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accessible to scientists not expert in that particular field.

Nele Boelaert

Dijet Angular Distributionsin Proton–Proton Collisions

Atffiffi

sp

= 7 TeV andffiffi

sp

= 14 TeV

Doctoral Thesis accepted byLund University, Sweden

123

AuthorDr. Nele BoelaertDepartment of PhysicsLund University22100 LundSwedene-mail: nele.boelaert@hep.lu.se

SupervisorProf. Torsten ÅkessonDepartment of PhysicsLund University22100 LundSwedene-mail: Torsten.Akesson@hep.lu.se

ISSN 2190-5053 e-ISSN 2190-5061ISBN 978-3-642-24596-1 e-ISBN 978-3-642-24597-8DOI 10.1007/978-3-642-24597-8Springer Heidelberg Dordrecht London New York

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Supervisor’s Foreword

One of the most common experimental methods in Physics is to illuminate a target,observe the pattern of the scattering, and learn something about the structure of thetarget. A famous example is of course the experiment of Rutherford in 1911, whenhe illuminated a gold foil with alpha particles and discovered the atomic nucleus.A later example is the electron scattering experiment using the Stanford LinearAccelerator which led to the discovery of the quarks inside the protons andneutrons. The highest resolution is obtained with the highest energy particles,and today, those are to be found at the Large Hadron Collider (LHC) at CERN.In the historic examples above, the targets were at rest in the laboratory, while thescattering is in a different rest-frame at a collider. Nevertheless, the principle is thesame. By studying the angular distribution of the scattered quarks and gluons, atthe LHC, their possible structure and the forces acting between them, are explored.This was the thesis topic of Dr Boelaert.

In 2006 the Physics Department at Lund University got the opportunity tolaunch a graduate school in High Energy Physics, thanks to a Marie Curie grantfrom the 6th framework programme of the European Union. It allowed sevenstudents to start as graduate students. The students came from Belgium, China,Denmark, Italy, Romania and UK, and studied and did their research together inLund during four years. I believe that this has given them and us, the permanentstaff, an experience for life. Nele Boelaert came to this group with a degree inEngineering Physics from the Technical University in Gent/Belgium and I had theprivilege to become her supervisor.

My interactions with her were a sequence of positive surprises in learning howmuch she had done, the quality of what she had done, and her innovative approach.

N. Boelaert started before the LHC became operational, and the original planwas that after a year of courses and a year of research preparation, she would havea few years of data from the LHC as basis for her thesis. However, like manyfrontier projects, the LHC encountered some delays. This gave her time to enterdeeper into the phenomenological aspects of the measurements to be done, but alsoreduced the prospects of the scientific potential of the data that would be at handfor the thesis. Nevertheless, the LHC started during the last year of her position in

v

Lund allowing her to get results from the first, but limited, data from this newfacility. This data was just a tiny first step into the vast space that the coming yearsof LHC operation will allow to be explored.

Her analysis has shown how well these measurements can be done, how wellour current theory, the Standard Model, describes the entering point into the spaceopened up the LHC, and has shown the precision of the understanding of ATLASat the LHC that has been built up by the scientific collaboration that constructedthis facility. Nele Boelaert’s thesis has set the best possible stage to pursue thisexploration in the years to come as the LHC integrates luminosity and increases itsenergy. Her thesis is very well structured and written, and provides an excellentintroduction for new graduate students to come.

Lund, August 2011 Torsten Åkesson

vi Supervisor’s Foreword

Acknowledgements

I would not have been able to complete this thesis without the help and influenceof many people.

First of all, I wish to thank my main supervisor Torsten, because his suggestionto work on dijet angular distributions has resulted into a very fascinating andversatile research project.

Else became my co-supervisor nearly two years ago. Her advice concerningmy research and work in the ATLAS collaboration has been extremely helpful.Else has given me the necessary confidence to grow and stand up inside thecollaboration.

My warmest gratitude goes to Torbjörn. As my theoretical co-supervisor, he hasled me successfully through my first phenomenology study. But his help has gonefar beyond that; he has always been eager to share his very broad experience withme, explaining me everything I wanted to know, and giving me insight in how toproceed with my work. I have taken up so many hours of his time without himshowing the least bit of impatience, and for all this I am very grateful.

I also wish to thank everybody who has been involved in setting up andorganizing the Lund-HEP EST graduate school, which has given me the oppor-tunity to start a PhD in high energy physics.

Part of my work consisted of using a Monte Carlo particle generator which wascreated by Leif. I appreciate very much the time he took for helping me use it andinterpret the results.

Furthermore, I want to thank the ATLAS collaboration for integrating me andgiving me scope to develop and learn. In particular, I wish to thank those people Ihave closely worked with on the dijet analysis: PO, Frederik, Lukas, Georgios andSing. Our group has been very successful, with results of the measurements beingpublished only a few months after the data had been recorded.

My work on ATLAS data quality was under the supervision of Michael, and Iwish to express my gratitude to him because he has taught me well in the field ofsoftware development and the ATLAS offline framework.

Here in Lund, I wish to thank Anders, the head of the division of ExperimentalHigh-Energy Physics, because he has given me excellent feedback on my thesis.

vii

Not only was he a very good listener to any kind of problem but he also always didwhatever he could to help solving them.

Nowadays computers cannot be left out when studying high energy physics.Even though they are such a great aid, they often don’t do what you want them todo. Fortunately, whenever I had a problem that seemed unsolvable, Richard wouldhelp me out. But more importantly, as my significant other, he has cared for me ina much broader context.

Finally I wish to thank my parents. They have been a constant and great supportthroughout my whole life. Without them, I wouldn’t even have started this PhDstudy.

This thesis work was partly financed from the Marie Curie Mobility-2 action ofthe European Union 6th framework programme. Swedish participation in ATLASwas granted by the Swedish Research Council (VR) and the Knut and AliceWallenberg foundation (KAW).

viii Acknowledgements

Abstract

Dijet angular distributions provide an excellent tool for looking at high transversemomentum parton interactions in order to study both QCD and new physicsprocesses. With the Large Hadron Collider (LHC) recently brought into use, anunprecedented energy regime has opened up. ATLAS is one of the experiments atthe LHC. Its high performance calorimeter system providing near hermetic cov-erage in the pseudorapidity range |g|\4.9, enables ATLAS to perform reliable jetmeasurements. Detailed Monte Carlo studies at

ffiffi

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= 14 TeV, the LHC designcollision energy, and at

ffiffi

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= 7 TeV, the collision energy foreseen for the initialyears of the LHC operation, clearly show that dijet angular distributions can beused to discriminate the Standard Model from a new physics model describinggravitational scattering and black hole formation in large extra dimensions. Whenconsidering only the shape of the distributions, both the theoretical and theexperimental uncertainties are predicted to be small in those regions where newphysics is expected to show up. The study at

ffiffi

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= 7 TeV indicates that ATLAS isalready sensitive to large extra-dimensional gravity mediated effects with 1 pb-1

of data. The first measurement of dijet angular distributions atffiffi

sp

= 7 TeV withATLAS was carried out in two mass bins, using data that were recorded early2010, corresponding to an integrated luminosity of about 15 nb-1. The measure-ment shows good agreement with QCD predictions and demonstrates that ATLASis ready to search for new physics in the dijet angular distributions with more data.

ix

List of Publications Related to this Thesis

1. Dijet angular distributions atffiffi

sp

= 14 TeVBy N. BoelaertPublished in Proceedings of Science (EPS-HEP 2009) 298

2. Software design for prompt assessment of time-varying data qualityBy N. Boelaert, M. D’Onofrio, A. Dotti, C. Guyot, M. Hauschild, R. Hawkings,B. Heinemann, A. Hocker, V. Kazazakis, E. Lytken, M. Martınez-Perez,R. McPherson, P. U. E. Onyisi, A. Schaetzel, R. Seuster and M. G. WilsonPublished as ATLAS internal note, ATL-COM-GEN-2010-002-Geneva: CERN,2010

3. Implementation of the GravADD generator in AthenaBy N. BoelaertPublished as ATLAS internal note, ATL-PHYS-INT-2010-012-Geneva:CERN, 2010

4. Dijet angular distributions atffiffi

sp

= 14 TeVBy N. Boelaert and T. ÅkessonarXiv:0905.3961 [hep-ph]Published in The European Physical Journal C, 33, (2010) 343–357

5. ATLAS sensitivity to contact interactions and large extra dimensions usingdijet events a

ffiffi

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= 7 TeVBy N. Boelaert, G. Choudalakis, P. O. Deviveiros, E. Feng, H. Li, J. Poveda,L. Pribyl, F. Ruehr and S. L. WuPublished as ATLAS internal note, ATL-COM-PHYS-2010-136-Geneva:CERN, 2010

6. High-pT dijet angular distributions in pp interactions atffiffi

sp

= 7 TeV measuredwith the ATLAS detector at the LHCBy N. Boelaert, R. Buckingham, S. L. Cheung, G. Choudalakis, T. Davidek,P. O. De-Viveiros, E. Feng, J. Frost, M. Kaneda, H. Li, H. Peng, L. Pribyl,M. Shupe, K. Terashi, S. L. WuPublished as ATLAS internal note, ATL-COM-PHYS-2010-359-Geneva:

xi

CERN, 2010Presented at the International Conference on High Energy Physics 2010,ParisPresented at LBNLMIT10, Cambridge, USA, a joint workshop betweenLawrence Berkeley National Laboratory and Massachusetts Institute ofTechnology

xii List of Publications Related to this Thesis

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Standard Model and Beyond . . . . . . . . . . . . . . . . . . . . . 11.2 High Energy Physics Experiments and the Large

Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 This Thesis: Dijet Angular Distributions at LHC Energies. . . . 61.4 Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Introduction to QCD and Collider Physics . . . . . . . . . . . . . . . . . 112.1 Quantum Chromodynamics (QCD) . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Perturbative QCD (pQCD). . . . . . . . . . . . . . . . . . . . 122.2 The Parton Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Hard Scattering Processes in Hadron Collisions . . . . . . . . . . . 172.4 Parton Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Hadronization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.6 Monte Carlo Event Generators . . . . . . . . . . . . . . . . . . . . . . . 22References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 NLO Monte Carlo Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 The Dipole Subtraction Method . . . . . . . . . . . . . . . . . . . . . . 26

3.2.1 General Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.2 NLOJET++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 The Phase Space Slicing Technique . . . . . . . . . . . . . . . . . . . 303.3.1 General Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 JETRAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Comparison of the Subtraction Method and the PhaseSpace Slicing Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

xiii

4 Dijet Physics at Colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1 Leading-Order Jet Pair Production . . . . . . . . . . . . . . . . . . . . 35

4.1.1 Massless Partons . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.2 Massive Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Dijet Angular Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 394.2.1 Parton Level Considerations . . . . . . . . . . . . . . . . . . 394.2.2 Hadron Level Considerations . . . . . . . . . . . . . . . . . . 41

4.3 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Gravitational Scattering and Black Holes in LargeExtra Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.1 Extra Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.1.1 Kaluza-Klein Mode Expansion and Reduction . . . . . . 455.1.2 Compactification on an Orbifold . . . . . . . . . . . . . . . 475.1.3 Types of Extra Dimensions . . . . . . . . . . . . . . . . . . . 485.1.4 Bounds on Extra Dimensions . . . . . . . . . . . . . . . . . . 48

5.2 The ADD-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2.1 Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2.2 Lowering the Planck Scale . . . . . . . . . . . . . . . . . . . 495.2.3 Implications for Low Energy Phenomenology . . . . . . 515.2.4 Kinematic Regimes. . . . . . . . . . . . . . . . . . . . . . . . . 525.2.5 Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3 Gravitational Scattering in the ADD Model . . . . . . . . . . . . . . 535.3.1 KK Reduction of the Graviton . . . . . . . . . . . . . . . . . 535.3.2 Scattering Amplitude . . . . . . . . . . . . . . . . . . . . . . . 545.3.3 Large Momentum Transfers:

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5.3.4 Small Momentum Transfers:ffiffi

sp� Ms . . . . . . . . . . . 56

5.3.5 Experimental Limits . . . . . . . . . . . . . . . . . . . . . . . . 575.4 Black Holes in the ADD Model . . . . . . . . . . . . . . . . . . . . . . 57

5.4.1 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.4.2 Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.5 The GravADD Generator. . . . . . . . . . . . . . . . . . . . . . . . . . . 595.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.5.2 Monte Carlo Generators in Athena . . . . . . . . . . . . . . 605.5.3 Model Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . 605.5.4 Implementation in the ATLAS Software

Framework Athena . . . . . . . . . . . . . . . . . . . . . . . . . 615.5.5 Use From Inside Athena . . . . . . . . . . . . . . . . . . . . . 62

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

xiv Contents

6 The ATLAS Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.1 Detector Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.1 The Jet Trigger Slice . . . . . . . . . . . . . . . . . . . . . . . 736.3 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.4 Data Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.4.1 Automatic Evaluation and Display ofData-Quality Histograms: Han and Handi . . . . . . . . 75

6.4.2 Prompt Assessment of Data-Quality DuringData Taking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.1 General Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7.1.1 Jet Reconstruction Performance Studies . . . . . . . . . . 847.2 Jet Finding Algorithms in ATLAS . . . . . . . . . . . . . . 857.2.1 Cone Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2.2 Sequential Recombination Algorithms. . . . . . . . . . . . 867.2.3 Anti-kT : the ATLAS Default Algorithm . . . . . . . . . . 87

7.3 Input for Jet Finding Algorithms . . . . . . . . . . . . . . . . . . . . . 877.4 Jet Energy Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.4.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.4.2 Step 1: Energy Hadronic Calibration. . . . . . . . . . . . . 917.4.3 Step 2: Offset Correction. . . . . . . . . . . . . . . . . . . . . 947.4.4 Step 3: ðg;/Þ Correction . . . . . . . . . . . . . . . . . . . . . 957.4.5 Step 4: Response Correction . . . . . . . . . . . . . . . . . . 957.4.6 Step 5: Resolution Improvement . . . . . . . . . . . . . . . 967.4.7 Step 6: Topology and Flavor Corrections . . . . . . . . . 97

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

8 Jet Reconstruction with 2010 ATLAS Data . . . . . . . . . . . . . . . . . 998.1 Jet Algorithm and Jet Calibration . . . . . . . . . . . . . . . . . . . . . 998.2 Data Quality Requirements and Event Cleaning . . . . . . . . . . . 99

8.2.1 Run Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.2.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008.2.3 Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.3 Jet Reconstruction Performance . . . . . . . . . . . . . . . . . . . . . . 1018.3.1 Jet Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . 101

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

9 Dijet Angular Distributions atffiffi

sp¼ 14 TeV:

A Phenomenology study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059.2 Kinematics Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Contents xv

9.3 QCD Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1079.4 Gravitational Scattering and Black Hole Formation

in Large Extra Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . 1169.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

10 Preparing ATLAS for the Measurement of Dijet AngularDistributions at

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10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12510.2 Trigger Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

10.2.1 Trigger Menu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12610.2.2 Trigger Efficiency Using the Tag

and Probe Method . . . . . . . . . . . . . . . . . . . . . . . . . 12610.3 Kinematic Cuts and Histogram Binning . . . . . . . . . . . . . . . . 129

10.3.1 Kinematic Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 12910.3.2 Binning in v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13010.3.3 QCD Distributions and Statistical Uncertainties

for 10 pb�1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.4 NLO QCD Calculations and k-Factors . . . . . . . . . . . . . . . . . 133

10.4.1 Calculating k-Factors: General Method . . . . . . . . . . . 13310.4.2 NLO QCD Calculations and k-Factors

for the Dijet Angular Distributions . . . . . . . . . . . . . . 13410.5 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

10.5.1 Renormalization and FactorizationScale Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 136

10.5.2 PDF Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 13810.6 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 139

10.6.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . 13910.6.2 Estimate of Experimental Uncertainties . . . . . . . . . . . 141

10.7 Data Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14310.8 Sensitivity to Black Hole Production and Gravitational

Scattering in Large Extra Dimensions . . . . . . . . . . . . . . . . . . 14510.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

11 Measurement of Dijet Angular Distributions by ATLAS . . . . . . . 15111.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15111.2 Data Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15111.3 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15211.4 Physics Selection Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15211.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

11.5.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 15411.5.2 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

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12 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15712.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15712.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Appendix A: Statistical Hypothesis Testing Using the FrequentistMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

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