EPJ manuscript No.(will be inserted by the editor)

Feasibility studies of time-like proton electromagnetic formfactors at PANDA at FAIRThe PANDA Collaboration

B. Singh1, W. Erni2, B. Krusche2, M. Steinacher2, N. Walford2, B. Liu3, H. Liu3, Z. Liu3, X. Shen3,C. Wang3, J. Zhao3, M. Albrecht4, M. Backwinkel4, T. Erlen4, M. Fink4, F. Heinsius4, T. Held4, T. Holtmann4,S. Jasper4, I. Keshk4, H. Koch4, B. Kopf4, M. Kuhlmann4, M. Kümmel4, S. Leiber4, M. Mikirtychyants4, P. Musiol4,A. Mustafa4, M. Pelizäus4, J. Pychy4, M. Richter4, C. Schnier4, T. Schröder4, C. Sowa4, M. Steinke4, T. Triffterer4,U. Wiedner4, M. Ball5, R. Beck5, C. Hammann5, B. Ketzer5, M. Kube5, P. Mahlberg5, M. Rossbach5, C. Schmidt5,R. Schmitz5, U. Thoma5, M. Urban5, D. Walther5, C. Wendel5, A. Wilson5, A. Bianconi6, M. Bragadireanu7,M. Caprini7, D. Pantea7, B. Patel8, W. Czyzycki9, M. Domagala9, G. Filo9, J. Jaworowski9, M. Krawczyk9,E. Lisowski9, F. Lisowski9, M. Michałek9, P. PoznaÅĎski9, J. PÅĆaÅijek9, K. Korcyl10, A. Kozela10, P. Kulessa10,P. Lebiedowicz10, K. Pysz10, W. Schäfer10, A. Szczurek10, T. Fiutowski11, M. Idzik11, B. Mindur11, D. Przyborowski11,K. Swientek11, J. Biernat12, B. Kamys12, S. Kistryn12, G. Korcyl12, W. Krzemien12, A. Magiera12, P. Moskal12,A. Pyszniak12, Z. Rudy12, P. Salabura12, J. Smyrski12, P. Strzempek12, A. Wronska12, I. Augustin13, R. Böhm13,I. Lehmann13, D. Nicmorus Marinescu13, L. Schmitt13, V. Varentsov13, M. Al-Turany14, H. Deppe14, R. Dzhygadlo14,A. Ehret14, H. Flemming14, A. Gerhardt14, K. Götzen14, A. Gromliuk14, L. Gruber14, R. Karabowicz14, R. Kliemt14,M. Krebs14, U. Kurilla14, D. Lehmann14, S. Löchner14, J. Lühning14, U. Lynen14, H. Orth14, M. Patsyuk14,K. Peters14, T. Saito14, G. Schepers14, C. J. Schmidt14, C. Schwarz14, J. Schwiening14, A. Täschner14, M. Traxler14,C. Ugur14, B. Voss14, P. Wieczorek14, A. Wilms14, M. Zühlsdorf14, V. Abazov15, G. Alexeev15, V. A. Arefiev15,V. Astakhov15, M. Yu. Barabanov15, B. V. Batyunya15, Y. Davydov15, V. Kh. Dodokhov15, A. Efremov15,A. Fechtchenko15, A. G. Fedunov15, A. Galoyan15, S. Grigoryan15, E. K. Koshurnikov15, Y. Yu. Lobanov15,V. I. Lobanov15, A. F. Makarov15, L. V. Malinina15, V. Malyshev15, A. G. Olshevskiy15, E. Perevalova15, A.A. Piskun15, T. Pocheptsov15, G. Pontecorvo15, V. Rodionov15, Y. Rogov15, R. Salmin15, A. Samartsev15, M.G. Sapozhnikov15, G. Shabratova15, N. B. Skachkov15, A. N. Skachkova15, E. A. Strokovsky15, M. Suleimanov15,R. Teshev15, V. Tokmenin15, V. Uzhinsky15, A. Vodopianov15, S. A. Zaporozhets15, N. I. Zhuravlev15, A. G. Zorin15,D. Branford16, D. Glazier16, D. Watts16, P. Woods16, M. Böhm17, A. Britting17, W. Eyrich17, A. Lehmann17,F. Uhlig17, S. Dobbs18, K. Seth18, A. Tomaradze18, T. Xiao18, D. Bettoni19, V. Carassiti19, A. Cotta Ramusino19,P. Dalpiaz19, A. Drago19, E. Fioravanti19, I. Garzia19, M. Savrie19, V. Akishina20, I. Kisel20, G. Kozlov20,M. Pugach20, M. Zyzak20, P. Gianotti21, C. Guaraldo21, V. Lucherini21, A. Bersani22, G. Bracco22, M. Macri22, R.F. Parodi22, K. Biguenko23, K. Brinkmann23, V. Di Pietro23, S. Diehl23, V. Dormenev23, P. Drexler23, M. Düren23,E. Etzelmüller23, M. Galuska24, E. Gutz23, C. Hahn23, A. Hayrapetyan23, M. Kesselkaul23, W. Kühn23, T. Kuske23, J.S. Lange23, Y. Liang23, O. Merle23, V. Metag23, M. Nanova23, S. Nazarenko23, R. Novotny23, T. Quagli23, S. Reiter23,J. Rieke23, C. Rosenbaum23, M. Schmidt23, R. Schnell23, H. Stenzel23, U. Thöring23, M. Ullrich23, M. N. Wagner23,T. Wasem23, B. Wohlfahrt23, H. Zaunick23, D. Ireland24, G. Rosner24, B. Seitz24, P.N. Deepak25, A. Kulkarni25,A. Apostolou26, M. Babai26, M. Kavatsyuk26, P. J. Lemmens26, M. Lindemulder26, H. Loehner26, J. Messchendorp26,P. Schakel26, H. Smit26, M. Tiemens26, J. C. van der Weele26, R. Veenstra26, S. Vejdani26, K. Dutta27, K. Kalita27,A. Kumar28, A. Roy28, H. Sohlbach29, M. Bai30, L. Bianchi30, M. Büscher30, L. Cao30, A. Cebulla30, R. Dosdall30,A. Gillitzer30, A. Goerres30, F. Goldenbaum30, D. Grunwald30, A. Herten30, Q. Hu30, G. Kemmerling30, H. Kleines30,A. Lehrach30, R. Nellen30, H. Ohm30, S. Orfanitski30, D. Prasuhn30, E. Prencipe30, J. Ritman30, S. Schadmand30,T. Sefzick30, V. Serdyuk30, G. Sterzenbach30, T. Stockmanns30, P. Wintz30, P. Wüstner30, H. Xu30, S. Li31, Z. Li31,Z. Sun31, H. Xu31, V. Rigato32, L. Isaksson33, P. Achenbach34, O. Corell34, A. Denig34, M. Distler34, M. Hoek34,A. Karavdina34, W. Lauth34, Z. Liu34, H. Merkel34, U. Müller34, J. Pochodzalla34, S. Sanchez34, S. Schlimme34,C. Sfienti34, M. Thiel34, H. Ahmadi35, S. Ahmed35, S. Bleser35, L. Capozza35, M. Cardinali35, A. Dbeyssi35,M. Deiseroth35, F. Feldbauer35, M. Fritsch35, B. Fröhlich35, P. Jasinski35, D. Kang35, D. Khaneft35 a, R. Klasen35,H. H. Leithoff35, D. Lin35, F. Maas35, S. Maldaner35, M. Marta35, M. Michel35, M. C. Mora Espí35, C. MoralesMorales35, C. Motzko35, F. Nerling35, O. Noll35, S. Pflüger35, A. Pitka35, D. Rodríguez Piñeiro35, A. Sanchez-Lorente35, M. Steinen35, R. Valente35, T. Weber35, M. Zambrana35, I. Zimmermann35, A. Fedorov36, M. Korjik36,O. Missevitch36, A. Boukharov37, O. Malyshev37, I. Marishev37, V. Balanutsa38, P. Balanutsa38, V. Chernetsky38,

a e-mail: khaneftd@kph.uni-mainz.de

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A. Demekhin38, A. Dolgolenko38, P. Fedorets38, A. Gerasimov38, V. Goryachev38, V. Chandratre39, V. Datar39,D. Dutta39, V. Jha39, H. Kumawat39, A.K. Mohanty39, A. Parmar39, B. Roy39, S. Dash40, M. Jadhav40, S. Kumar40,P. Sarin40, R. Varma40, S. Grieser41, A. Hergemöller41, B. Hetz41, A. Khoukaz41, J. P. Wessels41, K. Khosonthongkee42,C. Kobdaj42, A. Limphirat42, P. Srisawad42, Y. Yan42, M. Barnyakov43, A. Yu. Barnyakov43, K. Beloborodov43, A.E. Blinov43, V. E. Blinov43, V. S. Bobrovnikov43, S. Kononov43, E. A. Kravchenko43, I. A. Kuyanov43, K. Martin43,A. P. Onuchin43, S. Serednyakov43, A. Sokolov43, Y. Tikhonov43, E. Atomssa44, R. Kunne44, D. Marchand44,B. Ramstein44, J. van de Wiele44, Y. Wang44, G. Boca45, S. Costanza45, P. Genova45, P. Montagna45, A. Rotondi45,V. Abramov46, N. Belikov46, S. Bukreeva46, A. Davidenko46, A. Derevschikov46, Y. Goncharenko46, V. Grishin46,V. Kachanov46, V. Kormilitsin46, A. Levin46, Y. Melnik46, N. Minaev46, V. Mochalov46, D. Morozov46, L. Nogach46,S. Poslavskiy46, A. Ryazantsev46, S. Ryzhikov46, P. Semenov46, I. Shein46, A. Uzunian46, A. Vasiliev46, A. Yakutin46,E. Tomasi-Gustafsson47, U. Roy48, B. Yabsley49, S. Belostotski50, G. Gavrilov50, A. Izotov50, S. Manaenkov50,O. Miklukho50, D. Veretennikov50, A. Zhdanov50, A. Kashchuk51, O. Levitskaya51, Y. Naryshkin51, K. Suvorov51,K. Makonyi52, M. Preston52, P. Tegner52, D. Wölbing52, T. Bäck53, B. Cederwall53, A. K. Rai54, S. Godre55,D. Calvo56, S. Coli56, P. De Remigis56, A. Filippi56, G. Giraudo56, S. Lusso56, G. Mazza56, M. Mignone56,A. Rivetti56, R. Wheadon56, L. Zotti56, A. Amoroso57, M. P. Bussa57, L. Busso57, F. De Mori57, M. Destefanis57,L. Fava57, L. Ferrero57, M. Greco57, J. Hu57, L. Lavezzi57, M. Maggiora57, G. Maniscalco57, S. Marcello57, S. Sosio57,S. Spataro57, F. Balestra58, F. Iazzi58, R. Introzzi58, A. Lavagno58, J. Olave58, R. Birsa59, F. Bradamante59,A. Bressan59, A. Martin59, H. Calen60, W. Ikegami Andersson60, T. Johansson60, A. Kupsc60, P. Marciniewski60,M. Papenbrock60, J. Pettersson60, K. Schönning60, M. Wolke60, B. Galnander61, J. Diaz62, V. Pothodi Chackara63,A. Chlopik64, G. Kesik64, D. Melnychuk64, B. Slowinski64, A. Trzcinski64, M. Wojciechowski64, S. Wronka64,B. Zwieglinski64, P. Bühler65, J. Marton65, D. Steinschaden65, K. Suzuki65, E. Widmann65, and J. Zmeskal65

1 Aligarth Muslim University, Physics Department, Aligarth, India2 Universität Basel, Basel, Switzerland3 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China4 Universität Bochum, Institut für Experimentalphysik I, Bochum, Germany5 Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany6 Università di Brescia, Brescia, Italy7 Institutul National de C&D pentru Fizica si Inginerie Nucleara "Horia Hulubei", Bukarest-Magurele, Romania8 P.D. Patel Institute of Applied Science, Department of Physical Sciences, Changa, India9 University of Technology, Institute of Applied Informatics, Cracow, Poland

10 IFJ, Institute of Nuclear Physics PAN, Cracow, Poland11 AGH, University of Science and Technology, Cracow, Poland12 Instytut Fizyki, Uniwersytet Jagiellonski, Cracow, Poland13 FAIR, Facility for Antiproton and Ion Research in Europe, Darmstadt, Germany14 GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany15 Veksler-Baldin Laboratory of High Energies (VBLHE), Joint Institute for Nuclear Research, Dubna, Russia16 University of Edinburgh, Edinburgh, United Kingdom17 Friedrich Alexander Universität Erlangen-Nürnberg, Erlangen, Germany18 Northwestern University, Evanston, U.S.A.19 Università di Ferrara and INFN Sezione di Ferrara, Ferrara, Italy20 Frankfurt Institute for Advanced Studies, Frankfurt, Germany21 INFN Laboratori Nazionali di Frascati, Frascati, Italy22 INFN Sezione di Genova, Genova, Italy23 Justus Liebig-Universität Gieçen II. Physikalisches Institut, Gießen, Germany24 University of Glasgow, Glasgow, United Kingdom25 Birla Institute of Technology and Science - Pilani , K.K. Birla Goa Campus, Goa, India26 KVI-Center for Advanced Radiation Technology (CART), University of Groningen, Groningen, Netherlands27 Gauhati University, Physics Department, Guwahati, India28 Indian Institute of Technology Indore, School of Science, Indore, India29 Fachhochschule Südwestfalen, Iserlohn, Germany30 Forschungszentrum Jülich, Institut für Kernphysik, Jülich, Germany31 Chinese Academy of Science, Institute of Modern Physics, Lanzhou, China32 INFN Laboratori Nazionali di Legnaro, Legnaro, Italy33 Lunds Universitet, Department of Physics, Lund, Sweden34 Johannes Gutenberg-Universität, Institut für Kernphysik, Mainz, Germany35 Helmholtz-Institut Mainz, Mainz, Germany36 Research Institute for Nuclear Problems, Belarus State University, Minsk, Belarus37 Moscow Power Engineering Institute, Moscow, Russia38 Institute for Theoretical and Experimental Physics, Moscow, Russia39 Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai, India40 Indian Institute of Technology Bombay, Department of Physics, Mumbai, India

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41 Westfälische Wilhelms-Universität Münster, Münster, Germany42 Suranaree University of Technology, Nakhon Ratchasima, Thailand43 Budker Institute of Nuclear Physics, Novosibirsk, Russia44 Institut de Physique Nucléaire d’Orsay (UMR8608), CNRS/IN2P3 and Université Paris-sud, Orsay, France45 Dipartimento di Fisica, Università di Pavia, INFN Sezione di Pavia, Pavia, Italy46 Institute for High Energy Physics, Protvino, Russia47 IRFU, SPHN, CEA Saclay, Saclay, France48 Sikaha-Bhavana, Visva-Bharati, WB, Santiniketan, India49 University of Sidney, School of Physics, Sidney, Australia50 National Research Centre "Kurchatov Institute" B.P.Konstantinov Petersburg Nuclear Physics Institute, Gatchina, St.

Petersburg, Russia51 Petersburg Nuclear Physics Institute of Russian Academy of Science, Gatchina, St. Petersburg, Russia52 Stockholms Universitet, Stockholm, Sweden53 Kungliga Tekniska Högskolan, Stockholm, Sweden54 Sardar Vallabhbhai National Institute of Technology, Applied Physics Department, Surat, India55 Veer Narmad South Gujarat University, Department of Physics, Surat, India56 INFN Sezione di Torino, Torino, Italy57 Università di Torino and INFN Sezione di Torino, Torino, Italy58 Politecnico di Torino and INFN Sezione di Torino, Torino, Italy59 Università di Trieste and INFN Sezione di Trieste, Trieste, Italy60 Uppsala Universitet, Institutionen för fysik och astronomi, Uppsala, Sweden61 The Svedberg Laboratory, Uppsala, Sweden62 Instituto de Física Corpuscular, Universidad de Valencia-CSIC, Valencia, Spain63 Sardar Patel University, Physics Department, Vallabh Vidynagar, India64 National Centre for Nuclear Research, Warsaw, Poland65 Österreichische Akademie der Wissenschaften, Stefan Meyer Institut für Subatomare Physik, Wien, Austria

Received: date / Revised version: date

Abstract The results of simulations for future measurements of electromagnetic form factors at PANDA(FAIR) in frame of the PandaRoot software are reported. The statistical precision at which the protonform factors can be determined is estimated. The signal channel p̄p→ e+e− is studied on the basis of twodifferent but consistent procedures. The main background is identified in the p̄p → π+π− channel. Thesuppression of this background, the background versus signal efficiency, and the of the statistical errorson the extracted proton form factors have been also evaluated according to the two different procedures.The comparison with older predictions based on an old framework shows consistency of the results anda slightly better precision is achieved here in a large range of momentum transfer, assuming the nominalconditions of beam and detector performances.

3

1 Introduction

The PANDA [1] experiment at FAIR (Facility for Antipro-ton and Ion Research, at Darmstadt, Germany) will de-tect the products of the annihilation reactions induced byhigh intensity antiproton beams with momentum from 1.5to 15 GeV/c. The broad physics program includes char-monium spectroscopy, search for hybrids and glueballs,search for charm and strangeness in nuclei, as well as nuc-leon structure studies [2]. Here we focus on the extrac-tion of time-like (TL) proton electromagnetic form factors(FFs) through the measurement of the angular distribu-tion of the produced electron (positron) in the annihilationof proton-antiproton into an electron-positron pair.

Electromagnetic FFs are fundamental quantities whichdescribe the intrinsic electric and magnetic distributionsof hadrons. Assuming parity and time invariance, a had-ron with spin S is described by 2S + 1 independent FFs.Protons and neutrons (spin 1/2 particles) are then char-acterized by two FFs, the electric GE and the magnetic

GM . In TL region electromagnetic FFs have been associ-ated with the time evolution of these distributions [3].

Theoretically, the FFs enter in the parametrization ofthe proton electromagnetic current. They are experiment-ally accessible through measurements of differential andtotal cross sections for elastic ep scattering in the space-like (SL) region and p̄p ↔ e+e− in the TL region. It isassumed that the interaction occurs through one-photonexchange, which carries a momentum transfer squared q2

(corresponding to the total energy squared s in TL re-gion).

Although measurements have existed for decades [4],recently the possibility to apply the polarization transfermethod [5, 6] and to access with a high precision a widekinematical range, has raised new interest and new ques-tions in the field. The data from the JLab-GEp collabor-ation up to a value of the momentum transfer squared ofQ2 = −q2 ' 8.5 (GeV/c)2 showed that the electric andmagnetic distributions inside the proton are not the same,contrary to what was previously assumed: the ratio of theelectric to the magnetic FF, µpGE/GM (µp is the proton

4

magnetic moment) decreases almost linearly from unity asthe momentum transfer squared increases, approaching azero value.

In the TL region, the accuracy of the determinationof the proton FFs has been limited by the achievable lu-minosity of the e+e− colliders and p̄p annihilation exper-iments. Attempts have been made at LEAR [7], BABAR[8] and more recently at BESIII [9]. The FFs ratio shows adifferent trend, somehow inconsistent in the limit of com-bined systematic and statistic errors and definitely callsfor more precise experiments. The results of LEAR andBABAR disagree with each other up to 3σ significance,while BESIII measurements have large total uncertainties.

The PANDA experiment, designed with an averagepeak luminosity of L = 2 · 1032 cm−2s−1 in high luminos-ity mode, will bring new information in two respects: theprecision measurement of the angular distribution for theindividual determination of FFs, and the measurement ofthe integrated cross section for the extraction of a gener-alized FF up to larger values of s. These data are expectedto set a stringent test of nucleon models. In particular thehigh s-region brings information on analyticity propertiesof FFs and on the asymptotic q2 behavior predicted byperturbation Quantum ChromoDynamics (pQCD).

The FAIR facility and the PANDA experiment arein construction at Darmstadt (Germany). Simulations forthe different physics processes have been done or are inprogress. The feasibility of the FFs measurement with thePANDA detector, as suggested in Ref. [10], has been in-vestigated in Ref. [11]. The necessity to update that workis due to the fact that these first estimations were per-formed in the old framework i.e., BABAR based simula-tion framework with a simplified version of the PANDAdetector. Recently a lot of progress was made in the designof the detector. Prototypes of sub-detectors have beenbuilt. A series of performance tests have been carried outwhich provided data for improvements in the design. TheTechnical Design Reports of most of the detectors areavailable. Although the simulation and analysis softwareis still in progress, in parallel with the detector construc-tion, a realistic description of the sub-detectors and newalgorithms for the tracking and PID have been implemen-ted.

The need to perform the proposed analysis channelin the new PandaRoot software is due to the fact thatthe software used for the previous PANDA publication[11], did not contain a complete description of part ofthe detector, in particular, of the micro vertex detector(MVD), which was represented by sensors without pass-ive elements. The magnetic field had been kept constantand equal 2T, whereas in the PandaRoot [12] a realisticmagnetic field map, calculated with TOSCA software [13],has been implemented, as well as the digitization extrac-ted from experimental data. In the solenoid, the field maydecrease to 1 T, which worsens the resolution by a factorof two for beam momenta below 3 GeV/c. A more realisticdescription of PANDA sub-detectors and material budgetis now available.

In the version of PandaRoot used for this work, the de-scription of most of the sub-detectors has been completedwith passive materials, pipe, magnet yoke, etc. Moreover,during recent years GEANT4 [14] has undergone continu-ous improvement, concerning in particular, the shape ofthe electromagnetic shower.

The aim of this paper is to present a new simula-tion, based on a recent version of PandaRoot, in orderto check the validity of the assumptions previously usedand confirm the feasibility of the e+e− detection at a suf-ficient level of precision. In addition new and efficient ana-lysis tools have been developed for the extraction of thephysical information, which will be applied also to thetreatment of the experimental data. Full scale simulationswere performed on the HIMster cluster of the Helmholtz-Institut Mainz.

The paper is organized as following. The kinematic ofthe reactions of interest (signal and background) and theevaluation of the counting rates are described in Section 2.The detector is briefly described in Section 3. The stand-ard chain of the full simulation with PandaRoot and theprocedure to identify and analyze the signal and the back-ground channels, based on the properties of the kinematicsand the PID information from the sub-detectors, are de-scribed in Section 3. In Section 4 the results in terms ofthe protons FFs ratio R = |GE |/|GM |, individual FFs GE

and GM , the angular asymmetry A and the effective FFare presented. Finally, in Section 5 a number of sources ofsystematic uncertainties are discussed. Conclusions con-tain a summary and final remarks.

2 Basic formalism

Let us consider the reactions:

p̄(p1) + p(p2)→ `−(k1) + `+(k2), ` = e, µ, π, (1)

where the four-momenta of the particles are written inparentheses. In the center-of-mass (c.m.) system, the four-momenta are:

p1 = (E,p), p2 = (E,−p),

k1 = (E,k), k2 = (E,−k), p · k = pk cos θ, (2)

θ is the angle between the negative emitted particle andthe antiproton beam.

The cylindrical symmetry of the unpolarized binaryreactions around the beam axis originates an isotropic dis-tribution in the azimuthal angle φ. These reactions are twobody final state processes. The final particles are emittedback to back in the c.m. system and each of them, havingequal mass, carries half of the total energy of the system,E =

√s/2, where the invariant s is s = q2 = (p1 + p2)2 =

(k1 + k2)2.All leptons in the final state (e, µ, τ) bring the same

physical information on the electromagnetic hadron struc-ture. However, the experimental requirements for their de-tection are peculiar to each particle species. In this work

5

Figure 1: Tree-level contributing diagram to p̄p→ l+l−.

we focus on the electron-positron pair production, denom-inated the signal reaction and on the charged pion pairproduction, denominated the background reaction. Had-ron production is expected to be much larger than leptonproduction: the production of a charged pion pair is ∼ 106

times larger than an e+e− pair [15–17]. The signal andthe background reactions have very similar kinematicsbecause the mass of the electron is sufficiently close tothe pion mass in the energy scale of the PANDA ex-periment (for plab = 3.3 GeV/c the electron momentumspread is 0.58-3.82 GeV/c, while for the pions it is 0.92-3.5 GeV/c). Therefore, the kinematics plays a minor rolein the electron (positron)/pion separation. The discrim-ination between electrons and pions requires high per-formance PID detectors and precise momentum measure-ment. For example, the information on the electromag-netic shower induced by different charged particles in anelectromagnetic calorimeter does play an important rolefor the electron identification. The kinematical selectionhelps in the hadronic contribution suppression related tothe channels with more than two particles in the finalstates, or secondary particles coming from the interactionof primary particles with the detector material. Kinemat-ical selection is also very effective in suppressing the pres-ence of neutral pions, as it has been discussed in Refs.[11, 18]. Note that the cross section for the neutral pionpair production, π0π0, is ten times smaller compared toπ+π−.

2.1 The signal reaction

The expression of the hadron electromagnetic current forthe p̄p annihilation into two leptons is derived assumingone-photon exchange. The diagram which contributes tothe tree-level amplitude is shown in Fig. 1. The internalstructure of the hadrons is then parametrized in termsof two FFs, which are complex functions of q2, the fourmomentum squared of the virtual photon. For the case of

unpolarized particles the differential cross section has theform [15]:

dσ

d cos θ=πα2

2βs

[(1 + cos2 θ)|GM |2 +

1

τsin2 θ|GE |2

],

β =

√1− 1

τ, τ =

s

4m2(3)

where α is the electromagnetic fine-structure constant andm is the proton mass. This formula can be also written inequivalent form as [19]:

dσ

d cos θ= σ0

[1 +A cos2 θ

], (4)

where σ0 is the value of the differential cross section atθ = π/2 and A is an angular asymmetry which lies in therange −1 ≤ A ≤ 1 and can be written as a function of theFFs ratio as:

σ0 =πα2

2βs

(|GM |2 +

1

τ|GE |2

)A =

τ |GM |2 − |GE |2

τ |GM |2 + |GE |2=τ − R2

τ + R2 , (5)

where R = |GE |/|GM |.Let us note that taking the form (4), the fit function

reduces to a linear function (instead of quadratic) whereσ0 and A are the parameters to be extracted from theexperimental angular distribution. The linear fit on A issimpler than a quadratic fit on the ratio R. In the caseof R = 0, the minimisation procedure based on MINUIThas problems to converge, while the asymmetry A variessmoothly in the considered q2 interval, therefore, it is ex-pected to reduce instabilities and correlations in the fittingprocedure.

The angular range where the measurement can be per-formed is usually restricted to | cos θ| ≤ c̄, with c̄ = cos θmax.

The integrated cross section, σint, is

σint =

∫ c̄

−c̄

dσ

d cos θd cos θ = 2σ0 c̄

(1 +A3c̄2)

(6)

=πα2

2βsc̄

[(1 +

c̄2

3

)|GM |2 +

1

τ

(1− c̄2

3

)|GE |2

].

The total cross section, σtot, corresponds to c̄ = 1:

σtot = 2σ0

(1 +A3

)=

2πα2

3βs

[2|GM |2 +

|GE |2

τ

](7)

=2πα2|GM |2

3βs

[2 +

R2

τ

].

Being known the total cross section, one can define aneffective FF as:

|Fp|2 =3βsσtot

2πα2

(2 +

1

τ

) , (8)

6

or from the integrated cross section, as:

|Fp|2 =βs

πα2

σint

c̄

[(1 +

c̄2

3

)+

1

τ

(1− c̄2

3

)] , (9)

which is equivalent to the value extracted from cross sec-tion measurements, assuming |GE | = |GM |.

Literature offers several parameterizations of the pro-ton FFs (see review Refs. [20, 21]). The world data areillustrated Fig. 2. In Ref. [11] two parameterizations wereconsidered. Cross section parameters extracted from ex-perimental data of the known integrated experimental crosssection. Since then, new BABAR data are published [22,23], and suggest a steeper decrease with s.

The QCD inspired parameterization of |GE,M | is basedon analytical extension of the dipole formula from SL toTL region and corrected to avoid ’ghost’ poles in αs (thestrong interaction running constant) [33]:

|GQCDE,M | =

AQCD

q4[log2(q2/Λ2

QCD) + π2] , (10)

where AQCD = 89.45 (GeV/c)4 is obtained fitting the ex-perimental data and ΛQCD = 0.3 (GeV/c) is the QCDcut-off parameter. It is shown in Fig. 2 as a blue dash-dotted line.

The existing data on the TL effective FF is well repro-duced by the function proposed in Ref. [19]:

|GE,M | =A

1 + q2/m2a

GD,

GD = (1 + q2/q20)−2, (11)

where the numerator A is a constant extracted from the fitto the TL data. It is illustrated by a black solid line withthe nominal parameters A = 22.5, m2

a = 3.6 (GeV/c)2,and q2

0 = 0.71 (GeV/c)2. Note that an updated global fitwith a data set including 85 points (starting from s = 4GeV2) gives A(fit) = 71.5 (GeV/c)4 and m2

a(fit) = 0.85(GeV/c)2, with a value of χ2/NDF= 1.4 (red dashed line),overestimating the low energy data. These parameteriza-tions reproduce reasonably well the data in the consideredkinematical region. For the present evaluations, we chosethe parametrization from Eq. (11) with the nominal para-meters.

The expected counting rates are reported in Table 1,assuming R = |GE |/|GM | = 1, the parametrization fromEq. (11) and the angular range | cos θ| ≤ 0.8, and us-ing Eq. (3). Due to the PANDA detector acceptance, theelectron identification efficiency becomes very low above| cos θ| = 0.8 (see Section 4). For each kinematical point,Nint(e

+e−) and Nint(π+π−) correspond to an integrated

luminosity of 2 fb−1 (i.e., four months of measurementwith 100% efficiency at the maximum luminosity of L =2 · 1032 cm−2s−1).

As it was already mentioned, in the time-like regionFFs are complex functions but the unpolarized cross sec-tion contains only the moduli squared of the FFs. An ex-

periment with polarized antiproton beam and/or polar-ized proton target would allow to access the phase differ-ence of the proton FFs (Ref. [34]). The feasibility of im-plementing a transversely polarized proton target is underinvestigation.

2.2 The background reaction

In order to estimate the π+π− background in the inter-esting kinematical range, phenomenological parameteriza-tions for the differential cross sections have been developedand a new generator has been built (see Ref. [35]).

The difficulties for a consistent physics description arerelated to different aspects:

– The dominant reaction mechanism is changing withenergy and angle [36].

– At low energy, the angular distribution of the finalstate pions is measured [16]. A baryon exchange modelwas developed in Ref. [37], restricted to

√s < 1 GeV.

– At high energy, lack of statistics does not allow to bet-ter constraint the parameters [38, 39], to discriminateamong models.

– Model independent considerations based on crossingsymmetry or T-invariance, which help to connect therelevant reactions, in general can not be considered aspredictive [40].

Therefore the generator uses two different parameteriz-ations: in the low energy region, 0.79 ≤ plab ≤ 2.43 GeV/c(plab is the antiproton beam momentum in the laboratorysystem), the parameters of Legendre polynomials up tothe order of ten have been fitted to the data from Ref. [16].In the high energy region 5 ≤ plab < 12 GeV/c, the Reggeinspired parametrization from Ref. [17], previously tunedon data from Refs. [38, 39, 41, 42], was applied. In theintermediate region 2.43 GeV/c ≤ plab < 5 GeV/c, whereno data exist and the validity of the model is questionable,a soft interpolation is applied.

Differential cross sections are displayed in Fig. 3 for thep̄p → π+π− reaction, for different plab values. The func-tions used in the pion generator are shown in comparisonto the data sample.

The total cross section is shown in Fig. 4 as a functionof the antiproton momentum. Lack of data for plab = 4GeV/c does not allow to fix more precise parameter con-straints in the generator. The value at plab = 12 GeV/cfrom Ref. [42] should be considered as a lower limit. Forcomparison, the parametrization from the compilation inRef. [43], which reproduces the low momentum data, isalso shown.

The expected counting rates for the background chan-nel, as well as the total signal to background cross sectionratio, are reported in Table 1. One can see that, withinthe range | cos θ| ≤ 0.8, the annihilation into two chargedpions is about five to six orders of magnitudes larger thanthe production of a lepton pair.

7

]2[(GeV/c)2q5 10 15 20 25 30

|p

|F

0.1

0.2

0.3

(a)

]2[(GeV/c)2q10D

|/G

p|F

5

10

15

20

BABAR

E835

Fenice

PS170

E760

DM1

DM2

BES

BESIII

CLEO

(b)

Figure 2: q2 dependence of the world data for p̄p → e+e− and e+e− → p̄ + p. The effective proton TL FF, |FP |, isextracted from the annihilation cross sections assuming |GE | = |GM |: E835 [24, 25], Fenice [26], PS170 [7], E760 [27],DM1 [28], DM2 [29, 30], BES [31], BESIII [9], CLEO [32], BABAR [22, 23]. Different parameterizations are shownfrom Eq. (11) (black solid and red dashed lines) and from Eq. (10) (blue dash-dotted line) (see text).

s plab σint(e+e−) Nint(e

+e−) σint(π+π−) Nint(π

+π−)σint(π

+π−)

σint(e+e−)[(GeV/c)2] [GeV/c] [pb] [µb] ·10−6

5.40 1.70 415 830·103 101 202·109 0.247.27 2.78 55.6 111·103 13.1 262·108 0.248.20 3.30 24.8 496·102 2.96 592·107 0.1211.12 4.90 3.25 6503 0.56 111·107 0.1712.97 5.90 1.16 2328 0.23 455·106 0.2013.90 6.40 0.73 1465 0.15 302·106 0.21∗16.69 7.90 0.21 428 0.05 101·106 0.24∗22.29 10.90 0.03 61 0.01 205·105 0.34∗26.03 12.90 0.01 21∗27.90 13.90 0.66·10−2 13

Table 1: Integrated cross section σint in the range | cos θ| ≤ 0.8 and number of counts, for p̄p→ e+e− (parametrizationfrom Eq. (11)), p̄p → π+π−, corresponding to an integrated luminosity L = 2 fb−1, which is expected for each datapoint in four months of data taking with 100% efficiency. For the values of s marked with an ’*’ the full simulation hasnot been performed and the numbers are given for future references. The last value, s = 27.9 (GeV/c)2, is the highestvalue where the upper limit of the cross section can be measured at PANDA.

3 The PANDA experiment

3.1 The PANDA detector

The PANDA experiment is based on a broad physics pro-gram which requires 4π acceptance, high resolution andtracking capability, and excellent neutral and charged particleidentification in a high rate environment. The average in-teraction rate is expected to reach 20 MHz. The struc-ture and the components of the detector have been op-

timized following the experience gained at high energy ex-periments. The PANDA detector description and its per-formance can be found in [1]. We will mention the charac-teristics of the detectors which play an important role inthe FFs measurements.

An overall picture of the PANDA detector is shown inFig. 5. The size of the detector is about 13 m along thebeam direction. PANDA is a compact detector, with twomagnets, a central solenoid and a forward dipole. The (pel-let or jet) target is surrounded by a number of detectors.

8

θcos

­0.5 0 0.5

b]

µ [

θ/d

cos

σd

­310

­210

­110

1

10

210

310

Figure 3: Data and modeling of angular distributionsfor the reaction p̄p → π+π−, as a function of cos θ,for different values of the beam momentum: plab = 1.7GeV/c [16] (green triangles and dash-triple dotted line)plab = 5 GeV/c [38] (blue full squares and dash-dottedline); plab = 6.21 GeV/c [39] (black full circles and solidline). The results of the generator [35] are also given atplab = 3 GeV/c (red dotted line) and plab = 10 GeV/c(magenta dashed line).

The target tracker consists of the Micro Vertex Detector(MVD) [49] and the Straw Tubes Tracker (STT) to en-sure a precise vertex finding as well as spatial reconstruc-tion of the trajectories of charged particles in a broad mo-mentum range from about a few 100 MeV/c up to 8 GeV/cthrough energy loss measurement dE/dx [50]. The DIRC(Detection of Internally Reflected Cerenkov light) is usedfor particle identification at polar angles between 22◦ and140◦ and momentum up to 5 GeV/c [51].

The barrel is completed by an electromagnetic calor-imeter (EMC), consisting of Lead Tungstate (PbWO4)crystals, to assure an efficient photon detection from 30 MeVto 10 GeV [52] with energy resolution lower than 2%. Be-sides the cylindrical barrel of 11360 crystals, a forwardendcap (3856 crystals) and a backward endcap (600 crys-tals) are added.

Particles emitted at angles smaller than 22◦ are detec-ted by three planar stations of Gas Electron Multipliers(GEM) downstream of the target [53]. The muon iden-tification is performed by Iarocci proportional tubes andstrips, in the inner gap of the solenoid yoke and betweenthe hadron calorimeter planes, with a forward angular cov-erage up to 60◦ [54]. The Barrel DIRC is used for PID forparticles with momenta of 0.8 GeV/c up to about 5 GeV/c,at polar angles between 22◦ and 140◦ [55]. The achieved

[GeV/c]lab

p1 10

b]

µ [

σ

­410

­310

­210

­110

1

10

210

310

Figure 4: Total cross section for the reaction p̄p→ π+π−,as a function of the beam momentum in laboratory sys-tem, plab. The selected data are from references: [7] (blackopen circle), [44] (blue full circle), [45] (cyan full cross),[46] (red full diamonds), [47] (brown full stars), and [48](black open star). The result from [42] (green full square)corresponds to total backward cross section and has tobe considered as a lower limit. The solid line is the resultfrom the generator. The dashed line is the result of thecompilation from Ref. [43].

momentum resolution is expected to be ∆p/p ' 1.5% at1 GeV/c.

A data acquisition system capable of a fast continuousreadout followed by an intelligent software trigger is underdevelopment.

3.2 Simulation and analysis software

The offline software for the PANDA detector simulationand event reconstruction is PandaRoot, which is developedin the frame of the common framework for the futureFAIR experiments, FairRoot [56]. It is mainly based onthe object oriented data analysis framework ROOT [57]and allows us to run different transport models such asGeant4 [14], which is used in the present simulations. Dif-ferent reconstruction algorithms for tracking and PID areunder development and optimization in order to achievethe requirements of the experiment.

The various steps undergone by a simulation or ana-lysis of experimental data, using PandaRoot are illustratedin Fig. 6.

9

Figure 5: View of the PANDA detector.

Figure 6: Standard analysis chain in PandaRoot.

3.3 Generated events

The signal and background events can be produced bydifferent event generators according to the physics case.As mentioned in the previous section, the generator fromRef. [35] was used for the background p̄p → π+π− sim-ulation. Taking into account that the ratio of cross sec-tions σ(p̄p → π+π−)/σ(p̄p → e+e−) < 106, a number of108 events were generated for the reaction p̄p → π+π−

at each value of the three incident antiproton momentafrom Table 1, plab = 1.7, 3.3 and 6.4 GeV/c (s = 5.4,8.2, 13.9 GeV2, respectively). To be safe in proton FF

measurement, we need to achieve a background rejectionfactor on the order of 10−8. Monte Carlo angular distri-butions for negative pions are shown in Fig. 7, for theconsidered three incident antiproton momenta.

The EvtGen [58] generator was used to generate thesignal channel p̄p → e+e−. 106 events were generatedat different values of the antiproton momenta (Table 1).These events were used to determine the efficiency of thesignal channel with high precision. The final state leptonsare produced according to two models of the angular dis-tribution (see Section 4).

3.4 PID and kinematical variable reconstruction

In order to separate the signal from the background, anumber of criteria have been applied to the reconstructedevents, using the raw output of the PID and tracking sub-detectors as EMC, STT, MVD, and DIRC. In this Sectionthe most relevant reconstructed variables for the signalselection are described in detail.

The EMC provides many efficient variables that canbe used in the event selection, as for example, the lateralmoment, and the energy deposit in a specific crystal. Forelectromagnetic showers, most of the energy is typicallycontained in two to three crystals, while hadronic showersspread out over greater distances.Lateral moment is typic-ally small for electromagnetic showers in comparison withhadronic showers. EMC lateral moment for the signal andbackground events is shown in Fig. 8.

The ratio of the shower energy deposited in the calor-imeter to the reconstruted momentum of the track asso-ciated with the shower (EEMC/preco) is another standard

10

θcos­1 ­0.5 0 0.5 1

Eve

nts

0

2000

4000

6000

8000

10000

310×

­π

+π→pp

(a)θcos

­1 ­0.5 0 0.5 1

Eve

nts

0

5

10

15

20

25

30

35

610×

­π

+π→pp

(b)θcos

­1 ­0.5 0 0.5 1

Eve

nts

0

5

10

15

20

25

30

35

40

45

610×

­π

+π→pp

(c)

Figure 7: Angular distribution of the p̄p→ π+π− events generated using the model from Ref. [35] for different s values:(a) 5.4 GeV2, (b) 8.2 GeV2, (c) 13.9 GeV2.

EMC lateral moment

0 0.2 0.4 0.6 0.8 1

Events

0

20

40

60

80

100

120

140

160

180

200

220

310×

Figure 8: EMC lateral moment for the signal (bluesquares) and background (red circles) events.

variable for electron selection (Fig. 9). Due to the verylow electron mass the EEMC/preco ratio is close to unityfor the signal (Fig. 9a). The discontinuities that appearon the plot are due to the transition regions between thedifferent parts of the EMC. For the background (Fig. 9b),the distribution shows a double structure: a narrow peakat low EEMC/preco values, which is due to the energy lossby ionization, and another one around EEMC/preco = 0.4corresponding to the hadronic interactions. The tail of thelatter extends to much higher values, causing backgroundunder the electron peak.

Like the EMC, the STT produces a different signaldepending on the type of the particle passing through itsvolume. The energy loss per unit of length, dE/dxSTT , inthe STT as a function of the reconstructed momentum forthe signal and the background are shown in Fig. 9c andFig. 9d respectively. Though electron and pion dE/dxSTT

patterns overlap, a cut on deposited energy in the STTcan still be applied in order to partially suppress the pionbackground.

3.4.1 PID probabilities

Using the raw output of the EMC, STT, MVD, and DIRCdetectors, the probabilities of a reconstructed particle be-ing an electron or positron were calculated. Those prob-abilities can be calculated for each detector individually(PIDs) or as a combination of all of them (PIDc).

In this work, both types of probabilities PIDs and PIDc

were used in order to increase the signal efficiency and thebackground suppression factor. The distributions of PIDc

are shown in Fig. 10. For the signal, the distributions ofthe PIDc (Fig. 10a) have a maximum at PIDc = 1, wherethe generated electron and positron events are well iden-tified. The peak at 0.2 is related to the events which themethod used to calculate PIDs can not provide a decisionabout the type of the particle. In this case, the probabilitysplits equally into the five particle types (e, µ, K, π, andp). The same explanation holds for the highly populatedregion around PIDc = 0.3, where two or three particleshave the same behavior in some detectors. For the gener-ated background events, PIDc distributions are shown inFig. 10b. As expected, the distributions of PIDc have amaximum at zero.

11

1

10

210

310

p [GeV/c]0 1 2 3 4 5

[G

eV

/(G

eV

/c)]

reco

/pE

MC

E

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

­e+ e→pp

(a)

1

10

210

310

410

510

610

p [GeV/c]0 1 2 3 4 5

[G

eV

/(G

eV

/c)]

reco

/pE

MC

E

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

(b)

1

10

210

310

p [GeV/c]0 1 2 3 4 5

[a

.u.]

ST

Td

E/d

x

0

2

4

6

8

10

12

14

16

18

20

­e+ e→pp

(c)

1

10

210

310

410

510

610

p [GeV/c]0 1 2 3 4 5

[a

.u.]

ST

Td

E/d

x

0

2

4

6

8

10

12

14

16

18

20

­π

+π→pp

(d)

Figure 9: Detector response to the signal (left column) and the background (right column): (a,b) is the energy depositedin the EMC over the reconstructed momentum as a function of momentum, (c,d) is the energy loss per unit of lengthin the STT as a function of momentum at q2=8.2 (GeV/c)2.

3.4.2 Kinematical variables

The signal and background reactions are two body finalstate processes. The electrons or pions are emitted backto back in the c.m. system. Since all final state particlesare detected, their total energy is equal to that of the p̄psystem.

In Fig. 11, the relevant kinematical variables are presen-ted for both, generated and reconstructed Monte Carloevents, before the selection procedure, including the sig-nal and the background at q2=8.2 (GeV/c)2.

Unlike the momentum and energy of a charged particle,the polar angles as well as the azimuthal angles are not af-fected on average by the Bremsstrahlung emission duringthe travel of the particle through the detector.

The kinematical selection helps mainly for the sup-pression of the hadronic background contribution relatedto the channels with more than two particles in the finalstate or to eliminate secondary particles whose kinematicsis different from that of primary particles. After applyinga chosen set of cuts (see Sections 4.1 and 4.2), the ver-tex and the kinematic fits did not contribute to rejectionof the secondary particles nor to the signal-backgroundseparation.

4 Simulation of the signal

Two independent simulations have been performed for thesignal. In order to clarify the methods used in each one,

12

PID probability

0 0.2 0.4 0.6 0.8 1

Events

310

410

510

610 (a) )+

|e+

(ecPID

)­

|e­

(ecPID

PID probability

0 0.2 0.4 0.6 0.8 1

Events

510

610

710(b) )

+|e+

π (cPID

)­

|e­π (cPID

Figure 10: (a) Total PID probability for e+ to be identified as e+ PIDc(e+|e+) (red dashed) and e− to be identified as

e− PIDc(e−|e−) (black solid). (b) Total PID probability for π+ to be identified as e+ PIDc(π

+|e+) (red dashed) andπ− to be identified as e− PIDc(π

−|e−) (black solid).

we present in this Section their detailed description. Themain differences between them are related (i) to the an-gular distribution model used as input for the event gen-erator, (ii) the determination of the efficiency, and (iii)the fit of the reconstructed events after efficiency correc-tion. The comparison between the two simulations allowsus to study the effect of the statistical fluctuations, theefficiency determination, and the extraction of the protonFFs using different fit functions.

4.1 Method I

All signal events were generated using the differential crosssection expressed as a function of the proton electromag-netic FFs, Eq. (3). In order to calculate the annihilationcross section, Eq. (11) was used as parameterization of|GM |, together with the hypothesis that |GE | = |GM |.

Thus, assuming the integrated luminosity of L = 2fb−1 (four months of data taking) and 100% efficiency thenumber of the expected e+e− pairs in the range −0.8 <cos θ < 0.8 can be calculated. Table 1 shows the total crosssection and the expected number of events for differentvalues of s. The signal events were generated using Eq. (3)and table 1.

4.1.1 Particle identification

The event selection was done in two steps. First, eventsthat had exactly one positive and one negative reconstruc-

ted charged track were selected for further analysis. Thenumbers of reconstructed pairs of particles with an oppos-ite charge are shown in Fig. 12. One can see that only in10% of the cases is the multiplicity larger than one. If anevent had e.g. one positive and two negative particles, itwas considered as carrying a multiplicity of two, becausethe positive particle could be associated with either of thetwo negative particles.

After the preselection, all events were filtered througha set of additional criteria listed in table 2. These criteriawere chosen in order to maximize signal reconstructionefficiency while suppressing as many background eventsas possible. Some cuts were fixed throughout all values ofq2, when others are changed to better fit the detector’sresponse at different energies.

Table 3 shows the reconstruction efficiency for the sig-nal (e+e−) selection and the background (π+π−) suppres-sion for each value of q2.

4.1.2 Measurement of signal efficiency

An additional set of e+e− pairs, containing a significantlylarger sample, was simulated for each value of q2. The sig-nal efficiency was extracted from these separate samples.The fraction of reconstructed events which satisfies theselection criteria to the generated events was defined asthe signal efficiency. The angular distribution of generatedelectrons, reconstructed and identified events, and the re-

13

’ [degree]θ+θ

150 160 170 180 190 200 210

Events

1

10

210

310

410

510

610­e+ e→pp

(a)’| [degree]φ­φ|

150 160 170 180 190 200 210E

vents

1

10

210

310

410

510

­e+ e→pp

(b)

]2 [GeV/cinv

M

0 1 2 3 4 5

Events

1

10

210

310

410

510

610

­e+ e→pp

(c)

’ [degree]θ+θ

150 160 170 180 190 200 210

Events

1

10

210

310

410

510

610

710

810­

π+

π→pp

(d)

’| [degree]φ­φ|150 160 170 180 190 200 210

Events

1

10

210

310

410

510

610

710

810­

π+π→pp

(e)

]2 [GeV/cinv

M

0 1 2 3 4 5

Events

1

10

210

310

410

510

610

710

810­

π+

π→pp

(f)

Figure 11: Spectra of generated (black) and reconstructed (red) events for different kinematical variables for the signal(top row) and the background (bottom row) at q2 = 8.2 (GeV/c)2: (a,d) the sum of the polar angles, (b,e) the differenceof the azimuthal angles, (c,f) the invariant mass of two reconstructed particles.

q2 [(GeV/c)2] 5.4 7.3 8.2 11.1 12.9 13.9PIDc [%] >99 >99 >99 >99 >99 >99PIDs [%] >10 >10 >10 >10 >10 >10dE/dxSTT [a.u.] >5.8 >5.8 >5.8 >5.8 >5.8 >6.5EEMC/preco [GeV/(GeV/c)] >0.8 >0.8 >0.8 >0.8 >0.8 >0.8EMC LM - <0.75 <0.75 <0.75 <0.75 - -EMC E1 [GeV] >0.35 >0.35 >0.35 >0.35 >0.35 >0.35θ + θ′ [degree] 175 < θ + θ′ < 185|φ− φ′| [degree] 175 < |φ− φ′| < 185Minv [GeV/c2] - - >2.2 >2.2 >2.2 >2.7

Table 2: Criteria used to select the signal (e+e−) and suppress the background (π+π−) events (Method I). Cuts wereapplied in a series from top to bottom as listed in the table.

construction efficiency at s = 8.2 GeV2 are presented inFig. 13.

4.1.3 Extraction of the ratio R

To extract the FFs ratio R, the reconstructed angular dis-tributions first need to be corrected using the efficiencycorrection method described in Section 4.1.2. As a second

step of this procedure, the corrected angular distributionwas fitted using the following equation:

dσ

d cos θ=πα2

2βs|GM |2

[(1 + cos2 θ) +

R2

τsin2 θ

], (12)

where R is a free fit parameter. Equation (11) was usedto calculate the the value of GM for each q2. The recon-structed and corrected angular distribution of electronstogether with the fit are shown in Fig. 14. One can see that

14

Pair multiplicity0 2 4 6 8 10

Events

0

100

200

300

400

500

600

700

310×

Figure 12: Number of reconstructed pairs of particles, outof 106, with an opposite charge for p̄p→ e+e− at q2=8.2(GeV/c)2. Only events with one positive and one negativereconstructed tracks i.e., multiplicity 1, were selected.

q2 [(GeV/c)2] e+e− π+π−

5.4 50.9% 6.8 · 10−6%7.3 53.5% -8.2 46.3% 2.0 · 10−6%11.1 46.2% -12.9 46.6% -13.9 38.7% 2.9 · 10−6%

Table 3: Reconstruction efficiency for the criteria de-scribed in Section 4.1.1 for the signal (e+e−) and the back-ground (π+π−) for each value of q2 (Method I).

for lower values of q2, where the cross section is higher, theshape of the angular distribution is reconstructed very welland the errors are relatively small. At higher q2 the recon-structed angular distribution is distorted due to statisticalfluctuations. For q2=13.9 (GeV/c)2 the fit range was re-duced to | cos θ| < 0.7, because of the large uncertaintiesat cos θ = ±0.8. The value of χ2/NDF is roughly 1 for allbut the highest q2 where it doubles.

4.1.4 Individual extraction of |GE | and |GM |

To extract individual values of |GE | and |GM | the differen-tial cross sections were calculated, assuming an integratedluminosity of L=2 fb−1, and using

σi =Ni

L· 1

Wi, (13)

where Ni is the number of events in the i-th bin and Wi

is the bin width of the i-th bin. Cross section uncertainty

θcos1− 0.5− 0 0.5 1

Eve

nts

0

10000

20000

30000

40000

50000

60000

Re

co

nstr

uctio

n e

ffic

ien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 13: Angular distribution for p̄p → e+e− atq2=8.2 (GeV/c)2 of generated (red circles) and reconstruc-ted/identified (blue squares) electrons. The reconstructionefficiency (green triangles) corresponds to the y-axis scaleon the right.

∆σ was calculated in the following way:

∆σi =1

Wi

∆Ni

L. (14)

Each differential cross section is fitted using Eq. (3), whichincludes |GE | and |GM | as free parameters.

4.1.5 Results

After the fitting procedure, the ratio R and the individualvalues and errors of |GE | and |GM | are extracted fromthe fit. The extracted FFs ratio is shown in Fig. 15 to-gether with results of other experiments. As can be seenthe PANDA experiment is able to measure the FFs ra-tio with a high statistical precision, around 1%, at lowerq2, in comparison to other experiments, while providingadditional measurements in the higher q2 domain.

The residual values of |GE | and |GM |, including onlystatistical uncertainties, are shown in Fig. 16. |GM | canbe measured with a significantly lower uncertainty, withthe relative error on GE being 2%-9%, in contrast to |GE |,which is around 3%-45%, due to the suppression by thefactor of τ in the fit function. Table 4 shows the expectedvalues and errors of extracted |GE |, |GM |, R.

4.2 Method II

The second method allowed to verify the reproducibilityof the results and to check systematic effects. The signal(p̄p → e+e−) was generated with the EvtGen generatorin phase space (PHSP) angular distributions. A numberof 106 events was generated at each value of the three in-cident antiproton momenta plab =1.7, 3.3 and 6.4 GeV/c

15

θcos1− 0.5− 0 0.5 1

Events

0

10000

20000

30000

40000

50000

(a)

θcos1− 0.5− 0 0.5 1

Events

0

1000

2000

3000

4000

5000

6000

7000

8000

(b)

θcos1− 0.5− 0 0.5 1

Events

0

500

1000

1500

2000

2500

3000

3500

(c)

θcos1− 0.5− 0 0.5 1

Events

0

100

200

300

400

500

(d)

θcos1− 0.5− 0 0.5 1

Even

ts

0

50

100

150

200

250

(e)

θcos1− 0.5− 0 0.5 1

Even

ts

0

20

40

60

80

100

120

140

160

(f)

Figure 14: Reconstructed and corrected angular distribution of generated electrons (green squares) and the fit (redline) for different q2 values: (a) 5.4 (GeV/c)2, (b) 7.3 (GeV/c)2, (c) 8.2 (GeV/c)2, (d) 11.1 (GeV/c)2, (e) 12.9 (GeV/c)2,(f) 13.9 (GeV/c)2.

16

]2 [(GeV/c)2q4 6 8 10 12 14

R

0

0.5

1

1.5

2

2.5

3BaBar

LEAR

FENICE+DM2

E835

BESIII

PANDA Method I

Figure 15: Form factor ratio extracted from the presentsimulation (magenta circles) as a function of q2, com-pared with the existing data. Data are from Ref. [7] (redsquares), from Ref. [8] (black triangles), from Ref. [59](green cross and blue star).

q2 R±∆R |GE | ±∆|GE | |GM | ±∆|GM |(GeV/c)2

5.40 1.0068±0.0147 0.1216±0.0012 0.1208±0.00057.28 1.0682±0.0325 0.0620±0.0013 0.0580±0.00048.21 0.9959±0.0530 0.0435±0.0018 0.0437±0.000511.1 0.9618±0.1765 0.0190±0.0029 0.0197±0.000612.9 1.1982±0.3445 0.0148±0.0033 0.0123±0.000713.9 1.0208±0.5766 0.0108±0.0051 0.0106±0.0010

Table 4: Expected values and errors of extracted R, |GE |,and |GM | (Method I).

(q2 = 5.4, 8.2, and 13.9 (GeV/c)2, respectively). Such stat-istics allows to optimize the kinematical cuts on the vari-ables with the aim to reach the largest pion rejection.

The events for both channels were analyzed in twosteps. First, the events which have one positive and onenegative particle were selected. If the event contained morethan one positive or negative track, i.e. secondary particleswhich may be produced by the interaction of generatedprimary particles with the detector materials, the bestpair identified by one positive and one negative track (thebest back-to-back with respect to the c.m. polar angle)was selected. Second, the reconstructed variables, such asmomentum, deposited energy, PID probabilities, etc. ofthe selected events, were analyzed. The best selection re-jecting the pion background was studied. The latter stepis explained below.

4.2.1 PID probability and kinematical cuts

The cuts applied to the background and the signal eventsare reported in table 5, for q2=5.4, 8.2 and 13.9 (GeV/c)2.The cuts were optimized in order to reach the largest pion

q2 [(GeV/c)2] 5.4 8.2 13.9PIDc [%] >99 >99 >99.5PIDs [%] >10 >10 >10dE/dxSTT [a.u.] >6.5 >5.8 0 or >6.5? [GeV/(GeV/c)] >0.8 >0.8 >0.8EMC LM - <0.66 <0.75 <0.66EMC E1 [GeV] >0.35 >0.35 >0.35θ + θ′ [degree] 175 < θ + θ′ < 185|φ− φ′| [degree] 175 < |φ− φ′| < 185Minv [GeV/c2] - >2.2 >2.7

Table 5: PID probability and kinematical cuts used toselect the signal (e+e−) and suppress the background(π+π−) events (Method II).

rejection of the background, while maximizing the signalefficiency. The sequential effect of all cuts, i.e., when ap-plied in a sequence one after the other, as well as the indi-vidual impact of each single cut, are reported for s = 8.2GeV2 in table 6.

Cut individual ε [%] sequential ε [%]background signal background signal

Acceptance/tracking 83.7 86.4 83.7 86.4PIDc +PIDs 3.5×10−4 70.1 2.9×10−4 60.5dE/dxSTT 15.5 95.1 1.9×10−4 59.3EEMC/preco 4.3×10−2 93.5 1.1×10−4 58.7EMC E1 + LM 2.0 83.7 1.9×10−5 52.6Kinematical cuts 94.9 72.9 9.8×10−7 44.6

Table 6: Individual and sequential efficiency for the signaland the background after the cuts, for s=8.2 GeV2 and| cos θ| ≤ 0.8 (Method II).

The reconstructed signal events, after applying thecuts, as well as the generated MC events are shown inFig. 17 for q2=8.2 (GeV/c)2. The drop of reconstructedevents at cos θ = 0.65 (θlab ∼ 22.3◦) is due to the trans-ition region between the forward and the barrel EMC(Fig. 17).

4.2.2 Extraction of the signal efficiency

The signal efficiency was extracted from the events gen-erated according to PHSP, for each cos θ bin. The ratiobetween the PHSP reconstructed events after cuts R(c),and the MC events M(c) represents the signal efficiencyas a function of the angular distribution c = cos θ. It canbe written as:

ε(c) =R(c)

M(c). (15)

To the content of each bin of R(c), is attributed the error∆R(c) =

√R(c). The error on the efficiency was derived

using Eq. (15) as follows:

∆ε(c) =

√ε(c)

M(c). (16)

17

4 6 8 10 12 140.01−

0.008−

0.006−

0.004−

0.002−

0

0.002

0.004

0.006

0.008

0.01

4 6 8 10 12 140.01−

0.008−

0.006−

0.004−

0.002−

0

0.002

0.004

0.006

0.008

0.01

Figure 16: Residual values of |GE | (left panel) and |GM | (right panel) for different q2 values with statistical uncertaintiesonly (Method I).

θ cos

­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1

Eve

nts

10000

20000

30000

40000

50000

60000

0

0.2

0.4

0.6

0.8

1

Figure 17: Angular distribution in the c.m. system for theMonte Carlo events for e− (green asterisk) and e+ (bluetriangles) generated according to the PHSP, for s=8.2(GeV/c)2. The reconstructed events after the cuts are alsoshown for e− (black squares) and (e+) (red circles). Theright y-axis represents the efficiency values.

Equation 16 shows, that the statistical error in the effi-ciency depends on the number M(c) events and it can bereduced to very small values. The efficiency distribution of

q2 [(GeV/c)2] e+e− π+π−

5.4 41% 1.9 · 10−6%8.2 44.6% 9.8 · 10−7%13.9 40.8% 1.9 · 10−6%

Table 7: Efficiency of the signal (e+e−) and the back-ground (π+π−) integrated over the angular range | cos θ| ≤0.8 for each value of q2 (Method II).

the signal as a function of cos θ is shown in Figs. 17 and 18for q2=8.2, 5.4 and 13.9 (GeV/c)2. As mentioned above,the reaction mechanism for pion pair production changesas a function of energy and the shape of the efficiency isnot constant with respect to the energy. Due to the dropof the efficiency in the region | cos θ| > 0.8, the analysisfor the proton FF measurements is limited to the angularrange cos θ ∈ [−0.8, 0.8]. The integrated efficiency in thisregion is given in Table 7.

4.2.3 Physical events

The PHSP events, having a flat distribution of cos θ in thec.m. system, do not contain the physics of the proton FFs.Physical events follow the angular distribution of Eq. (4).Therefore, the MC histograms of cos θ were rescaled bythe weight ω(c) = 1 +A c2, where A is given according toa model for GE and GM .

Note that the simulation should not show any dif-ference between electrons and positrons. In one-photonexchange, the angular distribution in c.m. system is de-scribed by a forward-backward symmetric, even function,in cos θ. Possible contributions from radiative corrections

18

θ cos

­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8

∈

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(a)

θ cos

­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1

(b)

Figure 18: Signal efficiency for e+ (red circles) and e− (black squares) in the c.m. system: (a) q2=5.4 and (b) 13.9(GeV/c)2.

(i.e. two-photon exchange diagrams and interference betweeninitial and final state photon emissions) can introduce inprinciple odd contributions in cos θ leading to a forwardbackward asymmetry. Being a binary process, in the ab-sence of odd contributions in the amplitudes1 the detec-tion of an electron at a definite value of c is equivalent tothe detection of a positron at cos(π − θ).

In the real data analysis, the efficiency will be valid-ated using the experimental spectra. In this analysis, weconsidered and corrected for separated e+ and e− MCgenerated events, as some asymmetry appears at the levelof reconstruction attributed to the different interaction ofpositive and negative particles with matter. The electronsand protons are corrected by their determined efficiencies.

To determine the number of the physical MC eventsbefore reconstruction (P (c)) and the physical reconstruc-ted events (W (c)), three other samples for the reactionp̄p → e+e− were generated using the PHSP angular dis-tributions, for the three values of q2. The P (c) and W (c)histograms are rescaled by the weight w(c) for the caseR = 1, A = (τ − 1)/(τ + 1).

4.2.4 Normalization: observed events

The reconstructed physical events, W (c), were normal-ized according to the integrated counting rate Nint(e

+e−)given in Table 1, which depends on the energy of the sys-tem and the luminosity. The events which are expected to

1 This is the case in the present simulation: one photon ex-change is implied and the photon emission calculated with thePHOTOS package does not induce any asymmetry [60].

be observed were estimated as follows:

O(c) = W (c) · Nint(e+e−)∫ 0.8

−0.8P (c)dc

, (17)

with an error ∆O(c) =√O(c) since the experimental er-

ror will finally be given by the accumulated statistics ofthe detected events.

4.2.5 Efficiency correction and fit

The fit procedure was applied to the observed events afterthe correction by the efficiency, F (c):

F (c) = O(c)/ε(c), (18)

∆F (c)

F (c)=

√(∆O(c)

O(c)

)2

+

(∆ε(c)

ε(c)

)2

, (19)

where the error in the efficiency ∆ε(c) was taken intoaccount. For each q2 value, the distribution F (c) as afunction of c2 was fitted with a two-parameter function(straight line). The linear fit function is:

y = a0 + a1x, with x = c2, a0 ≡ σ0, a1 ≡ σ0A, (20)

where a0 and a1 are the parameters to be determinedby minimization. They are related to the physical FFs,through Eq. (5). The observed events, before (O(c)) andafter (F (c)) efficiency correction are shown in Fig. 19 forq2 = 5.4 (GeV/c)2.

19

θ2cos

0 0.2 0.4 0.6 0.8

Eve

nts

4000

6000

8000

10000

12000

Figure 19: Observed events before efficiency correctionO(c) (forward events (blue triangles) and backward events(orange stars)) and after efficiency correction F (c) (for-ward events (red circles) and backward events (greensquares), as a function of cos2 θ for q2 = 5.4 (GeV/c)2,assuming R = 1. The line is the linear fit. The abscissa forbackward (forward) events is shifted by +0.005 (-0.005)for better visualization.

The measurement of the angular asymmetry allows oneto determine the FF ratio through the relation:

R =

√τ

1−A1 +A

. (21)

In the limit of small errors, as long as first order statist-ical methods work, the error in R can be obtained fromstandard error propagation on A:

∆R =1

Rτ

(1 +A)2∆A. (22)

The results of the fit are reported in Table 8. The relativeerror on the proton FF ratio increases from about 1.4% atthe low energy point to 40% at q2 = 13.9 (GeV/c)2.

The advantage of the PHSP based generator methodis that the same simulation can be used to test differ-ent models, by weighting each event according to the ap-plied model, of the proton FFs at a fixed energy. Thepoints obtained from the present simulations and the pub-lished world data on the proton FF ratio are shown inFig. 20 for the different values of R predicted by theor-etical models. The curves are theoretical predictions fromvector dominance model (solid green line), extended Gary-Krüempelmann (blue dash-dotted), naive quark model (reddashed line) model where the parameters have been ad-justed as in Ref. [61], and Ref. [3] (black dotted). For a

q2 [(GeV/c)2] R A ∆R ∆A5.40 1 0.210 0.014 0.0148.21 1 0.400 0.050 0.04213.90 1 0.590 0.407 0.264

Table 8: Expected statistical errors on the angular asym-metry and the proton FF ratio, for different s values as-suming an integrated luminosity of 2 fb−1 (Method II).The second and the third columns are the theoretical val-ues (simulation inputs). The fourth and the fifth columnsare the results of the fit on the errors. The statistical errorsare extracted in the angular range | cos θ| ≤ 0.8.

]2 [(GeV/c)2q4 6 8 10 12 14

R

0

0.5

1

1.5

2

2.5

3BaBar

LEAR

E835

FENICE+DM2

PANDA Method II

BESIII

Figure 20: Expected statistical precision on the determin-ation of the proton FF ratio from the present simulation(magenta circles) as a function of q2, compared with theexisting data. Data are from Ref. [7] (red squares), fromRef. [8] (black triangles), from Ref. [59] (green cross andblue stars). The statistical errors are extracted in the an-gular range | cos θ| ≤ 0.8. Curves are theoretical predic-tions, as explained in the text.

fixed energy point, the relative error in the proton FF ra-tio increases when the ratio is approaching zero, giving ameaningless value at the highest energy point q2 = 13.9(GeV/c)2.

4.2.6 Statistical errors on |GE | and |GM |

In order to extract the FF ratio, the measurement of theslope of the linear distribution of the cross section as afunction of cos θ is sufficient. To obtain the individual er-rors and the values of |GE | and |GM |, one needs to knowthe absolute normalization. The normalization needs anabsolute luminosity measurement, which will be knownwith a few percent precision.

20

q2 [(GeV/c)2] |GM | = |GE | ∆|GM | ∆|GE |5.40 0.12 0.70× 10−3 0.10× 10−2

8.21 0.04 0.70× 10−3 0.20× 10−3

13.90 0.01 0.10× 10−2 0.35× 10−2

Table 9: Expected statistical errors in the proton FFs, fordifferent s values (Method II). The second column is thetheoretical value (simulation input). The third and fourthcolumns are the results of the fit. The statistical errors areextracted in the angular range | cos θ| ≤ 0.8.

The individual determination of |GE | and |GM | wasobtained from a two-parameter fit with the function ofEq. (4) on the histograms of the events after the efficiencycorrection as defined in Section 4.2.5:

y = a+ b cos2 θ (23)

where |GE | and |GM | were extracted from a = σ0L andb = σ0AL by

|GM |2 =(a+ b)

2N; |GE |2 = τ

(a− b)2N

; (24)

N =πα2

2βsL;

and their errors:

∆|GM |2 =1

2N√

(∆a)2 + (∆b)2.

∆|GE |2 =τ

2N√

(∆a)2 + (∆b)2. (25)

The results of the fits are reported in Table 9. Theinput values of |GM | = |GE | (Eq. (11) are recovered withinthe error ranges.

4.2.7 Extrapolation and projected data

The real efficiency will be corrected during the experi-ment using the physics events. The MC contains ingredi-ents that will be fine tuned on the data. Moreover, thecounting rates (i.e., the cross sections) are also affectedby an uncertainty: different models give different values,especially at large s, where they are not so constrained bythe data. The experimental error depends on the squareroot of the efficiency.

Figure 21 shows the integrated efficiencies for q2=5.4,8.2 and 13.9 (GeV/c)2 over the angular range | cos θ| ≤0.8. The efficiency at q2=16.7 and q2=29 (GeV/c)2 arecalculated assuming the same cuts as for s=13.9 (GeV/c)2.The curve is obtained by extrapolation of the efficiencypoints obtained from the present simulation.

The experimental situation for the generalized protonFF, Fp, which can be extracted from the integrated crosssection (see Eq. (9)), in the hypothesis |GE | = |GM | andusing the dipole parametrization for the magnetic FF,Eq. (11), is shown together with the world data in Fig. 22.

]2[(GeV/c)2q0 10 20 30

[%]

0

20

40

Figure 21: Integrated efficiency of the signal p̄p → e+e−

for q2 = 5.4, 8.2 and 13.9 (GeV/c)2 (black triangles)and calculated efficiency, assuming the same cuts as fors=13.9 (GeV/c)2, for q2 = 16.7 and q2 = 29 (GeV/c)2(red squares).

]2|[(GeV/c)2|q0 5 10 15 20 25 30 35 40

D|/G

p|F

1−10

1

10

GM(SL)

GE(SL)

GM(TL)

BaBarE835Fenice

PS170E760DM1DM2BESBESIIICLEOPANDA Method II

Figure 22: q2-dependence of the world data on the effect-ive proton TL FF, as extracted from the annihilation crosssection assuming |GE | = |GM |, and on the SL FFs. Theerrors obtained or extrapolated from the present simula-tion, for an integrated luminosity of 2 fb−1, are shown bythe black squares.

21

4.2.8 Results with the full and reduced luminosity mode

FAIR is designed to provide instantaneous luminosities upto 2 × 1032 cm−2 s−1. The results presented in this workcorrespond to an integrated luminosity of 2 fb−1 which canbe accumulated in about 4 months of data taking. Withthis number of the integrated luminosity, the proton FFratio (R=1) can be determined with a statistical preci-sion of 1.4, 5 and 40.7% at q2=5.4, 8.2 and 13.9 (GeV/c)2respectively (Table 8). A separate measurement of |GE |and |GM | is possible. The relative error on |GE | (|GM |)increases from about 0.8% (0.6%) at q2=5.4 (GeV/c)2 to37% (9%) at q2=13.9 (GeV/c)2 (Table 9). The proton ef-fective FF can be measured over a large momentum rangewith a precision ranging from 0.3% at the lowest energypoint up to 62.4% at q2=27.9 (GeV/c)2 (see Fig. 22).

For the start operation of PANDA, a reduced setup islikely, with 20 times lower luminosity. With an integratedluminosity of 0.2 fb−1 (8 months of data taking with thereduced scenario), the statistical error on the proton FFratio increases by a factor of ∼

√10 compared to the full

luminosity mode. As a consequence, the range of meas-urement of the FF ratio, |GE | and |GM | will be reducedto below ∼10 (GeV/c)2 (∆R/R ∼ 40% at 10 (GeV/c)2,estimated using Method II).

5 Systematic uncertainty

As a full systematic study requires both experimental dataand MC we are limited in our ability to estimate everypossible source. Therefore, below, we discuss some of thesources of systematic uncertainties which can be testedwith MC only. As detectors design and production goes on,and first test data are available, a more precise estimationof systematic errors will be feasible.

5.1 Luminosity measurement

The PANDA experiment will use p̄p elastic scattering forthe luminosity measurement. Based on the Ref. [62] thesystematic uncertainty on the luminosity measurementmight vary from 2% to 5% depending on the beam en-ergy, the p̄p elastic scattering parameterization, and p̄p in-elastic background contamination. We considered the rel-ative systematic luminosity uncertainty ∆L/L to be 4.0%,2.5%, and 2.2% for the q2=5.40, 8.21, and 13,9 (GeV/c)2respectively. Table 11 shows the impact of the luminosityuncertainty on the extraction precision of GE and GM .

5.2 Detector placement

Thanks to the almost 4π acceptance of the PANDA de-tector, misalignments of its different components will notaffect the determination of proton FFs. Known displace-ments will be corrected during the reconstruction step,while an effect of small, up to few hundred micrometers,positioning errors will be much smaller than it’s trackingresolution.

5.3 Pion background

Considering the achieved background rejection factor of108 we can estimate the effect of the misidentification ofbackground events as signal ones. The analysis in Sec. 4was repeated with signal and background events mixedtogether. The number of added background events wascalculated in accordance with achieved background sup-pression.

In addition, the cross section of the background chan-nel p̄p→ π+π− will be measured at PANDA with a veryhigh accuracy due to its high cross section. Therefore, sys-tematic errors due to the model of the background differ-ential cross section used in simulations is expected to benegligible. The impact of the background on the FFs pre-cision is shown in Table 11.

5.4 Sensitivity to cos θ odd contributions

The analysis above assumes even cos θ angular distribu-tions, as expected from the one-photon exchange mech-anism. However odd contributions may be present in thedata, due to either experimental or physical reasons. Onephysical issue related to odd cos θ terms is the presence oftwo-photon exchange (TPE) mechanism, which may playa role at large s (see overview Ref. [21]).

In the presence of TPE, the matrix element of the reac-tion p̄p → e+e− contains three complex amplitudes: G̃E ,G̃M and F3 [63], instead of two form factors. The dif-ferential cross section of p̄p → e+e− including the TPEcontributions, can be approximated as:

dσ

d cos θ=πα2

2q2

√τ

τ − 1D, (26)

with

D = ( 1 + cos2 θ)|GM |2 +1

τsin2 θ|GE |2

+ 2

√τ(τ − 1)

(GE

τ−GM

)F3 cos θ sin2 θ. (27)

Only the real part of the three amplitudes, denoted GE ,GM , and F3, is taken into account since their relativephases are not known. The purpose of this study is not todetermine the physical amplitudes, but to set a limit fora detectable odd cos θ contribution, eventually present inthe data wether it comes from a physical origin or from ex-perimental acceptance. The Monte Carlo histograms (pro-duced in PHSP) were rescaled according to Eq. (26) withR = 1 and F3/GM=0, 0.02, 0.05 and 0.20. We fitted theangular distributions by the function:

y = a0 + a1 cos2 θ + a2 cos θ(1− cos2 θ), (28)

where a2, directly related to the ratio F3/GM gives the re-lative size of odd contributions. The results of the fit arereported in Table 10. Below F3/GM=0.05, a2 is compat-ible with zero, indicating a sensitivity to an asymmetry

22

q2 [(GeV/c)2] F3/GM [%] a0 a1 a2 ∆R ∆A5.4 0 10045±34 2077±130 76±83 0.014 0.015.4 2 10045±34 2078±130 -0.6±83 0.014 0.015.4 5 10045±34 2077±130 -115±83 0.014 0.015.4 20 10045±34 2077±130 -687±83 0.014 0.018.2 0 579±6 231±24 -3.5±14.8 0.05 0.048.2 2 579±6 231±24 -19.9±15 0.05 0.048.2 5 579±6 231±24 -44.3±15 0.05 0.048.2 20 579±6 231±24 -166±15 0.05 0.0413.9 0 17±1 10±4.2 -0.1±2.6 0.4 0.2613.9 2 17±1 10±4.2 -1.4±2.6 0.4 0.2613.9 5 17±1 10±4.2 -3.4±2.6 0.4 0.2613.9 20 17±1 10±4.2 -13.4±2.6 0.4 0.25

Table 10: The results from the fit of the angular distributions using Eq. (28), for q2 = 5.4, 8.2 and 13.9 (GeV/c)2.

larger than 5% at q2=5.4 (GeV/c)2. The extraction of Rand A is not affected.

In case of the charge symmetric detection of electronsand protons the interference term between the one- andtwo-photon-exchange channels will not contribute to thedifferential cross section [63]. Since PANDA will be able todetect both electrons and positrons (exclusive processes)and the contribution of TPE is symmetric between them,the TPE contribution can be eliminated by adding elec-tron and positron angular distributions.

5.5 Contribution to FFs

The contribution of the luminosity and background tothe precision of extracted values of FFs are reported inTable 11 together with the statistics contribution. Thebackground contamination is on the level of few percentfor all values of q2. The luminosity uncertainty affects onlyGE and GM , since the luminosity measurement is notneeded for R determination. At lower q2 values, wherethe signal statistic is relatively high, the total uncertaintyis dominated by the background contamination and lu-minosity contributions. In the intermediate energy domainstatistic decreases and affects the total uncertainty on thesame level as systematic uncertainties. At higher q2, themain contribution to the total uncertainty is given by thestatistical error due to the small signal cross section.

6 Conclusion

Feasibility studies for the measurement of the process p̄p→e+e− at PANDA have been performed and reported inthis work. Full simulations for the processes p̄p → e+e−

have been carried out with the PandaRoot software. Anamount of 3 × 108 events for the main background pro-cess p̄p→ π+π− has been generated and reconstructed atthree energy points. A background suppression factor ofthe order of ∼ 108 has been achieved keeping a large andsufficient signal efficiency for the proton FF measurementsat PANDA. Two independent simulations have been per-formed for the signal using two models and numbers for

q2 Stat Systematic[(GeV/c)2] Bg Lumi Total

∆GE/GE

5.40 1.0% 0.3% 2.0% 2.3%8.21 4.2% 2.9% 1.3% 5.2%13.9 48% 3.1% 1.1% 48%

∆GM/GM

5.40 0.5% 2.8% 2.0% 3.4%8.21 1.2% 1.1% 1.3% 2.1%13.9 9.4% 1.0% 1.1% 9.5%

∆ R/R5.40 1.5% 2.9% n/a 3.3%8.21 5.3% 4.0% n/a 6.6%13.9 57% 4.1% n/a 57%

Table 11: Effect of systematic and statistic uncertainties,as well as their total contribution, on the precision of GE ,GM , and R. (Method I)

the generated events, two sets of event selection criteriaand two fit functions to extract the proton electromag-netic FFs. The results from the two simulations, assumingR = 1, are shown in Fig. 23, together with the existingexperimental data. For q2 = 5.4 and 8.2 (GeV/c)2, theresults are consistent between each other. At q2 = 13.9(GeV/c)2, Method I gives a larger statistical error thanMethod II: at this energy point, the number of events issmall and as a consequence the statistical fluctuations areimportant. This fact is not taken into account in MethodII where about 106 events have been generated and res-caled. Indeed, the statistical fluctuations are arbitrary andby repeating Method I multiple times one can obtain aGaussian distribution of the statistical error where themean, the most probable value, is equal to the error valueobtained with Method II. The error distribution on theangular asymmetry A is verified to be gussian symmetricup to this value of s.

The determination of the statistical uncertainties on Rhas been extended with Method II to different models ofproton FF ratio. For a fixed energy point, larger relativeerror has been obtained for R < 1 than for the case R=1.This result should be the same for both simulations since itdepends only on the number of statistics generated withinthe detector acceptance.

In comparison to the previous analysis [11], the de-scription of the detector is more realistic as well as the

23

]2 [(GeV/c)2q4 6 8 10 12 14

R

0

0.5

1

1.5

2

2.5

3BaBar

LEAR

FENICE+DM2

E835

BESIII

PANDA method I

PANDA method II

Figure 23: Expected statistical precision on the determ-ination of the proton FF ratio from the present simu-lations (magenta squares and blue down triangles) forR = 1 as a function of q2, compared with the existingdata. Data are from Ref. [7] (red squares), from Ref. [8](black up triangles), from Ref. [59] (green cross and bluestar). The statistical errors are extracted in the angularrange | cos θ| ≤ 0.8.

different steps of the reconstruction and the analysis. Thetotal signal efficiency is improved by 5–10% in compari-ons to the previous stdudies [11] due to the new selectionprocedure and new PID capabilities avaiable in the Panda-Root. However, the experimental cuts will finally be seton the real data.

The PANDA experiment at FAIR will extend the know-ledge of the TL electromagnetic FFs in a large kinematicalrange. The present results show that the statistical errorat q2 ≥ 14 (GeV/c)2 will be comparable to the one ob-tained by BABAR at ∼ 7 (GeV/c)2.

The study of the systematic uncertainties shows thatthe background misidentification and luminosity uncer-tainty dominate the total uncertainty at lower q2, whilein the high energy domain the total error is mainly influ-enced by the statistic due to the smaller p̄p→ e+e− crosssection. The total relative uncertainty of individual FFs isexpected to be around 2–47% and around 3–57% for theratio R.

The absolute cross section measurement depends es-sentially on the precision achieved in the luminosity meas-urement, which is expected to lye between 1% and 2%. ThePANDA experiment at FAIR will allow the individual de-termination of the FFs in the TL region, from 5.4 GeV/cto 13.9 GeV/c. This is essential for a global analysis of theFFs in the SL and TL regions, to test the models which ap-ply in the whole kinematical range and require analyticalcontinuation of FFs.

The moduli of the individual FFs GE and GM will bemeasured for the first time at BESIII using the data col-lected at 20 different beam energies between 4.0 and 9.5GeV2 [64]. A statistical precision on the FF ratio between

9% and 35% is expected. Based on these numbers, onecan see that PANDA will extend these measurements upto a higher energy range (14 GeV2), with a precision bet-ter than expected at BESIII or comparable in case of thereduced luminosity mode.

The modulus of the proton FFs ratio can be also meas-ured at Belle [65], using the initial state radiation (ISR)technique, with a comparable accuracy to the BABARdata . The Belle detector was operating on the KEKBe+e− collider [66]. An integrated luminosity of about 1040fb−1 was collected at KEKB between 1999 to 2010. Mostof the data were taken at the Y (4S) resonance. The up-graded facility of the KEKB collider (SuperKEKB) aimsto accumulate 50 ab−1 around 2021-2022 [67]. The BelleII experiment [68] at the superKEKB collider may providethe most accurate data on the proton FF ratio. Unlike thedirect production of the e+e− ↔ p̄p processes which allowa precise measurement of FFs in very thin bins of q2, theISR technique allows their extraction in wide bins of q2. Sofar, no estimation has been presented by the collaborationfor the FFs measurement at Belle and Belle II.

7 Acknowledgments

The success of this work relies critically on the expertiseand dedication of the computing organizations that sup-port PANDA. We acknowledge financial support from theScience and Technology Facilities Council (STFC), Brit-ish funding agency, Great Britain; the Bhabha AtomicResearch Center (BARC) and the Indian Institute ofTechnology, Mumbai, India; the Bundesministerium fürBildung und Forschung (BMBF), Germany; the Carl-Zeiss-Stiftung 21-0563-2.8/122/1 and 21-0563-2.8/131/1,Mainz, Germany; the Center for Advanced RadiationTechnology (KVI-CART), Gröningen, the Netherlands;the CNRS/IN2P3 and the Université Paris-Sud, France;the Deutsche Forschungsgemeinschaft (DFG), Germany;the Deutscher Akademischer Austauschdienst (DAAD),Germany; the Forschungszentrum Jülich GmbH, Jülich,Germany; the FP7 HP3 GA283286, European Commis-sion funding; the Gesellschaft für SchwerionenforschungGmbH (GSI), Darmstadt, Germany; the Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ger-many; the INTAS, European Commission funding; theInstitute of High Energy Physics (IHEP) and theChinese Academy of Sciences, Beijing, China; the Isti-tuto Nazionale di Fisica Nucleare (INFN), Italy; theMinisterio de Educación y Ciencia (MEC) under grantFPA2006-12120-C03-02, Spain; the Polish Ministry of Sci-ence and Higher Education (MNiSW) grant No. 2593/7,PR UE/2012/2, and the National Science Center (NCN)DEC-2013/09/N/ST2/02180, Poland; the State AtomicEnergy Corporation Rosatom, National Research CenterKurchatov Institute, Russia; the Schweizerischer Nation-alfonds zur Forderung der wissenschaftlichen Forschung(SNF), Switzerland; the Stefan Meyer Institut für Subato-mare Physik and the Österreichische Akademie der Wis-senschaften, Wien, Austria; the Swedish Research Coun-cil, Sweden.

24

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