of-mass energy, εi is the de-tector efficiency, Li is the integrated luminosity,and σbkg is a constant background cross section.The integral is extended over the energy acceptanceof the machine. The spin-averaged Breit-Wignercross section for a spin-J resonance of mass M andwidth Γ formed in pp annihilations is

σBW(w) =(2J + 1)(2S + 1)2

16πw2 − 4m2

(ΓinΓout/Γ) · ΓΓ2 + 4(w −M)2

;

(2.6)m and S are the (anti)proton mass and spin,while Γin and Γout are the partial resonance widthsfor the entrance (pp, in our case) and exit chan-nels. The Breit-Wigner cross section is correctedfor initial-state radiation to obtain σBWr [38, 39]:

σBWr(w) =

b

∫ w/2

0

dk

k

(2kw

)bσBW(

√w2 − 2kw) =

(2/w)b∫ (w/2)b

0

dt σBW(√w2 − 2t1/bw),

where the second form is more suitable for nu-merical integration and b(w) is the semiclassicalcollinearity factor [39], equal to 0.00753 at theψ(2S).

The resonance mass M , width Γ, ‘area’ A ≡(ΓinΓout/Γ) and the background cross section σbkg


CR

OS

S S

EC

TIO

N (

nb)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

pp → e+ e−

CR

OS

S S

EC

TIO

N (

nb)

0

5

10

15

pp → J ψ + X → e+ e− + X

Constant−orbit scan (stack 1)

CENTER−OF−MASS ENERGY (MeV)

3684 3685 3686 3687 3688

Constant−field scan (stack 29)

Figure 2.17: The observed cross section (excitation curve) for each channel (filled dots); the expected crosssection from the fit (open diamonds); the ‘bare’ resonance curves σBW from the fit (solid lines). The two bottomplots show the normalized energy distributions Bi (from Ref. [37]).

statistical systematicmass M 3 keV – J/ψ or ψ(2S) mass from resonant depolarization: 10 keV

– ∆L: 5 keV (single scan), 100 keV (scans at differentenergies)

width Γ 1.9 % – η: ∼5 %– ∆L (BPM noise): ∼ 5 keV

‘area’ ΓinΓout/Γ 1.5 % – efficiency: a few %– luminosity: a few %

Table 2.3: Summary of the sources of uncertainty in the resonance parameters. Statistical errors refer toN ≡ εLσ = 104 and scale as 1/

√N . It is assumed that the luminosity distribution is optimized and that the

beam width is negligible, and so they represent lower limits for a given N .


BEAM MOMENTUM p [GeV/c]

∂ fw

[keV

/Hz]

A

ND

∂ Lw

[keV

/mm

]

1 2 3 4 5 6 7 8 9 10 12 14

1

2357

10

20305070

100

200300500700

1000

∂fw∂Lw

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

HESRinjection

LHESR = 574 m

J ψ ψ(2S)

50

100

150

200

250

300

∆w

(∆p p)

∆w(∆

pp)

[k

eV/1

0−4]

Figure 2.18: Left vertical axis: partial derivatives ofthe centre-of-mass energy w with respect to revolutionfrequency f and orbit length L. Right vertical axis:energy spread in the centre of mass ∆w for a given mo-mentum spread ∆p/p.

energy spread in resonance width units ΓB Γ

stat

istic

al u

ncer

tain

ty in

the

wid

th (

%)

0.0 0.5 1.0 1.5 2.0

0

1

2

3

4

5

6

Figure 2.19: The amount of data is N ≡ εLσp = 104

in this example. An optimal luminosity distribution isassumed.

energy spread in resonance width units ΓB Γ

dist

ortio

n of

line

sha

pe (

%)

0.0 0.5 1.0 1.5 2.0

0

10

20

30

40

50

Figure 2.20: Distortion of the resonance shape as afunction of the ratio between energy spread (GaussianFWHM ΓB) and resonance width Γ.

are left as free parameters in the maximiza-tion of the log-likelihood function log(Λ) =∑i logP (µi, Ni), where P (µ,N) are Poisson prob-

abilities of observing N events when the mean is µ.Ni are the observed number of events, and σi ≡Ni/(εiLi) is the observed cross section. The areaparameter is usually chosen in the parameterizationof the resonance shape because it is proportional tothe total number of events in each channel. It isless correlated with the width than the product ofbranching fractions.

The detector determines the cross section (y-axis)measurements and their uncertainty. Here we focuson energy measurements (x-axis), their uncertaintyand their impact on the determination of resonanceparameters through Bi.

2.4.2 Mass Measurements

The centre-of-mass energy distribution Bi(w) of thepp system can be determined from the velocity ofthe antiproton beam, since revolution frequenciesand orbit lengths can be measured very precisely.

The revolution-frequency distribution of the an-tiprotons can be measured by detecting the Schot-tky noise signal generated by the coasting beam.The signal is sensed by a longitudinal Schottkypickup and recorded on a spectrum analyser. Anaccuracy of 0.05 Hz can be achieved on a revolutionfrequency of 0.52 MHz, over a wide dynamic rangein intensity (60 dBm), using commercial spectrum


analysers.

The beam is slightly bunched by an rf cavity operat-ing at f cav ∼ 0.52 MHz, the first harmonic (h = 1)of the revolution frequency. The beam is bunchedboth for stability (ion clearing) and for making thebeam position monitors (BPMs) sensitive to a por-tion of the beam. Therefore, recorded orbits refer toparticles bunched by the rf system, and their revolu-tion frequency is f rf = f cav/h. The bunched-beamrevolution frequency f rf is usually close to the av-erage revolution frequency of the beam. Each orbitconsists of several horizontal and vertical readings.BPM noise in an important consideration for preci-sion energy measurements.

From the BPM readings and the HESR latticemodel, differences ∆L in the length of one orbitand another can be calculated accurately. Themain systematic uncertainties come from lattice dif-ferences, from BPM calibrations, from bend-fielddrifts, and from neglecting second-order terms inthe orbit length. In the Fermilab Antiproton Ac-cumulator, the systematic uncertainty in ∆L wasestimated to be 0.05 mm out of 474 m during theE835 run within a single ψ(2S) scan [37], and about1 mm over the entire run.

The absolute length L of an orbit can be calculatedfrom a reference orbit of length L0: L = L0 + ∆L.The calibration of L0 is done by scanning a reso-nance (the ψ(2S), for instance) the mass of whichis precisely known from the resonant-depolarizationmethod in e+e− experiments [40].

For particles in the bunched portion of the beam(rf bucket), the relativistic parameters βrf and γrf

are calculated from their velocity vrf = f rf ·L, fromwhich the centre-of-mass energy w of the pp systemis calculated: wrf = w(f rf , L) ≡ m

√2 (1 + γrf).

(The superscript rf is omitted from orbit lengths be-cause they always refer to particles in the rf bucket.)In the charmonium region, this method yields goodaccuracies on w. Fig. 2.18 shows the magnitudeof the partial derivatives of w with respect to f rf

and L, ∂fw and ∂Lw. Being based upon veloc-ity measurements, the precision is quickly degradedas the beam energy increases. At constant L andrelativistic energies, the partial derivatives scaleas the fifth power of the centre-of-mass energy:∂f,Lw ∼ w5. From the uncertainties in the orbitlength and in the revolution frequency, it is reason-able to expect absolute measurements of the beamenergy with an uncertainty of the order of 0.1 MeVin the charmonium region.

2.4.3 Total and Partial Widths

For width and area determinations, energy differ-ences are crucial, and they must be determined pre-cisely. During normal data taking, the beam is keptnear the central orbit of the machine. A particularrun is chosen as the reference (subscript 0). En-ergy differences between the reference run and otherruns in the scan (subscript i), for particles in the rfbucket, are simply

wrfi − wrf

0 = w(f rfi , L0 + ∆Li)− w(f rf

0 , L0). (2.7)

Within the energy range of a resonance scan, thesedifferences are largely independent of the choiceof L0. For this reason, the absolute energy calibra-tion is irrelevant for width and area measurements.Only uncertainties coming from ∆L are to be con-sidered.

Once the energy wrfi for particles in the rf bucket

is known, the complete energy distribution is ob-tained from the Schottky spectrum using the rela-tion between frequency differences and momentumdifferences at constant magnetic field:

∆pp

= −1η

∆ff, (2.8)

where η is the energy-dependent phase-slip factorof the machine, which is one of the parameters gov-erning synchrotron oscillations. (The dependenceof η on beam energy is chosen during lattice de-sign; the variation of η within a scan can usually beneglected.) In terms of the centre-of-mass energy,

w − wrfi = −1

η

(βrfi )2(γrf

i )m2

wrfi

f − f rfi

f rfi

. (2.9)

Within a run, rf frequencies, beam-frequency spec-tra, and BPM readings are to be updated frequentlywith respect to expected variations in energy orluminosity. Frequency spectra can then trans-lated into centre-of-mass energy through Eq. 2.9,weighted by luminosity and summed, to obtainthe luminosity-weighted normalized energy spec-tra Bi(w) for each data-taking run.

The phase-slip factor is usually determined from theslope of the measured synchrotron frequency fs asa function of rf voltage settings V rf :

f2s = −η cosφs(f rf)2qV rf

2πhβ2Es, (2.10)

where φs is the synchronous phase, q is the particles’charge, Es their energy and β2 is the relativistic fac-tor. The main uncertainty comes from the absolutecalibration of the rf voltage and it is usually of theorder of a few percent.


The resonance width and area are affected by a sys-tematic error due to the uncertainty in η. This ef-fect is most noticeable when the beam width is notnegligible compared to the resonance width. Usu-ally, the resonance width and area are positivelycorrelated with the phase-slip factor. A larger ηimplies a narrower energy spectrum, as describedin Eq. 2.9. As a consequence, the fitted resonancewill more closely resemble the measured excitationcurve, yielding a larger resonance width.

For precision measurements, one needs a better esti-mate of the phase-slip factor or determinations thatare independent of η, or both. In E760, the ‘doublescan’ technique was used [38]. It yielded η with anuncertainty of 6 % at the ψ(2S) and width determi-nations largely independent of the phase-slip factor,but it had the disadvantage of being operationallycomplex. For E835, a new method of ‘complemen-tary scans’ was developed [37]. It resulted in a sim-ilar precision on η and arbitrarily small correlationsbetween resonance parameters and phase-slip fac-tor; the technique is also operationally simpler.

The resonance is scanned once on the central or-bit, as described above. A second scan is then per-formed at constant magnetic bend field. The energyof the beam is changed by moving the longitudinalstochastic-cooling pickups. The beam moves awayfrom the central orbit, and the range of energies islimited but appropriate for narrow resonances.

Since the magnetic field is constant, beam-energydifferences can be calculated independently of ∆L,directly from the revolution-frequency spectra andthe phase-slip factor, according to Eq. 2.9. A pivotrun is chosen (subscript p). The rf frequency of thisrun is used as a reference to calculate the energy forparticles in the rf bucket in other runs. These par-ticles have revolution frequency f rf

i and the energyis calculated as follows:

wrfi − wrf

p = −1η

(βrfp )2(γrf

p )m2

wrfp

f rfi − f rf

p

f rfp

. (2.11)

For the scan at constant magnetic field, this rela-tion is used instead of Eq. 2.7. Once the energy forparticles at f rf

i is known, the full energy spectrumwithin each run is obtained from Eq. 2.9, as usual.For the constant-field scan, the energy distributionsmay be obtained directly from the pivot energy bycalculating w − wrf

p , instead of using Eq. 2.11 firstand then Eq. 2.9. The two-step procedure is cho-sen because it is faster to rescale the energy spectrathan to re-calculate them from the frequency spec-tra when fitting for η. Numerically, the differencebetween the two calculations is negligible. More-over, the two-step procedure exposes how the width

depends on η.

Using this alternative energy measurement, thewidth and area determined from scans at constantmagnetic field are negatively correlated with η. Theincreasing width with increasing η is still present,as it is in scans at nearly constant orbit. But thedominant effect is that a larger η brings the energypoints in the excitation curve closer to the pivotpoint, making the width smaller.

The constant-orbit and the constant-field scan canbe combined. The resulting width has a dependenceon η that is intermediate between the two. An ap-propriate luminosity distribution can make the re-sulting curve practically horizontal. The combinedmeasurement is dominated by the statistical uncer-tainty. Moreover, thanks to this complementary be-havior, the width, area and phase-slip factor can bedetermined in a maximum-likelihood fit where η isalso a free parameter. Errors and correlations arethen obtained directly from the fit.

2.4.4 Line Shapes

The discussion so far was focused on the determi-nation of Breit-Wigner resonance parameters. Onemight also wish to determine the line shape of res-onances near the open charm threshold. The ques-tion then arises: how narrow should the beam be inorder to distort the line shape by less than a givenamount?

The distortion of the line shape can be characterizedby the maximum difference d between the physicalcross section σphys(w) and the observed cross sec-tion σobs(w) (arising from the convolution of thephysical cross section with the pp energy distribu-tion in the centre of mass B(w)), divided by thephysical cross section at the peak σpeak

phys :

d ≡ maxw|σphys(w)− σobs(w)| / σpeak

phys (2.12)

Fig. 2.20 shows the distortion d as a function of theratio between the FWHM of the energy distribution(assumed to be Gaussian) and the FWHM of theresonance (a Breit-Wigner, in this example). Forinstance, if a distortion of less than 10 % is needed,than the FWHM ratio needs to be smaller than0.43. If the FWHM of the resonance is Γ = 1 MeV,the rms of the energy distribution in the centre ofmass needs to be smaller than 0.18 MeV, corre-sponding to a momentum spread of 0.8 × 10−4 at6 GeV/c (see also Fig. 2.18).


2.4.5 Achievable Precision

From the above discussion, it is clear that somefeatures of the machine are essential for precisionmeasurements. Here is a list of the most importantrequirements:

• longitudinal Schottky pickups;

• low-noise horizontal and vertical BPMs, withfluctuations corresponding to less than 0.1 mmin the orbit length;

• small lattice differences between the energy ofthe calibration resonance and the energies ofinterest;

• absolute rf voltage calibration to within a fewpercent;

• motorized longitudinal cooling pickups, for ac-tive feedback on energy drifts and for constant-field scans.

Table 2.3 summarizes the sources of statistical andsystematic uncertainty in the resonance parameters.Statistical errors were normalized toN , the productof detector efficiency ε, total integrated luminosityL ≡ ∑Li, and peak cross section σp ≡ σBW(M):N ≡ εLσp = 104, in this example. Statistical un-certainties are affected by how the total integratedluminosity L is spent. Here we assume that the op-timal distribution is used [41]. For the numbers inthe table, it is also assumed that the beam widthis negligible, and so they represent lower limits fora given N . The uncertainty in the width is theone that is most affected by a larger beam energyspread. Its dependence on the ratio between energyspread and resonance width is shown in Fig. 2.19.

References

[1] M. Buscher et al., The Moscow-JulichFrozen-Pellet Target, in Hadron Spectroscopy,edited by A. Reis, C. Gobel, J. D. S. Borges,and J. Magnin, volume 814 of AmericanInstitute of Physics Conference Series, pages614–620, 2006.

[2] C. Ekstroem et al., Nucl. Instrum. Meth.A371, 572 (1996).

[3] A. V. Boukharov et al., Phys. Rev. Lett. 100,174505 (2008).

[4] Technical report, ATLAS Technical DesignReport 11, CERN/LHCC 98-13.

[5] Technical report, CMS Technical DesignReport 5, CERN/LHCC 98-6.

[6] B. Ketzer, Q. Weitzel, S. Paul, F. Sauli, andL. Ropelewski, Nucl. Instrum. Meth. A535,314 (2004).

[7] H. Staengle et al., Nucl. Instrum. Meth.A397, 261 (1997).

[8] K. Mengel et al., IEEE Trans. Nucl. Sci. 45,681 (1998).

[9] R. Novotny et al., IEEE Trans. Nucl. Sci. 47,1499 (2000).

[10] M. Hoek et al., Nucl. Instrum. Meth. A486,136 (2002).

[11] Technical Proposal, CERN/LHC 9.71.

[12] Technical Proposal, 1994, CERN/LHCC94-38, LHCC/P1.

[13] E.Auffray et al., Proceedings of SCINT99,Moscow, 1999.

[14] P. Abbon et al., Nucl. Instrum. Meth. A577,455 (2007).

[15] N. Akopov et al., Nucl. Instrum. Meth.A479, 511 (2002).

[16] G. S. Atoyan et al., Nucl. Instrum. Meth.A320, 144 (1992).

[17] G. David et al., Performance of the PHENIXEM calorimeter, Technical report, PHENIXTech. Note 236, 1996.

[18] A. Golutvin, (1994), HERA-B Tech. Note94-073.


[19] LHCb Technical Proposal CERN LHCC 98-4,LHCC/P4, 1998.

[20] I.-H. Chiang et al., (1999), KOPIO Proposal.

[21] H. Morii, (2004), Talk at NP04 Workshop atJ-PARC.

[22] G. Atoyan et al., Test beam study of theKOPIO Shashlyk calorimeter prototype, inProceedings of “CALOR 2004”, 2004.

[23] T. A. Armstrong et al., Phys. Lett. B385,479 (1996).

[24] Baseline Technical Report, subproject HESR,Technical report, Gesellschaft fur Schwerionen(GSI), Darmstadt, 2006.

[25] O. Boine-Frankenheim, R. Hasse,F. Hinterberger, A. Lehrach, andP. Zenkevich, Nucl. Instrum. Meth. A560,245 (2006).

[26] V. Parkhomchuk, Nucl. Instrum. Meth.A441, 9 (2000).

[27] A. H. Sørensen, Introduction to intrabeamscattering, in CERN Accelerator School:General accelerator physics, numberCERN-87-10, page 135, 1987.

[28] F. Hinterberger, T. Mayer-Kuckuk, andD. Prasuhn, Nucl. Instrum. Meth. A275, 239(1989).

[29] F. Hinterberger and D. Prasuhn, Nucl.Instrum. Meth. A279, 413 (1989).

[30] D. Reistad et al., Calculations on high-energyelectron cooling in the HESR, in Proceedingsof COOL 07 — Workshop on Beam Coolingand Related Topics, pages 44–48, BadKreuznach, Germany, 2007.

[31] H. Stockhorst et al., Stochastic CoolingDevelopments for the HESR at FAIR, inProc. of the European Accelerator ConferenceEPAC08, number THP055, page 3491, Genoa,Italy, 2008.

[32] A. Lehrach, O. Boine-Frankenheim,F. Hinterberger, R. Maier, and D. Prasuhn,Nucl. Instrum. Meth. A561, 289 (2006).

[33] F. Hinterberger, Monte carlo simulations ofThin Internal Target Scattering in Ceslius, inBeam-Target Interaction and Intra-beamScattering in the HESR Ring: Emittance,Momentum Resolution and Luminosity,Bericht des Forschungszentrum Julich, 2006,Jul-Report No. 4206.

[34] W.-M. Yao et al., Journal of Physics G33, 1(2006).

[35] A. Lehrach, IKP Annual Report Jul-4234,138 (2006).

[36] D. McGinnis, G. Stancari, and S. J. Werkema,Nucl. Instrum. Methods A 506, 205 (2003).

[37] M. Andreotti et al., Phys. Lett. B 654, 74(2007).

[38] T. A. Armstrong et al., Phys. Rev. D 47, 772(1993).

[39] D. C. Kennedy, Phys. Rev. D 46, 461 (1992).

[40] V. M. Aulchenko et al., Phys. Lett. B 573, 63(2003).

[41] A. Pesce, Studio della distribuzione ottimaledi luminosita per la misura dei parametri dirisonanza in fisica delle particelle (BScThesis, in Italian), 2007.

39

3 Software

The offline software which has been devised for thePANDA Physics Book benchmark studies follows anobject oriented approach, and most of the code hasbeen written in C++. Several well-tested softwaretools and packages from other HEP experiments areused and have been adapted to the PANDA needs.The software contains

• event generators with accurate decay modelsfor the individual physics channels as well asfor the relevant background channels,

• particle tracking through the complete PANDAdetector by using the GEANT4 transport code,

• the digitization which models the signals of theindividual detectors and their processing in thefront-end-electronics,

• the reconstruction and identification of chargedand neutral particles, providing lists of particlecandidates for the physics analysis and

• user friendly high level analysis tools which al-low to make use of vertex and kinematic fitsand to reconstruct extensive decay trees veryeasily.

3.1 Event Generation

For generating events representing the benchmarkreactions, EvtGen [1] was used. It allows to generatethe resonances of interest, taking into account theknown decay properties, including angular distri-butions, polarization, etc., and allows user defineddecay models.

For the simulation of the generic annihilation back-ground, the Dual Parton Model based generator,DPM, was used in the case of pp, and the Ultra-relativistic Quantum Molecular Dynamic model,UrQMD, in case of pN, which are described in moredetail in the following.

3.1.1 EvtGen Generator

EvtGen was first developed within the BaBar col-laboration, and originally it was designed for theneeds of studies at B-meson factories. The modu-lar design allows an easy extension to other physicschannels, and meanwhile EvtGen has been adaptedand used for ATLAS [2] and PANDA studies, too.

EvtGenmakes use of the formalism of spin densitymatrices. This enables the inclusion of spin effectsinto the simulation, and allows the user to studyangular distributions of particles in the final state.

The input data for each decay process are passedto the code as a complex amplitude. In cases wheremore than one complex amplitude are involved forthe same process, these are added before the decayprobabilities are calculated. Consequently, interfer-ence terms, which are of significant importance inmany channels studied with PANDA, are included.

The package also uses a novel nodal decay algo-rithm, where each decay step is treated indepen-dently, addressing the problem of cascade decays.In a conventional Monte Carlo generator, kinemat-ics for the whole chain would be generated at once,and the accept-reject decision applied on the result.This method is inefficient as a rejection leads to thewhole chain being regenerated from scratch. Thenode-wise method of EvtGen avoids this by gener-ating kinematics for each step separately. This ap-proach does lead to increasingly complex spin den-sity matrices being attached to the amplitudes foreach node, but the computation time required tocalculate these is very much less than what wouldbe needed to continually re-generate kinematics forthe whole decay tree.

EvtGen is controlled by means of a decay ta-ble, which lists all possible decay processes, theirbranching ratios and the decay model. A user de-cay table can be written to override the default tableand, thereby, exclude unwanted processes.

3.1.2 Dual Parton Model

The Dual Parton Model [3] is a synthesis ofthe Regge theory, topological expansions of QCD1/Nf or 1/Nc, and ideas from the parton model.The Regge theory gives the energy dependence ofhadron-hadron cross sections assuming various ex-changes of particles between projectile and targetin the t-channel. The cross sections are in a cor-respondence with diagrams of 1/N expansion. Thediagrams describe creation of unstable intermedi-ate s-channel states – quark-gluon strings or colourtubes.

The main objects of the model are constituentquarks having masses ∼ 300–350 MeV, strings, andstring junctions for baryons. It is assumed that


mesons consist of a quark and an antiquark whichare coupled by colour forces. The vortex lines ofthe field are concentrated in a small space regionforming a string-like configuration. So, mesons areconsidered as strings with small masses.

Baryons are assumed to consist of three quarks.Two possible string configurations in baryons wereconsidered: triangle and Mercedes star configura-tions [4, 5, 6, 7, 8, 9, 10]. Three strings are joinedin the central point in the Mercedes star case andgive the string junction.

Various processes are possible in baryon-antibaryoninteractions. Some of them are shown in Fig. 3.1where string junctions are presented by dashedlines. The diagram of Fig. 3.1a represents a pro-cess with string junction annihilation and creationof three strings. The diagram 3.1b describes quark-antiquark annihilation and string creation betweendiquark and anti-diquark. Quark-antiquark andstring junctions annihilation is shown in Fig. 3.1c.Finally, one string is created in the process ofFig. 3.1 e. After fragmentation of the strings,hadrons appear in the same way as in e+e−-annihilation. One can assume that excited stringswith complicated configuration are created in pro-cesses 3.1d and 3.1f. If the collision energy is suffi-ciently small, glueballs can be formed in the process3.1f. Mesons with constituent gluons can be createdin the process 3.1d.

The pomeron exchange is responsible for 2 stringsformation and diffraction dissociation (Fig. 3.1g and3.1h). They are dominant at high energies.

In the simplest approach it is assumed that the crosssections of the processes have an energy dependencegiven in Fig. 3.1 where s is the square of the totalenergy in the centre-of-mass system (CMS). Someof the processes (3.1d, 3.1f) have not a well-definedenergy dependence of the cross sections. Since it isusually assumed that their cross sections are small,we have neglected them.

A calculation of the cross sections is a rather com-plex procedure (see [11, 12]) because there are in-teractions in initial and final states. Here we followthe approach developed in Ref. [12]. The cross sec-tions calculated by us have a complicated energydependence. To reproduce it we have parametrised

Figure 3.1: The question marks mean that the corre-sponding estimations are absent.

the cross sections of Fig. 3.1 in the following form:

σa = 51.6/s0.5 − 58.8/s+ 16.4/s1.5,

σb = 77.4/s0.5 − 88.2/s+ 24.6/s1.5,

σc = 93/s− 106/s1.5 + 30/s2,

σd = σe = σf = 0,σg = 18.6/s0.08 − 33.5/s0.5 + 30.8/s,σh = 0,

where only the leading terms correspond to thatshown in Fig. 3.1. All cross sections are given inmb with s in GeV 2.

String masses are determined by kinematic proper-ties of quarks and antiquarks at their ends. Accord-ing to Ref. [3] we assume the following probabilitydistributions, dWi, in the processes 3.1a, 3.1c and3.1g:

dWa ∝ x−αR(0)+ dx+,

dWc ∝ x−αR(0)+ (1− x+)−αR(0)dx+,

dWg ∝ x−αR(0)+ (1− x+)αR()−2αN (0)dx+,


where x+ is the light-cone momentum fraction ofquarks, and αR(0) is the intercept of the non-vacuum reggeon trajectory.

The transverse momentum distribution of quarkshas been chosen in the form:

d2W = B2e−BpT d2pT , B = 4.5 (GeV/c)−1,

where pT is the transverse momentum, and B is theadjusted parameter.

The strings fragment into hadrons. The mechanismof the fragmentation is like the one applied in theLUND model [13, 14]. Here we use a code pro-posed by S. Ritter [15] with fragmentation func-tions (hadron distributions on light-cone momen-tum) taken from Refs. [16, 17]. Strings with smallmasses are considered as hadrons, and we put themon the mass-shell.

After the string fragmentation all unstable hadronsdecay. We simulate the processes with the help ofthe code DECAY [18].

The corresponding event generator has been devel-oped and tested successfully. It gives a possibilityto simulate the inelastic interactions as well as theelastic pp-scattering.

3.1.3 UrQMD

The Ultra-relativistic Quantum Molecular Dynamicmodel (UrQMD) [19, 20] is a microscopic modelbased on a phase space description of nuclear reac-tions. It describes the phenomenology of hadronicinteractions at low and intermediate energies (

√s <

5 GeV) in terms of interactions between knownhadrons and their resonances. At higher energies,√s > 5 GeV, the excitation of colour strings and

their subsequent fragmentation into hadrons aretaken into account in the UrQMD model.

The model is based on the covariant propagationof all hadrons considered on the (quasi-)particlelevel on classical trajectories in combination withstochastic binary scattering, colour string formationand resonance decay. It represents a Monte Carlosolution of a large set of coupled integro-differentialequations for the time evolution of the various phasespace densities of particle species i = N , ∆ , Λ,etc.. The main ingredients of the model are thecross sections of binary reactions, the two-body po-tentials and decay widths of resonances.

In the UrQMD model, the total cross section σtot

depends on the isospins of colliding particles, theirflavor and the c.m. energy. The total and elas-tic proton-proton and proton-neutron cross sections

are well known [21]. Since their functional depen-dence on

√s shows a complicated shape at low en-

ergies, UrQMD uses a lookup-table for those crosssections. The neutron-neutron cross section is as-sumed to be equal to the proton-proton cross sec-tion (isospin-symmetry). In the high energy limit(√s ≥ 5 GeV) the CERN/HERA parametrization

for the proton-proton cross section is used [21].

Baryon resonances are produced in two differentways, namely: hard production – N + N → ∆N ,∆∆, N∗N , etc. and soft production – π−+p→ ∆0,K−+p→ Λ∗ . . .

The cross sections of s-channel resonances forma-tion are fitted to measured data. Partial cross sec-tions are used to calculate the relative weights forthe different channels.

There are six channels for the excitation ofnon-strange resonances in the UrQMD model,namely NN → N∆1232, NN∗, N∆∗, ∆1232∆1232,∆1232N

∗, and ∆1232∆∗. The ∆1232 is explicitlylisted, whereas higher excitations of the ∆ reso-nance have been denoted as ∆∗. For each of these 6channels specific assumptions have been made withrespect to the form of the matrix element, and thefree parameters have been adjusted to the availableexperimental data.

Meson-baryon (MB) cross sections are dominatedby the formation of s-channel resonances, i.e. theformation of a transient state of mass m =

√s,

containing the total c.m. energy of the two in-coming hadrons. On the quark level such a pro-cess implies that a quark from the baryon annihi-lates an antiquark from the incoming meson. Atc.m. energies below 2.2 GeV, intermediate reso-nance states get excited. At higher energies thequark-antiquark annihilation processes become lessimportant. There, t-channel excitations of thehadrons dominate, where the exchange of mesonsand Pomeron exchange determine the total crosssection of the MB interaction [22].

To describe the total meson-meson (MM) reactioncross sections, the additive quark model and theprinciple of detailed balance, which assumes the re-versibility of the particle interactions, are used.

Resonance formation cross sections from the mea-sured decay properties of the possible resonances upto c.m. energies of 2.25 GeV for baryon resonanceand 1.7 GeV in the case of MM and MB reactionshave been calculated based on the principle. Abovethese energies collisions are modelled by the forma-tion of an s-channel string or, at higher energies (be-ginning at

√s = 3 GeV), by one or two t-channel

strings. In the strangeness channel elastic collisions


are possible for those meson-baryon combinationswhich can not form a resonance, while the creationof t-channel strings is always possible at sufficientlylarge energies. At high collision energies both crosssections become equal due to quark counting rules.

A parametrization proposed by Koch and Dover[23] is used in the UrQMD model for the baryon-antibaryon annihilation cross section. It is assumedthat the antiproton-neutron annihilation cross sec-tion is identical to the antiproton-proton annihila-tion cross section.

The potential interaction is based on a non-relativistic density-dependent Skyrme-type equa-tion of state with additional Yukawa- and Coulombpotentials. The Skyrme potential consists of asum of two- and a three-body interaction terms.The two-body term, which has a linear density de-pendence models the long range attractive compo-nent of the nucleon-nucleon interaction, whereas thethree-body term with its quadratic density depen-dence is responsible for the short range repulsivepart of the interaction. The parameters of the com-ponents are connected with the nuclear equation ofstate. Only the hard equation of state has beenimplemented into the current UrQMD model.

At the beginning of an event generation a target nu-cleus is modelled according to the Fermi-gas ansatz.The wave-function of the nucleus is defined as theproduct of nucleon wave-functions. A nucleon wave-function is represented by the Gauss function inthe configuration and momentum space. In con-figuration space, the centroids of the Gaussians arerandomly distributed within a sphere with radiusR(A), where R(A) is the nucleus radius. The ini-tial momenta of the nucleons are randomly chosenbetween 0 and the local Thomas-Fermi momentum.

The impact parameter of a collision is sampled ac-cording to the quadratic measure (dW ∼ bdb). Atgiven impact parameter, b, the centres of projec-tile and target are placed along the collision axis insuch a manner that the distance between the sur-faces of the projectile and the target is equal to3 fm. Momenta of nucleons are transformed in thesystem where the projectile and target have equalvelocities directed in different directions of the axis.After that the time propagation starts. During thecalculation, at the beginning of each time step eachparticle is checked whether it will collide within thattime step. A collision between two hadrons will oc-cur if d <

√σtot/π, where d and σtot are the im-

pact parameter and the total cross section of thetwo hadrons, respectively. After each binary colli-sion or decay the outgoing particles are checked forfurther collisions within the respective time step.

The hadron-hadron interactions at high energies aresimulated in 3 stages. According to the cross sec-tions, probabilities of interaction are defined (elas-tic, inelastic, antibaryon-baryon annihilation etc.),and a type of interaction is sampled. In the case ofinelastic collisions with string excitation, the kine-matic characteristics of strings are determined. Thestrings between quark and diquark (antiquark) fromthe same hadron are produced. The strings havethe continuous mass distribution f(M) ∝ 1/Mwith the masses M , limited by the total collisionenergy

√s: M1 + M2 ≤

√s. The remaining en-

ergy is equally distributed between the longitudinalmomenta of two produced strings.

The second stage of hadron-hadron interactions isrelated to string fragmentation. The fragmentationfunctions used in the UrQMD model are differentfrom the ones in the well-known LUND model [24].

The formation time of created hadrons is taken intoaccount in hadron-nucleus and nucleus-nucleus in-teractions.

The decay of the resonances proceeds according tothe branching ratios compiled by the Particle DataGroup [25]. The resonance decay products haveisotropic distributions in the rest frame of the reso-nance. If a resonance is among the outgoing parti-cles, its mass must first be determined according toa Breit-Wigner mass-distribution. If the resonancedecays into N > 2 particles, then the correspond-ing N -body phase space is used to calculate themomenta of the final particles.

The Pauli principle is applied to hadronic collisionsor decays by blocking the final state if the outgoingphase space is occupied.

The final state of a baryon-antibaryon annihilationis generated via the formation of two meson-strings.The available c.m. energy of the reaction is dis-tributed in equal parts to the two strings whichdecay in the rest frame of the reaction. On thequark level this procedure implies the annihilationof a quark-antiquark pair and the reordering ofthe remaining constituent quarks into newly pro-duced hadrons (additionally taking sea-quarks intoaccount). This model for the baryon-antibaryon an-nihilation thus follows the topology of a rearrange-ment graph.

The collision term in the UrQMD model con-tains 55 different baryon species (including nu-cleon, delta and hyperon resonances with massesup to 2.25 GeV) and 32 different meson species(including strange meson resonances with massesup to 1.9 GeV), which are supplemented by theircorresponding antiparticle and all isospin-projected


states. The states can either be produced in stringdecays, s-channel collisions or resonance decays.For excitations with masses larger than 2 GeV, astring picture is used. Full baryon/antibaryon sym-metry is included: the number of implementedbaryons therefore defines the number of antibaryonsin the model, and the antibaryon-antibaryon inter-action is defined via the baryon-baryon interactioncross sections.

A very important improvement of the UrQMDmodel was proposed in Ref. [26] where themodel was coupled with the Statistical Multi-fragmentation (SM) Model [27]. According toRef. [26], the UrQMD calculation is carried outup to a time scale referred to as the transitiontime ttr ∼ 100fm/c. The positions of the nucle-ons are then used to calculate the distribution ofmass and charge numbers of pre-fragments. In de-termining the mass and charge numbers of the pre-fragments, the minimum spanning tree method [28]is employed. A pre-fragment is formed if the dis-tances between nucleons are lower than 3 fm. Thetotal energy of each pre-fragment is determined inits rest frame by the Lorentz transformation. Theexcitation energy of a hot pre-fragment is calculatedas the difference between the binding energy of thehot pre-fragment and the binding energies of thispre-fragment in the ground state. The decay of thepre-fragments is described by the SM model.

We use the combination of the models for estima-tion of neutron production in p-interactions withnuclear targets.

3.2 Particle Tracking andDetector Simulation

The detector simulation is subdivided into twosteps. The first step is the propagation of the gener-ated particles through the PANDA detector by usingthe GEANT4 transport code [29, 30]. It takes intoaccount the full variety of interactions and decaysthat the different kinds of particles may undergo.The output of this first step is a collection of hits,which contain mainly the intersection points andenergy losses of all particles in the individual de-tector parts. Based on this information the digiti-zation step follows, which models the signals andtheir processing in the front-end-electronics of theindividual detectors, producing a digitised detectorresponse as similar as possible to beam data. Thisdesign ensures that in the future the same recon-struction code can be used for Monte Carlo and forbeam data. For performance reasons for some de-

tectors an effective smearing was used, which wasderived from Monte Carlo calculations using a fulldigitization.

3.2.1 Detector Setup

The geometry description of the PANDA detectoris based on the detector description database de-veloped by the CMS experiment [31]. It providesinterfaces between the geometry information storedin Extensible Markup Language (XML) files andthe corresponding transient objects of the individ-ual applications. The used XML schema consistsof type-safe XML constructs, abstract types, andhierarchical inheritance structures. This allows aneasy integration into a C++ environment.

Tools have been developed which are able to converttechnical drawings created by widely used Com-puter Aided Design (CAD) programs directly intothe XML based detector description. This makes itvery easy to add and remove geometries or to up-date modifications of specific detector parts in thesimulation.

The simulations have been done with the com-plete setup which was already described in detailin Sec. 2.2. The still not finally established Time-Of-Flight (TOF) and the Forward RICH detectorshave not been considered, and the Straw Tube op-tion has been used for the central tracker device.The Muon detector consists only of two scintillatorlayers instead of a multilayer scenario within theiron yoke which was the most favoured option dur-ing the implementation phase of the geometry intothe software. For the pp reactions the pellet sce-nario as an internal target has been chosen takinginto account the material budget of the target pipeand the pumping stations. The interaction pointhas been considered with a spread of σ=0.275 mmin each direction.

Fig. 3.2 shows the contributions of the subdetec-tors to the material which a particle has to traverseto reach the EMC as a function of θ. The materialthicknesses are presented in units of the correspond-ing radiation lengths X0.

3.2.2 Digitization

3.2.2.1 Readout of the Tracking Devices

3.2.2.1.1 Silicon Readout of the MVD The Mi-cro Vertex Detector (MVD) makes use of two dif-ferent silicon detector types, silicon strip and pixeldetectors. The readout of the silicon devices is


Figure 3.2: Contributions of the subdetectors to thematerial budget in front of the EMC in units of a radi-ation length X0 as a function of the polar angle θ.

for both types different and is treated differentlyin the digitization scheme. The signal in the sen-sor is formed by using the local trajectory withinthe detector material to calculate the correspond-ing channel relative to the readout matrix of thesensor. The hit position on the sensor surface de-fines the channel number and the deposited energythe charge collected by the electronics. The chan-nel mapping of the trajectory is done on both sidesof the sensor. In the case of the pixel detectors,the trajectory is projected to the surface and de-pending on its relative orientation, all excited pixelcells are calculated and the charge signal is sharedamong all pixel cells depending on the fraction ofthe local track. Strip sensors will be sensitive onboth sides and the formation of digitised channelsis done independently on both sides of the sensor.The procedure is similar to the pixel case but doneonly in one dimension.

The size of the readout structures are defined bythe size of the pixel cell or the spacing of the strips.These parameters can be changed interactively inorder to test various settings and have to meet thedimensions of the sensor. The channel is assignedto a frontend and a common number of 128 chan-nels per frontend have been chosen. In the case ofthe pixel detector the size of the ATLAS frontendchip was used as basis to assign a frontend num-ber to a certain channel. Since the electronics chipis bump bonded onto the surface of the detectorthe number of pixel cells per frontend is defined bythe dimension of the frontend chip. A threshold forthe electronics signal can be set and was chosen asstandard to an equivalent of 300 electrons which isa reasonable value for pixel detectors.

3.2.2.1.2 Straw Tube Tracker and Drift Cham-bers The digitization for the Straw Tube Tracker(STT) and the Drift Chambers (DCH) have beentreated in a similar way. Both devices consist ofwires inside an ArCO2 gas mixture volume. If acharged particle traverses this gas volume, the localhelix trajectory is derived from the correspondingGEANT4 intersection points. The drift time of theionization electrons is estimated from the smallestdistance of this helix trajectory to the wire dpoca.The uncertainty of the drift time is taken into ac-count by smearing dpoca with a Gaussian distribu-tion with a standard deviation of σ = 150µm forthe STT, and σ = 200µm for the DCH devices.

The average number of primary ionization electronsis the total deposited energy in the gas volume di-vided by the ionization energy of 27 eV for ArCO2.The energy signal of a straw tube is finally calcu-lated by taking into account Poisson statistics.

3.2.2.1.3 GEMs Readout Each GEM stationconsists of two detector planes. The distance be-tween the detector planes is 1 cm. It has been as-sumed that each detector plane has two strip de-tector layers with perpendicular orientation to eachother. The gas amplification process and the re-sponse of the strip detector has not been simulatedin detail. Instead, the entry point of a charged trackinto the detector plane has been taken directly fromGEANT4 and smeared with a Gaussian distributionof 70µm width in each strip orientation direction.

3.2.2.2 Readout of the DIRC Detectors

The light propagation in the Cerenkov radiators,the signal processing in the front-end-electronics,and the reconstruction of the Cerenkov angle havebeen modelled in a single effective step.

The resolution of the reconstructed Cerenkov angleσC is mainly driven by the uncertainty of the singlephoton angle σC,γ and the statistics of relativelysmall numbers of detected Cerenkov photons Nph:

σC =σC,γ√Nph

A single photon resolution of σC,γ = 10 mrad wasused, corresponding to the experience with existingDIRC detectors. The number of detected photonswas calculated from the velocity, β, of charged par-ticles passing through the quartz radiators and thepath length L within the radiator, via:

Nph = ε 2παL (1− 1β2n2

quartz

)(1

λmin− 1λmax

) ,


where α is the fine structure constant and nquartz =1.473 the refraction index of quartz. The sensi-tive wavelength interval, λmin–λmax, was chosen to[280 nm , 350 nm], and a total efficiency of ε = 7.5 %was used to take into account the transmission andreflectivity losses as well as the quantum efficiencyof the photo detectors. Fig. 3.3 shows the simu-lated number of photons for the Barrel DIRC as afunction of the polar angle for 1 GeV/c pions. Theaverage number of detected photons at a polar an-gle of 90, 20, increases by a factor of 2 for veryforward and backward directions.

Figure 3.3: The number of detected Cerenkov photonsversus the polar angle of pions with momenta of 1 GeV/c.

Fig. 3.4 shows the precision of the measuredCerenkov angle obtained with the digitization andreconstruction procedure described above. A fitwith a Gaussian distribution yields to a resolutionof σ = 2.33 mrad.

Figure 3.4: Difference between the reconstructed andexpected Cerenkov angle ∆ΘC for single 1 GeV/c pions.

3.2.2.3 EMC Scintillator Readout

For the EMC in the target spectrometer (TS EMC)reasonable properties of PbWO4 crystals at the op-erational temperature of -25C have been consid-ered. A Gaussian distribution with a σ of 1 MeVhas been used for the constant electronics noise.The statistical fluctuations were estimated by 80photo electrons per MeV produced in the LargeArea Avalanche Photo Diode (LAAPD). An excessnoise factor of 1.38 has been used, corresponding tothe measurements with the first LAAPD prototypeat an internal gain ofM = 50 (see [32]). This resultsin a photo statistics noise term of 0.41 %/

√E/GeV.

For the forward calorimeter (FS EMC) a Shashlykdetector consisting of lead-scintillator sandwiches isforeseen. Therefore, only a fraction of roughly 30 %of the energy are deposited in the scintillator ma-terial. Based on this energy deposit the electronicsnoise with σ = 3 MeV has been considered whichyields to a statistic noise term of 0.8 %/

√E/GeV.

3.2.2.4 Muon Detector Readout

Because the layout of the muon detector and itsreadout is still under investigation, a parametriseddigitization was used. The intersections of the par-ticle tracks with the scintillators of the muon de-tectors were derived from the detector hits pro-vided by the GEANT4 transport code. In the pro-cess of matching muon detector hits with recon-structed charged tracks, the uncertainties are domi-nated by the errors from the extrapolation of the re-constructed tracks to the muon detector, and there-fore the finite position resolution of the muon de-tector was neglected. The algorithm that was usedto deduce PID probabilities from the muon detectorhits will be described in Sec. 3.3.3.1.4.

3.3 Reconstruction

3.3.1 Charged Particle TrackReconstruction

3.3.1.1 MVD Cluster Reconstruction

The MVD provides very precise space point mea-surements as a basis for the track and vertex recon-struction. The hit resolution of individual MVDmeasurements is shown in Fig. 3.5 in the case ofthe pixel detector.

The distribution in Fig. 3.5 shows the difference be-tween the reconstructed position on the sensor and


Figure 3.5: The resolution of the reconstructed hitposition after clustering with respect to the simulatedvalue.

the generated Monte Carlo value. The broad con-tribution comes from hits where only one pixel iscontributing to the hit cluster and the narrow con-tribution from multi hit clusters. In the latter case,charge weighting between the pixel cells in the clus-ter can be used to calculate the mean position ofthe hit. Without using the energy information, theresolution of the position measurement would be

σgeom = p/√

12

where p is the size of the readout structure. Using100 × 100µm large pixel cells, the geometric reso-lution is σgeom = 28µm, which is the uncertaintyof the broader distribution caused by single pixelclusters. For high momentum particles the hit res-olution limits the overall track resolution whereasfor low momentum particles the small angle scat-tering is the limiting factor.

3.3.1.2 Global Track Reconstruction

The track object provides information about acharged particle path through space. It containsa collection of hits in the individual tracking sub-detectors. Each hit knows about the residual of thehit to a given reference trajectory and the precisionof the measurement. For example, the hit resid-ual of the STT is defined as the closest approach ofthe reference trajectory to the wire of the straw mi-nus the actual drift distance. In case of hits in theMVD or in a GEM station, the residual is defined asthe distance between the sensor and the referencetrack in the detector plane. An idealised patternrecognition has been used for track building basedon Monte Carlo information to assign reconstructedhits to their original tracks. Tracks which containless than eight detector hits were rejected.

The tracks in the target spectrometer are fitted withthe Kalman Filter algorithm, which considers notonly the measurements and their corresponding res-olutions but also the effect of the interaction withthe detector material, i.e. multiple scattering andenergy loss. A detailed description of the imple-mentation of the algorithm, which has been adaptedfrom the reconstruction software of the BaBar Col-laboration can be found in [33]. For simplificationa constant magnetic field parallel to the z-axis hasbeen assumed in the target spectrometer region. Atypical choice for the parametrization of the track ina solenoidal field is a five-parameter helix along theprinciple field direction z. The following parametervector P is used:

P = (d0, φ0, ω, z0, tanλ)

where d0 is the distance of closest approach to theorigin in the x-y plane, signed by the angular mo-mentum ~r × ~p at that point, φ0 is the angle in thex-y plane at closest approach, and z0 the distanceof closest approach to the origin in the z projec-tion. The parameter ω gives the curvature of thetrack in the x-y plane, and tanλ is the tangent ofthe track dip angle in the projection plane definedby the cylindrical coordinates ρ and z. The positionof the particle as a function of the x-y plane pro-jection of the flight length from the point of closestapproach l is given by:

x = sin(φ0 + ω · l)/ω − (1/ω + d0) sinφ0

y = − cos(φ0 + ω · l)/ω − (1/ω + d0) cosφ0

z = z0 + l · tanλ

The momentum of the track for a given magneticfield (0,0,B) is then:

px = q · c ·B/ω · cos(φ0 + ω · l)py = q · c ·B/ω · sin(φ0 + ω · l)pz = q · c ·B/ω · tanλ

The task of the track-fitting algorithm is to deter-mine the optimal parameter vector and its covari-ance matrix as a function of the flight length l inorder to create a representation of the track as apiecewise helix. In the physics analysis the parti-cle position and momentum can then be accessedthrough this piecewise helix representation.

Tracks which have hits in the target spectrometeras well as in the drift chambers of the forward spec-trometer are treated in the following way. From thehit residuals of the drift chambers a χ2 is calculated,where the propagation of the track through space isdone with a Runge-Kutta integration method. Forminimising the χ2 the package MINUIT [34] is used.


The result of the fit is a five-parameter helix andits covariant matrix at z = 1.9m. This informa-tion serves as a constraint for the Kalman Filter fit,where also the hits in the target spectrometer areconsidered.

Multiple scattering and energy loss effects dependon the mass of the particle. Therefore, the trackshave been refitted separately for all five particle hy-potheses (e, µ, π, K and p). This results in anadequate accuracy of the reconstructed kinematicsassigned to the individual particle species.

3.3.1.3 Tracking Performance

In the following the track reconstruction efficiency,the momentum resolution, and the spatial resolu-tion for reconstructed vertexes are shown, whichwere achieved for the chosen detector setup usingthe reconstruction software described above.

The upper histogram of Fig. 3.6 shows the obtainedtrack efficiency as a function of the transverse mo-mentum for single pions generated at a polar angleof 60. The efficiency is here defined as the ratio be-tween the number of tracks which fulfil only a lowcriterion on the accuracy of the reconstructed trans-verse momentum to the number of generated tracks.It is required that the difference between the recon-structed to the generated momentum is less than3 σ of its resolution. While above pt > 0.2 GeV/cmore than 90 % of the tracks are well measured, theefficiency decreases to 70 % for a transverse momen-tum of 0.1 GeV/c. These results are comparable tothe track efficiency for real data obtained with theBaBar detector (Fig. 3.6 and [35]).

Fig. 3.7 illustrates the reconstructed momentum forpions of 1 GeV/c momentum at a polar angle of 20.This example yields to a momentum resolution ofσp/p = 1 %.

The achieved vertex resolution is shown in Fig. 3.8for pions of 3 GeV/c momentum. Here all trackingdetectors were taken into account.

3.3.2 Photon Reconstruction

3.3.2.1 Reconstruction Algorithm

A photon entering one scintillator module of theEMC develops an electromagnetic shower which, ingeneral, extends over several modules. A contigu-ous area of such modules is called a cluster.

The energy deposits and the positions of all scin-tillator modules in a cluster allow a determinationof the four vector of the initial photon. Most of

Figure 3.6: The track reconstruction efficiency as afunction of the transverse momentum for pions at a po-lar angle of 60 (upper histogram).The lower histogram was taken from [35] and illustratesthe track reconstruction efficiency achieved at BaBar fortwo different operation modes of the central drift cham-ber.

Figure 3.7: The momentum resolution for pions of1 GeV/c momentum at a polar angle of 20.

the EMC reconstruction code used in the offlinesoftware is based on the cluster finding and bump-


Figure 3.8: The achieved vertex resolution for pionsof 3 GeV/c momentum.

splitting algorithms which were developed and suc-cessfully applied by the BaBar experiment [35, 36].

The first step of the cluster reconstruction is thefinding of a contiguous area of scintillator moduleswith energy deposit. The algorithm starts at themodule exhibiting the largest energy deposit. Itsneighbours are then added to the list of modules ifthe energy deposit is above a certain threshold Extl.The same procedure is continued on the neighboursof newly added modules until no module fulfils thethreshold criterion. Finally a cluster gets acceptedif the total energy deposit in the contiguous area isabove a second threshold Ecl.

The next step is the search for bumps within eachreconstructed cluster. A cluster can be formed bymore than one particle if the angular distances ofthe particles are small. In this case the cluster hasto be subdivided into regions which can be associ-

ated with the individual particles. This procedure iscalled the bump splitting. A bump is defined by a lo-cal maximum inside the cluster: The energy depositof one scintillator module Elocal must be aboveEmax, while all neighbour modules have smaller en-ergies. In addition the highest energy ENmax ofany of the N neighbouring modules must fulfil thefollowing requirement:

0.5 (N − 2.5) > ENmax /Elocal (3.1)

The total cluster energy is then shared between thebumps, taking into account the shower shape ofthe cluster. For this step an iterative algorithm isused, which assigns a weight wi to each scintilla-tor module, so that the bump energy is defined asEb =

∑i wiEi. Ei represents the energy deposit

in the iTH module and the sum runs over all mod-ules within the cluster. The module weight for eachbump is calculated by

wi =Ei exp(−2.5 ri / rm)∑j Ej exp(−2.5 rj / rm)

(3.2)

with

• rm = Moliere radius of the scintillator material,

• ri,rj = distance of the iTH and jTH module tothe centre of the bump, respectively, and

• index j runs over all modules.

The procedure is iterated until convergence. Thecentre position is always determined from theweights of the previous iteration and convergence isreached when the bump centre stays stable withina tolerance of 1 mm.

The spatial position of a bump is calculated via acentre-of-gravity method. The radial energy distri-bution, originating from a photon, decreases mainlyexponentially. Therefore, a logarithmic weightingwith

Wi = max(0, A(Eb) + ln(Ei/Eb)) (3.3)

was chosen, where only modules with positiveweights are used. The energy dependent factorA(Eb) varies between 2.1 for the lowest and 3.6 forthe highest photon energies.

3.3.2.2 Reconstruction Thresholds

The optimal choice for the three photon reconstruc-tion thresholds – as already explained in 3.3.2.1 –depends strongly on the light yield of the scintil-lator material and the electronics noise. To detect


TS EMC FW EMCExtl 3 MeV 8 MeVEcl 10 MeV 15 MeVEmax 20 MeV 10 MeV

Table 3.1: Reconstruction thresholds for the PbWO4

and Shashlyk calorimeter.

low energetic photons and to achieve a good energyresolution, the thresholds should be set as low aspossible. On the other hand, the thresholds mustbe sufficiently high for a suppression of misleadinglyreconstructed photons originating from the noise ofthe readout and from statistical fluctuations of theelectromagnetic showers. The single crystal thresh-old was set to 3 MeV of deposited energy, corre-sponding to the energy equivalent of 3 σ of the elec-tronics noise (see Sec. 3.2.2.3). All reconstructionthresholds for the TS EMC as well as for the FWEMC are listed in Table 3.1.

3.3.2.3 Leakage Corrections

The sum of the energy deposited in the scintillatormaterial of the calorimeters is in general less thanthe energy of the incident photon. While only a fewpercent is lost in the TS EMC, which mainly orig-inates from energy losses in the material betweenthe individual crystals, a fraction of roughly 70 %of the energy is deposited in the absorber materialfor the Shashlyk calorimeter.

The reconstructed energy of the photon in the TSEMC is expressed as a product of the measured to-tal energy deposit and a correction function whichdepends logarithmically on the energy and – dueto the layout – also on the polar angle. MonteCarlo simulations using single photons have beencarried out to determine the corrected photon en-ergy Eγ,cor = E∗f(lnE, θ) with the correction func-tion

f(lnE, θ) = exp(a0 + a1 lnE + a2 ln2E + a3 ln

3E

+a4 cos(θ) + a5 cos2(θ) + a6 cos3(θ)+a7 cos4(θ) + a8 cos5(θ)

+a9 lnE cos(θ))

Fig. 3.9 shows the result for the barrel part in theθ range between 22 and 90.

The energy leakage in the FW EMC is mainlydriven by the huge amount of absorber material andis just slightly caused by the geometry. Therefore, acorrection has been considered which only depends

Figure 3.9: The leakage correction function for thebarrel EMC in the θ range between 22 and 90.

on the collected energy. Fig. 3.10 shows the result-ing correction function for energies up to 5 GeV.

Figure 3.10: The leakage correction function depend-ing on the deposited energy for the Shashlyk calorime-ter.

3.3.3 Charged Particle Identification

Good particle identification for charged hadronsand leptons plays an essential role for PANDA andmust be guaranteed over a large momentum rangefrom 200 MeV/c up to approximately 10 GeV/c. Sev-eral subdetectors provide useful PID informationfor specific particle species and momenta. While en-ergy loss measurements within the trackers obtaingood criteria for the distinction between the differ-ent particle types below 1 GeV/c, the DIRC detectoris the most suitable device for the identification ofparticles with momenta above the Cerenkov thresh-old. Moreover, in combination with the tracking


detectors, the EMC is the most powerful detectorfor an efficient and clean electron identification, andthe Muon detector is designed for the separation ofmuons from the other particle species. The bestPID performance however can be obtained by tak-ing into consideration all available information ofall subdetectors.

The PID software is divided in two different parts.In the first stage the recognition is done for eachdetector individually, so that finally probabilitiesfor all five particle hypothesis (e, µ, π, K andp) are provided. The probabilities are normaliseduniquely by assuming same fluxes for each particlespecies.In the second stage the global PID combinesthis information by applying a standard likelihoodmethod. Based thereon, flexible tools can be usedwhich allow an optimization of efficiency and pu-rity, depending on the requirements of the particu-lar physics channel.

3.3.3.1 Subdetector PID

3.3.3.1.1 dE/dx Measurements The energyloss of particles in thin layers of material directlyprovides an access to the dE/dx. As can be seendirectly from the Bethe-Bloch formula, for a givenmomentum particles of different types have differ-ent specific energy losses, dE/dx. This propertycan be used for particle identification, as illustratedin Fig. 3.11. The method however suffers from twolimitations. First of all, at the crossing points, thereis no possibility to disentangle particles. Secondly,the distribution of the specific energy loss displaysa long tail which constitutes a limitation to the sep-aration, especially when large differences exist be-tween the different particle yields. Various methodshave been worked out to circumvent this second lim-itation. In PANDA, two detectors will give accessto a dE/dx measurement, the MVD detector setup,and the central spectrometer tracking system. Inthe present status of the simulation, only the StrawTube Tracker option has been investigated in de-tail. Although not discussed here, the TPC will alsobe able to give very good identification capabilitiesthrough dE/dx measurements.

3.3.3.1.1.1 MVD Although the number of re-constructed MVD hit points per track is limited to4 in the barrel section and 5-6 in the forward do-main the energy loss information provided by thereadout electronics can be used as part of the parti-cle identification decision. The ability of separatingdifferent particle species relies on an accurate en-

Figure 3.11: Typical truncated dE/dx plot as a func-tion of momentum for the 5 particle types

Figure 3.12: dE/dx information from the MVD ver-sus track momentum for protons (upper band), kaons(middle) and pions/muons/electrons (lower).

ergy loss information and a good knowledge of thetrack position with respect to the sensors. Contraryto the usual method of summing the individual hitmeasurements dEi/dxi to an energy loss informa-tion all hit measurements can be combined to a to-tal quantity

S =∑dEi∑dxi

n−1e

where n−1e is the electron density in silicon. The dEi

are the energy information from the reconstructedhit and the dxi are obtained by calculating thelength of the reconstructed track traversing the sen-sor material. This method gives a slightly smallerspread of the Landau-smeared energy loss. Fig. 3.12shows the calculated energy loss versus particle mo-


mentum for different particle types. Separation ispossible only for protons (upper band) and kaons(middle) from the lowest band which is a superpo-sition of pions, muons and electrons.

The width of the individual bands depends on theenergy-loss distribution which varies with momen-tum. To reproduce the distribution all uncertaintiesare merged into a single Gaussian-distributed errorwhich is added to the already Landau-distributedenergy loss. The distribution has to be calculatedusing numerical integration of the convolution inte-gral

w(s) =∫L(x)G(s− x)dx

with the parameters σ for the Gauss width, τ re-spectively for the Landau width and s, which isthe most probable value of the Landau distribution.The used parametrizations for the distributions are

Gσ(x) =1√2πσ

e−x2/σ2

for the Gauss distribution and

Lτ (x) =1πτ

∫ ∞0

e−t(ln t−x/τ) sin(πt)dt

for the scaled Landau distribution. For each par-ticle type the parameters were obtained indepen-dently by generating 3 × 105 single particle eventseach over a momentum range from 50 MeV/c to1.5 GeV/c. The energy loss distribution was fittedfor 25 MeV/c bins to get the parameters si, σi, τifor a given pi. The width parameters σ and τ forprotons are shown in Fig. 3.13 and the small inset

Figure 3.13: The change of the width parameters σand τ for protons.

shows the energy loss distribution for the momen-tum bin ∆p = 0.65 . . . 0.675 GeV/c. For all particletypes the evolution of the parameters s(p), σ(p) andτ(p) are fitted with polynomials and used as a basisfor the calculation of the particle hypothesis.

3.3.3.1.1.2 STT The energy loss of particlesthrough thin layers of gas provides an opportunityfor particle identification in a large domain of mo-mentum. However, when thicknesses as low as a fewmm of gas are considered, the fluctuations resultingfrom the relatively low number of primary collisions(less than 100 on a 1 cm Ar pathlength) give riseto an extended Landau tail in the energy loss dis-tribution. To circumvent this phenomenon whichcould result into a dramatic reduction of PID capa-bilities, truncation methods associated to differentaveraging procedures are often used. The truncatedarithmetic mean has been used in the framework ofPANDA. Moreover, as straw tubes are cylindricaldetectors, a path length determination is necessaryto calculate a dE/dx. A transverse resolution of150 µm was assumed. With the used hexagonalSTT setup, particles pass 24 straw tubes on aver-age in the angular range from 22 to 140. Thisnumber decreases rapidly to 8 straw tubes at 14.

A truncation parameter of 70, corresponding tokeeping 70 % of the smallest energy loss values, wasfound to be the best compromise between the res-olution defined by the Gaussian fit and the tailstill remaining after truncation. Parameters of theGaussians (µi and σi) were obtained and tabu-lated for all particle types over the angular range[14, 140] covered by the STT and for momentaranging from a minimum of 400 MeV/c up to themaximum allowed by kinematics in pp collisions at15 GeV/c. The dependence on the angle φ was notincluded in the simulation. However, the effect isexpected to be important only in the two 6 wide φangular regions at 90 and 270. Outside the abovementioned limits, a priori probabilities are sharedequally between all particle types e, µ, π,K and p.For a given triplet (p, θ, dE/dxtrunc), five a prioriprobabilities are calculated using the parameters ofthe Gaussians (µi,σi, i =, e, µ, π,K and p), prop-erly normalised. To take into account the role ofpossible non Gaussian tails, a lower limit on thelikelihood was set to 1 %. These likelihoods canthen be directly combined with the ones from theother detectors to calculate a global likelihood.

Fig. 3.14 shows the likelihoods for being identifiedas electrons for particles with momenta between0.2 GeV/c and 10 GeV/c and polar angles between14 and 140.

Whereas an efficiency above 98 % is observed forelectrons (see figure Fig. 3.15), the contaminationrate, that is the probability for another type of par-ticle (µ, π,K and p) to be identified as an electronvaries between 1 % and 16 %. One should. how-ever, note that these values are averaged over the


Figure 3.14: The distribution of the likelihoods forelectron identification, averaged over the whole STTangular range in the [0.2,10.] GeV/c momentum range.The peak at 0.2 corresponds to cases when all particlelikelihoods are finally set to the same value of 0.2: thishappens when all 5 first-guess likelihoods are below 1 %.

polar angle: at forward angles, the contaminationincreases as the result of the strong decrease of thenumber of hits in the straw tubes.

Figure 3.15: The efficiency for electrons in the mo-mentum range between 0.2 GeV/c and 10 GeV/c and thecontamination rates for the four other particle types,averaged over the whole STT angular range.

3.3.3.1.2 PID with DIRC Charged tracks areconsidered if they can be associated with the pro-duction of Cerenkov light in the DIRC detector.Based on the reconstructed momentum, the recon-structed path length of the particle in the quartzradiator and the particle hypotheses the expectedCerenkov angles and its errors are estimated. Com-pared with the measured Cerenkov angle the likeli-hood and significance level for each particle species

are calculated. As an example for the DIRC per-formance Fig. 3.16 shows the obtained kaon effi-ciency and contamination rate by applying a Loosekaon criterion on the DIRC PID. The loose crite-rion corresponds to the kaon probability of 30 %.While below the Cerenkov threshold of approxi-mately 500 MeV/c almost no kaon can be identifiedthe efficiency above the threshold is more than 80 %over the whole momentum range up to 5 GeV/c. Thefraction of pions misidentified as kaons is substan-tially less than 10−3 for momenta below 3 GeV/cand increases up to 10 % for 5 GeV/c.

Figure 3.16: The kaon efficiency and contaminationrate of the remaining particle species in different mo-mentum ranges by using the DIRC information.

3.3.3.1.3 Electron Identification with the EMCThe footprints of deposited energy in the calorime-ter differ distinctively for electrons, muons andhadrons. The most suitable property is the de-posited energy in the calorimeter. While muonsand hadrons in general lose only a certain fractionof their kinetic energy by ionization processes, elec-trons deposit their complete energy in an electro-magnetic shower. The ratio of the measured energydeposit in the calorimeter to the reconstructed trackmomentum (E/p) will be approximately unity. Dueto the fact that hadronic interactions can take place,hadrons can also have a higher E/p ratio than ex-pected from ionization. Figure Fig. 3.17 shows thereconstructed E/p fraction for electrons and pionsas a function of the momentum.

Furthermore, the shower shape of a cluster is help-ful to distinguish between electrons, muons andhadrons. Since the chosen size of the scintillatormodules corresponds to the Moliere radius of thematerial, the largest fraction of an electromagneticshower originating from an electron is contained in


Figure 3.17: E/p versus track momentum for elec-trons (green) and pions (black) in the momentum rangebetween 0.3 GeV/c and 5 GeV/c.

just a few modules. Instead, an hadronic showerwith a similar energy deposit is less concentrated.These differences are reflected in the shower shapeof the cluster, which can be characterised by thefollowing properties:

• E1/E9 which is the ratio of the energy de-posited in the central scintillator module andin the 3×3 module array containing the cen-tral module and the first innermost ring. Alsothe ratio between E9 and the energy deposit inthe 5×5 module array E25 is useful for electronidentification.

• The lateral moment of the cluster defined by

momLAT =n∑i=3

Eir2i /(

n∑i=3

Eir2i +E1r

20 +E2r

20)

with

– n: number of modules associated to theshower

– Ei: deposited energy in the iTH modulewith E1 ≥ E2 ≥ ... ≥ En

– ri: lateral distance between the centraland the iTH module

– r0: the average distance between twomodules.

• A set of Zernike moments which describe theenergy distribution within a cluster by radialand angular dependent polynomials. An ex-ample is given in Fig. 3.18, where the Zernikemoment 31 is depicted for each particle type.

Figure 3.18: Zernike moment for electrons, muons andhadrons.

Since a lot of partially correlated EMC propertiesare suitable for electron identification, a MultilayerPerceptron (MLP) with 10 input nodes, 13 hiddennodes, and one output node has been applied. Theadvantage of a neural network is that it can providea correlation between a set of input variables andone or several output variables without any knowl-edge of how the output formally depends on theinput. The training of the MLP has been donewith a data set of 850 k single tracks for each par-ticle species (e, µ, π, K and p) in the momentumrange between 200 MeV/c and 10 GeV/c in such away that the output values are constrained to be1 for electrons and -1 for all other particle types.10 input variables in total have been used, namelyE/p, p, the polar angle θ of the cluster, and 7 showershape parameters (E1/E9, E9/E25, the lateral mo-ment of the shower and 4 Zernike moments). Theresponse of the trained network to a test data setof single particles in the momentum range between300 MeV/c and 5 GeV/c is illustrated in Fig. 3.19.The logarithmically scaled histogram shows that analmost clean electron recognition with a quite smallcontamination of muons and hadrons can be ob-tained by applying a cut on the network output.

For the global PID a correlation between the net-work output and the PID likelihood of the EMChas been calculated. Fig. 3.20 shows the electronefficiency and contamination rate as a function ofmomentum achieved by requiring an electron likeli-hood fraction of the EMC of more than 95 %. Formomenta above 1 GeV/c one can see that the elec-tron efficiency is greater than 98 % while the con-tamination by other particles is substantially lessthan 1 %. For momenta below 1 GeV/c, the electronidentification based solely on the EMC information


Figure 3.19: MLP network output for electrons andthe other particle species in the momentum range be-tween 300 MeV/c and 5 GeV/c.

has a poor efficiency and an insufficient purity.

Figure 3.20: The electron efficiency and contamina-tion rate for muons, pions, kaons and protons in differ-ent momentum ranges by using the EMC information.

3.3.3.1.4 PID with the Muon Detector Theparticle ID for the muon detector is based on analgorithm which quantifies for each reconstructedcharged track the compatibility with the muon hy-pothesis. It propagates the charged particles fromthe tracking volume outward through the neigh-bouring detectors like DIRC and EMC and finallythrough the iron, where the scintillator layers ofthe muon device are located. This procedure takesinto account the obtained parameters of the globaltracking, the magnetic field as well as the muonenergy loss in the material and the effects of multi-ple scattering. Then the extrapolated intersectionpoints with the scintillators are compared with the

detected muon hit positions. In case the distancebetween the expected and the detected hit is smallerthan 12 cm, according to 4σ of the correspondingdistribution, the muon hit will be associated withthe corresponding charged track. Fig. 3.21 showsan example for the obtained spatial resolution be-tween the expected and the corresponding detectedhits. The distribution of the distance in x-directionfor generated single muons yields to a resolutionσx = 3.0 cm. Based on the numbers of associatedand expected muon hits, the likelihoods for eachparticle type are estimated.

The procedure results in a good muon identificationfor momenta above approximately 1 GeV/c. Whileelectrons can be completely suppressed, a contam-ination rate of only a few percent can be achievedfor hadrons.

Figure 3.21: The distribution of the distance in x-direction between the expected hits obtained by the ex-trapolation and the corresponding detected hits in themuon detector. This figure illustrates an example forgenerated single muon particles hitting on specific layerwithin the barrel yoke.

3.3.3.2 Global PID

The global PID, which combines the relevant in-formation of all subdetectors associated with onetrack, has been realised with a standard likelihoodmethod. Based on the likelihoods obtained by eachindividual subdetector the probability for a trackoriginating from a specific particle type p(k) is eval-uated from the likelihoods as follows:

p(k) =∏i pi(k)∑

j

∏i pi(j)

, (3.4)

where the product with index i runs over all con-sidered subdetectors and the sum with index j overthe five particle types e, µ, π, K and p.


Due to the variety of requirements imposed by thedifferent characteristics of the benchmark channelsvarious kinds of particle candidate lists dependingon different selection criteria on the global likeli-hood are provided for the analysis (see. Table 3.2).The usage of the so-called VeryLoose and Loosecandidate lists allows to achieve good efficiencies,and the Tight and VeryTight lists are optimisedto obtain a good purity with efficient backgroundrejection. Fig. 3.22 represents the performance ofthe global PID for the VeryTight list for kaon andelectron candidates, respectively.

candidate listparticle VeryLoose Loose Tight VeryTight

e 20 % 85 % 99 % 99.8 %µ 20 % 45 % 70 % 85 %π 20 % 30 % 55 % 70 %K 20 % 30 % 55 % 70 %p 20 % 30 % 55 % 70 %

Table 3.2: Selection criteria for the particle candidatelists provided for the analysis. The table represents theminimal values for the global likelihood (see. Eq. 3.4),which are required for the corresponding particle types.

3.4 Physics Analysis

The event data used for physics analysis is struc-tured in three levels of detail:

• the small TAG level contains brief event sum-mary data

• the Analysis Object Data (AOD) mainly con-sists of PID lists of particle candidates, and, inthe case of MC data, also of MC truth data.Most analysis jobs run on AOD data.

• the Event Summary Data (ESD), which holdsall reconstruction objects down to the detectorhits which are necessary to redo the track andneutral particle reconstruction, and to rebuildthe PID information. The detailed ESD datais needed only by very few analysis jobs.

This event data design directly supports the typicalanalysis tasks, which usually can be subdivided intothree steps:

• a fast event preselection that uses just the TAGdata

Figure 3.22: The kaon (upper histogram) and elec-tron (lower histogram) efficiency with the contamina-tion rate of the remaining particle species in differentmomentum ranges by applying VeryTight cuts on theglobal likelihood. The results are based on single parti-cles generated within the θ range between 25 and 140.

• an event reconstruction and refined event se-lection step using the AOD data. In the eventreconstruction, decay trees are built up, andgeometrical and kinematic fits are applied onthem. Cuts on the fit probabilities, invariantmasses or kinematic properties of the candi-dates are common to refine the event selectionin this step. The output of this analysis stepusually are n-tuple like data.

• in the last analysis step the event selection canbe further refined by applying cuts on the n-tuple data, and histogram fits or partial waveanalyses can be performed on the final set ofevents.


3.4.1 Analysis Tools

The used application framework provides filtermodules which allow a TAG based event selection.For events which do not pass this selection, only therelative small TAG has to be read in. This yieldsin a significant speed up of the analysis jobs.

The analysis user has the choice to reconstruct de-cay trees, perform geometrical and kinematic fits,and to refine the event selection by using Beta,BetaTools and the fitters provided by the analy-sis software [37] directly in an application frame-work module, or by defining the analysis in a moreabstract way using SimpleComposition tools. ThisTCL based high level analysis tool package providesan easy-to-learn user interface for the definition ofan analysis task and the production of n-tuples,and it allows to set up analysis jobs without theneed to compile any code. SimpleComposition aswell as Beta, BetaTools and the geometric and kine-matic fitters were taken over as well tested packagesfrom BaBar, and adapted and slightly extended forPANDA.

For the exclusive benchmark channels it turned outthat especially a 4C-fit of the reconstructed decaytree is a powerful tool to improve the data qual-ity and to suppress background. 4C-fits and cutson the results can also be defined in SimpleCom-position. Fig. 3.23 shows an example of a drasticimprovement of the mass resolution for a compositeparticle.

Figure 3.23: J/ψ π+ π− mass spectra from pp →Ψ(2S)π+ π− → J/ψ 2π+ 2π− before and after apply-ing a 4C-fit to the decay tree with requiring a commonvertex for J/ψ → e+e−.

site events [106] stored data [TB]Lyon 551 4.4GSI 308 2.4

Orsay 149 1.2Bochum 297 2.3

Table 3.3: Contributions of the computing sites to thePhysics Book simulation production.

The last n-tuple based analysis steps were carriedout utilising the ROOT [38] toolbox, which providespowerful, interactively usable instruments amongothers for cutting, histogramming, and fitting.

3.5 Data Production

3.5.1 Bookkeeping

The Monte Carlo data used for this document wereproduced in a centrally organised way. All simula-tion requests are stored in a MySQL database, andall job scripts and configuration files are producedautomatically by Perl and PHP scripts. Also thescanning of the log files of the simulation jobs is au-tomated, and the determined job status is noted inthe database, too.

The analysis users could get the actual status ofthe simulation production for an individual chan-nel from a web page. With a tool available in thePANDA software they could configure the input oftheir analysis jobs and split an analysis task into anadequate number of jobs, which could run in paral-lel on one of the batch farms.

3.5.2 Event Production

Because none of the involved computing sites listedin Table 3.3 had sufficient computing and storageresources available for PANDA, the data produc-tion for the simulation was distributed over foursites, namely the IPN in Orsay [39], the CCIN2P3in Lyon, the Ruhr-Universitat Bochum, and theGSI at Darmstadt. Table 3.3 lists the contributionsof the sites to the simulation production. In to-tal 22 · 106 signal events for 22 channels, 1002 · 106

dedicated background events including the domi-nant background reactions for the individual anal-yses and 280 · 106 generic background events wereproduced in 29 weeks. The typical event size was3.5 kByte for AOD and TAG data, and 4.4 kBytefor the ESD component.


The network bandwidth between the productionsites was limited and did not allow to copy overanalysis data from one site to another for a largenumber of events. Therefore, most analysis jobs ranat the site where the analysis data were produced.

3.5.3 Filter on Generator Level

The most time consuming parts of the data process-ing chain are the simulation and reconstruction. Incomparison to that, the first stage, namely the gen-eration of events, is in general few order of magni-tudes faster. In order to achieve the relevant num-ber of required background events, an event filteron the generator level has been applied for a cer-tain part of these data. The strategy is to consideronly those events which are possible candidates forpassing all the selection criteria in the analysis bycutting on the kinematics of the generated particles.

This technique was used especially for the relevantbackground of those benchmark channels whichcontain a J/ψ decaying to a e+e− pair. In this caseonly events have been processed completey if theinvariant mass of two charged particles is within acertain J/ψ mass window. This method will nowbe presented and justified in detail for the exampleJ/ψη.

3.5.3.1 Validation of the J/ψ Generator Filter

The ππη final state is one of the most importantbackground sources for the J/ψη channel. It hadto be justified that the generated mass of the ππsystem, with the pions falsely identified as electrons,can be limited to the J/ψ signal region.

Here a generator-level filter was applied in the fol-lowing way: the four-vectors of the pions were recal-culated with an electron mass hypothesis and werecombined afterwards. The resulting invariant massmust lie within [2.8; 3.2] GeV/c2, corresponding tothe J/ψ signal region. Another two data sampleswere created with the combined invariant mass be-tween [2.4; 2.8] GeV/c2 and [3.2; 3.6] GeV/c2, respec-tively, corresponding to the sideband regions belowand above the J/ψ signal region.

10 million events have been generated for each of thethree mass regions at a beam momentum of 8.6819GeV/c.

The pp → J/ψη → e+e−γγ analysis module wasrun on the reconstructed ππη data. The numberof reconstructed entries in the signal region in de-pendence of the electron PID criteria is shown inTable 3.4. In Fig. 3.24 the resulting reconstructed

Le+e− reconstr. eventse± e∓ SR SBl SBr> 0% > 0% 204269 0 0> 0% > 20% 18965> 20% > 20% 338> 20% > 85% 64> 85% > 85% 3> 85% > 99% 1> 99% > 99% 0

Table 3.4: Number of reconstructed J/ψη candidatesfrom the background mode ππη, for different electronPID criteria, in three regions of the generated invariantππ mass under electron mass hypothesis: J/ψ signal re-gion SR and left and right J/ψ sideband regions (SBland SBr, resp.).

J/ψη mass is shown after applying all cuts on thedata sample corresponding to the J/ψ signal region.No PID criteria have been applied on the false elec-tron candidates. About 200000 candidates are leftout of 10 million. For events from the J/ψ sidebandregions, there are no candidates left after apply-ing the same selection criteria. Fig. 3.25 shows thereconstruction efficiency on the Monte Carlo truthlevel.

Figure 3.24: Reconstructed J/ψη mass from the back-ground mode ππη, with the π+π− mass (under electronmass hypothesis) within the J/ψ signal region.

In summary, one can limit the production to eventswith a generated ππ mass which is close to the J/ψmass. With a filter efficiency of 14%, the productiontime can be reduced by a factor of 7.


Figure 3.25: Reconstruction efficiency for wronglyidentified e+e− pairs (Monte Carlo truth mass).

3.6 Software Developments

The development of a next-generation simulationand analysis framework for PANDA was initiatedat the end of 2006. The new software infrastruc-ture, called PANDAroot, is designed to improve theaccessibility for beginning users and developers, toincrease the flexibility to cope with future devel-opments and to enhance synergy with other nu-clear and high-energy physics experiments. In addi-tion, it will provide a complete reconstruction andpattern-recognition chain to overcome the short-comings of the older analysis framework. Most ofthe functionalities of the software infrastructure asdescribed in the previous sections have been embed-ded in PANDAroot as well. Below, only the most im-portant new elements of PANDAroot are described.

The core services for the detector simulation andoffline analysis are provided by the FAIRroot frame-work [40], which is based on the object-orienteddata analysis framework, ROOT [38], and the Vir-tual Monte-Carlo (VMC) interface [41]. FAIRrootenables the integration of a detailed magnetic fieldmap, advanced parameter handling with an inter-face to an Oracle database, the usage of a largeset of event generators, presently EvtGen, DPM,UrQMD, and Pluto, and, since recently, a graph-ical tool to display reconstructed or Monte Carlobased hits and tracks. Furthermore, a modular de-sign of the framework is guaranteed via a task mech-anism. With this, the developer can setup simu-lation, reconstruction, and analysis algorithms inwell-separated and exchangeable tasks, which theuser can exploit to compare different algorithms andmethods for his or her application. Fig. 3.26 depictsthe various ingredients of FAIRroot and its couplingto ROOT, VMC, and the two available branches,

PANDAroot and CBMroot.

The VMC interface allows to perform easily, e.g.without the need to alter the user code, simu-lations using various transport models, presentlyGeant3 [42], Geant4 [30], and Fluka [43]. For themodelling of the detector geometry, a vitalizationscheme, virtual geometry model (VGM), has beenemployed as well. The vitalization concept foreseesa transparent transition between older and newertransport models, thereby, improving the validityand lifetime of the framework significantly. Be-sides the option to run a simulation using one ofthe Monte-Carlo transport codes, the new frame-work includes a fast simulation package based ona parametrization of the individual detector re-sponses. The parametrization is obtained by a com-parison with the results from experimental data orfrom simulations using one of the full transportcode. The fast-simulation package is used to gener-ate large numbers of background events within anacceptable period of time.

Fig. 3.26 sketches the various simulation and anal-ysis steps which are part of the PANDAroot frame-work. The new framework enables a complete re-construction of tracks which does not depend uponthe true origin of hits given by the Monte Carlotransport code. For this, the information of thetransport model is pre-processed to simulate thesignals from the individual detector components.In Fig. 3.27 this procedure is indicated as digitizer.The data after this process represent the digitiseddetector response and are, therefore, comparablewith experimental data. The following part, re-construction, takes only this data as input to findtracks and to reconstruct the momenta, scatteringangles, and the type of particle. Note that such anunbiased reconstruction procedure allows to studybackground due to fake tracks and pileup effects aswell.

Efficient and fast algorithms, based on conformalmapping [44] or extended Riemann [45] techniques,can be exploited to find charged tracks, to correlatethem with the information of various PID detec-tors of PANDA and to use as a pre-fit for a moreprecise track-fitter package. A track follower basedon the well-tested GEANE package [42] combinedwith a generic Kalman filter provide a tool set tooptimise the momentum reconstruction for chargedparticles. With these algorithms and tools, the newframework enables a realistic and complete trackfinding and pattern recognition.

For a complete particle identification, the propa-gation of Cerenkov photons is simulated and ring-finding algorithms for the DIRC are being imple-


Figure 3.26: An illustration of the building blocks of FAIRroot. The framework inherits the functionalities ofROOT and Virtual Monte Carlo. The core elements of FAIRroot are indicated in the green box in the middle ofthe figure. The two boxes at the bottom of the figure represent the ingredients of the CBMroot and PANDArootbranches and both are based on FAIRroot.

Figure 3.27: A sketch of the simulation and recon-struction chain of PANDAroot.

mented. Furthermore, for the global particle iden-tification, multi-dimensional probability distribu-tions for the different particle types are providedusing the k-nearest neighbourhood technique [46]together with a very fast multi-variate classificationmethod based on self-organising maps [47].

For the higher-level analysis activities, the Rhopackage [48] have been embedded in the PANDArootframework. The Rho package is an analysis tool kitwhich is optimised for interactive work and perfor-

mance. It owes a lot to its predecessors, includingthe BETA package [37], which has been describedbriefly in the previous sections. Unlike Beta, Rhois based on the solid fundamentals of the ROOTframework and runs interactively on all comput-ing platforms supporting ROOT. The PANDArootframework is enriched with vertex and kinematic fit-ting tools, based on the KFitter package from theBelle collaboration [49].

The PANDAroot framework is designed to run on alarge variety of computing platforms. This has theadvantage that the software can be employed easilyon a GRID environment. The PANDA collaborationis presently expanding and maintaining an AliEN2

GRID network [50] in synergy with the Alice col-laboration and with the PANDAroot developments.A complete simulation and analysis chain has beentested successfully on the GRID which presentlyconsists of about ten sites and gradually expand-ing. In addition, advanced monitoring tools, basedon MonALISA, are being used in connection to theGRID and framework developments.

The development of the new simulation and anal-ysis framework ran in parallel with the physics-benchmark simulations for this report. Hence,nearly all the channels were so-far studied using the


predecessor of the PANDAroot framework. How-ever, one of the electromagnetic channels, namelypp → γγ, was simulated and analysed using PAN-DAroot. This channel depends primarily on the re-construction code of the electro-magnetic calorime-ter, which was successfully derived from the oldframework, and, therefore, identical to the codewhich was used for the studies of all other chan-nels. The new framework in combination with theGRID infrastructure will be used in the near fu-ture to perform simulations of an extended set ofbenchmark reactions.

References

[1] D. J. Lange, Nucl. Instrum. Meth. A462, 152(2001).

[2] J. Catmor, R. Jones, and M. Smizanska,Development of the EvtGen package for theLHC and ATLAS, Proc. of CHEP2006,Mumbai, India, September 2006.

[3] A. Capella, U. Sukhatme, C.-I. Tan, andJ. Tran Thanh Van, Phys. Rept. 236, 225(1994).

[4] X. Artru, Nucl. Phys. B85, 442 (1975).

[5] G. C. Rossi and G. Veneziano, Nucl. Phys.B123, 507 (1977).

[6] L. Montanet, G. C. Rossi, and G. Veneziano,Phys. Rept. 63, 149 (1980).

[7] T. T. Takahashi, H. Matsufuru, Y. Nemoto,and H. Suganuma, Phys. Rev. Lett. 86, 18(2001).

[8] G. S. Bali, Phys. Rept. 343, 1 (2001).

[9] D. S. Kuzmenko and Y. A. Simonov, Phys.Atom. Nucl. 64, 107 (2001).

[10] D. S. Kuzmenko and Y. A. Simonov, Phys.Atom. Nucl. 66, 950 (2003).

[11] A. B. Kaidalov and P. E. Volkovitsky, Z.Phys. C63, 517 (1994).

[12] V. V. Uzhinsky and A. S. Galoyan,hep-ph/0212369 (2002).

[13] B. Andersson, G. Gustafson, and C. Peterson,Zeit. Phys. C1, 105 (1979).

[14] B. Andersson, G. Gustafson, andT. Sjostrand, Zeit. Phys. C6, 235 (1980).

[15] S. Ritter, Comput. Phys. Commun. 31, 393(1984).

[16] A. B. Kaidalov, Yad. Fiz. 45, 1452 (1987).

[17] A. B. Kaidalov and O. I. Piskunova, Z. Phys.C30, 145 (1986).

[18] K. Hanssgen and S. Ritter, Comput. Phys.Commun. 31, 411 (1984).

[19] M. Bleicher et al., J. Phys. G25, 1859 (1999).

[20] S. A. Bass et al., Prog. Part. Nucl. Phys. 41,225 (1998).


[21] R. M. Barnett et al., Phys. Rev. D54, 1(1996).

[22] A. Donnachie and P. V. Landshoff, Phys.Lett. B296, 227 (1992).

[23] P. Koch, B. Muller, and J. Rafelski, Phys.Rept. 142, 167 (1986).

[24] B. Andersson, G. Gustafson, andB. Soderberg, Z. Phys. C20, 317 (1983).

[25] S. Eidelman et al., Phys. Lett. B592, 1+(2004), http://pdg.lbl.gov.

[26] K. Abdel-Waged, Phys. Rev. C67, 064610(2003).

[27] J. P. Bondorf, A. S. Botvina, A. S. Ilinov,I. N. Mishustin, and K. Sneppen, Phys. Rept.257, 133 (1995).

[28] C. Hartnack et al., Eur. Phys. J. A1, 151(1998).

[29] J. Allison et al., IEEE Transactions onNuclear Science 53, 270 (2006).

[30] S. Agostinelli et al., Nucl. Instrum. Meth.A506, 250 (2003).

[31] P. Arce et al., Nucl. Instrum. Meth. A502,687 (2003).

[32] Technical report, Technical Design Report forthe PANDA EMC, in progress.

[33] D. Brown, E. Charles, and D. Roberts, TheBaBar track fitting algorithm, Proc.Computing in High Energy PhysicsConference, Padova, 2000.

[34] F. James and M. Roos, Comput. Phys.Commun. 10, 343 (1975).

[35] B. Aubert et al., Nucl. Instrum. Meth. A479,1 (2002).

[36] P. Strother, Design and application of thereconstruction software for the BaBarcalorimeter, PhD thesis, 1998, University ofLondon and Imperial College, UK.

[37] R. Jacobsen, Beta: A High Level Toolkit forBaBar Physics Analysis, 1997, presented atConference on Computing in High EnergyPhysics, Berlin.

[38] R. Brun and F. Rademakers, Phys. Res.A389, 81 (1996 1997).

[39] Grille de Recherche d’Ile de France,http://www.grif.fr.

[40] FairRoot, Simulation and AnalysisFramework, http://fairroot.gsi.de.

[41] Virtual Monte Carlo,http://root.cern.ch/root/vmc.

[42] CERN Program Library W5013 (1991).

[43] FLUKA, http://www.fluka.org.

[44] P. Yepes, Nucl. Instr. and Meth. A380, 582(1996).

[45] R. Fruhwirth, A. Strandlie, andW. Waltenberger, Nucl. Instr. and Meth. inPhys. Res. A490, 366 (2002).

[46] R. Duda, P. Hart, and D. Stork, PatternClassification, Wiley Interscience ISBN:0-471-05669-3.

[47] T. Kohonen, Self-Organizing Maps, SpringerSeries in Information Sciences, Springer,Berlin, Heidelberg, New York(1995,1997,2001).

[48] Rho: A Set of Analysis Tools for ROOT,http://savannah.fzk.de/websites/hep/rho/.

[49] Belle Kinematic Fitter, http://hep.phys.s.u-tokyo.ac.jp/ jtanaka/BelleSoft/KFitter/.

[50] Alien2@GRID, http://alien.cern.ch.

63

4 Physics Performance

4.1 Overview

The PANDA experiment will use the antiprotonbeam from the HESR colliding with an internal pro-ton target and a general purpose spectrometer tocarry out a rich and diversified hadron physics pro-gram.

The experiment is being designed to fully exploitthe extraordinary physics potential arising fromthe availability of high-intensity, cooled antiprotonbeams. The aim of the rich experimental programis to improve our knowledge of the strong interac-tion and of hadron structure. Significant progressbeyond the present understanding of the field isexpected thanks to improvements in statistics andprecision of the data.

Many measurements are foreseen in PANDA.

• The study of QCD bound states is of fun-damental importance for a better, quantita-tive understanding of QCD. Particle spectracan be computed within the framework of non-relativistic potential models, effective field the-ories and Lattice QCD. Precision measure-ments are needed to distinguish between thedifferent approaches and identify the relevantdegrees of freedom. The measurements to becarried out in PANDA include charmonium, Dmeson and baryon spectroscopy. In addition tothat PANDA will look for exotic states such asgluonic hadrons (hybrids and glueballs), mul-tiquark and molecular states.

• Non-perturbative QCD Dynamics. In thequark picture hyperon pair production eitherinvolves the creation of a quark-antiquark pairor the knock out of such pairs out of the nu-cleon sea. Hence, the creation mechanism ofquark-antiquark pairs and their arrangementto hadrons can be studied by measuring the re-actions of the type pp→ Y Y , where Y denotesa hyperon. Furthermore the self-analysingweak decays of most hyperons give access tospin degrees of freedom for these reactions. Bycomparing several reactions involving differentquark flavours the OZI rule, and its possibleviolation, can be tested for different levels ofdisconnected quark-line diagrams separately.

• Study of Hadrons in Nuclear Matter.The study of medium modifications of hadrons

embedded in hadronic matter is aimed at un-derstanding the origin of hadron masses in thecontext of spontaneous chiral symmetry break-ing in QCD and its partial restoration in ahadronic environment. So far experiments havebeen focused on the light quark sector. Thehigh-intensity p beam of up to 15 GeV/c will al-low an extension of this program to the charmsector both for hadrons with hidden and opencharm. The in-medium masses of these statesare expected to be affected primarily by thegluon condensate. A complementary studyaims to unravel the onset of the regime wherethe Colour Transparency phenomenon revealsthe short distance dominance of some exclusivereactions.

• Hypernuclear Physics. Hypernuclei are sys-tems in which up or down quarks are re-placed by strange quarks. In this way a newquantum number, strangeness, is introducedinto the nucleus. Although single and doubleΛ-hypernuclei were discovered many decadesago, only 6 double Λ-hypernuclei are presentlyknown. The availability of p beams at FAIRwill allow efficient production of hypernucleiwith more than one strange hadron, makingPANDA competitive with planned dedicatedfacilities. This will open new perspectives fornuclear structure spectroscopy and for study-ing the forces between hyperons and nucleons.

• Electromagnetic Processes. In additionto the spectroscopic studies described abovePANDA will be able to investigate the struc-ture of the nucleon using electromagnetic pro-cesses, such as Deeply Virtual Compton Scat-tering (DCVS) and the process pp → e+e−,which will allow the determination of the elec-tromagnetic form factors of the proton in thetimelike region over an extended q2 region. Theassociated process pp→ e+e−π0 should revealthe shape of the meson cloud in the nucleonthrough the study of the Transition Distribu-tion Amplitudes describing the proton to piontransition.

• Electroweak Physics. With the high-intensity antiproton beam available at HESRa large number of D-mesons can be produced.This gives the possibility to observe rare weakdecays of these mesons allowing to study elec-


troweak physics by probing predictions of theStandard Model and searching for enhance-ments introduced by processes beyond theStandard Model.

In this chapter we will discuss in detail the vari-ous items of the PANDA physics program and wewill describe the Monte Carlo simulations whichhave been carried out on a number of benchmarkchannels to study acceptances, resolutions, back-ground rejection. In order to perform these stud-ies a number of tools have been developed, whichare described in detail in the previous chapter, andwhich include a full simulation of the detector re-sponse and a series of sophisticated reconstructionand analysis tools. These studies have allowed usto obtain reliable estimates for the performance ofthe PANDA experiment and the sensitivity of thevarious measurements.

4.2 QCD Bound States

4.2.1 The QCD Spectrum

The spectrum of charmonium, like bottomonium,is very similar (apart from the scale) to the spec-trum positronium. It is therefore suggestive to as-sume that cc an bb (so called conventional mesons)can be understood in the strong interaction in ananalogue way as positronium in electroweak inter-actions. This would imply a Coulomb-like potentialand a term which takes care of linear confinement.But this a/r+ br potential arising mainly from theexchange of one gluon is by far not sufficient toexplain the spectrum of hadrons. The coherent ex-change of gluons which manifest in a gluon tube isan important aspect when one wants to understandthe binding among strongly interacting particles.Together with mesic excitations and pure gluonicstates which are possible in QCD they are are usu-ally present in the wave function of hadrons and areoften referred to as Fock-States of the ground statemeson. The Fock-States may decouple from theground state and thus being individually observableas individual states. This happens if the lifetimeof the objects allow a partitioning into individualobjects (e.g. width smaller than the mass differ-ence). We see this usually happening for the firstrotational excitations of hadrons. For higher excita-tions they tend to end up in a continuum. Thereforethe QCD spectrum is richer than that of the naivequark model (see Fig. 4.1). We distinguish conven-tional, gluonic and mesic hadrons. Conventionalhadrons have been already discussed in Sec. 4.2.2.

Gluonic hadrons fall into two categories: glueballsand hybrids. Glueballs are predominantly excitedstates of glue while hybrids are resonances consist-ing largely of a quark, an antiquark, and excitedglue. The properties of glueballs and hybrids aredetermined by the long-distance features of QCDand their study will yield fundamental insight intothe structure of the QCD vacuum. Mesic hadronsare dimesons and/or tetra-quarks, often referred toas multi-quarks or baryonium. They may be viewedas a loosely bound meson-anti-meson system or adiquark-antidiquark ensemble.

The search for glueballs and hybrids has mainlybeen restricted to the mass region below 2.2 GeV/c2.Experimentally, it would be very rewarding to go tohigher masses because of the unavoidable problemsdue to the high density of normal qq mesons below2.5 GeV/c2.

In the search for glueballs, a narrow state at1500 MeV/c2, discovered in antiproton annihilationsby Crystal Barrel [2, 3, 4, 5, 6], is considered thebest candidate for the glueball ground state (JPC =0++). However, the mixing with nearby conven-tional scalar qq states makes the unique interpreta-tion as a glueball difficult.

Both cases indicate the problems of light quarkspectroscopy due to large widths, deteriorated line-shapes and mixing among states. Thus heavyquarks states are decay modes give a more unbi-ased view to the spectrum of QCD states.

In the past decades many resonances have been as-sociated with the quest of the existence of multi-quarks. The a0(980) and f0(975) were always be-lieved to have a strong KK. Now a lot of charmo-nium states are discussed in the same framework.

4.2.2 Charmonium

4.2.2.1 Introduction

Ever since its discovery in 1974 [7, 8] charmoniumhas been a powerful tool for the understanding ofthe strong interaction. The high mass of the c quark(mc ≈ 1.5 GeV/c2) makes it plausible to attempt adescription of the dynamical properties of the (cc)system in terms of non-relativistic potential mod-els, in which the functional form of the potentialis chosen to reproduce the asymptotic propertiesof the strong interaction. The free parameters inthese models are to be determined from a compar-ison with the experimental data.

Now, more than thirty years after the J/ψ discovery,charmonium physics continues to be an exciting and


4

5

6

7

8

9

10

11

12

JPC 0-+ 1-- 1+- 0++ 1++ 2++ 2-+ 2-- 3-- 3+- 3++exotic

1.5

2

2.5

3

3.5

4

4.5

5

2S+1LJ1S0

3S11P1

3P03P1

3P21D2

3D23D3

1F33F3 n.a.

m r

0

m/G

eV

1-+

ηcJ/Ψ

hc χc0

χc1χc2

0+-

2+-

0+-

glueballs

experimentDD**

DDCP-PACSColumbia

hybrids

Figure 4.1: Charmonium spectrum from LQCD. See [1] for details.

interesting field of research. The recent discoveriesof new states (η′c, X(3872)), and the exploitation ofthe B factories as rich sources of charmonium stateshave given rise to renewed interest in heavy quarko-nia, and stimulated a lot of experimental and the-oretical activities. The gross features of the char-monium spectrum are reasonably well described bypotential models, but these obviously cannot tellthe whole story: relativistic corrections are impor-tant and other effects, like coupled-channel effects,are significant and can considerably affect the prop-erties of the cc states. To explain the finer featuresof the charmonium system, model calculations andpredictions are made within various, complemen-tary theoretical frameworks. Substantial progressin an effective field theoretical approach, labelledNon-Relativistic QCD (NRQCD) has been achievedin recent years. This analytical approach makesit possible to expect significant progress in latticegauge theory calculations, which have become in-creasingly more capable of dealing quantitativelywith non-perturbative dynamics in all its aspects,starting from the first principles of QCD.

Experimental Study of Charmonium

Experimentally charmonium has been studiedmainly in e+e− and pp experiments.

In e+e− annihilations direct charmonium formationis possible only for states with the quantum num-bers of the photon JPC = 1−−, namely the J/ψ, ψ′

and ψ(3770) resonances. Precise measurements ofthe masses and widths of these states can be ob-tained from the energy of the electron and positronbeams, which are known with good accuracy. Allother states can be reached by means of other pro-duction mechanisms, such as photon-photon fusion,initial state radiation, B-meson decay and doublecharmonium.

On the other hand all cc states can be directlyformed in pp annihilations, through the coherentannihilation of the three quarks in the proton withthe three antiquarks in the antiproton. This tech-nique, originally proposed by P. Dalpiaz in 1979 [9],could be successfully employed a few years later atCERN and Fermilab thanks to the development ofstochastic cooling. With this method the massesand widths of all charmonium states can be mea-sured with excellent accuracy, determined by thevery precise knowledge of the initial pp state and


not limited by the resolution of the detector.

The parameters of a given resonance can be ex-tracted by measuring the formation rate for thatresonance as a function of the c.m. energy Ecm, asexplained in detail in section 2.4.1. As an illustra-

Figure 4.2: Resonance scan at the χc1 carried out atFermilab (a) and beam energy distribution in each datapoint (b).

tion of this technique we show in Fig. 4.2 a scan ofthe χc1 resonance carried out at the Fermilab an-tiproton accumulator by the E835 experiment [10]using the process pp → χc1 → J/ψγ. For eachpoint of the scan the horizontal error bar in (a) cor-responds to the width of the beam energy distribu-tion. The actual beam energy distribution is shownin (b). This scan allowed the E835 experiment tocarry out the most precise measurement of the mass(3510.719 ± 0.051 ± 0.019 MeV/c2) and total width(0.876± 0.045± 0.026 MeV) of this resonance.

The Charmonium Spectrum

The spectrum of charmonium states is shown inFig. 4.1. It consists of eight narrow states belowthe open charm threshold (3.73 GeV) and severaltens of states above the threshold.

All eight states below DD threshold are well es-tablished, but whereas the triplet states are mea-sured with very good accuracy, the same cannot besaid for the singlet states.

The ηc was discovered almost thirty years ago andmany measurements of its mass and total widthexist, with six new measurements in the last fouryears. Still the situation is far from satisfactory.The Particle Data Group (PDG) [11] value of themass is 2980.4 ± 1.2 MeV/c2, an average of eight

measurements with an internal confidence level of0.026: the error on the ηc mass is still as large as1.2 MeV/c2, to be compared with few tens of keV/c2

for the J/ψ and ψ′ and few hundreds of keV/c2 forthe χcJ states. The situation is even worse for thetotal width: the PDG average is 25.5 ± 3.4 MeV,with an overall confidence level of only 0.001 andindividual measurements ranging from 7 MeV to34.3 MeV. The most recent measurements haveshown that the ηc width is larger than was previ-ously believed, with values which are difficult to ac-commodate in quark models. This situation pointsto the need for new high-precision measurements ofthe ηc parameters.

The first experimental evidence of the ηc(2S) wasreported by the Crystal Ball collaboration [12],but this finding was not confirmed in subsequentsearches in pp or e+e− experiments. The ηc(2S)was finally discovered by the Belle collaboration [13]in the hadronic decay of the B meson B → K +ηc(2S) → K + (KsK

−π+) with a mass which wasincompatible with the Crystal Ball candidate. TheBelle finding was then confirmed by CLEO [14]and BaBar [15] which observed this state in two-photon fusion. The PDG value of the mass is3638 ± 4 MeV/c2, corresponding to a surprisinglysmall hyperfine splitting of 48± 4 MeV/c2, whereasthe total width is only measured with an accuracyof 50 %. The study of this state has just started andall its properties need to be measured with good ac-curacy.

The 1P1 state of charmonium (hc) is of particu-lar importance in the determination of the spin-dependent component of the qq confinement po-tential. The Fermilab experiment E760 reportedan hc candidate in the decay channel J/ψπ0 [16],with a mass of 3526.2 ± 0.15 ± 0.2 MeV/c2. Thisfinding was not confirmed by the successor exper-iment E835, which however observed an enhance-ment in the ηcγ [17] final state at a mass of 3525.8±0.2 ± 0.2 MeV/c2. The hc was finally observed bythe CLEO collaboration [18] in the process e+e− →ψ′ → hc + π0 with hc → ηc + γ, in which the ηcwas identified via its hadronic decays. They founda value for the mass of 3524.4±0.6±0.4 MeV/c2. Itis clear that the study of this state has just startedand that many more measurements will be neededto determine its properties, in particular the width.

The region above DD threshold is rich in inter-esting new physics. In this region, close to the DDthreshold, one expects to find the four 1D states.Of these only the 13D1, identified with the ψ(3770)resonance, has been found. The J = 2 states (11D2

and 13D2) are predicted to be narrow, because par-


ity conservation forbids their decay to DD. In addi-tion to the D states, the radial excitations of the Sand P states are predicted to occur above the opencharm threshold. None of these states have beenpositively identified.

The experimental knowledge of this energy regioncomes from data taken at the early e+e− experi-ments at SLAC and DESY and, more recently, atthe B-factories, CLEO-c and BES. The structuresand the higher vector states observed by the earlye+e− experiments have not all been confirmed bythe latest much more accurate measurements byBES [19, 20]. A lot of new states have recentlybeen discovered at the B-factories, mainly in thehadronic decays of the B meson: these new states(X, Y , Z ...) are associated with charmonium be-cause they decay predominantly into charmoniumstates such as the J/ψ or the ψ′, but their inter-pretation is far from obvious. The situation can beroughly summarised as follows:

• the Z(3931) [21], observed in two-photon fu-sion and decaying predominantly into DD, istentatively identified with the χc2(2P );

• the X(3940) [22], observed in double charmo-nium events, is tentatively identified with theηc(3S);

• for all other new states (X(3872), Y (3940),Y (4260), Y (4320) and so on) the interpreta-tion is not at all clear, with speculations rang-ing from the missing cc states, to molecules,tetraquark states, and hybrids. It is obviousthat further measurements are needed to de-termine the nature of these new resonances.

The main challenge of the next years will be thus tounderstand what these new states are and to matchthese experimental findings to the theoretical ex-pectations for charmonium above threshold.

Charmonium in PANDA

Charmonium spectroscopy is one of the main itemsin the experimental program of PANDA, and thedesign of the detector and of the accelerator areoptimised to be well suited for this kind of physics.PANDA will represent a substantial improvementover the Fermilab experiments E760 and E835:

• up to ten times higher instantaneous luminos-ity (L = 2 × 1032 cm−2s−1 in high-luminositymode, compared to 2× 1031 cm−2s−1 at Fermi-lab);

• better beam momentum resolution (∆p/p =10−5 in high-resolution mode, compared with10−4 at Fermilab);

• a better detector (higher angular coverage,magnetic field, ability to detect the hadronicdecay modes).

At full luminosity PANDA will be able to collectseveral thousand cc states per day. By means offine scans it will be possible to measure masses withaccuracies of the order of 100 keV and widths to10 % or better. The entire energy region below andabove open charm threshold will be explored.

4.2.2.2 Benchmark Channels

One of the main problems in the experimental studyof charmonium spectroscopy in pp annihilation isthe high hadronic background. It is therefore nec-essary to select those decays of charmonium whichare less affected by background. In general we canidentify four main classes of charmonium decay:

• decays with a J/ψ in the final state: cc→J/ψ + X, with J/ψ → e+e− or J/ψ → µ+µ−.These channels can be used to identify statessuch as the χcJ , the ψ′ or the X(3872). Thepresence of the lepton pair in the final statemakes these channels relatively clean, with themain background coming from misidentifiedπ+π− pairs. The analysis of these channels re-lies on the positive identification of the leptonpair in the final state, with an invariant masscompatible with the J/ψ. In case of an exclu-sive analysis (e.g. J/ψπ+π−) a further improve-ment on the signal to background ratio can beobtained by means of a kinematical fit;

• two- and three-photon decays can be usedto identify states such as the ηc, the η′c or thehc (via hc → ηc + γ → 3γ). The main back-ground comes from π0γ and π0π0 final states inwhich one or two photons are lost, either out-side the calorimeter acceptance or below thecalorimeter low-energy threshold. This back-ground can be calculated by measuring the π0γand π0π0 cross sections and then using MonteCarlo techniques to estimate the feed-down toγγ and 3γ. The analysis requires the presenceof the required number of photons in the finalstate, with a veto on π0s and charged particles.Also in this case a kinematical fit can help toimprove the background situation;

• decays to light hadrons. As stated pre-viously these decay modes are affected by a


large hadronic background. In this case sig-nal/background separation can be obtained bycutting on discriminating topological variablesor angular distributions, whenever possible.An example of such decay is hc → ηcγ → φφγ;

• decays to DD: charmonium states aboveopen charm threshold will generally be iden-tified by means of their decay to DD, unlessforbidden by some conservation rule.

In what follows we will present a discussion of indi-vidual benchmark channels.

4.2.2.3 pp→ J/ψ + X

A class of charmonium decays that will be studiedat PANDA presents a J/ψ in the final state result-ing, for example, from de-excitation of a higher levelcharmonia with the emission of hadrons or photons.The existence of a J/ψ in the final state representsa clean signature for the signal.In what follows we present the study of the bench-mark channels:

• pp→ J/ψπ+π− → e+e−π+π−;

• pp→ J/ψπ0π0 → e+e−γγγγ;

• pp→ χc1,c2γ → J/ψγγ → e+e−γγ;

• pp→ J/ψγ → e+e−γ;

• pp→ J/ψη.

In all these cases the analysis strategy will focus onthe detection of the J/ψ → e+e− in the final state,allowing an efficient rejection of the hadronic back-ground, followed by the full event reconstruction.The first step in the analysis is the reconstructionof the J/ψ candidate starting from the lepton pair,following this strategy:

1. select one electron candidate from chargedtracks with Loose PID criteria, and one elec-tron candidate with Tight PID criteria;

2. kinematical fit of both electrons in order to re-construct the J/ψ candidates with vertex con-straint;

3. probability of J/ψ vertex fit: PJ/ψ > 0.001.

This strategy was followed for each benchmarkchannel.Fig. 4.3 shows the invariant mass distribution of theJ/ψ candidates for pp→ Y (4260)→ J/ψπ+π−.

)2 Mass (GeV/c-e+Invariant e3.07 3.075 3.08 3.085 3.09 3.095 3.1 3.105 3.11 3.115 3.12

Cou

nts

0

50

100

150

200

250

300

Figure 4.3: Invariant e+e− mass reconstructed at√s = 4.260 GeV.

The results of the reconstructed J/ψ, at differentcentre-of-mass energies and for several channels, aresummarised in Table 4.1

We now turn to a detailed discussion of the fivebenchmark channels.

pp→ J/ψπ+π−

The reaction pp → J/ψπ+π− → e+e−π+π− hasbeen simulated for several centre-of-mass energies.Event selection is done in the following steps:

1. select a well reconstructed J/ψ in the event;

2. select two pion candidates from charged trackswith VeryLoose PID criteria;

3. kinematical fit of the J/ψπ+π− candidates withvertex constraint;

4. probability of J/ψπ+π− vertex fit: PJ/ψπ+π− >0.001.

Fig. 4.4 shows the confidence level of the fit for thedata simulated at

√s = 4.260 GeV.

After this selection, the reconstruction efficiencyand RMS of the invariant mass distribution are re-ported in Table 4.2.

As an example, we will discuss in more detail the re-sults obtained for this channel at the energy of theresonance Y (4260). This resonance was observedfor the first time by BaBar in Initial State Radia-tion events [23], in the decay Y (4260)→ J/ψπ+π−.The natural quantum number assignment for thisstate is JPC = 1−− and one of its possible interpre-tation is a hybrid.In Fig. 4.5 the invariant mass distribution for


Channel Events√s(GeV ) Mean (GeV) RMS (MeV)

J/ψπ+π− 25 k 3.526 3.097 2.525 k 3.686 3.097 3.925 k 3.872 3.097 4.325 k 4.260 3.097 7.025 k 4.600 3.097 5.725 k 5.000 3.097 6.4

J/ψπ0π0 360 k 4.260 3.096 8.8χc1γ 20 k 3.686 3.096 6.8

20 k 3.872 3.096 7.620 k 4.260 3.095 8.3

χc2γ 20 k 3.686 3.096 6.920 k 3.872 3.096 7.520 k 4.260 3.096 8.3

J/ψγ 100 k 3.510 3.097 3.1100 k 3.556 3.097 3.420 k 3.872 3.096 3.7

J/ψη 40 k 3.638 3.093 740 k 3.686 3.094 740 k 3.872 3.096 680 k 4.260 3.096 6

Table 4.1: Number of simulated events, mean value and RMS of the reconstructed J/ψ invariant mass distributionfor each energy and channel analysed, after 4C fit.

Confidence Level0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cou

nts

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Figure 4.4: The cut applied is PJ/ψπ+π− > 0.001.

Y (4260) candidates, obtained with the described se-lections, is presented.

In the simulation, the dipion invariant mass (mππ)distribution was implemented according to the fol-lowing parametrisation [24]:

dΓdmππ

∝ PHSP ·(m2ππ − λm2

π

)2(4.1)

where PHSP is the phase-space factor, mπ is thepion mass and λ is a parameter that can be obtainedfrom the data; in this analysis we used λ = 4.0

√s [GeV] Eff [%] RMS [MeV]3.526 27.52 3.73.686 30.90 5.73.872 32.07 8.34.260 32.58 13.44.600 30.60 18.55.000 29.70 24.3

Table 4.2: Efficiencies and RMS of the reconstructedJ/ψπ+π− invariant mass distributions for each energyanalysed.

[25]. This choice is motivated by measurements ofψ(2S)→ J/ψπ+π−, considering the fact that ψ′ andY (4260) have the same quantum numbers.Fig. 4.6 shows themππ distribution after the recon-

struction. The blue line is the result of the fit withthe theoretical formula, which is consistent with theinput data. The main background for this channelcomes from pp→ π+π−π+π− where two pions maybe misidentified as electrons and contaminate thesignal.The study of background contamination is doneonly at the Y (4260) energy. At

√s = 4.260 GeV the

cross section of the background reaction is approxi-mately equal to 0.046 mb [26], while using available


)2 Mass (GeV/c-π+πψInvariant J/4.2 4.22 4.24 4.26 4.28 4.3 4.32

Co

un

ts

0

50

100

150

200

250

300

350

400

Figure 4.5: Invariant J/ψπ+π− mass, in the case ofY(4260) resonance.

)2 (Gev/cππm0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Cou

nts

0

100

200

300

400

500

0.40±=4.32λ

Figure 4.6: The black line is the simulated and re-constructed data and the blue line is the fit with thetheoretical function. The result of λ after the fit seemsto be consistent with the input data.

data from E835 experiment [25], we can estimatethe cross section of pp → Y (4260) → J/ψπ+π− →e+e−π+π− to be about 60 pb.In order to estimate the signal/noise ratio, 55 Mbackground filtered events were simulated (filterefficiency: 16.66%). Only 60 events satisfy theselection criteria, and present an invariant massof the reconstructed J/ψ in the region between[2.8;3.2] GeV/c2, and none events show a peak at theJ/ψ mass. We conclude that the signal/noise ratiois about 2, so this channel could be well identifiedin PANDA.

pp→ J/ψπ0π0

With its excellent electromagnetic calorimeterPANDA will also be able to study the neutral dipiontransition into J/ψπ0π0 in great detail. In order todetermine the acceptance and background rejection

capability of the detector, Monte Carlo simulationshave been done for this channel at

√s = 4.26 GeV.

The event selection has been done in the fol-lowing way. The J/ψ is reconstructed throughthe decay mode e+e− with the same cuts asdescribed in the J/ψπ+π− selection. Photonsfrom π0 candidates must have an energy depositin the calorimeter larger than 20 MeV. Afterthe 4C fit with CL> 0.1 %, only those eventswith m(e+e−) within [3.07; 3.12] GeV/c2 and m(γγ)within [120; 150] MeV/c2 are accepted. In order toreduce background, the remaining events are fittedwith J/ψπ0π0 and J/ψηπ0 hypothesis. Only eventswith exactly one combination with CL(J/ψπ0π0)>0.1 % pass the event selection. Events with at leastone J/ψηπ0 combination with CL(J/ψηπ0)> 0.01 %are rejected.

The results are summarised in Table 4.3. Assum-ing a cross section for pp → J/ψπ0π0 → e+e−4γof 30 pb [25] at

√s = 4.26 GeV, PANDA will

be able to reconstruct about 40 events per day.The main background channels could be sufficientlysuppressed. Only 1 from 250 million simulatedπ+π−π0π0 events pass the event selection, whichresults in a signal/background ratio S/B= 25 .

Figure 4.7: Invariant dipion mass of J/ψπ0π0 candi-dates.

The dipion mass distribution which is simulatedwith the same shape as that of the decay ofY (4260) → J/ψπ+π− is shown in Fig. 4.7. Nostrong efficiency variation in the mπ0π0 spectrumis visible.

pp→ χcγ

For the study of radiative decays to χc, it is possibleto make use of the subsequent decay χc → J/ψγ.


channel assumed σ efficiencypp→ J/ψπ0π0 → e+e−4γ 30 pb 16.9 % nrec= 40 events / daybackground reactions:pp→ π+π−π0π0 → π+π−4γ 50µb 1 / 250M S/B= 25pp→ J/ψηπ0 → e+e−4γ <30 pb 0 / 20K S/B> 103

pp→ J/ψωπ0 → e+e−5γ <10 pb 4 / 20K S/B> 103

Table 4.3: Simulation results for the channel pp → J/ψπ0π0. To save computing time π+π−π0π0 events withmπ+π− < 2.4 GeV/c2 or mπ+π− > 3.4 GeV/c2 are rejected without detector simulation.

Starting from the J/ψ sample it is possible to adda photon to reconstruct the χc candidate; a secondphoton is then added to fully reconstruct the finalstate.We will consider the following processes:

pp→ χc1,c2γ → J/ψγγ → e+e−γγ . (4.2)

The event selection is done in the following steps:


2. select reconstructed photon candidates;

3. kinematic fit of the χc1,c2 candidates with ver-tex constraint;

4. probability of χc1,c2 vertex fit: Pχc1,c2 > 0.001;

5. probability of χc1,c2γ vertex fit: Pχc1,c2γ >0.001;

6. χc1,c2 mass window: [3.3,3.7] GeV.

The results for the reconstructed χc1,c2 are sum-marised in Table 4.4. Fig. 4.8 shows the χc1 in-variant mass distribution reconstructed at

√s =

3.686 GeV.

)2 Mass (GeV/cγψInvariant J/3.49 3.495 3.5 3.505 3.51 3.515 3.52 3.525 3.53 3.535 3.54

Cou

nts

0

50

100

150

200

250

300

Figure 4.8: Invariant J/ψγ mass at√s = 3.686 GeV.

According to the selection cuts described above, asecond photon is added to the reconstructed χc1,c2

in order to reconstruct the complete final state,where it is possible to perform the kinematical fitto the pp 4-momentum. The results of the recon-structed χc1,c2γ are summarised in Table 4.5:

Fig. 4.9 shows the χc1γ candidates reconstructed at√s = 3.686 GeV.

)2 Mass (GeV/cγ1

χInvariant 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72

Cou

nts

0

50

100

150

200

250

300

350

Figure 4.9: Invariant χc1γ mass at√s = 3.686 GeV.

The major background comes from pp→ π+π−π0.This study is done at the Y (4260) and X(3872) en-ergies.The cross section of the background reactions at√s= 4.260 GeV is approximately equal to 30µb

[26], while at√s=3.872 GeV the cross section is

about 0.29 mb [26].36 million filtered events (filter efficiency: 13.5%)were analysed at the Y (4260) energy and, for theχc1γ final state, only 7 events pass the selection,while for χc2γ only 8 event satisfy the selectioncriteria, corresponding to an effective backgroundcross-section of 0.8 pb and 0.9 pb respectively.68 million filtered events (filter efficiency: 12.7%)were analysed at the X(3872) energy and, for theχc1γ final state, only 12 events pass the selection,while for χc2γ only 15 event satisfy the selectioncriteria, corresponding to an effective backgroundcross-section of 6.5 pb and 8.1 pb respectively.Since the signal cross-section for these reactions


χc1 χc2√s[GeV ] Mean [GeV] RMS [MeV] Mean [MeV] RMS [MeV]3.686 3.510 5.5 3.556 5.53.872 3.509 6.9 3.556 6.14.260 3.510 7.0 3.556 7.4

Table 4.4: Mean value and RMS of the reconstructed J/ψγ candidates for each energy analysed for the radiativedecay of χc1,c2.

χc1 χc2√s[GeV ] Mean [GeV] Eff [%] RMS (MeV) Mean [GeV] Eff [%] RMS [MeV]3.686 3.687 28.88 7.6 3.686 29.13 8.53.872 3.875 29.98 14.3 3.873 28.78 10.84.260 4.262 28.61 15.5 4.262 29.26 15.4

Table 4.5: Mean value, efficiencies and RMS of the reconstructed χγ candidates for each energy analysed forthe radiative decay of χc1,c2.

is not known it is not possible to calculate a sig-nal/background ratios. However these simulationsshow that for these channels a very good back-ground suppression can be achieved.

pp→ J/ψγ

pp → χc → J/ψγ → e+e−γ is the most importantchannel to study the radiative decay and the angu-lar distribution of χc → J/ψγ.The first step is the reconstruction of a J/ψ fromelectron-positron decay and then, adding one pho-ton, one can reconstruct the J/ψγ candidate.Event selection is done in the following steps:


2. select reconstructed photon candidates;

3. kinematic fit of the J/ψγ candidates with ver-tex constraint;

4. probability of J/ψγ vertex fit: PJ/ψγ > 0.001.

According to the selection cuts described above, theresults of the reconstructed J/ψγ are summarised inTable 4.6.

Fig. 4.10 shows the J/ψγ candidates reconstructedat√s = 3.510 GeV.

The major background comes from pp→ π+π−π0.The study of background contamination is done atthe X(3872) and χc2 energies.The cross section of the background reaction is ap-proximately equal to 0.29 mb at

√s = 3.872 GeV

and 0.12 mb at√s = 3.556 GeV [26].

√s[GeV ] Mean [GeV] Eff[%] RMS [MeV]3.510 3.512 44.47 10.53.556 3.557 45.10 11.03.872 3.874 37.96 15.3

Table 4.6: Mean value, efficiencies and RMS of thereconstructed J/ψγ candidates for each energy analysed.

)2 Mass(GeV/cγψInvariant J/3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 3.56

Cou

nts

0200400600800

10001200

14001600

180020002200

Figure 4.10: Invariant J/ψγ mass at√s = 3.510 GeV.

The cross section for pp → χc2 → J/ψγ is, fromE835 measurements, about 2 nb [10]. The numberof simulated filtered background events was 26 Mand 68 M at

√s = 3.556 GeV and

√s = 3.872 GeV,

respectively. (filter efficiencies are 10.5% and 12.7%respectively). In the first case only 2 events pass theselection criteria, but if the constraint on the J/ψinvariant mass is applied, these events disappear. Inthe second case 13 events satisfy the selection cri-


teria; also in this case, for many background eventsthe 4C-fit does not converge so it is completely sup-pressed by the cut CL > 0.1 %.Since no background events survive the selectionwe can set upper limits for the effective backgroundcross-sections of 1.2 pb and 1.3 pb at the χc2 andX(3872) energies, respectively. For the χc2, wherethe signal cross section is known, this translates intoa signal/background ratio S/B of about 103.

pp→ J/ψη → e+e−γγ

The first step in the analysis of this channel is thereconstruction of a J/ψ via its electron decay; thesecond step is the reconstruction of a η candidatefrom two photons decay and then reconstruct theJ/ψη candidate.Event selection is done in the following steps:


2. select a well reconstructed η in the event;

3. kinematic fit with beam, J/ψ and η mass con-straints;

4. J/ψ mass window: [3.07;3.12] GeV/c2;

5. η mass window: [0.535;0.565] GeV/c2;

6. probability of J/ψη vertex fit: PJ/ψη > 0.001.

According to the selection cuts described above, theresults of the reconstructed J/ψη are summarised inTable 4.7.

√s Mean Eff FWHM

[GeV ] [GeV] [%] [MeV]3.638 3.645 15.7 13.686 3.686 18.8 53.872 3.872 18.6 114.260 4.260 18.8 18

Table 4.7: Mean value, efficiencies and RMS of thereconstructed J/ψη candidates for each energy analysed.These results are listed after a fit with mass constrainton J/ψ and η.

Fig. 4.11 shows the J/ψη candidates reconstructedat√s = 4.260 GeV.

For this signal channel we investigated the followingbackground reactions:

• pp→ J/ψπ0γ

• pp→ J/ψπ0π0

]2) [GeV/cηψm(J/4.2 4.22 4.24 4.26 4.28 4.3 4.32

2E

ntrie

s / 1

.2 M

eV/c

0

100

200

300

400

500

600

700

800

Inv. J/psi eta massInv. J/psi eta massFigure 4.11: Invariant J/ψη mass at√s = 4.260 GeV.

• pp→ J/ψηγ

• pp→ J/ψηπ0

• pp→ J/ψηη

• pp→ π+π−η

• pp→ π+π−π0

with π0 → γγ, η → γγ and J/ψ → e+e−. Mostcross sections for decays including a J/ψ have notbeen measured yet.

The cross sections and branching fractions for theJ/ψη signal and background modes are summarisedin Table 4.8. Table 4.9 presents the results of back-ground contamination studies.

4.2.2.4 pp→ hc → ηcγ

According to theoretical predictions and previousexperimental observations [17, 27] one of the mostpromising decay modes for the observation of the hcis its electromagnetic transition to the ground stateof charmonium

hc → ηc + γ (4.3)

where the energy of the photon is Eγ = 503 MeV.

The ηc can be detected through many exclusive de-cay modes, neutral (ηc → γγ) or hadronic.

In order to estimate the signal cross-section we cal-culate the value of the Breit-Wigner formula at theresonance peak ER:

σp =3πk2BppBηcγ (4.4)


Reaction pp→ √s [GeV] σ B

J/ψη 3.638 σs 2.34%×B(ηc(2S)→ J/ψη)J/ψπ0π0 3.638 σb 5.78%J/ψπ0γ 3.638 σb 5.84%J/ψηγ 3.638 σb 2.32%J/ψη 3.686 σs 0.07%

J/ψπ0π0 3.686 σb 5.78%J/ψπ0γ 3.686 σb 5.84%J/ψηγ 3.686 σb 2.32%J/ψη 3.872 σs 2.34%×B(X(3872))→ J/ψη)J/ψηπ0 3.872 σb 2.30%J/ψπ0π0 3.872 σb 5.78%J/ψπ0γ 3.872 σb 5.84%J/ψηγ 3.872 σb 2.32%π+π−π0 3.872 290 µb 98.80%J/ψη 4.260 σs 2.34%×B(Y (4260)→ J/ψη)J/ψηη 4.260 σb 0.92%J/ψηπ0 4.260 σb 2.30%J/ψπ0π0 4.260 σb 5.78%J/ψπ0γ 4.260 σb 5.84%J/ψηγ 4.260 σb 2.32%π+π−η 4.260 1.54 µb1 39.38%

π+π−π0π0 4.260 50 µb 97.61%π+π−π0 4.260 30±10 µb2 98.80%

Table 4.8: σs denotes the cross section for the formation of a given resonance in pp events, B the branchingfraction for the decay tree. σb is the cross section for the background mode in pp annihilation. 1) obtained fromDPM generator. 2) measured value at 8.8 GeV/c.

where k2 = (E2R−4m2

p)/4 and the Bs represent thebranching ratios into the initial and final states.

Using the value measured by E835 ΓppBηcγ=10 eVand assuming a value of 0.5 MeV for the hc widthwe obtain σp = 33 nb.

hc → ηc + γ → 3γ

We first consider the process hc → 3γ. This decaymode was observed at Fermilab by E835 [17]. It ischaracterised by a fairly clean final state, but thelow value of the ηc → γγ branching ratio (4.3·10−4)results in a relatively low event rate in comparisonwith the hadronic decay modes of ηc.

The main contributors to the background for the3γ final state are γs from the π0, η, η′ decay in γγdecay modes: the loss of one or more γs outside thedetector acceptance or below the energy thresholdof the calorimeter can result in a 3 γ final state.The background channels considered in this analysis

are presented in Table 4.10 with the correspondingcross-sections measured by E760 and E835 over theangular range in the CM system | cos(θCM )| < 0.6[28, 29].

The angular dependence for all the studied back-ground channels is strongly peaked in the forwardand backward direction, which is typical of two andthree meson production in proton-antiproton anni-hilation. For the Monte Carlo study the angulardependence of the cross-section was parametrisedby 6th or 7th order polynomials in cos(θCM ). As anexample we show the π0π0 angular distribution inFig. 4.12.

The number of Monte Carlo events used for thisanalysis for signal and all the background channelsare shown in Table 4.10.

The event selection is done in the following steps:

1. An ηc candidate is formed by pairing γ’s withan invariant mass in the window [2.6; 3.2] GeV.The third γ is added to this pair to form the


Decay pp→ √s [GeV] Suppression Signal to noise

J/ψπ0π0 3.638 > 105 6300σ/σbJ/ψπ0γ 3.638 > 105 6200σ/σbJ/ψηγ 3.638 5 1σ/σbJ/ψπ0π0 3.686 > 105 7600σ/σbJ/ψπ0γ 3.686 12500 900σ/σbJ/ψηγ 3.686 400 100σ/σbJ/ψηπ0 3.872 > 105 18800σ/σbJ/ψπ0π0 3.872 > 105 75σ/σbJ/ψπ0γ 3.872 8300 600σ/σbJ/ψηγ 3.872 2000 400σ/σbπ+π−π0 3.872 > 7 · 107 1σ/nbJ/ψηη 4.260 > 105 47700σ/σbJ/ψηπ0 4.260 > 105 19000σ/σbJ/ψπ0π0 4.260 > 105 7600σ/σbJ/ψπ0γ 4.260 3600 300σ/σbJ/ψηγ 4.260 3400 600σ/σbπ+π−η 4.260 > 7 · 107 500σ/nb

π+π−π0π0 4.260 > 1.4 · 108 20σ/nbπ+π−π0 4.260 > 1.7 · 108 15σ/nb

Table 4.9: Signal to noise ratios are given in terms of the unknown cross section σ or σ/nb.

Channel σ (nb) number of eventspp→ hc → 3γ 20 kpp→ π0π0 31.4 1.3 Mpp→ π0γ 1.4 100 kpp→ π0η 33.6 1.3 Mpp→ ηη 34.0 1.3 Mpp→ π0η′ 50.0 100 k

Table 4.10: The main background contributors tohc → 3γ with corresponding cross-section integratedover | cos(θCM )| < 0.6.

hc candidate.

2. A 4C-fit to beam energy-momentum is appliedto the hc candidate and the information on thehc and the updated information on the daugh-ter γ’s are stored into the root ntuple.

3. The following cuts are applied at the ntuplelevel to suppress the background.

(a) Events with 3 γ’s were selected. This cutkeeps 47 % of all signal events, whereasit rejects more than 90 % of all back-ground events (with the exception of theπ0γ channel).

(b) Cut on the confidence level of the 4C-fit:CL > 10−4.

Figure 4.12: Angular dependence of π0π0 cross-section in the CM system with parametrisation usedin Monte-Carlo simulation.

(c) Cut on the CM energy of the γ fromthe hc → ηcγ (Eγ) radiative transition:0.4 GeV< Eγ < 0.6 GeV.

(d) Angular cut | cos(θCM )| < 0.6, to rejectthe background which is strongly peakedin the forward and backward directions.The cos(θCM ) distributions for a back-ground channel (π0π0) and for the signalare shown in Fig. 4.13 and Fig. 4.14, re-spectively.

(e) The cut for invariant mass of combination


Figure 4.13: Distribution of reconstructed cos θ of theγ in CM system for pp→ π0π0 background.

Figure 4.14: Distribution of reconstructed cos θ of theγ in CM system from hc → ηcγ.

M(γ1, γ3) > 1.0GeV and M(γ2, γ3) >1.0GeV (the value of the cut is deter-mined by the η′ mass).

In Table 4.11 the selection efficiencies for differ-ent cuts are presented. Efficiencies are cumula-tive, i.e. applied one after another. Taking intoaccount the signal cross-section σpp→hc = 33 nb atresonance, branching ratio B(ηc → γγ) = 4.3 · 10−4

and background cross-sections it results in the ex-pected signal to background ratios presented in Ta-ble 4.12. The expected event rate for the luminos-ity in high luminosity mode L = 2 · 1032 cm−2s−1 is20 events/day, and for high resolution mode withL = 2 · 1031 cm−2s−1 2.0 events/day correspond-ingly.

hc → ηcγ → φφγ

As a benchmark channel with a hadronic decaymode of the ηc we study the φφ final state withB = 2.6 · 10−3. We detect the φ through the decaycorrespondingly φ→ K+K−, with B = 0.49 [11].

For the exclusive decay mode considered in thisstudy:

pp→ hc → ηcγ → φφγ → K+K−K+K−γ

the following 3 reactions are considered as the maincontributors to the background:

1. pp→ K+K−K+K−π0,

2. pp→ φK+K−π0,

3. pp→ φφπ0.

With one photon from the π0 decay undetectedthese reactions have the same final state particlesas the studied hc decay. As in the case of the threephoton decay discussed above, it is crucial to haveas low an energy threshold as possible in order toeffectively reject this background.Additional possible source of background is pp →K+K−π+π−π0. This reaction could contribute tobackground due to pion as kaon misidentification.

There are no experimental measurements, to ourbest knowledge, of the cross-sections for the firstthree background reactions, which are supposedto be main contributors to background. The onlyway to estimate their cross-sections was found touse the DPM (Dual Parton Model) event generator[30]. 2 · 107 events were generated with DPMat beam momentum pz = 5.609 GeV/c, whichcorresponds to the studied hc resonance. Thecorresponding numbers of events are 115 and 12for the first two background channels. No eventsfor the pp → φφπ0 reaction were observed. Withthe total pp cross-section at this beam momentumof 60 mb the cross-sections for the correspondingbackground channels are estimated at 345 nb, 60 nband below 3 nb, respectively.For pp → K+K−π+π−π0 the cross-section wasestimated by extrapolation from lower energyaccording to the total inelastic cross-section. Itgives an estimation σ = 30µb.

The number of analysed events are presented in Ta-ble 4.13.For the pp → K+K−π+π−π0 channel 15 millionsout of 20 millions events were simulated with filter


Cut hc π0γ π0π0 π0η ηη π0η′

preselection 0.70 0.43 0.14 8.2 · 10−2 4.0 · 10−2 8.5 · 10−2

3 γ 0.47 0.31 1.3 · 10−2 7.5 · 10−3 2.7 · 10−3 8.7 · 10−3

CL > 10−4 0.44 0.30 9.9 · 10−3 4.9 · 10−3 7.2 · 10−4 5.7 · 10−3

Eγ [0.4;0.6] GeV 0.43 0.12 3.9 · 10−3 2.0 · 10−3 2.8 · 10−4 2.3 · 10−3

| cos(θ)| < 0.6 0.22 9.2 · 10−2 2.7 · 10−3 1.1 · 10−3 7.0 · 10−5 7.5 · 10−4

m212,m

223 > 1.0 GeV 8.1 · 10−2 0 0 0 0 0

Table 4.11: Selection efficiencies for hc → 3γ and its background channels.

Channel S/B ratiopp→ π0π0 > 94pp→ π0γ > 164pp→ π0η > 88pp→ ηη > 87pp→ π0η′ > 250

Table 4.12: Signal to background ratio for hc → 3γand different background channels.

Channel N of eventspp→ hc → φφγ 20 kpp→ K+K−K+K−π0 6.2 Mpp→ φK+K−π0 200 kpp→ φφπ0 4.2 Mpp→ K+K−π+π−π0 5 M + 15 M

100 k

Table 4.13: The numbers of analysed events for hcdecay

on invariant mass of the pair of two kaons. Theevents with m(K+K−) in the range [0.95;1.2] GeVwere selected. The efficiency of the filter is 29.9 %,which gives effective number of simulated events ∼55 M.

The following selection criteria were applied:

1. φ candidates were defined as K+, K− pairswith invariant mass in the window [0.8;1.2] GeV. Two φ candidates in one event withinvariant mass in the window [2.6;3.2] GeV de-fined an ηc candidate which, combined with aneutral candidate, formed an hc candidate.

2. A 4C-fit to beam energy-momentum was ap-plied to the hc candidate, which was stored toa root ntuple together with the updated infor-mation on its decay products.

3. The following cuts are performed at the ntuple

level for additional background suppression:

(a) cut on the confidence level of the 4C-fit tobeam energy-momentum, CL > 0.05,

(b) ηc invariant mass [2.9;3.06] GeV,(c) Eγ within [0.4;0.6] GeV,(d) φ invariant mass [0.99;1.05] GeV,(e) no π0 candidates in the event, i.e. no 2γ

invariant mass in the range [0.115;0.15]GeV with 2 different low energy γ thresh-olds: 30 MeV and 10 MeV.

The efficiencies of the various cuts are given in Ta-ble 4.14 for the signal and three of considered back-ground channels.

Assuming the hc production cross-section of 33 nbat resonance, one obtains the signal to backgroundratios given in Table 4.15.

For the pp→ φφπ0 background channel the reduc-tion of low energy γ-ray threshold from 30 MeV to10 MeV gives a 19 % improvement in the signal tobackground ratio, for the pp→ φK+K−π0 the cor-responding improvement is 33 %.

With the final signal selection efficiency of 25 %and the assumed luminosity in high luminositymode of L = 2 · 1032 cm−2s−1 the expected signalevent rate is 92 events/day. For the high resolutionmode with L = 2 ·1031 cm−2s−1 the expected signalevent rate is 9 events/day.

4.2.2.5 pp→ DD

The main focus of this benchmark study is to assessthe ability to separate the charm signal from thelarge hadronic background. In addition to the de-tection of charmonium states above the DD thresh-old this is important for other major parts of thePANDA physics program, such as open charm spec-troscopy, the search for charmed hybrids decayingto DD and the investigation of rare decays and CPviolation in the D meson sector.


Selection criteria signal 4Kπ0 φK+K−π0 φφπ0 K+K−π+π−π0

pre-selection 0.51 9.8 · 10−3 1.3 · 10−2 4.9 · 10−2 9.0 · 10−6

CL > 0.05 0.36 1.5 · 10−3 2.0 · 10−3 7.0 · 10−3 4.0 · 10−8

m(ηc), Eγ 0.34 4.1 · 10−4 5.2 · 10−4 1.8 · 10−3 0m(φ) 0.31 4.5 · 10−6 1.2 · 10−4 1.7 · 10−3 0no π0(30MeV ) 0.26 2.7 · 10−6 4.5 · 10−5 9.2 · 10−4 0no π0(10MeV ) 0.24 1.8 · 10−6 3.0 · 10−5 7.1 · 10−4 0

Table 4.14: Efficiency of different event selection criteria.

channel Signal/Backgroundpp→ K+K−K+K−π0 8pp→ φK+K−π0 8pp→ φφπ0 > 10pp→ K+K−π+π−π0 > 12

Table 4.15: Signal to background ratio for different hcbackground channels

In order to study the tracking and PID reconstruc-tion capabilities of the proposed PANDA detector,two benchmark channels have been chosen with de-cays containing only charged particles (charge con-jugated states included):

• pp → D+D− with the decay D+ → K−π+π+

• pp → D∗+D∗− with the sequential decaysD∗+ → D0π+ and D0 → K−π+

Both channels were simulated at a beam energycorresponding to

√s = mcc, the Ψ(3770) for the

D+D− channel and the Ψ(4040) for the D∗+D∗−

channel, respectively. The production is donedirectly into a DD pair, which corresponds to≈ 40 MeV above the particular DD threshold.

The charm production cross sections close tothreshold in pp annihilations are unknown. To es-timate the DD production cross section a Breit-Wigner approach can be used to calculate the res-onant cross section, where the unknown branchingratios to pp are estimated by scaling the known ra-tio J/ψ → pp [31]. This method estimates onlythe strength of the resonance contribution to thecross section. The strength of the DD continuumproduction is unknown and to account for its con-tribution, the known decay branchings cc → DDhave been set to 100 %, which leads to assumptionsfor the cross sections of:

σ(pp→ Ψ(3770)→ D+D−) = 2.8nb

for the first channel, and

σ(pp→ Ψ(4040)→ D∗+D∗−) = 0.9nb

channel D+D− D∗+D∗−

decay D± → K∓π±π± D∗+ → D0π+

(9.2 %) (67.7 %)D0 → K−π+

(3.8 %)R 4 · 10−10 1 · 10−11

Table 4.16: Definition of the DD physics channels,relevant decay branching ratios and the expected ratiobetween signal and total pp cross section.

for the second channel, respectively. Taking into ac-count the branching ratios of the considered D me-son decays, the expected ratio R between the signaland the total pp cross section within this analysiscan be calculated. The values obtained are listed inTable 4.16 together with the branching ratios of theindividual D meson decays used in this analysis.

Using a value of 60 mb for the total pp cross sectionat the DD threshold the relevant production crosssection will thus be suppressed at least by ten ordersof magnitude.

The event selection requires all six charged tracksto be detected. D meson candidates are defined bymeans of loose mass windows of ∆m = ±0.3 GeV/c2

before vertex fitting is done. For theD+D− channelthree charged tracks are fitted to a common vertexand both D± meson candidates are combined tothe initial system, which has to meet kinematicallythe beam four-momentum. The confidence level forthe kinematic fit is required to be CLkin > 0.01.In events with more than two D± candidates thebest two are selected according to the χ2 value fromthe vertex fit and the momentum of the candidate,which should be closer to the kinematically allowedregion. Fig. 4.15 shows the invariant mass distri-bution of the D± candidates. The signal sample isfree of combinatorial background and the distribu-tion is well described by a fit containing a super-position of two Gaussian components (shown in theplot as dashed lines) with the individual widths of


Figure 4.15: Invariant D± mass distribution of pp→D+D− signal events.

σ1 = 11.2 MeV/c2 and σ2 = 7.4 MeV/c2. The overallsignal efficiency at this stage is ε = 39.9 %.

For the D∗+D∗− channel, again a loose mass win-dow is set in the preselection of the D0 candidate.A kaon and a pion track are combined and if acommon vertex is found, a pion is combined tothe previously selected D0 candidate to reconstructthe corresponding D∗± meson. If both D∗± arefound, the event is fitted kinematically to the four-momentum of the beam-target system. A confi-dence level CLkin > 0.01 is required. The invariantmasses of both D mesons are shown in Fig. 4.16.The right side shows the D0 invariant mass and theline shape is well described by a fit containing twoGaussian components with values σ1 = 15.2 MeV/c2

and σ2 = 28.3 MeV/c2. The left side of Fig. 4.16shows the invariant mass distribution of the D∗±

candidates after a 5C kinematic fit.

This additional mass constraint can be imposedsince the whole decay tree gets fitted. Togetherwith the beam four-momentum constraint, the in-dividual widths of the two Gaussian components areσ1 = 0.75 MeV/c2 and σ2 = 0.29 MeV/c2. Withoutthe additional constraint the width of the D∗ massdistribution would be of the same order as the D±

mass resolution. The efficiency for the 5C-fit getsonly slightly reduced from εsignal,4C = 27.4 % toεsignal,5C = 24.0 %.

In order to understand the general features of theanalysis the Dual Parton Model (DPM) was usedto produce background coming from pp annihi-lations. Only inelastic collisions including multi-prong events have been simulated. Because of thesmall ratio between the DD cross section and the

channel D+D− D∗+D∗− ratio to ppDPM 83 M - -3π+3π−π0 50 M 43 M 2.5 · 10−2

3π+3π− 10 M 14 M 5 · 10−3

K+K−2π+2π− 1 M 10 M 5 · 10−4

Table 4.17: Background channels for the DD analysiswith the corresponding number of simulated events andthe ratio to the total pp cross section.

total pp cross section, a very large number of eventsneeds to be generated. For this reason this generalstudy was carried out only for the D+D− chan-nel: 8.3 · 107 events were produced to test the anal-ysis, e.g. for the acceptance of events containingcharged track multiplicities equal or larger than sixand to check for possible detector-related effects.Only 11 events pass the analysis for the D+D−

channel, if no constraint on the decay vertex po-sition of the two D± candidates is applied . Theseevents contain two charged kaons and four pions inthe event. Since the DPM model generates the re-action channel pp → K+K−2π+2π− as a subset,the number of remaining events corresponds withinthe statistics with the suppression efficiency of theK+K−2π+2π− background channel.

In a second stage, in order to evaluate the abilityto suppress the background to a sufficient level, adetailed study of specific background reactions wasperformed. This includes channels with six chargedtracks in the final state, which could be kinemat-ically interpreted as signal events. The selectedchannels and the relative ratio to the total pp crosssection are given in Table 4.17:

To study the background arising from channels withcharged kaons and pions the non-resonant produc-tion of K+K−2π+2π− has been analysed, whichhas at least a 106 times higher cross section thanthe D+D− signal channel close to the productionat threshold. Fig. 4.17 compares the longitudinalvs. the transverse momentum component of the Dmeson candidate for signal (left) and backgroundevents (right). A constraint on the D± momentumvia the definition of a wide window in the two di-mensional momentum plane gives a reduction factorof ≈ 26 for background events. The cut has beenchosen to reject mainly those background eventswith too large transverse momenta, which would re-sult in lower values for the invariant D± mass. Theremaining events leave a non-peaking backgrounddistribution in the mass region defined by the loosemass window from the preselection. Thus, the re-maining background will be kinematically similar


Figure 4.16: Invariant mass distributions of the D∗± candidate (left) and the D0 candidates (right).

Figure 4.17: Momentum components of D± candidates for signal events (left) and for background events of thereaction pp→ K+K−2π+2π− background (right). The surrounded region shows the allow momentum range forD± candidates.

to signal events and can not be separated furtherby kinematical constraints.

Background events will be produced prompt at theinteraction point and can be in principle separatedby finding the D± decay vertices located separatedfrom the primary interaction point. Since the DDproduction was studied close to threshold and dueto the fixed-target character of the experiment, thedirection of the D± mesons will be close to thebeam axis with a small opening angle. The un-certainty in the location of the primary vertex isdetermined by the size of the beam spot along thebeam which is of the order of σz,prim ≈ 500µm.On the other hand, using the tracking system, amuch better resolution can be obtained for theD± decay vertex: σx,y ≈ 35µm in the transverse

plane and σz ≈ 80µm in beam direction, respec-tively. The reconstructed decay position of bothD± candidates can be used to reject backgroundevents. Fig. 4.18 shows the beam axis projectionof the difference vector of the two D± meson de-cay vertices for signal events (black histogram) andfor K+K−2π+2π− background events (hatched his-togram) after all kinematic constrains. Since thesimulation requirement for the DD channels is al-ready high, the amount of simulated backgroundevents was chosen to meet the level of signal gener-ation, under the conservative cross section assump-tion given above. The shape of the background dis-tribution has been scaled by a factor 105, whichis symbolised by an additional blue dashed line inFig. 4.18 and would correspond to an equal amount


Figure 4.18: Distribution of the difference of both re-constructed D± mesons as projection onto the beamaxis. Upper curve for signal lower for remaining back-ground events (see text for details).

of produced signal and background events. The ver-tical arrow represents a ∆z = 0.088 cm cut, wherethe area below both distributions is equal. Thiswould correspond to a signal to background ratio of1 : 1. The remaining signal efficiency after the addi-tional vertex cut is ε∆z(D+D−) = 7.8 %. The shapeof the background distribution can be assumed tobe the same like the blue shaded region, since onlyvertex constraints determine the shape of the back-ground distribution. An increase of the ∆z cut canfurther enhance the signal to background ratio.

The cross sections for the pionic channels are ac-cording to Table 4.17 a factor of fifty larger com-pared to the pp → K+K−2π+2π− background re-action. For both channels all produced events couldbe suppressed completely, even without demandinga larger kaon probability in the D± reconstruction.To obtain the efficiency for background events somecuts have been relaxed, e.g. the influence of the D±

momentum cut has been estimated in an analysiswithout kinematic fit.

For the benchmark channel pp → 3π+3π−π0 thekinematic suppression of this channel is strongercompared to the 3π+3π− channel, although thecross section for this particular channel is a fac-tor of five larger. The π0 is not reconstructed andin most cases the event does not fit to the initialbeam momentum. For the 3π+3π− channel, thesuppression factor caused by the kinematic fit forbackground events was estimated to be ≈ 2.6 ·10−4,whereas for the 3π+3π−π0 channel it was estimatedto ≈ 4.4 · 10−4, respectively. For both channels novertex constraints has been used. At this level theexpected signal to background ratio are better than2 : 1. Table 4.18 gives an overview about the ob-

tained efficiencies and the resulting signal to back-ground ratios. According to the investigation of theK+K−2π+2π− channel and additional cut to thereconstructed D± vertex positions would stronglyincrease the signal to background ratio.

For the second charmed benchmark channel pp →D∗+D∗− in total 107 events for the backgroundreaction K+K−2π+2π− have been analysed. Forthe generation of the background channels for thisphysics channel, a pre-filter has been used, whichfiltered those events, which does not have a D0 anda D∗± candidate in the event. Only ≈ 15 % of allevents passed the filter. For this preselection a widemass window of ∆m = 0.5 GeV/c has been set. Allsimulated events could be suppressed by the anal-ysis. This corresponds to a signal to backgroundratio of S/B ≈ 1 : 3. According to the analysisof this background channel for the D+D− signal,an additional suppression factor of 10 could be ob-tained by applying a cut on the difference of the D0

decay vertices of ∆z = 200µm . This constraintwould reduce the signal efficiency from ε = 24.0 %to ε = 12.7 % and the signal to background ratiowould improve to ≈ 3 : 2.

To estimate the contributions of the pionic back-ground channels pp → 3π+3π−(π0) to the back-ground of the D∗+D∗− signal channel, the totalof 5.7 · 107 background channels have been simu-lated (according to Table 4.17). This correspondsto a total of 3.5 · 108 events and no event passesthe analysis for both background channels. Toestimate the influence of the suppression of thekinematic fit, the pionic background channel havebeen analysed without kinematic fit and only afew events survive the preselection including vertexfits. The efficiencies to suppress the background aregiven in Table 4.19. Assuming at least a factor ofε5C−kin ≈ 10−4 for the influence of the kinematic fiton the background suppression, the expected signalto background ratio for the pionic channels wouldthan be larger than S : N > 12. This assumptionis still very conservative, since the additional con-straint on theD0 mass in the kinematic fit could notbe estimated and would increase the suppressionfactor for this background source. Therefore, thecontribution to the expected hadronic backgroundfrom the pionic channels is expected to be small.

Assuming the reaction cross sections of charmoniumproduction above the DD threshold to be in theorder of 3 nb for the D+D− and 0.9 nb for theD∗+D∗− production the expected numbers of re-constructed events per year of PANDA operation areat least 1.5 ·104 and 1.4 ·103, respectively. For theseestimations efficiencies of ε = 7.8 % for the D+D−


selection efficiency signal/backgroundselection D+D− 3π+3π− 3π+3π−π0 D+D−

3π+3π−D+D−

3π+3π−π0

preselection 0.43 5.4 · 10−3 9.6 · 10−4 - -4C-fit 0.40 1.4 · 10−6 4.2 · 10−7 0.02 0.015

D± momentum 0.40 < 1.1 · 10−8 < 3.6 · 10−9 > 2.7 > 1.8K± Loose PID 0.23 < 1.8 · 10−9 < 1.7 · 10−9 > 9.5 > 2.2

Table 4.18: Expected signal to background ratios for the D+D− channel to 3π+3π−(π0) background events.

selection efficiency signal/backgroundselection D∗+D∗− 3π+3π− 3π+3π−π0 D∗+D∗−

3π+3π−D∗+D∗−

3π+3π−π0

preselection 0.27 5.0 · 10−7 7.5 · 10−8 - -5C-fit 0.24 5.0 · 10−11 7.5 · 10−12 ≥ 8.8 ≥ 12.4

Table 4.19: Expected signal to background ratios for the D∗+D∗− channel to 3π+3π−(π0) background events.

channel and ε = 24.0 % for the D∗+D∗− channelhave been used. These values are obtained by usingonly the dominant charged decays of D mesons. In-cluding further decay channels should significantlyimprove the signal efficiency. Furthermore, thecross section estimates for the DD channels givenabove are conservative, compared to other estimatesusing a quark-gluon string model [32], the annihila-tion of a diquark pair [33] or the contribution of theDD molecule hypothesis to higher resonances abovethe DD threshold [34], which suggest values up to10 − 100 nb in the PANDA energy range. Thesemodels usually extrapolate from strange channels,where data exist, to the charmed region. This al-lows the study of DD close to threshold and wouldstrongly increase the expected signal yield for theDD signal channels.

4.2.2.6 hc Width Measurement

In order to assess the ability to measure narrowwidths we report a study of the sensitivity ofPANDA to the determination of the hc width. Forthis purpose we performed Monte Carlo simulationsof energy scans around the resonance. Events weregenerated at 10 different energies around the hcmass, each point corresponding to 5 days of runningthe experiment in high resolution mode.

The expected shape of the measured cross-section isthe convolution of the Breit-Wigner resonance curvewith the normalised beam energy distribution andan added background term. The expected number

of events at the ith data point is

νi =[ε×

∫Ldt

]i

×[σbkgd(E) +

σpΓ2R/4

(2π)1/2σi

×∫

e−(E−E′)2/2σ2i

(E′ −MR)2 + Γ2R/4

dE′]

(4.5)

where σi is the beam energy resolution at the ithdata point, ΓR and MR the resonance width andmass, L the luminosity and ε is an overall efficiencyand acceptance factor. To extract the resonance pa-rameters the likelihood function − lnL is minimisedassuming Poisson statistics, where

L =N∏j=1

νnjj e−νj

nj !(4.6)

For our simulation we assumed a signal to back-ground ratio of 8:1 and we used the signal recon-struction efficiency of the hc → ηcγ → φφγ chan-nel. The simulated data were fitted to the expectedsignal shape with 4 free parameters: ER, ΓR, σbkgd,σp. The background was assumed to be energy in-dependent. The study has been repeated for 3 dif-ferent values of the total width: ΓR = 0.5, 0.75,1.0 MeV. The results of the fit for 0.5 MeV and1.0 MeV are presented in Fig. 4.19. The extractedΓR’s with errors are summarised in Table 4.20.

4.2.2.7 Angular Distributions in the RadiativeDecay of χc

The measurement of the angular distribution in theradiative decays of the χc states provides informa-tion on the multipole structure of the radiative de-cay and the properties of the cc bound state. The


(a) (b)

Figure 4.19: Fit of hc resonance for Γ = 0.5 MeV (a) and Γ = 1 MeV (b)

ΓR,MC [MeV] ΓR,reco [MeV] ∆ΓR [MeV]1 0.92 0.24

0.75 0.72 0.180.5 0.52 0.14

Table 4.20: Reconstructed hc width.

process pp → J/ψγ → e+e−γ is dominated by thedipole term E1. M2 and E3 terms arise in the rel-ativistic treatment of the interaction between theelectromagnetic field and the quarkonium system.They contribute to the radiative width at the fewpercent level.The coupling between the set of χ states and pp isdescribed by four independent helicity amplitudes:

• χc0 is formed only through the helicity 0 chan-nel;

• χc1 is formed only through the helicity 1 chan-nel;

• χc2 can couple to both.

The angular distributions of the χc1 and χc2are described by four independent parameters:a2(χc1), a2(χc2), B2

0(χc2), a3(χc2).The fractional electric octupole amplitude, a3 ≈E3/E1 can contribute only to the χc2 decays, andis predicted to vanish in the single quark radiationmodel if the J/ψ is pure S-wave.For the fractional M2 amplitude a relativistic cal-culation yields [35]:

a2(χc1) = − Eγ4mc

(1 + κc) = −0.065(1 + κc) (4.7)

a2(χc2) = − 3√5Eγ4mc

(1 + κc) = −0.096(1 + κc)

(4.8)where κc is the anomalous magnetic moment of thec-quark.

Fig. 4.20 shows the angles used in the descriptionof the angular distribution:

• θ is the polar angle of the J/ψ with respect tothe antiproton in the pp centre of mass system;

• θ′ is the polar angle of the positron in the J/ψrest frame with respect to the J/ψ direction inthe χc rest system;

• φ′ is the azimuthal angle between the J/ψ decayplane and the χc plane.

γ

θ

χc

p

e+

e-J/ψ

θ’ Φ’

SS’

Figure 4.20: Definition of the angles for the angulardistribution of the radiative decay of the χc.


The theoretical value of the ratio between a2(χc1)and a2(χc2) is predicted to be independent of thec-quark mass and anomalous magnetic moment:(

a2(χ1)a2(χ2)

)Th

=√

53Eγ(χ1 → J/ψγ)Eγ(χ2 → J/ψγ)

= 0.676

(4.9)E835 measured for the first time this ratio and theresult is [36]:(

a2(χ1)a2(χ2)

)E835

= −0.02± 0.34 (4.10)

While the value of a2(χc2) agrees well with the pre-dictions of a simple theoretical model, the value ofa2(χc1) is lower than expected (for κc=0) and theratio between the two, which is independent of κc is≈ 2σ away from the prediction. This could indicatethe presence of competing mechanisms, lowering thevalue of the M2 amplitude at the χc1. Further, highstatistics measurements of these angular distribu-tions are needed to solve this question.In order to do that, following the results of E835, anew model of angular distribution was implementedusing the following parameters for the decay of χc1:

• production amplitudes: B0=0;

• decay amplitude: a2 = 0.002± 0.032± 0.004;

and for the decay of χc2:

• production amplitudes: B20 = 0.16+0.09

−0.10 ± 0.01;

• decay amplitude: a2 = −0.076+0.054−0.050 ± 0.009

and a3 = 0.020+0.055−0.044 ± 0.009.

The angular distributions for the three angles canbe approximately written, for the χc1, as:

W (cosθ) ∼ 1− 13 cos2 θ

W (cosθ′) ∼ 1− 13 cos2 θ′

and for the χc2:

W (cosθ) ∼ 1− 13 cos2 θ

W (cosθ′) ∼ 1 + 113 cos2 θ′

W (φ′) ∼ 1− 871 cos 2φ′

Fig. 4.21 and 4.22 present the results obtained forthe cos θ, cos θ′ and φ′ distributions after the gener-ation and reconstruction of the events for the decayof χc1,2 → J/ψγ. The top plots show the angledistributions corrected with the efficiency, which ispresented in the lower part of the plot.

The dip in the efficiency around cos(θ) ∼ −0.4 cor-responds to events in which the photons are emittedat a polar angle in the laboratory system of ∼ 20,in the transition zone between the target and for-ward electromagnetic calorimeters. The projectedangular distributions, after efficiency correction, areconsistent with the observation from E835.


θCos-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

Eff

icie

ncy

[%]

0

10

20

30

40

50

60

θCos-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8 1

Cou

nts

0

200

400

600

800

1000

1200

’θCos-1 -0.5 0 0.5 1

Eff

icie

ncy

[%]

0

10

20

30

40

50

’θCos-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8 1

Cou

nts

0

200

400

600

800

1000

1200

’φ0 0.5 1 1.5 2 2.5 3

Eff

icie

ncy

[%]

0

10

20

30

40

50

’φ0 0.5 1 1.5 2 2.5 3

Cou

nts

0

200

400

600

800

1000

1200

Figure 4.21: Results for cos θ, cos θ′ and φ′ after the generation and reconstruction of the events for χc1 decay.

θCos-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

Eff

icie

ncy

[%]

0

10

20

30

40

50

60

θCos-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8 1

Cou

nts

0

200

400

600

800

1000

1200

1400

’θCos-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

Eff

icie

ncy

[%]

0

10

20

30

40

50

’θCos-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8 1

Cou

nts

0

200

400

600

800

1000

1200

’φ0 0.5 1 1.5 2 2.5 3

Eff

icie

ncy

[%]

0

10

20

30

40

50

’φ0 0.5 1 1.5 2 2.5 3

Cou

nts

0

200

400

600

800

1000

1200

Figure 4.22: Results for cos θ, cos θ′ and φ′ after the generation and reconstruction of the events for χc2 decay.


4.2.3 Exotic Excitations

4.2.3.1 Hybrids - Gluonic Excitation of qqStates

The glue tube (often referred to as flux-tube)adds degrees of freedom which may manifest in vi-brations of the tube. The higher the excitationthe more units of angular momentum are carried.These different levels of excitation can be trans-lated into different potentials, one for each mode.Fig. 4.23 shows this together with the correspond-ing wave functions.

Hybrids with Exotic Quantum NumbersThe additional degrees of freedom (e.g. the vibra-tion of the glue tube) manifest themselves also in acontribution to the quantum numbers of the topol-ogy. In the simplest scenario this corresponds toadding the quantum numbers of a gluon (JP=1+ or1− depending on if it is a colour-electric or colour-magnetic excitation) to a simple qq pair. Thereforethey are often referred to as hybrids. This proce-dure creates e.g. for S-wave mesons 8 lowest lyinghybrid states (see Table 4.21).

An important experimental aspect here is that 3 outof these 8 states exhibit quantum numbers whichcan not be formed by a normal qq pair. Thereforethese quantum numbers are called exotic.

The most promising results for gluonic hadronshave come from antiproton annihilation experi-ments. Two particles, first seen in πN scatter-ing [38, 39] with exotic JPC = 1−+ quantum num-bers, π1(1400) [40] and π1(1600) [41] are clearly seenin pp annihilation at rest (for a more detailed listof observations see Table 4.22).

4.2.3.1.1 Charmonium HybridsExotic charmonia are expected to exist in the 3–5 GeV/c2 mass region where they could be resolvedand identified unambiguously.

Predictions for hybrids come mainly from calcula-tions based on the bag model, flux tube model, andconstituent gluon model and, recently, with increas-ing precision, from LQCD [50, 51]. For hybrids, thetheoretical results qualitatively agree, lending sup-port to the premise that the predicted propertiesare realistic. Charmonium hybrids can be expectedsince the effect of an extra gluonic degree of free-dom in meson-like systems is evident in the con-fining potentials for the ccg system (e.g. as derivedfrom LQCD calculations in the Born-Oppenheimerapproximation [51]).

Gluon(qq)8 1− (TM) 1+ (TE)1S0, 0−+ 1++ 1−−3S1, 1−− 0+− ← exotic 0−+

1+− 1−+ ← exotic2+− ← exotic 2−+

Table 4.21: The coupling of spins leads to 8 hybridstates for each pair of pseudoscalar and vector mesonswith equal isospin. Even in this simple case three JPC

combination are not allowed for conventional qq pairs.

The discussions have only been centred around thelowest-lying charmonium hybrids. Four of thesestates (JPC = 1−−, 0−+, 1−+, 2−+) correspondto a cc pair with JPC = 0−+ or 1−−, coupled to agluon in the lightest mode with JPC = 1−−. Theother four states (JPC = 1++, 0+−, 1+−, 2+−)with the gluon mode JPC = 1−+ are probablyheavier. All models agree that the lightest exoticstate would be 1−+. Predictions for the mass arelisted in Table 4.23. In addition to the lightestexotic state there are seven other hidden charmedhybrids to be discovered. The well accepted pic-ture is that the quartet 1−−,(0,1,2)−+ is lower inmass than 1++,(0,1,2)+−. The expected splittingis about 100-250 MeV from 1−+ to 0+− [52, 53].In addition there is fine-splitting within the hy-brid triplets, so that the levels are spread over afew hundred MeV (e.g. 4.14 GeV/c2 for 0−+ and4.52 GeV/c2 for 2−+) [54, 55] which was verified bylattice QCD [56]. The actual signature is thereforenot just an individual state, but also the pattern ofstates.

Charmonium hybrids are likely to be narrower sinceopen-charm decays are forbidden or suppressed be-low the DD

∗J + c.c. (often referred to as DD∗∗)

threshold. From experiments at LEAR we knowthat production rates of such qq states are similar tothose of states with exotic quantum numbers. Thus,we estimate that the cross sections for the formationand production of charmonium hybrids will be sim-ilar to those of normal charmonium states which isin the order of 120 pb (pp → J/ψπ0 [57]), in agree-ment with theoretical predictions [58]. The namingdefinitions of Table 4.24 are used for the subsequentdiscussions.

Production vs. FormationFormation experiments would generate non-exoticcharmonium hybrids with high cross sections whileproduction experiments would yield a charmoniumhybrid together with another particle, such as a


Figure 4.23: (a) Heavy quarkonium potentials and wave functions for different excitation levels from LQCD. Σdenotes normal one gluon exchange while the excited Π potentials are the lowest lying hybrid potentials. In thatcase, the attraction is not mediated by a single gluon but a string of gluons which carry angular momentum. (b)shows the charmonium spectrum from LQCD. The conventional charmonium states are on the right while thehybrids are found in column Πu and Σ−u . See [37] for details.

Experiment Exotic JPC Mass [MeV/c2] Width [MeV/c2] Decay Refs.E852 π1(1400) 1−+ 1359 +16

−14+10−24 314 +31

−29+9−66 ηπ [42]

Crystal Barrel π1(1400) 1−+ 1400 ±20±20 310 ±50 +50−30 ηπ [40]

Crystal Barrel π1(1400) 1−+ 1360 ±25 220 ±90 ηπ [43]Obelix π1(1400) 1−+ 1384 ±28 378 ±58 ρπ [44]E852 π1(1600) 1−+ 1593 ±8 +29

−47 168 ±20 +150−12 ρπ [45]

E852 π1(1600) 1−+ 1597 ±10 +45−10 340 ±40±50 η′π [45]

Crystal Barrel π1(1600) 1−+ 1590 ±50 280 ±75 b1π [46]Crystal Barrel π1(1600) 1−+ 1555 ±50 468 ±80 η′π [41]E852 π1(1600) 1−+ 1709 ±24±41 403 ±80±115 f1π [47]E852 π1(1600) 1−+ 1664 ±8±10 185 ±25±28 ωππ [48]E852 π1(2000) 1−+ 2001 ±30±92 333 ±52±49 f1π [47]E852 π1(2000) 1−+ 2014 ±20±16 230 ±32±73 ωππ [48]E852 h2(1950) 2+− 1954 ±8 138 ±3 ωππ [49]

Table 4.22: Light states with exotic quantum numbers. The experiment E852 at BNL was performed with apion beam on a hydrogen target, while Crystal Barrel was a pp spectroscopy experiment at LEAR.

π or an η. In pp annihilation, production exper-iments are the only way to obtain charmonium hy-brids with exotic quantum numbers. It is envisagedthat the first step of exploring charmonium hybrids

would consist of production measurements at thehighest antiproton energy available (Ep = 15 GeV,√s = 5.46 GeV/c2) and studying all possible pro-

duction channels available to cover exotics and non-


(a) m(ccg), 1−+ Group Ref.4 390±80±200 MILC97 [59]4 317±150 MILC99 [60]4 287 JKM99 [61]4 369±37±99 ZSU02 [62]

(b) m(ccg,1−+)-m(cc,1−−) Group Ref.1 340±80±200 MILC97 [59]1 220±150 MILC99 [60]1 323±130 CP-PACS99 [63]1 190 JKM99 [61]1 302±37±99 ZSU02 [62]

Table 4.23: Hybrid masses (a) and mass differences (b) from quenched LQCD. The results for the lightest JPC

exotic cluster around the threshold for DD∗∗

+ c.c. production.

χc1 1++ ψ 1−−

hc0 0+− ← exotic ηc0 0−+

hc1 1+− ηc1 1−+ ← exotichc2 2+− ← exotic ηc22−+

Table 4.24: Lowest lying charmonium hybrids corre-sponding to the definitions as in Table 4.21.

exotic states. The next step would consist of forma-tion measurements by scanning the antiproton en-ergy in small steps in the regions where promisinghints of hybrids have been observed in the produc-tion measurements, thus having a second check onthe static properties like the JPC assignment as wellas mass and width.

The discovery of such a reaction would necessitatea very good charmonium reconstruction efficiency.Thus, apart from the benchmark channels used forconventional charmonium, the charmed hybrid pro-duction in the mode pp → ηc1η → χc1π

0π0η (ηc1is often referred to as ψg) has also been used tostudy the detector performance in multi-body char-monium reactions (see Sec. 4.2.3.4).

Proposed MeasurementsThe main goal is to measure all low lying charmo-nium hybrid states. From the 8 states, it is possibleto measure 7 of them using three channels with acharmonium final state. The possible reactions are

pp → ηc0,1,2η → χc1π0π0η (4.11)

pp → hc0,1,2η → J/ψπ0π0η (4.12)

pp → ψη → J/ψω[π0 or η] (4.13)

Since the final states χc1π0π0η with χc1 → J/ψγand J/ψπ0π0η are very similar in terms of multiplic-ity and photon energies, the slightly more compli-cated channel (4.12) with a radiative charmoniumdecay and a charmonium hybrid mass of 4.3 GeV/c2

is used to test the sensitivity of the detector. Al-though a charmonium final state is likely an opencharm final state may also be possible and 7 of thealready mentioned 8 states may be accessed withthe final state DD∗. Thus the reactions

pp → [ηc0,1,2, hc0,1,2, χc1]η → DD∗η (4.14)

should be measured and will be also used as abenchmark channel with a charmonium hybridmass of about 4.3 GeV/c2. In order to ensure reason-able event statistics, D decays with high yields haveto be combined. In both cases, the charmonium andthe open charm channels are detailed partial wavedecomposition has to be performed to disentanglethe different waves. Since the experimental find-ings Y (3940) and Y (4320) are also discussed in theframework of hybrids, e.g. as vector charmoniumhybrid candidates they are also used as benchmarkchannels.

4.2.3.2 Glueballs - Gluonic Excitation of theQCD Vacuum

LQCD calculations make rather detailed predic-tions for the glueball mass spectrum in thequenched approximation disregarding light quarkloops [64]. For example, the calculated width ofapproximately 100 MeV/c2 [65] for the ground-stateglueball matches the experimental results. LQCDpredicts the presence of about 15 glueballs, some


with exotic quantum numbers in the mass rangeaccessible to the HESR.

Glueballs with exotic quantum numbers are calledoddballs which cannot mix with normal mesons. Asa consequence, they are predicted to be rather nar-row and easy to identify experimentally [66]. It isconceivable that comparing oddball properties withthose of non-exotic glueballs will reveal deep insightinto the presently unknown glueball structure sincethe spin structure of an oddball is different [66].The lightest oddball, with JPC = 2+− and a pre-dicted mass of 4.3 GeV/c2, would be well within therange of the proposed experimental program. Likecharmonium hybrids, glueballs can either be formeddirectly in the pp-annihilation process, or producedtogether with another particle. In both cases, theglueball decay into final states like φφ or φη wouldbe the most favourable reaction below 3.6 GeV/c2

while J/ψη and J/ψφ are the first choice for the moremassive states.

The indication for a tensor state around 2.2 GeV/c2

was found in the experiment of Jetset collaborationat LEAR [67]. The acquired statistics was not suffi-cient for the complementary reactions to be deter-mined. We plan to measure the pp → φφ channelwith statistics of two orders of magnitude higherthan in the previous experiments. Moreover, otherreactions of two vector particle production, suchas pp → ωω,K∗K∗, ρρ will be measured. How-ever, the best candidate for the pseudo-scalar glue-ball (ηL(1440)), studied comprehensively at LEARby the Obelix collaboration [68, 69, 70, 71, 72], isnot widely accepted to be a glueball signal becausethe calculations of LQCD predict its mass above2 GeV/c2. Therefore, new data on many glueballstates are needed to make a profound test of differ-ent model predictions.

It is worth stressing again that pp-annihilationspresent a unique possibility to search for heavierglueballs since alternative methods have severe lim-itations. The study of glueballs is a key to under-standing long-distance QCD. Every effort should bemade to identify them uniquely.

Light GlueballsSince decades light meson spectroscopy experimentstried to identify the lowest lying glueball states.Many high statistics experiments have been per-formed which delivered excellent information aboutthe scalar and pseudoscalar waves. Nevertheless,due to the unavoidable mixing problem and thelarge widths arising from missing or smooth damp-ing functions pinning down of the scalar glueballswill very difficult.

Figure 4.24: Glueball prediction from LQCD calcu-lations. See [73, 64] for details. While the region of theground-state glueball was investigated in the LEAR era(in particular by Crystal Barrel) are the tensor glueballand the spin exotic glueballs with JPC = 0+− and 2+−

important research topics for PANDA.

In light quark domain the tensor glueball is thebest candidate to look at from experimental means.There is potential mixture from two nonets (3P2

and 3F2) which sums up to 5 expected isoscalarstates, but SUF (3) forbids φφ decays to first orderfor the conventional qq states, while there is no sup-pression for a potential glueball. The mass for theglueball is expected in the range from 2.0 GeV/c2

to 2.5 GeV/c2. Thus the benchmark reaction ispp → f2(2000− 2500) → φφ.

Heavy OddballsSince glueballs don’t have to obey any OZI rule,they may decay in any open channel. For glue-balls above the open charm pair production thresh-old also decays in to D mesons and its excitationsshould be easily possible. The width is completelyunknown. Since a lot of channels are potentiallyopen, the heavy glueballs could be extremely wide.Nevertheless it is known from many other reactions,that nature seems to invest more likely in massrather than in breakup-momentum, thus giving theopportunity to look for oddballs in e.g. DD∗ de-cays. Decays of this kind are investigated for thesearch for charmonium hybrids. The final state tolook at is then DD∗η or DD∗π0. The lightest odd-balls are JPC = 2+− and 1+− (spectroscopic nameb0,2(4000− 5000)). Since they would appear in the


same open charm final states as charmonium hy-brids, the conclusions for these hybrid channels ap-ply also to the oddball search.

4.2.3.3 Multiquarks - Mesic Excitation of qqstates

It is an widely accepted paradigm, that mesic ex-citations are present in the wave functions of QCDbound states, like the pion cloud around the nucle-ons. The mesic excitation is - if at all - expected tobe loosely bound, thus resulting in extremely largewidths. In the vicinity of strong thresholds this maybe different and states with a potentially large ad-ditional mesic component can become substantiallymore narrow if they appear sub-threshold. This isfor example seen in the a0(980) and f0(975) pair,which are believed to be the ground state I = 1 andI = 0 scalar mesons, but strongly attracted by theKK threshold and with large (may be dominating)KK component in the wave function.

In the case of the extremely narrow X(3872) theDD∗ threshold has a dramatic impact on its wavefunction and dynamics. As discussed in the previ-ous section it was discovered in typical charmoniumreactions, but it does not really fit very well in anypotential model. One solution could be that it isdominated by a DD∗ bound state. Various calcu-lations show, that depending on the kind of object,the different dispersive effects would manifest in dif-ferent lineshapes [75, 74] (see also Fig. 4.25).


Study of pp → ηc1η → χc1π0π0η

For the production of ηc1 in pp → ηc1η it is as-sumed that the cross section is in the same order ofmagnitude as for the process pp → ψ(2S)η includ-ing conventional charmonium. The cross section forthis reaction is given in Ref. [76] to be (33±8) pb at√s = 5.38 GeV and is calculated from the crossed

process ψ(2S) → ηpp observed in e+e− annihila-tion.

The final state with 7 photons and an e+e− leptonpair originating from J/ψ decays has a distinctivesignature and separation from light hadron back-ground should be feasible. A source of backgroundare events with hidden charm, in particular eventsincluding a J/ψ meson. This type of backgroundhas been studied by analysing pp → χc0 π

0 π0 η,pp → χc1 π

0 η η, pp → χc1 π0 π0 π0 η and pp →

J/ψ π0 π0 π0 η. The hypothetical hybrid state is ab-sent in these reactions, but the χc0 and χc1 mesonsdecay via the same decay path as for the signal.

Therefore these events have a similar topology assignal events and could potentially pollute the ηc1signal.

Reaction σ Bpp→ηc1η 33 pb 0.82 %× B(ηc1 → χc1π

0π0)χc0π

0π0η 0.03 %χc1π

0ηη 0.32 %χc1π

0π0π0η 0.81 %J/ψπ0π0π0η 2.26 %

Table 4.25: Cross sections for signal and backgroundreactions. The table lists also the product of branchingfractions for the subsequent particle decays.

The number of analysed signal and backgroundevents is summarised in Table 4.26.

Reaction Eventspp→ηc1η 8 · 104

χc0π0π0η 8 · 104

χc1π0ηη 8 · 104

χc1π0π0π0η 8 · 104

J/ψπ0π0π0η 8 · 104

Table 4.26: Number of analysed signal and back-ground events. The J/ψ is considered only in the e+e−

decay mode.

Photon candidates are selected from the clustersfound in the EMC with the reconstruction algo-rithm explained in Sec. 3.3.2.1. Two photon candi-dates are combined and accepted as π0 and η can-didates if their invariant mass is within the inter-val [115;150] MeV/c2 and [470;610] MeV/c2, respec-tively.

From the J/ψ and photon candidates found in anevent χc1 → J/ψ γ candidates are formed, whoseinvariant mass is within the range [3.3;3.7] GeV/c2.From these χc1 π

0 π0 η candidates are created,where the same photon candidate does not occurmore than once in the final state. The corre-sponding tracks and photon candidates of the fi-nal state are kinematically fitted by constrainingtheir momentum and energy sum to the initial ppsystem and the invariant lepton candidates massto the J/ψ mass. Accepted candidates must havea confidence level of CL > 0.1 % and the invari-ant mass of the J/ψγ subsystem should be withinthe range [3.49; 3.53] GeV/c2, whereas the invariantmass of the η candidates must be within the inter-


Figure 4.25: Dispersive effects on the X(3872) from various authors: (left) Hanhardt et al. [74] and (right)

Braaten et al. [75]. The left figure shows differential rates for the J/ψπ+π− (first plot) and D0D∗0

(second

plot) for large J/ψπ+π− yield (solid curves) and D0D∗0

dominance (dashed curves). The right figure shows

the line shapes near the D0D∗0

threshold for X(3872) in the D0D∗0

channel. The line shapes are shown forthree different model settings corresponding to a bound state (solid line), virtual state (dashed line), and smoothexcitation (dotted line).

val [530; 565] MeV/c2. A FWHM of 13 MeV/c2 and9 MeV/c2 is observed for the η and χc1 signal re-spectively after the kinematic fit.

For the final event selection the same kinematic fitis repeated with additionally constraining the in-variant χc1, π0 and η mass to the correspondingnominal mass values. Candidates having a confi-dence level less than 0.1 % are rejected.

At this stage of the analysis 8.2% of the event arereconstructed, whereas for a fraction of 5.3% of thereconstructed events more than one χc1π0π0η com-bination is found per event. To ensure an unam-biguous reconstruction of the total event, eventswith a candidate multiplicity higher than one arerejected.

The invariant χc1π0π0 mass obtained after applica-tion of all selection criteria is shown in Fig. 4.26.The ηc1 signal has a FWHM of 30 MeV/c2. Thereconstruction efficiency is determined from thenumber of ηc1 signal entries in the mass range4.24− 4.33 GeV/c2 and is found to be 6.83 %.

The background suppression is estimated from thenumber of accepted background events after appli-cation of all selection criteria having a valid ηc1candidate whose invariant mass is within the sameinterval used to determine the reconstruction effi-ciency for signal events. In Table 4.27 the suppres-sion for the individual background channels is listedtogether with the expected signal to background ra-

]2) [GeV/c0π0πc1

χm(4.15 4.2 4.25 4.3 4.35 4.4 4.45

2E

ntrie

s / 3

MeV

/c

0

50

100

150

200

250

300

Figure 4.26: Invariant χc1π0π0 mass obtained for the

J/ψ → e+e− channel after application of all selectioncriteria.

tio S/B, which is reported in terms of

R =σSB(ηc1 → χc1π

0π0)σB

(4.15)

given by the unknown signal (background) crosssection σS (σB) and the branching fraction for theηc1 → χc1π

0π0 decay. Depending on the back-ground channel and reconstructed J/ψ decay modeS/B is varying between 250 − 10100R. For pp →


χc1π0π0π0η only a lower limit > 5530R is obtained.

If the cross sections σB for the background processesare not enhanced by more than an order of magni-tude over σSB(ηc1 → χc1π

0π0) very low contamina-tion of the signal from these processes is expected.

Reaction η S/B

pp→ [103] [103]χc0π

0π0η 5.33 10.1Rχc1π

0ηη 26.6 4.57Rχc1π

0π0π0η > 80 > 5.53RJ/ψπ0π0π0η 9.98 0.25R

Table 4.27: Background suppression η and the ηc1signal to background ratio S/B for the individual back-ground reactions in terms of R as defined in Eq. 4.15.

Background reactions including no charm but lightmesons in the final state have not been investigatedyet. The studies of the background types performedfor the charmonium states presented in this doc-ument proof that a clean reconstruction via theJ/ψ → e+e− decay mode is possible. Therefore thereconstruction of the ηc1 state via this decay shouldyield also a sufficient background suppression.

The expected number of reconstructed events perday is given by

N = σSB(ηc1 → χc1π0π0)× 4.81 nb−1, (4.16)

assuming a design luminosity of 2 · 1032cm−2s−1

with an efficiency of 50 %. As before said the crosssection for pp → ψ(2S)η is expected to be 33 pb.Assuming the same cross section for the produc-tion of the charmonium hybrid state this becomesN = 0.16B(ηc1 → χc1π

0π0) events per day.

Study of pp → ηc1η → DD∗ηTwo possible background reactions including open

charm decays leading to a similar event topology assignal events have been investigated. The first ispp → D0D

∗0π0, where the recoil η is absent and

the D and D∗ mesons decay via the same decaypath as for signal events. Secondly the reactionpp→ D0D

∗0η is investigated, where the recoil η is

present but either the D0 or the D0

meson (fromD∗0 → D

0π0 decay) is decaying into K−π+π0π0

and K+π−π0π0. This D0 decay mode is listed inPDG as seen and it is assumed for this study thatit’s branching fraction is 5%, comparable in the or-der of magnitude to other D meson decay modes in-cluding a charged kaon. The product of branching

fractions for the background and signal reactionsare shown in Table 4.28. π0 and η are selected in the

Reactionpp→ Bηc1η 0.47%× B(ηc1 → D0D

∗0)

D0D∗0η 3.2%× B(D0 → K−π+π0π0) = 0.16%∗

D0D∗0π0 1.17%

Table 4.28: The product of branching fractions for thesubsequent particle decays for signal and backgroundreactions. For the branching fraction marked with anasterisk (∗) B(D0 → K−π+π0π0) = 5% is assumed.

standard way discussed before. Pions and kaons areselected from charged particles in the event by ap-plying a likelihood based selection algorithm, wherea likelihood value of L > 0.2 is required to accept acandidate as a pion or kaon. All possible K+π−π0

combinations having an invariant mass in the range[1.7; 2.2] GeV/c2 in an event are formed and fittedby applying a π0 mass constraint and requiring acommon vertex for the tracks of the two chargedcandidates. A confidence level CL >0.1 % is re-quired to accept the candidates as D0 → K+π−π0

candidates. These are then used to form D0π0

candidates having an invariant mass in the inter-val [1.95; 2.05] GeV/c2, which are kinematically fit-ted applying a π0 mass constraint. If the fit yieldsa confidence level CL >0.1 % the D∗0 → D0π0 can-didate is accepted for further selection. AfterwardsD0D

∗0η combinations are formed and fitted by con-

straining the final state particles’ four-vectors to theinitial pp system momentum and energy. Further-more the invariant γγ mass of the π0 candidatesin the decay tree is constrained to the π0 mass. Aconfidence level of CL >0.1 % is required.

A confidence level of CL > 0.1% is required. Forfinal event selection the fit is repeated but with ad-ditional mass constraints on the D0, D∗0 and η can-didates. Candidates leading to a confidence levellower than 0.1% are discarded.

A χc1π0π0η candidate multiplicity higher than one

is observed in 9.5% of the reconstructed events.In order to avoid unambiguities in later analy-sis events with a higher multiplicity than one areare rejected. To estimate the reconstruction ef-ficiency only the correct combinations are consid-ered. The event yield is determined as the numberof D0D

∗0signal entries falling in the mass window

[4.24; 4.33] GeV/c2.

The obtained D0D∗0

invariant mass distributionis shown Fig. 4.27. A signal width (FWHM) of


22.5 MeV/c2 is observed. The reconstruction effi-ciency is 5.17%.

]2) [GeV/c*

Dm(D

4.15 4.2 4.25 4.3 4.35 4.4

2E

ntrie

s / 2

.5 M

eV/c

0

50

100

150

200

250

300

350

400

450

CCb MassCCb MassFigure 4.27: Invariant D0D

∗0mass obtained after the

kinematic fit with a momentum and energy constrainton the initial pp system as described in the text.

The background reactions pp → D0D∗0η (with

D0 → K+π−π0π0) and pp → D0D∗0π0 could be

suppressed by a factor > 1.6 · 105. Assuming equalcross sections for these processes and signal eventsand a branching fraction for D0 → K+π−π0π0

(which is listed by the PDG as seen) in the orderof 5 % the expected signal to noise ratio can be ex-pressed by

S

N>B(ηc1 → D0D

∗0)× 0.47 %× 5.17 %

(0.16 % + 1.17 %)× 5 · 10−6

= B(ηc1 → D0D∗0

)× 2.9 · 103, (4.17)

where the term B(ηc1 → D0D∗0

) is the unknownbranching fraction for the decay ηc1 → D0D

∗0.

With the assumed cross section of 33 pb and designluminosity L = 2·1032cm−2s−1 with an efficiency of50 % the expected number of reconstructed eventsper day is given by

N = B(ηc1 → D0D∗0

)× 0.077. (4.18)

In conclusion this study proofs that the reconstruc-tion of an object of a mass of ≈ 4 GeV/c2 decay-ing to open charm produced in pp annihilation at15 GeV/c with a recoiling η meson leading to a fi-nal state with high photon multiplicity is feasible.The low branching fractions of D mesons make theinclusion of other decay modes necessary to be sen-sitive for lower ηc1 branching fractions, but these

decays should be detectable with similar efficiencyas the decay mode presented in this study.

Study of Y (3940)→ J/ψω System in pp Forma-tionIn the following an exclusive study of the formationof Y (3940) in pp annihilation is presented. The J/ψis reconstructed from its decay to e+e−, whereasthe ω is reconstructed via the π+π−π0 decay mode.

As possible sources of background the reactions

• pp→ ψ(2S)π0 (ψ(2S)→ J/ψπ+π−)

• pp→ J/ψρ0π0 (ρ0 → π+π−)

• pp→ J/ψρ+π− (ρ+ → π0π+)

• pp→ π+π−π0ρ0 (ρ0 → π+π−)

• pp→ π+π−π−ρ+ (ρ+ → π0π+)

• pp→ π+π−ω (ω → π+π−π0)

have been considered.

None of the cross sections for these reactions havebeen measured in the energy range of the Y (3940).The cross sections for the reactions pp → π+π−πρand pp → π+π−ω have been measured in the

√s

energy range between 2.14 and 3.55 GeV [77].

For the channels including charmonium states onehas to distinguish between the formation processpp→ Y (3940) followed by the subsequent Y (3940)decay on the one hand and direct production of acharmonium state with an associated recoil mesonon the other hand. While the observed decay ofthe Y (3940) into J/ψω is considered to be isospinconserving, a decay into ψ(2S)π0 is isospin violat-ing and thus expected to be suppressed. Here thenon-resonant reaction pp → ψ(2S)π0 is consideredas a possible source of background. Ref. [76] quotesthe cross section for this process to be less than55 pb. In this study a value of 55 pb is assumed forthis process as a conservative estimate. Backgroundcould also arise from hypothetical isospin conserv-ing Y (3940) decays into J/ψρπ, with a possible in-termediate resonance decaying into ρπ. Since thetime-scales of the two processes are distinct, less in-terference between the final states is expected andthe background is considered to be incoherent tosignal. For the branching fractions of the Y (3940)into J/ψρ0π0 and J/ψρ+π− a ratio of 1 : 2 is as-sumed, a decay pattern which is expected for anisoscalar state.

Table 4.29 summarises the assumed cross sectionsand the branching fractions of the signal and back-ground reactions under study.


Reaction σ Bpp→Y → J/ψω σS 5.2 %× B(Y → J/ψω)π+π−π0ρ0 149µb∗ 100 %π+π−π−ρ+ 198µb∗ 100 %π+π−ω 23.9µb∗ 100 %ψ(2S)π0 55 pb 3.73 %Y → J/ψρπ σ 5.9 %× B(Y → J/ψρπ)

Table 4.29: Cross sections for signal and backgroundreactions. The table lists also the branching ratiosfor the subsequent particle decays. The cross sectionsmarked by an asterisk (∗) take already the branchingratios of subsequent particle decays into account andthe corresponding branching ratios are listed thereforeas 100 %. The reaction Y → J/ψρπ, which has its ownrelevance, is treated as background here.

The number of analysed signal and backgroundevents is summarised in Table 4.30. Signal eventshave been generated with phase space distribu-tion for the reaction Y (3940) → J/ψω. For theω → π+π−π0 a proper angular distribution is con-sidered. The background reactions pp → π+π−ωand pp→ π+π−πρ require a large amount of data.To simulate the demanded number of events withina sufficient time a J/ψ mass filter technique is ap-plied and the number of events analysed for thesereactions has to be corrected by the filter efficiency,which is also listed in Table 4.30.

Reaction pp→ Events Filter eff.J/ψω 2 · 104 100%π+π−π0ρ0 8.49 · 106 0.77%π+π−π−ρ+ 8.49 · 106 0.81%π+π−ω 9.9 · 106 9.15%J/ψπ−ρ+ 2.5 · 105 100%J/ψπ0ρ0 2.5 · 105 100%ψ(2S)π0 8 · 104 100%

Table 4.30: Summary of analysed events and the J/ψmass filter efficiency. For channels including charmo-nium states no filter is applied and the J/ψ is decayingto e+e− only.

The J/ψω system is reconstructed by combining theJ/ψ candidates found in an event with ω → π+π−π0

candidates. To form the latter, two candidates ofopposite charge, both identified as pions having alikelihood value L > 0.2 are combined together withπ0 → γγ candidates, composed from two photoncandidates having an invariant mass in the range[115; 150] MeV/c2.

All combinations of an event are fitted by constrain-ing the sum of the four-momenta of the final stateparticles to the initial beam energy and momen-tum and constraining the origin of the charged fi-nal state particles to a common vertex. Combina-tions where the fit yields a confidence level less than0.1 % are not considered for further analysis. TheJ/ψ and ω signal has a FWHM of 9 MeV/c2 and16.5 MeV/c2, respectively. An ω mass window of[750; 810] MeV/c2 is applied to cleanly select J/ψωcandidates. For the final event selection the ac-cepted candidates are fitted under the J/ψω hypoth-esis, where on top of the pp four-momentum con-straint mass constraints are applied to the J/ψ andπ0 candidates. Only candidates where the fit yieldsa confidence level L >0.1 % are considered further.

]2) [GeV/c-π+πψm(J/3.66 3.67 3.68 3.69 3.7 3.71

2E

ntrie

s / 0

.5 M

eV/c

0

100

200

300

400

500

600

VetoVetoFigure 4.28: Invariant J/ψπ+π− (J/ψ → e+e−) massof the accepted J/ψω candidates for signal and ψ(2S)π0

background events. The background distribution isshown on top of the signal distribution (shaded) andis normalised to the signal cross section and branchingfraction according to Table 4.29. The vertical lines in-dicate the mass region used for the ψ(2S) veto.

At this stage of the analysis in 0.16 % of the anal-ysed signal events more than one J/ψω candidateis found. The ambiguity is solved by selecting thecombination in the event which is leading to thehighest confidence level for the fit assuming theJ/ψω hypothesis. In 65 % of the cases the selectedcombination is corresponding to the generated com-bination and thus is the correct one. In total a neg-ligible fraction of 6 · 10−4 out of the signal events isreconstructed in the wrong combination.

The reconstruction efficiency is estimated sepa-rately for events reconstructed via the two differentJ/ψ decay modes. Only the correct combinations


are considered. The efficiency is found to be 14.7 %.The invariant J/ψω mass distribution obtained froma kinematic fit similar to the final fit applying theJ/ψ and π0 mass constraints, but removing the con-straint on the beam momentum and energy is shownin Fig. 4.29. The signal width (FWHM) is found tobe 14.4 MeV/c2.

]2) [GeV/cωψm(J/3.88 3.9 3.92 3.94 3.96 3.98 4

2E

ntrie

s / 1

.2 M

eV/c

0

200

400

600

800

1000

1200

Inv. J/psi omg massInv. J/psi omg massFigure 4.29: Invariant J/ψω mass distribution ob-tained after the kinematic fit applying the constraintsdescribed in the text.

In order to estimate the pollution of the signal fromthe considered background reactions, backgroundevents are analysed likewise as signal events and thenumber of reconstructed J/ψω candidates is deter-mined. The suppression η for a certain backgroundreaction is defined as the fraction of generated andaccepted events and is given in Table 4.31 for the in-dividual background channels. The expected signalto noise ratio is then given by

S

N=σSσB

BSBB

ε

η−1, (4.19)

where σs (σB) is the cross section and BS (BB) isthe product of branching fractions for signal (back-ground) reactions, and ε is the signal reconstruc-tion efficiency. Since the cross section σS and thebranching fraction B(Y → J/ψω) for the signal pro-cess pp → Y → J/ψω are not known the signal tonoise ratio is reported with respect to the productσ = σSB(Y → J/ψω). Table 4.31 summarises theexpected ratio S/B together with the suppressionfor the various background reactions.

A very good background suppression better than1 · 109 and 1 · 108 is achieved for the channels pp→π+π−πρ and pp → π+π−ω, respectively. Here the

Reaction η S/B

π+π−π0ρ0 > 1.1 · 109 > 56.5 σ/nbπ+π−π−ρ+ > 1.05 · 109 > 40.6 σ/nbπ+π−ω > 1.08 · 108 > 34.6 σ/nbψ(2S)π0 3.33 · 103 24.8 σ/pbJ/ψπ−ρ+ 25 4.90BRJ/ψπ0ρ0 22.1 7.65BR

Table 4.31: Observed background suppression η andthe expected signal to noise ratio S/B for the inves-tigated background reactions. The ratio S/B is re-ported for Y → J/ψπρ with respect to the unknownratio B = B(Y → J/ψω)/B(Y → J/ψρπ) of the branch-ing fractions for the reactions pp → Y → J/ψω andpp→ Y → J/ψρπ.

expected signal to noise ratio is better than 34 −56σ/nb, depending on the background channel.

For the ψ(2S)π0 background a S/B of 24.8σ/pb isobtained. Thus the expected signal pollution is verylow. For the two J/ψρπ channels a suppression bya factor of 20–28 is observed and the expected S/Bfor the sum of the two J/ψρπ charge combinationsis 5.58B, where B = B(Y → J/ψω)/B(Y → J/ψρπ).

Both reactions can be disentangled performing apartial wave analysis, which is out of the scope ofthis document. However, it should be noted thatthe ω → π+π−π0 decay has a distinct angular dis-tribution from the decay ρπ with ρ → ππ. The ωhelicity angle θh is defined as the angle between theπ+ and π0 momentum computed in the π+π− cen-tre of mass system. For signal events the cos θh dis-tribution is ∼ sin2 θh. The reconstructed θh distri-bution for signal and background events is shown inFig. 4.30 together with the reconstruction efficiencyin dependence of cos θh. The efficiency distributionshows only structures at extreme forward and back-ward angles and is homogeneous otherwise with re-spect to statistical uncertainties. A linear fit to theefficiency distribution yields a gradient consistentwith zero within statistical errors. Thus the an-gle θh can be cleanly reconstructed without signifi-cant distortion due to an inhomogeneity of the effi-ciency. The cos θh distribution reconstructed fromsignal events shows the expected ∼ sin2 θh depen-dence, which is distinct from the distribution ob-tained for background events. The result for back-ground events is derived assuming phase space dis-tribution for the Y → J/ψρπ decay. Depending onthe production process of the ρ meson its helicityand thus the angular distribution for ρ → ππ canvary. The two scenarios where the ρ decay angle is∼ sin2 and∼ cos2 have been tested by weighting the


generated events accordingly. The observed θh dis-tributions are independent of the assumed ρ → ππangular distribution. In conclusion it is expectedthat the J/ψω and J/ψρπ decay modes could be dis-entangled performing a partial wave analysis of theJ/ψπ+π+π0 final state.

Figure 4.30: Distribution of the helicity angle θh(top) for signal (black) and pp → J/ψρπ background(red) events. The distributions are normalised to thebranching fraction B(Y → J/ψω) and B(Y → J/ψρπ),respectively. Also shown is the reconstruction efficiencyin dependence of θh (bottom). The red line is the resultof a fit using a linear function.

The number of reconstructed events per day run-ning the accelerator at the Y (3940) peak positionand design luminosity of L = 2 · 1032 cm−2s−1 as-suming an efficiency of 50 % is given by

N = εS σ

∫Ldt = 66σ nb−1. (4.20)

Study of Y (4320) → ψ(2S)π+π− System inFormationIn this section the decay pp →ψ(2S)π+π−, ψ(2S) → J/ψπ+π−, J/ψ → e+e−

at a beam momentum of pp = 8.9578 GeV/c(corresponding to the Y (4320) resonance) isexamined.

The J/ψ → e+e− candidates are reconstructed asdescribed above. Both daughter candidates from aJ/ψ decay must be identified as electrons with a like-lihood L >85 %. The likelihood value for the parti-cle candidates identified as pions must be L > 0.2.All combinations found in an event are kinemat-ically fitted by constraining the sum of the four-vector of the final state particles to the initial beamenergy and momentum and constraining the originof the charged final state particles to originate from

a common vertex. Also a mass constraint is ap-plied on the J/ψ and ψ(2S) candidates (mass andbeam constraint - MBC). The fit is repeated withmass constraints only (M) and with beam/energyconstraints only (only beam constraint - BC).For accepted candidates the ψ(2S) (BC) is requiredto be within the interval [3.67; 3.71] GeV/c2 and theJ/ψ mass (BC) to be within [3.07; 3.12] GeV/c2. Theconfidence level of the fit (MBC) must be largerthan 0.1%. If more than one candidate in an eventpasses these selection criteria, the candidate withthe highest confidence level is chosen and the othersare rejected. Reconstructed ψ(2S)ππ candidatesfrom the signal mode which are accepted by thecriteria summarised above are checked if they arethe correct combination.The background channels are reconstructed in thesame way and pass the same selection criteria asthe signal modes, without an check for the rightcombination.

The reconstruction efficiency and the signal to noiseratio are examined only for the decay of J/ψ →e+e−.The ψ(2S)ππ signal region is defined as the in-terval from [4.29; 4.35] GeV/c2. The reconstructionefficiency is 14.9%. The reconstructed signal hasa mean of 4320 MeV/c2 and a width (FWHM) of13 MeV/c2.The cross section for the background mode pp →3π+3π− is 140µb (measured at a beam momentumof 8.8 GeV/c). The suppression is ηe+e− = 37 · 106.The signal to noise ratios is S/Bee = 700σ/µb,where σ = σS(pp → Y (4320))B(Y (4320) →ψ(2S)π+π−) is given in terms of the unknown sig-nal cross section and branching fraction.

Reaction Beam mom. events Filter eff.pp→ [GeV/c ] [%]

ψ(2S)π+π− 8.9578 20000 1003π+3π− 8.9578 106 0.67

Table 4.32: Signal and background modes for theψ(2S)π+π− analysis. For the generator level filter, seeSec. 3.5.3.

Study of the Formation Process pp →f2(2000 − 2500) → φφ The primary goal ofthis study is to proof the feasibility of the recon-struction of exotic states decaying into the favoureddecay channel φφ as a feasibility check for the longstanding quest about the ξ(2230). Since no explicitassumptions about the exotic particles propertieslike mass or angular momentum have been made


Reaction σ Bpp→

ψ(2S)π+π− σs(pp→ Y (4320)) 1.9%× B(Y (4320)→ ψ(2S)π+π−)3π+3π− 140µb 100%

Table 4.33: Cross sections and branching fractions for the ψ(2S)π+π− signal and background modes. Forthe subsequent J/ψ decay we use to the sole branching fraction to one lepton type. The cross section for thebackground mode has been measured at a beam momentum of 8.8 GeV/c.

Decay Eff. Suppr. Sig. to noisepp→ εS η S/B

ψ(2S)π+π− 14.9% − −3π+3π− − 37 · 106 700σ/µb

Table 4.34: Suppression η and signal to noise ratio forthe background modes of the ψ(2S)π+π− analysis. Thesignal to noise ratios are given in terms of the unknowncross section σ.

]2) [GeV/cππ(2S)ψm(4.24 4.26 4.28 4.3 4.32 4.34 4.36 4.38 4.4

2E

ntrie

s / 1

.6 M

eV/c

0

100

200

300

400

500

600

Inv. J/psi eta massInv. J/psi eta massFigure 4.31: Invariant mass distribution for ψ(2S)ππcandidates.

the simulation considered here comprises non reso-nant reactions of the type pp→ φφ without an in-termediate resonance as a minimum bias approach.The detection of a possible resonant structure re-quires an energy scan around the region of interestin order to measure the dynamic behaviour of thecross section σ(

√s).

Thus this investigation consists of the following twoparts:

1. Reconstruction of the signal

• determination of efficiency of signal

• estimate background level (signal to noiseratio S/B)

2. Simulation of an energy scan

• estimate the expected energy dependentcross section with the efficiency measure-ment from above

• estimate the required beam time to detectthe signal with a significance of 10σ fordifferent assumptions for the signal crosssection

Goal of the reconstruction is to determine the num-ber of reactions of the type

pp→ φφ→ K+K−K+K− (4.21)

together with the reconstruction efficiency.

Under the assumption that the efficiency will notchange very much for different energies in the re-gion around 2.5 GeV signal as well as backgroundevents have been generated at Ecms = 2.23 GeVcorresponding to an initial 4-vector

Pinit = (px, py, pz, E · c)= (0, 0, 1432, 2650) MeV/c, (4.22)

additionally modified according to an relative jitterp/dp = 10−5 accounting for the expected beam un-certainty. This is region where is has been foundevidence for the tensor (JPC = 2++) glueball can-didate ξ(2230) by the BES experiment [78].

Signal events have been generated with the eventgenerator EvtGen [79]. In order to determine thereconstruction efficiency with angular independentaccuracy the events have been generated accord-ing to phase space resulting in flat angular distri-butions.

The simulated decay chain was

pp → φφ (4.23)φ → K+K− (4.24)


The particular decay chain leads to a branching ra-tio related reduction factor of

fB = B(φ→ K+K−)2 · B(f2 → φφ)︸︷︷︸unknown!

= (0.492)2 · x < 0.242 (4.25)

As a conservative estimate we will assume thebranching ratio to be B(Glueball → φφ) = 0.2leading to a hypothetical factor fB = 0.05.

Table 4.35 summarises the datasets used for thesestudies.

Channel Number of eventspp→ φφ 50 kDPM generic 10 M

Table 4.35: Datasets for the φφ feasibility study.

The procedure for the reconstruction was:

1. Select kaon candidates from charged trackswith VeryLoose PID criterion1

2. Create a list of φ candidates by forming allcombinations of a negative with a positivecharged kaon candidate

3. Kinematic fit of the single φ candidates withvertex constraint

4. Create pp candidates by forming any validcombination of two φ-candidates

5. Kinematic 4-constraint fit of the pp candidateswith additional vertex constraint

Every of the so formed candidates had to fulfil thefollowing requirements:

1. Probability of φ vertex fit: Pφ > 0.001

2. Probability of pp kinematic fit: Ppp > 0.001

3. φ mass window: |m(K+K−) − mPDG(φ)| <10 MeV/c2

4. φφ mass window: |m(φφ) − 2.23GeV/c2| <30 MeV/c2

The latter criterion defines the signal region beingnecessary to determine the efficiency. Fig. 4.32 (a),(b) show the corresponding distributions accord-ing to the upper selection criteria for signal MonteCarlo data with kaon selection VeryLoose. Thedashed lines in (b) as well as the box in (a) cor-respond to the selected mass windows. In plot (b)

a superposition is shown of all reconstructed candi-dates.

In Fig. 4.32 (c), (d) the same plots are shown forgeneric background Monte Carlo data. No φ-signalis seen in the invariant masses m(K+K−) in plot(c) and the signal window in (d) has only one en-try, which disappears for tigher PID selection cri-teria. Therefore the conclusion concerning back-ground level from generic hadronic reactions is lim-ited for the time being. Nevertheless for cases with-out a single background event a limit is calculatedwith the assumption of one candidate in the signalregion.

To find an optimum for the PID criterion the se-lection has been repeated for all available criteriaVeryLoose, Loose, Tight and VeryTight. The re-sults are summarised in Table 4.36. Since for thePID requirements VeryLoose and Loose only oneevent and for Tight and VeryTight no backgroundevent was observed in the signal region the optimumwould be the most loose selection, since all calcu-lations are based on one single background eventin the region of interest. The expected signal-to-noise ratios extracted from this study vary between1:6 and better than 1:9. These values are consid-ered to have large uncertainties due to the directinfluence of the relative cross section of backgroundwith respect to the signal cross section σS , whichhas chosen to be 5 · 106.

It should be noted that only the order of magnitudeof the efficiency, i.e. ε ≈ 15-25 %, is important,since it only serves as input for the simulation ofthe energy scan.

Besides the fact that there will be uncorrelatedhadronic background due to misidentification orsecondary particles the main obstacle for a high pre-cision detection of a resonant structure in the crosssection will probably be the total cross section ofnon-resonant

pp→ φφ→ K+K−K+K− (4.26)

reactions being of the order of σpp→φφ ≈ 3-4µb inthat energy region, which has been measured by theJETSET experiment as shown in Fig. 4.36. Thesehave exactly the same signature as the signal reac-tions

pp→ X → φφ→ K+K−K+K− (4.27)

and thus are also kinematically not separable, e.g. by a 4 constraint fit. The only possibility todisentangle non-resonant from resonant reactions

1. See section 3.3.3 for details.


Channel rel. X-sec ε(VL)[%] ε(L)[%] ε(T)[%] ε(VT)[%]Signal 1 25.0 23.4 19.6 15.7DPM generic 5 · 106 6.7 · 10−5 6.7 · 10−5 < 6.7 · 10−5 < 6.7 · 10−5

r = S : N – 1 : 6 1 : 6 > 1 : 7 > 1 : 9

Table 4.36: PID optimisation summary. ε is the efficiency, VL, L, T, VT refer to the PID selection criteriadescribed in the text.

]2) [GeV/c-K+(K1m0.98 1 1.02 1.04 1.06 1.08 1.1

]2)

[GeV

/c-

K+(K 2

m

0.98

1

1.02

1.04

1.06

1.08

1.1

0

50

100

150

200

250

)2

φ) vs. m(1

φm(

]2) [GeV/cφφm(2.15 2.2 2.25 2.3

2yi

eld

/ 2.0

MeV

/c

0

200

400

600

800

1000

1200

1400

1600

1800

p) (mct match)pMass m( p) (mct match)pMass m(

]2) [GeV/c-K+(K1m0.98 1 1.02 1.04 1.06 1.08 1.1

]2)

[GeV

/c-

K+(K 2

m

0.98

1

1.02

1.04

1.06

1.08

1.1

)2

φ) vs. m(1

φm(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

)2

φ) vs. m(1

φm(

]2) [GeV/cφφm(2.15 2.2 2.25 2.3

2yi

eld

/ 2.0

MeV

/c

0

0.2

0.4

0.6

0.8

1

p) (mct match)pMass m( p) (mct match)pMass m(Figure 4.32: Distributions for reconstructed events for pp → φφ. (a) 2D plot of invariant masses m(φ1)vs. m(φ2) for signal events, (b) invariant mass m(φφ) with MC truth match for signal events. (c), (d) Thesame distributions for reconstructed background events generated with the DPM generator. Black histogramcorresponds to all reconstructed combinations, the shaded area represents combinations failing the MCT match.

(a) (b)

(c) (d)

is to perform a spin-parity or partial-wave analy-sis (PWA). For that purpose it might be crucial tohave a ’good’ i.e. flat behaviour of the efficiencydependence with respect to the intrinsic appearingangles of the decay. These are

• the K-decay angle θφ1 of the first φ,

• the K-decay angle θφ2 of the second φ and

• the angle φplane between the decay planes ofthe two φ-mesons, as illustrated in Fig. 4.33.


Since the initial pp system has been generated phasespace distributed the decay angle distributions ofthe φ’s are expected to be flat.

The efficiency as function of these angles has beendetermined by dividing the distribution of recon-structed candidates by the distribution of the corre-sponding quantity of generated particles. Fig. 4.34shows the results, in (a) for the φ-decay angle cos θφand in (b) for the angle φplane between the decayplanes.

It can be seen clearly that the efficiency is indepen-dent of any of the involved angles, thus making apotential PWA less difficult.

Figure 4.33: Angle φplane between the decay planesof the two φ’s.

φ1

φ2

K+

K−

K+K−

φplane

As previously indicated resonances in formation re-actions can only be detected via an energy scanaround the potential resonances pole mass. Close tothat energy the total cross section will be enhancedaccording to the line shape of the resonance whoseintensity could look like a Breit-Wigner distribution

BW(m) = A · 1π· Γ/2

(m−mR)2 + (Γ/2)2(4.28)

with Γ and mR being its total width and pole massrespectively and A being an arbitrary amplitude.This enhancement has to be separated in particularfrom the non resonant part of the total cross sec-tion. The JETSET experiment performed a mea-surement of exactly this total cross section of thereaction pp → φφ leading to a value σφφ ≈ 3-4µb,as shown in Fig. 4.36. For the following studies theempirical line fit shown has been considered as thebackground level upon which the signal shape hasto be detected. The curve explicitly was chosen as

σnon-res(m) = a+ b ·m (4.29)

with parameter values a = 92.8µb and b =−40µb/GeV/c2.

Figure of merit is the beam time necessary to mea-sure the signal cross section with a significance

S = σ/δσ of 10σ, for now neglecting the back-ground considerations for generic events discussedin the previous chapter.

The procedure for that purpose was:

1. Assumptions for parameters:

• Resonance pole mass: mpole =2235 MeV/c2

• Resonance full width: Γ = 15 MeV/c2

• Resonance branching ratio to signal chan-nel: B(f2 → φφ) = 0.2

• Integrated luminosity: L = 8.8 pb−1/day

• Energy window: ±50 MeV around polemass

• Number of equally distributed scan posi-tions: n = 25

• Reconstruction efficiency of φφ channel:ε = 0.25

2. Vary signal cross section σS at pole mass be-tween 1 nb and 1µb

3. Determine the approximate total beam time Tb

for the complete measurement to achieve sig-nificance of 10σ for the cross section measure-ment:

• Vary Tb arbitrarily an apply followingsteps until significance is 10σ

• Estimate number of expected backgroundentries for each scan energy Ei = mi · c2as

Bi = σnon-res(mi) · ε ·T b[d] · L

n(4.30)

• Estimate number of expected signal en-tries for Ei as

Si =BW(mi)

BW(mpole)· σS · ε

·B(f2 → φφ) · T b[d] · Ln

(4.31)

• Set contents of bin number i of the scanhistogram to ci = (Si +Bi)±

√Si +Bi

• Fit sum of signal function Eq. 4.28 andbackground function Eq. 4.29 to resultinghistogram and compute the significance asA/δA, where A is the fitted amplitude forthe resonant part of the fit model.


)dec1θcos(-1 -0.5 0 0.5 1

effi

cien

cy

0

0.05

0.1

0.15

0.2

0.25

0.3

)decθ efficiency(1

φ )decθ efficiency(1

φ

[rad]plane

φ0 1 2 3

effi

cien

cy

0

0.05

0.1

0.15

0.2

0.25

)plane

φefficiency( )plane

φefficiency(Figure 4.34: (a) Efficiency as function of the φ decay angle cos θφ. (b) Efficiency as function of the angle φplane

between the two decay planes.

(a) (b)

It turns out that the results reasonably behave ac-cording to statistics expectation, i.e. twice thebeam time results in a precision improved by a fac-tor√

2. Fig. 4.35 shows some of the correspondingplots with the fits performed to the total cross sec-tion (a) as well as to the estimated background sub-tracted signal cross section determined as the differ-ence of the total cross section and the backgroundexpectation computed from Eq. 4.29 (b). Both fitsagree quite reasonable as expected. It seems sur-prising that in particular in Fig. 4.35 (a) no signalis visible at all whereas the fit result has quite ahigh significance. This is due to the assumed highprecision of the data points reflected in the corre-sponding difference plots on the right hand side.Of course this evidently depends on the certaintyof signal and background line shapes.

Table 4.37 summarises the results for the studiesabove. The necessary beam times to achieve anaccuracy of 10σ significance vary from infeasiblehundreds to thousands of days with assumed signalcross section of σS < 10 nb down to comfortable”far less than a day” time windows for signal crosssections σS > 100 nb.

It shall be emphasised at this point that the resultsmight be too optimistic since idealised by the as-sumption of the correctness of the knowledge aboutthe total cross section measurement. Therefore thegiven beam time estimates might be considerablysensitive to the uncertainties which clearly can beseen in Fig. 4.36.

σS [nb] Beam time Tb (≈)1 13.7 y5 200 d10 50 d100 12 h500 0.5 h1000 7.2 min

Table 4.37: Beam times needed to achieve a signifi-cance of 10σ.


Prob 0.417[nb] Sσ 1.135± 9.543

] 2 [GeV/c0m 0.001± 2.234 ] 2/2 [GeV/cΓ 0.001± 0.007

bgA 0.000± 0.817 1a 0.002± 113.520 2a 0.001± -48.931

[GeV]cmsE2.2 2.22 2.24 2.26 2.28

b]µ [to

tσ

0

1

2

3

4

5

total cross sectiontotal cross section

Prob 0.988

[nb] Sσ 1.003± 9.543

] 2 [GeV/c0m 0.001± 2.234

] 2/2 [GeV/cΓ 0.001± 0.007

[GeV]cmsE2.2 2.22 2.24 2.26 2.28

[nb

]Sσ

-2

0

2

4

6

8

10

12

signal cross sectionsignal cross sectionFigure 4.35: Fits to the total cross section (a) and the derived signal cross section (b) for a scan with σS = 10nb and beam time according to Table 4.37.

(a) (b)

Figure 4.36: Cross section for the reaction pp → φφmeasured by the JETSET experiment. The yellowcurve represents a Breit-Wigner resonance, whose am-plitude is at CL =95 % upper limit for the productionof fJ(2230) at a mass of 2235 MeV /c2 and a width of15 MeV/c2 [80].


4.2.4 Heavy-Light Systems

Introduction

Consisting of a heavy and a light constituent, the Dmeson can be seen as the hydrogen atom of QCD.For the understanding of the strong interaction Dmesons are very interesting objects since they com-bine the aspect of the heavy quark as a static coloursource on one side, and the aspect of chiral symme-try breaking and restoration due to the presenceof the light quark on the other side. In the limitof infinite mass of the heavy quark (heavy quarklimit), the states of heavy-light mesons are degen-erate with respect to the spin degree of freedom ofthe heavy quark, and the total angular momentumof the light quark is conserved [81, 82]. In reality,the charm quark mass is not very much above thehadronic scale of ∼ 1 GeV, but still, similar to thehyperfine splitting in the hydrogen atom induced bythe proton spin, the spin orientation of the charmquark has only a small effect on the mass of thesystem.

Based on earlier observations of low-lying D me-son states, the phenomenological quark model wasthought to be able to describe the excitation spec-tra of heavy-light systems, and thus to predict alsothen unobserved D meson states with reasonableaccuracy [82, 83, 84, 85]. According to the quarkmodel systematics the lowest states are the S-wavestates with the spin singlet JP = 0− as groundstate (D) and the spin triplet JP = 1− as first ex-cited state (D∗), followed by the P -wave states withJP = 0+, 1+, 1+, 2+ (D0, D1, D

′1, D2). The physi-

cal JP = 1+ doublet (D1 with jPq = 12

+, D′1 withjPq = 3

2

+; jq is the total spin of the light quark)results from a mixing of 3P1 and 1P1 states, sincein heavy-light systems the total spin S = sq + sQis not a good quantum number. The experimen-tally observed non-strange D meson spectrum [86]was consistent with this pattern of six states, al-though for some of the states no spin-parity assign-ments could be given. In the spectrum of charmedstrange mesons the only states known with estab-lished spin-parity assignments before the recent dis-coveries were the pseudo-scalar ground state Ds

and the first excited vector state D∗s . Apart fromthis, a Ds(2536) and a Ds(2573) state had beenobserved [86].

Recent discoveries

The series of new observations in the charmo-nium spectrum at B and charm factories was ac-

companied by exciting new experimental resultson the spectrum of open charm mesons, start-ing with the unexpected discovery of a narrowDs(2317) state observed in the decay mode D+

s π0

by BaBar [87] in e+e− annihilation data at ener-gies near 10.6 GeV. Shortly after, this state wasconfirmed by CLEO [88] and Belle [89]. At thesame time, CLEO found a new, also narrow stateDs(2460) [88] decaying to D∗+s π0. This state wassubsequently also seen by Belle [89], and confirmedby BaBar [90, 91]. The width of both states is smallsince the Ds(2317) is lying below the DK thresh-old, and the Ds(2460) is below the D∗K thresh-old. Thus the Ds(2317) state cannot decay by kaonemission, and, with JP = 1+, decay with kaon emis-sion is also forbidden for the Ds(2460) state. De-cay to D(∗)

s with single pion emission is isospin for-bidden. The properties of the two states were fur-ther studied in [92, 93]. [93] gives upper limits ofthe width Γ < 3.8 MeV for the Ds(2317) state andΓ < 3.5 MeV for the Ds(2460) state. The observeddecay modes are consistent with spin-parity assign-ments JP = 0+ for the Ds(2317) state and JP = 1+

for the Ds(2460) state, respectively. The so far ob-served decay modes are [94] Ds(2317)+ → D+

s π0

and Ds(2460)+ → D∗+s π0, D+s γ,D

+s π

+π−. Very re-cently, another Ds meson state decaying into DKat a mass of 2.86 GeV/c2 and a larger width of∼ 47 MeV was observed at BaBar [95].

Theoretical Interpretation

These observations attracted much interest both inthe theoretical and the experimental hadron physicscommunity, since the new states don’t fit well intothe quark model predictions for heavy-light systemsin contrast to the previously known D meson states.The Ds(2317) state is typically 150 MeV or morebelow the quark model expectation. In particu-lar, it has been considered very difficult to repro-duce the mass difference between the 0+ and the 1+

state within the quark model [96]. Fig. 4.37 shows acomparison between the observed Ds spectrum andquark model calculations [84, 85] together with theDK and D∗K thresholds.

Long before the discovery of the new states, a modelbased on chiral symmetry was developed for heavy-light systems that predicted the mass splitting ofthe 0− − 0+ and 1− − 1+ to be related to the lightconstituent quark mass [97, 98]. Since in that ap-proach the D mesons, like the light quark fields inQCD, transform linearly under chiral SU(3) rota-tions the spectrum shows a doublet structure. Af-ter the discovery of the new states the scheme was


Figure 4.37: The Ds meson spectrum as predictedby Godfrey and Isgur [84] (solid lines) and Di Pierroand Eichten [85] (dashed lines). Experimental valuesare shown by points, the DK and D∗K thresholds ashorizontal lines. The figure is taken from [93].

applied to the new Ds states [99, 100] and shownto explain the low Ds(2317) mass and the identicalhyperfine splitting in the 0−−1−− and 0+−1+ dou-blets. Such results indicate the importance of chiralsymmetry for the understanding of the open-charmmeson spectrum.

The discovery of the scalar and axial-vector open-charm states triggered a series of theoretical worksstudying the new states in various frameworks. Fora recent review focusing on approaches with activequark degrees of freedom see Ref. [96]. The possi-bility that these states could have a simple cs struc-ture is discussed in Refs. [101, 102]. The predictedlevel scheme of typical quark models may, however,suggest that the scalar and axial-vector Ds mesonshave an exotic non-cs structure. For instancetetra-quark models for Ds states assume strong[cs]

[uu+ dd

]or [cq] [sq′] components in the wave

function [103, 104, 105, 106, 107, 108, 109, 110].However, tetra-quark models usually predict a largenumber of states in addition to the qq meson statesfor which there is little experimental evidence. InRefs. [111, 112, 113] the relevance of higher Fockstates involving mesonic degrees of freedom for thescalar states was investigated applying resonatinggroup methods to a quark model. The possibilitythat the scalar Ds may be a molecular DK statewas discussed in Ref. [114].

First systematic computations where open-charmresonances are generated in terms of hadronic de-grees of freedom were based on the chiral La-grangian written down for the Goldstone bosons

and the pseudo-scalar and vector D-meson groundstates [115, 116]. The approach is consistent withthe heavy-quark symmetry that arises in the limitof large charm quark mass. A natural explana-tion of the scalar and axial vector spectrum wasachieved, where for instance the scalar Ds statesare coupled-channel molecules with important DKbut also η Ds components. In contrast to the chiral-doubling approach of Ref. [97, 98] the chiral La-grangian assumes the D meson fields to transformnon-linearly under chiral transformation. As a con-sequence the arising spectrum is not necessarilygrouped into chiral doublets. In fact the leadingorder chiral interaction predicts weak attraction inexotic non cq channels. The existence of such statesdepend2 on the character of sub-leading order termsin the chiral Lagrangian. A recent study [117] pre-dicts exotic signals in the η D∗ and πD channels.

D Spectroscopy at PANDA

An important quantity possibly allowing to distin-guish between the different pictures is the decaywidth of the two Ds states [117, 118, 119, 120, 121,122]. So far their widths are only constrained by up-per limits of a few MeV due to detector resolution,which is not sensitive enough to draw conclusionson their internal structure. In the following, a dif-ferent experimental approach to determine the nar-row widths of these states is discussed. Very close tothreshold the energy dependence of the productioncross section for a narrow resonance can be calcu-lated in a model-independent way [123], and thisfunction is sensitive to the resonance width. Pro-vided the beam energy is sufficiently well known,thus the width of a narrow resonance can be deter-mined in a measurement of the energy dependenceof the production cross section around the energythreshold, without requiring the corresponding de-tector resolution in the reconstruction of the res-onance from the final state. With δp/p ' 10−5

the p momentum spread in the HESR is sufficientlysmall to allow the measurement of the DsJ widthsin a threshold scan of the reaction pp→ DsDsJ atPANDA down to values of ∼ 100 keV.

As an example, the study of the Ds0 width isspecifically discussed in the following sections re-lated to simulation studies which have been per-formed for this report. Future investigations of theD and Ds meson spectra at PANDA have howevera wider scope beyond this specific aspect. If anexotic structure of the newly found states as molec-ular or tetra-quark states should be established,an experimental D meson spectroscopy program


should search for the then missing quark modelstates with the identical quantum numbers. Fur-ther insight is expected from a comprehensive studyof the decay modes of both D and Ds mesons in-cluding also modes with small branching fraction.Recent theoretical studies have proposed to mea-sure the partial widths for various radiative decaysof the new Ds states, since these are predicted tobe distinctly different for a molecular or Qq struc-ture [117, 121, 122, 124, 125, 126, 127, 128]. Thisrequires to measure both the branching fractionsfor the radiative transition and the total width ofthe decaying state which is certainly an ambitiousgoal. For not too small total widths and transitionprobabilities this may however be possible.

So far only S and P wave states have been observedin both the D and the Ds spectrum. Informationon states with D wave and higher angular momentaare still missing. This is likely to be due to thelimitation in angular momentum in the productionprocess of D mesons studied up to now (e+e− an-nihilation and B meson decays). In contrast veryhigh partial waves are available in the pp entrancechannel which should also enhance the populationof states with high L values. As was discussed veryrecently [129], the exploration of the region of stateswith high angular momenta could be an importantstep to clarify the question whether or not chiralsymmetry is restored in hadrons at high excitationenergies.

Simulated Signal Channels

For this report simulation studies focus on the iden-tification of the Ds0(2317) and the determinationof its width, based on the reaction channel pp →D±s D

∗s0(2317)∓. The recoiling D∗s0(2317) is identi-

fied inclusively without specifying its decay mode,as will be discussed below. Signal events have beengenerated which the event generator EvtGen[79]with the intrinsic width of the D∗s0(2317) set toΓ = 0.1 MeV for the study of signal reconstruction.A data set for signal events (=Signal 1) was gener-ated in the following way:

pp → D±s D∗s0(2317)∓ (4.32)

D±s → φπ±, φ→ K+K− (4.33)D∗s0(2317)∓ → anything (4.34)

A second data set with equal number of events(=Signal 2) was generated completely inclusive, i.e.

pp → D±s D∗s0(2317)∓ (4.35)

D±s → anything (4.36)D∗s0(2317)∓ → anything (4.37)

in order to allow an independent determination ofthe reconstruction efficiency.

Since the D∗s0(2317) width with its present upperexperimental limit Γ < 3.5 MeV [94] is smaller thanthe detector resolution, it cannot be measured di-rectly. Instead, it can be deduced from a mea-surement of the shape of the excitation function ofD∗s0(2317) production very close to threshold. Thesimulation studies thus also address an energy scanof the signal channel around the threshold energyand explore how well the shape of the excitationfunction can be determined.

Background Channels

In order to estimate the background level severalspecific reaction channels with a Ds meson in thefinal state with identical decay mode as the signalevents have been investigated. To fill the availablephase space at the threshold of the signal chan-nel of 354 MeV, background channels with pions orphotons in addition to the second Ds meson havebeen considered. Furthermore, a generic hadronicbackground sample created using the event gener-ator DpmGen based on the dual parton model [130]has been analysed. Table 4.38 lists the investigateddata sets. The data sets were generated at 5 MeVabove the nominal D±s D

∗s0(2317)∓ threshold.

Analysis Strategy

Corresponding to the goal of the simulation studyof D∗s0(2317)∓ production the analysis consists oftwo separated steps:

1. Reconstruct the signal at given energy:

• determine the efficiency of the signal re-construction• estimate the background level (signal to

noise ratio S/N)

2. Simulate the energy dependence:

• generate the relevant distributions for thesignal events based on the results fromstep 1 at selected energies, and determinethe number of signal and backgroundevents• determine the shape of the excitation

function• deduce width and mass of the D∗s0(2317)∓

state

These analysis steps will be briefly discussed in thefollowing.


Channel Number of eventspp→ D±s D

∗s0(2317)∓ (Signal 1) 40 k

pp→ D±s D∗s0(2317)∓, D±s → any (Signal 2) 40 k

pp→ D±s D∓s π

0 40 kpp→ D±s D

∓s 2π0 40 k

pp→ D±s D∓s π

+π− 40 kpp→ D±s D

∗∓s 40 k

pp→ D±s D∗∓s π0 40 k

pp→ D±s D∓s γ 40 k

pp→ D±s D∗∓s γ 40 k

DPM generic 10.5 M

Table 4.38: The data sets to evaluate signal reconstruction efficiency and signal-to-noise ratio.

Exclusive and inclusive signal reconstruction

The optimum signal to noise ratio is achieved in afull exclusive reconstruction of all particles emerg-ing in the decay chains of the primary particles pro-duced in the reaction. On the other hand, dueto the small branching ratios involved the signalevent rate based on a single decay chain will be verysmall. In the simulation studies these small branch-ing ratios reduce the significance of the achievedbackground suppression factor at given size of theanalysed background sample. Therefore, as will beargued below, a different approach using inclusiveD∗s0(2317) identification is pursued here.

The D±s meson has many decay branches. As chan-nel with reasonable efficiency and with character-istic strangeness content the D±s → φπ± decaybranch with φ → K+K− was selected. The com-bined branching ratio is

fB,Ds = B(D±s → φπ±) · B(φ→ K+K−) == 0.044 · 0.492 = 0.022.

Since the only known decay channel of theD∗s0(2317) is the isospin violating D∗s0(2317) →D±s π

0 decay (with unknown branching fraction) onealso needs to reconstruct the π0 → 2γ and the sec-ond D±s in the above channel for a full exclusivereconstruction resulting in the total branching ra-tio factor

fB,excl = B(D∗s0(2317)→ Dsπ0)︸︷︷︸

unknown

·B(D±s → φπ±)2 ·

·B(φ→ K+K−)2 · B(π0 → 2γ) << 4.6 · 10−4.

The branching ratio B(D∗s0(2317) → Dsπ0) is ex-

pected to be very close to one. With the assump-tion of σ = 1 nb signal cross section at threshold,an integrated luminosity of about L = 9000/nb per

day and efficiency ε ≈ 0.2 this results in an expectednumber of efficiency and branching ratio correctedsignal reactions of

Nexcl = σ · L · ε · fB,excl ≈ 9000 · 0.2 · 4.6 · 10−4 == 0.8 detected signals/day.

Such low event rates would require a very long run-ning time for the measurement of the excitationfunction. It therefore doesn’t seem promising toonly use this specific final state for the identifica-tion of the pp → D±s D

∗s0(2317)∓ reaction, but to

include an as large as possible number of specificchannels in the decay chain in order to increase theevent rate in the exclusive reconstruction.

The task to simulate many different channels ishowever beyond the scope of this report. Thesimulations are therefore focused on the questionwhether an inclusive reconstruction of theD±s decaywith the identification of the recoiling D∗s0(2317)∓

via the missing mass method, which would resultin higher event rates, yields sufficient backgroundsuppression for signal identification. To enhance thesignal to background ratio kinematic correlations inthe event are exploited, as discussed below. In caseof the inclusive reconstruction the expected numberof reactions which can be detected is estimated tobe

Nincl = σ · L · ε · fB,Ds < 9000 · 0.2 · 0.022 == 40 detected signals/day.

Hence, to collect a reasonable number like 500events only around two weeks of beam time wouldbe required.

Event selection criteria

D±s candidates were created in the following way:


1. Select kaon candidates from charged trackswith VeryLoose PID criterion2 (will be tight-ened later for better S/B ratio)

2. Create a list of φ candidates by forming allcombinations of a negative with a positivecharged kaon candidate

3. Kinematic fit of the single φ candidates withvertex constraint

4. Select pion candidates from charged trackswith VeryLoose PID criterion

5. Combine φ candidates with pion candidates toform D±s candidates

6. Kinematic fit of the D±s candidates with vertexconstraint

]2 [GeV/cmissm2.25 2.3 2.35 2.4

2yi

eld

/ 2.0

MeV

/c

0

200

400

600

800

1000

1200

1400

*)s0

aka m(Dmissm *)s0

aka m(DmissmFigure 4.38: Missing mass spectrum obtained for theD±s candidates based on the known 4-momentum of theinitial pp system. The black histogram corresponds toall reconstructed combinations of the required particlesin the final state, the green filled area represents thosecombinations which fail the MCT match criterion (ex-planation see text).

On the candidates preselected in this way the fol-lowing requirements were applied in addition:

1. Probability of φ vertex fit: Pφ > 0.001

2. Probability of D±s vertex fit: PDs > 0.001

3. φ mass window: |m(K+K−) − mPDG(φ)| <10 MeV/c2

4. φ decay angle3: | cos θdec| > 0.5

5. D±s mass window: |m(φπ±) − mPDG(D±s )| <30 MeV/c2

Fig. 4.38 shows the D±s missing mass spectrum ob-tained with the selection criteria listed above. Theblack histogram represents all reconstructed candi-dates whereas the green filled area corresponds tocandidates failing the so called Monte Carlo Truth(MTC) match4. Both D±s and D∗s0(2317)∓ peaksare reconstructed with a resolution of about 10-15 MeV/c2.

In a completely exclusive analysis a 4-constraint fitto the sum of the 4-momenta of the final state par-ticles as given by the 4-momentum vector of theinitial pp state in general improves the signal qual-ity significantly. As the D∗s0(2317) decay is not re-constructed, this is not possible here. However, thereconstructed D±s and D∗s0(2317)∓ masses are kine-matically anti-correlated as a consequence of theirproduction very close to the threshold energy. Thiscorrelation, as shown in Fig. 4.39 (left) is exploitedin order to enhance the signal to noise ratio. Thepeak of the msum = m(D±s ) +m(D∗s0(2317)∓) summass appears to have a width of about 1 MeV/c2

only. Therefore in this analysis the sum mass msum

is used as quantity to count the number of signalevents. It will be demonstrated later that back-ground channels exhibit a different behaviour andcan be reasonably well separated from the signal inthis projection.

The obtained msum spectrum is fit with a Voigtdistribution, i.e. a convolution of a Breit-Wignerwith a Gaussian distribution, with phase spacedamping5. However, due to the absence of back-ground within the signal events the reconstructionefficiency can simply be determined by counting thenumber of events in the range

4280 MeV/c2 < msum < 4291 MeV/c2 (4.38)

2. See section 3.3.3 for details.

3. The decay angle is defined as the angle between thedirection of motion of the reconstructed φ candidate in thelaboratory frame and the direction of motion of one of thekaons in the frame of the φ.

4. The Monte Carlo Truth match checks whether or nota decay tree has been exactly reconstructed the way it wasgenerated.

5. This function is given by

f(m) = A ·hR+∞−∞ G(x′;m0, σ) ∗BW (m− x′;m0,Γ) dx′

i×

1

1+exp“m−mqτ

” with a Gaussian G(m), a non-relativistic

Breit-Wigner function BW (m), an intensity parameter A,running variable m, resonance pole mass m0, resonancewidth Γ, reconstruction resolution σ, phase space limit mqand decay parameter τ (all except A in [GeV/c2 ]).


]2) [GeV/cπ φm(1.9 1.95 2 2.05

]2 [

GeV

/cm

iss

m

2.25

2.3

2.35

2.4

Ds vs. mmissm Ds vs. mmissm

A 0.052± 4.795 0m 0.000± 4.286

σ 0.000± 0.001 Γ 0.000± 0.001

qm 0.000± 4.289 τ 0.000± 0.001

]2 [GeV/cmiss + mDsm4.27 4.28 4.29

2yi

eld

/ 0.3

MeV

/c

0

200

400

600

800

1000

1200

1400

1600

1800

(mc match)Ds + mmissSum m (mc match)Ds + mmissSum mFigure 4.39: Reconstruction of signal events type 1. (Left) Correlation of missing mass and invariant D±s mass.(Right) The sum mass mmiss +m(D±s ). The number of signal events is evaluated as the number of entries in theinterval between the vertical red lines.

which is marked by the two vertical lines in Fig. 4.39(right). For the particular example here withVeryLoose kaon identification we find S = 14490entries in the signal region corresponding to an effi-ciency of ε = 36.2% An efficiency of the same mag-nitude is independently found by the analysis ofcompletely inclusive events (Signal 2), where alsothe recoiling Ds decays generically.

Background

Background channels as listed in Table 4.38 havebeen analysed. Fig. 4.40 shows as an example back-ground distributions due to the pp → D±s D

∓s π

0

reaction obtained for the VeryLoose kaon candi-date selection. Left and right panels of Fig. 4.40show the reconstructed D±s missing mass and themsum = m(D±s ) +m(D∗s0(2317)∓) sum mass distri-butions, respectively. For this as well as the otherspecific background channels the msum distributionfollows a phase space distribution which is well de-scribed by an Argus function 6.

In the background sample generated with DPM- known to be inadequate for the simulation ofcharmed hadron production - no significant amountof D±s mesons are correctly reconstructed. With theVeryLoose kaon candidate selection very few out of5 M generated events are found in the msum windowbetween 4280 MeV/c2 and 4291 MeV/c2.

Results

In order to find the selection criteria for the max-imum signal significance many parameters have tobe varied. At the present stage of the study onlythe influence of the kaon identification quality hasbeen systematically analysed.

Four different selection criteria VeryLoose, Loose,Tight and VeryTight based on a global PID like-lihood function L are available with requirementsaccording to tab. 3.2.

All these four criteria for kaon identification wereapplied to the selection procedure, resulting in dif-ferent numbers of residual candidates for signal andbackground in the msum signal region. The ex-pected signal-to-noise ratio rSB depending on thePID selection criterion can only be given based onrelative cross sections of the background channelsas compared to that of the signal. Since all crosssections are unknown, as reference value for the sig-nal and for all purely hadronic background chan-nels 50 nb is assumed, whereas the reference valueis scaled down by a factor 10 to 5 nb for channelswith photons in the final state. The S/B ratio forall considered specific background channels basedon this assumption is given in Table 4.39. TheS/B ratio for the generic background obtained withDPM corresponds to an assumed ratio of the back-

6. Here the Argus function is defined as fbg(m) = As ·m ·p

1 − (m/m0)2 · expˆc ·`1 − (m/m0)2

´˜with amplitude

parameter As, phase space limit m0 and shape parameter c.


]2 [GeV/cmissm2.25 2.3 2.35 2.4

2yi

eld

/ 2.0

MeV

/c

0

50

100

150

200

250

300

*)s0

aka m(Dmissm *)s0

aka m(Dmissm

0m 0.000± 4.291 c 12.098± -17.348

A 3.692± 39.374

]2 [GeV/cmiss + mDsm4.27 4.28 4.29

2yi

eld

/ 0.3

MeV

/c

0

5

10

15

20

25

30

(mc match)Ds + mmissSum m (mc match)Ds + mmissSum mFigure 4.40: Background channel 1: pp → D±s D

∓s π

0. (Left) Reconstructed D±s missing mass distribu-tion. (Right) Obtained sum mass distribution: the number of background events is evaluated in the interval4280 MeV/c2 < 4291 MeV/c2 as indicated by the vertical red lines. The black histogram corresponds to all recon-structed combinations of the required particles in the final state, the green filled area represents those combinationswhich fail the MCT match criterion (explanation see text).

Channel rel. X-sec ε(VL)[%] ε(L)[%] ε(T)[%] ε(VT)[%]Signal 1 36.2 28.1 21.0 19.0pp→ D±s D

∓s π

0 1 0.8 0.6 0.5 0.4pp→ D±s D

∓s 2π0 1 6.9 5.2 4.0 3.6

pp→ D±s D∓s π

+π− 1 8.1 6.1 4.6 4.2pp→ D±s D

∗∓s 1 0.0 0.0 0.0 0.0

pp→ D±s D∗∓s π0 1 3.7 2.8 2.1 1.9

pp→ D±s D∓s γ 0.1 0.6 0.4 0.3 0.3

pp→ D±s D∗∓s γ 0.1 1.1 0.9 0.6 0.6

DPM generic 106 2.5 · 10−4 4.5 · 10−5 1.9 · 10−5 1.9 · 10−5

rSB (w/ DPM) – 1 : 318 1 : 74 1 : 43 1 : 47rSB (w/o DPM) – 1.86 1.90 1.89 1.88

Table 4.39: Results of the simulation studies of signal reconstruction and background suppression. Only relativecross sections are given. ε denotes the signal reconstruction efficiency for the signal channel and the fake signalfinding probability for the studied background channels, respectively. The resulting values for the signal-to-noiseratio rSB including or excluding the generic DPM background are also given (see text).

ground to signal cross section of 106. Using the sig-nal selection criteria described above, 3 events outof 10.5 · 106 DPM background events are found inthe signal region. For a kaon selection based on cri-terion Tight this corresponds to an expected ratioof rSB ≈ 1 : 43.

Although this value has a large statistical uncer-tainty, this indicates that it may be difficult to mea-sure an excitation function based on the inclusivereconstruction method described above. Therefore,an even larger DPM background sample was also

analysed with the exclusive reconstruction of theD±s D

∗s0(2317)∓ → φπ±π0φπ∓ decay chain. None

of 4.0 · 107 DPM background events survived thesignal selection cuts using the VeryLoose kaon se-lection criterion. Further background suppressioncan be expected from using a tighter kaon selec-tion criterion, and particularly, from a cut on theD+s and D−s decay vertices. Unfortunately, due the

small branching ratio to the final state, the non-observation of fake events only corresponds to anestimated lower limit of signal-to-background ratioS/B > 1 : 623. In order to obtain a more sig-


nificant result on the achievable background sup-pression, much larger background samples have tobe generated and analysed. In addition, the sametype of exclusive analysis needs to be repeated fordifferent decay chains, in order to acquire a highersignal event rate. Both tasks are beyond the scopeof the present report, and will be pursued in futurestudies.

Simulation of a Near-Threshold Energy Scan

Excitation function

At small excess energies above threshold governedby S-waves the energy dependence of the cross sec-tion for the reaction a+b→ 1+2 where the two finalstate particles (i = 1, 2) have Breit-Wigner spectralfunctions

ρi(m) =1π· Γi/2

(m−mRi)2 + (Γi/2)2(4.39)

with resonances pole mass and width mRi and Γi isgiven by the integral [131]

σ(s) = |M |2∫ +∞

−∞dm1∫ +∞

−∞dm2 ρ1(m1)ρ2(m2) · p ·Θ(

√s−m1 −m2).

Here m1 and m2 are the running masses,√s is the

total centre-of-mass energy, M the matrix elementof the process, and p the momentum of the tworesonances in the centre-of-mass frame. Substitut-ing Breit-Wigner spectral functions with zero widthfor the Ds meson, and the centre-of-mass momenta,one obtains a simplified relation for the energy de-pendence (with md ≡ m(Ds)) [131]:

σ(s)|M |2 =

Γ4π√s

∫ √s−md−∞

(4.40)

dm

√[s− (m+md)2] · [s− (m−md)2]

(m−mR)2 + (Γ/2)2.

Scan procedure

The simulated energy scan for this write-up is basedon several simplifying assumptions.

Apart from the effects due to energy dependentshifts of the kinematic limit in the Argus functionmodelling the background distributions of the spe-cific channels considered, the background level isassumed to be energy independent within the small

energy range in which the excitation function is sim-ulated. Also the signal reconstruction efficiency isassumed to be constant for all energy steps.

The momentum spread of the beam is only takeninto account in a simplified way, namely by an ad-ditional contribution to the energy selected in thescan procedure. In a fully correct treatment the ef-fective excitation function instead consists of a con-volution of the energy spread with the theoreticalexcitation function for infinitely small momentumspread.

The following parameters are selected:

• The width ΓDs0 of the D∗s0(2317).

• The spent beam time Tbeam for the completemeasurement; a signal cross section of σS =1 nb at threshold energy Ethr and an integratedluminosity of L = 9 pb−1/day is assumed.

• The energy region ∆Emax below and above thethreshold to be scanned.

• The number n of the taken measurementswithin the energy scan (→ ∆E = 2 ·∆Emax/n)

• The signal-to-noise ratio rSB

• The signal reconstruction efficiency ε · fB,Ds

The number of signal events at each energy step iscomputed according to

Si = σ(Ei/c2) · Ltot

n· ε · fB,Ds =

= σS ·fex(Ei + δE)fex(Ethr)

· L · Tbeam

n· ε · fB,Ds

where δE corresponds to the uncertainty of thebeam energy, and is randomly selected within aGaussian distribution of 150 keV width, and fex isgiven by the value of the integral in equation 4.40.

The signal-to-background ratio rSB listed above isvalid at the highest energy En of the scan. Accord-ing to the lower number of signal events at the lowerenergies within the scan the value of rSB is scaleddown appropriately, assuming constant backgroundapart from a phase space correction.

Results

So far a few combinations of parameters have beenexplored in the simulation of the energy scan of thepp → D±s D

∗s0(2317)∓ reaction. No attempt was

made to find the global optimum of the procedure,which would require a systematic investigation of


[MeV]s4284 4285 4286 4287 4288

yiel

d

020406080

100120140160180200

220 Rm 0.528± 2317.412 RΓ 0.304± 1.160

A 25.824± 86.101

Rm 0.528± 2317.412 RΓ 0.304± 1.160

A 25.824± 86.101

GraphFigure 4.41: Fit of the excitation function obtainedfrom the reconstructed signal events, shown by the fullgreen line. The red dotted line shows the excitationfunction corresponding to the generated events.

a high-dimensional parameter space. The resultobtained for a specific parameter set is shown inFig. 4.41. The selected parameters (scan 1) are:

• T = 14 d, rSB = 1 : 3, Γ = 1 MeV/c2, ∆Emax =2 MeV, n = 12.

For this parameter set the fit yields

m = 2317.41±0.53 MeV/c2, Γ = 1.16±0.30 MeV/c2,(4.41)

to be compared with the input values m =2317.30 MeV/c2 and Γ = 1.00 MeV/c2, respectively.

The same procedure with a parameter set corre-sponding to a much smaller S/B ratio

• T = 28 d, rSB = 1 : 30, Γ = 0.5 MeV/c2,∆Emax = 1 MeV, n = 12

did not allow to deduce a meaningful fit result forthe D∗s0(2317) width.


4.2.5 Strange and Charmed Baryons

Introduction

An understanding of the baryon excitation spec-trum is one of the prime goals of non-perturbativeQCD. In the nucleon sector, where most of the ex-perimental information is available and where theexperimental effort is still being concentrated, it isfound that the agreement with quark model predic-tions is astonishingly small: some of the low-lyingstates are not at the energies predicted, whereasmany of the predicted higher lying states have notbeen seen experimentally [11]. The latter aspecthas been discussed as the problem of ’missing reso-nances’ [132], and different explanations have beensuggested. For example a quark-diquark structureof baryons would reduce the number of internal de-grees of freedom, and thus the number of states.Another reason could be a lack of experimental sen-sitivity, since resonance excitation and detected fi-nal states have so far been largely based on pionicmodes [11]. It is also not clear to which extent theobserved states are three-quark excitations or gov-erned by meson-baryon dynamics. In the approachof chiral coupled channel dynamics [133, 134, 135],based on the conjecture that the only genuine qqqstates are the octet and decuplet ground states, itis attempted to describe all excited baryon statesas dynamically generated resonances.

Strange Baryons

The question to which extent the excitation spec-tra of baryons consisting of light quarks (u, d, s) fol-low the systematics of SU(3) flavor symmetry, re-quires knowledge not only on N∗ and ∆ spectrabut also on those of all species of strange baryons,i.e. of Λ, Σ, Ξ, and Ω hyperons. However, as oneadds strangeness as an additional degree of free-dom to the baryonic constituents, the experimen-tal data quality becomes increasingly poor. This isalready the case for the Λ and Σ spectrum, whererecent observations of new states [136, 137] are wait-ing for confirmation and interpretation. The database is particularly scarce for S = −2 and S = −3baryons. Ξ and Ω excited states have in generalbeen seen as bumps in inclusive experiments only,without determination of spin and parity quantumnumbers. The 2006 edition of the Review of Parti-cle Physics [11] explicitly mentions that ”nothing ofsignificance on Ξ resonances has been added sincethe 1988 edition”. A large fraction of the data hasbeen obtained with low statistics in bubble cham-ber experiments. Apart from the Ξ octet and de-

cuplet (Ξ(1530)P13) ground states spin and par-ity assignments only exist for the three-star reso-nances Ξ(1820)D13 and Ξ(2030), but their assign-ment is labelled as ”merely educated guesses” in[11]. More recent information on masses, widths,and decay modes of the Ξ0(1690), Ξ−(1820), andΞ−(1950) states was delivered by the WA89 exper-iment [138, 139]. The Ξ0(1690) state was also seenin Λ+

c decays at Belle [140] and at BaBar [141]. Thelatter study favours a spin 1/2 assignment to thisstate, and confirms the JP = 3/2+ assignment forthe Ξ0(1530) state.

Almost nothing is known on the excitation spec-trum of the Ω baryon: no assignment exists for anyof the three seen excited states (one three-star, twotwo-star resonances). Table 4.40 gives an overviewof the assignment of known baryonic states in thelight quark sector [11].

Recent theoretical work on the Ξ and Ω spectrum isfound in Refs [142, 143]. Due to the lack of experi-mental data, most of the calculated states have noexperimental counterpart and their existence needsverification. Ref. [143] also estimates two-body de-cay widths, and obtains values of less than 50 MeVfor some of the states.

Table 4.40: Quark-model assignments for some of theknown baryon states in flavor-spin SU(6) basis. Part ofthe spin-parity assignments are not well established andneed confirmation (taken from [11]).


Baryon Spectroscopy with PANDA

The PANDA experiment is well-suited for a compre-hensive baryon spectroscopy program, in particularin the spectroscopy of (multi-)strange and possiblyalso charmed baryons. In pp collisions, a large frac-tion of the inelastic cross section is associated withchannels resulting in a baryon antibaryon pair inthe final state. As an example, at 3 GeV/c p mo-mentum the total pp cross section is 77 mb, the in-elastic cross section is 53 mb, with a one to one ra-tio of baryonic final states and of annihilation intomesons. At higher p momenta the yield of chan-nels with baryonic final states exceeds that of themesonic channels, e.g. at pp = 12 GeV/c the ratio is∼2.2. To a large extent reactions with baryonic finalstates proceed via excited states giving access to thedecay modes of the populated resonances and to theangular distributions of the decay particles. A par-ticular benefit of using antiprotons in the study of(multi-)strange and charmed baryons is that in ppcollisions no production of extra kaons or D mesonsis required for strangeness or charm conservation,respectively. This reduces the energy threshold ase.g. compared to pp collisions and thus the num-ber of background channels. In addition, the re-quirement that the patterns found in baryon andantibaryon channels have to be identical reducesthe systematic experimental errors. Strange, multi-strange and charmed baryons are characterised bytheir or their daughters’ displaced decay vertices,which can be identified thanks to the good trackingcapability of the PANDA tracking detectors (MVD,central tracker, tracking detectors of the forwardspectrometer).

Production cross sections for Ξ resonances are ex-pected to be of the same order as for ground stateΞ production, i.e. for the reaction pp → ΞΞ forwhich a cross section up to 2µb has been mea-sured [144, 145]. The Ξ∗(Ξ

∗) yields will thus be

sufficiently high to allow good statistics studiesanalysing the various Ξ∗ decay modes such as Ξπ,Ξππ, ΛK, ΣK, Ξη, and others. Given the ex-tremely scarce experimental information on the Ξexcitation spectrum available, the discovery poten-tial of PANDA seems to be particularly large for Ξresonances. One should also note that Ξ resonancesare in general much narrower than nucleon or ∆resonances which helps to separate contributions ofdifferent states.

The very poorly known Ω spectrum can also bestudied, however the creation of an additional sspair has to be paid by a reduction of the cross sec-tion. No experimental data exist for the reactionpp → ΩΩ, its predicted maximum cross section is

∼2 nb [32], to our knowledge the only existing theo-retical estimate. Some confidence in this predictionmay be drawn from the consistency of calculatedcross sections with experimental data for other bi-nary reactions in pp collisions [32]. At a luminosityof 1032 cm−2s−1 a cross section of 2 nb would stillcorrespond to ∼700 produced ΩΩ pairs per hourwhich allows to identify excited Ω states and theirmost important decay modes.

For all non-charmed baryons the HESR energyrange is sufficient to access excitation energies upto the continuum regime, and thus to populate thecomplete discrete part of the spectrum. Dependingon the hyperon resonances and their decay modes tobe studied, the p beam momentum should be cho-sen such that the excess energy above the thresholdfor the respective final state is as low as possible inorder to limit the number of partial waves and tofacilitate the separation of different resonances.

Also for pp → ΛcΛc, ΣcΣc, ΛcΣc/ΛcΣc reactionsno experimental data exist. For the Λ−c Λ+

c finalstate [32] predicts a cross section up to 0.2µb whichis much larger than for ΩΩ. However, the decaylength of the Λ+

c hyperon is only cτ(Λ+c ) = 60µm,

which is too short to be detected by its displacedvertex. It has only few percent branching for chan-nels with a Λ hyperon in the final state which couldbe easily identified by its delayed decay. Thus,in order to estimate the capability of PANDA toidentify final states with charmed baryons, detailedsimulations of these channels are being planned.One should also note that for charmed baryon reso-nances the range of excitation energies accessible isrestricted due to the kinematic limit at the HESR of√s = 5.5 GeV, which allows to populate excitation

energies up to 0.93 GeV and 0.76 GeV above the Λcand Σc ground states, respectively.

Recent theoretical studies using a chiral coupledchannel approach [146, 147] predict the existence ofnarrow crypto-exotic baryon resonances with hid-den charm. In particular, these calculations find anarrow resonance at 3.52 GeV/c2 being a coupled-channel bound state of ηcΛ and DΣc which shoulddominantly decay to η′N . Whereas the exotic orcrypto-exotic baryon resonances for systems withopen charm ranging from C = −1 to C = +3also found as dynamically generated states in thesame approach [146, 147] are not accessible withinthe HESR energy range, we see a good perspec-tive to confirm or to rule out the existence of nar-row crypto-exotic baryons with hidden charm in themass range between 3 GeV/c2 and 4 GeV/c2 in thePANDA experiment.


Benchmark Channels

In the context of baryon spectroscopy, the reaction

pp→ Ξ+

Ξ−π0

withΞ− → Λπ−,Λ→ pπ−

(and c.c.) has been chosen as benchmark chan-nel for the simulation studies. As a first step, theevents have been generated isotropically over thephase space. The goal of these simulation studiesis to reconstruct Ξ−π0 pairs (and c.c.) as one ofthe daughter states in the decay of Ξ resonances,to deduce the acceptance function of the PANDAdetector - and thus the capability to determine thepopulation of the three-body final state across thefull Dalitz plot, and to explore the suppression ofthe presumed dominant background channels. Thecapability of identifying specific Ξ resonances withtheir quantum numbers in the presence of a con-tinuum distribution and other Ξ resonances in thesame final state involves a partial wave analysis,which is beyond the scope of the studies for thisreport.

Figure 4.42: Schematic illustration of the investi-

gated pp→ Ξ+

Ξ−π0 reaction with the considered decaybranches. The reaction is characterised by four delayeddecay vertices.

In order to take into account possible interactionsof the charged Ξ baryons with the detector mate-rial and their bending in the magnetic field withintheir propagation before decay (cτ = 4.9 cm), theirdecays are not generated on event generator levelbut within the GEANT4 detector simulation.

The selected antiproton beam momentum is pp =6.57 GeV/c corresponding to a maximum Ξπ invari-ant mass of 2.45 GeV/c2. For the pp→ ΞΞ reactionat this incident momentum Ref. [32] predicts a crosssection of about 0.3µb. In the following this valueis also used as estimate for the pp→ ΞΞπ0 reaction,taking into account that the predicted ΞΞ cross sec-tion is below the measured value.

Background Reactions

The following background channels are considered:

(a) pp→ ΛΛπ+π−π0 → ppπ+π−π+π−π0

(b) pp → Σ(1385)+Σ(1385)−π0 → ΛΛπ+π−π0 →ppπ+π−π+π−π0

(c) pp→ ppπ+π−π+π−π0

(d) DPM generic background

The background channel (a) is expected to be themain background source since it has the identi-cal final state as the signal, and since it also hasthe same intermediate state characterised by a ΛΛpair. This background will be suppressed by re-quiring the Ξ and Ξ delayed decays according toa decay length cτ = 4.9 cm visible in a kink inthe charged particle track. In addition good Λπ−

(Λπ+) invariant mass resolution helps to distinguishthe Ξ− (Ξ

+) mass peak from the Λπ− (Λπ+) con-

tinuum. The cross section for this channel is notknown. For the reactions pp→ ΛΛπ+π− and pp→ΛΛ2π+2π− Ref. [148] lists a measured cross sectionof (59±12)µb and (8±4)µb at pp = 6.93 GeV/c, re-spectively. In the following a cross section of 70µbfor process (a) is assumed.

In reality, intermediate and final states of chan-nel (a) are expected to have some contributionfrom Σ(1385)− (and c.c.) production accordingto channel (b). Even if this fraction is small, itmight be of concern due to the relatively closemasses of Σ(1385)− and Ξ− to be reconstructedfrom Λπ− pairs (and c.c.). The cross section forthis channel is also not known. For the reactionpp→ Σ(1385)−Σ(1385)+ Ref. [148] lists a measuredcross section of (14 ± 3)µb at pp = 5.7 GeV/c. Inthe following a cross section of 20µb for process (b)is assumed.

Channel (c) is expected to have the largest cross sec-tion of the specific background reactions consideredhere, however it has no delayed decays and shouldbe suppressed very efficiently by requiring delayedΛ and Λ vertices. For this channel Ref. [148] lists a


cross section of (280 ± 30)µb at pp = 6.94 GeV/c.In the following a cross section of 300µb for process(c) is assumed.

Analysis Strategy

The following selection criteria are chosen in orderto discriminate signal and background events:

1. p and π− (p and π+) are fitted to a commonvertex with χ probability P > 0.001. Pro-ton candidates are selected from charged trackswith VeryLoose PID criteria, pion candidatesfrom all charged tracks.

2. The mass of Λ, Λ candidates has to fulfil thecondition 1.105 GeV/c2 < mΛ < 1.125 GeV/c2.

3. Λ and π− (Λ and π+) are fitted to a commonvertex with χ probability P > 0.001.

4. The mass of Ξ−, Ξ+

candidates has to fulfil thecondition 1.31 GeV/c2 < mΞ < 1.33 GeV/c2.

5. 2γ candidates with E > 25 MeV each are com-bined to a π0 candidate within a mass window110 MeV/c2 < mπ0 < 160 MeV/c2.

6. Ξ− and Ξ+

are fitted to a common vertex withthe assumption that the π0 is emitted from thesame vertex. In addition constraints on thetotal 4-momentum are set. Combinations withχ probability P < 0.001 are rejected.

7. Only events containing exactly one combina-tion of particles fulfilling all criteria listedabove are further considered.

8. The Ξ−, Ξ+

decay vertices have to fulfil thecondition that the sum of their distances fromthe interaction point is larger than 2 cm.

9. The complete event is refitted with mass con-straints on the Ξ−, Ξ

+, Λ, Λ, and π0.

Simulation Results

For the signal and all background channels theppπ+π−π+π−π0 final state has been investigated.The size of the analysed signal and background sam-ples is given in Table 4.41.

Table 4.42 shows the signal efficiency and the num-ber of remaining background events depending ofthe cut condition on the sum of the distances of the

Channel Number of eventspp→ Ξ+Ξ−π0 8.13 · 105

pp→ ΛΛπ+π−π0 8 · 105

pp→ Σ(1385)−Σ(1385)+π0 8 · 105

pp→ ppπ+π−π+π−π0 3 · 105

DPM generic 2 · 107

Table 4.41: Number of events simulated for signaland background channels. For the signal and the spe-cific background channels the number refers to theppπ+π−π+π−π0.

Ξ and Ξ decay vertices from the interaction pointD

(IP )

ΞΞ= dist(Ξ− IP) + dist(Ξ− IP). The selection

D(IP )

ΞΞ> 2 cm is used for further analysis. With

this selection the signal reconstruction efficiency isabout 16%. Taking into account a luminosity ofL = 9000/nb per day, a cross section σ = 0.3µb,and the branching fraction of the final state, thiscorresponds to 1.7 · 105 reconstructed signal eventsper day.

Based on the selection criteria, 4 remaining eventsare found in the background channel pp →ΛΛπ+π−π0, whereas no events survive the selectioncriteria in the other specific background channelsand in the DPM generic background sample. Basedon the cross sections assumed for signal and back-ground channels as given above, the resulting valuesfor signal-to-background ratio are much larger thanone in all cases:

(a) S/B = 135 for pp→ ΛΛπ+π−π0

(b) S/B > 1896 for pp→ Σ(1385)−Σ(1385)+π0

(c) S/B > 47 for pp→ ppπ+π−π+π−π0

(d) S/B > 19 for DPM generic.

Fig. 4.43 shows the invariant mass resolution in thereconstruction of a Ξ−π0 pair which is relevant forthe determination of width and pole position of Ξresonances as a function of the Ξ−π0 invariant mass.Fig. 4.44, showing the ratio of the number of re-constructed events relative to that of the generatedMonte Carlo events in a Dalitz plot of the Ξ

+Ξ−π0

final state, demonstrates that the reconstruction ef-ficiency varies smoothly across the 3-body phasespace at average values of ∼ 15 %.


Channel ε(D(IP )

ΞΞ> 2 cm ε(D(IP )

ΞΞ> 4 cm ε(D(IP )

ΞΞ> 6 cm

pp→ ΞΞπ0 15.8 % 15.0 % 13.9 %

NB(D(IP )

ΞΞ> 2 cm NB(D(IP )

ΞΞ> 4 cm NB(D(IP )

ΞΞ> 6 cm

pp→ ΛΛπ+π−π0 4 2 1pp→ Σ(1385)−Σ(1385)+π0 0 0 0pp→ ppπ+π−π+π−π0 0 0 0DPM generic 0 0 0

Table 4.42: Signal efficiency and remaining number of background events depending on the cut condition on theΞ and Ξ decay vertices (explanation see text).

Figure 4.43: Resolution achieved in the invariant massof reconstructed Ξ−π0 pairs as a function of the Ξπ0

invariant mass.

Figure 4.44: Dalitz plot showing the reconstruction

efficiency for the pp→ Ξ+

Ξ−π0 reaction.


4.3 Non-perturbative QCDDynamics

An effective description of reactions in hadronphysics relies on the identification of the relevantdegrees of freedom. At highest energies quark andgluon degrees of freedom seem to describe the ob-served reactions very accurately. The energy regimefor pp collisions at HESR is well suited to study theonset of hadron degrees of freedom. In this regimeboth ansatze are viable. Thus they can be exper-imentally tested separately and compared to eachother.

The simplest final state in proton antiproton col-lisions is two mesons. Depending on the momen-tum transfer (Mandelstam variable t), the scatter-ing amplitude is purely hadronic (small t) or isbetter described in terms of the quark content ofthe hadrons. Indeed the success of the dimensionalquark counting rules for large angle exclusive scat-tering suggests that the amplitude factorises in ashort distance quark subprocess and light cone wavefunctions of the lowest Fock state of the participat-ing hadrons. Whereas experimental data exist forproton proton elastic scattering, not much is knownon all the channels which are open in antiprotonproton scattering. Moreover the coexistence of twomechanisms as indicated by the proton proton datais an unsettled question in the other cases. It isvery likely that the transition from one mechanismto another occurs in the Panda energy range.

In the quark picture hyperon pair production eitherinvolves the creation of a quark-antiquark pair orthe knock out of such pairs out of the nucleon sea.Hence, the creation mechanism of quark-antiquarkpairs and their arrangement to hadrons can be stud-ied by measuring the reactions of the type pp →Y Y , where Y denotes a hyperon. By comparingseveral reactions involving different quark flavoursthe OZI rule [149, 150, 151], and its possible vio-lation, can be tested for different levels of discon-nected quark-line diagrams separately.

The parity violating weak decay of most groundstate hyperons introduces an asymmetry in the dis-tribution of the decay particles. This is quantifiedby the decay asymmetry parameter and gives ac-cess to spin degrees of freedom for these processes,both to the antihyperon/hyperon polarisation andspin correlations. One open question is how theseobservables relate to the underlying degrees of free-dom.

All strange hyperons, as well as single charmed hy-perons are energetically accessible in pp collisions at

HESR. A systematic investigation of these reactionswill bring new information on single and multiplestrangeness production and its dependence on spinobservables. This is particularly true above 2 GeV/cwhere practically nothing is known about the differ-ential distributions and spin observables. The largeamount of observables accessible and high statisticsPANDA data will allow for a partial wave analysis.Thus it will be possible to pin down relevant quan-tum numbers, coupling constants and possibly findnew resonances.

4.3.1 Previous Experiments

The pp → ΛΛ process can be considered as aprototype reaction in the study of production ofstrangeness. This reaction exhibits strong polari-sation phenomena and spin correlation parameterscan be extracted when both the Λ and Λ are recon-structed. The PS185 experiment at LEAR has pro-vided high quality data on the pp → ΛΛ reactionfrom threshold (1.436 GeV/c) up to 2 GeV/c [152]which was the maximum momentum of LEAR (seeFig. 4.45). The data above 2 GeV/c are dominatedby low statistics bubble chamber experiments andno data exist above 7 GeV/c. Little, if anything, isknown about the pp→ Y Y reaction in the multiplestrangeness sector. Only total cross sections basedon a few events have been measured in the doublestrangeness channel, i.e. the production of Ξ hyper-ons [148]. Nothing at all is known about this reac-tion for charmed hyperons. All the available dataon the total cross section for the pp→ Y Y reactionis summarised in Fig. 4.45. The high statistics datasamples from PS185 comprises 40k completely re-constructed pp → ΛΛ events [153]. Correspondingbubble chamber experiments have, at most, a fewhundred complete events [148]. There is one counterexperiment at 6 GeV/c with comparable statistics toPS185 [154], but normally only one hyperon couldbe reconstructed for the events which meant thatno spin correlation could be measured.

One example which shows the strength of hyperonpair production in pp annihilations is the following:By measuring spin correlations in the PS185 experi-ment, it has been shown that the ΛΛ pairs are prac-tically always produced in a triplet state [152]. Itis natural to associate this with the spin degrees offreedom in the creation process of the ss pair sincethe spin of the Λ hyperon is primarily carried by itsstrange quark. In other words, the ss pair is pre-dominantly created in a triplet state. The LEARdata were taken near threshold; and one should ver-ify that this feature persists as one goes up in mo-

118 PANDA - Strong interaction studies with antiprotonsσ

[μ

b]

pp → ΛΛ

→ ΛΣ + c. c.

→ Σ− Σ

→ Σ Σ

→ Σ Σ−

→ Ξ Ξ

→ Ξ Ξ−

Λc ΛcΞΞ ΩΩΛΣ ΣΣΛΛ

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2 4 6 8 10 12 14

Momentum [GeV/c] Momentum [GeV/c]

1000

100

10

1

0.1

0.01

0

0

0 0

0 0

+

+

+

Figure 4.45: Total cross sections for the pp → Y Y reaction in the momentum range of the HESR. The figureto the left is an expanded view of the threshold region, which reveals channels of single strangeness production.The figure to the right shows the experimental situation for momenta above 2 GeV/c [152, 148]. The absence of

error bars for some Ξ+

Ξ− points are because they are missing in reference [144]. The upper limits in red alsorefer to this channel. The arrows pointing to the momentum axis indicate the threshold momenta for the differenthyperon families.

mentum transfer into the more perturbative region.Both meson-exchange models and models based onthe constituent quark model have been applied tothe near threshold data from LEAR and both give arelatively good description of the main features ofthe data [155, 156]. The triplet state is producedby assuming that the ss pair is created with thequantum number of the vacuum, 3P0, or with thegluon quantum number, 3S1, for the quark basedmodels. Alternatively, it has been suggested thatss pairs may be extracted from the nucleon or anti-nucleon sea instead of being created in the reactionitself [157]. In this scenario the triplet state wouldreflect the fact that the ss pairs are polarised in thenucleon sea. In meson-exchange models, the tripletstate is interpreted as being due to a strong ten-sor force generated by the exchange of K and K∗

mesons.

4.3.2 Experimental Aims

As seen from Fig. 4.45 any measurement of hyperonpair production in the PANDA energy regime willsignificantly improve the data set. Even in ΛΛ pro-duction, where a large data set exists, data pointsat momenta above 2 GeV/c and a cross check at lowmomenta would help understanding the productionmechanism. For all other hyperon pairs PANDAwill provide the first conclusive insights on the be-haviour of the total cross section and first differ-ential cross sections. The very first measurementscan be provided for the pair production of charmed

hyperons.

Spin observables for the ΞΞ reaction can be ex-tracted similarly to the ΛΛ case. This will allowfor detailed comparisons between the ss and sssscreation processes. A comparison between the ΛΛchannel, which filters isospin I = 0, to the ΛΣ0

channel (including its charge conjugate channel),which forces I = 1, gives opportunities to study theisospin dependence of strangeness production. Inthe naive quark model the spin of the Σ0 is oppo-site to that of its constituent strange quark . Thisshould lead to differences in the spin correlationsif they are related to the spin state of the createdss-pair. Studies on the production of charmed hy-perons will allow for detailed comparisons betweenthe cc and the ss creation processes. This may helpto disentangle the perturbative contributions fromthe non-perturbative ones, as the charm productionwill be mainly probing the hard processes while thestrangeness production will be influenced by non-perturbative effects.

4.3.3 Reconstruction of the pp→ Y YReaction

Two-body kinematics together with the relativelylong lifetime of strange hyperons makes the iden-tification and reconstruction of Y Y events ratherstraightforward. The identification of these reac-tion channels involve practically always the recon-struction of a ΛΛ pair as can be seen from the main


decay channels listed in Table 4.43.

The PANDA detector allows for the reconstructionof both neutral and charged hyperons, due to itscapabilities to track charged particles, to detectphotons and discriminate between almost all sta-ble particles. For neutral hyperons with chargeddecay modes, e.g. the Λ→ pπ− decay channel, thedecay vertex outside the interaction region is recon-structed. Neutral strange hyperons, apart from theΛ, are accompanied by photons, which will be de-tected in the electromagnetic calorimeter. The re-construction of charged hyperons involve the iden-tification of tracks from the interaction region thatexhibit a “kink” that signals the hyperon decay.

A good understanding of the response and recon-struction of tracks that originate well outside ofthe interaction region is important for these stud-ies. This is further emphasised when extracting spinobservables. The parity violating weak decay of hy-perons gives a decay distribution in its own restframe according to

I (θB) =1

4π(1 + αY P

Y cos θB), (4.42)

where θB is the baryon emission angle with respectto the spin direction of the decaying hyperon, αYis the decay asymmetry parameter (listed in Ta-ble 4.43) and PY is the hyperon polarisation. Thecoordinate system used in the analysis is given inFig. 4.46. The axes are chosen such that a maxi-mum use of parity conservation can be made.

Spin observables can be extracted for all strangehyperons, with the exception of Σ− and Ω− wherethe decay asymmetry parameter is too small. TheΣ0 hyperon decays via the parity conserving elec-tromagnetic interaction but spin observables can beextracted from the subsequent Λ→ pπ− decay via

I (θp) =1

4π

(1− 1

3αΛP

Σ0cos θp

). (4.43)

The measured cross sections for production of sin-gle and doubly strange hyperons range from a µb toa hundred µb. These cross sections are comfortablyhigh with hundred thousands of events producedper hour already at nominal luminosity. Nothingis experimentally known of the cross section fortriple strangeness production, i. e. the reactionpp→ Ω

+Ω−. The only existing theoretical estimate

predicts maximum cross section of ∼ 2 nb [32] whichwould correspond to ∼ 700 produced Ω

+Ω− pairs

per hour at a luminosity of 1032cm−2s−1. This issufficient for a measurement of the total cross sec-tion and the differential angular distribution. No

spin observables will be directly accessible for thisreaction due to the very small decay asymmetry pa-rameter.

There is only one estimate for the cross section ofthe pp→ Λ

−c Λ+

c reaction predicting it to be as highas 0.2µb [32]. The asymmetry parameter in theΛ+c → Λπ+ decay is comfortably large to access

spin observables. The challenges in studying thisreaction via this decay channel is that its branch-ing ratio is only 1%. In fact, all decay channels forthe Λ+

c have branching ratios of the order of 1 %or less [11]. The decay length cτ of the Λ+

c cannotbe used to identify the reaction as it is only 60µm.However, the Λ+

c and its antiparticle decay into Λand Λ, which have a long decay length. The reac-tion may be identified against a large backgroundas it is possible to additionally pin down the inter-action vertex by the reconstruction of the chargedpions from the Λ+

c decay.

It is worthwhile to note that the decay pattern givenfor all charmed hyperons listed in Table 4.43 will al-ways lead to the appearance of a Λ particle. It istherefore important to acquire a good understand-ing of the reconstruction of Λ particles in PANDA.


Among the variety of channels of hyperon pair pro-duction accessible at PANDA, the channels pp →ΛΛ and Ξ

+Ξ− haven been chosen to prove our prin-

ciple ability to reconstruct the angular and polar-isation distributions. These channels exhibit thefollowing features which makes them well suited fora case study.

• pp→ ΛΛ. Though well studied close tothreshold this basic channel provides an essen-tial tool to understand the reconstruction ca-pabilities for all hyperon pair production re-actions at PANDA. This is mainly due to thefact that most hyperons decay such that a Λ(Λ)particle is produced in an intermediate state(see Table 4.43). This is also the case for theexcited baryons (see sec. 4.2.5). Hence, a de-tailed understanding of the reconstruction andidentification of Λ or Λ particles in PANDA de-tector is very important for many aspects ofthe PANDA physics programme. The recon-struction of the Λ decay products (mostly fromΛ→ pπ+ and Λ→ pπ−) differs from ordinarycharged particle reconstruction in PANDA asthe charged particles do not stem from the in-teraction point. This displaced vertex posesa challenge to reconstruction algorithms and


Table 4.43: Properties of strange and charmed ground state hyperons [11] that are energetically accessible atPANDA. The hyperon, its valence quark composition, mass, decay length cτ , main decay mode, branching ratioB and the decay asymmetry parameter αY are listed.

Hyperon Quarks Mass [MeV/c2 ] cτ [cm] Main decay B [%] αYΛ uds 1116 8.0 pπ− 64 +0.64

Σ+ uus 1189 2.4 pπ0 52 -0.98Σ0 uds 1193 2.2 · 10−9 Λγ 100 -Σ− dds 1197 2.4 nπ− 100 -0.07Ξ0 uss 1315 8.7 Λπ0 99 -0.41Ξ− dss 1321 4.9 Λπ− 100 -0.46Ω− sss 1672 2.5 ΛK− 68 -0.03

Λ+c udc 2286 6.0 · 10−3 Λπ+ 1 -0.91(15)

Σ++c uuc 2454 Λ+

c π+ 100

Σ+c udc 2453 Λ+

c π0 100

Σ0c ddc 2454 Λ+

c π− 100

Ξ+c usc 2468 1.2 · 10−2 Ξ−π+π+ seen

Ξ0c dsc 2471 2.9 · 10−3 Ξ−π+ seen -0.6(4)

Ω0c ssc 2697 1.9 · 10−3 Ω−π+ seen

θ

mY

nY

pp

m j =n× l j

n=

rki ×rk fr

ki ×rk f

l j =k j

nY

lY

lY

mY

Y

YθB

Figure 4.46: Coordinate system for the pp → Y Y reaction. θ is the centre-of-mass (CM) scattering angle, ~kiand ~kf are the initial p beam and the final antihyperon momentum vectors in the CM system, respectively. These

two vectors define the scattering plane and also the pseudovector ~n = ~ki × ~kf which is normal to the scatteringplane. These vectors are then used to define a coordinate system for the antihyperon/hyperon rest frame with

one axis along ~n and the two other axes in the scattering plane. The direction of the jth particle momentum bkj(j = Y or Y ) in the CM system is taken as the blj axis. The handiness of the coordinate system is taken to beright handed.

special attention has to be drawn to back-ground reduction. The extension and compari-son of the well measured near-threshold data tohigher momenta makes the study of this chan-nel also interesting in its own right.

• pp→ Ξ+

Ξ−. This channel probes the track-ing capability near the interaction region toa much larger extent than the Λ pair pro-duction. This will also be a reaction wherePANDA will provide first differential distribu-tions. For the simulation we therefore assumedan isotropic distribution in the CM system toinvestigate how well this can be reconstructed

with PANDA.

Study of the pp→ ΛΛ Reaction.Monte Carlo data for this reaction have been gen-erated and analysed at three incoming momenta,1.64 GeV/c, 4 GeV/c and 15 GeV/c. Approximately106 events were generated for each of the three beammomenta. The lowest momentum corresponds tothe near threshold region where high quality dataexist from the PS185 experiment at LEAR. The datafor this momentum were generated according to theexperimental angular distribution [153]. An empiri-cal function composed of two exponential functionsand four parameters in total was used to generate


the corresponding angular distributions at the twohigher momenta as suggested in Ref. [154],

dσ/dt′ = aebt′+ cedt

′. (4.44)

Here, t′ = − 12 t′max(1−cos θCM ) is the reduced four-

momentum transfer squared, where mass effects areremoved from the full four momentum transfer

t = m2p +m2

Λ −s

2+

12t′max cos θCM (4.45)

with t′max =√

(s− 4m2p)(s− 4m2

Λ).

The polarisation was assumed to follow a sin 2θCM

dependence for all momenta. The reconstruction ofthe events was done consecutively in the followingsteps:

1. Identified pairs of antiprotons(protons) andπ+(π−) were fitted to a common vertex underthe hypothesis of stemming from a Λ(Λ). Theχ2 of the fit was then required to be > 0.001.

2. The invariant pπ+ and pπ− masses of the re-constructed Λ and Λ, respectively, are requiredto be within about 4σ of the Λ mass, i.e.1.110 GeV/c2 ≤ M ≤ 1.120 GeV/c2. (See alsoFig. 4.47.)

3. The remaining events are fitted to the pp →ΛΛ hypothesis in a tree-fit. Again, the χ2 ofthe fit was then required to be > 0.001.

4. Finally, cuts on the Λ and Λ vertices are ap-plied. An effective cut on the displaced verticeswas found to be the requirement that the sumof both path lengths is above 2 cm.

These criteria result in global reconstruction effi-ciencies of 0.11, 0.24 and 0.14 for the pp → ΛΛreaction in the charged decay mode at 1.64 GeV/c,4 GeV/c and 15 GeV/c, respectively. The reasonfor the lower efficiency at 1.64 GeV is that thereare many pions produced with momenta below50 MeV/c at this momentum. These cannot bereconstructed as will be shown in the discussionon polarisation below. The lower efficiency at15 GeV/c is primarily due to a higher loss of tracksin the beam pipe. This is a result of the veryforward peaked angular distribution. The recon-structed Λ mass at 1.64 GeV/c is shown in Fig. 4.47.The Λ mass is reconstructed obtaining a sigma of1.2 MeV/c2 at this momentum. Similar mass reso-lutions are obtained at the higher momenta.

The spatial distributions of decay vertices for gen-erated Λ events are shown in Fig. 4.48. The lower

m [GeV/c2]1.105 1.11 1.115 1.12 1.1250

1000

2000

3000

4000

5000

6000

# o

f ev

ents

Λ

Figure 4.47: Reconstructed pπ+ invariant mass for Λcandidates from the pp → ΛΛ reaction at 1.64 GeV/c(histogram) and a Gaussian fit to the distribution(smooth curve). The distributions at 4 and 15 GeV/cshow a similar behaviour.

figure shows the distribution at 1.64 GeV/c andthe upper figure the corresponding distribution at15 GeV/c. This illustrates the origin of the chargedtracks from the ΛΛ reaction. No strong dependen-cies on the vertex position in the reconstruction ef-ficiencies are found (apart from obvious geometricalconstraints). The decay vertices are reconstructedwith a sigma ranging from 0.6 mm at 1.64 GeV/cto 2.8 mm at 15 GeV/c. The z component of thevertex is dominating the uncertainty and this nat-urally increases with higher beam momenta as theparticles are emitted in smaller angles.

Centre-of-mass angular distributions for the out-going Λ at 1.64 GeV/c and 4 GeV/c are shown inFig. 4.49. The Monte Carlo generated events arethe black histograms and the angular dependenciesare taken from references [153] and [154], respec-tively. The red histograms show the correspondingreconstructed angular distributions (multiplied bya factor of 10 to account roughly for the overall effi-ciency). It is seen that the experimental acceptancecovers the whole angular region for this reactionat 1.64 GeV/c. The lack of events at higher anglesat 4 GeV/c is due to the exponential fall off of thegenerated angular distribution (see Eq. 4.44) andthis is further emphasised at 15 GeV/c. The loss inthe very forward direction is due to losses of eventswith tracks in the beam pipe region. It has beenverified that the acceptance is covering the full an-gular region at the two higher momenta as well, byanalysing Monte Carlo event samples with isotropicCM angular distributions. This means that, afteracceptance correction, the full centre-of-mass angu-lar distributions of the outgoing hyperons can be


Figure 4.48: Λ decay vertex coordinates at beam mo-menta of 1.64 GeV/c (upper panel) and 15 GeV/c (lowerpanel) for phase space distributed events.

deduced for this reaction over the full momentumrange of HESR.

The analysis of spin observables requires the knowl-edge of the angular distribution of the hyperondecay particles, the proton and pion, in the restframe of the hyperon. This angular distribution isisotropic for the unpolarised case. The coordinatesystem that is used for this reconstruction is givenin Fig. 4.46. It should be noted that the axes ofthis coordinate system vary from event to event. Inthis coordinate system the projections onto the land m axes are isotropic independently of the hy-peron polarisation. The distribution along the naxis will exhibit a slope equal to αΛP

Λ. Here αΛ isthe decay asymmetry parameter and PΛ is the po-larisation (see Eq. 4.42). CP conservation requiresthat PΛ = PΛ. Fig. 4.51 shows the projections ofthe decay antiproton emission vector along the l, nand m axes for reconstructed non-polarised eventsat 1.64 GeV/c. These distributions are clearly non-isotropic for all projections which shows that thePANDA acceptance is inhomogeneous for these reac-tions. Such distributions will therefore be used foracceptance corrections in the extraction of the po-larisation. The non-isotropies are related to an inef-ficiency to reconstruct low-energy pions in PANDA.

That low-energy pions cannot be reconstructed ef-ficiently can be seen in Fig. 4.50 which shows theabsolute value of the π+ momentum in the labora-tory system from the Λ decay at 1.64 GeV/c . The

5000

10000

15000

20000

25000

30000

35000

40000

45000

CMΘcos-1 -0.5 0 0.5 11

10

210

310

410

510

pp→ ΛΛ, 1.64 GeV/c

MC dataReconstructed data x10

pp→ ΛΛ, 4 GeV/c

MC dataReconstructed data x10

# of

eve

nts

# o

f ev

ents

Figure 4.49: Centre-of-mass angular distributions forthe Λ hyperon from the pp→ ΛΛ reaction at 1.64 GeV/c(upper figure) and 4 GeV/c (lower figure). The MonteCarlo generated angular distributions are shown inblack; the reconstructed angular distributions (multi-plied by a factor of ten) are shown in red.

black histogram shows the Monte Carlo generatedevents and the red histogram shows the momentafrom the reconstructed events multiplied by a fac-tor of ten. It is clear from this picture that pionswith momenta lower than about 50 MeV/c are notreconstructed. This is also the origin of the non-isotropies in Fig. 4.51. The same pattern is seen athigher momenta, but the magnitude of the effect de-creases with increasing beam momentum since theamount of low energy pions decreases with increas-ing beam momentum.

The polarisation distributions are extracted by ap-plying the method of moments [158] with accep-tance correction functions from non-polarised datain bins of cos θCM. The polarisation is finally ex-tracted using both hyperon polarisations, i.e. (PΛ+PΛ)/2. The extracted polarisations at 1.64 GeV/c


momentum [GeV/c]+π0 0.1 0.2 0.3 0.40

5000

10000

15000

20000

25000

30000

35000

40000 #

of

even

ts

Figure 4.50: Absolute value of the pion momentum inthe laboratory system from the Λ decay 1.64 GeV/c. Theblack histogram is Monte Carlo data and the red his-togram shows the reconstructed events. The histogramfor the reconstructed has been multiplied by a factor often.

and 4 GeV/c are shown in Fig. 4.52 together withthe superimposed sin 2θCM function which is usedto generate the polarisation data. The large errorbars at the higher angles at 4 GeV/c is due to thefunctional form for the angular distribution whichstrongly suppresses events at large CM emission an-gles. This is further emphasised at 15 GeV/c wherereasonable statistics is only acquired at the upper-most angular bins. The background for this channelis treated in section 4.3.3.2.

Study of the pp→ Ξ+

Ξ− Reaction.Approximately 2·106 Monte Carlo events have beengenerated and analysed at 4 GeV/c for this reaction.This momentum was chosen because it is also usedfor analysing events for the ΛΛ channel. No ex-perimental information on angular distributions areavailable for the pp → Ξ

+Ξ− channel. The pro-

duction of two ss quark-pairs in this reaction willmost likely lead to a less steep angular distributionthan in the ΛΛ case. An isotropic CM angular dis-tribution was therefore chosen. The reconstructedangular distribution will then directly give the an-gular acceptance for the process. A sin 2θCM func-tion was used for the polarisation. The reactionwas studied in the Ξ

+ → Λπ+ → pπ+π+(Ξ− →Λπ− → pπ−π−) decay channel which is illustratedin Fig. 4.53.

The reconstruction was made in the following steps:

500

1000

1500

2000

2500

3000

pΘcos-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

500

1000

1500

2000

2500

3000

3500

# of

eve

nts

#

of e

vent

s

# o

f eve

nts

l

m

n

Figure 4.51: Angular distributions of p from theΛ → pπ+ decay reconstructed in the PANDA accep-tance in the hyperon rest frame according to the coor-dinate system defined in Fig. 4.46.

1. Identified pairs of antiprotons(protons) andπ+(π−) were fitted to a common vertex undera Λ(Λ) hypothesis. The χ2 of the fit was thenrequired to be > 0.001.

2. The invariant pπ+ masses of the reconstructedΛ and Λ are required to be close to the Λ mass,1.100 GeV/c2 ≤ M ≤ 1.300 GeV/c2.

124 PANDA - Strong interaction studies with antiprotonspolarisation

-1

-0.5

0

0.5

1

1.5

CMΘcos-1 -0.5 0 0.5 1

polarisation

-1.5

-1

-0.5

0

0.5

1

1.64 GeV/c

4 GeV/c

Figure 4.52: Reconstructed polarisation from pp →ΛΛ reaction at 1.64 GeV/c (upper figure) and 4 GeV/c(lower figure). The solid line is the sin 2θCM functionthat is used to generate the polarisation.

Figure 4.53: Schematic illustration of the topology

for the investigated pp → Ξ+

Ξ− reaction. The charac-teristic pattern of this reaction is four separated decayvertices

3. Pairs of Λ(Λ) and π+(π−) are fitted to a com-

mon vertex under a Ξ+

(Ξ−) hypothesis. Theχ2 of the fit was then required to be > 0.001.

4. The invariant mass of the reconstructed Ξ+

and Ξ− are required to be close to the Ξ− mass,i.e. 1.30 GeV/c2 ≤ M ≤ 1.35 GeV/c2.

5. The remaining events are fitted to the pp →Ξ

+Ξ− hypothesis in a tree-fit. The χ2 of the

fit was then required to be > 0.001.

These criteria result in an overall reconstruction ef-ficiency of about 0.19. The reconstructed invariantΞ

+mass is shown in Fig. 4.54. The Ξ

+mass is re-

constructed with a sigma of 2.1 MeV/c2. The sigmaof reconstructed Λ mass is 1.7 MeV/c2. The Ξ andΛ decay vertices are reconstructed with a sigma of5.2 mm and 4.7 mm, respectively. The dominatingcontribution is the resolution in the z direction.

]2 [GeV/cΞm1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335 1.34

# of

eve

nts

0

500

1000

1500

2000

2500

3000

Figure 4.54: Reconstructed Ξ+

mass for the pp →Ξ

+Ξ reaction at 4 GeV/c.

The reconstructed Ξ+

centre-of-mass angular distri-bution is shown in Fig. 4.55. The acceptance doesnot vary more than a factor of two over the fullangular range which means that the distributioncan be extracted with small statistical uncertain-ties in all angular bins. The dip in the forward andbackward directions are primarily related to eventswhere one track is lost in the beam pipe region.One must correct for the bending of the chargedΞ tracks in the transverse direction to get the cor-rect production momentum vector. This is done byapplying the formula [11]

R =p⊥B0.3

, (4.46)

where R is the radius of curvature in meters, p⊥ themomentum component in the transverse directionin GeV/c and B the magnetic field in Tesla. Thiscorrection improves the resolution in the x and y


components of the production momentum vector ofthe Ξ particles from 5.3 MeV/c to 1.9 MeV/c.

ΞΘcos-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

reco

nstr

ucti

on e

ffic

ienc

y

0

0.02

0.04

0.06

0.08

0.10.12

0.14

0.16

0.18

0.2

0.22

Figure 4.55: Centre-of-mass angular distribution for

the pp → Ξ+

Ξ− reaction at 4 GeV/c from isotropicallygenerated events reconstructed in the PANDA accep-tance.

The analysis of polarisation is done in the same wayas for the ΛΛ case described in the previous section.Here one analyses the distribution of the Ξ decayparticles, Λ and π, in the Ξ rest frame. The cosinedistributions of the Λ distribution look quite simi-lar to the corresponding p distribution for the ΛΛcase. Fig. 4.56 shows the extracted polarisation,using P = (PΞ

+

+ PΞ−)/2. The generated polari-sation is very well reproduced by the reconstructedevents when corrected for the PANDA acceptance.

ΞΘcos-1 -0.5 0 0.5 1

polarisation

-1.5

-1

-0.5

0

0.5

1

1.5

Figure 4.56: Reconstructed polarisation for the pp→Ξ

+Ξ− reaction at 4 GeV/c. The solid line is the sin 2θCM

function used to generate the polarisation.

4.3.3.2 Background Reactions

The PS185 experiment at LEAR showed that thepp→ ΛΛ reaction can be extracted with low back-

ground near the threshold. The background wasof the order of (5-10) % which primarily came fromquasi-free production on carbon from the CH2 tar-get [153]. We therefore anticipate a much lowerbackground in this kinematical region when us-ing pure hydrogen pellets. The remaining back-ground reactions that have been considered for thepp→ ΛΛ channel are:

(a) pp→ ppπ+π−

(b) pp→ ΛΣ0

(c) pp→ ΛΣ(1385)

(d) pp→ Σ0Σ0

(e) Dual Parton Model (DPM)

These channels could potentially mimic the ΛΛchannel by producing a ppπ+π− system in the finalstate. It should be noted that channels (b), (c) and(d) are of interest in their own right, but are treatedhere as a background. The only hyperon channelthat is energetically accessible at 1.64 GeV/c is theΛΛ channel and therefore was only reaction (a) con-sidered at this momentum. At 4 GeV/c there areseveral hyperons channels with a ΛΛ pair presentas a result of Σ0 decays in addition to reaction (a).The same reactions were studied at 15 GeV/c to-gether with the DPM. 1M events were generatedand analysed for reaction (a) at 1.64 GeV/c and15 GeV/c and the DPM. 300k events were generatedand analysed for the other background channels atall momenta and reaction (a) at at 4 GeV. Theresult of this background study is summarised inTable 4.44.

At 1.64 GeV/c we can expect a background well be-low 1 %, as anticipated from the PS185 results. Thebackground will be somewhat higher at 4 GeV/c dueto the increase of the cross section for reaction (a)and the presence of several neutral hyperon chan-nels. The result is that we can expect a backgroundof the order of a percent at this momentum. Due tothe large inelastic cross section the largest source ofbackground at the highest momentum is assumedto stem from the DPM process. This backgroundwould not be greater than a few percent, however.Hyperon resonances, not considered here, could beadditional sources of background. This backgroundand the Σ0 channels would be suppressed by apply-ing a χ2 test on these hypotheses.

The pp → Ξ+

Ξ− channel involves four well sepa-rated decay vertices. Thus any background channelwith a different decay pattern can be suppressed


Channel 1.64 GeV/c Rec. eff. σ [µb] Signalpp→ ΛΛ 0.11 64 1pp→ ppπ+π− 1.2 · 10−5 ∼ 10 4.2 · 10−5

Channel 4 GeV/cpp→ ΛΛ 0.23 ∼ 50 1pp→ ppπ+π− < 3 · 10−6 3.5 · 103 < 2.2 · 10−3

pp→ ΛΣ0 5.1 · 10−4 ∼ 50 2.2 · 10−3

pp→ ΛΣ(1385) < 3 · 10−6 ∼ 50 < 1.3 · 10−5

pp→ Σ0Σ0 < 3 · 10−6 ∼ 50 < 1.3 · 10−5

Channel 15 GeV/cpp→ ΛΛ 0.14 ∼ 10 1pp→ ppπ+π− < 1 · 10−6 1 · 103 < 2 · 10−3

pp→ ΛΣ0 2.3 · 10−3 ∼ 10 1.6 · 10−2

pp→ ΛΣ(1385) 3.3 · 10−5 60 1.4 · 10−3

pp→ Σ0Σ0 3.0 · 10−4 ∼ 10 2.1 · 10−3

DPM < 1 · 10−6 5 · 104 < .09Channel 4 GeV/c Rec. eff. σ (µb) Signalpp→ Ξ

+Ξ− 0.19 ∼ 2 1

pp→ Σ+

(1385)Σ−(1385) < 1 · 10−6 ∼ 60 < 2 · 10−4

Table 4.44: Background for pp→ ΛΛ and pp→ Ξ+

Ξ−. The reconstruction efficiencies give the probability for agenerated background events to be identified as a physics event. The cross sections are taken from refs. [153, 148]or extrapolated from the latter. The cross sections and branching ratios into the charged decay mode is takeninto account in the signal number which gives the normalised probability for a background reaction event to beidentified as a physics event.

imposing a constraint on this pattern. A channelwhich has the same ΛΛπ+π− final state is the

pp→ Σ+(1385)Σ−(1385)

reaction. We therefore consider it as the mainsource of background. This channel has one or-der of magnitude higher cross section. However,the contamination from the 1 M events generatedand analysed is negligible as can be seen in Ta-ble 4.44. The low level of remaining background isalso confirmed in the background studies made forthe pp → Ξ

+Ξ−π0 channel at a somewhat higher

momentum in section 4.2.5 where more backgroundchannels were studied.

4.3.3.3 Simulation Results

This study shows that the benchmark channelspp → ΛΛ and pp → Ξ

+Ξ− can be well recon-

structed in PANDA. There is acceptance over thefull angular range and the whole momentum rangeof HESR for the ΛΛ channel. The same will mostlikely hold true also for the Σ0 channels due to thekinematical similarities. There is also full CM ac-ceptance for the Ξ

+Ξ− channel at 4 GeV/c, and

most likely over the full momentum range fromthreshold.

Acceptance corrections have to be applied to obtainthe final results due to the loss of particles in thebeam pipe direction and the loss of pions below 50MeV/c. The angular differential cross section andthe polarisation can be extracted to high precisionafter those corrections.The count rates will be high for the studied chan-nels. Table 4.45 gives the expected count ratesfor the benchmark channels in their charged de-cay mode channels in PANDA at a luminosity of2 · 1032cm−2s−1, ranging from a few 10 per secondfor the Ξ

+Ξ− channel up to a thousand per second

for the ΛΛ channel.

Momentum [GeV/c] Reaction Rate [s−1]1.64 pp→ ΛΛ 580

4 pp→ ΛΛ 980pp→ Ξ

+Ξ− 30

15 pp→ ΛΛ 120

Table 4.45: Estimated count rates into their chargeddecay mode for the benchmark channels at a luminosityof 2 · 1032cm−2s−1


The high count rate together with the expectedlow background, not more than a few percent,makes the study of antihyperon-hyperon pairs verypromising.

4.3.4 Two-Meson Production in pp-Annihilation at Large Angle

The scale for the onset of the pQCD regime canonly be deduced from experiments, and this topichas been much discussed recently especially withregards to the recent electromagnetic form factormeasurements at JLab. This onset may well beprocess-dependent.

Figure 4.57: s10dσ/dt as a function of ln(s) for the ppelastic scattering at θCM = 90.

Pions are copiously produced in pp annihilation.At large angle (s ∼ −t ∼ −u Λ2

QCD), Thetransition to a perturbative QCD description isexpected in the energy range covered by PANDA.

The scaling power law s−n, where n+ 2 is the totalnumber of elementary constituents in the initial andfinal state, for exclusive two-body hard scatteringhas been in the focus of high energy scattering the-ory ever since the first suggestion in the early 70’sof the constituent counting rules [159, 160]. Thesubsequent hard pQCD approach to the deriva-tion of the constituent counting rules has beendeveloped in late 70’s-early 80’s and is known asthe Efremov-Radyushkin-Brodsky-Lepage (ERBL)evolution technique [161, 162].

There remains an open and hot issue of the so-called Landshoff independent scattering mechanism

Figure 4.58: Short-distance QCD diagram for the pro-cess pp→ π+π−. (a) is the Brodsky-Farrar mechanismwhile (b) represents the Landshoff one.

Figure 4.59: s8dσ/dt as a function of ln(s) for thepp→ π+π− reaction at θCM = 90.

[163] which may be important at accessible valuesof s in the PANDA energy range. Some indicationcomes from the experimentally observed oscillatorys-dependence of s10dσ/dt in elastic p p scattering


(see Fig. 4.57) which may be understood as a signalof the interference of the Brodsky-Farrar and Land-shoff mechanisms [164]. For pp → π+π− a typicalshort-distance QCD diagram and the correspond-ing Landshoff process are shown in Fig. 4.58 [165].Available data are shown in Fig. 4.59 [166, 167, 168].Unfortunately, the measurements are not at highenough energy to clarify the issue.

This oscillation scenario could be investigated inPANDA in the two pion channel. Expected count-ing rates at s = 13.5 GeV2 for one week of beamtime at full luminosity are of the order of a few 106

within a 0.1 wide cosθ bin at θCM = 60.

Spin and flavour of other two meson channels(KK, φφ, ρρ) should help to understand better thedynamics.


4.4 Hadrons in the NuclearMedium

The study of hadron properties at finite nucleardensities has a long history. As the most funda-mental aspect, the change of hadron masses insidethe nuclear medium has been proposed to reflect amodification of the chiral symmetry breaking pat-tern of QCD due to the finite density, and thus tobe an indicator of changes of quark condensates. Inparticular, attractive mass shifts reflecting the re-duced quark pair condensate at finite density havebeen predicted for vector mesons [169, 170]. As theongoing theoretical discussion on this issue (see re-cent review articles like [171]) demonstrates, the re-lation between the nuclear density dependence of in-medium masses and chiral condensates is howevernot a direct one. Furthermore, it is important tonote that in-medium mass shifts of hadrons, reflect-ing the real part of a nuclear potential, are drivenby low energy interactions. The most significantmedium effects are thus expected for hadrons whichare at rest or have a small momentum relative to thenuclear environment, whereas the non-observationof mass shifts at high momenta not necessarily im-plies the absence of nuclear potentials. For ex-perimental studies of hadron in-medium proper-ties therefore appropriate conditions of the reactionkinematics have to be selected. Due to the releasedannihilation energy of almost 2 GeV hadrons pro-duced in antiproton-nucleon collisions may be im-planted in the nuclear environment at much lowermomenta than e.g. in proton induced reactions.

Numerous experiments using proton-nucleus,photon-nucleus, or nucleus-nucleus collisionshave been, at least partially, devoted to deducein-medium mass shifts or nuclear potentials ofhadrons in the light quark sector (u,d,s), both forvector mesons [172, 173, 174, 175, 176, 177], and forpseudo-scalar mesons [178, 179, 180, 181, 182, 183,184, 185, 186]. Only in part of the experiments themesons were studied at low momenta relative tothe nuclear environment, where possibly significantmedium effects may be expected.

Besides the mass shift also the change of the widthof hadrons inside the nuclear medium is an impor-tant observable. In general the width will increasedue to the opening of decay channels which arenot accessible in the vacuum. The measurement ofthe modification of a hadron’s width in the nuclearmedium therefore yields information on its inelas-tic interactions, which is otherwise very difficult toaccess for unstable hadrons. In the case of veryshort-lived mesons decaying inside the nucleus, the

in-medium width may be measured directly. As analternative approach, the measurement of the trans-parency ratio determined from the production crosssection with different target nuclei allows to deducethe in-medium width of mesons [187, 188].

For some observables, the effect of the nuclearmedium becomes surprisingly small: this is theColour transparency phenomenon which is relatedto the gauge nature of strong interactions. Thestudy of exclusive hard reactions in a nuclearmedium constitutes a way to test the factorisa-tion of a short distance process occurring betweencolour neutral objects whose transverse size is con-trolled by the hardness of the collision (measuredby the momentum transfer t). Moreover the nuclearmedium may even be able to filter out the non shortdistance dominated part of the amplitude. Thesephenomena and their possible study with PANDAis discussed in section 4.4.5.

4.4.1 In-Medium Properties ofCharmed Hadrons

The energy range of the HESR and the detectioncapabilities of the PANDA detector in principle al-low to extend studies of the in-medium properties ofhadrons into the charm sector by using antiproton-nucleus collisions as entrance channel. The in-medium properties of both D mesons and charmo-nium states have been studied theoretically in dif-ferent approaches (for a review on the earlier worksee [189]). In analogy to the K/K splitting in nu-clear matter phenomenological estimates using aquark-meson coupling model [190, 191] predict anin-medium mass splitting between D and D mesonsof about 100 MeV, and an attractive D meson (D+,D0) potential with a depth of more than −100 MeVat normal nuclear density ρ = ρ0. A downwardshift of the DD average mass by about 50 MeV wasobtained in a QCD sum rule estimate [192]. TheQCD sum rule analysis of Refs. [189, 193] predictsa D+ − D− mass splitting of more than 50 MeVwith the a downward shift of the D+/D− aver-age mass by about the same order of magnitudeat ρ = ρ0. A more involved coupled channel ap-proach [194, 195, 196] reveals a complicated struc-ture of D+ mesons (and equivalently D0 mesons)which is not appropriately described by two simpleparameters denoting in-medium mass and width,respectively. Inside the nuclear medium the in-elastic charm exchange channels DNN → ΛcNand DN → πΛc are open at threshold resultingin a low mass component reflecting Λc-hole excita-tion. Nuclear binding effects for charmonium have


been studied theoretically almost 20 years ago [197],but the binding effect was later found to be rathersmall, namely between 5 and 10 MeV for J/ψ andηc states [198, 199]. Large attractive mass shiftsof ∼ 100 MeV in normal nuclear matter were pre-dicted for higher-lying charmonium states resultingfrom the QCD second order Stark effect due to thechange of the gluon condensate [200, 201].

Different experimental methods were discussed toobserve signals of the D meson mass modifica-tion in nuclear matter. It was proposed [191] tostudy subthreshold production of D and D mesonsin antiproton-nucleus collisions, where reduced in-medium masses should be visible in an enhance-ment of the production cross section. A lower-ing of the in-medium DD threshold has been pre-dicted to result in a dramatic increase of the ψ(2S)and ψ(3770) width, since in free space these statesare rather narrow due to their vicinity to the DDthreshold [192]. Using a Multiple Scattering MonteCarlo approach [202] it was however found that thecollisional width of these charmonium states in thenuclear medium is much larger than their width infree space already for unchanged D/D masses. Tak-ing the collisional width and D/D re-scattering intoaccount, no effect of attractive nuclear potentialssurvived in the DD channel, and only a very smalleffect in the di-lepton channel.

It has also been proposed to study the elemen-tary DN and DN interaction more directly in pdcollisions by using the spectator nucleon in thedeuteron as secondary target, as discussed for theelastic DDN cross section in [203]. Inelastic chan-nels with charm exchange like pd → ΛcN(π) orpd → ΣcN(π) might also be studied. Recently,the DN interaction with its energy dependence wasstudied in a combined meson exchange and quark-gluon dynamics approach [204]. It was found thatthe DN cross section is by about a factor two largerthan the KN cross section within the range up toabout 150 MeV above threshold. In the nucleon restframe this corresponds to a D momentum of about1.4 GeV/c.

Due to the high mass of charmed hadrons, it isvery difficult to realise the conditions at which theirmedium properties are experimentally accessible.For D mesons produced in direct annihilation pro-cesses in antiproton-nucleus collisions the conditionof low momentum, which is required to be sen-sitive to nuclear medium effects, is kinematicallynot fulfilled. For example, at threshold the D/Dmeson momentum is 3.2 GeV/c. Lower D/D mo-menta can be reached by using backward produc-tion at higher beam energies, but at the highest

HESR beam momentum of 15 GeV/c the minimumD/D momentum is still 1.67 GeV/c. The interest-ing regime of momenta below 1 GeV/c can only bereached in complicated two- or multi-step reactionswith correspondingly small cross sections. Qual-itatively, the same holds for charmonium statesproduced in pA collisions. Presently it is neitherknown to which extent the discussed observablesare still sensitive to nuclear potentials at high D/Dor charmonium momenta relative to the nuclearmedium, or if more complicated processes slowingdown charmed hadrons inside a nucleus can be ex-perimentally identified. Therefore the study of pos-sible mass modifications of charmed hadrons in nu-clear matter is considered as a long term physicsgoal based on further theoretical studies on the re-action dynamics, and on the exploration of the ex-perimental capability to identify more complicatedprocesses. It will however not be in the focus of thephysics program during the first years of PANDAoperation.

4.4.2 Charmonium Dissociation

Apart from the determination of nuclear potentialsof charmed hadrons, specific well-defined problemsexist to which the study of antiproton-nucleus col-lisions with PANDA can contribute valuable infor-mation. As an important issue in this respect wesee the still open question of the J/ψN dissocia-tion cross section. This cross section is as yet ex-perimentally unknown, except for indirect informa-tion deduced from high-energy J/ψ production fromnuclear targets. A J/ψN cross section σJ/ψN =3.5 ± 0.8 mb has been deduced by measuring J/ψphoto-production from nuclei with a mean photonenergy of 17 GeV/c [205]. The J/ψ momentum in thenuclear rest frame was not explicitly determined. In[206] the authors analysed proton-nucleus collisionswith beam energies between 200 and 800 GeV/c andfound as absorption cross section σ = 7.3± 0.6 mb,also without explicitly specifying the J/ψ momen-tum in the nuclear rest frame. In an analysis of re-cent measurements of J/ψ and ψ′ production in pAcollisions at 400 and 450 GeV/c [207, 208] the NA50Collaboration finds σabs(J/ψ) = 4.6 ± 0.6 mb andσabs(ψ′) = 10.0 ± 1.5 mb. The authors of [208] ex-plicitly mention the energy dependence of J/ψ andψ′ absorption as a still open question. Recently,nuclear shadowing effects of J/ψ mesons were alsostudied in d + Au collisions in the PHENIX experi-ment at RHIC at the much higher energy

√sNN =

200 GeV/c, resulting in a deduced J/ψ breakup crosssection of σbreakup = 2.8+1.7

−1.4 mb [209, 210].


Apart from being a quantity of its own in-terest, the J/ψN dissociation cross section isclosely related to the attempt of identifying quark-gluon plasma (QGP) formation in ultra-relativisticnucleus-nucleus collisions. A significant additional,so-called anomalous suppression of the J/ψ yieldin high-energy nucleus-nucleus collisions had beenpredicted due to colour screening of cc pairs in aQGP environment [211]. In fact, the CERN-SPSexperiments have observed a J/ψ suppression effectincreasing with the size of the interacting nuclearsystem, and interpreted this as signature for QGPformation [212, 213, 214]. The validity of such aninterpretation is however based on the knowledgeof the ”normal” suppression effect due to J/ψ dis-sociation in a hadronic environment. Nuclear J/ψabsorption can so far only be deduced from mod-els [215, 216, 217] since the available data do notcover the kinematic regime relevant for the inter-pretation of the J/ψ suppression effect seen in theSPS heavy ion data, since e.g. J/ψN dissocia-tion processes will in general occur at higher rel-ative momenta in 400 GeV/c pA collisions than in158 GeV/c/u Pb + Pb collisions with partial stop-ping of the nuclear matter. Ref. [216] gives a rangefrom ∼ 1 mb to ∼ 7 mb for the uncertainty of theestimated values of the J/ψ-nucleon cross section.In cold nuclear matter J/ψ mesons can dissociatevia the reaction J/ψN → DΛc at plab ≥ 1.84 GeV/c,whereas dissociation via J/ψN → DDN requiresplab ≥ 5.17 GeV/c. Therefore the J/ψN dissocia-tion cross section will be strongly momentum de-pendent, and it is important to supply experimen-tal information on this dependence particularly atlower momenta.

4.4.3 J/ψ N Dissociation Cross Sectionin pA Collisions

In antiproton-nucleus collisions the J/ψN dissocia-tion cross section can be determined for momentaaround 4 GeV/c with very little model dependence,in contrast to its values deduced from the previousstudies as discussed in section 4.4.2. The J/ψ mo-mentum inside the nuclear medium is constrainedby the condition that the pp→ J/ψ formation pro-ceeds ’on resonance’ with a target proton (pp =4.1 GeV/c). The determination of the J/ψN dissoci-ation cross section is, in principle, straight forward:the J/ψ production cross section is measured fordifferent target nuclei of mass number ranging fromlight (d) to heavy (Xe or Au), by scanning the pbeam momentum across the J/ψ yield profile whosewidth is essentially given by the internal target nu-

cleon momentum distribution. The internal nuclearmomentum distribution is sufficiently well known.The J/ψ is identified by its decay branch to µ+µ−

or e+e−. The attenuation of the J/ψ yield per effec-tive target proton as a function of the target massis a direct measure for the J/ψN dissociation crosssection, which can be deduced by a Glauber typeanalysis. Note that a study of pd collisions ’on theJ/ψ resonance’ allows an exclusive measurement ofthe final state, and thus with the spectator neutronas secondary target should give direct access to thecross section for specific J/ψn reactions [203].

Figure 4.60: Simulated cross section for resonant J/ψproduction on nuclear protons with internal Fermi mo-mentum distribution as a function of the antiproton mo-mentum [218].

In a second step these studies may be extendedto higher charmonium states like the ψ′ (ψ(2S))which requires p momenta around 6.2 GeV/c for res-onant production. This would also allow to de-termine the cross section for the inelastic processψ′N → J/ψN [219] which is also relevant for the in-terpretation of the ultra-relativistic heavy ion data.Measurement of ψ′ production on nuclear targets ismore difficult since the ψ′ yield will be considerablysmaller than that of J/ψ. Neglecting absorption, theestimated ratio of the production cross sections isσpA→ψ′X/σpA→J/ψX ' 0.03, based on the Breit-Wigner formula with the known [220] widths andpp branching ratios. Absorption effects will furtherreduce this ratio, since due to the larger size of theψ′ a larger absorption cross section is expected thanfor J/ψ. At low momenta in the nuclear rest frame


the lower thresholds for dissociation processes willalso play an important role and enhance the ratio ofψ′ to J/ψ absorption. In contrast to the J/ψN sys-tem as discussed above, the ψ′N → DΛc channelis already open at threshold, and the dissociationvia J/ψN → DDN is also open at the p momentachosen for resonant ψ′ production (in the nucleonrest frame the ψ′ threshold momentum for DD dis-sociation is 1.28 GeV/c).

Benchmark Channels

The simulation studies for this report, in the con-text of antiproton nucleus collisions, focus on as-pects relevant for the determination of the J/ψ-nucleon dissociation cross section. The reactionstudied is:

p 40Ca→ J/ψX → e+e−X

The incident p momentum is 4.05 GeV/c2, corre-sponding to resonant J/ψ formation with a protonat rest in the target nucleus. Goal of the simula-tions is to study the identification of the J/ψ signalin e+e−pairs, and to explore the suppression of pre-sumed dominant background channels. No attemptis made at the present stage to simulate the fullexperiment required to determine the J/ψN disso-ciation cross section, and to estimate its achievablestatistical and systematic errors. The full exper-iment will comprise the measurement of absolutecross sections for J/ψ production on a series of tar-get nuclei ranging from very light to heavy (e.g. 2H,N, Ne, Ar, Kr, Xe) including a p momentum scanacross the J/ψ excitation function in each case.

A dedicated event generator for the reaction pA→J/ψX [221] has been used to generate 80 thousandevents of the signal channel. The event generator in-cludes realistic Fermi momentum distributions andaverage nuclear binding effects of the nuclear tar-get protons, as well as p and J/ψ absorption in thenuclear medium.

Various criteria are conceivable to select the J/ψ →e+e− signal events based on the two-body kinemat-ics of the process with a slow target nucleon and onthe identification of the e+e− pair. The conditionsselected in the simulation studies are given in detaillater.

Background Reactions

As compared to resonant J/ψ formation with anantiproton hitting a free target proton at a crosssection of ∼ 5µb, J/ψ production on a nucleus is

reduced roughly by a factor 1000 due to the nuclearFermi momentum, and thus the peak cross sectionis estimated to be a few nb. In contrast, the totalantiproton-nucleus cross section, dominated by an-nihilation and inelastic hadronic processes on targetnucleons, is approximately given by the geometri-cal cross section of the order of 1 b. Taking intoaccount the ∼ 6 % branching for the e+e− decay,the rate of hadronic background reactions is almost10 orders of magnitude larger than that of the J/ψsignal. Obviously, it is not possible to simulate thedetector response for a sample of unspecific back-ground events which is large enough to test back-ground suppression at a relative signal level below10−9. The background suppression and signal de-tection capability can therefore only be estimatedby using extrapolations based on certain assump-tions.

Annihilation of antiprotons with one of the nucleartarget protons into π+ π− pairs without creation ofother particles or high momentum transfer to tar-get nucleons is considered to be the most dangerousbackground channel to a di-leptonic J/ψ signal be-cause of a possible misidentification of π+ π− pairsas e+e− pairs. A suppression of these backgroundevents by kinematic selection criteria is not pos-sible. Experimental data on the reaction pp →π+π− at energies above the LEAR energy rangeare scarce. Ref [148] lists a total cross section of7± 5µb at pp = 4 GeV/c. Angular distributions forpp → π+π− have been measured up to p momen-tum pp = 0.78 GeV/c [222] whereas for pp → π0π0

differential cross sections at total pp centre-of-massenergies in the charmonium mass range have beenmeasured by the Fermilab E760 and E835 experi-ments for part of the angular range [223, 224].

Samples of 26.4 million background events for4.05 GeV/c p on 40Ca have been created by using theUrQMD event generator [225, 226] in the standardversion (i.e. statistical de-excitation of the systemby emission of low energy particles is neglected).This sample is representative for unspecific back-ground in pA collisions. Since it is difficult to de-cide which event patterns create background in thedi-leptonic J/ψ signal at a level below 10−9 no filterto the UrQMD events has been applied before prop-agation through the detector. In addition a sampleof 3 · 107 pp → π+π− background events was gen-erated. Since at the considered energy no experi-mental data on π+ π− angular distributions in ppcollisions exist, the parametrisation of the π0π0 an-gular distribution measured by the E835 experimentwas used [224].


4.4.3.1 Simulation Results

The first step in the analysis is the computa-tion of the invariant mass of selected pairs of e−

and e+ candidates. Four e± candidate lists havebeen defined - the VeryLoose, Loose, Tight, andVeryTight lists. In Fig. 4.61 the e+e− invariantmass distributions using the different lists are dis-played.

]2) [GeV/c- + e+Invariant mass (e0 0.5 1 1.5 2 2.5 3 3.5 4

coun

ts

1

10

210

310

410

510Candidate lists

very loose: 89/02loose: 82/01tight: 67/01very tight: 47/01MC true: 89

]2) [GeV/c+ + e-Invariant mass (e0 0.5 1 1.5 2 2.5 3 3.5 4

coun

ts

-110

1

10

210

310

410

510Candidate lists

very loose: 1.00

loose: 0.08tight: 0.06

very tight: 0.04

Figure 4.61: Reconstructed invariant mass distribu-tion of e+e− pair candidates for the signal events (upperpanel) and for the UrQMD background events (lowerpanel).

The upper panel contains the signal events, whereasthe lower panel shows the corresponding distribu-tions obtained for the UrQMD background events.The two numbers given in the legend of the upperpanel are the percentages of reconstructed true andand fake J/ψ mesons, respectively, at a minimumreconstructed mass of 2.0 GeV/c2.

The green line, labelled with MC true, repre-sents the true mass distribution for the VeryLooselist. The reconstruction efficiency decreases from∼ 89 % with the VeryLoose list to ∼ 47 % with theVeryTight list. With the available statistics thenumber of fake J/ψ meson candidates in the con-sidered invariant mass region is zero for all cases.In the lower panel, showing the background dis-tributions, the number in the legend is the frac-

tion of reconstructed fake J/ψ mesons with respectto the number obtained with the VeryLoose list.The mass distribution decreases strongly with in-creasing mass. Except for the VeryLoose list thereare only few background events in the mass rangeabove 2 GeV/c2. With the available number of sim-ulated background events, using the Loose list 5background events survive in this mass range. Withthe Tight list 1 event, with the VeryTight list nobackground event is found above 2 GeV/c2.

A realistic ratio of the numbers of background andsignal events reflecting the cross section ratio of1010 may however require additional cuts for fur-ther background suppression. The simple topologyof the signal events helps to select the signal eventsfrom the dominating background. The typical fea-tures which can be exploited to suppress the back-ground are listed below:

1. the two leptons emerge from the main vertex

2. the total momentum approximately equals theincident p momentum (Pz(e+) + Pz(e−) ≈Pz(p))

The total perpendicular momentum approximatelyvanishes (P⊥(e+) ≈ −P⊥(e−)) which implies that

3. in the centre of mass system the angle betweenthe two leptons Φ(e+, e−) is ∼ 180

4. the absolute values of the perpendicular mo-menta of the two leptons is approximatelyequal (|P⊥(e+))| ≈ |P⊥(e−)|)

The momentum relations are only approximatelyvalid because of the Fermi-motion of the protons inthe target nuclei.

The cuts deduced from these characteristic featuresare shown in Fig. 4.62. The panels on the left sidecontain the signal events, whereas the right sidepanels show the background events using the Looselist. The red lines represent possible cuts to sepa-rate signal and background. The used cuts are ex-plicitly given in Table 4.46. In addition, not shownin the figure, a condition in the x− y plane on theprimary interaction vertex at the target can be set.

The efficiencies of these cuts in combination withthe Loose e± candidate list are listed in Table 4.46.In case of the signal the numbers represent the frac-tion of true J/ψ mesons which are reconstructedand accepted by the given cut in the invariant massrange above 2 GeV/c2. In case of the background thegiven fraction is the number of accepted e+e− pairs


) [GeV/c]-(ezP-1 0 1 2 3 4 5

) [G

eV/c

]+

(e zP

-1

0

1

2

3

4

5

0

0.05

0.1

0.15

0.2

0.25

0.3

) [GeV/c]-(ezP-1 0 1 2 3 4 5

) [G

eV/c

]+

(e zP

-1

0

1

2

3

4

5

0

1

2

3

4

5

6

) [radian]+, e-(eCMΦ0 0.5 1 1.5 2 2.5 3 3.5 4

coun

ts

1

10

210

310

410

) [radian]+, e-(eCMΦ0 0.5 1 1.5 2 2.5 3 3.5 4

coun

ts

10

210

310

410

0

0.05

0.1

0.15

0.2

0.25

0.3

) [GeV/c]- (eP0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

) [G

eV/c

]+

(e

P

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

0.2

0.4

0.6

0.8

1

1.2

) [GeV/c]- (eP0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

) [G

eV/c

]+

(e

P

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Figure 4.62: Distributions used to suppress the background to the J/ψ signal: Left panels are for signal events,right panels show the UrQMD background distributions. Upper panels show the longitudinal momentum of e−

versus that of e+, middle panels show the azimuthal angle φ(e+, e−) between e+ and e− in the centre of masssystem, and lower panels show the perpendicular momentum of e− versus that of e+. The red lines represent cutsto enhance the signal to background ratio. The 2D-histograms are normalised to contain 100 events.

with a reconstructed invariant mass above 2 GeV/c2

relative to the number of simulated events.

The combination of all four cuts efficiently enhancesthe signal to background ratio. Figure 4.63 showsthe invariant mass distribution after application ofthe combined cut. With the given statistics noUrQMD background events are left in the inves-tigated mass range. Therefore the fraction of ac-cepted UrQMD background events shown in Ta-ble 4.46 represents a lower limit for the achievablebackground suppression. On the other hand 73 %of the true J/ψ mesons are accepted. Note that thiscombination of Loose list and software cuts is con-

siderably more efficient than simply using a morestringent list to enhance the signal to backgroundrelation.

The black line in Fig. 4.63 shows an estimate ofthe remaining background with 8 · 1014 simulatedUrQMD background events (1010 times the num-ber of signal events). The distribution is assumed tofollow an exponential function which was fit to theLoose list distribution shown in the lower panel ofFig. 4.61 and was scaled accordingly. This estimateindicates that also with the realistic relation of sig-nal and background events it should be possible tomeasure J/ψ production in antiproton-nucleus col-


Table 4.46: Definition of cuts and their selection efficiency in combination with the Loose e± candidate list forthe J/ψ → e+e− signal, the generic UrQMD, and specific background channel π+ π−. The numbers are computedfor e+e− invariant masses above a minimum mass of 2 GeV/c2. vx, vy are the x, y coordinates of the primaryvertex.

cut fraction acceptedsignal background

UrQMD π+ π−√v2x + v2

y < 1 mm 0.77 3.8 · 10−8 4.1 · 10−6

Pz(e+) + Pz(e−) > 2.0 GeV/c 0.77 2.3 · 10−7 4.9 · 10−6

Φ(e+, e−) > 2.5 rad 0.77 1.5 · 10−7 4.9 · 10−6

[P⊥(e+) + P⊥(e−)] > 1 GeV/c & | arctan(P⊥(e+)P⊥(e−)

)− 45| < 15 0.73 3.8 · 10−8 2.8 · 10−6

combined (IMe+e− > 2.0 GeV/c2) 0.73 < 3.8 · 10−8 2.4 · 10−6

lisions with acceptable signal to background ratio.

]2) [GeV/c+ + e-Invariant mass (e0 0.5 1 1.5 2 2.5 3 3.5 4

coun

ts

-110

1

10

210

310

410

510

610

710

810Background (26.4 Mio.)

Signal (80 k)

-Background (30 Mio.)-π+π

)14ext. Bckgnd. (8 x 10

Figure 4.63: Invariant mass distribution of e+e− paircandidates for signal (blue), UrQMD background (red),and π+ π− background (magenta) events. The esti-mated distribution for an UrQMD background samplescaled up to 1010 times the number of signal events isshown by the black line.

In addition, as specific background channel, the re-action pp → π+π− at the same incident momen-tum of 4.05 GeV/c has been studied. To mimicthe contribution of this 2-charged-pion annihila-tion channel with a nuclear target, the momentumof the target proton was smeared isotropically ac-cording to a Gaussian distribution with a widthof σp = 180 MeV/c. Assuming σpp→π+π− = 10µbat the upper limit within the experimental uncer-tainty [148] together with an A2/3 scaling for thenuclear target and a signal cross section of 0.1 nb, asuppression factor of minimum 10−5 is required tokeep the signal level above possible background duethe π+ π− channel. The right most column in Ta-ble 4.46 shows the fraction of π+ π− pairs which areerroneously accepted as e+e− pairs from J/ψ decay.

The corresponding invariant mass spectrum of π+

π− pairs accepted out of 30 million generated pp→π+π− events is represented in Fig. 4.61 by the ma-genta distribution.

The suppression factor of 2.4 · 10−6 obtained withthe combined cut is smaller than the required valueand indicates that a signal-to-background ratio withrespect to the π+ π− channel above one can beachieved.

4.4.4 Antibaryons and AntikaonsProduced in pA Collisions

Although not covered in the simulation section ofthis write-up, it is worth mentioning that the specialkinematics of p induced reactions combined withthe detection capabilities of PANDA opens the op-portunity to study the in-medium properties of anumber of hadrons in the light quark sector whichcan be produced at rest or at very small momentainside nuclei. This is e.g. the case for p, Λ, and K,for which the nuclear potential is a quantity of in-terest, but could not be determined experimentallyup to now.

The antiproton-nucleon interaction at low energiesis dominated by annihilation. As a consequence ofthe strong absorption effects constraints deducedfrom the energy levels of antiprotonic atoms orfrom low energy antiproton-nucleus scattering onthe depth of the real part of the p nuclear potentialhave large uncertainties. In theoretical work G par-ity transformation has been proposed as a conceptto provide a link between the NN and NN inter-action at most for distances where the meson ex-change picture is applicable [227], whereas at shortdistances the quark-gluon structure of baryons mayquestion the validity of this approach. Based on Gparity transformation relativistic mean field mod-


els predict a depth of the p nuclear potential aslarge as −700 MeV [228, 229, 230]. The depthof phenomenological potentials deduced from an-tiprotonic atoms [231, 232, 233] and from sub-threshold antiproton production in nucleus-nucleusand in proton-nucleus collisions [234, 235, 236].ranges at lower values, typically between −100and −350 MeV. Therefore better experimental con-straints on the nuclear antiproton potential, whichmay help to elucidate the role of the quark-gluonstructure of baryons for the short-range baryon-antibaryon force, are needed.

The study of antiproton-nucleus collisions at highenergy opens new opportunities: in this case theantiproton can penetrate into the interior of the nu-cleus, and probe the nuclear potential quasi at restby backward scattering from a nuclear proton. Anattractive p potential will be visible in forward pro-tons having a higher momentum than the incidentantiproton which is a very sensitive signature. Thecross section for pA → pX with a recoil proton atθ ' 0 is expected to be comfortably large despitenuclear absorption effects for the incident antipro-ton and the outgoing recoil proton. The nuclear an-tiproton potential reflects itself in the missing massdistribution of the fast forward proton.

The same method of low recoil momentum produc-tion is applicable for Λ antihyperons in the reactionpp→ ΛΛ on a nuclear proton with Λ emission closeto 0. This may for the first time give access to theproperties of Λ antihyperons inside nuclei, since noexperimental information on the nuclear potentialof antihyperons exists so far.

nucleus

p_

p

quasi-boundantihyperon

hyperon

nucleus

p_

p

antihyperon

hyperon

Figure 4.64: Schematic illustration of reactions giv-ing access to the nuclear potential of Λ antihyperons:recoilless Λ production with Λ missing mass measure-ment(left), and comparison of Λ and Λ transverse mo-mentum distribution (right).

In addition, for larger momenta of the producedhadrons, quantitative information on the ’differ-ence’ between baryon and antibaryon potentials andhence on the potential of antibaryons may be ob-tained via exclusive antibaryon-baryon pairs pro-duced close to threshold after an antiproton-protonannihilation within a complex nucleus [237]. Once

these hyperons leave the nucleus and are detected,their asymptotic momentum distributions will re-flect the depth of the respective potentials. Adeeply attractive potential for one species could re-sult in a momentum distribution of antihyperonswhich is very different from that of the coincidenthyperon. Thus event-by-event momentum correla-tion of coincident baryon-antibaryon pairs can pro-vide a direct and quantitative probe for the nuclearpotentials. Fig. 4.64 schematically illustrates bothexperimental approaches to access nuclear poten-tials of Λ antihyperons as described above. Bothmethods may be used in the same experiment tostudy baryon and antibaryon in-medium propertiesover a larger range of momenta.

Due to its mass being very close to that of the nu-cleon, recoilless production is also possible for theφ meson, and hence also for the antikaon as oneof the decay particles emitted at very low momen-tum in the φ rest frame. This may give accessto the nuclear potential for φ mesons and for an-tikaons. We therefore propose to explore the re-action pp → φφ → K+K−K+K− at θ ' 0 onnuclear target protons.

In these reactions the produced slow hadrons arevery likely to be absorbed in the nuclear mediumand not to be detected directly. However a mea-surement of the φ or φK+ missing mass may allowto identify the reaction channel, and to deduce thein-medium properties of φ or K− mesons, respec-tively. In the latter case it is experimentally chal-lenging to detect and identify a low momentum K+

meson.

4.4.5 Colour Transparency

Colour transparency (CT) [238, 239, 240] is the pre-dicted phenomenon of reduced strong interactionsunder certain conditions, and in particular when ahard scattering process occurs, which selects smalltransverse size components in hadronic wave func-tions, and thus triggers a coherent cancellation ofperturbative interactions. Colour transparency istightly connected to the property of asymptoticfreedom in QCD and is expected to occur in manykinds of quasi-exclusive reactions with either elec-tron or hadron beams. A large energy scale isneeded (large quark masses or large transverse mo-menta) for the coloured degrees of freedom to berelevant, and an exclusivity condition is necessary.The concept of colour transparency is related to thenotion of nuclear filtering, which is the conversionof quark wave functions in hadrons to smaller trans-verse space dimensions by interaction with a nuclear


medium.

At high energy, colour transparency has been an es-sential element of the diffractive physics program atHERA as it forms the basis of the QCD factorisationtheorem for production of vector mesons. At FNAL,perturbative QCD prediction of CT was found to beconsistent with the observation of coherent diffrac-tive dissociation of 500 GeV pions into di-jets offthe nuclei [241].

At intermediate energies colour transparency of themagnitude predicted by the colour diffusion model[242] was reported recently in the electroproduc-tion of pions at JLAB [243]. Hence, the presence ofcolour transparency for mesons is now established.Baryons are much more complicated objects thanmesons in particular due to the more important roleplayed by the chiral degrees of freedom. So lookingfor onset of colour transparency for baryon interac-tions is complementary to the meson case.

Among the various experiments where colour trans-parency may be probed, we select here two exam-ples which should be feasible in the PANDA set-up.

4.4.5.1 Antiproton - Nucleon Annihilation in aHadron Pair at Large Angle

The exclusive reactions

pN→ ππ , KK , pN

and the corresponding ones on a nuclear target

pA→ ππ(A− 1)∗ , KK(A− 1)∗ , pN(A− 1)∗

should be perturbatively calculable at large energiesand fixed large scattering angle. The QCD analysisof these processes usually distinguishes two compet-itive mechanisms: the Brodsky-Farrar-Lepage hardscattering of small-sized objects and the Landshoffindependent scattering process where the scatteredobjects have one large transverse size. The differentphase structure of the two interfering amplitudesgives rise to a pattern of oscillatory cross section[244, 245] which has been seen at beam energies inthe 5-15 GeV range for p p collisions.

The pioneering colour transparency experiments[246, 247] involving hadronic hard scattering wasdone at BNL by the group of Carroll et al.. Aproton beam was used to study pA → p′p′′(A −1)∗. Data was taken simultaneously on six tar-gets, namely 1H, 7Li, 12C, 27Al, 64Cu and 207Pb.The reaction was identified via measurement of thethree-momentum of one proton, the direction ofthe second proton, and using veto counters to ex-clude events with production of extra hadrons but

Figure 4.65: The transparency ratio for the elasticproton-proton scattering at large angle, as measured atBNL [246, 247], compared with the oscillatory behaviourpredicted by Ref.[248, 249].

allowing the residual nucleus to be left in the ex-cited state. In the subsequent experiment whichwas focusing on the measurements with the carbontarget momenta of both nucleons were measured.The experiments introduced and reported the trans-parency ratio, T (pN , A) defined by T = (dσ(pA →p′p′′(A− 1)∗/dt)/Zdσ(pp→ p′p′′)/dt at 90 degreesin the centre of mass. The data of the two ex-periments are consistent in observing a rise fromthe value which agrees with the Glauber theory atpN ∼ 6 GeV/c to the value which is about two timeslarger than the Glauber value for pN ∼ 9.5 GeV/cand falls back to the Glauber level again at highermomenta all the way up to 14.4 GeV/c. This oscil-latory energy dependence of the transparency ratiolead to some debate between different theoreticalexplanations [242, 248, 249, 250, 251]. Fig. 4.65shows the BNL data together with the Ralston-Pireinterpretation [248, 249]. These authors infer therise and fall pattern in the colour transparency ratiofrom the different rates of final state interactions ina nuclear medium connected to the different physicsunderlying the two possible processes.

The scientific case between the different ways of un-derstanding the CT phenomenon should be clearedby adding more precise data from other exclusivereactions, such as the exclusive annihilation chan-nels of an antiproton with a nucleon bound in anucleus. The relative weights of the different mech-anisms of production are process-dependent and itis thus crucial to analyse various processes beforeclaiming that colour transparency indeed occurs atintermediate energies for reactions with baryons.


The antiproton beam delivered by FAIR has theright energy and luminosity to access this controver-sial question. The energies of the produced mesonsare at least as high in this case as in the CT ex-periment at JLAB, so the freezing of the qq systemis strong enough not to mask CT effects. PANDAhas the capacities to measure in both in vacuum(proton target) and in a nuclear environment thereactions

pN → ππ pN → KK pN → pN

at various large angles and at various energies inthe right domain where the transition to pertur-bative QCD may occur and cross sections are stillmeasurable. Doing experiments at a few beam en-ergy values and on a few typical nuclear targets(1H, 2H, 12C, 27Al, 58Ni) should allow to plot thetransparency ratio with a good precision for variouscentre of mass angle bins. Simulations already per-formed in the framework of the background analysisof the time-like form factor measurement, namelythe reaction pp → π+π−, show that the hadronidentification (π+,K+, p or their antiparticles) iseasy to perform. Kinematically, the separation fromthe process leading to an additional π is as good asin the case of the reaction on the proton.

4.4.5.2 Colour transparency in charmoniumproduction

Charmonium states will be produced in the nu-clear media in the same resonance reactions as thosewhich will be studied in pp collisions. A possibilityto use these processes for studies of CT was firstsuggested in Ref. [252]. A subsequent detailed anal-ysis of the effects of CT and Fermi motion was per-formed in Ref. [253]. It found that CT effects dueto squeezing of the incoming antiproton are smallsince the incident energy is small leading two a shortcoherence length for the incident and final particles.The effect of the Fermi motion is large but well un-der control. What is unique about this reaction isthat at these energies charmonium is formed veryclose (≤ 1fm) to the interaction point, hence onegets a possibility to check the main premise of CTthat small objects interact with nucleons with smallcross sections. The ability to select states of vary-ing size: J/ψ, χc, ψ

′ will allow to investigate howthe interaction strength depends on the transversesize of the system. A nontrivial consequence of thisphenomenon is an A-dependent polarisation of theχ states [254] due to filtering of cc configurationsof smaller transverse size. The study of this phe-nomenon is also important for understanding the

dynamics of charmonium production in heavy ioncollisions.


4.5 Hypernuclear Physics

Quantum Chromo Dynamics (QCD) is the theoryof the force responsible for the binding of nucleonsand nuclei and thus of a significant fraction of theordinary matter in our universe. While the internalstructure of hadrons and the spectra of their ex-cited states are important aspects of QCD, it is atleast equally important to understand how nuclearphysics emerges in a more rigorous way out of QCDand how nuclear structures - nuclei on the smallscale and dense stellar objects on the large scale -are formed [255]. For example, the presence of hy-perons in neutron star cores is expected to lower themaximum mass of neutron (e.g. ref.[256]). Recentmeasurements of a few large masses of pulsars inbinaries with white dwarfs could be used to put ad-ditional (astrophysical) constraints on the hyperon-nucleon interaction (e.g. ref.[256]). However, thereis at present no clear picture emerging as to whatkind of matter exists in the cores of neutron stars[257, 258, 259].

A hyperon bound in a nucleus offers a selectiveprobe of the hadronic many-body problem as it isnot restricted by the Pauli principle in populatingall possible nuclear states, in contrast to neutronsand protons. On one hand a strange baryon em-bedded in a nuclear system may serve as a sensi-tive probe for the nuclear structure and its possiblemodification due to the presence of the hyperon. Onthe other hand properties of hyperons may changedramatically if implanted inside a nucleus. There-fore a nucleus may serve as a laboratory offering aunique possibility to study basic properties of hy-perons and strange exotic objects. Thus hypernu-clear physics represents an interdisciplinary sciencelinking many fields of particle, nuclear and many-body physics (Fig. 4.66).

4.5.1 Physics Goals

4.5.1.1 Hypernuclei Probing Nuclear Structure

While it is difficult to study nucleons deeply boundin ordinary nuclei, a Λ hyperon not suffering fromPauli blocking can form deeply bound hypernuclearstates which are directly accessible in experiments.In turn, the presence of a hyperon inside the nu-clear medium may give rise to new nuclear struc-tures which cannot be seen in normal nuclei con-sisting only of nucleons. Furthermore, a comparisonof ordinary nuclei and hypernuclei may reveal newinsights in key questions in nuclear physics like forexample the origin of the nuclear spin-orbit force

astrophysics

many-bodysystems

particlephysics

nuclearstructure

nuclearreaction

hot nuclearmedium

QCD and chiral

symmetry

hadronstructure

hyper-nuclei

nuclearphysics

Figure 4.66: Hypernuclei and their link to other fieldsof physics.

[260].

An important goal is to measure the level spec-tra and decay properties of hypernuclei is in or-der to test the energies and wave functions frommicroscopic structure models. Indeed recent cal-culations of light nuclei based on modern nucleon-nucleon potentials, which also incorporate multi-nucleon interactions, are able to describe the ex-citation spectra of light nuclei with a very high pre-cision of 1-2% [261, 262, 263, 264]. A challengingnew approach to hyperon interactions and struc-ture of hypernuclei is the relativistic density func-tional theory. This is a full quantum field theoryenabling an ab initio description of strongly inter-acting many-body system in terms of mesons andbaryons by deriving the in-medium baryon-baryoninteractions from free space interactions by meansof Dirac-Brueckner theory [265, 266]. The field the-oretical approach is also the appropriate startingpoint for the connection to QCD-inspired descrip-tions based for example on chiral effective field the-ory (χEFT ) [267, 268]. At present, χEFT is wellunderstood for low-energy meson-meson [269] andmeson-baryon dynamics in the vacuum [133, 270]and infinite nuclear matter[271, 272]. A task leftfor the future is to obtain the same degree of un-derstanding for processes in a finite nuclear envi-ronment. Present nuclear structure calculations ofthe light nuclei in χEFT [264, 273, 274, 275] signalsignificant progress.

It is this progress made in our theoretical under-standing of nuclei which nurtures the hope that de-tailed information on excitation spectra of hypernu-


clei and their structure will provide unique informa-tion on the hyperon-nucleon and - in case of doublehypernuclei – on the hyperon-hyperon interactions.

Figure 4.67: Present knowledge on hypernuclei. Onlyvery few individual events of double hypernuclei havebeen detected and identified so far.

4.5.1.2 Hypernuclei: Baryon-BaryonInteraction

While the nucleon-nucleon scattering was exten-sively studied since the 50’s, direct experimentalinvestigations for the YN interactions are still verysparse. Because of their short lifetimes, hyperontargets are not available. Low-momentum hyperonsare very difficult to produce and hyperon-protonscattering is only feasible via the double-scatteringtechnique [276, 277]. There are only a few hundredslow-momentum Λ-N and Σ±-N scattering eventsavailable and there is essentially no data on Ξ-Nor Ω-N scattering.

In single hypernuclei the description of hyperons oc-cupying the allowed single-particle states is withoutthe complications encountered in ordinary nuclei,like pairing interactions and so on. The strength ofthe Λ-N strong interaction may be extracted witha description of single-particle states by rather wellknown wave functions. Furthermore, the decom-position into the different spin-dependent contri-butions may be analysed. For these contributions,significantly different predictions exist for examplefrom meson exchange-current and quark models.

It is also clear that a detailed and consistent un-derstanding of the quark aspect of the baryon-baryon forces in the SU(3) space will not be pos-sible as long as experimental information on thehyperon-hyperon channel is not at our disposal.

Since scattering experiments between two hyperonsare impractical, the precise spectroscopy of multi-strange hypernuclei at PANDA will provide a uniqueapproach to explore the hyperon-hyperon interac-tion. So far only very few individual events of dou-ble hypernuclei have been detected and identified(Fig. 4.67).

4.5.1.3 Hypernuclei: Weak Decays

Once a hypernucleus has reached its ground state,it can only decay via a strangeness-changing weakinteraction. Because of the low Q-value for free-Λmesonic decay at rest of only 40 MeV, the mesonicdecay of a Λ → Nπ bound in a nucleus (BΛ ≥ -27 MeV; see e.g. Ref. [278]) is disfavoured by thePauli principle and is only for light nuclei still siz-able (see Fig. 4.68). In contrast, processes likeΛN → NN and ΛΛ → ΛN are allowed, openinga unique window for the four-baryon, strangenessnon-conserving interaction. Moreover, in doublehypernuclei hyperon induced non-mesonic weak de-cays ΛΛ → ΛN and ΛΛ → ΣN are possible [279,280, 281] giving unique access to the ΛΛK coupling.

Figure 4.68: Measured ratio of non-mesonic (ΛN →NN) to mesonic (Λ→ Nπ) hypernuclear decay widthsas a function of the nuclear mass [282].

In the simulation presented below we consider onlythe case of two subsequent pionic decays whichamounts to typically 10% of all weak decays of thelight double hypernuclei (c.f. Fig. 4.68). Consider-ing in the future also non-mesonic decays the eventstatistics may therefore increase significantly.


4.5.1.4 Multi-Strange Atoms

It is interesting to note that the different S=-2 sys-tems - Ξ−-atoms and single Ξ−-hypernuclei on oneside and double ΛΛ hypernuclei on the other side -provide complementary information on the baryonforce: on the one-meson exchange level strangemesons with I=1/2 do not contribute to the Ξ-N in-teraction. On the other hand, only strange mesonsact in the ΞN -ΛΛ coupling while only non-strangemesons contribute in the Λ-Λ interaction [283, 284].Indeed, hyperatoms created during the capture pro-cess of the hyperon will supply additional informa-tion on the hyperon-nucleus interaction. X- raysfrom π−, K−, p and Σ− atoms have already beenstudied in several experiments in the past. At J-PARC first precise studies of Ξ-atoms are planned[285]. At PANDA not only Ξ− atoms but also Ω−

atoms can be studied for the first time thus provid-ing unique information on the nuclear optical poten-tial of Ω− baryons. The Ω hyperon is particularlyinteresting because due to it’s long lifetime and it’sspin of 3/2 it is the only ’elementary’ baryon witha non-vanishing spectroscopic quadrupole moment.Since the quadrupole moment of the Ω is mainly de-termined by the one-gluon exchange contribution tothe quark-quark interaction [286, 287] it’s measure-ment represents a unique benchmark for our under-standing of the quark-quark interaction.

4.5.1.5 Hypernuclei: Doorway to Exotic QuarkStates

The claimed observation of pentaquark states placesalso the question for other exotic quark states onthe agenda. Thus the possible existence of an S=-2 six quark (uuddss) H-dibaryon [288, 289] repre-sents another challenging topic of ΛΛ hypernuclearphysics. Because of their long lifetimes double Λ hy-pernuclei may serve as ’breeder’ for the H-particle.Although some theories predict the H-dibaryon tobe stable ([290] and references therein), the obser-vation of several double hypernuclei makes the exis-tence of a strongly bound free H-dibaryon unlikely.However, since the mass of the H-particle mightdrop inside a nucleus [290] and due to hyperon mix-ing [291, 292, 293, 294] it might be possible to ob-serve traces of a H-dibaryon even if it is unboundin free space by a detailed study of the energy levelsin double hypernuclei.

4.5.2 Experimental Integration andSimulation

In the PANDA experiment, bound states of Ξ hy-pernuclei will be used as a gateway to form doubleΛ hypernuclei [295]. The production of low momen-tum Ξ− hyperons and their capture in atomic levelsis therefore essential for the experiment. At PANDA

the reactions p + p → Ξ−Ξ+

and p + n → Ξ−Ξ0

followed by re-scattering of the Ξ− within the pri-mary target nucleus will be employed (Fig. 4.69).After stopping the Ξ− in an external secondarytarget, the formed Ξ hypernuclei will be convertedinto double Λ hypernuclei. This two-step produc-tion mechanism requires major additions to theusual simulation package PandaRoot as well as thePANDA setup (Fig. 2.8 in Sec. 2.2). Mandatoryfor this experiment is a modular and highly flexiblesetup of the central PANDA detector:

Ξ-3 GeV/c

Kaons_Ξ trigger

p_

ΛΛ

captureof Ξ- in

secondarytarget;atomic

transistion

hyperon-antihyperonproduction

at threshold; rescattering

γ

γ

+28MeV

Ξ-p→ΛΛconversionγ-decay andweak decay

12C

9Be, 10,11B or 12,13C

Figure 4.69: Various steps of the double hypernucleusproduction in PANDA.

• A primary carbon target at the entrance to thecentral tracking detector of PANDA. To avoidunnecessary radiation damage to the micro ver-tex detectors surrounding the nominal targetregion, these detectors will be removed duringthe hypernucleus runs.


• A small secondary active sandwich target com-posed of silicon detectors and 9Be, 10,11B or12,13C absorbers to slow down and stop the Ξ−

and to identify the weak decay products.

• To detect the γ-rays from the excited doublehypernuclei an array of 15 n-type Germaniumtriple Cluster-arrays will be added. To max-imise the detection efficiency the γ-detectorsmust be arranged as close as possible to thetarget. Hereby the main limitation is the loadof particles from p-nucleus reactions. Since theγ-rays from the slowly moving hypernuclei isemitted nearly isotropic the Ge-detectors willbe arranged at backward angles.

4.5.2.1 Simulation of Hyperon Production

At present high statistics production of hyperon-antihyperon pairs in antiproton-nucleus are notpractical within full microscopic transport calcula-tions like UrQMD. We therefore employed an eventgenerator [296] which is based on an Intra NuclearCascade model and which takes as a main ingredi-ent the re-scattering of the antihyperons and hyper-ons in the target nucleus into account.

Target nuclei with larger mass are more efficient forre-scattering of the produced primary particles andhence for the emission of low momentum Ξ− hy-perons. However, heavier targets increase the neu-tron and x-ray background in the germanium de-tectors. Furthermore, Coulomb scattering in heavyprimary targets leads to significant losses of an-tiprotons. Therefore it is foreseen to use thin car-bon micro-ribbons [297] as a primary target in theHESR ring. For the present simulations 106 Ξ−Ξpairs were generated. At the incident momentumof 3 GeV/c we expect a cross section per nucleon of2µb [298]. For comparison, at PANDA a luminosityof 1032cm−2s−1 for p+12C reactions corresponds toabout 700000 produced Ξ−Ξ pairs per hour. Out ofthe produced 1 million pairs, 50505 contain low mo-mentum Ξ− with momentum less than 500 MeV/c.

4.5.2.2 Deceleration of Ξ− Hyperons in aSecondary Target

In order to limit the number of possible transitionsand thus to increase the possible signal to back-ground ratio, the experiment will focus on light sec-ondary target nuclei with mass number A0 ≤ 13.Since the identification of the double hypernucleihas to rely on the unique assignment of the de-tected γ-transitions, different isotopically enrichedlight absorbers (9Be, 10,11B, 12,13C) will be used. In

the following we consider as an example the case of12C absorbers in all four quadrants of the secondarytarget.

The geometry of the target (see Fig. 2.9 in Sec. 2.2)is essentially determined by the lifetime of thehyperons and their stopping time in solid mate-rial: only hyperons with momenta smaller thanabout 500 MeV/c have a non-negligible chance tobe stopped prior to their free decay. From 50505

X(cm)-3 -2 -1 0 1 2 3

Y (

cm)

-3

-2

-1

0

1

2

3

0

2

4

6

8

10

12

14

16

18

20

stopped Xi- X-Y distribution

Figure 4.70: The figure marks the stopping pointsof the Ξ− hyperons within the target in the x-y planetransverse to the beam direction. The rectangles indi-cate the outlines of the four target segments. All foursegments are equipped with 12C absorbers.

produced events which contained a Ξ− with a labo-ratory momentum less than 500 MeV/c, 7396 hyper-ons are stopped within the secondary target. Themajority of the hyperons are stopped in the mostinner layers of the sandwich structure (Fig. 4.70).The typical momenta of these stopped Ξ− are inthe range of 200 MeV/c (see lower part of Fig. 4.71).

Recently Yamada and co-workers studied withinthe framework of the doorway double-Λ hypernu-clear picture [299] the production of double-Λ hy-pernuclei for stopped Ξ− particles in 12C [300]. Perstopped Ξ− they predict a total double-Λ hyper-nucleus production probability of 4.7%. An evenlarger probability of 11.1% was recently obtained byHirata et al. within the Antisymmetrised MolecularDynamics approach [301, 302]. Since the presentstudies concentrate on the production of doublehypernuclei, a full microscopic simulation of theatomic cascade and capture of the Ξ− hyperons isnot performed. For the final rate estimate we as-sume a Ξ−p → ΛΛ conversion probability of only


(GeV/c)z

longitudinal momentum P-0.1 0 0.1 0.2 0.3 0.4 0.5

(G

eV/c

)t

tran

save

rsal

mo

men

tum

P

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

5

10

15

20

25

30

35

40

(GeV/c)z

longitudinal momentum P-0.1 0 0.1 0.2 0.3 0.4 0.5

(G

eV/c

)t

tran

save

rsal

mo

men

tum

P

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

5

10

15

20

25

Figure 4.71: Transverse vs. longitudinal momen-tum distribution of Ξ− with transverse and longitudinalmomenta less than 500 MeV/c (upper part) and thosestopped within the secondary target (lower part).

5%. Of course for the study of hyperatoms the sim-ulations need to be complemented in this aspect.

4.5.2.3 Population of Excited States in DoubleHypernuclei

For light nuclei even a relatively small excitationenergy may be comparable with their binding en-ergy. Model calculations [303, 304, 284] show thatthe width for the conversion of a Ξ− and a protoninto two Λ’s is around 2–5 MeV, i.e. the conver-sion is rather fast and takes less than 100 fm/c.In this case we assume that the principal mecha-nism of de-excitation is the explosive decay of theexcited nucleus into several smaller clusters. To de-scribe this break-up process we have developed [305]a model which is similar to the famous Fermi modelfor particle production in nuclear reactions [306].In the microcanonical model we consider all possi-ble break-up channels, which satisfy the mass num-ber, hyperon number (i.e. strangeness), charge, en-ergy and momenta conservations, and take into ac-

count the competition between these channels. Pre-viously, this model was applied rather successfullyfor the description of break-up of conventional lightnuclei in nuclear reactions initiated by protons, pi-ons, antiprotons and ions [307, 308, 309, 310]. Theprecision was around 20–50% for the descriptionof experimental yields of different fragments. Thisprecision is sufficient for the present analysis of hy-pernucleus decay, since the main uncertainly is inunknown masses and energy levels of the producedhyperfragments.

For double hypernuclei the experimental informa-tion is restricted to a few cases only [311, 312, 313,314, 315]. Except for the 6

ΛΛHe nucleus reported inRef. [315] the interpretation of the observed eventsis however not unique [311, 316, 317, 318, 319].Furthermore no direct experimental information onpossible excited states is at hand (see e.g. discus-sion in Ref. [318]). Therefore, theoretical predic-tions of bound and exited states of double hyper-nuclei by Hiyama and co-workers [318] were used inthe present model calculation for nuclei with massnumber 6≤ A0 ≤10. For the mirror nuclei 5

ΛΛH and5ΛΛHe there seems to be a consensus that these nu-clei are indeed bound [292, 294, 320, 321, 322]. Inview of the theoretical uncertainties, we assumedin our calculations a value for the Λ-Λ bond en-ergy ∆BΛΛ=1 MeV for both nuclei. In case of 4

ΛΛHthe experimental situation is ambiguous [314, 319]and also the various model calculations predictan unbound [323] or only slightly bound nucleus[324, 325, 322].

Also for heavier nuclei several particle stable excitedstates are expected [300]. The ground state mass ofthese double hypernuclei was estimated from theknown masses of single hypernuclei and adopting afixed value for ∆BΛΛ of 1 MeV. Furthermore, thecalculations of Hiyama and co-workers [318] signalthat in the mass range relevant for this work thelevel structure of particle stable double hypernu-clei resembles the level scheme of the correspondingcore nucleus. The excitation spectrum of doublehypernuclei with A≥11 was therefore assumed tobe given by that of the corresponding core nucleus.Only states below the lowest particle decay thresh-old were considered in the present calculations.

For hypernuclei with a single Λ particle, we use theexperimental masses and excited states which aresummarised in various reviews (e.g. Ref. [326, 278]).In case of the production of conventional nuclearfragments in a break-up channel, we adopt theirexperimental ground states masses, and take intoaccount their excited states, which are stable re-spective to emission of nucleons (see nuclear tables,


e.g. [327]). Masses of fragments in excited stateswere calculated by adding the corresponding exci-tation energy to their ground state masses.

10-4

10-3

10-2

10-1

100

-25 -20 -15 -10 -5 0

Yie

ld p

er e

vent

Ξ- Binding energy [MeV]

12C target

DHP g.s.DHP ex. s.

SHP g.s.SHP ex.s.

THP g.s and g.s.THP g.s and ex. s.

THP ex. s.

Figure 4.72: Production probability of ground (g.s.)and excited states (ex.s.) in conventional nuclear frag-ments and in one single (SHP), twin (THP) and dou-ble hypernuclei (DHP) after the capture of a Ξ− in a12C nucleus and its conversion into two Λ hyperons pre-dicted by a statistical decay model.

The main reaction which we analyse is the break-upof an excited hypernucleus with double strangenessproduced after absorption of stopped Ξ−. Unfor-tunately, the excitation energies of the producedhypernuclei are not well known, since this conver-sion may happen at different energy levels, anda part of the released energy may be lost. Themaximum energy available in this case is Emax =(M(Ξ−)+Mtarget)c2. In order to take into accounta possible reduction of this energy because of theΞ− binding the calculations were performed for arange of energies less than Emax.

The Fermi break-up events were generated by com-paring probabilities of all possible channels withMonte–Carlo methods. The Coulomb expansionstage was not considered explicitly for such lightsystems. The momentum distributions of the fi-nal break-up products were obtained by a randomgeneration over the whole accessible phase space,determined by the total kinetic energy, taking intoaccount exact energy and momentum conservationlaws. For this purpose we applied a very effectivealgorithm proposed by G.I. Kopylov [328].

Fig. 4.72 shows as an example the production ofground (g.s.) and excited (ex.s.) states of conven-tional nuclear fragments as well as single (SHP),twin (THP) and double (DHP) hypernuclei in caseof a 12C target as a function of the assumed Ξ−

binding energy. According to these calculations ex-cited states in double hypernuclei (green triangles)

10-3

10-2

10-1

-25 -20 -15 -10 -5 0

Ξ- Binding energy [MeV]

8Λ ΛLi

10-3

10-2

10-1

9Λ ΛLi

10-3

10-2

10-1 9Λ ΛBe

ground s.1st ex.s.2nd ex.s.3nd ex.s.

10-3

10-2

10-1 Y

ield

per

eve

nt

10Λ ΛBe

10-3

10-2

10-1

11Λ ΛBe

10-3

10-2

10-1

12Λ ΛBe

10-3

10-2

10-1

12C target

12Λ ΛB

Figure 4.73: Excited states in 11ΛΛBe, 10

ΛΛBe and 9ΛΛLi

dominate over a wide range of the Ξ− binding energy.

are produced with significant probability. Fig. 4.73shows the population of the different accessible dou-ble hypernuclei. For the 12C target, excited statesin 11

ΛΛBe, 10ΛΛBe and 9

ΛΛLi dominate over a wide rangeof the assumed Ξ− binding energy.

Very little is established experimentally on the in-teraction of Ξ hyperons with nuclei. Various anal-yses (see e.g. [329, 330]) suggest a nuclear poten-tial well depth around 20 MeV. Calculations of light


Ξ atoms [331] predict that the conversion of thecaptured Ξ− from excited states with correspond-ingly small binding energies dominates. In a nu-clear emulsion experiment a Ξ− capture at rest withtwo single hyperfragments has been observed [332]which was interpreted as Ξ− + C →4

Λ H +9Λ Be

reaction. The deduced binding energy of the Ξ−

varied between 0.62 MeV and 3.70 MeV, dependingwhether only one out of the two hyperfragments orboth fragments were produced in an excited particlestable state. Therefore for the present simulation ofthe γ-ray spectra a Ξ− binding energy of 4 MeV wasadopted. As can be seen from Fig. 4.73 this choiceof the binding energy is not crucial for the final γ-ray yield.

4.5.2.4 Gamma Detection

In the next step the excited particle stable statesof double hypernuclei as well as excited states ofconventional nuclei and single hypernuclei producedduring the decay process de-excite via γ-ray emis-sion. For the high resolution spectroscopy of excitedhypernuclear states a position sensitive Germaniumγ–array [333] has been implemented in the stan-dard PANDA framework PandaRoot(see Fig. 2.8).To describe the response of these detectors, pro-cesses which are relevant for the interaction of theemitted photons with matter such as pair produc-tion, Compton scattering and the photoelectric ef-fect have been taken into account.

Gamma-ray Energy (MeV)0 1 2 3 4 5 6 7 8 9 10

dN

/dE

0

10

20

30

40

50

60 Total energy spectra

Figure 4.74: The statistics of the simulations corre-sponds to a data taking time of about two weeks.

Fig. 4.74 shows the total energy spectrum summedover all germanium detectors for all events where

a Ξ− has been stopped in the secondary target.Note, that the size of the bins (50keV) in thisplot is significantly larger than the resolution ofthe germanium detectors expected even for highdata rates at normal conditions (3.4 keV at 110 kHz[334]). Even after 100 days of operation at PANDAand an integrated neutron fluence of about 6·109

neutrons/cm2, we expect a degradation of the res-olution by less than a factor of 3 to no more than10 keV [335]. Several peaks seen in the spectrumaround 1, 1.68 and 3 MeV are associated with γ-transitions in various hypernuclei. However, for aclear assignment of these lines obviously additionalexperimental information will be needed.

4.5.2.5 Weak Decays of Hypernuclei

For the light hypernuclei relevant for the plannedexperiments the non-mesonic and mesonic decaysare of similar importance. In the following we willfocus on the case of two subsequent mesonic weakdecays of the produced double and single hyper-nuclei. For the light nuclei discussed below thisamounts to about 10% of the total decay width (seeFig. 4.68). Since the momenta of the two pions arestrongly correlated their coincident measurementprovides an effective method to tag the productionof a double hypernucleus. Moreover, the momentaof the two pions are a fingerprint of the hypernu-cleus respective its binding energy.

In PANDA the pions are tracked in the silicon stripdetectors of the secondary target. In the presentconfiguration silicon strip detectors with a pitch of100µm and a two-dimensional readout are imple-mented. For the reconstruction the standard soft-ware package of PANDA was applied. Since mostΞ− stop in the first few millimetres of the secondarytarget, the efficiency for tracking both pions pro-duced in the subsequent weak decays is rather high.After the statistical decay of the 7396 produced ex-cited Ξ− hypernuclei, 14883 charged tracks are re-constructed out of which 8133 tracks are assignedas a π− candidate.

The upper part of Fig. 4.75 shows the momentumcorrelation of all negative pion candidates from thesecondary 12C target. The various bumps corre-sponding to different double hypernuclei are markedby different colours. The good separation of the dif-ferent double hypernuclei provides an efficient selec-tion criterion for their decays.

The lower parts of Fig. 4.75 show the γ-ray spec-tra gated on the four regions indicated in the two-dimensional scatter plot. In the plots (a) and (d)the 1.684 MeV 1

2

+ and the 2.86 MeV 2+ states of


(GeV/c)HighP0.04 0.06 0.08 0.1 0.12 0.14

(G

eV/c

)L

ow

P

0.04

0.06

0.08

0.1

0.12

0.14 ΛΛ11 Be

ΛΛ9Li

Λ4+HΛ

9Be

ΛΛ10 Be


coun

ts

0

2

4

6

8

10

12

14

BeΛΛ

11a) BeΛΛ

11a)


coun

ts

0

2

4

6

8

10

12

14

LiΛΛ

9b) LiΛΛ

9b)


coun

ts

0

2

4

6

8

10

12

14

HΛ4Be +

Λ9d) HΛ

4Be +Λ9d)


coun

ts

0

2

4

6

8

10

12

BeΛΛ

10d) BeΛΛ

10d)

Figure 4.75: The expected γ-transitions energies fromsingle and double hypernuclei are marked by the arrows.

11ΛΛBe and 10

ΛΛBe, respectively, can clearly be identi-fied. Because of the limited statistics in the presentsimulations and the decreasing photopeak efficiencyat high photon energies, the strongly populatedhigh lying states in 9

ΛΛLi at 4.55 and 5.96 MeV can-not be identified in (b). The two dominant peaksseen in part (c) result from the decays of excitedsingle hyperfragments produced in the Ξ− +C →4

Λ

H +9Λ Be reaction, i.e. 4

ΛH at an excitation energyof 1.08 MeV [336, 337] and 9

ΛBe at an excitationenergy of 3.029 and 3.060 MeV [338, 339].

In the present simulation several intermediate steps,which do not effect the kinematics and hence thedetection of the decay products, have not been con-sidered on an event-by-event basis. Of course, these

points are relevant for the final expected count rate:

• a capture and conversion probability of the Ξ−

of 5-10%.

• typical probability of a double mesonic decayof 10% (c.f. Fig. 4.68).

• availability of data taking 50% .

With these additional factors taken into account,the spectra shown in Fig. 4.75 correspond to a run-ning time at PANDA of about two weeks. It isalso important to realise that gating on double non-mesonic weak decays or on mixed weak decays maysignificantly improve the final rate by up to a factor10.

4.5.2.6 Background

theta(degree)0 20 40 60 80 100 120 140 160 1800

200

400

600

800

1000

1200protons

kaons

pions

neutrons

Figure 4.76: The Germanium detectors will be af-fected mainly by particles emitted at backward axialangle.

Incident kinetic energy (GeV)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

dN

/dE

0

10

20

30

40

50

60

70

80

90

100

neutrons

protons

Figure 4.77: The main contribution to a possible ra-diation damage of the detector is provided by neutrons.


Particles produced simultaneously with the doublehypernuclei do not significantly disturb the γ-raydetection. The main limitation is the load of theCluster–array by the high particles rate from uncor-related background reactions. The pp→ Ξ−Ξ crosssection of 2µb is about a factor 2500 smaller thanthe inelastic pp cross section of 50mb at 3 GeV/c.Charged particles and low energy neutrons whichare emitted into the region covered by the Ge de-tectors will undergo electromagnetic and nuclear in-teractions and will thus contribute to the signal ofthe detector. The total energy spectra in the crys-tal has been obtained summing up event by eventthe energy contributions of the particles impingingon the Ge array.

Background reactions have been calculated by us-ing the UrQMD+SMM [340] event Generator. Atpresent, it is not possible to simulate the detec-tor response for a sample of unspecific backgroundevents which is large enough to test backgroundsuppression in all details. The background suppres-sion and signal detection capability can thereforeonly be estimated by using extrapolations basedon simplified assumptions. For the present analysis10000 p +12 C interactions at 3 GeV/c were gener-ated. Most of the produced charged and neutralsparticles are emitted into the forward region notcovered by the Germanium array (see Fig. 4.76).Charged particles emitted into backward axial an-gles are very low in kinetic energy, and will be ab-sorbed to a large fraction in the material surround-ing the primary target. More critical are neutronsemitted into the backward direction which also con-tribute to the radiation damage of the detector.Fig. 4.77 shows the kinetic energy distribution ofprotons and neutrons entering the surface of theGermanium detectors.

The total energy spectra resulting from the back-ground simulation have been filtered by using thesame technique as it was done for the signal events.Particularly the same cuts on correlated pion candi-dates have been applied to the background events,in order to obtained the corresponding backgroundspectrum for each of the hypernuclei channels. For11ΛΛBe as well as 10

ΛΛBe only one single event survivedthe cuts. Both of these events had an energy depo-sition in the germanium detector exceeding 10 MeVsignificantly.

Several further improvements of the backgroundsuppression are expected by exploring the topologyof the sequential weak decays. This includes theanalysis of tracks not pointing to the primary tar-get, multiplicity jumps in the detector planes andthe energy deposition in the secondary target. Fur-

thermore kaons detected in the central detector ofPANDA at forward angles can be used to tag the Ξproduction.


4.6 The Structure of theNucleon UsingElectromagnetic Processes

4.6.1 Partonic Picture of HardExclusive pp-AnnihilationProcesses

Introduction

A wide area of the physics program of PANDAconcerns studies of the non-perturbative region ofQCD. However, the experimental setup foreseen of-fers the opportunity to study also a certain classof hard exclusive processes that give insight intoan intermediate region, which marks the transitiontowards increasingly important perturbative QCDeffects.

In the recent years, the theoretical framework ofgeneralised parton distributions (GPDs) has beendeveloped, which allows treating hard exclusive pro-cesses in lepton scattering experiments on a firmQCD basis [341, 342, 343, 344]. This is possibleunder suitable conditions where one can factoriseshort and long distance contributions to the reac-tion mechanism. Being related to non-diagonal ma-trix elements, GPDs do not represent any longera mere probability, but rather the interference be-tween amplitudes describing different parton con-figurations of the nucleon, thus giving access tovarious momentum correlations. Their importancewas first stressed in studies of deeply virtual Comp-ton scattering (DVCS)[345, 346, 347], for which itcould be rigorously proven that the QCD handbagdiagram (see Fig. 4.78) dominates the process in

p

γ∗ γq

soft

hardx− ξ

e´

e

x+ ξ

p´GPD

Figure 4.78: DVCS can be described by the hand-bag diagram, as there is factorisation between the upper‘hard’ part of the diagram which is described by pertur-bative QCD and QED, and a lower ‘soft’ part that isdescribed by GPDs.

certain kinematical domains and that factorisationholds, i.e. that the process is divided into a hardperturbative QCD process and a soft part of thediagram which is parametrised by GPDs. The ap-plication of perturbative QCD is possible in DVCSdue to the hard scale defined by the large virtualityQ2 of the exchanged photon. A second example forthe application of the handbag formalism is wideangle Compton scattering (WACS). Here the hardscale is related to the large transverse momentumof the final state photons.

The important question which arises is whether theconcepts that are used in lepton scattering exper-iments have universal applicability and can there-fore be used in studies of pp-annihilation processeswith the crossed kinematics. The crossed diagramof WACS is the process pp → γγ with emission ofthe two final state photons at large polar angle inthe CM system (see Fig. 4.79). It can be shown that

p γ

p γ

GD

A

Figure 4.79: The handbag diagram may describe theinverted WACS process pp→ γγ at PANDA energies.

the handbag approach is not appropriate to describethe crossed channel WACS neither at very small norat very large energies [348, 349]. However, thereare strong arguments and first experimental indica-tions that the handbag approach is appropriate atthe intermediate energy regime where PANDA op-erates [350, 351], even though a rigorous proof offactorisation has not been achieved yet. The corre-sponding amplitudes that parametrise the soft partof the annihilation process (i.e. the counterpartsof GPDs) are called generalised distribution ampli-tudes (GDAs). The measurement of the processpp→ γγ as a function of s and t is an experimentalchallenge, due to the smallness of the cross section.The high luminosity and the excellent detector, es-pecially the 4π electromagnetic calorimeter, shouldenable PANDA to separate this process from thelarge hadronic background.


A second, much more abundant process that canbe described in terms of handbag diagrams is pp→π0γ. In contrast to WACS, in this case one pho-ton is replaced by a pseudo-scalar meson, but oth-erwise the theoretical description is similar. Firstexperimental results from the Fermilab experimentE760 indicate that the handbag approach is ap-propriate to accommodate the data in the ranges ∼ 8.5− 13.5 GeV2 [350].

The handbag approach (i.e. the factorisation as-sumption) is suitable for the description of furtherreactions, like pp → Mγ where M is any neutralmeson (e.g. a ρ0) or pp → γ∗γ, where γ∗ decaysinto an e+e−- or µ+µ−-pair. The latter process isdescribed by the crossed diagram of DVCS. Unfor-tunately, the factorisation proof in DVCS γ∗p→ γpis not applicable for the crossed diagram pp→ γ∗γ,as the virtuality Q2 of the final state γ∗ is limitedto be smaller than s, in contradiction to the as-sumption made in the proof of factorisation of thisdiagram in DVCS kinematics.

In a complementary theoretical approach, the pro-cess pp→ γ∗γ is not described by the handbag dia-gram but by so-called transition distribution ampli-tudes (TDAs) [352, 353] that parametrise the tran-sition of a proton into a (virtual) photon accordingto the diagram in Fig. 4.80. In a similar way theexclusive meson production pp → γ∗π0 can be de-scribed (see Fig. 4.108).

P

P

q

p

u u d

γ∗

γ

~p ′

~q ′

e−

e+

TDA

Figure 4.80: The production of a hard virtual photon(upper part) is a hard sub-process that factorises fromthe lower part, which can be described by a hadron tophoton transition distribution amplitude (TDA).

The theoretical understanding of GPDs and relatedunintegrated distributions is just at its beginning.There is an extended experimental endeavour bylepton scattering experiments at DESY, CERN andJLAB to get access to these powerful distributions.PANDA has the chance to join this quest for an

improved description of the nucleon structure bymeasuring the crossed-channel counterparts of thesedistributions in hard exclusive processes with vari-ous final states in a new kinematical region. Newinsights into the applicability and universality ofthese novel QCD approaches can be expected.

Crossed-Channel Compton Scattering

It has been argued [354] that the crossed-channelCompton scattering, namely exclusive proton-antiproton annihilation into two photons, pp→ γγcan also be described in a generalised parton pic-ture at large s with |t|, |u| ∼ s. The two photonsare predominantly emitted in the annihilation of asingle “fast” quark and antiquark originating fromthe proton and antiproton. The new double dis-tributions, describing the transition of the pp sys-tem to a qq pair, can be related to the timelikenucleon form factors; by crossing symmetry theyare also connected with the usual quark/antiquarkdistributions in the nucleon. With a model for thedouble partonic distributions one can compute thepp → γγ amplitude from the handbag graphs ofFig. 4.79. The result for the helicity-averaged dif-ferential cross section is

dσ

d cos θ=

2πα2ems

R2V (s) cos2 θ +R2

A(s)sin2 θ

(4.47)

with the energy dependency of the squared formfactors R2

V (s) and R2A(s) depicted in Fig. 4.81.

Figure 4.81: The squared form factors R2V (s) (solid

line) and R2A(s) (dashed line), as calculated from the

double distribution model (Fig. 2 of ref. [354])

Recent measurements of the time-reversed processγγ → pp by the BELLE collaboration [351] tendto confirm the predicted asymptotic behaviour athigher energies, however at intermediate energies(2.5 – 4 GeV) they can not be entirely explained bythe existing theoretical models.


Hard Exclusive Meson Production

Besides detecting pp → γγ, hard exclusive mesonproduction, like pp → γπ0, can also provide valu-able information about the structure of the proton.In treating this process, one can adopt as start-

p

p γ

π0

GD

A

Figure 4.82: The blob on the right hand side repre-sents the parametrised general dynamics for qq → γπ0

ing point the assumption of the handbag factori-sation of the amplitude for the kinematical regions,−t,−u Λ2 (see Fig. 4.82), where Λ is a typicalhadronic scale of the order of 1 GeV, as in [350]. Acomparison with existing Fermilab E760 data [355]concerning both the energy dependence of the inte-grated cross section and angular distribution of thedifferential cross section makes it possible to have areliable prediction for the differential cross sectionof pp→ γγ at PANDA, as shown in Fig. 4.83.

!"# !"$ !"% !"& !"& !"% !"$ !"#!!"!'!"!(!"!)!"!*

,-

!! . '! /01 ! "# "2"3" # $$4

Figure 4.83: Cross section prediction for the angulardistribution at s = 20 GeV2 for PANDA taken fromref. [350] .

There is also an approach to describe hard exclusivemeson production by transition distribution ampli-tudes for reactions like pp→ γ∗π0 → e+e−π0. De-tails are described in ref. [356].

Simulation of pp→ γγ and pp→ γπ0

In order to test the possibility of detection of boththe pp → γγ and pp → γπ0 reactions, MonteCarlo simulations were run within the PANDARootframework. The main goal of these studies was toestimate the ability of the PANDA detector systemto separate useful physics events from the back-ground.

The main background for the crossed channelCompton scattering pp → γγ comes from reac-tions with neutral hadrons in the final states, likepp → π0π0 or pp → γπ0. After a comparison ofthe various cross sections of interest at PANDA en-ergies, given in Fig. 4.84, it can be concluded that

[GeV]s2.5 3 3.5 4 4.5 5

[nb

arn

]to

tσ

-310

-210

-110

1

10

210

in cms° >53θ

π0 π0

π γ0

BELLEγγηc

Figure 4.84: The results correspond to particles with| cos(θ)| < 0.6 in the centre of mass system (Refs. [357,350, 351]).

the number of the exclusive background events con-sidered is roughly three (respectively two) orders ofmagnitudes higher than the number of the eventsof interest. This result has been taken into accountall along our studies.

The background has a significant constituent orig-inating in reactions with charged particles in thefinal states. These events are supposed to be ve-toed by the detector subsystems that are sensitiveto charged particles, however a systematic study ofthem was not yet performed.

In order to test the detector response, γγ, π0γ andπ0π0 events were generated using EvtGen. For theangular distribution of γγ events Eq. 4.47 fitted tothe BELLE data [351] was used, for π0γ results sim-ilar to the one in Fig. 4.83 in [350] were consid-ered, the π0π0 distribution follows the one given


by Ong and Van de Wiele [357]. The centre ofmass angle of the generated particles was limitedby | cos(θ)| < 0.6.

)θcos(-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

)θN

/co

s(

1

10

210

310

410

510

610 0π0π

γ0π γγ

) | < 0.6θGenerated: | cos(

Figure 4.85: Angular distribution of generated parti-cles in the centre of mass system, as seen by the detec-tor.

Fig. 4.85 gives the distribution of reconstructedevents in the electromagnetic calorimeter. The in-fluence of the asymmetric detector system is clearlyvisible, which introduces a difference between theangular distribution of particles moving in forwardor backward direction. Noticeably, detected parti-cles seem to be found also outside the | cos(θ)| < 0.6angular limit, a feature caused by the finite digiti-sation in the detector.

For the reconstruction of γγ events the followingalgorithm was used:

• Identify all the bumps in the electromagneticcalorimeter and order them according to theirenergy in the centre of mass system.

• Associate single photons with the first twobumps of highest cms-energy.

• Evaluate the kinematic factor

Kγγ ∼√|~pp − ~pγ1 − ~pγ2 |2 + |EL − Eγ1 − Eγ2 |2

×

1√~p2γ1

+ E2γ1

+1√

~p2γ2

+ E2γ2

(4.48)

Events with γπ0 in the final state are reconstructedin a slightly different way:

• Order the bumps in the EMC as above.

• Associate a single photon to the first one, thephotons from π0 to the next two of them.

• Evaluate the kinematic factor Kγπ0 similar toEq. 4.48

First a comparison of the kinematic factors for thesignal and background is performed, followed by acut on the value of the kinematic factor in orderto further eliminate possible misidentifications. Fi-nally, a cut on the number of hits in the EMC isapplied to differentiate between photons and pions.

In Fig. 4.86 and 4.87 preliminary results on the sep-arability of γγ, γπ0 and π0π0 events are presented.Four different pp centre of mass energies (

√s = 2.5,

3.5, 4 and 5.5 GeV) were considered, and for all en-ergies events of the type γγ, π0γ and π0π0 weregenerated in the | cos(θ)| < 0.6 angular interval.A full simulation of the detector system was per-formed and the event recognition algorithms withthe corresponding cuts were applied.

(GeV)s2.5 3 3.5 4 4.5 5 5.5

%

0

5

10

15

20

25

-eventsγγEvents left after Separation looking for

% γγ % x1000πγ % x10000π0π

Figure 4.86: Separation of γγ events from the neu-tral background γπ0 and π0π0 is possible using MonteCarlo corrections. The number of misidentified γπ0

(π0π0) events and their statistical error were magni-fied by a factor 102, (103) to match the limited MonteCarlo statistics to the abundance of the background inthe experiment.

To obtain a realistic picture, the ratio of the crosssections (see Fig. 4.84) for the various processes in-volved must be taken into account, when evaluatingthe possibility of detecting an useful physics signal.Therefore, lacking the necessary Monte Carlo statis-tics, the numbers of π0γ and π0π0 events misiden-tified as γγ have to be multiplied by factors of 100and 1000, respectively (see Fig. 4.86). A similarapproach was taken while identifying π0γ events(Fig. 4.87). In this case the number of misiden-tified π0π0 events were multiplied only by a factorof 10.

After this selection and normalisation, the γγ sig-nal is at the same level as the pion background,which means that the extraction of cross sectionsfor this class of events should be possible by the useof Monte Carlo corrections over the full kinematical


range of PANDA. The studies are still very prelimi-nary and only simple cuts were applied, so that weare positive that more sophisticated cuts in futurewill improve the situation.

The separation of exclusive γπ0 events is clearlypossible over the full energy range after applyingthe above simple cuts as shown in Fig. 4.87.

(GeV)s2.5 3 3.5 4 4.5 5 5.5

%

10

20

30

40

50

-events0πγEvents left after Separation looking for

Events0πγ

Events % x100π0π

Figure 4.87: Separation of γπ0 events from the neutralbackground. The number of misidentified π0π0 eventsand their statistical error were magnified by a factor 10.

Conclusions

First simulation results of the processes pp → γγand pp → γπ0 suggest that these interesting ex-clusive reactions can be successfully measured atPANDA. The performance of the EMC plays a cru-cial role for the measurement of these processes. Amore detailed study of the event recognition algo-rithms and the applied cuts, as well as consider-ably increased Monte Carlo statistics are requiredfor more precise predictions.


4.6.2 Transverse Parton DistributionFunctions in Drell-YanProduction

Theoretical Introduction

In a Drell-Yan (DY) process p(↑)p(↑) → µ+µ−X two(eventually polarised) hadrons H1 and H2 annihi-late into a lepton-antilepton pair ll; hadrons carrymomenta P1 and P2 respectively (P 2

1,2 = M21,2) and

spins S1, S2 (S1,2 · P1,2 = 0), the ll momenta be-ing k1, k2 (k2

1,2 ∼ 0). Relevant kinematic variablesare the initial squared energy in the centre-of-mass(CM) frame s = (P1 + P2)2, and the time-like mo-mentum transfer q2 ≡ Q2 = (k1 + k2)2 ≥ 0 directlyrelated to the final state invariant mass (Q2 ≡M2

ll).

In the DIS regime, defined by the limit Q2, s→∞(0 ≤ τ = Q2/s ≤ 1), a DY process can be de-scribed factorising an elementary annihilation pro-cess qq → ll with two soft correlation functions de-scribing the annihilating antiparton (1) and parton(2) distributions in the parent hadrons:

Φ(p1;P1, S1) =∫d4z

(2π)4e−ip1·z 〈P1S1|ψ(z) ψ(0)|P1, S1〉 ,

Φ(p2;P2, S2) = (4.49)∫d4z

(2π)4eip2·z 〈P2, S2|ψ(0)ψ(z)|P2, S2〉 .

The dominant contribution in leading order is de-picted in Fig. 4.88 [358], provided that M is con-strained inside a range where the elementary anni-hilation can be safely assumed to proceed througha virtual photon converting into the final ll.

At Q2 → ∞ the parton momenta p1,2 are ap-proximately aligned with the corresponding hadronand antihadron momenta P1,2, the correspondinglight-cone fractions of the parton momenta beingx1,2 = p1,2

P1,2' Q2

2P1,2·q (q = p1,2, by momentum con-servation [359]); momenta p1,2T (often addressedin the literature as k⊥), the intrinsic transverse-momenta of the partons in the parent hadron w.r.t.the axis defined by the corresponding hadron 3-momentum Ps1,2, are bound by the momentumconservation q

T= p1T +p2T , where q

Tis the trans-

verse momentum of the final lepton pair.

Figure 4.88: The leading-twist contribution to theDrell-Yan dilepton production [358]; the correlationfunctions for the annihilating hadrons Φ and Φ can beparametrised considering explicitly their dependence onthe transverse parton momenta p1T and p2T [360], thusleading to Eq. 4.52.

Since in semi-inclusive processes the annihilationdirection is not known and a convenient refer-ence frame is needed; the Gottfried-Jackson (GJ)frame and the u-channel frame being other popularchoices, the most commonly adopted frame is theso called Collins-Soper frame [361] (see fig. 4.89),defined by:

t =q

Q, z =

x1P1

Q− x2P2

Q, h =

qT

|qT| (4.50)

where azimuthal angles lie in the plane perpendic-ular to t and z: φ and φS1,2 are respectively theangles of h and of the nucleon spin S1,2T with re-spect to the lepton plane.

Figure 4.89: The Collins-Soper (CS) frame [361].

In the so-called collinear kinematics approach(p1,2T ∼ 0, i.e. neglecting dependencies on the k⊥),at leading twist (i.e. twist-two) the quark struc-ture of an hadron can be described by three PartonDistribution Functions (PDF): the number densityf1(x) (a.k.a. unpolarised distribution), the longitu-dinal polarisation distribution g1(x) (a.k.a. helicitydistribution) and the transverse polarisation h1(x)


(a.k.a. Transversity). The density function f1(x) isthe probability of finding a quark with fraction x ofthe parent hadron longitudinal momentum, regard-less of its spins orientation; g1(x) describes the he-licity of a quark in a longitudinally polarised quark,i.e. the asymmetry between the number densitiesof the quarks with a given momentum fraction xand with spins parallel and antiparallel to the par-ent hadron spin; the Transversity h1(x) describesthe asymmetry between the number densities of thequarks with a given momentum fraction x and withspins parallel and antiparallel to that of a trans-versely polarised hadron. The latter PDF has noprobabilistic interpretation in the helicity basis, andbeing chirally odd it could not be observed in thehistorical DIS experiments. This is the reason whywhile the former two PDF’s have been studied atgreat length, the Transversity h1(x), historically in-troduced right for DY processes [358], has been ne-glected for a very long time and rediscovered only inthe beginning of the 90’s [362], yet being a leading-twist distribution [358, 362, 363]. The current PDFnomenclature has been introduced by Jaffe and Ji[364] and reflects the leading-twist nature of thethree considered PDF’s (the 1 subscript). The threePDF’s are linked by the well-known Soffer inequal-ity (2|h1| ≤ (f1 + g1)) [365].

In collinear kinematics a factorised pQCD approachcannot interpret even the experimental unpolarisedcross sections for inclusive particle production inhigh-energy hadron-hadron production [366]; onlyrecently NLO calculations including threshold re-summation effects have been developed [367], inreasonable agreement with inclusive cross sectionsintegrated over the hadron rapidity range, but therapidity-dependent case is still under investigation.The collinear kinematics approach is also not suit-able to describe the DY production at low lepton-pair transverse momentum: no transverse momen-tum can be generated in the collinear LO approxi-mation.

The role of parton’s intrinsic transverse momentumhas thus to be explicitly accounted for; since theearly interest [368, 369] huge efforts have been ded-icated to provide a full set of Transverse-MomentumDependent (TMD) PDF’s and Fragmentation Func-tions (FF). The generalisation of the pQCD factori-sation theorem to the TMD scenario has been for-mally proved for the DY processes [361]; at lead-ing twist eight independent TMD PDF distribu-tions are needed to describe the nucleonic structureand the nucleonic correlator can be parametrisedas [360]:

Φ(x,pT , S) =12

f1 /n+ + f⊥1T

εµνρσγµnν+p

ρTS

σT

M+(SLg1L +

p⊥ · STM

g1T

)γ5/n+

+h1T iσµνγ5nµ+S

νT

(SLh

⊥1L +

p⊥ · STM

h⊥1T

)iσµνγ

5nµ+pνT

M+ h⊥1

σµνpµTn

ν+

M

,(4.51)

where n± are auxiliary light-like vectors, M is thenucleon mass, and all the TMD PDF’s depend onx and |p⊥| (e.g. f1 = f1(x,p2

T )). This form ofthe TMD approach is also addressed in the liter-ature as Generalised Parton Model (GPM). Sev-eral notations are used for the TMD’s nomenclature[370, 371]; in the one [372] adopted in Eq. 4.51, f ,g and h refer respectively to unpolarised, longitu-dinally polarised and transversely polarised quarks,to longitudinal and transverse hadron polarisation(subscripts L and T ), at leading twist (subscript1), explicitly dependent on intrinsic momenta (apex⊥). The three TMD PDF’s f1(x,p2

T ), g1L(x,p2T )

and h1T (x,p2T ), upon integration on p2

T yield re-spectively f1(x), g1(x) and h1(x); the other TMDPDF’s cancel out upon integration on p2

T .

The relevant TMD PDF’s for the physics programproposed at PANDA are: h⊥1 (a.k.a. Boer-Mulders,BM, function), the distribution of transversely po-larised partons in unpolarised hadrons; f⊥1T (a.k.a.Sivers function) and h1T (a.k.a. Transversity), thedistributions of respectively unpolarised and trans-versely polarised partons in a transversely polarisednucleon. These PDF’s will be described in detailsin the next sub-section, while reviewing the experi-mental data available from the literature and theirinterpretation.

It was stated before that the DY production at lowlepton-pair transverse momentum can not be in-terpreted in the framework of collinear kinematics;the energy evolution of the spin and TMD distri-butions had been discussed in [373] resumming the


large logarithms arising in perturbative calculationsfor SIDIS and DY process at low transverse mo-mentum. To extend the validity of the TMD fac-torisation approach from the very small qT rangeto the moderate transverse momentum region (yetwith qT Q) soft gluon radiation has to be ac-counted for by the mean of Sudakov factors includedby proper resummation; the outcome is a suppres-sion of the TMD azimuthal asymmetries that be-comes more important with rising energy [374].

It should be stressed that theoretical approachesother than the TMD formalism do exist; in par-ticular the one considering twist-three effects incollinear pQCD, whose origin dates back to [375],allows to evaluate the azimuthal asymmetries inthe framework of pQCD generalised factorisationtheorems with the introduction of new twist-threequark-gluon correlator functions convoluted withordinary twist-two parton distribution functionsand a short-distance hard scattering part; suchfunctions do not have a simple partonic interpre-tation, being expectation values between hadronicstates of three field operators. See Ref. [376] for amore detailed discussion of such functions and oftheir relation with SSA.

A comparison of the twist-three and of the TMD ap-proaches [377, 378, 379, 380] to SIDIS and DY pro-cesses shows how both mechanisms, yet having dif-ferent validity domains, describe the same physicsin the overlapping kinematic region. In the twist-three approach domain (large lepton pair transversemomentum and photon virtuality: qT , Q ΛQCD)

twist-three quark-gluon correlations can lead to thespin-dependent cross section; at qT ' ΛQCD Qsingle spin asymmetries (SSA) can be generatedfrom spin-dependent TMD quark distributions; inthe overlapping domain ΛQCD qT Q, qT islarge enough for the asymmetry to be a twist-threeeffect but at the same time a qT Q allows for theTMD factorisation formalism. The connections be-tween such different formalisms lead to strong con-straints on those phenomenological studies aimingat the dynamics underlying transverse SSA.

Experimental Data and TheoreticalInterpretations

We will focus herewith on the unpolarised andsingle-polarised DY processes, that can be accessedin the PANDA scenario respectively since the verybeginning and when a polarised target will eventu-ally become available; nevertheless double-polarisedDY processes will be shortly addressed as well, be-ing the most promising scenario to access transver-sity effects in the nucleon dynamics, even if in such acase an antiproton polarisation is needed, and sucha polarisation can eventually be provided only inlater FAIR stages.

The Unpolarised Case: pp→ l+l−XThe TMD leading-twist parametrisation of Φ andΦ [360] leads to the following fully differential crosssection for the unpolarised DY process [359]:

dσo

dΩdx1dx2dqT=

α2

12Q2

∑f

e2f

(1 + cos2 θ

)F[ff1 f

f1

]

+f sin2 θ cos 2φF[(

2h · p1T h · p2T − p1T · p2T

) h⊥ f1 h⊥ f1

M1M2

] , (4.52)

α being the fine structure constant, ef the chargeof a parton with flavour f . The TMD PDF’s are

convoluted with their antiparton partners accord-ing to:

F[ff1 f

f1

]≡∫dp1T dp2T δ (p1T + p2T − q

T)[ff1 (x1,p1T ) ff1 (x2,p2T ) + (1↔ 2)

]. (4.53)


Cross section (4.52), when considered differential in√τ and x

Fonly (τ = x1x2 and the Feynman param-

eter xF

= x1−x2) scales as d2σ/d√τdxf ∼ 1/s, in-

fluencing the choice of the kinematical set-up, whileafter integrating on all the kinematic variables butthe angular distribution, at leading order in αs be-comes:

1σo

dσo

dΩ=

34π

1λ+ 3

(1 + λ cos2 θ + (4.54)

+µ sin2 θ cosφ+ν

2sin2 θ cos 2φ

)In a naive parton model approach the assump-tion of massless quarks leads to a transversely po-larised virtual photon, so that λ = 1, µ = ν =0 and dσ/d cos θ ∼ 1 + cos2 θ; such predictionsare confirmed by both LO and NLO perturbativeQCD calculations [381]. The so called Lam-Tungrule [382, 383, 384] λ = 1 − 2ν, analogous to theCallan-Gross relation in DIS, should hold in any ref-erence frame and be unaffected by first-order QCDcorrections [384], even if it could be influenced byparton intrinsic motions and other ”soft” effects.

Experimental data from NA3 [385] and NA10 [386,387] Collaborations at CERN and from theE615 [388] Collaboration at Fermilab for muon pairsproduction with π− beams at different momenta(140÷286 GeV/c) on 2H and W targets have shownno evidence of a CM energy dependence or a nucleardependence of the angular distribution parametersλ, µ and ν. Data for the former two parameters,leading to λ ∼ 1 and µ ∼ 0 as predicted, are mostlyindependent of the considered kinematic region, ex-cept a slight reduction of λ at high x1 (the light-conefraction of the parton in the pion) that has been in-terpreted with higher-twist effects [389, 390]. Butthese experimental data show a relevant cos 2φ de-pendence with a deviation from zero for ν at highqT , depending on

√s, that tops at larger qT val-

ues ν ∼ 0.30 in CERN data [387] and ν ∼ 0.73 inFermilab data [388], clearly departing from pQCDexpectations. Other mechanisms, like higher twistsor factorisation breaking terms at NLO, are not ableto explain such a relevant violation of the Lam-Tungrelation [391, 392, 389].

This is not the case if we consider the TMD ap-proach, where the convolution of the two BM func-tions h⊥ f1 and h⊥ f1 in the last term of Eq. 4.52allows for a leading-twist (hence large) cos 2φ az-imuthal dependence [359]. Since the BM func-

tion describes the transverse polarisation of par-tons in unpolarised hadrons, it is intimately con-nected to the orbital motion of the parton insidethe hadron; the product h⊥1 h

⊥1 brings a change of

two units in the orbital angular momentum, lead-ing to an angular dependence on 2φ. The BMfunction is a chirally-odd PDF, it cannot be ex-tracted from DIS data [393], and can be accessedonly through its convolution with another chirally-odd quantity: itself (Eq. 4.52) in the unpolarisedDY, or the Transversity h1T in the single-polarisedDY (Eq. 4.56 of the next sub-section) [359].

Other mechanisms, like the role of QCD-vacuumstructure in hadron-hadron scattering [394, 381,395], has been considered as well, and more recentlythe cos 2φ azimuthal dependence of the unpolarisedDY process pp → µ+µ−X has been studied in thequark-diquark spectator approach [396].

Very recent data from E866/NuSea [397] Collabo-ration at FNAL for muon pairs production with a800 GeV/c proton beam on 2H haven’t shown anysignificant cos 2φ azimuthal dependence, constrain-ing thus those theoretical models predicting largerazimuthal dependencies originating from QCD vac-uum effects, and pointing toward an almost vanish-ing sea-quark BM function, much smaller than thatrelated to valence quarks [360].

Moreover contributions to a cos 2φ azimuthalasymmetry for DY dilepton production with(anti)nucleon on nuclear targets could arise fromthe nuclear distortion of the hadronic projectilewave function, typically a spin-orbit effect occurringon the nuclear surface [398]; this effect, expected tobe on the percent level, should be added to the oneoriginating from the elementary hard event.

The Single-Polarised Case: pp↑ → µ+µ−XWhen one of the annihilating hadrons is trans-versely polarised, in a TMD approach at leading-twist a further polarised term shows up in the crosssection:

dσ

dΩdx1dx2dqT=

dσo

dΩdx1dx2dqT+

d∆σ↑

dΩdx1dx2dqT(4.55)

where dσo/dΩdx1dx2dqT is the unpolarised crosssection defined in Eq. 4.52. The polarisedd∆σ↑/dΩdx1dx2dqT [359]:


d∆σ↑

dΩdx1dx2dqT=

α2

12sQ2

∑f

e2f |S2T |

(1 + cos2 θ

)sin(φ− φS2)F

[h · p2T

ff1 f⊥ f1T

M2

]

− sin2 θ sin(φ+ φS2)F[h · p1T

h⊥ f1 hf1TM1

](4.56)

− sin2 θ sin(3φ− φS2)F[(

4h · p1T (h · p2T )2 − 2h · p2T p1T · p2T − h · p1T p22T

) h⊥ f1 h⊥ f1T

2M1M22

]

depends explicitly on the Sivers function f⊥ f1T , onthe Transversity hf1T and on the BM function h⊥ f1T ;sum is extended on the parton flavour f .

Eq. 4.56 shows how a powerful tool can be theDrell-Yan production of muon pairs, since selectingthe proper angular dependence both the BM andthe Sivers functions can be accessed. A spin asym-metry weighted by sin(φ− φS2) leads to the convo-lution of f⊥ f1T with the known distribution ff1 in amechanism similar to the Sivers effect in DIS withlepton beams [399]. The asymmetry defined weight-ing for sin(φ+ φS2) leads to the convolution of hf1Twith h⊥ f1 in a mechanism similar to the Collins ef-fect [400]; since h⊥ f1 contribute at leading twist tothe unpolarised cross section as well (Eq. 4.52), acombined analysis of the cos 2φ and sin(φ+φS2) mo-ments of azimuthal asymmetries respectively in theunpolarised and in the single-polarised Drell-Yancross sections should allow for the determination ofboth PDF’s at the same time in a single experimen-tal scenario.

The Transversity distribution h1T is not diagonalin the parton helicity basis, since involves a helic-ity flipping mechanism at parton level. It is hencechirally-odd, since at leading twist chirality and he-licity are identical, and this is reason why it can-not be accessed in DIS as well: QED and QCDfor massless quarks conserve helicity, and thus h1T

pertains the ”soft” domain where the chiral symme-try of QCD is (spontaneously) broken. To be mea-sured in a (chirally-even) cross-section or asymme-try it needs another chiral-odd partner, in contrastwith the unpolarised and the helicity distributionfunctions, both chiral-even (see for a review alsoRefs. [401, 371]). In the transverse spin basis h1T

is diagonal and can be interpreted as the differencebetween the probabilities to find a quark polarisedalong the transverse proton polarisation and againstit. In a nucleon (and more generally in any spin 1

2hadron) it has no gluonic counterpart, due to themismatch in the change of helicity units, and its

evolution is hence decoupled from radiative gluons;it also decouples from charge-even qq configurationsof the Dirac sea, because it is odd also under chargeconjugation transformations. The prediction of itsweaker evolution [401] could represent a basic testof QCD in the non-perturbative domain.

The Sivers function f⊥1T (originally suggested in[402, 399]) is a T-odd chirally-even p⊥-odd dis-tribution describing how the distribution of unpo-larised quarks is affected by the transverse polar-isation of the parent proton. It appears at lead-ing twist in semi-inclusive DIS (SIDIS) processeslike lp↑ → l′πX [403] or pp↑ → πX [404], whereit is responsible of the so-called Sivers effect, theazimuthal asymmetric distribution of the detectedpions depending on the direction of the target po-larisation, since it is proportional [360, 370] to thefunction ∆Nf of Refs. [405, 406] (also addressedin the literature as ”Sivers function”). Its rele-vance for the PANDA physics program is related tothe azimuthal asymmetries in single-polarised DYpp↑ → l+l−X (Eq. 4.56): a measurement of a non-vanishing asymmetry would be a direct evidence ofthe orbital angular momentum of quarks [407].

The Sivers function was originally expected to van-ish [400] in DY, due to parity and time reversalinvariance in the light-cone gauge, but the role ofthe presence of Wilson lines had been reconsidered[408] since under time-reversal the future-pointingWilson lines are replaced by past-pointing Wilsonlines. The corresponding transverse gauge link isresponsible of the gauge invariance of TMD partondistributions [409] and at the same time of the at-tractive final state interactions (FSI) in SIDIS andof the repulsive initial state interactions (ISI) in DY[400, 410]. Since in the latter case the past-pointingWilson lines allow as well an appropriate factorisa-tion of the Drell-Yan process [408, 411], the correctresult is not a vanishing Sivers function in DY, butrather a Sivers function showing opposite signs in


SIDIS and in DY:

f⊥ f1T |SIDIS = f⊥ f1T |DY (4.57)

preserving hence the universality of the TMD spin-dependent PDF’s. Huge theoretical efforts havebeen aimed to investigate the role of the gauge linksin TMD distributions [412, 409, 413, 414, 373, 415],with a focus on the gauge invariance of the TMDPDF’s and on the proper QCD factorisation at lead-ing twist for SIDIS and DY processes; the evalua-tion of the Sivers function in the DY di-lepton pro-duction could allow for a strong test on the univer-sality of the TMD PDF’s.

As pointed out by theoretical predictions basedon the Sivers effect from SIDIS experimental data,large SSA are expected for DY processes at the largeenergy scale foreseen in the later phases of the FAIRproject [416, 417, 418, 416, 419], while the Siversasymmetry at RHIC could be measured only at highrapidity and should be strongly sensitive to the sea-quark Sivers distributions [419].

Two TMD mechanisms has been discussed untilnow, that could lead to transverse SSA’s in theDY process pp↑ → µ+µ−X: the Sivers effect andthe Boer-Mulders effect (which involves also theTransversity distribution); in such exclusive pro-cess, and this is the main advantage with respectto inclusive processes like pp → h + X, the mea-surement of the lepton-pair angular distribution au-tomatically allows to select one specific effect. Asystematic calculation of all leading-twist PDF’sin the nucleon has been performed in the frame-work of a diquark spectator model [420]. Butother mechanisms that could also generate SSA’sin the DY process had been proposed in the lit-erature [421, 422, 423, 424], based on higher twistquark-gluon correlation functions in a generalisedpQCD factorisation theorem approach [425]: insuch cases the asymmetries depend on the anglebetween the proton polarisation direction and thefinal lepton pair plane [361], and vanish upon cor-responding angular integrations.

The Sivers function f⊥1T has recently attracted thedeepest interests in the spin physics community.Besides being a T-odd TMD PDF, it describes howthe distribution of unpolarised quarks is distortedby the transverse polarisation of the parent hadron,and as such it contains information’s on the orbitalmotion of hidden confined partons and their spatialdistribution [426]. Besides, it offers a natural link

between microscopic properties of confined elemen-tary constituents and hadronic measurable quanti-ties, such as the nucleon anomalous magnetic mo-ment [427]. And the prediction of Eq. 4.57 is astrong test of the universality of TMD PDF’s.

Recently, very precise data for SSA involving f⊥1T(the Sivers effect) have been obtained for the SIDISprocess on transversely polarised protons [428, 429,430]. Three different parametrisation of f⊥1T [416,418, 431] have been extracted from the HERMESdata (see for a comparison among the various ap-proaches Ref. [432]), showing a relevant non zeroeffect. On the contrary COMPASS data for non-identified [433, 434] and identified hadrons [435]show small effects, compatible with zero withinthe statistical errors, interpreted in term of a can-cellation between the u- and d-quark contribu-tions [435, 436, 437, 438]. Although SIDIS databy HERMES and COMPASS do not constrain thelarge transverse momentum region, at lower trans-verse momentum they show a serious conflict aslong as Sivers effects are concerned, in particularconsidering the latest data from COMPASS [439]that show Sivers asymmetries compatible with zeroboth for positive and negative hadrons.

New efforts are in progress either to explain the nonzero Sivers effects in p− p collisions by the mean ofscalar and spin-orbit re-scattering terms [440], ei-ther to account for the new data from COMPASSupdating the present parametrisations [441]. An in-dependent evaluation of the Sivers distribution f⊥1Tin the single-polarised DY processes at FAIR wouldcertainly contribute to the present (and probablylong lasting) challenge to the spin physics commu-nity.

The Dream Option: p↑p↑ → µ+µ−XAlthough the Transversity h1T can be accessedin the single-polarised DY, convoluted with h⊥1(Eq. 4.56), the simplest scenario to extract theTransversity function h1T is the fully polarised DY,as originally proposed in Ref. [358]: it allows for adirect access to h1T , without its convolution withany other PDF, but it requires a reasonable an-tiproton polarisation; such a dream option couldbe accessed only in the very last stage of the FAIRproject, as proposed in [442] and in [443].

In a TMD approach at leading twist the fully po-larised cross section, after integrating upon dq

T,

becomes [444]:


dσ↑↑

dx1 dx2 dΩ=

α2

12q2

[(1 + cos2 θ)

∑f

e2f f

f1 (x1) ff1 (x2) + sin2 θ cos 2φ

ν(x1, x2)2

+|ST1 | |ST2 | sin2 θ cos(2φ− φ

S1− φ

S2)∑f

e2f h

f1T (x1)hf1T (x2) + (1↔ 2)

],(4.58)

where φSi

is the azimuthal angle of the transversespin of hadron i as it is measured with respect tothe lepton plane in a plane perpendicular to z andt of the CS frame (Fig. 4.89); the contribution from

h⊥ f1T is hidden in the function ν, while to access theTransversity distribution hf1T a double spin asym-metry can be defined:

ATT

=dσ↑↑ − dσ↑↓dσ↑↑ + dσ↑↓

= |ST1 | |ST2 |

sin2 θ

1 + cos2 θcos(2φ− φ

S1− φ

S2)

∑f e

2f h

f1T (x1)hf1T (x2) + (1↔ 2)∑

f e2f f

f1 (x1) ff1 (x2) + (1↔ 2)

(4.59)

The asymmetry depends at leading order onhf1T squared, without contribution from sea-quarkPDF’s nor convolution with fragmentation func-tions as in SIDIS, providing then the best possiblescenario to access Transversity.

The asymmetry in Eq. 4.59 could in principle beaccessed at RHIC as well, in the polarised DY pro-cess p↑p↑ → l+l−X, the first process suggested toaccess Transversity at leading order [358]. But insuch a case it would depend on sea-quark PDF’s,since it would involve the Transversity of an an-tiquark in a transversely polarised proton. More-over, NLO simulations in the RHIC CM energyrange [445, 446] have shown an ATT strongly sup-pressed by QCD evolution and by a Soffer boundon the percent level. On the contrary makinguse of the FAIR’s antiproton beams the asymme-try would involve Transversities of valence partonsonly [447, 448].

Total Cross SectionThe full expression of the leading-twist differentialcross section for the Drell-Yan H

(↑)1 H

(↑)2 → l+l−X

process can be found in the Appendix of Ref. [359]

The clear systematics in the literature showinga production of Drell-Yan pairs distributed with〈|qT |〉 > 1GeV/c and depending on

√s, suggests

that sizeable QCD corrections are needed beyond asimple Quark Parton Model (QPM) approach, sinceconfinement alone induces much smaller quark in-

trinsic transverse momenta. The involved higherorder Feynman diagrams typically show qq annihi-lations into gluons or quark-gluon scattering [388].Two main levels of approximation had been used inthe literature [449]. The first one is the so-calledLeading-Log Approximation (LLA), where the lead-ing logarithmic corrections to the DY cross sectioncan be re-summed at any order in the strong cou-pling constant αs, introducing in the PDF’s an ad-ditional scale dependence on M2

ll. The so-called

DGLAP evolution can be obtained by describingthe functions with parameters explicitly dependingon logM2 (see Ref. [450] and Apps. A, B and Din Ref. [388] for further details). The second ap-proximation level in the QCD higher order correc-tions, the so-called Next-to-Leading-Log Approxi-mation (NLLA), is performed including in the cal-culation all processes at first order in αs involv-ing a quark, an antiquark and a gluon [449], andleads to sizeable effects, approximately doublingthe pure QPM cross-section. Such a correctionsis roughly independent of x

Fand M2 (except for

the kinematical upper limits) and it is usually indi-cated as the K factor. K-factors depend on thechoice of the parametrisation of the distributionfunctions through their normalisation [451], andscale as

√τ [388].

The azimuthal asymmetries, which are defined asratios of cross sections, should be pretty robustw.r.t. such kind of QCD corrections, since the cor-rections in the numerator and in the denominator


should approximately compensate each other [445].

But this is not the case if we consider the(un)polarised cross-section. DY processes at highCM energy show reduced K-factors, but the rel-evant role of higher-order perturbative QCD cor-rections [452], in terms of the available fixed-order contributions as well as of all-order soft-gluon re-summations, leads to large enhancementsof the unpolarised DY dilepton production in thePANDA kinematic regime, due to soft gluon emis-sion near partonic threshold; the unpolarised crosssection for DY dilepton production at PANDA ener-gies is thus matter of investigation itself, and couldprovide information on the relation of perturbativeand non-perturbative dynamics in hadronic scatter-ing [452].

The PANDA Scenario

The unpolarised and the single-polarised Drell-Yanpp(↑) → µ+µ−X can be investigated with thePANDA spectrometer (the former case since the

very beginning, the latter if a polarised target wouldbe developed) and the HESR antiproton beam. Insuch a scenario a beam energy of 15 GeV on theprotons at rest in the fixed target can provide acentre of mass energy up to s ' 30 GeV2.

The handbag diagram of Fig. 4.88 is the dominantcontribution only for a CM energy s much biggerthan the involved hadron masses. Moreover the di-lepton mass Mll should not belong to the hadronicresonance region, in order to select for the elemen-tary process an annihilation into a virtual photon;this is the reason why the DY di-lepton productionis usually investigated in the so-called ”safe region”:4 GeV ≤Mll ≤ 9 GeV, between the ψ′ and the firstΥ resonance.

In the DIS regime we can define, in terms of thelight-cone momentum fractions, the parameter τ =x1x2 and the invariant x

F= x1 − x2 (fraction of

the total available longitudinal momentum in thecollision CM frame); the unpolarised cross sectiondσ0 of Eq. 4.52, kept differential in M2

ll≡ Q2 and

integrated upon dτ :

dσo

dM2dxF

=4πα2

91

M2s(x1 + x2)

∑f

e2f

[ff1 (x1) ff1 (x2) + (1↔ 2)

](4.60)

shows the scaling in the CM energy s experimen-tally confirmed [453] and the enhanced productionof di-lepton pairs at lower M2

ll.

In the PANDA scenario the upper limit of the ”saferegion” M < 9 GeV is beyond the accessible kine-matic region: since for a p beam on a p fixed targetis M2 = τ s = τ 2Mp(Mp + Ep) ∼ τ 2MpEp, evenconsidering the limit τ ∼ 1, i.e. the case in whichall the available CM energy is transferred to thevirtual photon, an M ∼ 9 GeV would correspondto an antiproton beam energy Ep ∼ 40 GeV. Thelower cut M > 4 GeV selects then a phase spaceregion 0.5 . τ . 1 limited to very high values ofboth x1 and x2. To release the constraint on thelower cut, the 1.5 GeV ≤ M ≤ 2.5 GeV portionof the di-lepton mass spectrum can be consideredas well: a region not overlapping the φ and J/ψresonances, that leads to two major benefits in thePANDA scenario: a wider accessible τ range (asshown in Fig. 4.90) and a larger cross section (seeEq. 4.60 and Ref. [454]).

The expected integrated cross section for pp →l+l−X at s = 30 GeV2 in the 1.5 GeV ≤ M ≤

2.5 GeV is σ01.5≤M≤2.5 ∼ 0.8 nb [454]; assuming the

design luminosity of the High Resolution mode (seeTab. 2.1 in Sec. 2.3.1) L = 2 · 1032 cm−2 s−1, theexpected rate for the DY production of µ-coupleswould hence be:

R = 2 · 1032cm−2 s−1 × 0.8 · 10−33cm−2 = 0.16 s−1

(4.61)The cross section at s = 30 GeV2 is expected todrop dramatically in the ”safe-region” to σ0

4≤M≤9 ∼0.4 pb [454]; since the resulting rate for the DY pro-cesses would be incompatible with a detailed inves-tigation in the PANDA framework, the focus willbe herewith on the 1.5 GeV ≤M ≤ 2.5 GeV regiononly.

Simulations

The investigation of the (un)polarised DY pp(↑) →µ+µ−X process in the scenario and with the kine-matic conditions described above in this sectionis certainly a difficult task; to probe its feasibil-ity Monte-Carlo simulations have been performed,based on the event generator kindly provided us by


A. Bianconi (a more detailed description of such agenerator can be found in Ref. [454, 455]). Thisis the very same event generator involved in thefeasibility studies performed for the polarised DYπ±p↑ → µ+µ−X process at the CM energy

√s ∼ 14

GeV reachable at COMPASS [456, 457], and for thepolarised DY pp↑ → µ+µ−X process at the CM en-ergy

√s = 200 GeV reachable at the Relativistic

Heavy-Ion Collider (RHIC) of BNL [458].

The main goal of the Monte-Carlo simulations re-ported herewith is to estimate the number of eventsrequired for the DY program at PANDA, in orderto access unambiguous information on the PDF’sof interest, namely the BM function h⊥1 in thepp → µ+µ−X process and the Sivers functionf⊥1T , the Transversity h1T and the h⊥1 again in thepp↑ → µ+µ−X process. The effects of the kine-matic cuts above described and of the acceptanceintroduced by the PANDA spectrometer, and thepossibility to probe the dependence of the experi-mental asymmetries on the kinematics have to beinvestigated as well.

An estimation of the fully polarised case is beyondthe scope of the present discussion; see Ref. [459,447, 448] for the predictions of double-spin asym-metries in different experimental scenarios at FAIRin the case of the fully polarised DY process.

For each one of the two investigated processes 480Kevents have been generated at s = 30 GeV2 in or-der to satisfy the following kinematic cuts: a di-lepton invariant mass 1.5 GeV ≤ M ≤ 2.5 GeV,a di-lepton transverse momentum q

T> 1 GeV/c,

and a polar angle for the µ+ in the CS frame60 ≤ θCSµ+ ≤ 120. The second cut, together withthe rejection factor introduced by the iron in themagnet, is necessary to select the DY signal eventsfrom the hadronic background, as will be discussedlater in this section; the latter cut is aimed to se-lect the azimuthal θCSµ+ -region where the azimuthalasymmetries are expected to be larger (at θCSµ+ ∼ π

2

[454]).

If the simulations had included also events in thesafe-region (4 GeV ≤ M ≤ 9 GeV) the phasespace for large τ = x1x2 would have been anywayscarcely populated, since the virtual photon intro-duces a 1/M2 ∝ 1/τ factor in the cross section ofEq. 4.60, which thus decreases for increasing τ (with0 ≤ τ ≤ 1). The PDF’s become hence negligible forx1x2 → 1 and events accumulate in the phase spacepart corresponding to small τ .

This is indeed the case of Fig. 4.90, reporting thex1 vs x2 scatter-plot for the generated sample ofunpolarised DY di-lepton production. The upper

right corner of the figure corresponds to the limitτ → 1, when all the available CM energy is trans-ferred to the virtual photon, and is depleted by thecut 1.5 GeV ≤M ≤ 2.5 GeV; such a cut selects theregion 0.075 ≤ τ ≤ 2.1, and the distribution be-comes more and more dense approaching the lowerridge. The line bisecting the plot at 45 correspondsto xF ∼ 0; parallel lines above and below indicatexF > 0 and xF < 0, corresponding in the labora-tory frame respectively to ”forward” (small θLABµ+ )and ”backward” (large θLABµ+ ) events.

Figure 4.90: The correlation between the two light-cone momentum fractions of the parton momenta x1,2

for the 480K DY events generated with the AndreaBianconi’s generator [454] for the unpolarised pp →l+l−X processes at s = 30 GeV2 in the following kine-matic conditions: a di-lepton invariant mass 1.5 ≤M2ll ≤ 2.5 GeV, a transverse momentum of the lepton

pair qT > 1 GeV/c and a polar angle for the µ+ in theCollins-Soffer frame 60 ≤ θCSµ+ ≤ 120.

Figure 4.91: The azimuthal asymmetry between crosssections related to positive and negative values of thecos2φ term in Eq. 4.52 for 480K events of the unpo-larised DY process pp → l+l−X in the same kinematicconditions of Fig. 4.90. The asymmetry is evaluatedin xp bins for a di-lepton pair transverse momentum1 ≤ qT ≤ 2 GeV/c (squares) or 2 ≤ qT ≤ 3 GeV/c (tri-angles). Error bars reflect statistical errors only.


Figure 4.92: The single-spin azimuthal asymmetries Asin(φ−φS2 )

T and Asin(φ+φS2 )

T between cross sections relatedto positive and negative values respectively of the two sin(φ− φS2) and sin(φ+ φS2) terms in Eq. 4.56, for 480Kevents of the single-polarised DY process pp↑ → l+l−X in the same kinematic conditions of Fig. 4.90. Theasymmetries are evaluated in xp bins for a di-lepton pair transverse momentum 1 ≤ qT ≤ 2 GeV/c (squares) or2 ≤ qT ≤ 3 GeV/c (triangles). Error bars reflect statistical errors only.

The azimuthal asymmetry related in the CS frameto the cos2φ term of Eq. 4.52 and Eq. 4.54 (an asym-metry that leads to the BM function h⊥1 ) has beenevaluated for muon pairs with transverse momen-tum 1 < qT < 2 GeV/c or 2 < qT < 3 GeV/c inxp bins (xp being the light-cone momentum frac-tion of the parton in the proton) over the range0.2 < xp < 0.8, where according to the phase spacedistribution of Fig. 4.90 the statistics is reasonablylarge. The asymmetry Acos2φ has been obtainedconsidering all the 480K unpolarised pp → l+l−Xevents generated by the Andrea Bianconi’s genera-tor [454], tuned to reproduce the most recent ex-perimental data available in the literature [388].For each xp bin and qT cut two event samples arestored, corresponding respectively to positive andnegative values of cos2φ; the resulting asymmetryAcos2φ = (U −D)/(U + D) between cross sectionswith positive (U) and negative (D) values of cos2φis shown in Fig. 4.91. Error bars represent statisti-cal errors only; since the asymmetry has been evalu-ated considering the whole sample of the generatedevents, both the asymmetry itself and its error barsshown in Fig. 4.91 are not folded with the accep-tance of the PANDA spectrometer.

The azimuthal asymmetry related to h⊥1 is henceexpected to be not negligible, experimentally mea-surable in the PANDA energy range, with errorsgood enough to allow for the investigation of thedependence of the asymmetry on the relevant kine-matic variables such as the transverse momentumof the lepton pair qT . Such an investigation is of ut-termost importance in order to probe the existence

of a possible inversion of the trend in the energydependence of the asymmetries, to balance soft andhard effects in this kind of processes.

In the case of the single-polarised DY process pp↑ →µ+µ−X two different SSA’s can be defined; a firstone, Asin(φ−φS2 )

T , weighted by the factor sin(φ−φS2)(Eq. 4.56) and related to the Sivers function f⊥1T ;a second one, Asin(φ+φS2 )

T , weighted by the factorsin(φ + φS2) (Eq. 4.56) and related to the convo-lution of the Transversity h1T with the BM func-tion h⊥1 . The single-polarised DY sample have beengenerated under the assumptions described in Sec.A of [454] but assuming the simpler functional hy-pothesis 〈h1(xp)〉/〈f1(xp)〉 = 1. The procedure todetermine the two asymmetries is the analogous ofthat used to evaluate the unpolarised asymmetry:for each xp bin four sample of events are stored,for positive (U±) and negative (D±) values of thefactors respectively sin(φ + φS2) and sin(φ − φS2).The resulting asymmetries A

sin(φ±φS2 )

T = (U± −D±)/(U±+D±) are plotted in Fig. 4.92 in xp bins inthe range 0.2 < xp < 0.8, separately for muon pairswith transverse momentum 1 < qT < 2 GeV/c or2 < qT < 3 GeV/c. The asymmetries have been ob-tained considering the whole sample of 480K eventsgenerated for the single-polarised DY process andare hence not affected by the spectrometer accep-tance; error bars represent statistical errors only.

Under the assumptions above described the asym-metry A

sin(φ+φS2 )

T is expected to be relevant, andalso in this case the investigation of the dependenceof the asymmetry on the di-lepton transverse mo-


Figure 4.93: Estimated kinematic acceptance for the unpolarised DY process in the same kinematic conditions ofFig. 4.90. A ”Monte Carlo through” has been performed considering the preliminary estimation of the minimumiron thickness required to resolve the DY signal from the hadronic background. Left panel shows the accessible τregion and the events accumulating toward low values of the transverse momentum of the lepton pair qT in theCollins-Soper frame. The central and the right panels show the scatter plots respectively of the momenta and ofthe transverse momenta of the two outgoing muons in the laboratory Frame frame.

mentum qT should be possible. This is not thecase for the asymmetry A

sin(φ−φS2 )

T , predicted tobe much smaller and with a strongly reduced de-pendence on qT .

For each one of the two simulated DY processesthe generated events have then been propagatedthrough the PANDA spectrometer (Sec. 2.2) in or-der to evaluate the global acceptance introduced bythe experimental layout, i.e. the geometrical ac-ceptance and the events’ loss due to the materialbudgets, in particular the ones introduced by theElectromagnetic Calorimeter and by the iron of themagnet (in which the muon detectors will be em-bedded).

The iron shield is mandatory in order to separatethe muon couples produced in the investigated DYprocesses from the pion couples coming from thehadronic background; in fact the required combinedrejection factor that has to be provided by the ex-perimental apparatus itself and by the events’ re-construction is very large. The total pp annihila-tion cross section in the PANDA energy range isσpp ∼ 50 mb; once accounted for its diffractive com-ponent, the global cross section for pion productionin the final state is of the order of some tens ofmb. Since the DY expected cross section [454] is ofthe order of the nb, the required rejection factor is∼ 107.

The extended simulations needed to investigate the

Figure 4.94: The statistical errors for the asymmetries of Figures 4.91 and 4.92 expected once they are foldedwith the PANDA global acceptance (see text for a more detailed discussion), for a di-lepton pair transversemomentum 1 ≤ qT ≤ 2 GeV/c (left panel) or 2 ≤ qT ≤ 3 GeV/c (right panel). The ”Monte Carlo through” hasbeen performed for each one of the two sets of 480K events generated for unpolarised and single-polarised DYprocesses, in the same kinematic conditions of Fig. 4.90, considering the preliminary estimation of the minimumiron thickness required to resolve the DY signal from the hadronic background.


background rejection are actually still in progress.Nevertheless their preliminary indications point to-ward a scheme in which the required rejection factorcould be achieved by the mean of: the depletion ofthe pions’ sample due to their interaction with theiron in the PANDA solenoid; a set of kinematic cutsin order to select in the event reconstruction stagethe DY processes (the most effective ones being therequirement of a di-muon pair transverse momen-tum qT ≥ 1 GeV/c and of a reaction vertex in thetarget region); a kinematically constrained refit ofthe final state in order to reject the residual con-tamination from the hadronic background. To bal-ance the best possible background rejection and theminimum DY events loss, the geometry of the ironin the barrel and in the endcap of the solenoid hasto be segmented, in order to host embedded muoncounters. The minimum iron thickness required toachieve such a large rejection factor determines thepreliminary global acceptance of the apparatus forthe DY processes.

The preliminary indications for such an acceptancefrom the extended simulation in progress, point toa reduction by a factor of ∼ 2 of the total cross-section σ0 quoted above in this section. That wouldrescale Eq. 4.61 to the corresponding rate expectedfor those DY muon pairs that can be detected andresolved from the hadronic background in thesekinematic conditions by the PANDA spectrometer:R = 2 · 1032 cm−2s−1 × 0.8 · 10−33 cm−2 × 1

2 =0.08 s−1, i.e. ∼ 200K events/month, not accountingfor the various experimental efficiencies.

The plots in Fig. 4.93 show few of the most rele-vant kinematic distributions for those unpolarisedDY events surviving the (preliminarily estimated)minimum iron thickness required to resolve the DYsignal from the hadronic background; i.e., thosekinematic distributions are folded with the globalacceptance of the PANDA spectrometer.

The most unwanted effect of the PANDA spectrome-ter acceptance is the introduction of sizeable fake in-strumental asymmetries, heavily depending on thegeometrical cut introduced in the muons polar an-gle distribution in the laboratory frame by the holein the endcap around the beam pipe (varying onthe azimuthal angle φLABµ± but being in the averageθLABµ± ≥ 7). Such an effect will have to be carefully

accounted for in the analysis stage and can be par-tially reduced including in the considered DY sam-ple also those events for which (one of) the outgoingmuons can be detected in the Forward Spectrometer(FS) (See Sec. 2.2).

The plots in Fig. 4.94 show the expected statisticalerrors for the three considered azimuthal asymme-tries once the effects of the preliminary PANDA ac-ceptance, and namely the consequent reduction inthe statistics, are accounted for. The estimatederrors show how the PANDA spectrometer shouldbe able to detect and experimentally evaluate theabove described azimuthal asymmetries, even ifthey were rather small.

Conclusions

The DY production of muon pairs is an excellenttool to access transverse spin effects within the nu-cleon. As stated before in this Section, the double-polarised case would really be a ”dream option”,allowing to access the Transversity distribution h1T

directly and without any convolution with otherPDF’s; unfortunately it is beyond the initial scopeof the PANDA physics program. But even con-sidering the unpolarised and the single-polarisedcases only, the Boer-Mulders distribution h⊥1 andthe Sivers distribution f⊥1T could be accesses as well,and in a single experimental scenario. To accessthe latter a polarised target is needed, an elementnot yet included in the present PANDA layout butby many indicated as an almost necessary upgrade,while the former can be accessed since the very be-ginning of the PANDA activities.

A DY program in PANDA, besides addressing thepresent excitement in the spin physics communitydriven by the discrepancies among the most recentSIDIS data for the Sivers function, would allow forthe evaluation of three of the most hunted PDF’sin a kinematic region were the valence contributionsare expected to be dominant.

A large rejection factor is needed to resolve theDY processes from the hadronic background; a de-tailed evaluation of the hadronic background in thePANDA scenario is in progress, in order to completethe feasibility studies relative to the spin physicsprogram.


4.6.3 Electromagnetic Form Factors inthe Time-like Region

4.6.3.1 Introduction

The electromagnetic probe is an excellent tool to in-vestigate the structure of the nucleon. The PANDA-experiment offers the unique possibility to make aprecise determination of the electromagnetic formfactors in the time-like region with unprecedentedaccuracy. The electric (GE) and magnetic (GM)form factors of the proton parametrise the hadroniccurrent in the matrix element for elastic electronscattering (e− + p → e− + p) and in its crossedprocess annihilation (pp → e+e−) as shown inFig. 4.95. The form factors (FF) measured in elec-tron scattering are intimately connected with thosemeasured in the annihilation process. Moreoverthey are observables that can probe our understand-ing of the nucleon structure in the regime of nonper-turbative QCD as well as at higher energies whereperturbative QCD applies.

The interaction of the electron with the nucleonis described by the exchange of one photon withspace-like four momentum transfer q2. The leptonvertex is described completely within QED and onthe nucleon vertex, the structure of the nucleon isparametrised by two real scalar functions dependingon one variable q2 only. These real functions are theDirac form factor F1

p,n and the Pauli form factorF2

p,n, or as a linear combination of Fp,n1,2 the Sachsform factors GE

p,n and GMp,n. The standard way

of writing the matrix element for elastic electronproton scattering in the framework of one-photonexchange is:

M =e2

q2u(k2) γµ u(k1) u(p2) [F1(q2) γµ

+iσµνq

ν

2mpF2(q2)] u(p1), (4.62)

k1(p1) and k2(p2) are the four-momenta of the ini-tial and final electron (nucleon) represented by thespinors u(k) (u(p)) and u(k) (u(p)), mp is the nu-cleon mass, q = k1 − k2, q2 < 0. Applying crossingsymmetry yields the matrix element for pp→ e+e−

where k2(p2) changes sign so that q2 = s.

The form factors are analytic functions of the fourmomentum transfer q2 ranging from q2 = −∞ toq2 = +∞. While in electron scattering the formfactors can be accessed in the range of negative q2

(space-like), the annihilation process allows to ac-cess positive q2 (time-like) starting from the thresh-old of q2 = 4m2

p. Unitarity of the matrix elementrequires that space-like form factors are real func-

tions of q2 while for time-like q2 they are complexfunctions. In the Breit frame, space-like FFs have

p

e−

p′

e′−

p

p

e−

e+

Figure 4.95: Feynman diagrams for elastics elec-tron scattering (left) and its crossed channel pp →e+e− (right) which will be measured with the PANDA-detector.

concrete interpretations, since they are the Fouriertransforms of the spatial charge (GE) and the mag-netisation distribution (GM) of the proton. Theirslope at q2 = 0 directly yields the charge and mag-netisation radius of the proton. In time-like region,FFs reflect the frequency spectrum of the electro-magnetic response of the nucleon. That way twocomplementary aspects of nucleon structure can bestudied and ask for a full and complete descrip-tion of the electromagnetic form factors over thefull kinematical range of q2.

Impact from Electron Scattering Data

The experimental determination of the electromag-netic form factors of the nucleon has triggered largeexperimental programs at all major facilities sincethey have long served as one of the testing groundsfor our understanding of nucleon structure rangingfrom the low-q2 regime of QCD up to the high en-ergy perturbative regime. Basically all models ofnonperturbative QCD, which are using effective de-grees of freedom, have been used to estimate thenucleon form factors[460]. For example differentconstituent quark models, skyrmion type of mod-els, bag models and more recently a framework likechiral perturbation theory and lattice gauge theoryhave been applied.

Due to their analyticity space-like and time-likeform factors are intimately connected by the ap-plication of dispersion relations which are an ap-plication of Cauchy’s integral formula. Perturba-tive QCD makes predictions for the large q2 be-haviour of the connection between space-like regionand time-like region. Space-like form factors areconnected to the recent developments using non-perturbative generalised parton distributions.


The interest in the time-like form factors of thenucleon has been renewed by the recent measure-ment at JLAB using the polarisation transfer andtarget asymmetry method, showing that the ratioof µpGE/GM (µp magnetic moment of the proton)deviates from unity and is in contrast to the re-sults derived from Rosenbluth separation technique[461, 462, 463, 464, 465]. While this discrepancy ismost probably connected with radiative corrections,it has been shown, that the polarisation transfermethod is much less sensitive to those effects. Itseems that GE is approaching zero around a q2 of8 (GeV/c)2 while GM follows a dipole form factorindicating that the charge distribution has a hardsurface in contrast to the magnetisation distribu-tion. This surprising result has reopened the ques-tion on the determination of GE and GM in thetime-like domain which are complex functions. Al-most all experiments so far have determined |GM| inthe time-like domain using the hypothesis of equal-ity between GE and GM which is fulfilled strictlyonly at threshold. The recent JLAB results, yieldinga different q2 behaviour for GE and GM add to themotivation of individual determination of time likeform factors, which was not obtained up to now andwhich will be possible with the PANDA-experiment.Only two experiments had enough statistics to de-termine the ratio of |GE|/|GM| independently fromany hypothesis and which have so far reached con-tradicting results with large experimental uncer-tainties. The determination of the electromagneticform factors in the time-like domain at low to inter-mediate momentum transfer is therefore regardedto be an open question.

Existing Data on Time-like Form Factors

The PANDA experiment offers a unique opportu-nity to determine the moduli of the complex formfactors in the time-like domain, by measuring theangular distribution of the process pp→ e+e− in aq2 range from about 5 (GeV/c)2 up to 14 (GeV/c)2.A determination of the magnetic form factor up toa q2 of 22 (GeV/c)2 will be possible by measuringthe total cross section.

The differential cross section for unpolarised initialand final states of the process pp→ e+e− is [466]:

dσd cos θ

=πα2(~c)2

8m2p

√τ (τ − 1)

[|GM |2(1 + cos2 θ

)+|GE |2τ

(1− cos2 θ

)](4.63)

with τ = q2/4m2p. A measurement of this differ-

ential cross section over a wide range of cos θ al-

lows an independent determination of the moduli|GE(q2)| and |GM(q2)| of the electromagnetic formfactors and has been attempted by a number of ex-periments [467, 468]. Fig. 4.96 gives a summary

]2[(GeV/c)2q2 4 6 8 10 12 14 16 18 20

|M

|G-210

-110

Babar

E835FenicePS170E760

DM1DM2BES

CLEO

Figure 4.96: World data on the modulus |GM| of thetime-like magnetic form factor extracted from differentexperiments using pp→ e+e−,e+e− → pp, and e+e− →γpp. In all cases, the hypothesis of R = |GE|/|GM| = 1has been used to analyse the data.

on the world data on the modulus |GM| of thetime-like magnetic form factor extracted from dif-ferent experiments using pp → e+e−,e+e− → pp,and e+e− → γpp. In all cases, the hypothesis of|GE| = |GM| has been used to analyse the data us-ing the integrated differential cross section.

So far only two experiments have collected enoughstatistics in order to analyse the angular distribu-tion and extract |GE| and |GM| independently (seeFig. 4.97).

The PANDA experiment is planned to have un-precedented luminosity and rich particle identifica-tion capabilities, which are necessary in order todiscriminate against the very large background ofpp → π−π+. It is about 106 times higher in crosssection. We show here the strategy how to reach aπ−π+ rejection factor of about 108 using the parti-cle identification capabilities of each detector.

Any sizeable two-photon exchange contribution inthe time-like domain, which is regarded to be oneof the radiative correction processes responsible forthe discrepancy between Rosenbluth and polari-sation transfer method, can be detected in thesame measurement since it introduces a forward-backward asymmetry in the angular distribution


-2.5

0

2.5

5

7.5

4 5 6 7 8q2 (GeV2/c2)

µpG

Ep /GMp

BABARPS-170FENICE+DM2GE

p(4Mp2)=GM

p (4Mp2)

Dispersive approach

Figure 4.97: The data from the LEAR experimentPS170 and recent BABAR data have been alternativelyused as an input to a dispersion relation analysis ofthe electromagnetic form factors. The recent data fromJLAB have been used as an input for the space-like re-gion. The green band gives the dispersion relation fitresult on |GE|/|GM| when using the PS170 data in thetime-like region and the yellow band gives the result forthe BABAR data. The present accuracy in the ratio ofR = |GE|/|GM| is of order 50 % while a future mea-surement using the PANDA experiment at the designluminosity yields a statistical error of order few % orbetter after 107 s in this region of q2.

which otherwise is symmetric in one-photon ex-change [469, 470].

A large experimental activity is coming from B-factory e+e−-colliders where the energy is fixed toa bb-resonance. The process of initial state radi-ation e+e− → ppγ (ISR), where the variable en-ergy γ from an initial state electron is used in or-der to ”scan” the q2 of the virtual photon probingthe form factors, is used at those B-factories. TheBABAR experiment has recently published resultsfor the ratio R = |GE|/|GM|, but is penalised bythe fact, that the luminosity for e+e− → ppγ isthen suppressed in average by factors of 105 to 106

as compared to the direct e+e−-luminosity and can-not so far compete with the proposed measurementat PANDA.

An analogous process to ISR would be the emis-sion of a π by one of the pp in the initial statewhich would lower the q2 of the virtual photon atthe annihilation vertex. That way, one could reachthe otherwise unaccessible range below the thresh-old and measure the form factors down to lower q2.Vector meson dominance and hypothetical baryo-nium states could be accessed that way. Anotherpossible extension of the program could be a possi-bility to access the axial form factor in time-like do-main, by using a neutron (deuteron) target [471]. Inanalogy to pion electroproduction, the chiral Ward-identities could be used here to extract the axial

form factor in the time-like domain, for which nodata exist at all. First estimates of cross sectionsfor both, subthreshold electromagnetic form factorsand an axial form factor measurement have beenperformed, but more theoretical work and simula-tions is necessary [471].

Another way to reach the subthreshold region wouldbe to study the EM annihilation on a nucleus, usinga fast bound proton which is off-mass-shell. In par-ticular, the reaction could be done on deuterium(p + d → e+e−n) at low beam momentum (1.5GeV/c), with the final neutron as a missing particle.First estimates have been performed regarding thecount rate and the missing mass resolution. Back-ground rejection remains to be studied in detail.

4.6.3.2 Simulations

Time-like form factors (TLFF) measurementsthrough the reaction pp → e+e− (or µ+µ−) re-quire the complete identification of the 2 outgoingleptons. The shape of the angular distribution pro-vides a direct access to the moduli of the two protonform factors |GM| and |GE| (see 4.6.3.1). We havestudied two aspects concerning the determinationof |GM| and |GE| with the PANDA detector: thebackground conditions which will eventually limitthe purity of the lepton signal and the sensitivityto the shape of the angular distribution after recon-structing the lepton signal in the PANDA detector.The integrated cross section of the signal reactionpp→ e+e− was modelled by a fit to the world datawhere the following Ansatz for GM had been used(see details in [472] ):

|GM | =a(

1 +q2

m2a

)GD (4.64)

GD =1(

1 +q2

m2d

)2 ,

m2a = 3.6(GeV/c)2,

m2d = 0.71(GeV/c)2

GD denotes the usual dipole-form factor, a = 22.5is a normalisation constant and ma is an additionalparameter describing the deviation from a dipole.m2a = 3.6 ± 0.9 GeV2, md is the usual dipole-mass

parameter.

The upper plot of Fig. 4.98 shows the magnetictime-like proton form factor |GM | which has beenused in the signal simulations described here. Thelower part of Fig. 4.98 shows the integrated crosssection dependence versus q2. The plot shows the


individual contributions of |GE | and |GM | to thetotal cross section. One sees that the sensitivity tothe electric form factor decreases with increasing q2

due to the kinematic factor 1/τ in front of |GE | (τ= q2

4m2p, see Eq. 4.63).

]2[(GeV/c)2q5 10 15 20 25 30

-210

-110

|M

|G

]2[(GeV/c)2q5 10 15 20 25 30

Tot

al C

ross

Sec

tion

[pb]

-310

-210

-110

1

10

210 ]M = G

ETotal Cross Section [ GMagnetic contributionElectric contribution

Figure 4.98: The upper plot shows the modulus of themagnetic time-like proton form factor |GM | which hasbeen used in the simulations of the process pp→ e+e−

described here. The lower plot gives the integratedpp→ e+e− cross section as a function of q2. Also shownis the cross section contribution from magnetic and elec-tric form factors under the assumption of |GE| = |GM|.

Due to the fact that the world data on time-likeform factors have been analysed under the assump-tion that |GE | = |GM |, we can determine and fit thetotal cross section as shown in Fig. 4.98. The knowl-edge of the ratio R = |GE|/|GM| at present is verylimited, dispersion theory allows values between 0and 3 for certain q2-values (see Fig. 4.97). In orderto study the sensitivity to the ratio of |GE|/|GM|we have used the measured total cross section toestimate the total number of counts and have simu-lated the reaction pp→ e+e− with different angulardistributions according to R = 0, 1, 3 and the q2-dependence of GM according to equation Eq. 4.64.Fig. 4.99 shows angular distributions for several as-sumptions on |GE|/|GM|. Table 4.47 summarisesthe simulated event numbers reached for the signalsimulation (pp → e+e− and pp → µ+µ−) and themost important background channels (pp→ π+π−,pp→ π0π0).

Due to the very low cross sections of the process

q2 [GeV2] e+e− µ+µ− π+π− π0π0

5.4 4× 106 4× 106 - -7.21 4× 106 4× 106 - -8.21 4× 106 4× 106 108 3× 106

11.03 4× 106 4× 106 - -12.9 4× 106 4× 106 108 3× 106

16.7 4× 106 4× 106 2.108 3× 106

22.3 4× 106 - - -

Table 4.47: The number of simulated events reachedfor the simulation of the signal (pp → e+e− and pp →µ+µ−) and for the background reactions (pp → π+π−

and pp → π0π0). For the signal case we have created106-events each for the cases |GE| = 0, |GE| = |GM| and|GE| = 3|GM| plus an isotropic e+e−-distribution foracceptance and efficiency corrections. We have studiedthree cases for the final state of π0π0: a) both π0 decayinto 2 gammas, b) one of the final state π0π0 is decayingto 100% into e+e−γ (Dalitz decay) and, c) both finalstate π0π0 do 100 % Dalitz decay.

pp → e+e−, rejection of the other channels mustbe very efficient. The first and most important typeof background arises from misidentified hadrons inbinary reactions (π+π− and K+K−) , where bothcharged hadrons are misidentified as electrons andpositrons. The thickness of the electromagneticcalorimeter (about 20 radiation lengths X0) corre-sponds to slightly more the one nuclear interactionlength λ0, so that we expect for about 30% of the pi-ons nuclear reactions among which charge exchangereactions are especially harmfull. Reactions where aπ+ converts to a π0 with its subsequent decay into 2photons inside the EMC will deposit energy of thesame order as an electron with the same momen-tum. This has been completely taken into accountin additional simulations used for the determinationof the PID-likelihood.

The cross sections of the processes with π+π− orK+K− in the final state are of the same order ofmagnitude. However, the kaon mass is substantiallyhigher than the pion mass, so rejection through PIDand kinematical constraints is more efficient for theK+K− channel.

Consequently, the π+π− background channel wassimulated as the first step. The correspondingangular distributions (see Fig. 4.100) were takenfrom measured data and extrapolated where nec-essary [473, 474, 475, 476, 29]. The ratio of π+π−

to e+e− cross sections, which varies from 105 at| cos θCM | = 0 up to 3 · 106 at | cos θCM | = 0.8, isthen properly taken into account in the simulation.

The second kind of background arises from exit


CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Nu

mb

er o

f C

ou

nts

0

10

20

30

40

50

60

70

80310×

2=5.4 (GeV/c)2q

CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Nu

mb

er o

f C

ou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

310×

= 0EG M = GEG

M = 3 GEG

2=8.2 (GeV/c)2q

CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Nu

mb

er o

f C

ou

nts

0

20

40

60

80

100

120

140

160

2=13.9 (GeV/c)2q

Figure 4.99: Event generator distributions (events before particle tracking and reconstruction) for pp → e+e−

for three different values of q2. The three different distributions in each plot show the angular distribution inthe centre of mass frame (CMS), for the different models: |GE| = 0 (red), |GE| = |GM| (blue) and |GE| = 3|GM|(green). The number of expected counts for each model at the same q2 are the same. The error bars denote thestatistical errors where no efficiency correction has been taken into account.

CMθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

[nb/

sr]

Ω/dσd

-410

-310

-210

-110

1

10

210

(dSigdOme/(2*3.14)):cosTHE

]2 = 8.21 [ (GeV/c)2, q-π+π →p p

Figure 4.100: Angular distribution of pp → π+π−

as used in the simulation. The phenomenological fit todata has been further symmetrized in cos θCM .

channels of the type e+e−X, where X might be acombination of mesons, photons, and lepton pairs.In addition to the direct production from the ppinteractions, such final states can also arise whena produced gamma materialises before reaching thetracking detectors. Due to the high resolution ofthe tracking system, channels, where the missingmass is of the order or larger than the π0 mass, arerejected very efficiently. Considering the involved

cross sections, the main problem therefore arisesfrom e+e− pairs, each one coming from the decay ofone of the two π0s produced in pp→ π0π0 reaction.This can happen, either from Dalitz decay of π0 orafter photon conversion following the direct decay.The reaction pp → π0π0 has therefore been sim-ulated, using the same cross sections and angulardistributions as for the pp→ π+π−. Three-body fi-nal state background reactions involving 2 oppositecharged hadrons and a neutral massive particle (π0

or heavier meson) are much easier to separate, sincekinematical considerations can then provide addi-tional constraints which can be used to cut very ef-ficiently the corresponding background. They havenot yet been simulated.

The background events from π+π− and π0π0 wereanalysed under the hypothesis of having an e+e−-pair. Analogously, the π+π− events have been re-analysed under the hypothesis of having a µ+µ−-pair. The same analysis cuts and kinematical fitconstraints have then been applied to the e+e− sig-nal sample (µ+µ−- sample respectively) in order tocreate the signal distributions. Different cuts onthe PID were used as described in Sec. 3.3.3, corre-sponding to different thresholds on the global like-lihood (see Table 3.2).


Special attention has been paid to the π0π0 channel.The photons from the main π0-decay can eventu-ally convert to e+e−-pairs in the PANDA detector,notably in the beam pipe before the tracking de-tectors. Those e+e−-pairs fulfil all PID cuts butcan very efficiently be suppressed by the kinemati-cal constraints. In addition, we studied the case ofone (two respectively) π0 decaying via the Dalitz-channel (π0 → e+e−γ). The e+e− from Dalitz de-cay again fulfil all PID cuts for electrons, but again,can be efficiently rejected due to kinematical con-straints. One should note, that the branching ratiofor Dalitz decay is of order 1%, i.e. the probabilitythat both π0 decay via the Dalitz process is about10−4.

Extensive simulations have been made for the e+e−

channel and are discussed below (see Table 4.47).Measuring the µ+µ− channel could be a very in-teresting and complementary channel too which westudied at different q2-values. We can not concludehere on the case of muons, more simulations areneeded.

4.6.3.3 Background Analysis

Separating e+e− from π+π− In the analysis ofthe process pp → e+e−, the most severe back-ground comes from two pion final states, namelypp→ π+π− and pp→ π0π0. The large ratio of thecross section for pion final states versus lepton finalstates (of order 106) requires a large event sampleof order 108 in order to show that the lepton signalpollution by pion final states is below 1 %. For thisreason, we have simulated the background processesfor π+π− final states with very high statistics onlyat 3 incident momenta, where we have chosen a lowmomentum, a medium momentum value and thehighest momentum value, where we can access formfactors: 3.3 GeV/c (q2 = 8.21 GeV2), 5.84 GeV/c(q2 = 12.9 GeV2), and 7.86 GeV/c (q2 = 16.7 GeV2)(see Table 4.47) . The effect of different cuts inthe global PID are shown in Table 4.48. For thepp → e+e−-signal processes, particles at CMS-angels of | cos θCM | > 0.8, one of the electrons hitsthe forward spectrometer, which is less powerfulconcerning the e+e− reconstruction. Since we don’tuse this region of CMS-angle for our simulationsof the signal channel, π+π− events were simulatedonly in a restricted range ([-0.8,0.8]) of cos θCM val-ues. Outside this interval, there are no data onmeasured pp → π+π− cross sections and the ex-trapolation by phenomenological models introduceslarge uncertainties due to the steep rise of the crosssection in this cos θCM region. However, as will be

shown in the next subsection, the acceptance for thesignal is very low close to | cos θCM | = 1 and there-fore the uncertainty in the background cross sectionin the interval outside ([-0.8,0.8]) of cos θCM is thennot relevant.

q2((GeV/c)2) 8.2 12.9 16.7no cut 108 108 2. 108

VL 46.8 90 k 140 kL 425 1.2 k 3 kT 31 70 120VT 2 5 6CL∗ 8. 105 1. 106 2.5 106

Table 4.48: Number of π+π− events, misidentified ase+e−, left after the different cuts applied for 3 differ-ent q2 values. The CL∗ cut requires 2 kinematicalfit conditions to be fulfilled, namely CL ≥ 0.001 andCLe+e− ≥ 10CLπ+π− . Please note that the suppres-sion factor of about 100 from the CL∗ cut is indepen-dent from the cut in the PID-probability. By requiringboth, PID-cut and CL∗ cut, we expect a total suppres-sion factor of order 109 to 1010

Fig. 4.101 displays the effect of the different PIDcuts. Only the VeryTight cut, corresponding to aglobal likelihood greater than 99.8 % (and at least a10 % minimum likelihood on each subdetector) onboth positive and negative charged candidates canbe used. Combining one VeryTight with one Tightcandidate is by far not efficient enough to suppressthe background. Additionally the Confidence Level(CL∗) cut resulting from the kinematic refit wasused to efficiently reduce the background. This CL∗

cut requires 2 conditions to be fulfilled, namely CL≥ 0.001 and CLe+e− ≥ 10CLπ+π− . It gives an in-dependent rejection factor of the order of 100, onlyslightly depending on energy. The contaminationof signal e+e− events by background π+π− ones isgiven for all 3 simulated q2 values in Table 4.48.Using VeryTight cuts together with the conditionsCL∗ then allows to reach an overall rejection fac-tor greater than 109 up to 1010. Within these con-ditions, the contamination of the e+e− signal byπ+π− will be well below 1% and will therefore notaffect the precision for extracting the magnetic andthe electric proton form factors.

The contamination of signal events by backgroundπ0π0 ones is shown in the figure Fig. 4.102. In thiscase, electrons are indeed detected and correctlyidentified as such. They originate from 3 differentchannels, namely the double π0 Dalitz decay, one π0

Dalitz decay associated to a photon conversion fromthe other π0, or 2 photon conversions from the 2 π0.The first one scales as the π0 Dalitz decay branch-


CM!cos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

CM!Nu

mbe

r of e

vent

s/0.

1 co

s

1

10

210

310

410

510

610

710

Monte Carlo trueVery LooseLooseTightVery TightVery Tight and CL*

Figure 4.101: Centre of mass distribution of pionsmisidentified as electrons after the different PID cuts atq2 = 8.21(GeV/c)2. The CL∗ cut provides an indepen-dent rejection factor of the order of 100, thus rejectingvery efficiently the 2 remaining events after the VT cut.

ing ratio Γγe+e− squared, The second one scales asΓγe+e− times the conversion probability in the de-tector material. the third one scales as the conver-sion probability squared. In all cases the final stateis a 6-body one (2e+, 2e−, 2γ). From the first case,shown on the left part of the figure, one can de-duce that kinematical constraints and PANDA her-meticity provide a rejection of at least a factor 104.This factor applies as well to the case with 2 photonconversion. As a result, we can say that the π0π0

channel can be rejected by a factor close to 108.

Separating µ+µ− from π+π− The same full-scale simulations were used to analyse the rejectionof π+π− when using the PID cuts adapted to theselection of µ+µ− pairs. There are two major effectsthat limit our ability to discriminate the µ+µ− sig-nal from the background π+π−: the in-flight decayof pions and the unsufficient iron yoke thickness. Inthe former case muons from decaying pions in theclose vicinity of the target behave like muons frompp-annihilation. In the latter case, the backgroundis due to pions which did not interact strongly withiron and are detected by the muon counters. Sincepion and muon masses are not very different, parti-cle identification through specific energy loss dE/dxor Cerenkov radiation is of very little help. Thecalorimeter only provides a rejection factor for pi-ons, but is however of the order of 2/3. Prelimi-nary results obtained with simulations done in thepresent framework show that the extraction of the

µ+µ− channel will be difficult.

4.6.3.4 Signal Analysis

e+e− Channel. Signal events for the processespp → e+e− and pp → µ+µ− have been simulated.The electromagnetic form factors span the regimefrom nonperturbative QCD to perturbative QCDat higher energies that is why we simulated eventsat 8 different energies. In the simulations presentedhere, we concentrate on the extraction of the ratio|GE |/|GM |. Due to the kinematical factor 1/τ infront of |GE |, the sensitivity to |GE | from the crosssection measurement decreases with rising beammomentum (see Fig. 4.98). Table 4.49 gives theexpected number of events for different antiprotonbeam momenta. For a given q2 we used the sametotal number of expected events for the different as-sumptions on the ratio |GE |/|GM |. We have applied

p q2 number ofGeV/c (GeV/c)2 events

1.70 5.40 1071 k2.87 7.27 124 k3.30 8.21 64 k4.85 11.03 90945.86 12.90 31986.37 13.84 20037.88 16.66 58010.9 22.29 82

Table 4.49: Expected counting rates for e+e− cor-responding to an integrated luminosity of 2fb−1 (107s corresponding to about 4 months at L = 2 ·1032cm−2s−1)

the same cuts concerning particle identification andkinematical constraints as for the background chan-nels described in the previous paragraph. Fig. 4.103indicates the reconstruction efficiency as a functionof cos θCM for different cuts for q2 = 8.21 (GeV/c)2.For the VeryTight cut, one can note the impor-tant drop corresponding to the loss of the PIDcapabilities. Holes or drops in the spectrum cor-respond to regions where detector transitions oc-cur,e.g. transition between the barrel part of thecalorimeter and the forward end cap at θlab = 22

(| cos θCM | = 0.33) or loss of STT dE/dx identifi-cation at θlab = 14 (| cos θCM | = 0.67). Fig. 4.104shows the total reconstruction efficiency, integratedover an interval in cos θCM of [-0.8,0.8]. The re-construction efficiency decreases for large q2 values.In addition to the drop in reconstruction efficiency,the cross section decreases with rising q2 and the


CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

# ev

ents

1

10

210

310

410

510

CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

# ev

ents

1

10

210

310

410

510

Montecarlo True events

Reconstructed events

CL*

Montecarlo True events

Reconstructed events

CL*

CMθcos

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

# ev

ents

1

10

210

310

410

510

Figure 4.102: Centre of mass distribution of events after different cuts for the 3 different channels (see text).The top curves are the π0π0 angular distributions whereas the other curves display the angular distribution ofe+e−. The green line of remaining background after the cuts in kinematical fit constraints is not visible sincethere are zero background events left.

CMθcos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Rec

onst

ruct

ion

Effi

cien

cy

0

0.2

0.4

0.6

0.8

1

1.2

ReconstructedVery LooseLooseTightVery TightCL*Very Tight && CL*

]2 = 8.2 [(GeV/c)2, q- e+ e→p p

Cos(theta*)Figure 4.103: Reconstruction efficiency as a functionof cosθCM at one example of beam energy correspondingto q2 = 8.21 (GeV/c)2 for the different different PIDcuts and kinematical constraints. The values quotedare averaged over a bin interval of 0.1, but still showthe drop in efficiency at the transitions between barreland forward end cap detector parts.

sensitivity for |GE | decreases too. For a q2 above14 (GeV/c)2 a measurement of the total cross sectionwill still be possible with unprecedented accuracy,yielding a determination of |GM |. An e+e− angu-

]2 [(GeV/c)2q4 6 8 10 12 14 16 18 20 22 24

Rec

onst

ruct

ion

Effi

cien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Very Tight

CL*Very Tight && CL*

blank

-e+ e→p p

Figure 4.104: Overall integrated reconstruction effi-ciency as a function of q2 applying kinematical con-straints and PID cuts, integrated over an interval incos θCM of [-0.8,0.8] (red curve). The effect of applyingthe kinematial constraints only (CL∗, black curve) andPID cuts only (blue curve) are shown separately .

lar distribution is shown for q2 = 8.21(GeV/c)2 forone model assumption (|GE | = |GM |) in Fig. 4.105.The event generator output is shown together withthe reconstructed event distribution. We apply ac-ceptance and reconstruction efficiency corrections,


CM!cos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

CM!Nu

mbe

r of e

vent

s/0.

1 co

s

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Reco

nstru

ctio

n ef

ficie

ncy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2=8.2 (GeV/c)2; q-e+ e"pp

Monte Carlo trueReconstructed eventsCorrected eventsCorrection

Figure 4.105: The figure shows the angular distribu-tion of e+e− pairs in the centre of mass system. Theblack symbols denote the distribution at the outputof the event generator (Monte Carlo). The red sym-bols denote the distribution of the reconstructed e+e−-pairs. An acceptance and reconstruction efficiency cor-rection (blue points) has been determined from an e+e−

data sample which is isotropically distributed in the CM(right scale). The angular distribution of the recon-structed and efficiency corrected e+e− pairs in the cen-tre of mass system at q2 = 8.21(GeV/c)2 (green points).The corrected angular distribution, fits nicely to theMonte Carlo one, the ratio R = |GE |/|GM | is extractedfrom a fit to the angular distribution. Only statisticalerrors have been taken into account.

determined from an independent isotropical e+e−

distribution. We have simulated the e+e− distri-butions for all q2-values given in table Table 4.47and for all three assumptions on |GE |/|GM | plusisotropic case. Reconstruction efficiency correctionshave been determined for every q2 from the isotropice+e− distribution. We fitted every resulting e+e−-distribution with a linear 2 parameter function inorder to determine the error on R. Fig. 4.106 sum-marises the results for the case |GE | = |GM |. Theyellow band represents a parametrisation of the er-rors of the fits on R. The results for the cases|GE | = 0 and |GE | = 3|GM | are similar. The dif-ferent curves correspond to theory estimates [477].It shows that the separation of the 2 Form Fac-tors can be made almost up to 14 GeV2. In thelow q2 region, PANDA will be able to improve theerror bars by an order of magnitude compared tothe most recent BaBar data, and will consequentlyseverely constrain the theoretical predictions whichtoday display quite a large dispersion.

]2[(GeV/c)2q4 6 8 10 12 14

R

0

0.5

1

1.5

2

2.5

3

Figure 4.106: The expected error of the ratio R =|GE|/|GM| is given as a function of q2. The yellow bandrepresents the errors from the fits to the efficiency cor-rected e+e− distributions at the 8 q2 values and is plot-ted up to q2 = 14(GeV/c)2. The results for the cases|GE | = 0 and |GE | = 3|GM | look similar. The datapoints from PS170 and BABAR are shown as well asthree theoretical expectations for R = |GE|/|GM|. Inthe low q2 region, PANDA will be able to improve theerror bars by an order of magnitude.

µ+µ− Channel. Measuring the µ+µ− channelcould be a very interesting and complementarychannel to e+e−. It was studied at different q2 val-ues and corresponding efficiencies were determined.Their cos θCM behaviour is different from the e+e−

channel, since they are strongly dependent on thegeometry of the muon counters and on the thicknessof the iron yoke. At high q2, the average efficiency isonly slightly smaller than for e+e−, but drops dra-matically at low q2, reaching values below 10 % overan extended cosθCM interval at q2 = 5.4(GeV/c)2.

4.6.3.5 Conclusion

In extended simulations, we have shown, that it ispossible to reject the most important backgroundprocess pp → π+π− with a rejection factor of atleast 109. The resulting contamination of the sig-nal process pp → e+e− data sample is expectedto be well below 1 % and can therefore be safelyneglected.

Our studies have been performed without explicitassumptions on the accuracy of a luminosity mea-surement. For this we can extract the ratioR = |GE|/|GM| with unprecedented precision up


to 14 (GeV/c)2. A factor 10 improved experimentalprecision is expected with respect to present worlddata. Fig. 4.107 shows the expected accuracy onthe PANDA measurements in comparison with theworld data, under the assumption that R = 1. Witha precise luminosity measurement, we can not onlydetermine the ratio R but also the absolute anddifferential cross section up to 22 (GeV/c)2. More-over separate determination of |GE| and |GM| canbe made below 14 (GeV/c)2.

In contrast to the e+e− case, the situation for theprocess pp → µ+µ− is different. Due to the simi-lar mass of muon and pion PID capabilities are notsufficient to arrive at a clean separation of pionsagainst muons. Our simulations show, that a mea-surement of the electromagnetic form factors usingmuons is much less promising. Further studies arerequired.

Polarisation degree of freedom, either on the targetside or with transversely polarised p-beam wouldallow to access the imaginary part of the complexform factors. For example with a transversely po-larised target only one could already determine thephase difference of the two form factors.

Outlook on Transition Distribution Amplitudes(TDA)

The amplitude of the process

p(pp)p(pp)→ γ?(q)π(pπ)→ `+(p`+)`−(p`−)π(pπ)(4.65)

at small t = (pπ − pp)2 (or at small u = (pπ − pp)2)and large lepton pair invariant mass squared q2

has been shown to factorise into a short-distanceperturbatively calculable matrix element and long-distance dominated antiproton Distribution Ampli-tudes (DA) and proton to pion Transition Distribu-tion Amplitudes (TDA), as shown in Fig. 4.108.

Transition Distribution Amplitudes [352, 353,478] are universal non-perturbative objects describ-ing the transitions between two different particles( e.g. p → π, p → γ). They are defined from theFourier transform of a matrix element of a three-quark-light-cone operator between a proton and ameson state. They obey QCD evolution equationswhich follow from the renormalisation-group equa-tion of the three-quark operator. Their Q2 depen-dence is thus completely under control. To definethe transition distribution amplitudes from a nu-cleon to a pseudoscalar meson, we introduce light-

]2[(GeV/c)2q5 10 15 20 25 30

|M

|G

-310

-210

-110

BabarE835FenicePS170E760

DM1DM2BES

CLEO

PANDASim

Figure 4.107: Present world data on |GM| (extractedusing the hypothesis R = |GE|/|GM| = 1) are showntogether with the expected accuracy by measuring pp→e+e− with the PANDA experiment at FAIR. Each pointcorresponds to an integrated luminosity of 2 fb−1.

Figure 4.108: The factorisation of the process pp →e+e−π0

cone coordinates v± = (v0 ± v3)/√

2 and trans-verse components vT = (v1, v2) for any four-vectorv. The skewedness variable ξ = −∆+/2P+ with∆ = p′ − p and P = (p + p′)/2 describes the loss


of plus-momentum of the incident hadron in theproton → meson transition. The exchanged quarkscarry light cone fractions of + momenta labelledby x1, x2 and x3, and their supports are within[−1 + ξ, 1 + ξ]. Momentum conservation impliesthat

∑i xi = 2ξ .

As in the case of generalised parton distributionsthe simultaneous presence of two transverse scalesQ2 and −t, allows through a Fourier transform tomap the impact parameter dependence of the scat-tering amplitude. In the case under study, the t−dependence of the N → π transition distributionamplitude allows in its ERBL region (namely, whenall xi > 0) a transverse scan of the location of thesmall sized (of the order of 1/Q ) hard core madeof three quarks when a pion carries the rest of themomentum of the nucleon. This may be phrasedalternatively as detecting the transverse mean po-sition of a pion inside the proton.

Cross section estimates have been calculated usinga TDA ansatz inspired by soft pion theorems in Ref.[356]. They show that measurable rates up to Q2

values of the order a few GeV2 are expected withthe designed beam luminosity. Detailed simulationshave not yet been done, but the rate estimates show,that the process is accessible with the design lumi-nosity.

0.01

0.1

1

10

100

6 12 18 24 30

dσ /d

t| ∆T=

0 (n

b/G

eV2 )

W2 (GeV2) (a)

|pzπ|=0

|pzπ|=155 MeV

Figure 4.109: (a) Differential cross section dσ/dt forpp → γ?π0 as a function a W 2 for |pzπ| = 0 (lowercurve) and |pzπ| = M/6. (b) Differential cross sectiondσ/(dtdQ2) for pp → `+`−π0 as a function of Q2 forvarious beam energies.


4.7 Electroweak Physics

With the high-intensity antiproton beam availableat HESR a large number of D-mesons can be pro-duced. This gives the possibility to observe rareweak decays of these mesons allowing to study elec-troweak physics by probing predictions of the Stan-dard Model and searching for enhancements intro-duced by processes beyond the Standard Model.Since the studied processes are very rare and smalldeviations are looked for statistics is the main factorin this class of measurements. This implies to per-form them at highest possible luminosity, best byeven extending the antiproton production rate be-yond the anticipated 2×107/s. However a longtermparasitic measurement in parallel to spectroscopyand other topics whenever D mesons are producedcan also provide an interesting statistics over someyears.

4.7.1 CP-Violation and Mixing in theCharm-Sector

CP violation [479] has been observed in neutral kaonand in neutral B meson decays [480, 481]. RecentlyBaBar has seen evidence for mixing of D and D[482]. The observed lifetime differences are howeverin no contradiction to the Standard Model.

In the standard model, CP violation arises froma single phase entering the Cabibbo-Kobayashi-Maskawa (CKM) matrix. As a result, two elementsof this matrix, i.e. Vub and Vtd have large phases.The elements have small magnitudes and involvethe third generation and CP violation is small inthe K0 system. The violation is predicted to beeven smaller in the D0 system [483]. Thus, a devia-tion from the small standard model effect indicating”new physics” can be more easily distinguished inexperiments in the D meson system. An enhancedmass difference of mixing D and D mesons wouldconstitute a deviation form the Standard Model.However lifetime difference mostly occur throughlong range interaction of common final states andcan be enhanced simply by a strong phase.

Working with D mesons produced at the DDthreshold has advantages arising from the strongcorrelation of the DD pair which is kept in thehadronisation process. Formed near threshold,asymmetries are not expected in the productionprocess and the observation of one D meson revealsthe quantum numbers of the other one when pro-duced in a charge symmetric environment (flavortagging). Thus, flavor mixing of DD and CP viola-

tion can be searched for in analogy to methods inthe B-system produced on the Υ(4S) [484].

The two-body channels pp → ψ(3770) → DDand pp → ψ(4040) → D∗D∗ may serve to in-vestigate the open charm reconstruction abilities ofPANDA. As shown in section 4.2.2.5 D mesons canbe reconstructed well in PANDA. The open ques-tion is the value of the production cross-section forpp → DD. In section 4.2.2.5 a very conservativeestimate derived from the decay width J/Ψ → ppof about 3 nb was given. On the other hand Kroll instudies for SuperLEAR calculated a cross section ofup to 200 nb for this process [485]. For a measure-ment of αCP ∼ 10−3 as predicted by the StandardModel the production of 109 D meson pairs wouldbe required, which at a production cross section of200 nb would correspond to 3 years of running atL = 2 · 1032 cm−2s−1, but would be out of reach atthe conservative lower limit of the cross section.

4.7.2 CP-Violation in Hyperon Decays

In self-analysing two-body decays of hyperons thepolarisation of the mother particle can be obtaineddirectly from the daughters. In these decays the or-bital angular momentum of the final state can beL = 0, 1, in other words the decay amplitude canbe an S-wave or a P -wave. Having two amplitudes,interference can occur and CP-violating phases canenter. There are two characteristic parameters,which govern the decay dynamics: The quantity αdenotes the asymmetry of the decay angular distri-bution, the quantity β gives the decay-baryon polar-isation. With these quantities and the decay widthΓ, CP asymmetries can be formed [486]:

A = αΓ+αΓαΓ−αΓ

≈ α+αα−α B = βΓ+βΓ

βΓ−βΓ≈ β+β

β−β D = Γ+ΓΓ−Γ

For the asymmetry A, standard model predictionsare of the order ≈ 2×10−5. Some models beyondthe standard model predict CP asymmetries of theorder of several 10−4. To reach the standard modellimit about 1010 Hyperon decays have to be recon-structed, which could be done within one year underideal conditions. The detector for this experimentrequires good vertex reconstruction, excellent par-ticle identification both in forward direction and atlarge angles and reliable long term stability.

4.7.3 Rare Decays

The study of rare decays can open a window ontophysics beyond the standard model since it probesthe violation of fundamental symmetries. Lepton


flavor number violating decays, e.g. D0 → µe orD± → πµe, could be searched for. Flavor changingneutral currents like in the decay D0 → µ+µ− canoccur in the standard model through box graphsor weak penguin graphs with branching fractionssmaller than 10−15. However, the signatures of thedecays are clean leaving hope for their observation,if processes exist that boost the decay branch.

References

[1] N. Brambilla et al., hep-ph/0412158 (2004).

[2] C. Amsler et al., Phys. Lett. B342, 433(1995).


[4] A. Abele et al., Phys. Lett. B385, 425(1996).

[5] A. Abele et al., Eur. Phys. J. C19, 667(2001).


[7] J. Aubert et al., Phys. Rev. Lett. 33, 1404(1974).

[8] J. Augustin et al., Phys. Rev. Lett. 33, 1406(1974).

[9] P. Dalpiaz, Charmonium and other onia atminimum energy, in Karlsruhe 1979,Proceedings, Physics With Cooled LowEnergetic Antiprotons, edited by H. Poth,pages 111–124, 1979.

[10] M. Andreotti et al., Nucl. Phys. B 717, 34(2005).

[11] W.-M. Yao et al., J. of Phys. G 33, 1 (2006).

[12] C. Edwards et al., Phys. Rev. Lett. 48, 70(1982).

[13] S. Choi et al., Phys. Rev. Lett. 89, 102001(2002).

[14] D. Asner et al., Phys. Rev. Lett. 92, 142001(2004).

[15] B. Aubert et al., Phys. Rev. Lett. 92,142002 (2004).

[16] T. Armstrong et al., Phys. Rev. Lett. 69,2337 (1992).

[17] M. Andreotti et al., Phys. Rev. D72, 032001(2005).

[18] J. Rosner et al., Phys. Rev. Lett. 95, 102003(2005).

[19] J. Bai et al., Phys. Rev. Lett. 84, 594200(2000).

[20] J. Bai et al., Phys. Rev. Lett. 88, 101802(2002).


[21] S. Uehara et al., Phys. Rev. Lett. 96,082003 (2006).

[22] K. Abe et al., Phys. Rev. Lett. 94, 182002(2005).


[24] T.N.Pham, B.Pire, and T. Truong, Phys.Lett. B61, 183 (1976).

[25] M. Negrini, Measurement of the branchingratios ψ′ → JψX in the experiment E835 atFNAL, PhD thesis, University of Ferrara,2003.

[26] V. Flaminio et al., CERN-HERA 70-03(1970).

[27] J. L. Rosner et al., Phys. Rev. Lett. 95,102003 (2005).

[28] M. Andreotti et al., Phys. Rev. D72, 112002(2005).

[29] T. A. Armstrong et al., Phys. Rev. D56,2509 (1997).

[30] A. Capella et al., Phys. Rept. 236, 225(1994).

[31] PANDA Technical Progress Report,Technical report, FAIR-ESAC, 2005.

[32] A. Kaidalov and P. Volkovitsky, Z. Phys. C63, 517 (1994).

[33] P. Kroll, B. Quadder, and W. Schweiger,Nuclear Physics B 316, 373 (1989).

[34] E. Braaten, Physical Review D (Particlesand Fields) 77, 034019 (2008).

[35] K. Sebastian, H. Grotch, and F. L. Ridener,Phys. Rev. D45, 3163 (1992).

[36] M. Ambrogiani et al., Phys. Rev. D65,05002 (2002).

[37] K. Juge, J. Kuti, and C. Morningstar, Phys.Rev. Lett. 90, 161601 (2003).

[38] D. Thompson et al., Phys. Rev. Lett. 79,1630 (1997).

[39] G. Adams et al., Phys. Rev. Lett. 81, 5760(1998).


[41] J. Reinnarth, Nucl. Phys. A692, 268c(2001).

[42] S. U. Chung et al., Phys. Rev. D65, 072001(2002).


[44] P. Salvini et al., Eur. Phys. J. C35, 21(2004).

[45] E. I. Ivanov et al., Phys. Rev. Lett. 86, 3977(2001).

[46] S. U. Chung and E. Klempt, Phys. Lett.B563, 83 (2003).

[47] J. Kuhn et al., Phys. Lett. B595, 109(2004).

[48] M. Lu et al., hep-ex/0405044.

[49] G. Adams, Talk given at the First GHPMeeting of the APS, Chicago, 2004.

[50] P. Chen, X. Liao, and T. Manke, Nucl.Phys. Proc. Suppl. 94, 342 (2001).

[51] C. Michael, in Proceedings of “HeavyFlavours 8”, 1999.

[52] K. Juge, J. Kuti, and C. Morningstar, Nucl.Phys. (Proc. Suppl.) B83, 304 (2000).

[53] T. Manke et al., Phys. Rev. D57, 3829(1998).

[54] P. Page, PhD thesis, 1995.

[55] J. Merlin and J. Paton, Phys. Rev. D35,1668 (1987).

[56] K. Juge, J. Kuti, and C. Morningstar, Nucl.Phys. (Proc. Suppl.) B86, 397 (2000), Phys.Lett. B478, 151 (2000).

[57] R. Cester, in Proceedings of the “SuperLEAR Workshop”, pages 91–103, Zurich,1991.

[58] M. Gaillard, L. Maiani, and R. Petronzio,Phys. Lett. B110, 489 (1982).

[59] C. Bernard et al., Phys. Rev. D56, 7039(1997).

[60] C. Bernard et al., Nucl. Phys. (Proc. Suppl.)B73, 264 (1999).

[61] K. Juge, J. Kuti, and C. Morningstar, Phys.Rev. Lett. 82, 4400 (1999).


[62] Z.-H. Mei and X.-Q. Luo, Int. J. Mod.PHys. A18, 5713 (2003), hep-lat/0206012.

[63] T. Manke et al., Nucl. Phys. (Proc. Suppl.)B82, 4396 (1999).

[64] C. Morningstar and M. Peardon, Phys. Rev.D60, 34509 (1999).

[65] J. Sexton, A. Vaccarino, and D. Weingarten,Phys. Rev. Lett. 75, 4563 (1995).

[66] P. Page, in Proceedings of the “pbar2000Workshop”, edited by D. Kaplan andH. Rubin, pages 55–64, Chicago, 2001.

[67] R. Jones, in Proceedings of the workshop“Gluonic excitations”, Jefferson Lab, 2003,in print.

[68] A. Bertin et al., Phys. Lett. B361, 187(1995).



[71] C. Cicalo et al., Phys. Lett. B462, 453(1999).

[72] F. Nichitiu et al., Phys. Lett. B545, 261(2002).

[73] C. Morningstar and M. Peardon, Phys. Rev.D56, 4043 (1997).

[74] C. Hanhart, Y. S. Kalashnikova, A. E.Kudryavtsev, and A. V. Nefediev, Phys.Rev. D76, 034007 (2007).

[75] E. Braaten and M. Lu, Phys. Rev. D77,014029 (2008).

[76] A. Lundborg, T. Barnes, and U. Wiedner,Phys. Rev. D73, 096003 (2006).

[77] J. Clayton et al., Nucl. Phys. B30, 605(1971).

[78] J. Z. Bai et al., Phys. Rev. Lett. 76, 3502(1996).

[79] D. J. Lange, Nucl. Instrum. Meth. A462,152 (2001).

[80] C. Evangelista et al., Phys. Rev. D57, 5370(1998).

[81] A. De Rujula, H. Georgi, and S. L. Glashow,Phys. Rev. Lett. 37, 785 (1976).

[82] N. Isgur and M. B. Wise, Phys. Rev. Lett.66, 1130 (1991).

[83] S. Godfrey and R. Kokoski, Phys. Rev.D43, 1679 (1991).

[84] S. Godfrey and N. Isgur, Phys. Rev. D32,189 (1985).

[85] M. Di Pierro and E. Eichten, Phys. Rev.D64, 114004 (2001).

[86] K. Hagiwara et al., Phys. Rev. D66, 010001(2002).


[88] D. Besson et al., Phys. Rev. D68, 032002(2003).

[89] P. Krokovny et al., Phys. Rev. Lett. 91,262002 (2003).

[90] B. Aubert et al., Phys. Rev. D69, 031101(2004).




[94] http://pdglive.lbl.gov.

[95] B. Aubert, Phys. Rev. Lett. 97, 222001(2006).

[96] E. Swanson, Phys. Rept. 429, 243 (2006).

[97] M. A. Nowak, M. Rho, and I. Zahed, Phys.Rev. D48, 4370 (1993).

[98] W. A. Bardeen and C. T. Hill, Phys. Rev.D49, 409 (1994).

[99] W. A. Bardeen, E. J. Eichten, and C. T.Hill, Phys. Rev. D68, 054024 (2003).

[100] M. A. Nowak, M. Rho, and I. Zahed, ActaPhys. Polon. B35, 2377 (2004).

[101] R. N. Cahn and J. D. Jackson, Phys. Rev.D68, 037502 (2003).

[102] O. Lakhina and E. S. Swanson, Phys. Lett.B650, 159 (2007).

[103] K. Terasaki, Phys. Rev. D68, 011501 (2003).


[104] A. Hayashigaki and K. Terasaki, Prog.Theor. Phys. 114, 1191 (2006).

[105] H.-Y. Cheng and W.-S. Hou, Phys. Lett.B566, 193 (2003).

[106] L. Maiani, F. Piccinini, A. D. Polosa, andV. Riquer, Phys. Rev. Lett. 93, 212002(2004).

[107] L. Maiani, F. Piccinini, A. D. Polosa, andV. Riquer, Phys. Rev. D71, 014028 (2005).

[108] Y.-Q. Chen and X.-Q. Li, Phys. Rev. Lett.93, 232001 (2004).

[109] M. E. Bracco, A. Lozea, R. D. Matheus,F. S. Navarra, and M. Nielsen, Phys. Lett.B624, 217 (2005).

[110] M. Nielsen, R. D. Matheus, F. S. Navarra,M. E. Bracco, and A. Lozea, AIP Conf.Proc. 814, 528 (2006).

[111] E. van Beveren and G. Rupp, Phys. Rev.Lett. 91, 012003 (2003).

[112] D. S. Hwang and D.-W. Kim, Phys. Lett.B601, 137 (2004).

[113] D. S. Hwang and D. W. Kim, J. Phys. Conf.Ser. 9, 63 (2005).

[114] T. Barnes, F. E. Close, and H. J. Lipkin,Phys. Rev. D68, 054006 (2003).



[117] M. Lutz and M. Soyeur,arXiv:hep-ph/0710.1545.

[118] F. P. Sassen and S. Krewald, Int. J. Mod.Phys. A20, 705 (2005).

[119] F.-K. Guo, S. Krewald, and U.-G. Meißner,arXiv:hep-ph/0712.2953.

[120] F. Sassen, PhD thesis, Universitat Bonn,2005.

[121] A. Faessler, T. Gutsche, V. E. Lyubovitskij,and Y.-L. Ma, Phys. Rev. D76, 014005(2007).

[122] A. Faessler, T. Gutsche, V. E. Lyubovitskij,and Y.-L. Ma, Phys. Rev. D76, 114008(2007).

[123] C. Hanhart, priv. comm., 2005.

[124] T. Mehen and R. P. Springer, Phys. Rev.D70, 074014 (2004).

[125] F. E. Close and E. S. Swanson, Phys. Rev.D72, 094004 (2005).

[126] P. Colangelo and F. De Fazio, Phys. Lett.B570, 180 (2003).

[127] P. Colangelo, F. De Fazio, and A. Ozpineci,Phys. Rev. D72, 074004 (2005).

[128] X. Liu, Y.-M. Yu, S.-M. Zhao, and X.-Q. Li,Eur. Phys. J. C47, 445 (2006).

[129] M. Shifman and A. Vainshtein, Phys. Rev.D77, 034002 (2008).

[130] A. Capella, U. Sukhatme, C.-I. Tan, andJ. Tran Thanh Van, Phys. Rept. 236, 225(1994).

[131] C. Hanhart, priv. comm., 2006.

[132] E. Klempt, Phys. Rev. C66, 058201 (2002).




[136] I. Zychor et al., Phys. Rev. Lett. 96, 012002(2006).

[137] M. I. Adamovich et al., Eur. Phys. J. C50,535 (2007).



[140] K. Abe et al., Phys. Lett. B524, 33 (2002).

[141] V. Ziegler, PhD thesis, University of Iowa,2007, report SLAC-R-868.

[142] U. Loring, B. C. Metsch, and H. R. Petry,Eur. Phys. J. A10, 447 (2001).

[143] V. Guzey and M. V. Polyakov,arXiv:hep-ph/0512355, 2005.

[144] C. Baltay et al., Phys. Rev. 140, B1027(1965).


[145] B. Musgrave, Nuov. Cim. 35, 735 (1965).


[147] M. F. M. Lutz and J. Hofmann, Int. J. Mod.Phys. A21, 5496 (2006).

[148] V. Flaminio, W. Moorhead, D. Morrison,and N. Rivoire, Report CERN-HERA 84-01,1984.

[149] S. Okubo, Phys. Lett. 5, 165 (1963).

[150] G. Zweig, CERN report TH-401.

[151] J. Iizuka, Prog. Theor. Phys. Suppl. 38, 21(1966).

[152] T. Johansson, Antihyperon-hyperonproduction in antiproton-proton collisions,in AIP Conf. Proc. Eight Int. Conf. on LowEnergy Antiproton Physics, page 95, 2003.

[153] P. D. Barnes et al., Phys. Rev. C 54, 1877(1996).

[154] H. Becker et al., Nucl. Phys. B 141, 48(1978).

[155] E. Klempt et al., Phys. Rept. 368, 119(2002).

[156] M. Alberg, Nucl. Phys. A 692, 47c (2001).

[157] M. Alberg, J. Ellis, and D. Kharzeev, Phys.Lett. B 356, 113 (1995).

[158] A. G. Frodesen, O. Skjeggestad, andH. Tøfte, Probability and Statistics inParticle Physics, Universitetsforlaget,Bergen, 1979.

[159] S. Brodsky and G. Farrar, Phys. Rev. Lett.31, 1153 (1973).

[160] V. Matveev et al., Lett. Nuovo Cimento 7,719 (1972).

[161] A. V. Efremov and A. V. Radyushki, Phys.Lett. B94, 245 (1980).

[162] G. P. Lepage and S. Brodsky, Phys. Rev.D22, 2157 (1980).

[163] P. Landshoff, Phys. Rev. D10, 1024 (1974).

[164] J. P. Ralston and B. Pire, Phys. Rev. Lett.49, 1605 (1982).

[165] C. E. Carlson et al., Phys. Rev. D 46, 2891(1992).

[166] A. Eide et al., Nucl. Phys. B 60, 173 (1973).

[167] E. Eisenhandler et al., Nucl. Phys. B 96,109 (1975).

[168] T. Buran et al., Nucl. Phys. B 116, 51(1976).

[169] G. Brown and M. Rho, Phys. Rev. Lett. 66,2720 (1991).

[170] T. Hatsuda and S. Lee, Phys. Rev. C 46, 34(1992).

[171] U. Mosel, arXiv:0801.49701 [hep-ph], 2008.

[172] D. Trnka et al., Phys. Rev. Lett 94, 191303(2005).

[173] M. Naruki et al., Phys. Rev. Lett. 96,092301 (2006).

[174] R. Muto et al., Phys. Rev. Lett. 98, 042501(2007).

[175] R. Nasseripour et al., Phys. Rev. Lett 99,262302 (2007).

[176] G. Agakishiev et al., Phys. Rev. Lett 75,1272 (1995).

[177] R. Arnaldi et al., Phys. Rev. Lett. 96,162302 (2006).

[178] T. Yamazaki et al., Z. Phys. A 355, 219(1996).

[179] H. Geissel et al., Phys. Rev. Lett. 88,122301 (2002).

[180] K. Suzuki et al., Phys. Rev. Lett. 92, 072302(2004).

[181] J. G. Messchendorp et al., Phys. Rev. Lett.89, 222302 (2002).

[182] M. Nekipelov et al., Phys. Lett. B 540, 207(2002).

[183] Z. Rudy et al., Eur. Phys. J. A 15, 303(2002).

[184] R. Barth et al., Phys. Rev. Lett. 78, 4007(1997).

[185] F. Laue et al., Phys. Rev. Lett. 82, 1640(1999).

[186] M. Pfeiffer et al., Phys. Rev. Lett. 92,252001 (2004).

[187] M. Kotulla et al., Phys. Rev. Lett. 100,192302 (2008).


[188] T. Ishikawa et al., Phys. Lett. B608, 215(2005).

[189] W. Weise, in Proc. Int. Workshop on theStructure of Hadrons, Hischegg, Austria,2001.

[190] K. Tsushima, D. Lu, A. Thomas, K. Saito,and R. Landau, Phys. Rev. C 59, 2824(1999).

[191] A. Sibirtsev, K. Tsushima, and A. Thomas,Eur. Phys. J. A 6, 351 (1999).

[192] A. Hayashigaki et al., Phys. Lett. B 487, 96(2000).

[193] P. Morath, PhD thesis, TU Munchen, 2001.

[194] L. Tolos, J. Schaffner-Bielich, and A. Mishra,Phys. Rev. C 70, 025203 (2004).

[195] M. Lutz and C. Korpa, Phys. Lett. B 633,43 (2006).

[196] T. Mizutani and A. Ramos, Phys. Rev. C74, 065201 (2006).

[197] S. Brodsky, I. Schmidt, and G. de Teramond,Phys. Rev. Lett. 64, 1011 (1990).

[198] S. Brodsky and G. Miller, Phys. Lett. B412, 125 (1997).

[199] F. Klingl et al., Phys. Rev. Lett. 82, 3396(1999).

[200] S. Lee and C. Ko, Prog. Theor. Phys. Suppl.149, 173 (2003).

[201] S. Lee, in Proc. 10th Int. Conf. on HadronSpectroscopy (Hadron’03), Aschaffenburg,2003, [arXiv:nucl-th/0310080].

[202] Y. Golubeva, E. Bratkovskaya, W. Cassing,and L. Kondratyuk, Eur. Phys. J. A 17, 275(2003).

[203] W. Cassing, Y. Golubeva, andL. Kondratyuk, Eur. Phys. J. A 7, 279(2000).

[204] J. Haidenbauer, G. Krein, U.-G. Meißner,and A. Sibirtsev, Eur. Phys. J. A 33, 107(2007).

[205] R. Anderson et al., Phys. Rev. Lett. 38, 263(1977).

[206] D. Kharzeev, C. Lourenco, M. Nardi, andH. Satz, Z. Phys. C 74, 307 (1997).

[207] B. Alessandro et al., Eur. Phys. J. C33, 31(2004).

[208] B. Alessandro et al., Eur. Phys. J. C 48, 329(2006).

[209] S. S. Adler et al., Phys. Rev. Lett. 96,012304 (2006).

[210] A. Adare et al., Phys. Rev. C77, 024912(2008).

[211] T. Matsui and H. Satz, Phys. Lett. B 178,416 (1986).

[212] B. Alessandro et al., Eur. Phys. J. C 39, 335(2005).

[213] R. Arnaldi et al., Eur. Phys. J. C 43, 167(2005).

[214] R. Arnaldi et al., Phys. Rev. Lett. 99,132302 (2007).

[215] A. Sibirtsev, K. Tsushima, and A. W.Thomas, Phys. Rev. C63, 044906 (2001).

[216] A. Sibirtsev, K. Tsushima, and A. Thomas,Phys. Rev. C 75, 064903 (2007).

[217] J. Hilbert, N. Black, T. Barnes, andE. Swanson, Phys. Rev. C 75, 064907(2007).

[218] K. Seth, in Proc. Int. Workshop on theStructure of Hadrons, Hischegg, Austria,2001.

[219] L. Gerland, L. Frankfurt, and M. Strikman,Phys. Lett. B 619, 95 (2005).

[220] W.-M. Yao et al., J. Phys. G 33, 1 (2006).

[221] A. Sibirtsev, 2008, priv. communication.

[222] T. Tanimori et al., Phys. Rev. Lett. 55,1835 (1985).


[224] M. Andreotti et al., Phys. Rev. Lett. 91,091801 (2003).

[225] M. Bleicher et al., J. Phys. G25, 1859(1999).

[226] S. A. Bass et al., Prog. Part. Nucl. Phys. 41,225 (1998).

[227] A. Faessler, G. Lubeck, and K. Shimizu,Phys. Rev. D26, 3280 (1982).


[228] T. Burvenich et al., Phys. Lett. B 542, 261(2002).

[229] I. N. Mishustin, L. M. Satarov, T. J.Burvenich, H. Stocker, and W. Greiner,Phys. Rev. C71, 035201 (2005).

[230] A. Larionov, I. Mishustin, L. Saratov, andW. Greiner, arXiv:0802.1845 [nucl-th](2008).

[231] C.-Y. Wong, A. Kerman, G. Satchler, andA. Mackellar, Phys. Rev. C 29, 574 (1984).

[232] C. Batty, E. Friedman, and A. Gal, Phys.Rept. 287, 385 (1997).

[233] E. Friedman, A. Gal, and J. Mares, Nucl.Phys. A 761, 283 (2005).

[234] S. Teis, W. Cassing, T. Maruyama, andU. Mosel, Phys. Rev. C 50, 388 (1994).

[235] C. Spieles et al., Phys. Rev. C53, 2011(1996).

[236] A. Sibirtsev, W. Cassing, G. I. Lykasov, andM. V. Rzyanin, Nucl. Phys. A632, 131(1998).

[237] J. Pochodzalla, Phys. Lett. B669, 306(2008).

[238] P. Jain, B. Pire, and J. P. Ralston, Phys.Rept. 271, 67 (1996).

[239] L. Frankfurt, G. A. Miller, and M. Strikman,Comments Nucl. Part. Phys. 21, 1 (1992).

[240] L. L. Frankfurt, G. A. Miller, andM. Strikman, Ann. Rev. Nucl. Part. Sci. 44,501 (1994).

[241] E. M. Aitala et al., Phys. Rev. Lett. 86,4773 (2001).

[242] G. R. Farrar, H. Liu, L. L. Frankfurt, andM. I. Strikman, Phys. Rev. Lett. 61, 686(1988).

[243] B. Clasie et al., Phys. Rev. Lett. 99, 242502(2007).

[244] B. Pire and J. P. Ralston, Phys. Lett. B117,233 (1982).


[246] A. S. Carroll et al., Phys. Rev. Lett. 61,1698 (1988).

[247] J. L. S. Aclander et al., Phys. Rev. C70,015208 (2004).



[250] S. J. Brodsky and G. F. de Teramond, Phys.Rev. Lett. 60, 1924 (1988).

[251] B. K. Jennings and G. A. Miller, Phys. Lett.B236, 209 (1990).

[252] S. J. Brodsky and A. H. Mueller, Phys. Lett.B206, 685 (1988).

[253] G. R. Farrar, L. L. Frankfurt, M. I.Strikman, and H. Liu, Nucl. Phys. B345,125 (1990).

[254] L. Gerland, L. Frankfurt, M. Strikman,H. Stoecker, and W. Greiner, Phys. Rev.Lett. 81, 762 (1998).

[255] W. Greiner, Int. Journal of Modern PhysicsE 5, 1 (1995).

[256] P. Haensel, A.Y.Potekhin, and D. Yakovlev,Neutron Stars 1. Equation of state andstructure, Springer, 2007.

[257] F. Weber, R. Negreiros, and P. Rosenfield,Springer Lecture Notes ,arXiv:arXiv:0705.2708.

[258] T. K. Jha, H. Mishra, and V. Sreekanth,Phys. Rev. C 77, 045801 (2008).

[259] H. Dapo, B.-J. Schafer, and J. Wambach,arXiv:0811.29391 [nucl-th].

[260] N. Kaiser and W. Weise, Phys. Rev. C 71,015203 (2005).

[261] R. B. Wiringa and S. C. Pieper, Phys. Rev.Lett. 89, 182501 (2002).

[262] S. C. Pieper, R. B. Wiringa, and J. Carlson,Phys. Rev. C 70, 054325 (2004).

[263] S. C. Pieper, Quantum Monte CarloCalculations of Light Nuclei, in Lecturenotes for Course CLXIX - ”NuclearStructure far from Stability: New Physicsand new Technology”, 2007,arXiv:0711.1500v1 [nucl-th].

[264] I. Stetcu, B. Barrett, and U. van Kolck,Phys. Rev. C 73, 037307 (2006).


[265] C. Keil, F. Hofmann, and H. Lenske, Phys.Rev. C 61, 06401 (2000).

[266] F. Hofmann, C. Keil, and H. Lenske, Phys.Rev. C 64, 034314 (2001).

[267] S. Beane, P. Bedaque, A. Parreno, andM. Savage, Nucl. Phys. A 747, 55 (2005).

[268] M. Savage, Baryon-baryon interactions fromthe lattice, in Proc. of the IX InternationalConference on Hypernuclear and StrangeParticle Physics, edited by J. Pochodzallaand T. Walcher, page 301, SIF andSpringer-Verlag Berlin Heidelberg, 2007,arXiv: 0612063 [nucl-th].

[269] A. G. Nicola and J. Pelaez, Phys. Rev. D65, 054009 (2002).

[270] H. Polinder, J. Haidenbauer, and U.-G. M.ner, Nucl. Phys. A 779, 244 (2006).

[271] L. Tolos, A. Ramos, and E. Oset, Phys. Rev.C 74, 015203 (2006).

[272] M. Lutz, C. Korpa, and M. Moeller, Nucl.Phys. A 808, 124 (2008).

[273] I. Stetcu, B. Barrett, and U. van Kolck,Phys. Lett. B 653, 358 (2007).

[274] B. Borasoy, E. Epelbaum, H. Krebs, D. Lee,and U.-G. Meißner, Eur. Phys. J. A 31, 105(2007).

[275] P. Navratil et al., Light nuclei from chiralEFT interactions, in Proceedings of the 20thEuropean Conference on Few-Body Problemsin Physics (EFB20), 2007.

[276] Y. Kondo et al., Nucl. Phys. A 676, 371(2000).

[277] J. Ahn et al., Phys. Lett. B 633, 214 (2006).

[278] O. Hashimoto and H. Tamura, Prog. Part.Nucl. Phys. 57, 566 (2006).

[279] K. Itonaga, T. Ueda, and T. Motoba, Nucl.Phys. A 691, 197c (2001).

[280] A. Parreno, A. Ramos, and C. Bennhold,Nucl. Phys. A 65, 015205 (2001).

[281] K. Sasaki, T. Inoue, and M. Oka, Nucl.Phys. A 726, 349 (2003).

[282] J. Dubach, G. B. Feldman, B. R. Holstein,and L. de la Torre, Ann. Phys. 249, 146(1996).

[283] T. Motoba, Nucl. Phys. A 691, 231c (2001).

[284] T. Rijken and Y. Yamamoto,arXiv:hep-ph/0207358v1.

[285] K. Tanida et al., Plan for the measurementof Ξ−-atomic X rays at J-PARC, in Proc. ofthe IX International Conference onHypernuclear and Strange Particle Physics,edited by J. Pochodzalla and T. Walcher,page 145, SIF and Springer-Verlag BerlinHeidelberg, 2007.

[286] A. Buchmann, Z. Naturforschung 52, 877(1997).

[287] A. Buchmann and R. F. Lebed, Phys. Rev.D 67, 016002 (2003).

[288] R. Jaffe, Phys. Rev. Lett. 38, 195 (1977).

[289] R. Jaffe, Phys. Rev. Lett. 38, 617E (1977).

[290] T. Sakai, K. Shimizu, and K. Yazaki, Prog.Theor. Phys. Suppl. 137, 121 (2000).

[291] T. Yamada and C. Nakamoto, Phys. Rev. C62, 034319 (2000).

[292] K. S. Myint, S. Shinmura, and Y. Akaishi,Eur. Phys. J. A 16, 21 (2003).

[293] I. Afnan and B. Gibson, Phys. Rev. C 67,017001 (2003).

[294] I. Filikhin, A. Gal, and V. Suslov, Phys.Rev. C 68, 024002 (2003).

[295] J. Pochodzalla, Nucl. Phys. A 754, 430c(2005).

[296] F. Ferro, M. Agnello, F. Iazzi, andK. Szymanska, Nucl. Phys. A 789, 209(2007).

[297] W. R. Lozowski, D. Steski, H. Huang, andC. Naylor, Nucl. Instr. and Meth. in PhysicsResearch A 590, 157 (2008).

[298] P. V. A.B. Kaidalov, Z. Phy. C 63, 517(1994).

[299] T. Yamada and K. Ikeda, Nucl. Phys.A585, 79c, 1995.

[300] T. Yamada and K. Ikeda, Phys. Rev. C 56,3216 (1997).

[301] Y. Hirata, Y. Nara, A. Ohnishi, T. Harada,and J. Randrup, Nucl. Phys. A 639, 389c(1998).


[302] Y. Hirata, Y. Nara, A. Ohnishi, T. Harada,and J. Randrup, Prog. Theor. Phys. 102, 89(1999).

[303] D. Millener, C. Dover, and A. Gal, Prog.Theor. Phys. Suppl. 117, 307 (1994).

[304] K. Ikeda et al., Prog. Theor. Phys. 91, 747(1994).

[305] A. S. Lorente, A. Botvina, andJ. Pochodzalla, (in preparation).

[306] E. Fermi, Progr. Theor. Phys. 5, 570 (1950).

[307] J. Bondorf, A. Botvina, A. Iljinov,I. Mishustin, and K. Sneppen, Phys. Rep.257, 133 (1995).

[308] A. Botvina, Y. Golubeva, and A. Iljinov,INR, P-0657, Moscow (1990).

[309] A. Botvina et al., Z. Phys. A 345, 413(1993).

[310] A. Sudov et al., Nucl. Phys. A 554, 223(1993).

[311] M. Danysz et al., Nucl. Phys. 49, 121 (1963).

[312] D. Prowse, Phys. Rev. Lett 17, 782 (1966).

[313] S. Aoki et al., Prog. Theor. Phys. 85, 1287(1991).

[314] J. Ahn et al., Phys. Rev. Lett. 87, 132504(2001).

[315] H. Takahashi et al., Phys. Rev. Lett. 87,212501 (2001).

[316] R. Dalitz et al., Proc. R. Soc. Lond. A 426,1 (1989).

[317] C. Dover, D. Millener, A. Gal, and D. Davis,Phys. Rev. C 44, 1905 (1991).

[318] E. Hiyama et al., Phys. Rev. C 66, 024007(2002).

[319] S. Randeniya and E. Hungerford, Phys. Rev.C 76, 064308 (2007).

[320] D. Lanskoy and Y. Yamamoto, Phys. Rev. C69, 014303 (2004).

[321] M. Shoeb, Phys. Rev. C 69, 054003 (2004).

[322] H. Nemura, S. Shinmura, Y. Akaishi, andK. S. Myint, Phys. Rev. Lett. 94, 202502(2005).

[323] I. Filikhin and A. Gal, Phys. Rev. Lett. 89,172502 (2002).

[324] H. Nemura, Y. Akaishi, and K. S. Myint,Phys. Rev. C 67, 051001(R) (2003).

[325] M. Shoeb, Phys. Rev. C 71, 024004 (2005).

[326] H. Bando, T. Motoba, and J. Zofka, Int. J.Mod. Phys. A5, 4021 (1990).

[327] F. Ajzenberg-Selove, Nucl. Phys. A 433, 1(1985).

[328] G. Kopylov, Principles of resonancekinematics, Moscow, 1970.

[329] C. Dover and A. Gal, Ann. Phys. 147, 309(1983).

[330] E. Friedman and A. Gal, Phys, Report 452,89 (2007).

[331] C. J. Batty, E. Friedman, and A. Gal, Phys.Rev. C 59, 295 (1999).

[332] S. Aoki et al., Phys. Lett. B 355, 45 (1995).

[333] A. S. Lorente et al., Nucl. Inst. Meth A 573,410 (2007).

[334] M. Kavatsyuk et al., GSI Annual report(2007).

[335] P. Leleux et al., Astronomy andAstrophysics 411, L85 (2003).

[336] A. Bamberger et al., Nucl. Phys. B 60, 1(1973).

[337] M. Bedjidian et al., Phys. Lett. 62, 467(1976).

[338] M. May et al., Phys. Rev. Lett. 51, 2085(1983).

[339] H. Akikawa et al., Phys. Rev. Lett. 88,082501 (2002).

[340] A. Galoyan, Private Comunication.

[341] A. V. Belitsky and A. V. Radyushkin, Phys.Rept. 418, 1 (2005).

[342] X. Ji, Ann. Rev. Nucl. Part. Sci. 54, 413(2004).

[343] M. Diehl, Phys. Rept. 388, 41 (2003).

[344] K. Goeke, M. V. Polyakov, andM. Vanderhaeghen, Prog. Part. Nucl. Phys.47, 401 (2001).


[345] X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997).

[346] A. V. Radyushkin, Phys. Lett. B380, 417(1996).

[347] X.-D. Ji, Phys. Rev. D55, 7114 (1997).

[348] A. V. Radyushkin, Phys. Rev. D58, 114008(1998).

[349] M. Diehl, T. Feldmann, R. Jakob, andP. Kroll, Eur. Phys. J. C8, 409 (1999).

[350] P. Kroll and A. Schafer, Eur. Phys. J. A26,89 (2005).

[351] C.-C. Kuo et al., Phys. Lett. B621, 41(2005).

[352] B. Pire and L. Szymanowski, Phys. Rev.D71, 111501 (2005).

[353] B. Pire and L. Szymanowski, Phys. Lett.B622, 83 (2005).

[354] A. Freund, A. V. Radyushkin, A. Schafer,and C. Weiss, Phys. Rev. Lett. 90, 092001(2003).


[356] J. Lansberg, B. Pire, and L. Szymanowski,Phys. Rev. D76, 111502 (2007).

[357] S. Ong and J. Van de Wiele,HAL:in2p3-00222925 (2008) .

[358] J. P. Ralston and D. E. Soper, Nucl. Phys.B152, 109 (1979).

[359] D. Boer, Phys. Rev. D60, 014012 (1999).

[360] D. Boer and P. J. Mulders, Phys. Rev. D57,5780 (1998).

[361] J. C. Collins and D. E. Soper, Phys. Rev.D16, 2219 (1977).

[362] X. Artru and M. Mekhfi, Z. Phys. C45, 669(1990).

[363] J. L. Cortes, B. Pire, and J. P. Ralston, Z.Phys. C55, 409 (1992).

[364] R. L. Jaffe and X.-D. Ji, Phys. Rev. Lett.67, 552 (1991).

[365] J. Soffer, Phys. Rev. Lett. 74, 1292 (1995).

[366] C. Bourrely and J. Soffer, Eur. Phys. J.C36, 371 (2004).

[367] D. de Florian and W. Vogelsang, Phys. Rev.D71, 114004 (2005).

[368] R. D. Field and R. P. Feynman, Phys. Rev.D15, 2590 (1977).

[369] R. P. Feynman, R. D. Field, and G. C. Fox,Phys. Rev. D18, 3320 (1978).

[370] A. Bacchetta, U. D’Alesio, M. Diehl, andC. A. Miller, Phys. Rev. D70, 117504(2004).

[371] V. Barone, A. Drago, and P. G. Ratcliffe,Phys. Rept. 359, 1 (2002).

[372] P. J. Mulders and R. D. Tangerman, Nucl.Phys. B461, 197 (1996).

[373] A. Idilbi, X.-d. Ji, J.-P. Ma, and F. Yuan,Phys. Rev. D70, 074021 (2004).

[374] D. Boer, Nucl. Phys. B603, 195 (2001).

[375] G. L. Kane, J. Pumplin, and W. Repko,Phys. Rev. Lett. 41, 1689 (1978).

[376] U. D’Alesio and F. Murgia, Prog. Part.Nucl. Phys. 61 2008, 394 (2008).

[377] X. Ji, J.-W. Qiu, W. Vogelsang, andF. Yuan, Phys. Rev. Lett. 97, 082002 (2006).

[378] X. Ji, J.-w. Qiu, W. Vogelsang, and F. Yuan,Phys. Rev. D73, 094017 (2006).

[379] X. Ji, J.-W. Qiu, W. Vogelsang, andF. Yuan, Phys. Lett. B638, 178 (2006).

[380] Y. Koike, W. Vogelsang, and F. Yuan, Phys.Lett. B659, 878 (2008).

[381] A. Brandenburg, O. Nachtmann, andE. Mirkes, Z. Phys. C60, 697 (1993).

[382] C. S. Lam and W.-K. Tung, Phys. Rev.D18, 2447 (1978).

[383] C. S. Lam and W.-K. Tung, Phys. Lett.B80, 228 (1979).

[384] C. S. Lam and W.-K. Tung, Phys. Rev.D21, 2712 (1980).

[385] J. Badier et al., Zeit. Phys. C11, 195 (1981).

[386] S. Falciano et al., Z. Phys. C31, 513 (1986).

[387] M. Guanziroli et al., Z. Phys. C37, 545(1988).

[388] J. S. Conway et al., Phys. Rev. D39, 92(1989).


[389] E. L. Berger and S. J. Brodsky, Phys. Rev.Lett. 42, 940 (1979).

[390] E. L. Berger, Z. Phys. C4, 289 (1980).

[391] A. Brandenburg, S. J. Brodsky, V. V.Khoze, and D. Mueller, Phys. Rev. Lett. 73,939 (1994).

[392] K. J. Eskola, P. Hoyer, M. Vanttinen, andR. Vogt, Phys. Lett. B333, 526 (1994).

[393] R. L. Jaffe and X.-D. Ji, Phys. Rev. Lett.71, 2547 (1993).

[394] O. Nachtmann and A. Reiter, Z. Phys. C24,283 (1984).

[395] D. Boer, A. Brandenburg, O. Nachtmann,and A. Utermann, Eur. Phys. J. C40, 55(2005).

[396] L. P. Gamberg and G. R. Goldstein, Phys.Lett. B650, 362 (2007).

[397] L. Y. Zhu et al., Phys. Rev. Lett. 99, 082301(2007).

[398] A. Bianconi and M. Radici, J. Phys. G31,645 (2005).

[399] D. W. Sivers, Phys. Rev. D43, 261 (1991).

[400] J. C. Collins, Nucl. Phys. B396, 161 (1993).

[401] R. L. Jaffe, hep-ph/9602236 (1996).

[402] D. W. Sivers, Phys. Rev. D41, 83 (1990).

[403] A. V. Efremov, K. Goeke, and P. Schweitzer,Phys. Lett. B568, 63 (2003).

[404] M. Anselmino, M. Boglione, U. D’Alesio,E. Leader, and F. Murgia, Phys. Rev. D71,014002 (2005).

[405] M. Anselmino, M. Boglione, and F. Murgia,Phys. Lett. B362, 164 (1995).

[406] M. Anselmino, A. Drago, and F. Murgia,hep-ph/9703303 (1997).

[407] U. Elschenbroich, G. Schnell, and R. Seidl,hep-ex/0405017 (2004).

[408] J. C. Collins, Phys. Lett. B536, 43 (2002).

[409] A. V. Belitsky, X. Ji, and F. Yuan, Nucl.Phys. B656, 165 (2003).

[410] S. J. Brodsky, D. S. Hwang, and I. Schmidt,Phys. Lett. B530, 99 (2002).

[411] S. J. Brodsky, D. S. Hwang, and I. Schmidt,Nucl. Phys. B642, 344 (2002).

[412] X.-d. Ji and F. Yuan, Phys. Lett. B543, 66(2002).

[413] X.-d. Ji, J.-p. Ma, and F. Yuan, Phys. Rev.D71, 034005 (2005).

[414] X.-d. Ji, J.-P. Ma, and F. Yuan, Phys. Lett.B597, 299 (2004).

[415] A. Idilbi, X.-d. Ji, and F. Yuan, Phys. Lett.B625, 253 (2005).

[416] M. Anselmino et al., Phys. Rev. D72,094007 (2005).

[417] A. V. Efremov, K. Goeke, S. Menzel,A. Metz, and P. Schweitzer, Phys. Lett.B612, 233 (2005).

[418] W. Vogelsang and F. Yuan, Phys. Rev.D72, 054028 (2005).

[419] J. C. Collins et al., Phys. Rev. D73, 094023(2006).

[420] A. Bacchetta, F. Conti, and M. Radici,arXiv:0807.0323 (2008).

[421] N. Hammon, O. Teryaev, and A. Schafer,Phys. Lett. B390, 409 (1997).

[422] D. Boer, P. J. Mulders, and O. V. Teryaev,Phys. Rev. D57, 3057 (1998).

[423] D. Boer and P. J. Mulders, Nucl. Phys.B569, 505 (2000).

[424] D. Boer and J.-w. Qiu, Phys. Rev. D65,034008 (2002).

[425] J.-w. Qiu and G. Sterman, Phys. Rev. D59,014004 (1999).

[426] M. Burkardt and D. S. Hwang, Phys. Rev.D69, 074032 (2004).

[427] M. Burkardt and G. Schnell, Phys. Rev.D74, 013002 (2006).

[428] A. Airapetian et al., Phys. Rev. Lett. 94,012002 (2005).

[429] M. Diefenthaler, AIP Conf. Proc. 792, 933(2005).

[430] M. Diefenthaler, hep-ex 0706.2242, Proc. ofMunich 2007 Deep-inelastic scattering , 579(2007).


[431] J. C. Collins et al., hep-ph/0510342, Proc. ofThe International Workshop on TransversePolarisation Phenomena in Hard Processes(Transversity 2005) (2005).

[432] M. Anselmino et al., hep-ph/0511017, Proc.of The International Workshop onTransverse Polarisation Phenomena in HardProcesses (Transversity 2005) (2005).

[433] V. Y. Alexakhin et al., Phys. Rev. Lett. 94,202002 (2005).

[434] E. S. Ageev et al., Nucl. Phys. B765, 31(2007).

[435] M. Alekseev et al., Phys. Lett. B673, 127(2009).

[436] A. Courtoy, S. Scopetta, and V. Vento,hep-ph/0811.2368, Proc. of InternationalWorkshop On Diffraction In High EnergyPhysics (Diffraction 2008) (2008).

[437] A. V. Efremov, K. Goeke, and P. Schweitzer,Czech. J. Phys. 56, F181 (2006).

[438] A. V. Efremov, K. Goeke, and P. Schweitzer,Phys. Rev. D73, 094025 (2006).

[439] S. Levorato, hep-ex/0808.0086, Proc. of IIInternational Workshop on TransversePolarisation Phenomena in Hard Processes(Transversity 2008) (2008).

[440] A. Bianconi, J. Phys. G35, 115003 (2008).

[441] M. Anselmino et al., hep-ph/0809.3743,Proc. of II International Workshop onTransverse Polarisation Phenomena in HardProcesses (Transversity 2008) (2008).

[442] V. Abazov et al., ASSIA LOI, The structureof the nucleon: A study of spin-dependentinteractions with antiprotons,hep-ex/0507077, 2004.

[443] PAX LOI,http://www.fz-juelich.de/ikp/pax.

[444] R. D. Tangerman and P. J. Mulders, Phys.Rev. D51, 3357 (1995).

[445] O. Martin, A. Schafer, M. Stratmann, andW. Vogelsang, Phys. Rev. D57, 3084 (1998).

[446] V. Barone, T. Calarco, and A. Drago, Phys.Rev. D56, 527 (1997).

[447] A. V. Efremov, K. Goeke, and P. Schweitzer,Eur. Phys. J. C35, 207 (2004).

[448] M. Anselmino, V. Barone, A. Drago, andN. N. Nikolaev, Phys. Lett. B594, 97 (2004).

[449] G. Altarelli, R. K. Ellis, and G. Martinelli,Nucl. Phys. B157, 461 (1979).

[450] A. J. Buras and K. J. F. Gaemers, Nucl.Phys. B132, 249 (1978).

[451] E. Anassontzis et al., Phys. Rev. D38, 1377(1988).

[452] H. Shimizu, G. Sterman, W. Vogelsang, andH. Yokoya, Phys. Rev. D71, 114007 (2005).

[453] G. Moreno et al., Phys. Rev. D43, 2815(1991).

[454] A. Bianconi and M. Radici, Phys. Rev.D71, 074014 (2005).

[455] A. Bianconi, Nucl. Instrum. Meth. A593,562 (2008).


[457] A. Bianconi and M. Radici, J. Phys. G34,1595 (2007).



[460] C. F. Perdrisat, V. Punjabi, andM. Vanderhaeghen, Prog. Part. Nucl. Phys.59, 694 (2007).

[461] M. Jones et al., Phys. Rev. Lett 84, 1398(2000).

[462] O. Gayou et al., Phys. Rev. Lett 88, 092301(2002).

[463] O. Gayou et al., Phys. Rev. C 71, 055202(2005).

[464] M. Jones et al., Phys. Rev. C 74, 035201(2006).

[465] V. Punjabi et al., Phys. Rev. C71, 055202(2005).

[466] A. Zichichi et al., Nuovo Cim. 24, 170(1962).

[467] M. Ambrogiani et al., Phys. Rev. D60,032002 (1999), and references therein.



[469] G. I. Gakh and E. Tomasi-Gustafsson, Nucl.Phys. A771, 169 (2006).

[470] G. I. Gakh and E. Tomasi-Gustafsson, Nucl.Phys. A761, 120 (2005).

[471] C. Adamuscin, E. Kuraev,E. Tomasi-Gustafsson, and F. Maas,Phys.Rev. C75, 045205 (2007).

[472] E. Tomasi-Gustafsson and M. P. Rekalo,Phys.Lett. B504, 291 (2001).

[473] E. Eisenhandler et al., Nucl. Phys. B 96,109 (1975).

[474] T. Buran et al., Nucl. Phys. B 116, 51(1976).

[475] T. Berglund et al., Nucl. Phys. B 137, 276(1978).

[476] R. Dulude et al., Phys. Lett 79B, 329(1978).

[477] E. Tomasi-Gustafsson, F. Lacroix,C. Duterte, and G. I. Gakh, Eur. Phys. J.A24, 419 (2005).

[478] J. P. Lansberg, B. Pire, and L. Szymanowski,Nucl. Phys. Proc. Suppl. 184, 239 (2008).

[479] I. Bigi, Surveys High Energy Phys. 12, 269(1998).




[483] G. Burdman, hep-ph/9407378.

[484] P. Harrison and H. Quinn, editors, TheBabar Physics Book, SLAC, 1998,SLAC-R-504.

[485] P. Kroll, Invited talk at SuperLEARWorkshop, Zurich, Switzerland, Oct 9-12,1991.

[486] N. H. Hamann, Prepared for SUPERLEARWorkshop, Zurich, Swizterland, 9-12 Oct1991.

191

5 Summary and Outlook

Software and Data Production

The aim of the PANDA Physics Book benchmarkstudies was to demonstrate the feasibility of theplanned physics program and moreover to showthe expected physics performance for the upcom-ing measurements with the PANDA detector. Thisrequires accurate simulation studies of the physicschannels of interest and of the relevant backgroundby taking into account the complete PANDA de-tector. A huge number of background events wereneeded because the total pp cross section in this en-ergy regime is between 50 - 100 mb and comparedto that the cross sections of the most physics chan-nels are expected to be very low and are typicallyin the order of pb or nb. In order to meet theserequirements an offline software has been devisedfollowing an object oriented approach and makinguse of several well-tested software tools and pack-ages from other HEP experiments. These packageshave been adapted to the PANDA needs.

The generation and processing of the data is sub-divided into a couple of well defined stages: Theevent generation, the particle tracking utilising theGEANT4 transport code, the digitisation, whichmodels the signals and their processing in the front-end electronics of the detectors, the reconstruction,which finally creates lists of particle candidates, andat the last stage, the physics analysis. For this finalstep the software provides besides low-level anal-ysis tools also high-level analysis tools which allowto reconstruct decay trees, perform geometrical andkinematic fits, and to refine the event selection in avery easy and user friendly manner.

The very time consuming data production has beenorganised in a central way and was distributed overfour computing farms at IPNO in Orsay, at CCIN2P3in Lyon, at the Ruhr-Universitat Bochum, and atthe GSI at Darmstadt. Approximately 1011 eventsin total have been generated. Sophisticated filtershave been applied on this event generator level, sothat finally 22 · 106 signal events for 22 channels,1002 · 106 dedicated background events includingthe dominant background reactions for the individ-ual analyses, and 280·106 generic background eventshave been simulated and reconstructed in 29 weeks.The bookkeeping for this data production has beenrealised using a MySQL database in such a way thatall job scripts and configuration files get producedautomatically by Perl and PHP scripts.

The development of this software has been startedafter the preparation of the PANDA TechnicalProgress Report in spring 2005. In parallel to theseactivities a new software project has been initiatedin autumn 2006, with the aim to realise a next-generation software for PANDA. The objectives forthis new software, called PANDAroot, are to im-prove the accessibility for beginning users and de-velopers, to increase the flexibility to cope withfuture developments and to enhance synergy withother particle physics experiments. The core ser-vices are provided by the FAIRroot code, which isbased on the object-oriented ROOT software andwhich makes use of the Virtual Monte-Carlo (VMC)interface. Two physics cases have been investigatedby making use of the PANDAroot software, namelythe crossed channel compton scattering and the hy-pernuclei physics.

Physics Case and Outlook

Thanks to the software tools developed and sum-marised above the performance of the detector andthe sensitivity to the various physics channels havebeen estimated reliably in terms of geometrical ac-ceptance, resolution and signal/background ratios.

For the benchmark channels chosen for this reportthe simulations show that the final states of interestcan be detected with good efficiency and that thebackground contamination is at an acceptable level.This demonstrates the feasibility of the plannedphysics programme.

The experimental setup used in this report is not fi-nal: some detector components are still undergoingR&D and will be finalised in the coming months.For this reason the results presented here are tobe regarded as preliminary. Further improvementswill come from the new software framework beingdeveloped as well as from advances in the back-ground simulations. Progress in theoretical calcu-lations will yield better estimates of presently un-known cross sections, which will result in more reli-able evaluations of signal/background ratios. A newversion of the physics book is planned, which willreflect the progress described above and which willfeature a more complete list of benchmark channels.


Acknowledgments

We acknowledge financial support fromthe Bundesministerium fur Bildung undForschung (bmbf), the Deutsche Forschungs-gemeinschaft (DFG), the Forschungszen-trum Julich GmbH, Julich, the Universityof Groningen, Netherlands, the Gesellschaftfur Schwerionenforschung mbH (GSI),Darmstadt, the Helmholtz-GemeinschaftDeutscher Forschungszentren (HGF), theSchweizerischer Nationalfonds zur Forderungder wissenschaftlichen Forschung (SNF), theRussian funding agency “State Corpora-tion for Atomic Energy Rosatom”, theCNRS/IN2P3 and the Universite Paris-sud,the British funding agency “Science andTechnology Facilities Council” (STFC),the Instituto Nazionale di Fisica Nucleare(INFN), the Swedish Research Council, thePolish Ministry of Science and Higher Edu-cation, the European Community FP6 FAIRDesign Study: DIRACsecondary-Beams,contract number 515873, the EuropeanCommunity FP6 Integrated InfrastructureInitiative: HadronPhysics, contract numberRII3-CT-2004-506078, and the DeutscherAkademischer Austauschdienst (DAAD).


ADC Analog to Digital Converter

AOD Analysis Object Data

APD Avalanche Photo Diode

API Application Programming Interface

ASIC Application Specific Integrated Circuit

ATLAS A Toroidal LHC ApparatuS

BNL Brookhaven National Laboratory

CAD Computer Aided Design

CDR Conceptual Design Report

CERN Conseil European pour la Recherche Nu-cleaire

CKM Cabbibo-Kobayashi-Maskawa

CL Confidence Level

CLAS CEBAF Large Acceptance Spectrometer

COMPASS Common Muon Proton Apparatusfor Structure and Spectroscopy

COSY Cooler Synchrotron

CT Central Tracker

CVS Code Versioning System

DAQ Data Acquisition

DCH Drist Chambers

DESY Deutsches Elektronensynchrotron

DIRC Detector for Internally Reflected CherenkovLight

DPM Dual Parton Model

DSP Digital Signal Processor

DVCS Deeply Virtual Compton Scattering

DY Drell-Yan

EMC Electromagnetic Calorimeter

ESD Event Summary Data

EU European Union

FADC Flash ADC

FAIR Facility for Antiproton and Ion Research

FE Front-End

FEE Front-End Electronics

FNAL Fermi National Laboratory

FPGA Field Programmable Gate Array

FS Forward Spectrometer

GEM Gas Electron Multiplier

GPD Generalized Parton Distribution

GSI Gesellschaft fur Schwerionenforschnung

HC Hadron Calorimeter

HESR High Energy Storage Ring

HFG Hermann von Helmholtz-GemeinschaftDeutscher Forschungszentren

HV High Voltage

ISR Initial State Radiation

IP Interaction point

IN2P3 Institut National de Physique Nucleaire etde Physique des Particules

INFN Istituto Nazionale di Fisica Nucleare

KVI Kernfysisch Versneller Instituut

LAAPD Large Area APD

LEAR Low Energy Antiproton Ring

LED Light Emission Diode

LH Likelihood

LHC Large Hadron Collider

LOI Letter of Intent

LQCD Lattice QCD

MAPS Monolithic Active Pixel Sensor

MC Monte Carlo

MDC Mini Drift Chamber

MLP Multilayer Perzeptron

MUD Muon Detector

MVD Micro Vertex Detector

NRQCD Non-Relativistic QCD

PHP Hypertext Preprocessor

PID Particle Identification

PMT Photomultiplier

PSI Paul Scherrer Institute


PWA Partial Wave Analysis

PWO Lead Tungstate

QA Quality Assurance

QCD Quantum Chromo Dynamics

QED Quantum Electrodynamics

RICH Ring Imaging Cherenkov Counter

SLAC Stanford Linear Accelerator Center

SQL Structured Query Language

SSA Single Spin Asymmetry

SSL Secure Socket Layer

STT Straw Tube Tracker

TCL Tool Command Language

TCS Trigger Control System

TDA Transition Distribution Amplitude

TDC Time to Digital Converter

TLFF Time-like Form Factor

TOF Time-of-Flight Detector

TOP Time-of-Propagation

ToT Time-over-Threshold

TPC Time Projection Chamber

TS Target Spectrometer

TSL The Svedberg Laboratory

UrQMD Ultra-relativistic Quantum MolecularDynamic

VGM Virtual Geometry Model

VMC Virtual Monte Carlo

WACS Wide Angle Compton Scattering

XML Extensible Markup Language

197

List of Figures

1.1 The running of the strong couplingconstant as function of the scale µ [1]. 2

1.2 LQCD results divided by experimen-tal values for selected quantities inhadronic physics. . . . . . . . . . . . 4

1.3 The LQCD glueball spectrum inpure SU(3) gauge theory [6]. . . . . . 5

1.4 LQCD predictions for the charmo-nium, the glueball and the spin-exotic cc-glue hybrids spectrum inquenched lattice QCD. . . . . . . . . 7

2.1 Artistic view of the PANDA Detector 14

2.2 Side view of the target spectrometer 15

2.3 Schematic of the target and beampipe setup with pumps. . . . . . . . 15

2.4 The Micro-vertex detector of PANDA 17

2.5 Straw Tube Tracker in the TargetSpectrometer . . . . . . . . . . . . . 18

2.6 GEM Time Projection Chamber inthe Target Spectrometer . . . . . . . 18

2.7 The PANDA barrel and end-cap EMC 20

2.8 Integration of the secondary targetand the germanium Cluster–array inthe PANDA detector. . . . . . . . . . 21

2.9 Layout out the secondary sandwichtarget. . . . . . . . . . . . . . . . . . 21

2.10 Design of the γ–ray spectroscopysetup with 15 germanium cluster de-tector, each comprising 3 germaniumcrystals. . . . . . . . . . . . . . . . . 21

2.11 Schematic overview of the luminositymonitor concept. . . . . . . . . . . . 23

2.12 Top view of the experimental area . 26

2.13 Schematic view of the HESR. . . . . 28

2.14 Time dependent luminosity duringthe cycle L(t) versus the time in thecycle. Different measures for beampreparation are indicated. . . . . . . 29

2.15 Cycle average luminosity vs. cycletime at 1.5 (left) and 15 GeV/c (right). 29

2.16 Maximum average luminosityLmaxvs. atomic charge Z for threedifferent beam momenta. . . . . . . . 30

2.17 ψ(2S) resonance scans. . . . . . . . . 32

2.18 Kinematical factors used in the de-termination of the centre-of-mass en-ergy from the velocity of antiprotonsin the rf bucket. . . . . . . . . . . . . 33

2.19 Statistical uncertainty in the reso-nance width as a function of the ra-tio between energy spread (GaussianFWHM ΓB) and resonance width Γ. 33

2.20 Distortion of the resonance shape asa function of the ratio between en-ergy spread (Gaussian FWHM ΓB)and resonance width Γ. . . . . . . . 33

3.1 Possible processes in pp-interactionsand their estimated energy depen-dencies. . . . . . . . . . . . . . . . . 40

3.2 Material budget in front of the EMC 44

3.3 The number of detected Cerenkovphotons versus the polar angle of pions 45

3.4 Difference between the reconstructedand the expected Cerenkov angle . . 45

3.5 Pixel hit resolution on sensor coordi-nates . . . . . . . . . . . . . . . . . . 46

3.6 Tracking reconstruction efficiency . . 47

3.7 The momentum resolution for pionsmomentum of 1 GeV/c momentum ata polar angle of 20 . . . . . . . . . . 47

3.8 The vertex resolution for pions of p =3 GeV/c momentum. . . . . . . . . . 48

3.9 Leakage correction function for thebarrel EMC in the θ range between22 and 90 . . . . . . . . . . . . . . 49

3.10 Leakage correction function depend-ing on the deposited energy for theShashlyk calorimeter . . . . . . . . . 49

3.11 Typical truncated dE/dx plot . . . . 50

3.12 dE/dx versus track momentum inthe MVD for different particle species 50

3.13 Width parameters of the energy lossinformation from the MVD . . . . . 51

3.14 Distribution of the likelihood forelectron identification. . . . . . . . . 52


3.15 Efficiency for electrons and contam-ination rate for the 4 other particletypes. . . . . . . . . . . . . . . . . . 52

3.16 Kaon efficiency and contaminationrate of the remaining particle speciesin different momentum ranges by us-ing the DIRC information . . . . . . 52

3.17 E/p versus track momentum for elec-trons and pions . . . . . . . . . . . . 53

3.18 Zernike moment 31 for electrons,muons and hadrons. . . . . . . . . . 53

3.19 MLP network output for electronsand the other particle species in themomentum range between 300 MeV/cand 5 GeV/c. . . . . . . . . . . . . . . 54

3.20 Electron efficiency and contamina-tion rate for muons, pions, kaonsand protons in different momentumranges by using the EMC information. 54

3.21 The distribution of the distance in x-direction between the expected hitsobtained by the extrapolation andthe corresponding detected hits inthe muon detector for generated sin-gle muon particles. . . . . . . . . . . 54

3.22 Kaon and electron efficiency with thecontamination rate of the remainingparticle species in different momen-tum ranges by applying VeryTightPID cuts . . . . . . . . . . . . . . . . 55

3.23 Improving the J/ψπ+π− mass reso-lution by applying a kinematic fit . . 56

3.24 Reconstructed J/ψη mass from thebackground mode ππη . . . . . . . . 57

3.25 Reconstruction efficiency for wronglyidentified e+e− pairs (truth mass) . 58

3.26 Functionality of FAIRroot . . . . . . 59

3.27 Flow diagram of PANDAroot . . . . . 59

4.1 Charmonium spectrum from LQCD 65

4.2 Resonance scan at the χc1. . . . . . 66

4.3 Invariant e+e− mass reconstructedat√s = 4.260 GeV. . . . . . . . . . . 68

4.4 Confidence level of the kinematicalfit to J/ψπ+π− for the data simu-lated at

√s = 4.260 GeV energy. . . 69

4.5 Invariant J/ψπ+π− mass, in the caseof Y(4260) resonance. . . . . . . . . 70

4.6 Invariant dipion mass of Y(4260)candidates. . . . . . . . . . . . . . . 70

4.7 Invariant dipion mass of J/ψπ0π0

candidates. . . . . . . . . . . . . . . 70

4.8 Invariant J/ψγ mass at√s =

3.686 GeV. . . . . . . . . . . . . . . . 71

4.9 Invariant χc1γ mass at√s =

3.686 GeV. . . . . . . . . . . . . . . . 71

4.10 Invariant J/ψγ mass at√s =

3.510 GeV. . . . . . . . . . . . . . . . 72

4.11 Invariant J/ψη mass at√s =

4.260 GeV. . . . . . . . . . . . . . . . 73

4.12 Angular dependence of π0π0 cross-section with parametrisation used inMonte-Carlo simulation. . . . . . . . 75

4.13 Distribution of reconstructed cos θ ofthe γ in CM system for pp → π0π0

background. . . . . . . . . . . . . . . 76

4.14 Distribution of reconstructed cos θ ofthe γ in CM system from hc → ηcγ. 76

4.15 Invariant D± mass distribution ofpp→ D+D− signal events . . . . . . 79

4.16 Invariant D∗± and D0 mass distribu-tions . . . . . . . . . . . . . . . . . . 80

4.17 Momentum components of D± can-didates for signal and for backgroundevents . . . . . . . . . . . . . . . . . 80

4.19 Fit of hc resonance for Γ = 0.5 MeV(a) and Γ = 1 MeV (b) . . . . . . . . 83

4.20 Definition of the angles for the angu-lar distribution of the radiative decayof the χc. . . . . . . . . . . . . . . . 83

4.21 Results for cos θ, cos θ′ and φ′ afterthe generation and reconstruction ofthe events for χc1 decay. . . . . . . . 85

4.22 Results for cos θ, cos θ′ and φ′ afterthe generation and reconstruction ofthe events for χc2 decay. . . . . . . . 85

4.23 Charmonium potentials and hybridspectrum from LQCD . . . . . . . . 87

4.24 Glueball prediction from LQCD cal-culations . . . . . . . . . . . . . . . . 89

4.25 Dispersive effects on the X(3872) . . 91

4.26 Invariant χc1π0π0 mass . . . . . . . 91

4.27 Invariant D0D∗0

mass . . . . . . . . 93

4.28 Invariant J/ψπ+π− (J/ψ → e+e−) mass 94

4.29 Invariant J/ψω mass distribution . . 95


4.30 Distribution of the helicity angles inJ/ψω . . . . . . . . . . . . . . . . . . 96

4.31 Invariant mass distribution forψ(2S)ππ candidates. . . . . . . . . . 97

4.32 Reconstructed events for pp→ φφ . 99

4.33 Angle between φ decay planes. . . . 100

4.34 Angular dependent efficiencies . . . . 101

4.35 Cross section scan examples . . . . . 102

4.36 Cross section measurement pp→ φφby JETSET. . . . . . . . . . . . . . . 102

4.37 The Ds spectrum and quark modelpredictions . . . . . . . . . . . . . . 104

4.38 Missing mass spectrum obtained forthe D±s candidates . . . . . . . . . . 107

4.39 Reconstruction of signal events type 1 108

4.40 Background channel 1: pp →D±s D

∓s π

0. . . . . . . . . . . . . . . . 109

4.41 Fit of the excitation function ob-tained from the reconstructed signalevents . . . . . . . . . . . . . . . . . 111

4.42 Schematic illustration of the investi-gated pp→ Ξ

+Ξ−π0 reaction . . . . 114

4.43 Ξ−π0 invariant mass resolution . . . 116

4.44 Dalitz plot showing the Ξ+

Ξ−π0 re-construction efficiency . . . . . . . . 116

4.45 Total cross sections for the pp→ Y Yreaction. . . . . . . . . . . . . . . . . 118

4.46 Coordinate system for the pp→ Y Yreaction. . . . . . . . . . . . . . . . . 120

4.47 Reconstructed pπ+ invariant massfor Λ candidates from the pp → ΛΛreaction. . . . . . . . . . . . . . . . . 121

4.48 Λ decay vertex distributions. . . . . 122

4.49 CM angular distributions for thepp→ ΛΛ reaction. . . . . . . . . . . 122

4.50 Pion momentum distributions in thelaboratory system from the Λ decay1.64 GeV/c. . . . . . . . . . . . . . . 123

4.51 Reconstructed p angular distribu-tions from the Λ→ pπ+ decay. . . . 123

4.52 Reconstructed polarisations from thepp→ ΛΛ reaction. . . . . . . . . . . 124

4.53 Topology of the pp→ Ξ+

Ξ− reaction. 124

4.54 Reconstructed Ξ+

mass for the pp→Ξ

+Ξ reaction. . . . . . . . . . . . . . 124

4.55 Reconstructed CM angular distribu-tion for the pp→ Ξ

+Ξ− reaction. . . 125

4.56 Reconstructed polarisation for thepp→ Ξ

+Ξ− reaction. . . . . . . . . 125

4.57 oscillatory behaviour of elastic pp . . 127

4.58 Feynman diagram . . . . . . . . . . 127

4.59 oscillation . . . . . . . . . . . . . . . 127

4.60 Simulated cross section for resonantJ/ψ production on nuclear protons . 131

4.61 Reconstructed invariant mass distri-bution of e+e− pair candidates forsignal and background . . . . . . . . 133

4.62 Distributions used to suppress thebackground to the J/ψ signal . . . . 134

4.63 Invariant mass distribution of e+e−

pair candidates for signal, UrQMD,and π+ π− events . . . . . . . . . . . 135

4.64 Schematic illustration of reactionsgiving access to the nuclear potentialof Λ antihyperons . . . . . . . . . . . 136

4.65 The transparency ratio for the elasticproton-proton scattering . . . . . . . 137

4.66 Hypernuclei and their link to otherfields of physics. . . . . . . . . . . . 139

4.67 Present knowledge on hypernuclei.Only very few individual events ofdouble hypernuclei have been de-tected and identified so far. . . . . . 140

4.68 Measured ratio of non-mesonic(ΛN → NN) to mesonic (Λ → Nπ)hypernuclear decay widths as afunction of the nuclear mass [282]. . 140

4.69 Various steps of the double hypernu-cleus production in PANDA. . . . . . 141

4.70 Layout out the secondary sandwichtarget used in the present simulations. 142

4.71 Transverse vs. longitudinal momen-tum distribution of Ξ− with trans-verse and longitudinal momenta lessthan 500 MeV/c (upper part) andthose stopped within the secondarytarget (lower part). . . . . . . . . . . 143


4.72 Production probability of ground(g.s.) and excited states (ex.s.) inconventional nuclear fragments andin one single (SHP), twin (THP) anddouble hypernuclei (DHP) after thecapture of a Ξ− in a 12C nucleus andits conversion into two Λ hyperonspredicted by a statistical decay model.144

4.73 Production probability of groundand excited states of accessible dou-ble hypernuclei after the capture ofa Ξ− in a 12C nucleus and the Ξ−

conversion into two Λ hyperons. . . . 144

4.74 Total γ-ray spectrum resulting fromthe decay of double hypernuclei pro-duced in a 12C target and detectedin the germanium array and beforeadditional cuts. . . . . . . . . . . . . 145

4.75 Upper part: Momentum correlationof all negative pion candidates re-sulting from the decay of double hy-pernuclei in a secondary 12C target.Lower part: γ-spectrum detected inthe Ge-array by cutting on the twopion momenta. . . . . . . . . . . . . 146

4.76 Distribution of produced particlesfrom background reactions. . . . . . 146

4.77 Incident kinetic energy of protonsand neutrons entering the Germa-nium detector surface. . . . . . . . . 146

4.78 DVCS can be described by the hand-bag diagram, as there is factorisa-tion between the upper ‘hard’ partof the diagram which is described byperturbative QCD and QED, and alower ‘soft’ part that is described byGPDs. . . . . . . . . . . . . . . . . . 148

4.79 The handbag diagram may describethe inverted WACS process pp→ γγat PANDA energies. . . . . . . . . . 148

4.80 The production of a hard virtualphoton (upper part) is a hard sub-process that factorises from the lowerpart, which can be described by ahadron to photon transition distribu-tion amplitude (TDA). . . . . . . . 149

4.81 The squared form factors R2V (s)

(solid line) and R2A(s) (dashed line),

as calculated from the double distri-bution model (Fig. 2 of ref. [354]) . 149

4.82 The handbag contribution to pp →γπ0 at large but non-asymptotic s. . 150

4.83 Cross section prediction for the an-gular distribution at s = 20 GeV2 forPANDA taken from ref. [350] . . . . 150

4.84 Cross sections for processes with γγ,π0γ and π0π0 in the final state, fordifferent PANDA energies. . . . . . . 150

4.85 Angular distribution of generatedparticles in the centre of mass sys-tem, as seen by the detector. . . . . 151

4.86 Separation of γγ events from theneutral background γπ0 and π0π0 ispossible using Monte Carlo corrections.151

4.87 Separation of γπ0 events from theneutral background. . . . . . . . . . 152

4.88 Leading-twist contribution to theDrell-Yan dilepton production . . . . 153

4.89 The Collins-Soper frame . . . . . . . 153

4.90 Light-cone momentum fractionsscatter plot for unpolarised DYdi-lepton production. . . . . . . . . . 161

4.91 The azimuthal asymmetry for theunpolarised DY process pp→ l+l−X. 161

4.92 The azimuthal asymmetries for thesingle-polarised DY process pp↑ →l+l−X. . . . . . . . . . . . . . . . . . 162

4.93 PANDA acceptance for the unpo-larised DY process pp→ l+l−X. . . 163

4.94 Expected statistical errors for SSAin the (un)polarised DY processpp(↑) → l+l−X folded with PANDAacceptance. . . . . . . . . . . . . . . 163

4.95 Feynman diagrams for elastic scat-tering and annihilation . . . . . . . . 165

4.96 World data on the modulus |GM| ofthe time-like magnetic form factor . 166

4.97 Recent dispersion theory results on|GE|/|GM| from BABAR data. . . . . 167

4.98 e+e− cross section as a function of q2. 168

4.99 e+e− cross section as a function ofθCMS . . . . . . . . . . . . . . . . . . 169

4.100Symetrized angular distribution ofπ+π− at 8.21. . . . . . . . . . . . . . 169

4.101Angular distribution of misidentifiedpions. . . . . . . . . . . . . . . . . . 171

4.102Distribution of misidentified pi0 . . . 172

4.103e+e− reconstruction efficiency atq2 = 8.21 (GeV/c)2 . . . . . . . . . . 172


4.104Integrated e+e− reconstruction effi-ciency versus q2. . . . . . . . . . . . 172

4.105Reconstructed angular e+e− distri-bution at q2 = 8.21(GeV/c)2 . . . . . 173

4.106precision on ratio GE/GM as a func-tion of q2 . . . . . . . . . . . . . . . 173

4.107PANDA results . . . . . . . . . . . . 174

4.108The factorisation of the process pp→e+e−π0 . . . . . . . . . . . . . . . . 174

4.109Theoretical cross section estimatesfor accessing TDAs. . . . . . . . . . 175

203

List of Tables

2.1 Injection parameters, experimentalrequirements and operation modes. . 28

2.2 Upper limit for relative beam lossrate, 1/e beam lifetime tp, and max-imum average luminosity Lmax for aH2 pellet target. . . . . . . . . . . . 29

2.3 Summary of the sources of uncer-tainty in the resonance parameters . 32

3.1 Reconstruction thresholds for thePbWO4 and Shashlyk calorimeter . . 49

3.2 Selection criteria for the particle can-didate lists . . . . . . . . . . . . . . 55

3.3 Contributions of the computing sitesto the Physics Book simulation pro-duction . . . . . . . . . . . . . . . . 56

3.4 Number of reconstructed J/ψη can-didates from the background modeππη, for different electron PID cri-teria, in three regions of the gener-ated invariant ππ mass under elec-tron mass hypothesis . . . . . . . . . 57

4.1 Number of simulated events, meanvalue and RMS of the reconstructedJ/ψ . . . . . . . . . . . . . . . . . . . 69

4.2 Efficiencies and RMS of the recon-structed J/ψπ+π− invariant massdistributions . . . . . . . . . . . . . . 69

4.3 results J/ψπ0π0 . . . . . . . . . . . . 71

4.4 Various properties of reconstructedJ/ψγ candidates for the radiative de-cay of χc1,c2 . . . . . . . . . . . . . . 72

4.5 Various properties of reconstructedχγ candidates for the radiative de-cay of χc1,c2 . . . . . . . . . . . . . . 72

4.6 Various properties of reconstructedJ/ψγ candidates . . . . . . . . . . . . 72

4.7 Various properties of reconstructedJ/ψη candidates . . . . . . . . . . . . 73

4.8 Cross sections and branching frac-tions for the J/ψη signal and back-ground modes. . . . . . . . . . . . . 74

4.9 Suppression η and signal to noise ra-tio for the background modes of theJ/ψη analysis. . . . . . . . . . . . . . 75

4.10 The main background contributorsto hc → 3γ . . . . . . . . . . . . . . 75

4.11 Selection efficiencies for hc → 3γ andits background channels. . . . . . . . 77

4.12 Signal to background ratio for hc →3γ and different background channels. 77

4.13 The numbers of analysed events forhc decay . . . . . . . . . . . . . . . . 77

4.14 Efficiency of different event selectioncriteria . . . . . . . . . . . . . . . . . 78

4.15 Signal to background ratio for differ-ent hc background channels . . . . . 78

4.16 Definition of the DD physics chan-nels, relevant decay branching ratiosand the expected ratio between sig-nal and total pp cross section . . . . 78

4.17 Background channels for the DDanalysis and amount of simulatedevents . . . . . . . . . . . . . . . . . 79

4.18 Signal to background ratio for thepp→ D+D− channel . . . . . . . . . 82

4.19 Signal to background ratio for thepp→ D∗+D∗− channel . . . . . . . . 82

4.20 Reconstructed hc width. . . . . . . . 83

4.21 The 8 lowest lying hybrid states . . . 86

4.22 Light states with exotic quantumnumbers . . . . . . . . . . . . . . . . 87

4.23 LQCD predictions for the lightestspin exotic hybrid . . . . . . . . . . 88

4.24 Lowest lying charmonium hybridscorresponding to the definitions as inTable 4.21. . . . . . . . . . . . . . . 88

4.25 Cross sections for the charmoniumhybrid channel . . . . . . . . . . . . 90

4.26 Signal and background events for thecharmonium hybrid analysis . . . . . 90

4.27 ηc1η signal to background ratio . . . 92

4.28 Decay branching ratios for opencharm production . . . . . . . . . . . 92

4.29 Cross sections for signal and back-ground reactions . . . . . . . . . . . 94


4.30 Summary of analysed events and theJ/ψ mass filter efficiency. For chan-nels including charmonium states nofilter is applied and the J/ψ is decay-ing to e+e− only. . . . . . . . . . . . 94

4.31 Background suppression and S/B forY (3940)→ J/ψω . . . . . . . . . . . 95

4.32 Signal and background modes for theψ(2S)π+π− analysis. For the gener-ator level filter, see Sec. 3.5.3. . . . . 96

4.33 Cross sections and branching frac-tions for the ψ(2S)π+π− signal andbackground modes . . . . . . . . . . 97

4.34 Suppression η and signal to noise ra-tio for the background modes of theψ(2S)π+π− analysis . . . . . . . . . 97

4.35 Datasets for the φφ feasibility study. 98

4.36 PID optimisation summary. . . . . . 99

4.37 Beam times needed to achieve a sig-nificance of 10σ. . . . . . . . . . . . 101

4.38 The data sets to evaluate signal re-construction efficiency and signal-to-noise ratio . . . . . . . . . . . . . . . 106

4.39 Results of the simulation studiesof signal reconstruction and back-ground suppression . . . . . . . . . . 109

4.40 Quark-model assignments for someof the known baryon states . . . . . 112

4.41 Number of events simulated for sig-nal and background channels . . . . 115

4.42 Signal efficiency and remaining num-ber of background events . . . . . . 116

4.43 Properties of strange and charmedground state hyperons . . . . . . . . 120

4.44 Background for pp→ ΛΛ and pp→Ξ

+Ξ− . . . . . . . . . . . . . . . . . 126

4.45 Estimated count rates into theircharged decay mode for the designluminosity . . . . . . . . . . . . . . . 126

4.46 Definition of cuts for the e+e− analysis135

4.47 Electromagnetic form factor simula-tion statistics . . . . . . . . . . . . . 168

4.48 Rejection efficiency for pions . . . . 170

4.49 Expected signal counting rates fore+e− . . . . . . . . . . . . . . . . . . 171

physics performance report for: panda strong interaction ... · fair/panda/physics book vii preface...

Documents