MEASUREMENT OF NEUTRAL CURRENT ELECTRON ...

MEASUREMENT OF NEUTRAL CURRENT ELECTRON-PROTONCROSS SECTIONS WITH LONGITUDINALLY POLARISED

ELECTRONS USING THE ZEUS DETECTOR

SYED UMER NOOR

A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATESTUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTSFOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

GRADUATE PROGRAM IN PHYSICS AND ASTRONOMYYORK UNIVERSITY

TORONTO, ONTARIODECEMBER 2007

MEASUREMENT OF NEUTRAL CURRENTELECTRON-PROTON CROSS SECTIONSWITH LONGITUDINALLY POLARISED


by Syed Umer Noor

a dissertation submitted to the Faculty of Graduate Stud-ies of York University in partial fulfilment of the require-ments for the degree of

DOCTOR OF PHILOSOPHYc© 2008

Permission has been granted to: a) YORK UNIVER-SITY LIBRARIES to lend or sell copies of this disserta-tion in paper, microform or electronic formats, and b) LI-BRARY AND ARCHIVES CANADA to reproduce, lend,distribute, or sell copies of this dissertation anywhere inthe world in microform, paper or electronic formats andto authorise or procure the reproduction, loan, distribu-tion or sale of copies of this dissertation anywhere in theworld in microform, paper or electronic formats.

The author reserves other publication rights, and nei-ther the dissertation nor extensive extracts for it maybe printed or otherwise reproduced without the author’swritten permission.

MEASUREMENT OF NEUTRAL CURRENT ELECTRON-PROTONCROSS SECTIONS WITH LONGITUDINALLY POLARISED


by Syed Umer Noor

By virtue of submitting this document electronically, the author certifies that thisis a true electronic equivalent of the copy of the dissertation approved by YorkUniversity for the award of the degree. No alteration of the content has occurredand if there are any minor variations in formatting, they are as a result of theconversion to Adobe Acrobat format (or similar software application).

Examination Committee Members:

1. A. Kumarakrishnan

2. S. Menary

3. W. Taylor

4. P. Taylor

5. I. McDade

6. D. Bailey

Abstract

Neutral current (NC) electron-proton deep inelastic scattering (DIS) cross sections

with negatively and positively longitudinally polarised electrons are measured at

high momentum transfer squared (Q2 > 185 GeV2) using the ZEUS detector at

HERA. The HERA accelerator provides e±p collisions at a centre-of-mass energy

of 318 GeV, allowing high Q2 interactions which are sensitive to the weak force

contribution to the NC process. The e−p scattering data analysed corresponds to

an integrated luminosity of 177.2 pb−1, and is the largest amount of e−p data ever

recorded at ZEUS. Single-differential cross sections and reduced double-differential

cross sections are measured and agree well with the predictions of the Standard

Model. The two major results of this thesis are the first observation of parity

violation in NC e−p DIS at distances down to 10−18 m, and the measurement of the

structure functions xF3 and xF γZ3 , which are proportional to the proton valence

quark distribution, with the best precision to date.

iv

Dedicated to my mother and the memory of my father

v

Acknowledgements

This PhD has been one of the most fruitful endeavours I have ever undertaken, and

there are a number of people who have helped me along the way.

Firstly, I thank my supervisor Sampa for her support and guidance. I have

been very lucky to work with such a kind-hearted supervisor. I thank the NC e−p

analysis team; Yongdok who performed an enormous amount of excellent work in

tandem with my analysis and Kunihiro who has expertly guided us both. It has

been a pleasure to work closely with such delightful people. I thank everyone in the

High Q2 group, especially Enrico, Alex, James, Catherine, Katherine, and Micha l

for all their help. I express my gratitude to Richard who patiently taught me how

to perform my first analysis. I also thank all the Trigger group members, especially

Alessandro and Yuji, for their advice.

The Canadian group at DESY has been very supportive, and I thank the re-

search associates Mara, Serguei, and Roberval for their endless help, and professors

Scott, John, and Francois for their guidance. I thank the Canadian students, in

vi

particular Jerome, Ying, Jeff, Trevor, Chuanlei, and Jason, for all the good times.

Life at DESY was made much richer by the impromptu games of football/baseball

and outings for lunch. Many thanks to John, Tom, Billy, Dan, Avraam, Elıas,

Alessandro, Matt, and Tim for great laughs. I especially thank Jerome and John

for being such great friends. In addition to living in Hamburg, I also had the

pleasure of living in Tsukuba for 6 weeks to work on the NC analysis side-by-side

with Yongdok. I am grateful to all the members of the ZEUS KEK group for their

hospitality and I especially thank Katsuo for being a kind host.

I have shared an office with many friendly people at York, including George,

Brian, Steve, and Slavic. I thank Scott, Marko, and Wendy for their guidance at

York, and I thank Brad for his help with my lab. TAs. Whilst living in Hamburg

and Toronto, I have generated lots of paperwork and needed help with living ar-

rangements, so I especially thank Marlene and Lauren at York, and Susan and the

international office at DESY for their huge efforts.

I would not have made it this far without the love from my mother and late

father, the constant encouragement from my brother and sister, and the warm-

hearted support from my mother-in-law and brother-in-law. Finally, I cannot thank

my wife enough for sticking by me through the ups and downs of the PhD. She is

my true treasure and I am deeply grateful for her love.

vii

Contributions to the ZEUS experiment

I have been a member of the Canadian group of the ZEUS collaboration since

autumn 2003. During this time, I have had the privilege of being part of an inter-

national collaboration of approximately 400 physicists, and the opportunity to be

involved in the running of a large and exciting experiment. The ZEUS experiment

is located in Hamburg, Germany, and I have worked on site for almost two years,

between 2003-2006, and undertaken regular 8-hour shifts at the experiment.

From January 2005 to June 2006 I was part of the team responsible for the

Third Level Trigger (TLT). My duties included maintaining the filter code, verifying

code updates submitted by various physics groups, and migrating the TLT online

histograms to a widely used website.

I became a member of the High Q2 physics group in 2005 and joined the group

of volunteers that monitored data quality histograms. From October 2005 to June

2006 I was the trigger representative for the High Q2 physics group. My duties

entailed implementing changes to the trigger slots maintained by our group and

viii

investigating problems raised by either my physics group or the trigger experts.

The analysis presented in this thesis began in January 2005 and is based on

electron-proton data recorded between 2005-2006. The NC analysis is important

for the ZEUS collaboration as a whole, as there are many events with which to

study the performance of the detector. I joined the luminosity working group in

2005 and presented evidence that the luminosity monitor was performing well. I

worked closely with other High Q2 members to devise a new method of correcting

the effect of hadronic particles scattering off detector components (the backsplash

effect).

The NC DIS analysis is a springboard for other analyses such as the QCD fits

which provide parton density functions. I provided the QCD fitters at ZEUS with

the latest NC DIS cross sections and uncertainties. I was also part of the ZEUS

and H1 working group that combined results between the two collider experiments

at HERA for the best statistical impact. I contributed to the first ever public

ZEUS and H1 combined result of the structure function xF γZ3 and the polarisation

asymmetry A±, both presented at the 33rd International Conference on High Energy

Physics.

The main result of my thesis is the first observation of parity violation in NC e−p

DIS at distances down to 10−18 m through a measurement of the polarisation asym-

metry A−, and also the most precise measurement of the structure functions xF3

ix

and xF γZ3 , which are sensitive to the proton valence quark momentum distribution.

I have presented my work on behalf of the ZEUS collaboration at the 14th

International Workshop on Deep Inelastic Scattering (DIS 2006) in Japan and the

conference Rencontres de Moriond: QCD and Hadronic Interactions (Moriond QCD

2007) in Italy. I also submitted a contribution to the proceedings of the 33rd

International Conference on High Energy Physics (ICHEP 2006) in Russia. After

close collaboration between myself, Yongdok Ri, Kunihiro Nagano, and Sampa

Bhadra, a paper based on the HERA II NC e−p DIS analysis has been submitted

to the management at ZEUS for review.

x

Contents

Abstract iv

Acknowledgements vi

Contributions to the ZEUS experiment viii

Table of Contents xi

List of Tables xvii

List of Figures xxii

1 Introduction 1

2 Theory 5

2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

xi

2.2 The structure of the proton . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Quark-parton model . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Quantum chromodynamics . . . . . . . . . . . . . . . . . . . 15

2.2.3 QCD improved parton model . . . . . . . . . . . . . . . . . 17

2.2.4 Parton Density Functions . . . . . . . . . . . . . . . . . . . 19

2.3 The electromagnetic and weak interactions . . . . . . . . . . . . . . 22

2.4 The neutral current cross section . . . . . . . . . . . . . . . . . . . 27

3 HERA and the ZEUS detector 36

3.1 HERA collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.1 Proton and electron beams . . . . . . . . . . . . . . . . . . . 40

3.1.2 Spin rotators and polarimetry . . . . . . . . . . . . . . . . . 41

3.2 ZEUS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 Uranium Calorimeter . . . . . . . . . . . . . . . . . . . . . . 45

3.2.2 Central Tracking Detector . . . . . . . . . . . . . . . . . . . 48

3.2.3 Luminosity detector . . . . . . . . . . . . . . . . . . . . . . 50

3.2.4 Background rejection . . . . . . . . . . . . . . . . . . . . . . 50

3.2.5 Trigger and data acquisition . . . . . . . . . . . . . . . . . . 51

4 Monte Carlo Simulation 55

4.1 DIS Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xii

4.2 Photoproduction Monte Carlo . . . . . . . . . . . . . . . . . . . . . 58

4.3 Detector simulation and software environment . . . . . . . . . . . . 60

4.4 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Reconstruction of Kinematic Variables 65

5.1 Electron reconstruction method . . . . . . . . . . . . . . . . . . . . 70

5.2 Jacquet-Blondel reconstruction method . . . . . . . . . . . . . . . . 71

5.3 Double Angle reconstruction method . . . . . . . . . . . . . . . . . 71

5.4 Bias and resolutions of reconstruction methods . . . . . . . . . . . . 72

6 Event Reconstruction 77

6.1 Track and vertex reconstruction . . . . . . . . . . . . . . . . . . . . 77

6.2 Longitudinal vertex reweighting . . . . . . . . . . . . . . . . . . . . 78

6.3 Electron identification . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.4 Electron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4.1 RCAL electron energy . . . . . . . . . . . . . . . . . . . . . 82

6.4.2 BCAL electron energy . . . . . . . . . . . . . . . . . . . . . 83

6.4.3 FCAL electron energy . . . . . . . . . . . . . . . . . . . . . 84

6.5 Calorimeter alignment . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.6 Hadronic final state reconstruction . . . . . . . . . . . . . . . . . . 85

6.6.1 Hadronic energy scale . . . . . . . . . . . . . . . . . . . . . 86

xiii

6.6.2 Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 88

6.6.3 Investigation into the hadronic angle . . . . . . . . . . . . . 89

7 Backsplash in the Hadronic Final State 93

7.1 Updating the backsplash correction . . . . . . . . . . . . . . . . . . 95

7.2 New jet-based approach . . . . . . . . . . . . . . . . . . . . . . . . 96

7.3 Results using new jet-based approach . . . . . . . . . . . . . . . . . 100

8 Event Selection 109

8.1 Event characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.2 Background characteristics . . . . . . . . . . . . . . . . . . . . . . . 115

8.2.1 Photoproduction . . . . . . . . . . . . . . . . . . . . . . . . 115

8.2.2 Beam-gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.2.3 Halo and cosmic muons . . . . . . . . . . . . . . . . . . . . . 116

8.2.4 Elastic QED Compton . . . . . . . . . . . . . . . . . . . . . 117

8.3 Data preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.3.1 First Level Trigger . . . . . . . . . . . . . . . . . . . . . . . 118

8.3.2 Second Level Trigger . . . . . . . . . . . . . . . . . . . . . . 119

8.3.3 Third Level Trigger . . . . . . . . . . . . . . . . . . . . . . . 120

8.3.4 Data quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

8.4 Data sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

xiv

8.5 Offline event selection . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9 Cross section extraction and uncertainties 131

9.1 Cross section calculation and bin selection . . . . . . . . . . . . . . 131

9.2 Statistical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 137

9.3 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 139

9.3.1 Background rejection . . . . . . . . . . . . . . . . . . . . . . 140

9.3.2 Electron purity and hadronic final state . . . . . . . . . . . . 141

9.3.3 Calorimeter energy and alignment . . . . . . . . . . . . . . . 143

10 Results and discussion 150

10.1 Single-differential cross sections . . . . . . . . . . . . . . . . . . . . 150

10.2 Reduced cross sections . . . . . . . . . . . . . . . . . . . . . . . . . 161

10.3 The structure functions xF3 and xF γZ3 . . . . . . . . . . . . . . . . 166

11 Summary and outlook 172

A Acronyms 176

B Trigger slots 178

B.1 First Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

B.2 Second Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 181

xv

C Comparisons between electron finders 183

D Extracting cross sections using the Electron method 186

E Tables of Results 190

Bibliography 224

xvi

List of Tables

2.1 The fundamental fermions of the Standard Model . . . . . . . . . . 6

2.2 The force carriers of the SM . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Definition of DIS kinematic variables . . . . . . . . . . . . . . . . . 10

2.4 The charge and third component of the weak isospin for the charged

leptons and quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Monte Carlo samples used to simulate NC e−p DIS data at Q2 >

185 GeV2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

8.1 Distribution of selected events in the calorimeter . . . . . . . . . . . 111

8.2 The integrated luminosity and polarisation of the data analysed . . 122

10.1 A χ2 test of the ratio of the polarised dσ/dx and dσ/dy cross sections

for Q2 > 185 GeV2 and Q2 > 3000 GeV2 . . . . . . . . . . . . . . . . 161

xvii

E.1 The single differential cross section dσ/dx for Q2 > 185 GeV2 mea-

sured using the combined 05-06 e−p data set (L = 177.2 pb−1, Pe =

−0.04) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191


sured using the negatively polarised 05-06 e−p data set (L = 105.4 pb−1, Pe =

−0.27) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192


sured using the positively polarised 05-06 e−p data set (L = 71.8 pb−1, Pe =

+0.30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193



−0.04) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194



−0.27) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195



+0.30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

xviii

E.7 The single differential cross section dσ/dy for Q2 > 185 GeV2 mea-


−0.04) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197



−0.27) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198



+0.30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199



−0.04) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200



−0.27) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201



+0.30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

xix

E.13 The single differential cross section dσ/dQ2 measured using the com-

bined 05-06 e−p data set (L = 177.2 pb−1, Pe = −0.04). This table

is continued in Table E.14. . . . . . . . . . . . . . . . . . . . . . . . 203

E.14 Continuation of Table E.13. . . . . . . . . . . . . . . . . . . . . . . 204

E.15 The single differential cross section dσ/dQ2 measured using the neg-

atively polarised 05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27).

This table is continued in Table E.16. . . . . . . . . . . . . . . . . . 205


E.17 The single differential cross section dσ/dQ2 measured using the pos-

itively polarised 05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30).

This table is continued in Table E.18. . . . . . . . . . . . . . . . . . 207


E.19 The polarisation asymmetry measured using negatively and posi-

tively polarised 05-06 e−p data (L = 105.4 pb−1, Pe = −0.27 and

L = 71.8 pb−1, Pe = +0.30 respectively) . . . . . . . . . . . . . . . . 209

E.20 The reduced cross section σ measured using the combined 05-06 e−p

data set (L = 177.2 pb−1, Pe corrected to zero). This table is contin-

ued in Tables E.21 -E.23. . . . . . . . . . . . . . . . . . . . . . . . . 210



xx


E.24 The reduced cross section σ measured using the negatively polarised

05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27). This table is

continued in Tables E.25 -E.27. . . . . . . . . . . . . . . . . . . . . 214




E.28 The reduced cross section σ measured using the positively polarised

05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30). This table is con-

tinued in Tables E.29 -E.31. . . . . . . . . . . . . . . . . . . . . . . 218




E.32 The structure function xF3 extracted using the combined 05-06 e−p

data set (L = 177.2 pb−1, Pe corrected to zero) and previously pub-

lished NC e+p DIS results (L = 63.2 pb−1, Pe = 0) . . . . . . . . . . 222

E.33 The interference structure function xF γZ3 at Q2 = 5000 GeV2 . . . . 223

xxi

List of Figures

2.1 Inelastic e − proton collision approximated as an incoherent sum of

e − parton scatters . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 The structure function νW2 determined at SLAC . . . . . . . . . . 13

2.3 The electromagnetic and strong coupling strengths . . . . . . . . . 16

2.4 Leading order QCD additions to the quark-parton model . . . . . . 17

2.5 The evolution of the proton structure with increasing resolution . . 18

2.6 A sketch of F2 versus x and F2 versus Q2 . . . . . . . . . . . . . . . 18

2.7 The structure function F ep2 as a function of Q2 at different values of x 19

2.8 The proton valence quarks, sea quarks, and gluon parton density

functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.9 The mixture of weak isospin and hypercharge carriers that forms the

observable photon and Z boson . . . . . . . . . . . . . . . . . . . . 25

2.10 Measurement of dσ/dQ2 versus Q2 in NC e±p scattering at HERA . 26

2.11 Feynman diagrams contributing to the Born-level NC cross section . 28

xxii

2.12 Contributions of the terms including F2, xF3 and FL to the reduced

cross section as predicted by the SM . . . . . . . . . . . . . . . . . 31

2.13 The σ(e−p) distribution versus Q2 at different polarisation values as

predicted by the SM . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.14 The σ(e±p) distributions versus Q2 as predicted by the SM . . . . . 34

2.15 The contribution of the xF γZ3 and xF Z

3 terms to structure function

xF3 versus x at fixed Q2 values as predicted by the SM . . . . . . . 35

3.1 A schematic view of the HERA collider and pre-accelerator rings . . 37

3.2 The integrated luminosity delivered by HERA, and the integrated

luminosity recorded by ZEUS during the HERA-II data taking period 39

3.3 Kinematic region accessible at ZEUS and other DIS experiments . . 40

3.4 A sketch of the HERA ring showing the spin rotators, polarimeters

and experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.5 Overview of the ZEUS detector cut along the beam-pipe . . . . . . 44

3.6 The ZEUS coordinate system . . . . . . . . . . . . . . . . . . . . . 45

3.7 The showering of different types of particles in the CAL . . . . . . . 46

3.8 Sketch of the CAL sections in the x − z plane . . . . . . . . . . . . 46

3.9 An octant of the CTD divided into superlayers. . . . . . . . . . . . 49

3.10 Sketch of the ZEUS trigger chain . . . . . . . . . . . . . . . . . . . 54

xxiii

4.1 Electroweak radiative corrections to the Born-level NC DIS process 56

4.2 The development of the hadronic final state in a DIS ep collision . . 57

4.3 Examples of the direct and resolved photoproduction processes . . . 59

4.4 The stages in a typical ZEUS analysis . . . . . . . . . . . . . . . . . 61

4.5 Reconstructed MC Q2 distribution before and after Q2 reweighting

and normalising to the integrated luminosity of the data . . . . . . 63

5.1 The ep NC DIS interaction in the QPM . . . . . . . . . . . . . . . . 66

5.2 The event topology of NC DIS events shown on the x−Q2 kinematic

plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3 Isolines of measured quantities shown on the x − Q2 kinematic plane 69

5.4 The resolution and bias when reconstructing Q2 using the Electron,

JB, and DA methods . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.5 The resolution and bias when reconstructing x using the Electron,

JB, and DA methods . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.6 The resolution and bias when reconstructing y using the Electron,

JB, and DA methods . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.1 The Gaussian fits applied to the ZV TX distribution. . . . . . . . . . 78

6.2 Electron energy distribution before and after corrections . . . . . . 81

6.3 RCAL electron energy scale . . . . . . . . . . . . . . . . . . . . . . 83

xxiv

6.4 Hadronic energy scale determined from pT,h/pT,DA versus γh and θe 87

6.5 Control plots (Data/MC) of variables related to the hadronic energy

after applying a MC hadronic energy scales . . . . . . . . . . . . . . 88

6.6 The prediction of γh using the Electron method . . . . . . . . . . . 91

6.7 The prediction of γh using jets . . . . . . . . . . . . . . . . . . . . . 92

7.1 Original approach (HERA I method) to identify a non-backsplash

control sample using MC events . . . . . . . . . . . . . . . . . . . . 94

7.2 Hadronic angle description due to the backsplash correction . . . . 95

7.3 New approach to identifying a non-backsplash control sample using

jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.4 Measuring γmax using the control sample . . . . . . . . . . . . . . . 99

7.5 The mean of Gaussian fits applied to γmax in bins of γh . . . . . . . 102

7.6 Distributions of γh using the original and new backsplash corrections 103

7.7 The bias ∆γh = γrec − γtrue versus ytrue in bins of x for the old and

new backsplash corrections and with no backsplash correction . . . 106

7.8 The resolution in ∆γh = γrec − γtrue versus ytrue in bins of x for the

old and new backsplash corrections and with no backsplash correction107

7.9 The γh distribution when using the backsplash correction only for

forward events such that γh < 90 . . . . . . . . . . . . . . . . . . . 108

7.10 Energy removed by backsplash cut in bins of γh . . . . . . . . . . . 108

xxv

8.1 Event display of a typical NC DIS event . . . . . . . . . . . . . . . 110

8.2 Data to MC comparison of variables used in the event selection . . 112

8.3 Data to MC comparison of variables used in the event selection and

the kinematic variables . . . . . . . . . . . . . . . . . . . . . . . . . 113

8.4 The integrated luminosity of the data used in the NC e−p DIS anal-

ysis as a function of electron longitudinal polarisation . . . . . . . . 122

8.5 The run-by-run event yield for the data used in the NC e−p DIS

analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

8.6 Data events displayed on the x − Q2 plane after the full NC DIS

selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

9.1 The generated kinematic variables for high x and high y MC events

compared with the measured MC events . . . . . . . . . . . . . . . 135

9.2 Efficiency, purity and acceptance in bins of dσ/dx, dσ/dy, and dσ/dQ2136

9.3 Efficiency and purity in the reduced cross section bins . . . . . . . . 137

9.4 Statistical error in the reduced cross section bins . . . . . . . . . . . 139

9.5 Systematic uncertainties in dσ/dQ2 . . . . . . . . . . . . . . . . . . 145

9.6 Systematic uncertainties in dσ/dx . . . . . . . . . . . . . . . . . . . 146

9.7 Systematic uncertainties in dσ/dy . . . . . . . . . . . . . . . . . . . 147

9.8 Individual systematic uncertainties in σ shown on the kinematic plane148

9.9 Individual systematic uncertainties in σ shown in terms of bin number149

xxvi

10.1 Measurements of dσ/dQ2, dσ/dx, and dσ/dy using the entire 2005-06

e−p data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

10.2 Data/SM for dσ/dQ2 . . . . . . . . . . . . . . . . . . . . . . . . . . 153

10.3 Data/SM for dσ/dx and dσ/dy . . . . . . . . . . . . . . . . . . . . 154

10.4 Measurement of dσ/dQ2 versus Q2 for positively and negatively lon-

gitudinally polarised electrons . . . . . . . . . . . . . . . . . . . . . 155

10.5 Measurement of the polarisation asymmetry (A−) versus Q2 . . . . 157

10.6 A χ2 test of the polarisation asymmetry measurement . . . . . . . . 158

10.7 Measurement of dσ/dx versus x for positively and negatively longi-

tudinally polarised electrons . . . . . . . . . . . . . . . . . . . . . . 159

10.8 Measurement of dσ/dy versus y for positively and negatively longi-

tudinally polarised electrons . . . . . . . . . . . . . . . . . . . . . . 160

10.9 Reduced cross sections versus x for positively and negatively po-

larised electrons in fixed bins of Q2 . . . . . . . . . . . . . . . . . . 163

10.10Reduced cross sections versus x for the total e−p data set compared

with previously measured e+p from 1999 . . . . . . . . . . . . . . . 164

10.11Data/SM for the reduced cross sections . . . . . . . . . . . . . . . . 165

10.12The structure function xF3 versus x in fixed bins of Q2 . . . . . . . 167

10.13Previous measurements of xF γZ3 (also known as xG3) made by the

ZEUS and BCDMS collaborations. . . . . . . . . . . . . . . . . . . 168

xxvii

10.14The interference structure function xF γZ3 versus x in fixed bins of Q2 169

10.15The interference structure function xF γZ3 versus x extrapolated to

Q2 = 5000 GeV2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

11.1 Fractional uncertainty of ZEUS-JETS PDFs and ZEUS-Pol PDFs . 174

11.2 Measurement of the polarisation asymmetry (A±) by the ZEUS and

H1 collaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

B.1 A sketch of the energy sums used at the CFLT . . . . . . . . . . . . 180

C.1 Data/MC distributions for certain variables involved in the event se-

lection of NC DIS events, compared between the EM and SINISTRA

electron finders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

C.2 Percentage amount of PHP events in the single differential cross sec-

tions and reduced cross section, compared between the EM and SIN-

ISTRA electron finders . . . . . . . . . . . . . . . . . . . . . . . . . 185

D.1 Data/SM for dσ/dQ2 reconstructed using the Electron method . . . 187

D.2 Data/SM for dσ/dx and dσ/dy reconstructed using the Electron

method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

D.3 Data/SM for reduced cross sections reconstructed using the Electron

method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

xxviii

1 Introduction

Leptons and quarks are the fundamental particles that are normally associated with

matter. However, only the leptons are seen bare, as the quarks are confined into

bound states called hadrons. The HERA1 accelerator collides electrons or positrons

with protons (collision denoted as ep) at a centre-of-mass energy of 318 GeV, pro-

viding high-momentum probes with a spatial resolution small enough to reveal the

quarks inside the proton. Such highly energetic interactions also allow the exchange

of the massive force carriers of the weak force. The behaviour of the weak inter-

action and the structure of the proton is being studied at HERA using the ZEUS

detector.

Interactions with a large momentum transfer squared (Q2) between the electron

and proton are studied in this thesis. The wavelength (λ) of the exchanged force

carrier, for example a photon, is related to the momentum transfer by λ ∝ 1/√

Q2.

Therefore, higher Q2 interactions probe the proton to a higher resolution, revealing

1The frequently used acronyms are listed in Appendix A.

1

the dynamic structure of the proton. This process is called deep inelastic scattering

(DIS), as the force carrier probes ‘deep’ inside the proton and the momentum

transfer is large enough to break the proton apart (an inelastic collision). The

DIS interaction can be studied in neutral current (NC) exchanges. Neutral current

interactions are mediated by electrically neutral particles, the photon (γ) and the

Z boson. The massless γ exchange dominates the low momentum transfer squared

region, where Q2 is much smaller than the mass of the Z boson squared (M2Z ∼

(91 GeV)2). The Z boson, which is one of the weak force carriers, contributes

significantly to the NC interaction probability at Q2 & M2Z .

The weak force does not conserve parity, which is the operation of reversing the

signs of the coordinate axes. This means that the weak force couples to a particle

with a different strength if the momentum of the particle is reversed (and the in-

trinsic spin direction of the particle remains the same). This relates directly to the

helicity of a particle, which is the projection of the particle’s spin onto its direction

of motion. This is particularly relevant, as HERA has delivered negatively and pos-

itively longitudinally polarised electron beams (electron spin aligned approximately

parallel to electron momentum) to ZEUS for the first time. The helicity dependence

of the NC e−p DIS cross section (related to the probability of two particles interact-

ing) becomes significant at high Q2, so the observation of interactions at the highest

accessible Q2 is important. The cross section asymmetry due to polarisation can

2

be measured from the single differential cross section dσ/dQ2 using negatively and

positively longitudinally polarised electron beams. Parity violation can be mea-

sured at extremely small distances due to the large centre-of-mass energy provided

by HERA, which leads to an accessible spatial resolution of λ ∝ 1/√

Q2 ∼ 10−18 m.

The weak force couples with a different strength in unpolarised e−p and e+p

collisions due to parity violation. This so-called charge asymmetry can be explored

by comparing NC e−p DIS cross sections with published ZEUS measurements of

e+p cross sections. The NC cross section contains proton structure functions which

parameterise the complicated make-up of the proton. The parity violating terms

due to charge asymmetry are absorbed into the structure function xF3. The struc-

ture function xF3 can be measured by taking the difference of the e−p and e+p

cross sections. The structure function xF3 contains terms for pure Z boson ex-

change (xF Z3 ) and γ − Z interference (xF γZ

3 ). The interference structure function

xF γZ3 can be calculated from xF3, and is proportional to the difference of quark and

anti-quark momentum densities inside the proton. By assuming the virtual quark

sea inside the proton provides as many quarks as anti-quarks, xF γZ3 gives the shape

and magnitude of the proton valence quark momentum distribution. The integral

of xF γZ3 can be compared to a sum rule related to the number of valence quarks

inside the proton.

The goal of this thesis is to use the ZEUS detector to measure parity violation

3

in NC e−p DIS for the first time at distances down to ∼ 10−18 m, and also to gain

information on the proton valence quark momentum distribution. This has been

achieved using the largest amount of e−p scattering data ever recorded at ZEUS.

The cross section measurements are the most precise to date and can be used to

test the Standard Model of particle physics.

This thesis is organised into 10 chapters. The theory relevant to this analysis is

outlined in Chapter 2. The HERA collider and the ZEUS detector are introduced

in Chapter 3. The simulation of NC ep DIS, the methods used to reconstruct

kinematic variables such as Q2, and the techniques used to reconstruct events from

detector signals are described in Chapters 4 − 7. The selection criteria used to

obtain a NC data sample is outlined in Chapter 8. The cross section binning and

the determination of uncertainties in the cross sections is discussed in Chapter 9.

The main results and conclusions are presented in Chapters 10 − 11.

4

2 Theory

The fundamental particles and forces that embody the Standard Model of particle

physics are introduced in this chapter. The role that particle colliders perform and

the importance of the cross section measurements that will be presented in this

thesis will also be discussed.

2.1 The Standard Model

The known fundamental particles and forces (except gravity) are described by the

Standard Model (SM), a framework of calculational rules that have been proven to

describe the quantum world to great accuracy. Elementary particles can be grouped

according to their intrinsic spin. Matter contains spin 1/2 particles called fermions

(half-integer spin particles). The particles that govern the electromagnetic, weak

and strong forces contain spin 1 and are called bosons (integer spin particles).

5

2.1.1 Matter

Matter Family 1 Family 2 Family 3 Qe Colour

Quarksup (u)

down (d)

charm (c)

strange (s)

top (t)

bottom (b)

+2/3

−1/3

r, g or b

Leptonse-neutrino (νe)

electron (e−)

µ-neut.(νµ)

muon (µ−)

τ -neut.(ντ )

tau (τ−)

0

−1

None

Table 2.1: The fundamental fermions of the Standard Model. The electric charge,

Qe, and colour charge for each particle is given.

The fermions that make up all known matter are given in Table (2.1). Each fermion

has a respective anti-particle partner (usually denoted by a bar above the symbol),

which has the same mass but opposite charge. The quarks differ from the leptons

as they contain colour charge, and are therefore subject to the strong force which

confines them into colour neutral bound states (hadrons). Three-quark colour neu-

tral states (baryons) can be formed by a r, g and b quark, and qq pairs (mesons)

are formed through colour combinations such as rr.

The first family in Table (2.1) contains the lightest2 particles (me ∼ 0.51 MeV,

mu = 1.5−3 MeV, md = 3−7 MeV [1]). Mass increases with family number, and the

top quark is the heaviest known particle (mt ∼ 174 GeV). Neutrinos are assumed

2The dimensions of mass can be written as GeV/c2, but as the convention ~ = c = 1 is usedit is customary to express mass, energy and momentum in units of GeV.

6

to be massless in the SM, though experiments have proved they have a very small

mass [1].

2.1.2 Forces

Force carriers Interaction Qe Mass ( GeV)

photon (γ) Electromagnetic 0 0

Z Weak 0 ∼ 91.2

W± Weak ± 1 ∼ 80.4

gluons (g) Strong 0 0

Table 2.2: The force carriers of the SM shown with their electric charge Qe and

mass [1].

The bosons that mediate the electromagnetic, weak and strong interactions are

given in Table (2.2). The photon mediates the electromagnetic force and interacts

with any electrically charged particle. The Z and W± bosons govern the weak

force and couple to all fermions. The direct electron-quark interaction is mediated

by the electrically neutral γ and Z bosons or the electrically charged W± bosons.

These interactions are grouped into neutral current (NC) or charged current (CC)

processes, depending on the electric charge of the boson. The framework governing

electromagnetic and weak interactions is unified under electroweak theory.

7

The gluons mediate the strong force and carry colour charge. They only couple

to other coloured particles, namely gluons and quarks. The theory of the strong

force is described by quantum chromodynamics (QCD).

2.2 The structure of the proton

A knowledge of the proton structure is needed to understand ep DIS. The first

successful model describing the proton structure was the quark-parton model, which

describes the proton as a collection of free point-like particles. This model was

improved by the introduction of QCD, which describes the confinement of quarks

inside the proton due to gluon exchange.

2.2.1 Quark-parton model

The quark-parton model (QPM) states that the nucleon is made up of free point-like

particles, referred to as partons. Therefore, the inelastic electron-proton collision

can be approximated as an incoherent sum of elastic electron-parton scatters. This

is illustrated in Fig. (2.1) using Feynman diagrams (a visual tool used to calcu-

late the cross section for a particular process). The inelastic cross section is then

constructed by combining the point-like elastic cross sections with proton struc-

ture functions which parameterise the dynamic proton composition, denoted by a

hashed circle in Fig. (2.1).

8

Kinematic variables used to characterise DIS are described in Table (2.3), and

are derived from the four-momenta denoted in Fig. (2.1). The most relevant kine-

matic variables for this thesis are Q2, which determines the spatial resolution of

the mediated force carrier, and x which is the fraction of the proton momentum

carried by the struck parton. Only these two variables are needed to characterise a

DIS event fully, as the kinematic variables are related by the centre-of-mass energy

squared provided by the collider, s = Q2/xy. The variable y is the fractional en-

ergy transferred by the electron in the proton’s rest frame, and is also related to the

electron scattering angle in the centre-of-mass frame (θ∗) via 1−y = (1+cos θ∗)/2.

γ(q) or Z(q)

proton (p)

e−(k) e−(k′)

=∑

i

[ γ(q) or Z(q)

partoni (xp)

proton (p)

e−(k) e−(k′)

]

Figure 2.1: The approximation of the NC inelastic e − proton collision (left) as an

incoherent sum of e − parton scatters (right). The four-momenta of the particles

are shown in brackets.

9

Kinematic variable Description

s = (k + p)2 ≈ 4EeEp Centre-of-mass energy (√

s), where Ee andEp

are the initial electron and proton energies.

Q2 = −q2 = −(k − k′)2 Resolving power of the exchanged boson,

0≤Q2≤s related to its wavelength by λ ∝ 1/Q.

x = Q2

2p·q Fraction of the proton momentum carried

0≤x≤1 by the struck parton.

y = p·qp·k = Q2

sxFractional energy transferred by the electron

0≤y≤1 in the rest frame of the proton.

Table 2.3: Definition of DIS kinematic variables using Fig. (2.1). Note that at the

HERA accelerator, Ee and Ep are fixed.

The probability of an interaction between particles is expressed through cross

sections. The general form of the ep DIS cross section is given by

dσ ∼ LeαβW αβ, (2.1)

where Leαβ and W αβ are the leptonic and hadronic tensors, respectively. If the low

Q2 region is considered (Q2 ≪ M2Z), such that the parity-violating weak force can

be ignored, the hadronic tensor can be written as [2]

W αβ = W1(q2, ν)(−gαβ +qαqβ

q2) +

W2(q2, ν)

M2(pα − p · q

q2qα)(pβ − p · q

q2qβ), (2.2)

10

where W1 and W2 are structure functions, gαβ is the metric tensor, p and q are

the four-momenta of the incoming proton and exchanged photon (as shown in

Fig. (2.1)), M is the proton mass, and ν = p · q/M .

The leptonic tensor can be written as

Leαβ = 2(k′

αkβ + k′βkα − k′ · kgαβ), (2.3)

where k and k′ are the four-momenta of the incoming and outgoing electron. By

contracting the leptonic and hadronic tensors in the laboratory frame one can write

the following [2]:

d2σ(ep → eX)

dΩdE ′ =4α2E ′2

Q4(2W1(Q2, ν) sin2 θ

2+ W2(Q

2, ν) cos2 θ

2), (2.4)

where ep → eX signifies the DIS process (the proton breaks up), E ′ is the energy

of the scattered electron, α is the QED coupling constant (giving the strength of

the electromagnetic force), dΩ is an element of solid angle and θ is the electron

scattering angle in the laboratory frame.

The foundation of the QPM is that the incoherent sum of elastic electron-parton

scattering can describe the inelastic electron-proton scattering process. Therefore,

to understand ep → eX scattering one can consider the point-like elastic scattering

cross section eµ → eµ [2]:

d2σ(eµ → eµ)

dΩdE ′ =4α2E ′2

Q4

(

cos2 θ

2+

Q2

2m2µ

sin2 θ

2

)

δ

(

ν − Q2

2mµ

)

, (2.5)

11

where mµ is the mass of the muon. By comparing Eqns. (2.4) and (2.5), the

structure functions can be expressed as

2mW1(ν, Q2) =

Q2

2mνδ

(

1 − Q2

2mν

)

, νW2(ν, Q2) = δ

(

1 − Q2

2mν

)

, (2.6)

where m is the parton mass. This signifies that the structure functions do not

depend on Q2 or ν separately but rather on a dimensionless quantity Q2

2mν. In this

case the following substitutions can be made [2]:

MW1(ν, Q2) → F1(x), (2.7)

νW2(ν, Q2) → F2(x), (2.8)

where x = Q2/2Mν is the fraction of the proton’s momentum as described in

Table (2.3). This agrees with the measurements of νW2 from ep DIS experiments

at the Stanford Linear Accelerator (SLAC) published in 1972 [3], shown in Fig. (2.2)

at a fixed value of x = 0.25 versus Q2. The SLAC measurements showed that in a

limited region in x, the structure functions do not depend on Q2. This means that

an increase in the spatial resolution of the photon (or in other words hitting the

objects harder) does not reveal further structure inside the proton, as the probe is

effectively interacting with free point-like partons. This phenomenon is known as

scaling.

12

Figure 2.2: The structure function νW2 determined by ep DIS at SLAC [4]. The

icons represent separate electron scattering angles. The structure function is seen

to be independent of the momentum transfer squared (q2 = Q2 in this plot) within

errors for x = 1ω

= 0.25.

The structure functions contain the sum of the momenta of the partons inside

the proton:

F2(x) =∑

i

e2i xfi(x), (2.9)

F1 =1

2xF2(x), (2.10)

where ei is the electric charge of parton i, and fi(x)dx is the probability of finding

a parton with proton momentum fraction x → x + dx, the so-called parton density

function (PDF). All the momentum fractions add up to unity:

∑

i

∫ 1

0

xfi(x)dx = 1, (2.11)

13

where the sum runs over all the partons, including the electrically neutral ones

which do not interact with the photon.

If the partons are assumed to be quarks, the proton can be considered as three

valence quarks (uud) and a sea of virtual qq pairs. The valence quarks provide

the proton with quantum numbers and the sea quarks (u, u, d, d, s, s, etc.) provide

higher mass quarks and anti-quarks. If the contribution to the proton content from

the heaviest quarks is neglected, the proton structure function F ep2 can be written

explicitly in terms of the three lightest quarks (u, d and s):

F ep2 (x) =

(

2

3

)2

x[u(x) + u(x)] +

(

−1

3

)2

x[d(x) + d(x) + s(x) + s(x)]. (2.12)

Each sea quark can be assigned a momentum probability distribution S(x) such

that F ep2 (x) can be expressed as

F ep2 (x) =

4

9xuv(x) +

1

9xdv(x) +

4

3xS(x), (2.13)

where uv and dv are the probability distributions of the proton valence quarks.

Measurements of F ep2 and F en

2 [2] showed that the quarks and anti-quarks con-

tributed to approximately half of the momentum of the nucleons. The other half

of the momentum of the nucleon is attributed to electrically neutral partons that

do not interact with the photon. These partons, unaccounted for by the QPM, are

called gluons, the force carriers of the strong force which is described by quantum

chromodynamics.

14

2.2.2 Quantum chromodynamics

Quantum chromodynamics (QCD) describes the strong interaction between quarks

and gluons. The charge of QCD is colour (r, g, b, r, g and b) and the strong force is

mediated through the exchange of massless, coloured gluons. The gluons can cou-

ple to themselves, which leads to the strong force behaving very differently to the

electromagnetic force as shown in Fig. (2.3). The strong coupling constant (αs),

which determines the strength of the strong interaction, increases as a coloured

charge moves further from another coloured charge. This phenomenon is known as

confinement, and is in stark contrast to the quantum electrodynamic (QED) cou-

pling constant (α), which tends to the asymptotic limit of 1/137 at large distances.

As more work is put into separating quarks, the energy contained in the strong field

becomes large enough to promote a quark-antiquark pair from the vacuum sea into

reality. This effectively lowers the potential energy of the system and acts to bind

quarks into neutral colour states (for example, rr or rbg). The proton is broken up

in ep DIS, but the quarks inside the proton cannot emerge as free particles. The

bare quarks fragment into ‘jets’ of colourless bound states (such as mesons), which

are collimated along the direction of the original partons.

Figure (2.3) shows that at small distances (high energies), αs becomes small.

High energy interactions take place in a shorter time scale than the inter-quark

15

interactions, such that the quarks can be considered as free particles. This is

known as asymptotic freedom. A factor√

αs is attached to each QCD vertex in

a Feynman diagram, as shown in Fig. (2.3), such that additional gluon or quark

vertices add extra orders of αs to the cross section calculation. The smallness of αs

at high energies allows perturbative techniques to be used effectively in QCD. The

leading order (LO) QCD additions to the QPM are shown in Fig. (2.4).

e

e

γ√

α q

q

g√

αs

Stro

ng c

oupl

ing

stre

ngth

Distance from charge

Confinement barrier

Ele

ctro

mag

netic

cou

plin

g st

reng

th

Distance from charge

α ≈ 1/137 Proton radius ∼ 1 fmαs ≈ 0.12

αs ≈ 1

0.002 fm (Q2 ∼ M 2Z)

Figure 2.3: The top diagrams show the coupling constants attached to QED and

QCD vertices due to photon and gluon emission. The bottom diagrams show the

change in coupling strength with distance.

16

proton

ee

(c)(b)(a)√

αs√

αs

√α

√α

√α

√α

√α

√α

Figure 2.4: The QPM (a) and leading order QCD additions (b,c). The QED and

QCD coupling constants α and αs are shown.

2.2.3 QCD improved parton model

Quantum chromodynamics describes the gluons that the QPM could not account

for, and in turn predicts that the structure functions depend on Q2. As the proton is

probed to higher energies, the resolution of the exchanged boson becomes sensitive

to quarks emitting gluons and the splitting of gluons into qq pairs, as illustrated in

Fig. (2.5).

The structure function F2 is proportional to the sum of the quark and anti-

quark densities. Therefore, F2 increases with Q2 at low x as more qq pairs are seen,

and decreases with Q2 at high x as high momentum quarks are less likely to be

observed due to gluon emission. This phenomenon is known as scaling violation

and is illustrated in Fig. (2.6). The scaling effect seen by previous DIS experiments,

shown in Fig. (2.2), was due to the limited x and Q2 range of the measurement

(x = 0.25 and 1 GeV2 < Q2 < 8 GeV2). Measurements at HERA of F2 versus Q2

17

at fixed x values are shown in Fig. (2.7). The increase and decrease of F2 with Q2

in the approximate region of x < 0.1 and x > 0.1 overwhelmingly confirms scaling

violation. The theoretical predictions of QCD are able to describe the measurements

of F2 over four orders of magnitude in Q2 and over three orders of magnitude in x.

Proton

Proton

Proton

(a)

(b)

(c)

Three valence quarks

Bound quarks

Qua

rk d

ensi

ty

x

Qua

rk d

ensi

ty

xsea

valence

Bound quarks + splittingwavelength A

wavelength B

1/3

Qua

rk d

ensi

ty

x

Figure 2.5: The evolution of the proton structure with increasing resolution from

(a) to (c). Note that in picture (c), a higher Q2 probe (wavelength B) is required

to see the low x behaviour of a gluon splitting into quarks.

high Q2

low Q2

Q2

low x

high x

scaling violation

scaling violation

scaling

F2 F2

x ∼ 0.1

x

Figure 2.6: A sketch of F2 versus x (left) and F2 versus Q2 (right).

18

HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log

10(x

)

Q2(GeV2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5 x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

Figure 2.7: The structure function F ep2 as a function of Q2 at different values of

x as measured at HERA (ZEUS and H1) and fixed target experiments [5]. The

theoretical predictions from QCD as calculated from ZEUS and H1 PDF fits are

shown as lines.

2.2.4 Parton Density Functions

Quantum chromodynamics describes the Q2 evolution of the PDFs, but the x de-

pendence of the PDFs must come from experiments as perturbative QCD cannot

19

be solved at long distances (∼ 1 fm) where αs becomes large. Experimental data

can be fitted at certain initial Q2 values to obtain the proton PDF, which then can

be evolved to other values of Q2 using the DGLAP equations [6–8].

The PDFs used in this thesis are those produced by the ZEUS collaboration

(ZEUS-JETS [9]) and the CTEQ theory group [10]. The ZEUS-JETS PDFs for the

valence quarks, quark sea, and gluons are parameterised at Q20 = 7 GeV2 using the

following functional form:

xf(x) = p1xp2(1 − x)p3(1 + p4x), (2.14)

where p1,2,3,4 are fit parameters constrained by factors such as momentum sum rules

(for example, Eqn. (2.11)). The ZEUS-JETS fit relies entirely on ZEUS measure-

ments of structure functions and jet production. Neutral current measurements

at low x (x . 0.01) provide information on the sea and gluon distributions, while

sensitivity to the valence quarks are provided by high Q2 (Q2 & 200 GeV2) NC and

CC data. Jet production rates are used to gain information on the gluon, as the

rate of jet production depends directly on the gluon PDF through diagrams such

as Fig. (2.4b). The CTEQ PDFs are generally parameterised in the same form

as Eqn. (2.14) and use data from many different experiments. The measurements

include fixed target data (muon and neutrino scattering off a fixed nuclear target)

to gain information on the valence quarks and jet cross sections from pp collisions

to gain information on gluon densities.

20

The advantage of using only ZEUS data for the ZEUS-JETS PDF is that there

is generally a better understanding of the experimental systematic uncertainties as

only one experiment is considered. However, this also limits the statistical precision

of the data. The ZEUS-JETS PDFs for the valence quarks, sea quarks and gluons

are shown in Fig. (2.8). The PDFs show that the valence quarks are populated in

the high-x region and the uv density is twice as large as the dv density because the

proton is a uud bound state. Note the similarities between the PDFs and the quark

density shown in Fig. (2.5c), as the gluons and sea quarks dominate the low x region

(the gluon and sea quark PDFs are scaled by a factor of 0.05 in Fig. (2.8)). The

PDF uncertainties stem from model and experimental uncertainties. The inclusion

of cross section measurements presented in this thesis will impact the valence quark

PDF uncertainties by improving the statistical precision of the data set. The con-

straint of the proton PDF uncertainties is of great importance, especially for the

Large Hadron Collider (LHC), which is planning to deliver proton-proton collisions

at a centre-of-mass energy of 14 TeV in 2008.

21

0

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

ZEUS-JETS fit)=0.11802

Z(Msα tot. uncert.

ZEUS-O fit

ZEUS-S fit

CTEQ6M MRST2001

x

xf

ZEUS

2 = 10 GeV2Q

vxu

vxd

0.05)×xS (

0.05)×xg (

0

0.2

0.4

0.6

0.8

1

Figure 2.8: The proton valence quarks (uv, dv), sea quarks (S), and gluon (g) PDFs

from the ZEUS-JETS fit and other QCD fits [9]. The gluon and sea quark PDFs

are scaled by a factor of 0.05.

2.3 The electromagnetic and weak interactions

The weak force ignores electric and colour charge, but prefers left-handed (LH) par-

ticles and right-handed (RH) anti-particles, in stark contrast to the electromagnetic

and strong force which both ignore handedness. The handedness of a particle is re-

lated to its helicity, which is the component of the spin of a particle projected along

22

its direction of motion. If the spin vector is aligned with or against the direction

of motion, the particle is called right-handed or left-handed, respectively. There-

fore, the weak interaction does not remain invariant under parity transformations

(reversing the signs of the coordinate axes).

The electroweak model groups the electron-type leptons, for example, into two

sets [11]:

le =

νe

e−

L

, e−R. (2.15)

As the neutrino is assumed to be massless in the SM, it is predicted to be only

left-handed. A quantum number known as weak isospin (T ) is introduced, such

that it is conserved in the left-handed and right-handed groups. The neutrino is

electrically neutral but the electron is charged, therefore a further quantum number

called hypercharge (Y ) is introduced such that the electric charge difference can

stem from weak isospin values. The electric charge for a fermion f is defined by

ef = e(T 3f + Yf/2), (2.16)

where e is the positron charge, and T 3 is the third component of the weak isospin.

The values of T 3 and the electric charge for the charged leptons and quarks are

shown in Table (2.3).

23

Leptons ee T 3e Quarks eq T 3

q

e−L -1 -1/2 uL 2/3 1/2

e−R -1 0 uR 2/3 0

e+L 1 1/2 dL -1/3 -1/2

e+R 1 0 dR -1/3 0

Table 2.4: The charge and third component of the weak isospin for the charged

leptons and quarks.

The electroweak model demands that the form of the interaction between fields

is invariant under weak isospin and hypercharge changes. To maintain invariance

under local isospin and hypercharge transformations the W 0 and B0 gauge particles

are introduced (but not observed in nature) [11]. Electric charge is defined in

Eqn. (2.16) as a mixture of weak isospin and weak hypercharge, so the photon is

in fact a mixture of W 0 and B0 particles. The W 0 and B0 wavefunctions also mix

to produce the Z boson. The mixture is governed by the weak-mixing angle θW as

illustrated in Fig. (2.9).

24

θW

B0

θW γ

W 0

cos θW = MW/MZ

Z

Figure 2.9: The weak isospin and hypercharge carriers mix to form the observable

photon and Z boson. MW and MZ are the masses of the W and Z bosons.

Coupling terms related to the Z boson interaction with LH and RH fermions

are expressed through axial-vector (af) and vector (vf ) couplings [12]:

af = T 3f , vf = T 3

f − 2ef sin2 θW . (2.17)

The coupling terms are combined with PDFs to form the proton structure functions,

which are discussed further in Section 2.4.

Figure (2.10) shows the single-differential cross section dσ/dQ2 versus Q2 in NC

e±p DIS measured at HERA by the ZEUS and H1 collaborations (using data taken

between 1994 and 2000). Note that the measured cross sections cover more than

two orders of magnitude in Q2 and fall by six orders of magnitude with increas-

ing Q2. The low Q2 region (Q2 . 1000 GeV2) is dominated by photon exchange,

and the effects of Z exchange are noticeable at higher Q2. The difference between

e−p and e+p cross sections is due to the parity violating weak interaction, which

25

distinguishes between matter and anti-matter as a result of helicity effects. Also,

helicity conservation imposes an isotropic scattering angle for eLqL and eRqR inter-

actions in the eq centre-of-mass frame. However, a suppression factor proportional

to (1 + cos θ∗)2 ∝ (1 − y)2, where θ∗ is the electron scattering angle in the centre-

of-mass frame, is imposed for eLqR and eRqL processes [13].

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

103

104

HERA Neutral Current

H1 e+p 94-00

ZEUS (prel.) e+p 99-00

SM e+p (CTEQ6D)

H1 e-p

ZEUS e-p 98-99

SM e-p (CTEQ6D)

y < 0.9

Q2 (GeV2)

dσ/

dQ

2 (p

b/G

eV2 )

Figure 2.10: Measurement of dσ/dQ2 versus Q2 in NC e±p scattering at HERA

by the ZEUS and H1 collaborations. The blue (red) icons represent measurements

with e+p (e−p) collisions. The e−p cross sections will be updated in this thesis

using data from 2005-06. The curves represent SM predictions using CTEQ PDFs.

26

2.4 The neutral current cross section

The lowest electroweak order (Born-level) double differential cross section for DIS

polarised lepton scattering with an unpolarised proton can be represented as [14]

d2σ(e±p)

dxdQ2= σγ + σ±

γZ(λ) + σ±Z (λ), (2.18)

where λ is the helicity of the lepton (λ = +1 for a RH particle and λ = −1 for

a LH particle) and σγ , σγZ and σZ are cross sections for photon exchange, γ − Z

interference, and Z boson exchange, respectively. To calculate the theoretical cross

section of a particular event, one specifies the initial and final states, and selects

all the Feynman diagrams to connect them. The Born-level diagrams for the eq

process are shown in Fig. (2.11). The mathematical expression for each diagram is

calculated by multiplying the wavefunctions of each quanta to give the amplitude

for the sub-process. The sub-processes are added to give the total amplitude, which

is squared to give the probability of the interaction occurring. The γ−Z interference

interaction can be understood from this procedure, outlined in Fig. (2.11).

27

NC cross section ∝γ

q

e−

q

e−

eq

ee

+(ve, ae)

(vq, aq)

Z

q

e−

q

e−

2

Figure 2.11: Feynman diagrams contributing to the Born-level NC cross section.

The coupling constants e, v, and a refer to the electric charge, vector coupling, and

axial-vector coupling, respectively.

The cross section can be written explicitly in terms of the structure functions

F2, xF3 , and FL = F2 − 2xF1 [15]:

d2σ(e±p)

dxdQ2=

2πα2

xQ4[Y+F2(x, Q2) ∓ Y−xF3(x, Q2) − y2FL(x, Q2)], (2.19)

where α is the QED coupling constant and Y± ≡ 1 ± (1 − y)2.

The xF3 structure function contains terms only relating to Z exchange and

γ−Z interference and describes the parity violating part of the cross section due to

charge asymmetry. The difference between e+p and e−p unpolarised cross sections

is totally contained within xF3. This is reflected by the ∓ sign attached to the xF3

term in Eqn. (2.19), which depends on the charge of the lepton. The xF3 structure

function is proportional to the difference of quarks and anti-quarks in the proton.

By assuming that the quark and the anti-quark densities from the sea quarks cancel

(a LO QCD assumption), the xF3 structure function is proportional to the valence

28

quark momentum density.

The FL structure function is related to the absorption cross section of longitudi-

nally polarised photons. In the QPM, FL = F2−2xF1 = 0 (as shown in Eqn. (2.10))

as fermions cannot absorb longitudinally polarised photons without violating he-

licity conservation. However, QCD allows the interaction through gluon emission.

Therefore, FL describes the gluon distribution inside the proton.

The F2 structure function contains terms related to γ, γ − Z, and Z exchange,

and dominates the cross section at low Q2 due to the photon being massless. The

structure function F2 is proportional to the sum of the quark and the anti-quark

PDFs.

The structure functions are written in terms of contributions from γ and Z

exchange and γ − Z interference at LO QCD as [14]

[

F γ2 , F γZ

2 , F Z2

]

= x∑

q

[e2q , 2eqvq, v

2q + a2

q ](q(x, Q2) + q(x, Q2)), (2.20)

[

xF γZ3 , xF Z

3

]

= 2x∑

q

[eqaq, vqaq](q(x, Q2) − q(x, Q2)) ∝ qvalence, (2.21)

FL(x, Q2) ∝ g(x, Q2), (2.22)

where vq and aq are the vector and axial-vector couplings of a quark flavour q, and

eq is the quark’s electric charge and g(x, Q2) is the gluon density.

The double differential cross section can be divided by kinematic terms to define

29

the reduced cross section

σe±p =xQ4

2πα2

1

Y+

d2σ(e±p)

dxdQ2= F2(x, Q2) ∓ Y−

Y+

xF3(x, Q2) − y2

Y+

FL(x, Q2), (2.23)

where the structure functions F2 and xF3 are described in more detail in Eqns. (2.24

- 2.25). Figure (2.12) shows the theoretical prediction of σe−p and the magnitude

of each term on the right-hand side of Eqn. (2.23). Note that the term y2

Y+FL

contributes less than one percent to the reduced cross section in the Q2 and x

region considered.

The structure functions F2 and xF3 depend on the lepton charge, the lepton

beam longitudinal polarisation (Pe), the mass of the Z and W bosons (MZ and

MW ), and the weak-mixing angle (θW ), to give the following [14]:

F±2 = F γ

2 + k(−ve ∓ Peae)FγZ2 + k2(v2

e + a2e ± 2Peveae)F

Z2 , (2.24)

xF±3 = k(−ae ∓ Peve)xF γZ

3 + k2(2veae ± Pe(v2e + a2

e))xF Z3 , (2.25)

where the structure functions for γ, γ−Z and Z exchange are detailed in Eqns. (2.20

- 2.21) and k = 1

4 sin2 θW cos2 θW

Q2

Q2+M2Z

is proportional to the ratio of the Z and photon

propagators (expressions used to describe the propagation of virtual particles). The

SM values of the vector and axial-vector coupling of the electron to the Z boson are

ve = −1/2 + 2 sin2 θW and ae = −1/2. The longitudinal polarisation of the electron

beam (Pe) is defined using the number of left-handed (NL) and right-handed (NR)

30

electrons in the beam, and can be written as

Pe =NR − NL

NR + NL. (2.26)

Note that Pe = +1 for a RH beam, and Pe = −1 for a LH beam. The dependence of

σ(e−p) with Pe is presented in Fig. (2.13), showing that the cross section increases

(decreases) with negatively (positively) longitudinally polarised electrons due to the

parity violating weak interaction.

)2 (GeV2Q310 410

Arb

. un

its

-0.10

0.10.20.30.40.50.60.7

x = 0.25; SM, ZEUS-JETS PDF

red. cross section (e-p)

2F

3) xF+ / Y

-(Y

L) F+ / Y2-(y

Figure 2.12: Contributions of the terms including F2, xF3 and FL to the reduced

cross section as predicted by the SM using ZEUS-JETS PDFs at x = 0.25.

31

)2 (GeV2Q310 410

0.20.25

0.30.350.4

0.450.5

0.550.6

0.65 x = 0.25; SM, ZEUS-JETS PDF

Unpol. red. cross section (e-p)

Pol. = -100%

Pol. = -30%

Pol. = +30%

Pol. = +100%

~ σ

Figure 2.13: The σ(e−p) distribution versus Q2 at different polarisation values as

predicted by the SM at x = 0.25.

Parity violation due to the polarisation of the electron beam can be directly

measured using the charge dependent polarisation asymmetry, defined by [16]

A± =2

P+ − P−

σ±(P+) − σ±(P−)

σ±(P+) + σ±(P−), (2.27)

where P+ and P− are the values of the positive and negative electron polarisations,

and σ±(P ) is the cross section measured at a particular polarisation for e±p colli-

sions. The polarisation asymmetry is a direct measure for electroweak effects as it

is approximately equal to the structure function ratio

A± ≈ ∓kaeF γZ

2

F γ2

, (2.28)

32

which is proportional to coupling combinations aevq. The weak force contributes

a greater effect to the NC cross section at high Q2, so the polarisation asymmetry

will grow in magnitude with Q2. The measurement of the polarisation asymmetry

in e−p scattering (A−) is one of the goals of this thesis.

The other major goal for this thesis is to extract the structure function xF3

from the e±p unpolarised reduced cross sections (using Eqn. (2.23)):

xF3(x, Q2) =Y+

2Y−(σe−p − σe+p). (2.29)

The difference between the e±p reduced cross sections grows with Q2 as shown in

Fig. (2.14). This highlights the motivation to measure events at high Q2 to be

sensitive to the xF3 contribution to the cross section. The structure function xF3

can be written as

xF3 = −aekxF γZ3 + 2veaek

2xF Z3 , (2.30)

using Eqn. (2.25) and Pe = 0. The theoretical prediction of xF3 versus x at fixed

Q2 values and the magnitude of the terms on the right of Eqn. (2.30) is plotted in

Fig. (2.15), clearly showing that the xF γZ3 term dominates xF3. By inserting the

charge and axial-vector coupling into Eqn. (2.21), one can write the interference

structure function as

xF γZ3 =

x

3(2uv + dv + 2∆u + ∆d), (2.31)

where ∆u = (usea − u + c − c) and ∆d = (dsea − d + s − s). The ∆ terms can be

33

neglected in LO QCD to provide the following sum rule [17]:

∫ 1

0

xF γZ3

dx

x=

1

3

∫ 1

0

(2uv + dv) =5

3, (2.32)

where the QCD radiative corrections are ∼ −5% [17]. Therefore, the structure

function xF γZ3 is determined directly from the valence quark distribution.

The theoretical predictions of parity violation and the structure of the proton

have been discussed in this chapter. The following chapters now deal with the

exciting prospect of using the wealth of experimental data from ZEUS to confront

the SM predictions.

)2 (GeV2Q310 410

0

0.1

0.2

0.3

0.4

0.5

0.6 x = 0.25; SM, ZEUS-JETS PDF

red. cross section (e-p)

red. cross section (e+p)

~ σ

Figure 2.14: The σ(e±p) distributions versus Q2 as predicted by the SM at x = 0.25.

The difference between σ(e±p) is contained in the structure function xF3.

34

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.010.020.03

0.040.050.06

2 = 1500 GeV2Q3xF

3 Zγ

k xFe-a

3Z xF2 ke ae2v

SM, ZEUS-JETS PDF

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.010.020.03

0.040.050.06

x0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.020.040.060.08

0.10.120.140.160.18

0.2

2 = 30000 GeV2Q3xF

3 Zγ

k xFe-a

3Z xF2 ke ae2v

SM, ZEUS-JETS PDF

x0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.020.040.060.08

0.10.120.140.160.18

0.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.0002

0.0004

0.0006

0.0008

0.001

2 = 1500 GeV2Q

3Z xF2 ke ae2v

Zoomed plot

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.0002

0.0004

0.0006

0.0008

0.001

x0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.0010.0020.0030.0040.0050.0060.0070.0080.009

0.01

2 = 30000 GeV2Q

3Z xF2 ke ae2v

Zoomed plot

x0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.0010.0020.0030.0040.0050.0060.0070.0080.009

0.01

x0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.0010.0020.0030.0040.0050.0060.0070.0080.009

0.01

Figure 2.15: The contribution of the xF γZ3 and xF Z

3 terms to structure function

xF3 versus x at Q2 = 1500 GeV2 (left) and Q2 = 30000 GeV2 (right) as predicted by

the SM. The lower plots highlight the small contribution from the term containing

xF Z3 .

35

3 HERA and the ZEUS detector

This chapter outlines the HERA accelerator, some key ZEUS detector components,

and the process of recording data.

3.1 HERA collider

The Hadron Elektron Ring Anlage (HERA) accelerator [18] collides protons with

electrons or positrons3 at high energies, and is the only such collider in the world. It

is located at the Deutsches Electronen Synchrotron (DESY) laboratory in Germany.

The HERA collider is located approximately 20 m underground inside a tunnel

with a circumference of 6.3 km in which protons and electrons are accelerated inde-

pendently in opposite directions. A schematic view of HERA and the experimental

halls can be seen in Fig. (3.1). The two beams are brought together to create colli-

sions in the South and North experimental halls, where the ZEUS [19] and H1 [20]

detectors are located. In the East hall, the HERMES experiment [21] uses only the

3The term ‘electrons’ will be generally used to denote both electrons and positrons for thischapter.

36

electron beam and inserts their own polarised gas target. The West hall was used

by the HERA-B experiment [22], which inserted a wire target in the proton ring.

The beams are collided by guiding magnets that deflect the proton beam into

the same vacuum pipe as the electron beam. The proton beam is deflected back into

its own ring after the interaction region, with 96 ns between each bunch crossing.

The proton and electron beam energies delivered for the data analysed in this

thesis are 920 GeV and 27.5 GeV, respectively, resulting in a centre-of-mass energy

of 318 GeV.

360m R=7

97m

360m

920 GeV

Protons

Hall West

Hall North

Hall East

Hall South

PETRA

HERA 40 GeV Protons

14 GeV Electrons

p e

e p

H1

ZEUS

HERMES

HERA B

27.5 GeV

electrons

Figure 3.1: A schematic view of the HERA collider and pre-accelerator rings. The

proton and electron beams are brought together at the centre of the ZEUS and H1

experiments in the South and North halls.

37

A key component for the effectiveness of a colliding-beam machine is the collision

rate in the interaction region. The reaction rate is given by

R = σL, (3.1)

where σ is the interaction cross section and L is the instantaneous luminosity. The

instantaneous luminosity can be expressed as [12]

L = fnN1N2

A, (3.2)

where N1 and N2 are the number of particles in each bunch, n is the number of

bunches in either beam around the ring, f is the revolution frequency, and A is the

effective cross-sectional area of the beam overlap. The units of L are effectively the

number of collisions per unit area per unit time.

Regular data taking for the collider experiments began in 1992. During a three

year shutdown period starting in 2000, a major luminosity upgrade was achieved at

HERA mainly through a reduction in the cross-sectional area of the beams. Also

during this period, spin rotators were installed in the collider ring to deliver posi-

tively and negatively longitudinally polarised electron beams. The pre-upgrade and

post-upgrade phases are known as HERA-I and HERA-II. The integrated luminos-

ity (L =∫

Ldt) delivered for these two periods is shown in Fig. (3.2). The data

presented in this thesis is based on e−p data from HERA-II. The massive increase

in luminosity is of direct relevance to this thesis, as it has allowed an improved

38

statistical precision in the high Q2 region where the effects of parity violation in

NC cross sections will be most visible.

In the spring of 2007, the HERA accelerator group lowered the proton energy

for a measurement of the FL structure function. This was HERA’s final swan-song,

as it shut down permanently in July 2007.

HERA delivered

0

100

200

300

400

500

600

700

800

0 500 1000 1500 2000 2500days of running

Inte

gra

ted

Lu

min

osi

ty (

pb

-1)

days of running

Inte

gra

ted

Lu

min

osi

ty (

pb

-1)

days of running

Inte

gra

ted

Lu

min

osi

ty (

pb

-1)

days of running

Inte

gra

ted

Lu

min

osi

ty (

pb

-1)

ZEUS Luminosity 2002 - 2007

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300 350Days of running

Inte

gra

ted

Lu

min

osi

ty (

pb

-1)

Figure 3.2: The integrated luminosity delivered by HERA (left), and the integrated

luminosity recorded by ZEUS during the HERA-II data taking period (right). This

thesis is based upon e−p data recorded during 2005 − 06.

The ZEUS detector has access to ep collisions in the kinematic range of 10−6 .

x . 1 and 0.1 GeV2 . Q2 . 50, 000 GeV2. This vast kinematic range is shown in

Fig. (3.3) compared with fixed target DIS experiments (for example, an accelerated

beam of muons or neutrinos impinging on a fixed target). The ZEUS measurements

39

reach several orders of magnitude higher in Q2 than the fixed target experiments,

leading to extensive QCD and electroweak studies.

y=1 (

HERA √s=32

0 GeV

)

x

Q2 (

GeV

2 )

E665, SLAC

CCFR, NMC, BCDMS,

Fixed Target Experiments:

ZEUS

H1

10-1

1

10

10 2

10 3

10 4

10 5

10-6

10-5

10-4

10-3

10-2

10-1

1

Figure 3.3: Kinematic region accessible at the HERA collider experiments, ZEUS

and H1, compared with other fixed target DIS experiments [23].

3.1.1 Proton and electron beams

The proton beam begins its life as H− ions. These ions are accelerated to 7.5 GeV

and then the electrons are stripped off the ions. The protons are then accelerated

to 40 GeV in a pre-accelerator ring and then finally injected into HERA. Supercon-

ducting dipole and quadrupole magnets guide the protons around the ring, and the

40

beam is accelerated to 920 GeV using radio frequency cavities.

The electrons are collected by heating a filament, and are accelerated to 14 GeV

in the pre-accelerator ring and then finally to 27.5 GeV in the HERA ring. Syn-

chrotron radiation is emitted as charged particles are contained within the accel-

erator ring. Synchrotron radiation is inversely proportional to the mass of the

accelerated particle, and as the electron is approximately 1800 times lighter than

the proton, the electron beam is much more susceptible to energy loss due to syn-

chrotron radiation (e → eγ). Therefore, the maximum energy of the electron beam

possible at HERA is much lower than the proton beam energy.

3.1.2 Spin rotators and polarimetry

Electrons in a storage ring can become polarised antiparallel to the guiding mag-

netic field due to the emission of synchrotron radiation [24]. The projection of the

electron’s spin onto the vertical axis may flip direction, and a small difference in

the probability of the spin flipping from up-to-down and down-to-up causes a po-

larisation effect. This phenomenon is known as the Sokolov-Ternov effect [25], and

causes a transverse polarisation in the electron beam that builds up over time (t)

through the relation [26]

P (t) = PST (1 − e−t/τST ), (3.3)

41

where PST is the asymptotic polarisation (0.92) and τST is the polarisation rise

time constant (37 minutes at HERA). The maximum polarisation is not realised at

HERA due to effects such as de-focused beams.

However, longitudinally polarised electron beams are of interest, as the projec-

tion of the spin of a particle in the direction of its motion defines its helicity. Lon-

gitudinally polarised electron beams are achieved at HERA via spin rotators [26],

which consist of interleaved horizontal and vertical bending magnets.

The polarisation of the electron beam (Pe) is measured by two independent

polarimeters, the Transverse polarimeter (TPOL) [24, 27] and the Longitudinal

polarimeter (LPOL) [28]. The uncertainty on the polarisation measurement using

either the TPOL or LPOL is ∼ 4% [29]. Figure (3.4) illustrates the position of the

spin rotators and polarimeters at the HERA ring with respect to the experiments.

42

BeamDirection

Polarimeter

TransversePolarimeter

Spin Rotator

Spin Rotator

pe

Spin RotatorSpin Rotator

Spin Rotator

Spin Rotator

Longitudinal

Figure 3.4: A schematic view of HERA showing the location of the spin rotators,

polarimeters and experiments. The short arrows denote whether the electron po-

larisation is transverse or longitudinal with respect to the direction of motion.

3.2 ZEUS detector

The ZEUS detector [19] is located 30 m underground, is roughly the size of a three

storey building, and weighs approximately 3600 tonnes. It is centred around an

interaction region where the electron and proton beams meet. Tracking detectors

and calorimetry surround the interaction point. A side-view of the ZEUS detector

is shown in Fig. (3.5).

43

Figure 3.5: Overview of the ZEUS detector cut along the beam-pipe. The electron

beam enters the detector from the left and the proton beam enters from the right.

Detector parts are labelled by acronyms, with the most relevant components for

this thesis described in the text.

All angles and directions are made with respect to the ZEUS reference frame,

as illustrated in Fig. (3.6). The z axis points along the proton beam line, x points

towards the centre of HERA, and y points upwards, perpendicular to the beam.

The proton and electron beam directions are referred to as the forward and rear

directions, respectively. The angles θ and φ represent the polar and azimuthal

angles. The polar angle can be transformed into a Lorentz additive variable called

44

the pseudo-rapidity η = − ln(tan θ/2).

y

xHERA centre

z

r

e

p

Figure 3.6: The ZEUS coordinate system.

3.2.1 Uranium Calorimeter

The calorimeter is used to measure the energy of a particle by its total absorp-

tion and to measure the position of the energy deposit. The uranium sampling

calorimeter (CAL) [30, 31] is a sandwich of absorber (depleted uranium) and de-

tector (plastic scintillator) layers of thickness 3.3 mm and 2.6 mm, respectively. As

a particle enters the absorber it interacts with the uranium layer generating sec-

ondary particles, which in turn develop into a shower. Eventually all, or almost all,

of the energy of the incident particle is deposited into the calorimeter and is mea-

sured using the light yield from the scintillators. This method ensures that neutral

particles can be detected. Figure (3.7) shows the typical development of a shower

for different types of particles. Electrons and photons shower electromagnetically

as soon as they enter the CAL, but hadronic showers are deeper and broader.

45

Figure 3.7: The showering of different types of particles in the CAL. The uranium

and scintillator layers are shown.

x

z

HAC1

CENTRAL TRACKING

FORWARD

TRACKING

SOLENOID

HAC1HAC2

1.5 m .9 m

RC

AL

EM

C

HA

C1

HA

C2

FC

AL

EM

C

BCAL EMC

3.3 m

θ=1.6rad

27.5 GeVelectrons

920 GeVprotons

θ=0.1rad

θ=0.64rad θ

θ=3.0rad

=2.3rad

BCAL RCALFCAL

Figure 3.8: Sketch of the CAL sections in the x−z plane. Polar angles corresponding

to the edges of the CTD and the boundaries between CAL sections are shown.

The CAL covers 99.7% of the solid angle around the interaction point and is

46

divided into three sections; the forward (FCAL), barrel (BCAL) and rear (RCAL)

calorimeters as shown in Fig. (3.8). Each section contains electromagnetic (EMC)

and hadronic (HAC) parts, with the EMC closest to the interaction point. Each

CAL section is divided transversely into towers, and longitudinally into an EMC

section, and either one HAC section in the RCAL or two HAC sections in the FCAL

and BCAL. This asymmetry is due to the large boost of the proton beam direction.

The light generated in the scintillator is collected by photomultiplier tubes (PMTs),

light guides, and wavelength shifters on both sides of the towers. The position of

an energy deposit is measured using the imbalance between these two signals.

The CAL energy resolutions as measured under test beam conditions are

σ(E)/E = 0.18/√

E( GeV) for purely electromagnetic deposits and σ(E)/E =

0.35/√

E( GeV) for hadrons. The angular resolution is 0.1 mrad and the time res-

olution is 1 ns for energy deposits larger than 4.5 GeV.

3.2.1.1 Presampler

Particles must traverse detector material as they travel from the interaction point

to the CAL. This intervening material, such as cables and magnets, are collectively

known as dead material. The energy loss due to interactions with dead material

is related to the number of particles (multiplicity) measured at the CAL. The

presampler [32] measures the multiplicity of particles entering the FCAL and RCAL,

47

and consists of 20 × 20 cm2 scintillator tiles read out by PMTs. Event-by-event

information from the presampler and the CAL is used in this analysis to quantify

the energy loss in the RCAL due to dead material.

3.2.2 Central Tracking Detector

The Central Tracking Detector (CTD) [33] is a cylindrical drift chamber that mea-

sures the path of charged particles. A thin superconducting solenoid outside the

CTD provides a uniform magnetic field of 1.4 T, allowing the CTD to measure the

momentum of charged particles.

The CTD is 2.05 m in length, with an inner and outer radius of 18 cm and

79 cm, respectively, and covers a polar angle region of 15 < θ < 164. The CTD

contains many wires strung in a frame filled with a gas mixture of mostly argon.

Charged particles passing through the CTD ionise the gas, and the resulting ions

and electrons drift towards the negative and positive sensor wires. This produces

electrical signals which are used to determine the path of the charged particle.

Particle identification is also possible through measurements of the mean energy

loss dE/dx of charged particles traversing the gas inside the CTD.

The CTD wires are organised into 9 concentric superlayers (as shown in Fig. (3.9))

with alternating superlayers running either parallel to the beam line (axial super-

layers) or with an angle of 5 to the beam line (stereo superlayers). This small angle

48

allows measurements in r − φ and z with a resolution of ∼ 200 µm and ∼ 2 mm.

The momentum resolution of tracks that traverse through all CTD layers is

σ(pT )/pT = 0.0058pT ⊕0.0065⊕0.0014/pT (pT in GeV). The first term is related to

the resolution of the CTD hits and the second and third terms are due to multiple

scattering.

x

y

z

O

u

t

e

re

l

e

c

t

r

o

s

t

a

t

i

cs

c

r

e

e

n

S u p e r l

a

y

e

r

n

u

m

b

e

r

S

t

e

r

e

o

a

n

g

l

e

I

n

n

e

re

l

e

c

t

r

o

s

t

a

t

i

cs

c

r

e

e

n

1

2

45

89

3

67

+ 0

.

0

0+ 4

.

9

8

- 5 .

5

3

+ 5

.

6

2

- 5 .

5

1

+ 0

.

0

0

+ 0

.

0

0

+ 0

.

0

0

+ 0

.

0

0

Figure 3.9: An octant of the CTD divided into superlayers, with stereo angles

shown.

3.2.2.1 Microvertex Detector

The Microvertex Detector (MVD) [34] is a semiconductor (silicon) tracking detector

positioned close to the interaction point, between the CTD and the beam-pipe,

covering a polar angle of 7 < θ < 170. The MVD measurements are used in

49

combination with CTD information in this thesis to reconstruct a more precise

measurement of the event vertex position.

3.2.3 Luminosity detector

The luminosity is measured by studying photons produced in ep bremsstrahlung

(ep → eγp), the so called Bethe-Heitler process. This is a QED process that is well

understood so the theoretical cross section can be used to obtain a measurement of

the instantaneous luminosity (L) using

L = Rep/σobsB−H , (3.4)

where Rep is the observed rate for Bethe-Heitler events and σobsB−H is the theo-

retical cross section corrected for detector acceptance. The Photon Calorimeter

(PCAL) [35] is used in this analysis to measure the ep bremsstrahlung rate and

determine the integrated luminosity (L =∫

Ldt). The fractional uncertainty on

the integrated luminosity measurement is 3.5%.

3.2.4 Background rejection

There are certain background processes that need to be controlled at ZEUS:

• Beam-gas: These interactions arise mainly between the proton beam and

residual gas in the beam-pipe, causing hadronic energy deposits in the CAL

50

• Halo muons: The interaction between the proton beam and beam-gas or the

beam-pipe itself can produce charged pions which decay into muons that

travel parallel to the proton beam

• Cosmic muons: Interactions between cosmic rays and the upper atmosphere

of the earth produce muons that pass through the detector

Detector components used to reduce background events are outlined below.

The Veto Wall [19] consists of scintillators supported by an iron wall and is

positioned at z = −7.5 m. Its main purpose is to block proton halo muons from

entering the detector and take measurements which can be used to reject halo muon

events. The C5 counter [36] is a scintillator located at z = −1.2 m. It takes timing

measurements of the electron and proton beam which are used to veto events that

do not occur at the correct time. Muon chambers and a backing calorimeter [19]

surround the uranium calorimeter and can be used reject proton halo muons and

cosmic muons.

3.2.5 Trigger and data acquisition

The ZEUS detector delivers an enormous event rate of 10 MHz, a large percent-

age of which are background events such as beam-gas interactions. Therefore, the

events recorded by ZEUS are filtered using triggers. The trigger system [37] is de-

51

signed to reduce the event rate to a maximum of 10 Hz of interesting ep events. The

trigger is based on three levels which are illustrated in Fig. (3.10) and are described

below.

First Level Trigger (FLT)

The main purpose of the FLT is to reduce the event rate by rejecting background

events such as beam-gas interactions. The time between bunch crossings is 96 ns,

which is too fast to make a trigger decision, so the information is stored in a 5 µs

long pipeline until a decision is made. Each detector component involved at the

FLT contains dedicated hardware used to compute triggering information. This in-

formation is sent to the Global First Level Trigger (GFLT) which decides whether

to pass the event onto the second level trigger.

Second Level Trigger (SLT)

The second-level processors have more time (3 − 4 ms) for processing than the

first level processors (∼ 2 µs), and the available data is more complete. Therefore,

the SLT components can process data more accurately through measurements such

as the vertex position. Each detector component at the SLT calculates triggering

information locally and sends processed information to the Global Second Level

Trigger (GSLT) which includes filters designed to accept certain physics processes.

52

The complete event information is then passed on to the Event Builder (EVB)

which formats the data and passes it on to the third level trigger.

Third Level Trigger (TLT)

The TLT consists of a computer farm able to reconstruct the event fully and use

sophisticated algorithms such as electron-finders to categorise events and calculate

kinematic variables such as Q2, x and y. These filters are software based and can be

changed to suit the needs of the physics groups or tightened to reduce rates when

background conditions are high. The accepted events are written to a mass storage

tape for re-processing with complete detector calibrations and full reconstruction

software.

53

CTD

CTDFLT

Global

Accept/Reject

OtherComponents

Front End

5µS

Pip

elin

eCTDSLT

Accept/Reject

Eve

nt B

uffe

r

CTD ...

Event Builder

Third Level Trigger

cpu cpu cpu cpu cpu cpu

Offline Tape

CAL

CALFLT

Front End

CALSLT

Eve

nt B

uffe

r

CAL ...

First LevelTrigger

Global

OtherComponents

Second LevelTrigger

Rate107 Hz

200 Hz

35 Hz

5 Hz

5µS

Pip

elin

e

Fast ClearAccept/Abort

Figure 3.10: A sketch of the ZEUS trigger chain, with the approximate event rate

shown on the left. Note that in 2006 the CTD-SLT was phased out in favour of the

Global Tracking Trigger.

54

4 Monte Carlo Simulation

A measurement of the cross section requires a thorough understanding of the de-

tector efficiency, the acceptance of events and the resolution of measured variables.

Monte Carlo (MC) simulations are used to determine these factors, so that the

detector measurements can be used to extract cross sections. The generation of the

final state particles for the NC ep DIS process and the simulation of the detector

is outlined in this chapter.

4.1 DIS Monte Carlo

The generation of final state particles in an ep DIS process requires theoretical

descriptions of the processes involved or approximations through phenomenological

models. The QED radiative corrections to the simplest NC DIS process (Born-

level) are shown in Fig. (4.1). These diagrams contain a photon radiated before

and after the ep interaction, known as initial state radiation (ISR) and final state

radiation (FSR), and also virtual loops.

55

The development of the hadronic final state (HFS) in an ep DIS interaction is

shown in Fig. (4.2). The ep interaction occurs at time t = 0, before which the

interacting quark may radiate gluons. After the γq interaction, particles are pro-

duced (parton cascade) as the strong force grows large enough to pull virtual qq

pairs from the vacuum sea. Following this, the coloured partons are confined into

bound states of colourless hadrons in a process called hadronisation or fragmenta-

tion. These hadrons are the objects seen in the detector and are collimated into

jets of particles emanating from the direction of the original particles inside the

proton.

(a) (b) (c) (d)

γ, Z0

proton

e−

e−

Figure 4.1: Electroweak radiative corrections to the Born-level NC DIS process.

Figures (a) and (b) show final and initial state radiation. Figures (c) and (d) show

vertex and self-energy corrections.

56

protonat rest

t → – ∞ t → + ∞t = t0 t = 0

boost

initial state radiation

final state radiation

Q02 Q2

partoncascade

hadronisation

"jet"hadrons

"beam"hadrons

proton remnant

γ

Figure 4.2: The development of the hadronic final state in a DIS ep collision [38].

The shaded ovals at t → ∞ represent the hadrons seen in the detector.

The event generator DJANGOH 1.3 [39] was used to generate NC events in DIS

including both QED and QCD radiative effects, and CTEQ5D PDFs [10] were used

to parameterise the proton structure. The HERACLES generator [40] is used in

DJANGOH to describe the electroweak radiative corrections shown in Fig. (4.1).

The DJANGOH generator is also an interface to the ARIADNE [41] program

that describes the initial development of the hadronic final state called the parton

cascade. This cannot be described completely by perturbative QCD, so a phe-

nomenological model is used as a suitable approximation. ARIADNE uses the

57

Colour Dipole Method (CDM), which treats the struck quark and proton remnant

as a colour dipole. The energy contained in the dipole radiates more coloured ob-

jects creating more dipoles until a minimum energy is reached. At this point a

set of coloured quarks and gluons are generated. The final step is to simulate the

hadronisation process to generate all the final state hadrons. This is done using

the Lund string model in JETSET [42]. This model incorporates the strong force

in terms of strings that connect quarks. As a quark moves further away from other

quarks, the potential energy contained within the strings increases until the strings

snap and a new qq pair is created. This process is repeated until the available

energy is fully contained within the hadrons created.

4.2 Photoproduction Monte Carlo

A major source of background to the NC ep DIS cross section measurement is

photoproduction (PHP), which is the process mediated by a quasi-real photon. In

these events the electron scatters off the proton at very low angles and is usually

lost undetected through the rear beam-pipe.

However, a PHP event may be classified as DIS if a photon is falsely identified as

an electron. This may occur if, for example, a high energy photon is detected in the

calorimeter with a misidentified track pointing towards the energy deposit. A PHP

event is much more likely to be observed than a DIS event, as the NC differential

58

cross section is proportional to 1/Q4. This leads to a significant amount of PHP

background in a DIS measurement. However, this background can be minimised

by using event selection criteria, such as electron energy thresholds, as discussed in

Chapter 8.

The PHP content is determined from two different processes. The direct PHP

process occurs when the photon interacts as a point-like particle with the proton.

In contrast, the resolved process involves the hadronic structure of the photon, as

the photon can fluctuate into a partonic system and subsequently transfer only a

fraction of its momentum in the interaction. The direct and resolved PHP processes,

as illustrated in Fig. (4.3), are combined to determine the PHP content in a DIS

measurement. The HERWIG 5.9 generator [43] was used to generate both PHP

MC samples.

p

e

p

e -

Figure 4.3: Examples of the direct (left) and resolved (right) photoproduction

process.

59

4.3 Detector simulation and software environment

After the final state particles have been generated, the detector response is sim-

ulated. The first stage is to simulate the interaction of the particles with the

detector. This is done using a program called MOZART [44], based on the sim-

ulation program GEANT [45], that provides the shape, material, and position of

detector components. Also, the propagation of particles through the whole detector

is simulated, taking into account energy loss, multiple scattering, and the effect of

the magnetic field. After the detector response is simulated, the three trigger levels

are simulated (using a package called CZAR) and then finally a full reconstruction

of the event is performed (using software called ZEPHYR) such that the simulated

events can be directly compared with data.

The process of passing generated events through the detector simulation, trigger

simulation, and event reconstruction is done using the FUNNEL facility [46], which

produces MC events using computing power across the world. The MC production

capacity has been increased since 2004 using a Grid-enabled extension of FUNNEL

which exploits the large number of computing Grid sites designed for the Large

Hadron Collider (LHC). At the time of writing, the Grid simulates approximately

20 million ZEUS events per week [47], roughly four times the FUNNEL production

capacity.

60

The stages in a typical ZEUS analysis are shown in Fig. (4.4), starting from

raw detector signals and the physics event generators, and ending with an offline

event analysis. The analysis framework used in this analysis is ORANGE [48], a

software library that executes standard ZEUS analysis routines, such as electron

finders and calorimeter energy corrections. ORANGE version 2006a.3 was used in

this analysis.

(ZEPHYR)

(ORANGE)

Trigger Chain

FLT

SLT

TLT

Event Reconstruction

Offline Event Analysis

(AMADEUS)

Physics Event Generation

(MOZART)

Detector Simulation

Trigger Simulation

(CZAR)

Figure 4.4: The stages in a typical ZEUS analysis, adapted from [49]. On the left

side are the simulated events and on the right are the measured data events. The

software packages are shown in brackets.

61

4.4 Monte Carlo samples

The NC ep DIS differential cross section depends on a 1/Q4 term, so it is economical

to generate NC events at different Q2 thresholds. This means that a large sample

of low Q2 MC is needed to describe the data, but a relatively small amount of high

Q2 MC is needed. To smooth out the Q2 distribution and normalise the MC to the

integrated luminosity of the data (Ldata) each MC event i is weighted by

weighti =Ldata

LMCi

, (4.1)

where LMCi is the total integrated luminosity of the MC samples generated using a

Q2 threshold lower than the Q2 of event i. The result of the reweighting process is

shown in Fig. (4.5).

The PHP MC events were generated using transverse energy or transverse mo-

mentum thresholds (ET > 30 GeV or PT > 6 GeV) to minimise the size of the MC

samples. A normalisation factor of 1.7 was applied to the final PHP sample, derived

from MC comparisons with a PHP enriched data sample [50].

The MC samples shown in Table (4.1) were used to simulate the NC DIS signal

and PHP background for the NC e−p DIS cross section measurement at Q2 >

185 GeV2. Note that the data analysed (described in Section 8.4) corresponds to

an integrated luminosity of 177.2 pb−1.

62

)2 (GeVrec2Q

310 410

Eve

nts

410

510

(a)

)2 (GeVrec2Q

310 410

Eve

nts

1

10

210

310

410

NC MC

NC data

-1Lumi = 177pb

(b)

Figure 4.5: Reconstructed MC Q2 distribution (a) before and (b) after Q2 reweight-

ing and normalising to the integrated luminosity of the data. The MC is generated

above Q2 thresholds indicated by dashed lines. The Q2 values shown are recon-

structed using the Double Angle method described in Chapter 5. The selection

criteria described in Chapter 8 is applied to both data and MC (resulting in a

small dip at Q2 ≈ 600 GeV2).

63

Process Cuts σ (pb) L ( pb−1) Events

NC DIS Q2had > 100 GeV2 8161 9.78 × 102 8 × 106

> 400 1197 1.59 × 103 2 × 106

> 1250 217.3 5.56 × 103 1 × 106

> 2500 71.87 6.96 × 103 5 × 105

> 5000 21.73 2.30 × 104 5 × 105

> 10000 5.383 4.82 × 104 3 × 105

> 20000 0.8518 1.17 × 105 1 × 105

> 30000 0.1867 3.21 × 105 6 × 104

> 40000 0.04311 4.17 × 105 2 × 104

> 50000 0.009312 2.09 × 106 2 × 104

Direct PHP PT > 6 GeV or 2830 200.6 6 × 105

ET > 30 GeV

Resolved PHP PT > 6 GeV or 11900 197.8 2 × 106

ET > 30 GeV

Table 4.1: The NC DIS and PHP Monte Carlo samples used to simulate NC e−p

DIS data at Q2 > 185 GeV2 with an integrated luminosity of 177.2 pb−1. The cross

section (σ), integrated luminosity (L) and approximate amount of events are shown.

The generated Q2had values are calculated from the scattered electron and hadronic

final state.

64

5 Reconstruction of Kinematic Variables

Lorentz invariant quantities are used to describe the kinematic region being probed

in the ep interaction. These kinematic variables can be calculated using the energies

and scattering angles of the electron and hadronic system.

The NC ep DIS interaction in the quark-parton model (QPM) is shown in

Fig. (5.1), with the four-momentum of the incoming electron and proton denoted

as k and P , and the four-momentum of the outgoing electron and struck quark

denoted by k′ and P ′. The four-momentum of the initial and final state particles

can be written as

k =

Ee

0

0

−Ee

, k′ =

E ′e

E ′e sin θ cos φ

E ′e sin θ sin φ

E ′e cos θ

, P =

Ep

0

0

Ep

, P ′ =

Eh

px,h

py,h

pz,h

,

(5.1)

where θ and φ are the polar and azimuthal angle of the scattered electron, re-

spectively, and the energies Ee, E′e, Ep and Eh correspond to the electron beam,

65

scattered electron, proton beam, and struck quark, respectively.

γ, Z0(q)

quark (xP )

struck quark (P ′)

proton (P )

e−(k) e−(k′)

Figure 5.1: The ep NC DIS interaction in the QPM.

By taking the QPM approximation, the four-momentum of the struck quark

(P ′) can be measured by adding the four-momenta of all the hadronic particles

not associated with the proton remnant (as shown in Fig. (4.2)). An obstacle to

this process is the loss of particles through the forward beam-pipe. This can be

minimised by using quantities such as the hadronic transverse momentum (pT,h)

and the difference between the energy and longitudinal momentum of the hadronic

final state (δh), which are defined by

p2T,h = p2

x,h + p2y,h = (

h∑

i

Ei sin θi cos φi)2 + (

h∑

i

Ei sin θi sin φi)2, (5.2)

δh = (E − pz)h =h

∑

i

(Ei − pz,i) =h

∑

i

Ei(1 − cos θi), (5.3)

66

where the sum runs over all the final state particles apart from the electron, and

θ and φ correspond to the polar and azimuthal angle, respectively. These quan-

tities are not heavily influenced by particles lost down the forward beam-pipe, as

these particles will have a low transverse momentum and have an energy approxi-

mately equal to their longitudinal momentum. Using the QPM approximation, the

scattering angle of the struck quark, γh, is calculated using

cos γh =p2

T,h − δ2h

p2T,h + δ2

h

. (5.4)

The event topology of NC DIS events is shown in Fig. (5.2) displayed on the

x − Q2 kinematic plane. It can be seen that the hadronic system contains a large

amount of energy at high x, and that the electron is scattered by larger angles

as Q2 increases. The hadronic angle is generally pointing in the proton direction

except at high y, where a large amount of energy is transferred from the electron

to the proton. The NC cross sections to be presented in this thesis are measured

at Q2 > 185 GeV2. Note that the topology of such events changes significantly

between, for example, x = 0.2 and x = 0.01 as the hadronic angle points towards

the FCAL or the BCAL. The isolines of measured variables on the x−Q2 kinematic

plane are shown in Fig. (5.3).

67

x-510 -410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

y=1

y=0.1

y=0.0

1

y=0.0

01

y=0.0

001

Event TopologyScattered electron

Hadronic system

zeθ

hγ

E-scale: 27.5GeV

Figure 5.2: The event topology of NC DIS events shown on the x − Q2 kinematic

plane [50]. The red arrows indicate the scattering polar angle of the electron at a

given x and Q2 value and the blue arrows denote the hadronic angle. The arrow

lengths are proportional to the final state energy.

68

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

step)°

isolines (20eθ

°175

°35

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

isolines (5GeV step)e’

E

27.5

GeV

22.5

GeV

32.5 GeV

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

isolines (4GeV step)T,hP

4 GeV

40 GeV

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

2 step)× isolines (hδ

0.5 G

eV

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

step)°

isolines (20h

γ

°10

°17

0

x-410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

y=1

y=0.1

y=0.0

1

y=0.0

01

2 step)× isolines (hE

27.5

GeV

6.87

5 G

eV

440

GeV

Figure 5.3: Isolines of measured quantities shown on the x−Q2 kinematic plane [50].

The scattered electron angle θe, energy of the scattered electron E ′e, transverse mo-

mentum of the hadronic system PT,h, hadronic energy minus the hadronic longitu-

dinal momentum δh, hadronic angle γh and the hadronic energy Eh are shown.

69

The energies E ′e, Eh and angles θ, γh are used to reconstruct the Lorentz invari-

ant kinematic variables that characterise the interaction. The kinematic variables

can be calculated using information only from the scattered electron, exclusively

from the hadronic final state, or a combination of the two. Three different methods

to reconstruct the kinematic variables are introduced below.

5.1 Electron reconstruction method

The Electron method [51] only uses information from the scattered electron to

reconstruct the kinematic variables:

Q2el = 2EeE

′e(1 + cos θ) = 4EeE

′e cos2 θ

2, (5.5)

yel = 1 − E ′e

2Ee(1 − cos θ) = 1 − E ′

e

Eesin2 θ

2, (5.6)

xel =Q2

syel

=E ′

e cos2 θ2

Ep(1 − E′e

Eesin2 θ

2). (5.7)

It can be seen from Fig. (5.3) that when the scattered electron has an energy close to

the beam energy (27.5 GeV), the event becomes independent of Q2 at fixed x. This

area of phase space is known as the ‘kinematic peak’ region, and leads to a poor

resolution of the electron method as a small variation in the energy measurement

leads to a significant change in the kinematic variables.

70

5.2 Jacquet-Blondel reconstruction method

The Jacquet-Blondel method (JB) [52] relies exclusively on measurements from the

hadronic final state. This is the only viable method for CC analyses as the final

state lepton is a neutrino which escapes undetected. The kinematic variables are

reconstructed using

Q2JB =

∑hi (p2

x,i + p2y,i)

1 − yJB=

p2T,h

1 − yJB, (5.8)

yJB =

∑hi (Ei − pz,i)

2Ee=

δh

2Ee, (5.9)

xJB =Q2

JB

syJB

, (5.10)

where the sums run over all the hadronic energy clusters.

5.3 Double Angle reconstruction method

The Double Angle method (DA) [51] uses the polar angles of the scattered electron,

θ, and the scattered quark, γh. It combines information from the final state lepton

and hadronic system, without a strong dependence on the calorimeter energy scale.

The kinematic variables are given by the following formulae:

Q2DA = 4E2

e

sin γh(1 + cos θ)

sin γh + sin θ − sin(θ + γh), (5.11)

yDA =sin θ(1 − cos γh)

sin γh + sin θ − sin(θ + γh), (5.12)

71

xDA =Ee

Ep

sin γh + sin θ + sin(θ + γh)

sin γh + sin θ − sin(θ + γh). (5.13)

The DA method is a useful tool in predicting the measured electron energy using

only scattering angles. This value (EDA) can be reconstructed using a DA kinematic

variable with the Electron method formula (Eqn. (5.5)):

EDA =Q2

DA

2Ee(1 + cos θ), (5.14)

where Ee is the electron beam energy. Energies predicted by the DA method are

used to check potential energy losses in the detector, as discussed in Chapter 6.

5.4 Bias and resolutions of reconstruction methods

The choice of a reconstruction method depends on how well it reproduces the

true kinematic variables. This can be done by comparing the generated kinematic

variable in MC simulation with the reconstructed variable using the reconstruction

method. For example, the resolution and bias of the DA method in Q2 can be

determined using the width and mean of the distribution

Q2gen − Q2

DA

Q2gen

. (5.15)

The bias and resolutions of the three reconstruction methods, Electron, JB and

DA, are shown in Figs. (5.4 - 5.6). The distributions are displayed on the x − Q2

plane at approximately the correct bins.

72

The DA method generally performs better than the other two methods when

reconstructing Q2, x and y over most of the kinematic plane. The Electron method

performs well at high y when reconstructing Q2, x and y, but introduces a large bias

and resolution at low y as a small change in the electron energy can severely bias

the reconstructed variable. The JB method is competitive at high x in x and y but

a large bias and resolution is seen in other kinematic regions and in Q2. Therefore,

the DA method is chosen to calculate NC ep DIS cross sections.

73

x

-210 -110 1

)2 (

GeV

2Q

310

410

510 bias2Q

Electron Method

JB Method

DA Method

generated

2 ) / Qreconstructed2 - Q

generated

2( Q

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.001 < x < 0.004

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 50000218000 < Q0.25 < x < 1.0

Figure 5.4: The resolution and bias in Q2 using the Electron, JB, and DA methods.

The distributions are displayed on the x − Q2 plane at the approximate bins.

74

x

-210 -110 1

)2 (

GeV

2Q

310

410

510 x Bias

Electron Method

JB Method

DA Method

generated ) / xreconstructed - x

generated( x

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.001 < x < 0.004

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 50000218000 < Q0.25 < x < 1.0

Figure 5.5: The resolution and bias in x using the Electron, JB, and DA methods.


75

x

-210 -110 1

)2 (

GeV

2Q

310

410

510 y Bias

Electron Method

JB Method

DA Method

generated ) / y

reconstructed - y

generated( y

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.001 < x < 0.004

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 3002100 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 8002300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.004 < x < 0.016

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 22002800 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.016 < x < 0.064

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 630022200 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.064 < x < 0.25

-0.4 -0.2 0 0.2 0.4

< 1800026300 < Q0.25 < x < 1.0

-0.4 -0.2 0 0.2 0.4

< 50000218000 < Q0.25 < x < 1.0

Figure 5.6: The resolution and bias in y using the Electron, JB, and DA methods.


76

6 Event Reconstruction

The signals recorded by the various detector components need to be interpreted

and combined to reconstruct the measured event. This chapter outlines some of

the corrections and algorithms used to reconstruct a NC DIS event.

6.1 Track and vertex reconstruction

Track reconstruction begins with a pattern recognition algorithm [53], which exam-

ines all the CTD hits (digitised signals in each CTD wire) to determine a track seed

formed from three hits in the outermost CTD superlayer. The pattern recognition

then proceeds inwards in the x−y plane towards the interaction point. The output

from the CTD is used as an input to a Kalman filter for the MVD [54]. This works

inwards, towards the interaction point, adding MVD hits to the CTD information

and accounting for effects such as material in the MVD and the beam-pipe. As

the track seed is extrapolated inwards, more hits are attributed to the track, which

improves the precision of the fit. Finally, the position of the event vertex is assigned.

77

6.2 Longitudinal vertex reweighting

The measurement of longitudinal vertex position (ZV TX) is important as it is the

reference point to measure the polar angle of the scattered electron. The vertex

position drifts slightly during HERA operation as accelerator optics are tuned.

To have an accurate description of the ZV TX position, the ZV TX distribution was

fitted [55] with Gaussian distributions using a large sample of NC DIS from 2005-06.

The fit was performed using five Gaussian distributions; one central Gaussian and

four others to fit the satellite peaks as shown in Fig. (6.1). The parameterisations

from these fits were used to reweight the MC events.

Z vertex (cm)-100 -80 -60 -40 -20 0 20 40 60 80 100

Eve

nts

210

310

410

510

Figure 6.1: The Gaussian fits applied to the ZV TX data distribution [55].

78

6.3 Electron identification

An electron finder algorithm is used to identify electron candidates. The main

task of an electron finder is to distinguish electromagnetic and hadronic energy

clusters measured in the EMC and HAC cells [56]. The main electron finder for

this analysis, called EM, has been designed particularly for the high Q2 region,

where the electron is scattered by a large angle and is found in the BCAL or

FCAL sections (see Fig. (3.8) for a sketch of the CAL). Another electron finder

named SINISTRA, tuned especially for lower Q2 events (electrons scattered into

the RCAL), was used as a systematic check.

The EM electron finder [57] combines CAL and CTD information to identify

and reconstruct the scattered electron, whilst rejecting other final state particles

that may mimic the signature of an electron. At first, CAL ‘clusters’ are formed by

grouping CAL cells [58]. The cluster angle is then determined by taking the polar

angle between the cluster centre and the event vertex. A matching track is also

required if the cluster is within the CTD acceptance. A matched track is assigned if

the distance of closest approach between the extrapolated track and cluster centre

is within 10 cm. Several variables are then used to evaluate whether a CAL cluster

is a scattered electron candidate, including the difference in θ and φ between the

track and cluster, the fraction of the cluster energy measured in the HAC layers,

79

and parameters related to the width of the electron shower. Each of the variables

is transformed into a sub-probability with a large sub-probability related to a likely

electron candidate. An EM grand probability is assigned by taking the product of

all the sub-probabilities. The electron candidate is accepted if the grand probability

is above a certain threshold determined from MC studies.

The SINISTRA electron finder [59] is based on a neural network using CAL

information, and is tuned especially for electrons with a small scattering angle (low

Q2) penetrating the RCAL. This electron finder identifies the scattered electron

based on the shape of the shower it produces in the CAL. The inputs to the neural

net are the CAL cell energies and the output is the probability for each cluster to

be electromagnetic.

6.4 Electron energy

The CAL measurement of the electron energy is altered by some effects. As the

electron passes from the interaction point to the CAL, it must traverse detector

material such as magnets. This material reduces the true energy of the particle,

due to energy lost in interactions. Also the CAL surface is not uniform as there

are gaps between modules and towers. The corrections for these effects [50] are

discussed in the following sections. The electron energy distribution before and

after all corrections is shown in Fig. (6.2).

80

(GeV)e’

E0 10 20 30 40 50

Eve

nts

10000

20000

30000

40000

Whole CALUncorrected

(GeV)e’

E0 10 20 30 40 50

Eve

nts

10000

20000

30000

40000

Whole CALCorrected

(GeV)e’

E0 10 20 30

Eve

nts

10000

20000DataNC + PHP MCPHP MC

RCAL

(GeV)e’

E0 10 20 30

Eve

nts

10000

20000 RCAL

(GeV)e’

E0 20 40 60

Eve

nts

2000

4000BCAL

(GeV)e’

E0 20 40 60

Eve

nts

2000

4000 BCAL

(GeV)e’

E0 100 200 300

Eve

nts

50

100

150FCAL

(GeV)e’

E0 100 200 300

Eve

nts

50

100

150

FCAL

Figure 6.2: Electron energy distribution before (left) and after (right) corrections.

The dots represent data, the blue histogram represents PHP MC, and the yellow

histogram represents NC + PHP MC. From top to bottom is shown the energy

measured in the entire CAL, the RCAL, the BCAL, and the FCAL. The dashed

line indicates the cut of E ′e > 10 GeV applied in the final event selection.

81

6.4.1 RCAL electron energy

The energy loss due to dead-material is proportional to the particle multiplicity

due to these extra interactions. The rear presampler (PRES) can be used to mea-

sure the particle multiplicity from the deposited energy and so correct the electron

energy event-by-event. The energy loss can be quantified using the electron energy

predicted by the DA method (EDA). This reference energy is convenient as it is

calculated using the electron angle and hadronic angle, so is relatively insensitive

to the energy scale of the CAL sections.

The presampler correction [50] is parameterised by fitting a linear function to

the electron energy loss, E ′e −EDA, versus the energy deposited in the PRES inde-

pendently for data and MC. However, there are events in which the PRES energy

measurements are not valid. In these cases a dead-material map of the detector is

used, which simulates the location and type of dead-material inside the detector.

The energy loss through non-uniformity effects were also applied [60].

After these corrections are made the scale and resolution of the electron energy

was determined from the ratio E ′e/EDA as a function of EDA or the electron position

at the RCAL surface. The RCAL energy scale uncertainty was determined to be

2% by considering the data to MC comparison in Fig. (6.3) and an energy smearing

factor of 3.4% was determined for the MC events [50].

82

(GeV)DAE10 20 30

DA

/Eeco

rE

0.9

0.95

1

1.05

1.1 0.000±Data: mean = 0.996 0.000±MC : mean = 1.000

(GeV)DAE10 20 30

Dat

a/M

CD

A/E

ecor

E

0.96

0.98

1

1.02

1.04 0.000±Data/MC: mean = 0.997

R(cm)100 150

DA

/Eeco

rE

0.9

0.95

1

1.05

1.1 0.000±Data: mean = 0.997 0.000±MC : mean = 1.000

R(cm)100 150

Dat

a/M

CD

A/E

ecor

E0.96

0.98

1

1.02

1.04 0.000±Data/MC: mean = 0.997

Figure 6.3: RCAL electron energy scale [50] determined from E ′e/EDA versus EDA

(top) and electron position R =√

x2 + y2 (bottom). Data and MC events are

shown overlaid on the left and the ratio data/MC is shown on the right.

6.4.2 BCAL electron energy

The dead-material map is used in conjunction with parameterisations obtained in

test beam studies of the CAL [61] to correct the BCAL electron energy. The data

energy was determined to be scaled down by 2% and an energy dependent smearing

factor for the MC was applied [50].

83

6.4.3 FCAL electron energy

The dead-material map and non-uniformity corrections were used for events with

an electron scattered into the FCAL. The scale and smearing factors were derived

from a Gaussian fit to the ratio Ecorrectede /EDA. The data energy was shown to

require a 2% scale increase and a 3.7% smear was determined for MC events [50].

6.5 Calorimeter alignment

The polar angle of the scattered electron (θe) is reconstructed using CAL energy

deposit positions (if the electron is outside the acceptance of the CTD) or combined

with CAL and tracking information to achieve a better reconstruction. Therefore,

an accurate measurement of the CAL position with respect to the ZEUS reference

frame (set by the CTD) is of great importance as θe is used to reconstruct kinematic

variables. The CAL is opened and closed during detector shutdown periods, so the

CAL-CTD alignment can change slightly over time.

The alignment study [50] was done separately for the RCAL, BCAL and FCAL,

as these CAL sections are physically separate. The study was done in the RCAL and

FCAL using the difference between the CAL energy position and the extrapolated

CTD track position of the scattered electron. The alignment study in the BCAL

was performed by measuring the z position of the CAL module boundaries through

84

calculations of E ′e/EDA as a function of the z position.

The RCAL was shown to be aligned within 2 mm in x, y, and z [50]. The BCAL

was shown to be aligned within 1 mm in the z direction [50]. A 4 mm shift in y in the

FCAL was seen in data [50] and is corrected in the final analysis. After correcting

this shift in y, the position uncertainty at the FCAL is conservatively taken as

2 mm. All alignment factors are incorporated into the systematic uncertainties of

the final analysis by varying the θe measurement in the MC by ±1 mrad.

6.6 Hadronic final state reconstruction

The scattering angle of the struck quark, as approximated by the QPM, is calculated

from the distribution of particles associated with the hadronic final state (HFS). The

software package CorAndCut [62] is used to reconstruct the HFS in this analysis.

The CorAndCut package corrects the HFS for energy losses due to interactions with

dead material, energy losses in the boundaries between the BCAL and F/RCAL

(the so-called super-cracks) and energy overestimations for low energy deposits.

The energy losses were studied using distributions of the reconstructed and

generated MC hadronic energy. The dead material effect is treated using a fit of

the energy loss with respect to the amount of inactive material traversed. The

super-crack energy losses were parameterised using distributions of the energy loss

versus the hadronic angle.

85

The energy overestimation is attributed to different threshold cuts for HAC and

EMC cells, and the difference in CAL response to ionisation loss and showering.

Both effects cause an over-estimation of the energy of low energy hadrons, which is

corrected using an extrapolation function based on the energy behaviour in terms

of the energy fraction deposited into EMC sections.

The ‘backsplash effect’, also treated by CorAndCut, occurs when hadronic en-

ergy is redirected due to interactions with material in the detector. A study was

performed to update the backsplash correction for the HERA-II running period and

is discussed in Chapter 7.

6.6.1 Hadronic energy scale

The hadronic energy scale was investigated by comparing the hadronic transverse

momentum (pT,h) with the value predicted by the DA method (pT,DA). The mea-

surements shown in Fig. (6.4) confirm that the MC agrees with the data generally

within a percent, so the hadronic energy scale uncertainty is assigned to be 1%.

However, there are some interesting features in the pT,h/pT,DA distribution, such as

a fluctuation of up to 3% in the data to MC comparison at low hadronic angles

(γh < 0.5 rad). The effect of this discrepancy on the NC analysis was investigated by

reweighting the MC hadronic energy by a scale determined from the ratio between

data and MC values of pT,h/pT,DA with γh. The new scaling factors improve the

86

MC description of the hadronic variables (E−pZ)h and pT,h, as shown in Fig. (6.5),

however there is no effect on the hadronic angle γh as the scales simply cancel. The

NC cross sections are calculated using the DA method, so the final results are most

affected by changes to γh, rather than (E−pZ)h and pT,h separately. Also, γh cannot

be used to assign hadronic energy scales separately to the CAL sections. Therefore,

this hadronic energy reweighting routine was not used in the final analysis.

(rad.)h

γ0 0.5 1 1.5 2 2.5 3

T,D

A /P

T,h

P

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

)-1DATA (177 pbNC MC

(rad.)h

γ0 0.5 1 1.5 2 2.5 3

(D

AT

A/M

C)

T,D

A /P

T,h

P

0.950.960.970.980.99

11.011.021.031.041.05

Mean = 1.00381

(rad.)eθ0 0.5 1 1.5 2 2.5 3

T,D

A /P

T,h

P

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1


(rad.)eθ0 0.5 1 1.5 2 2.5 3

(D

AT

A/M

C)

T,D

A /P

T,h

P

0.950.960.970.980.99

11.011.021.031.041.05

Mean = 1.00351

Figure 6.4: Hadronic energy scale determined from pT,h/pT,DA versus γh and θe.

The data and MC values are shown as filled and empty circles, respectively. The

data to MC ratio is shown on the right.

87

(rad.)h

γ0 0.5 1 1.5 2 2.5 3

T,D

A /P

T,h

P

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1


Figure 6.5: The pT,h/pT,DA measurement versus γh after applying MC hadronic

energy reweighting scales is shown on the left. The middle and right plots show

the data/MC distributions of variables related to the hadronic energy. The black

and red dots correspond to the values before and after applying the MC hadronic

energy reweighting scales.

6.6.2 Jet reconstruction

A jet-finder can be used to cluster hadronic particles into collimated jets and is an

alternate approach to using all the hadronic deposits in the CAL to characterise

the HFS. The jet-finder used for systematic studies in this thesis is called the

‘longitudinally invariant kT clustering algorithm’ [63]. The energies (E) and angles

(θ and φ) of the input particles to the jet-finder are combined to make the quantities

ET = E sin θ and pseudo-rapidity η = − ln(tan θ/2). The pseudo-rapidity is used

as it is the longitudinally invariant polar angle, as a Lorentz boost along the z axis

changes this quantity by an additive constant.

88

The combination of particles relies on two distance parameters [64]. For each

particle (i) a distance parameter di = E2T,i is assigned, and for each pair of particles

(i and j) a distance parameter is defined using

dij = min(E2T,i, E

2T,j)[(ηi − ηj)

2 + (φi − φj)2]. (6.1)

If the smallest of all the d parameters is of type di then particle i is considered to

be complete and is removed from further clustering. If the minimum d parameter is

dij then the particles j and i are combined to form a particle k using the following

equations:

ET,k = ET,i + ET,j, ηk =1

ET,k(ηiET,i + ηjET,j), φk =

1

ET,k(φiET,i + φjET,j).

(6.2)

This process is repeated until all the particles have been accounted for. A selection

process using ET and η thresholds can be used to determine the final sample of

jets. The clustering algorithm does not impose any fixed geometry on the jet

shape, however the shape is generally contained within a cone of radius one in the

η − φ plane [63].

6.6.3 Investigation into the hadronic angle

The hadronic angle, γh, is calculated using Eqn. (5.4) by measuring the energy and

position of all the hadronic final state particles in the CAL. This is the nominal

89

method used in this thesis. To investigate any possible bias in this method, one

can compare the γh values with different reconstruction methods.

The Electron reconstruction method (described in Section 5.1) can be used to

reconstruct kinematic variables (Q2, x and y) using θe and E ′e, and then a prediction

of the hadronic variables can be made using Eqns. (5.8 - 5.10). This is a way to

predict γh without using any information from the hadronic final state. The jet

finder described in the previous section can calculate γh using Eqns. (5.8 - 5.10)

with the sums running over every jet in the event instead of the individual energy

deposits. For this study the kT jet-clustering algorithm was used to calculate the

jet four-momenta using CAL energy deposits. The jets were required to have a

minimum transverse energy of ET,jet > 4 GeV and to be found within the main

detector acceptance of −2.5 < ηjet < 2.5.

The predicted values of γh using these two alternate reconstruction methods,

the Electron and jets method, are shown in Figs. (6.6 - 6.7). The alternate re-

construction methods for γh agree well with the nominal method, within ±0.1 rad,

indicating that the HFS is understood well.

90

γh comparison with Electron method

[rad]h,Ele

γ0 1 2 3

Eve

nts

5000

10000

[rad]h,Ele

γ0 1 2 3

Eve

nts

5000

10000

< 0.5γ0.0 <

[rad]h,Ele

γ0 1 2 3E

vent

s

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NC + PHP MC

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hγ-0.4-0.2 0 0.2 0.4

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nts

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hγ-0.4-0.2 0 0.2 0.4

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nts

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[rad

]h,

Ele

γ

0

1

2

3Data

0

500

1000

1500

2000

2500

3000

[rad]γ0 1 2 3

[rad

]h,

Ele

γ

0

1

2

3MC

Figure 6.6: The prediction of γh using the Electron method (γh,Ele). The left plots

show γh,Ele in bins of γh and the middle plots show γh − γh,Ele in bins of γh. The

dots represent NC DIS data and the yellow histogram shows the NC MC. The right

plots show the nominal γh measurement versus γh,Ele using a colour scheme to show

the density of points.

91

γh comparison with jets method

[rad]h,Jet

γ0 1 2 3

Eve

nts

5000

10000

15000

20000

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s

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20003000

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NC + PHP MC

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nts

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1000

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nts

500

1000 < 3.0γ2.5 <

0

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6000

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[rad

]h,

Jet

γ

0

1

2

3Data

0

1000

2000

3000

4000

5000

6000

[rad]γ0 1 2 3

[rad

]h,

Jet

γ

0

1

2

3MC

Figure 6.7: The prediction of γh using jets (γh,Jet). The left plots show γh,Jet in bins

of γh and the middle plots show γh − γh,Jet in bins of γh. The dots represent NC

DIS data and the yellow histogram shows the NC MC. The right plots show the

nominal γh measurement versus γh,Jet using a colour scheme to show the density of

points.

92

7 Backsplash in the Hadronic Final State

The kinematic variables Q2, x and y are used for cross section calculations and are

reconstructed from the energies and scattering angles of the final state particles

found in the detector. An accurate measurement of the hadronic final state is

crucial to correctly reconstruct the kinematic variables. The backsplash effect is

one process that can bias the HFS measurements.

Backsplash occurs whenever particles scatter off detector material and leave

energy deposits in other parts of the calorimeter. A sketch of this process is shown

in Fig. (7.1). As the HFS is usually concentrated in the forward direction (the

proton beam direction), the overall effect of backsplash deposits is an increase in

the hadronic angle of the event (γh). The γh distribution reconstructed before and

after the backsplash correction designed for HERA I is shown in Fig. (7.2). The

backsplash effect noticeably biases the measurement, smearing the low γh peak. An

update to the backsplash correction for HERA II data is presented in this chapter.

93

True

pointentry True

pointentry

BCAL

FCAL RCAL

electron proton

Hadronic particle Scatter

DISTANCE D

Scatter

(1) Run over each final state particle in MC (2) Cone island created for each particle separately

(3) Extrapolate true entry point at CAL afterscatterings

(4) Use distance D to define a control sampleD < 40 cm

Island detected

Island detected

Island detected

Figure 7.1: Original approach (HERA I method) to identify a non-backsplash con-

trol sample using MC events. The sketch shows the CAL cut along the beam-pipe

with a single particle track overlayed.

94

Figure 7.2: The hadronic angle description using the original backsplash correction

in CorAndCut is shown on the left and without any correction is shown on the

right. The dots are data, and the yellow histogram is NC MC.

7.1 Updating the backsplash correction

The CorAndCut software package used to reconstruct the HFS includes a back-

splash correction derived using HERA I MC [62]. Since the HERA II upgrade,

detector material has been added to ZEUS such as tracking detectors in the for-

ward direction. The object of this study was to update the backsplash correction

for HERA II data. The original method for identifying backsplash energy deposits

relied on parameters derived from the MC simulation, so there was an interest in

developing a new method that could also use data to tune the backsplash correction.

This would avoid a dependence on the MC simulation of the backsplash effect.

The backsplash correction is derived from a control sample of events which are

judged to contain a minimal amount of backsplashed energy. The determination of

95

the control sample is the key step in the entire method, as parameters are tuned

from this sample of events (described in the next section).

The original backsplash method identified a control sample by using the distance

from the true entry position of a particle at the CAL surface to the position of the

energy deposit, as illustrated in Fig. (7.1). The true entry position is determined by

extrapolating the track of a particle, from the point where a scatter occurs, to the

CAL surface. This position is then compared with the location of the energy deposit

(grouped into an object called a cone island) of the same particle in the CAL. The

distance (D) between these two positions can then be used to identify a control

sample of events which are judged to contain no backsplashed energy (D < 40 cm).

This method can only be developed using MC events as these detailed trajectories

are not known for data.

7.2 New jet-based approach

The new method developed in this study is based on grouping the HFS into jets

of collimated particles. The kT clustering algorithm does not impose a shape upon

the jets, but the jet shape is generally contained within a cone of radius one in

the η − φ plane. This is the foundation of the new method to identify a control

sample, as islands which are found far behind the jet axis (away from the proton

beam direction) are possible backsplash candidates. An arbitrarily large cone size

96

of R =√

∆η2 + ∆φ2 < 1.5 was used to determine the control sample (∆η = ηjet −

ηisl, ∆φ = φjet − φisl), from which parameters can be tuned to reject backsplashed

islands.

The stages for identifying a non-backsplash control sample of events using the

new jets method is illustrated in Fig. (7.3). The kT jet algorithm is used to find

the most backward jet (pointing furthest away from the proton beam direction) in

an event and is assigned as the reference jet. Then the CAL is scanned for energy

deposits backward from the reference jet. The distance between the reference jet

axis and the energy deposits is used to identify backsplash deposits. The jet shape

is exploited by requiring a control sample of events with energy deposits within

a cone of R < 1.5 about the reference jet, and then using this control sample to

derive backsplash parameters. The advantage of this method is that data and MC

can be used to tune the backsplash cut, as jet finders can be used on both.

97

Event not

islands

used in controlsample due to these

(1) Run jet finder over event (2) Take jet pointing furthest back as reference

(3) Run cone island routine (4) Draw cone of R = 1.5 around jet axis to definecontrol sample using island furthest backward in cone

reference jet

BCAL

electron

FCAL RCAL

jet 1jet 1jet 2

proton

reference jet

islands

Figure 7.3: New approach to identifying a non-backsplash control sample using

jets. The angular separation between the jet and a hadronic energy cluster is used

to determine a good control sample.

From this control sample an angle called γmax is defined, which in the jet method

study is the polar angle of the furthest backward island in the event, as illustrated

in Fig. (7.4). The functional form of γmax can then be parameterised in terms of γh

using the control sample. The angle γmax is crucial to the backsplash correction,

as it determines the angle behind which low energy deposits may be rejected as

98

backsplash energy (away from the proton beam direction). Note that only the

islands behind the main hadronic activity are rejected, to avoid the complicated

coloured region between jets.

γmaxγh

Once control sample defined, measure hadronic angleand γmax event-by-event

Figure 7.4: Measuring γmax using the control sample. The polar angle of the most

backward island (away from the proton direction) in the control sample is identified

as γmax.

Once the γmax function in terms of γh has been determined, the backsplash cut

is then performed in the following manner,

1. Calculate the hadronic angle, γh, from all islands in the CAL

2. γmax is determined from γh (using the functional form derived from the control

sample)

3. Remove low energy islands with Eisl < 3 GeV and θisl > γmax

99

4. Repeat from step one until the difference between two successive γh values is

less than 1%

The cut of Eisl < 3 GeV was derived in the original backsplash study [62] from the

energy distribution of backsplashed islands.

7.3 Results using new jet-based approach

The new jets-based approach uses the following selection to define a control sample,

which is then used to determine the functional form of γmax.

• Jet selection: The kT clustering algorithm is used to select jets with ET,jet >

4 GeV. The jets are limited to those away from the beam-pipe holes such

that −2.5 < ηjet < 2.5. The jet with the smallest η, in other words pointing

furthest backward, is selected as the reference jet.

• Control sample selection: The angular difference in η and φ between the

reference jet and a particular island is used to determine whether the event be-

longs to the control sample. This sample is defined by ∆R =√

∆η2 + ∆φ2 <

1.5.

The γmax function for HERA II was parameterised using NC data collected from

2005 with an integrated luminosity of 122 pb−1, selected using the criteria detailed

in Chapter 8. The NC DIS MC detailed in Chapter 4 was also used to parameterise

100

γmax. Therefore two separate γmax functions can be determined for HERA II based

on data and MC simulation. Gaussian fits were made to the γmax distribution in

bins of γh to determine the functional form of γmax. The mean and spread of these

Gaussian fits were used to create the γmax vs γh plots shown in Figs. (7.5). The

data and MC show very similar distributions. The curve downwards to zero at low

γh is due to η approaching large values at small polar angles. As γh decreases, a

cone in the η−φ plane corresponds to a tighter cone in θ−φ plane. The jets method

generally predicts smaller γmax values than the original method. This indicates the

jets method predicts the hadronic particles are contained within a smaller angular

region.

To evaluate the effectiveness of the new γmax parameters, the hadronic angle

was studied when using the original or new backsplash correction, as shown in

Fig. (7.6). The MC describes the data well, though the MC slightly overshoots the

data (∼ 5%) at γh ∼ 0.5 rad.

101

[rad]γ0 0.5 1 1.5 2 2.5 3

[ra

d]

MA

Xγ

0

0.5

1

1.5

2

2.5

3

)-1HERA II DATA (122pbFit to DATAHERA II MCFit to MCOriginal Function

[rad]γ0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

[ra

d]

MA

Xγ

0.4

0.5

0.6

0.7

0.8

0.9

1

)-1HERA II DATA (122pbFit to DATAHERA II MCFit to MCOriginal Function

Figure 7.5: The mean of Gaussian fits applied to γmax in bins of γh. The left

plot is for the whole detector coverage and the right plot focuses on the low γh

region. Circles and squares show data and MC measurements, respectively, with

lines showing a quadratic fit (extrapolated to zero) and a linear fit applied. The

dashed line shows the original γmax function (using the HERA I method), and the

solid black line indicates γmax = γh.

102

(rad.)γ0 1 2 3

5000100001500020000250003000035000

maxγOriginal

(rad.)γ0 0.5 1 1.5 2 2.5 3

DA

TA

/MC

0.8

0.85

0.9

0.95

1

1.05

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maxγData para. in

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1.05

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(rad.)γ0 0.5 1 1.5 2 2.5 3

DA

TA

/MC

0.8

0.85

0.9

0.95

1

1.05

1.1

Figure 7.6: Distributions of γh using the original backsplash correction derived

from the HERA I method (top), the new correction using data derived parameters

(middle), and MC derived parameters (bottom). The left column shows data on

top of MC (dots and histogram, respectively) and on the right shows the ratio

data/MC.

103

The bias and resolution of the hadronic angle is calculated using the recon-

structed and generated (true) MC variables. Figures (7.7 - 7.8) show the bias

and resolution using ∆γh = γrec − γtrue versus ytrue in fixed bins of x. Values are

compared between the old and new backsplash parameters and when using no back-

splash correction. The results show the importance of the backsplash correction,

as the bias is corrected from 0.15 rad to 0.03 rad at low y and high x. The new

γmax parameters perform similarly to the original γmax function, however the new

parameters slightly over-correct γh by ∼ 0.03 rad in the highest y bins (y > 0.9) or

very low x. This over-correction occurs as the new γmax function enforces a tighter

cut at high γh than the original parameters (see Fig. (7.5)).

A remedy for this over-correction at high y was to limit the backsplash cut to

events with γh < 90. It is the forward region that is particularly important for the

backsplash cut, as most of the hadronic material travels forward due to the high

proton beam energy. This constraint successfully fixed the over-correction problem,

however a significant drop in the γh distribution was seen at 90, corresponding

to the boundary at which the backsplash correction was switched off. This is

shown clearly in Fig. (7.9). A significant change in the shape of γh would cause

complications in calculating kinematic variables, so it was decided to close this

avenue and continue with using the backsplash correction over the entire γh region.

104

The energy cut by the new backsplash correction (using data derived param-

eters) is shown in Fig. (7.10) in bins of γh. The shape of the energy distribution

is slightly different between data and MC particularly for γh < 20, but the level

of agreement is reasonable considering that the MC may not be reproducing the

backsplash effect perfectly.

This concludes a study that was an update of the backsplash correction for

HERA II and the development of a method to identify backsplash energy using

data instead of relying only on the MC simulation. The new backsplash parameters

(γmax) perform well, studies of ∆γh = γrec − γtrue show that at low y and high

x the bias is corrected from 0.15 rad to 0.03 rad. The bias and resolution of γh

compares well between the old and new backsplash parameters, however a small

over-correction of ∼ 0.03 rad is seen at highest y (y > 0.9). However, the biggest

benefit to using the new backsplash parameters is that one does not need to rely

only on the MC to tune the backsplash parameters. The new backsplash parameters

derived using data were used for the main NC analysis and the parameters derived

from the MC were used to calculate systematic uncertainties for the NC DIS cross

sections, as discussed further in Section 9.3.2.

105

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.003 < x < 0.01No backsplash cut

maxγHERA I (derived using MC)

maxγNew

(derived using Data)max

γNew

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.01 < x < 0.05

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.05 < x < 0.1

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.1 < x < 0.3

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.3 < x < 0.5

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

0.5 < x < 0.7

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(ra

d.)

γ ∆

0

0.05

0.1

0.15

0.2

Figure 7.7: The bias ∆γh = γrec −γtrue versus ytrue in bins of x for the old and new

backsplash corrections and with no backsplash correction.

106

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2No backsplash cut

maxγHERA I (derived using MC)

maxγNew

(derived using Data)max

γNew

0.003 < x < 0.01

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

0.01 < x < 0.05

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

0.05 < x < 0.1

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

0.1 < x < 0.3

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

0.3 < x < 0.5

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

0.5 < x < 0.7

truey

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

γ ∆σ

0

0.05

0.1

0.15

0.2

Figure 7.8: The resolution in ∆γh = γrec − γtrue versus ytrue in bins of x for the old

and new backsplash corrections and with no backsplash correction.

107

Figure 7.9: The γh distribution when using the backsplash correction only for

forward events such that γh < 90. The dots are the data and the yellow histogram

is the MC. The plot on the right is a blow-up of the γh ∼ 90 region.

(GeV)removedCorr. E0 1 2 3 4 5 6 7 8 9 10

Eve

nts

210

310

410° < 10γ < ° 0


Eve

nts

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nts

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Eve

nts

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310 ° < 170γ < ° 160


Eve

nts

-110

1

10° < 180γ < ° 170

Figure 7.10: Energy removed by new backsplash cut (after dead material correc-

tions) in bins of γh. The dots represent data and the yellow histogram represent

NC MC events.

108

8 Event Selection

A NC ep DIS interaction is characterised by the detection of a scattered electron.

The selection criteria used to extract a NC signal is discussed in this chapter.

8.1 Event characteristics

Figure (8.1) shows an event display [65] of a NC DIS event (Q2 ∼ 7000 GeV2,

x ∼ 0.15) found at ZEUS. The event display shows the tracks and energy deposits

associated with final state particles. A clean NC DIS event will have an isolated

scattered electron that is well balanced in transverse momentum with the hadronic

final state. Note that the topology of this event is very similar to an event at

Q2 ∼ 7000 GeV2, x ∼ 0.15 shown in Fig. (5.2).

The vast majority of NC events are measured at low Q2 because the NC DIS

differential cross section is proportional to 1/Q4, as described in Eqn. (2.19). These

types of events contain an electron scattered at a low angle and hitting the RCAL.

As the Q2 of the interaction increases the electron is scattered at larger angles.

109

The higher Q2 events (Q2 & 500 GeV2) typically contain an electron found in the

BCAL. The very highest Q2 events contain an electron scattered into the FCAL.

The percentage of events selected in this analysis with a scattered electron in the

RCAL, BCAL or FCAL is shown in Table (8.1).

(a) (b)

Figure 8.1: Event display of a typical NC DIS event (Q2 ∼ 7000 GeV2, x ∼ 0.15).

Display (a) shows the x − y plane, looking through the beam-pipe, and figure (b)

shows the z − y plane with the electron (proton) coming in from the left (right).

The CAL is shown in blue and surrounds the tracking detectors, with the CTD

shown in light brown. The purple lines represent the measured particle tracks, the

blue lines are the tracks extrapolated to the CAL, and the area of the red rectangles

are proportional to the magnitude of the energy deposits measured by the CAL.

110

CAL section of Polar angle of Percentage of total

electron energy deposit scattered electron (rad.) NC DIS events

RCAL θe > 2.3 71.9%

BCAL 0.6 < θe < 2.3 27.9%

FCAL θe < 0.6 0.2%

Table 8.1: Distribution of selected events in the calorimeter. Note that a cut of

Q2 > 185 GeV2 is used to define the kinematic region of the data sample.

Events with an electron scattered into the FCAL are rare, corresponding to only

0.2% of the total NC DIS events selected in this thesis. However, these scarce events

are important to test the weak force, as the massive Z boson exchange contribution

to the NC cross section becomes significant at high Q2.

The variables used for event selection are shown in Figs. (8.2 - 8.3) and will be

described in detail throughout this chapter.

111

-105-06 e-p, L = 177 pb

Data

MC (NC + PHP)

PHP MCEM Prob.

-410-3

10 -210 -110

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nts

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0 10 20 30 40

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(1-xJB

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2)DA

(1-xJB

y-3

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nts

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310

410

Figure 8.2: Data to MC comparison of variables used in the event selection (ab-

breviations explained in Sections 8.1 and 8.5). Data is shown as dots, PHP MC is

shown in blue, and NC + PHP MC is shown in yellow. All selection cuts are applied

apart from the particular variable displayed. Red lines indicate cut thresholds.

112

0

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)

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MC (NC + PHP)

PHP MC

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Figure 8.3: Data to MC comparison of variables used in the event selection (abbre-

viations explained in Sections 8.1 and 8.5). The 2D histograms are colour coded

to show the density of events. The 1D histograms show data as dots, PHP MC in

blue, and NC + PHP MC in yellow. Red lines indicate cut thresholds.

113

A useful quantity for event selection is the difference between the energy and

longitudinal momentum of all final state particles, given by

δ = (E − pz) =∑

i

(Ei − pz,i) =∑

i

Ei(1 − cos θi), (8.1)

where the sum runs over all energy deposits. The advantage of such a quantity

is that it is insensitive to objects lost down the forward beam-pipe, such as the

proton remnant. Undetected particles that escape through the forward beam-pipe

contribute little δ as the difference between the energy and longitudinal momentum

approximately cancel.

Another important quantity is the net transverse energy and momentum defined

by

ET =∑

i

Ei sin θi, (8.2)

p2T = p2

x + p2y = (

∑

i

Ei sin θi cos φi)2 + (

∑

i

Ei sin θi sin φi)2, (8.3)

where the sum runs over all energy deposits. A clean NC event should be mea-

sured with ET and pT close to zero due to energy and momentum conservation.

These quantities can be used to reject background events such as cosmic muons

penetrating the detector.

114

8.2 Background characteristics

Background events must be limited to enhance the high Q2 NC DIS signal. The

relevant types of background for this analysis are discussed in the following sections.

8.2.1 Photoproduction

Photoproduction, as discussed in Section 4.2, is defined by events with a quasi-

real photon exchanged. In a PHP event the electron is typically lost undetected

down the rear beam-pipe resulting in a δ measurement close to zero. However, in

a perfectly measured NC DIS event, where the detector covers all angular regions,

δ is equal to

E − pz ≈ Ee − (−Ee) + Ep − Ep = 2Ee = 55 GeV, (8.4)

where Ee and Ep are the initial beam energies of the electron and proton, respec-

tively. A minimum cut on δ is therefore useful for rejecting PHP events.

The PHP cross section is much larger than the high Q2 DIS signal, so a small

number of PHP events will manage to pass the NC DIS event selection. To account

for this, PHP MC events are used to estimate the number of PHP events still

remaining in the sample. This contamination is subtracted from the final number

of NC DIS data events for each cross section measurement. The PHP content is at

most 2% in the highest y bin of dσ/dy.

115

8.2.2 Beam-gas

The beam-pipe is maintained under a vacuum pressure of 0.1 nTorr (≈ 1×10−8Pa)

[66], but residual gas atoms, called beam-gas, remain in the vacuum chamber.

Beam-gas interactions with the proton or electron beam which occur before the

beams have reached the detector can be effectively rejected by the Veto Wall and

timing constraints on the calorimeter energy deposits. However due to the high

rate of beam-gas interactions, beam-gas events can occur in coincidence with an

interesting physics event. This is known as an overlaid event and usually contributes

a large E − pz. These background events can also be controlled using ET and pT

measurements, as these quantities are typically much larger than zero.

8.2.3 Halo and cosmic muons

Beam halo muons are mainly created from the decay of charged pions (π− → µνµ),

which are produced through interactions between the proton beam and material

around the beam-pipe. Cosmic muons originate from interactions between cos-

mic rays and the earth’s upper atmosphere, creating muons that penetrate mostly

through the top of the detector. Both types of background can be rejected by tim-

ing constraints on the calorimeter deposits, as these muons will not hit the opposite

ends of the detector simultaneously and are not likely to coincide (within ∼ 10 ns)

116

with a bunch crossing. These background events can also be rejected using the

imbalance in ET and pT .

8.2.4 Elastic QED Compton

QED Compton scattering refers to the process where the initial or final state elec-

tron radiates a photon (ISR and FSR, respectively). The inelastic QED Compton

scattering process, where the proton breaks up, is included in the MC simulation

and has been shown to be well understood [67]. However, it is preferable to reject

the elastic QED Compton process, ep → eγp, as it has a clean topology. The mea-

sured energy comes almost entirely from the electron and photon, and these two

objects are well balanced in φ and ET .

8.3 Data preselection

The first opportunity to select events is during actual data taking, referred to as

online event selection. A cocktail of triggers selected from the three levels are

chosen to reject background events, and enhance the NC DIS signal. Data quality

monitoring is also used to reject events recorded while problems occurred in any of

the critical detector components.

117

8.3.1 First Level Trigger

Information from the CAL (CFLT) and the CTD (CTD-FLT) are used to trigger

on interesting events. The event requirements concentrate on the summed CFLT

quantities, isolated deposits in the EMC sections, and good tracks found at the

CTD-FLT. Several vetoes are also used to reject background events. A general list

of the requirements used is shown below, with full details of the trigger slots in

Appendix B.1.

• Require one of the following energy sums, with a looser cut applied if a good

track is found at the CTD-FLT. Energy sums are defined in Fig. (B.1)

– Transverse energy (ET ) ≥ 20 GeV

– EMC energy ≥ 30 GeV

– Barrel EMC energy (BEMC) ≥ 4.8 GeV or Rear EMC energy (REMC)

≥ 3.4 GeV if a good track is found in the CTD

– Isolated EMC deposit in RCAL (> 4 GeV) or BCAL (> 3 GeV)

• Vetoes

– Timing information from components such as the Veto Wall and C5

counters should be consistent with the ep bunch crossing

118

– Beam-gas rejection by checking for tracks not emerging from the event

vertex

8.3.2 Second Level Trigger

The physics selection at the SLT is based on accepting events that appear to be

DIS with a good scattered electron candidate. High transverse energy slots are used

in parallel to accept the highest Q2 events. Timing measurements at the CAL are

used to veto background events. A general list of the requirements are listed below

with a full account of the trigger slots in Appendix B.2.

• Physics selection based on one of the following requirements

– An electron candidate with energy greater than 5 GeV, E−pz > 29 GeV

and energy deposits above 10 GeV or 2.5 GeV in the forward calorimetry

or the B/RCAL EMC sections, respectively

– A transverse energy above 35 GeV

• Vetoes

– To avoid cosmic muons, the event is rejected if the energy deposit in the

top half of the BCAL arrives more than 10 ns earlier than measurements

in the bottom BCAL half

119

– The event is vetoed due to beam-gas or halo muons if the time difference

between energy deposits in the FCAL and RCAL exceeds 8 ns, or if either

measurement is not within 8 ns of the planned ep bunch crossing

– Reject any events with a CAL spark from a faulty PMT or if the total

energy is close to zero (. 0.5 GeV)

8.3.3 Third Level Trigger

The TLT is the final step in the trigger chain and as a result has more time to

make decisions. A tracking package is implemented to give a more precise ZV TX

position, which leads to a better E − pz measurement. Electron finder algorithms

are employed to identify NC DIS events and ensure a good electron candidate is

available. Muon chambers are also used in combination with the CAL and CTD to

reject cosmic and halo muon events.

The physics selection was based upon the following requirements (slot TLT

DIS03):

• DIS FLT and SLT slots: Certain FLT and SLT slots were required to begin

a full DIS trigger chain. The FLT slots require a minimum CAL energy, an

isolated EMC deposit, or high ET . The SLT slots reinforce these requirements

and adds a minimum E − pz cut

120

• (E − pz) + 2 × ELumi−γ > 30 GeV, where ELumi−γ is the energy of a radiated

photon detected in the luminosity monitor

• E − pz < 100 GeV to reject overlaid events

• Ee > 4 GeV using either of the two electron finder algorithms available for

this slot

8.3.4 Data quality

To ensure the data was recorded reliably a logical bit called EVTAKE was used

to indicate the essential detector components were working well. This includes the

CTD, the luminosity monitor, and the CAL. Similar variables called MVDTAKE

and POLTAKE were also used to ensure that the MVD and the polarimeters were

in full working order during data taking.

8.4 Data sample

The data analysed was collected in 2005-06 and corresponds to an integrated lumi-

nosity of 177.2 pb−1. This is split between positively and negatively polarised data

as shown in Table. (8.2).

121

Data set Integrated luminosity Luminosity weighted polarisation

Total 177.2 pb−1 Pe = −0.04

Positively polarised 71.8 pb−1 Pe = +0.30

Negatively polarised 105.4 pb−1 Pe = −0.27

Table 8.2: The integrated luminosity and polarisation of the data analysed.

The integrated luminosity as a function of electron beam polarisation is dis-

played in Fig. (8.4). The run-by-run event yield is shown in Fig. (8.5), showing the

number of NC events measured divided by the luminosity. The yield is stable and

does not indicate any problems during data taking.

eP-0.6 -0.4 -0.2 0 0.2 0.4 0.6

)-1

Lu

min

osi

ty (

pb

0

2

4

6

8

10 -1Total Lumi. = 177.2 pb-1 = -0.27, Lumi. = 105.4 pbeLH data: P-1 = +0.30, Lumi. = 71.8 pbeRH data: P

Figure 8.4: The integrated luminosity of the data used in the NC e−p DIS analysis

as a function of electron longitudinal polarisation (Pe).

122

ZEUS run number52000 53000 54000 55000 56000 57000 58000 59000 60000

NC

evt

s / L

um

i (p

b)

00.5

11.5

22.5

33.5

4Runs taken from Jan. 2005 to June 2006

Data grouped into approx. 10000 events

Figure 8.5: The run-by-run event yield for the data used in the NC e−p DIS analysis.

The data is grouped into sets of 10,000 events and the points are shown at the

averaged run number.

8.5 Offline event selection

The following criteria was used to select the final NC e−p DIS sample. The distri-

butions of each variable used in the event selection are shown in Figs. (8.2 - 8.3).

The final data sample is shown on the x − Q2 plane in Fig. (8.6).

• EM electron candidate: The electron candidates are ordered, with the first

candidate most likely to be the true DIS electron. The ordering algorithm

takes into consideration the electron energy, position, and EM probability

value.

• Electron Probability: The EM probability, discussed in Section 6.3, is used

to enhance the purity of the electron candidates. A cut of EMprob > 0.001 is

123

used.

• Isolated electron: If the scattered electron is measured close to a hadronic

shower in the CAL it is difficult to determine which energy deposits belong

to the electron. This can be evaluated by checking the amount of energy

deposited close to the electron candidate, but not associated with the elec-

tron. The area close to the electron position is determined using a cone

of radius Rcone =√

(∆φ)2 + (∆η)2 = 0.8, where η is the pseudo-rapidity,

η = − ln(tan θ2). The electron is considered to be isolated if Econe

not−ele < 5 GeV.

• Electron energy: Low energy neutral pions in PHP events can decay into

photons, ‘faking’ an electron signal in the CAL. The PHP background can

be controlled by imposing a lower threshold on the electron energy (E ′e) of

10 GeV.

• Electron track inside the acceptance region of the CTD: The electron

is considered to be within the acceptance region of the CTD if the CTD

exit radius of the track is greater than 45 cm. This implies that the electron

reached at least CTD superlayer 4, ensuring a good polar angle measurement.

The following cuts were made when the electron is inside the acceptance of

the CTD,

– Track matching: The distance of closest approach (DCA) between the

124

calorimeter cluster and the endpoint of the extrapolated CTD track is

required to be less than 10 cm. This rejects events where a photon is

wrongly associated with a track in the CTD.

– Electron track momentum: A cut of ptrke > 3 GeV increases the

probability that the track belongs to the scattered electron, and not to

a low energy charged particle.

– Distance to module edge (DME): The calorimeter is divided into

modules, and energy measurements close to the module edges can be

unreliable. Therefore, events are rejected if the electron track is extrap-

olated to be within 1.5 cm of a calorimeter module edge.

• Electron forward of the acceptance region of the CTD: In this region

the CTD tracking information is not reliable, so one cannot easily distinguish

a photon from an electron. Therefore, the electron candidate transverse mo-

mentum (pT,e) is required to be above 30 GeV.

• Super-cracks: The term ’super-cracks’ refers to the edges of the BCAL next

to the RCAL and FCAL. Energy measurements are biased in these areas due

to large amounts of dead-material such as structural supports. Therefore,

the event is rejected if the scattered electron is found in the super-cracks,

corresponding to the regions -98.5 cm < ze < -104 cm and 164 cm < ze <

125

174 cm.

• Pipes in front of the RCAL: A small region of the RCAL is masked by

pipes that carry helium to and from the superconducting solenoid. This area

can be avoided by rejecting events in the RCAL where the energy cluster of

the electron candidate or the extrapolated track endpoint falls in the region

|xe| < 10 cm and ye > 10 cm.

• Radius of electron position at RCAL: Measurements from the outer

regions of the RCAL are not simulated well, as it is partially overlapped by

the BCAL. Therefore, events are rejected when the electron has been found

in the RCAL with a position radius of RRCALe =

√

x2e + y2

e > 175 cm.

• Longitudinal event vertex: Most ep collisions occur at ZV TX ≈ 0 cm, but

satellite peaks are observed in the distribution approximately 50 cm either

side of the central region. Therefore, the ZV TX distribution is restricted to a

central region of |ZV TX | < 50 cm.

• E - pz: As discussed in Section 8.2.1, a perfectly measured NC DIS event

would be measured with E−pz = 55 GeV, however PHP events are populated

at low E−pz values. Therefore, a cut of E−pz > 38 GeV is used to reject PHP

events. An upper cut of E − pz < 65 GeV is used to remove overlaid events

where the NC ep DIS interaction occurs in coincidence with a background

126

process, such as proton beam-gas interactions.

• Kinematic variable ye: When the electron candidate is detected in the

FCAL region, such that tracking is unavailable, a photon could be misiden-

tified as the scattered electron. In this case the measured energy and polar

angle would be low. This can be exploited using the kinematic variable y

reconstructed using the Electron method (ye), given by

ye = 1 − E ′e

Ee(1 − cos θ), (8.5)

which becomes large for such events. Therefore, a cut of ye < 0.95 is used to

reduce the PHP background.

• Transverse momentum balance: The transverse momentum (pT ) of a

perfectly measured NC event would be zero, but the resolution on the pT

measurement is approximately√

ET . A cut of pT√ET

< 4 GeV1/2 rejects events

with a significant imbalance in pT , usually arising from cosmic muons or beam-

gas events. At low ET , the pT√ET

quantity enters an unphysical region where

pT is larger than ET . This is accounted for by adding a cut of of pT

ET< 0.7.

• Projection of γh on to the FCAL (RFCALh ): At very low values of γh, the

energy deposits in the FCAL are usually a fraction of the actual energy of

the current jet, as much of the HFS is lost down the forward beam-hole. To

avoid this situation, events are rejected when the forward projection of the

127

hadronic angle falls within a radius of 20 cm from the centre of the forward

beam-hole.

• MC validity: The MC is not valid at very low y and high x due to missing

higher order QED corrections [68]. This kinematic region is avoided using the

cut yJB(1−xDA)2 > 0.004. The JB and DA reconstruction methods are used

as they are suitable for low y and high x events, respectively, as discussed in

Chapter 5.

• Elastic QED Compton rejection: These events are identified by finding an

electron and photon candidate in opposite regions in φ, and the two candidates

contain almost all the energy in the event, as detailed below [50]:

– |φe − φγ| > 3 rad

– 0.8 < peT /pγ

T < 1.2

– (ETotalCAL − Ee

CAL − EγCAL) < 3 GeV

where the notation e and γ refer to the electron and photon candidate.

• Kinematic region: The kinematic region is constrained using variables re-

constructed using the Double Angle method. The events are restricted to the

high Q2 region using Q2DA > 185 GeV2. A yDA < 0.9 cut is imposed to avoid

extrapolating to the full y range, otherwise correction factors of up to 10%

128

are needed due to the ye < 0.95 selection cut.

The distributions of all the variables used in the event selection is shown in

Figs. (8.2 - 8.3) for data and MC events. The MC is able to describe the data well,

which is important for the cross section extraction procedure. The calculated cross

sections are most sensitive to the variables used in the DA reconstruction method,

namely θe and γh, which are well reproduced by the MC. The small dips in the θe

distribution at approximately 2.2 rad and 0.6 rad are due to the super-crack cuts at

the BCAL boundaries with the RCAL and FCAL. These dips are propagated into

the Q2DA distribution.

The final data sample is shown on the x − Q2 plane in Fig. (8.6). The data is

mostly populated at the Q2 threshold and in the middle x region of approximately

0.01, however an impressive reach in Q2 and x is accessed. The largest momentum

transfer event selected in this analysis is Q2 ≈ 48000 GeV2 corresponding to a

spatial resolution of ∼ 9 × 10−19 m. An arc is noticeable on the kinematic plane

across the x range in the region Q2 . 600 GeV2 due to the super-crack cut.

129

0

20

40

60

80

100

120

140

160

180

x-310 -210 -110

)2 (

GeV

2Q

310

410

2 > 185 GeV2Qy < 0.9

> 20 cmFCALγ

R > 0.0042y(1-x)

> 10 GeVeE

2005/06 NC e-p data

Figure 8.6: Data events displayed on the x−Q2 plane after the full NC DIS selection.

The lines represent selection cuts which limit the kinematic region.

130

9 Cross section extraction and uncertainties

Experimental measurements are compared directly with theoretical predictions us-

ing cross sections. The process of calculating cross sections and the statistical and

systematic uncertainties of the final results are described in this chapter.

9.1 Cross section calculation and bin selection

A cross section bin is the interval in a particular variable in which events can be

counted. The definition of the cross section in a particular bin is given by

σ =N

L , (9.1)

where N is the number of events measured and L is the integrated luminosity of

the sample. However there are a number of corrections to be made:

1. Only a sub-sample of the total number of events can be measured due to the

geometry of detector and the selection criteria used to obtain the sample. The

acceptance correction is determined using the number of MC events generated

and measured (reconstructed) in a given bin via NgenMC/N rec

MC.

131

2. The total cross section for data and MC events includes QED radiative correc-

tions. To obtain the Born-level cross section one applies a radiative correction

σBornint /σrad

int , where the theoretical cross sections are integrated over the bin

width.

3. To measure the Born-level cross section at a particular bin-centre one applies

a bin-centring correction σBornbin−centre/σ

Bornint .

Using these corrections and the relation NgenMC/L = σrad

int , one can measure the Born-

level cross section dσ/dQ2, for example, using

(

dσ

dQ2

)measured

=Ndata − Nbg

N recMC

(

dσ

dQ2

)Born

bin-centre

, (9.2)

where Ndata, Nbg, and N recMC are the number of events measured in a certain bin

using data, background PHP MC, and NC MC, respectively.

Monte Carlo events generated (before simulating the detector response) and

reconstructed (after simulating the passage of generated events through the detec-

tor) in a given bin were used to determine whether the bin was appropriate for a

cross section measurement. Figures (9.1 (a)) and (9.1 (b)) show that the high x

and high y MC events are reconstructed (measured) at larger Q2 values than the

generated Q2 values. This is due to the selection cuts on the electron energy (E ′e),

the projection of γh on to the FCAL (RFCALh ), and the quantity y(1 − x)2. This

discrepancy between generated and measured MC events was addressed by raising

132

the measured Q2 > 185 GeV2 requirement to Q2 > 3000 GeV2 for the highest x and

y bins for the extraction of dσ/dx and dσ/dy. This ensured that the MC events

were generated and measured at comparable Q2 values.

The binning was chosen to be be proportionate to the resolutions of the kine-

matic variables [50], and to reflect the data statistical uncertainties. The bins in

σ were also chosen to be compatible with a previous NC e+p DIS measurement at

ZEUS [69] such that an extraction of the structure function xF3 was possible with-

out bin extrapolation. The suitability of the bins was investigated using variables

called efficiency, purity and acceptance defined as

Efficiency in bin i =Ngen∩rec

i

Ngeni

,

Purity in bin i =Ngen∩rec

i

N reci

,

Acceptance in bin i =Efficiency

Purity=

Ngeni

N reci

, (9.3)

where Ngen and N rec are the number of generated and reconstructed MC events in

bin i. The purity indicates the amount of migration over bin boundaries due to the

smearing of generated event variables after reconstruction. As bin widths decrease

so does the purity, as it is more likely for a generated event to be reconstructed in

a neighbouring bin. The efficiency is the fraction of events that are measured in

their true kinematic bin, and measures the suitability of the selection criteria for a

given bin. Finally, the acceptance quantifies effects such as detector geometry and

133

selection criteria, which limit the kinematic range in which cross sections can be

measured.

The efficiency, purity and acceptance for dσ/dQ2, dσ/dx, and dσ/dy are shown

in Fig. (9.2). Note that for dσ/dx and dσ/dy, the efficiency, purity and acceptance

are shown for Q2 > 185 GeV2 and Q2 > 3000 GeV2. Any bins with a very low

efficiency or purity would indicate that the binning is not suitable for a particular

kinematic region or the bin width is too small. However, the binning is shown

to be reasonable, with the purity typically above 50%, and the efficiency above

40%, dropping lower at very high x or y. The efficiency drops when the electron

is found near the boundaries between the BCAL and F/RCAL, as these events are

generated but rejected during the selection process (through the super-crack cut).

Events measured with a very low γh are rejected using the cut on the projection

of γh onto the face of the FCAL (RFCALh > 20 cm), which causes the efficiency to

drop at high x. The efficiency also drops at high y as the electron energy becomes

lower, so events are more likely to be rejected via the E ′e > 10 GeV cut.

134

(a) Highest x values (x > 0.6)

0

1

2

3

4

5

6

7

8

9

hadronicx-310 -210 -110

)2 (

GeV

2 hadr

onic

Q

310

410 > 20 cmhFCALR

> 0.0042y(1-x)

Generated

0

0.05

0.1

0.15

0.2

0.25

hadronicx-310 -210 -110

)2 (

GeV

2 hadr

onic

Q

310

410 > 20 cmhFCALR

> 0.0042y(1-x)

Measured

(b) Highest y values (y > 0.85)

0

5

10

15

20

25

30

35

hadronicy0 0.2 0.4 0.6 0.8 1

)2 (

GeV

2 hadr

onic

Q

310

410

> 10 GeVeE

Generated

0

0.5

1

1.5

2

2.5

3

hadronicy0 0.2 0.4 0.6 0.8 1

)2 (

GeV

2 hadr

onic

Q

310

410

> 10 GeVeE

Measured

Figure 9.1: The generated kinematic variables (Q2had, xhad and yhad) for (a) high x

and (b) high y MC events compared with the measured MC events. The density

of events is represented by a colour gradient, and selection cuts which limit the

kinematic plane are shown.

135

(a) (b)

x-210 -110 1

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1/dxσd

2 > 185 GeV2Q2 > 3000 GeV2Q

x-210 -110 1

Pu

rity

0

0.2

0.4

0.6

0.8

1

x-210 -110 1

Acc

epta

nce

0

0.2

0.4

0.6

0.8

1

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1/dyσd

2 > 185 GeV2Q2 > 3000 GeV2Q

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Pu

rity

0

0.2

0.4

0.6

0.8

1

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Acc

epta

nce

0

0.2

0.4

0.6

0.8

1

(c)

)2 (GeV2Q310 410

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

12/dQσd

)2 (GeV2Q310 410

Pu

rity

0

0.2

0.4

0.6

0.8

1

)2 (GeV2Q310 410

Acc

epta

nce

0

0.2

0.4

0.6

0.8

1

Figure 9.2: Efficiency, purity and acceptance in bins of (a) dσ/dx, (b) dσ/dy, and

(c) dσ/dQ2.

136

The efficiency and purity of the double differential cross section bins are shown

in Fig. (9.3) and are typically above 40% and 50%, respectively. The super-crack cut

causes low efficiencies in a band stretching across x in the region Q2 ∼ 200 GeV2 −

600 GeV2.

x-310 -210 -110 1

)2 (

GeV

2Q

310

410

Efficiency > 80% > 70% > 60% > 50% > 40% > 30%

> 80% > 70% > 60% > 50% > 40% > 30%

x-310 -210 -110 1

)2 (

GeV

2Q

310

410

Purity > 80% > 70% > 60% > 50% > 40% > 30%

> 80% > 70% > 60% > 50% > 40% > 30%

Figure 9.3: Efficiency (left) and purity (right) in the reduced cross section bins.

9.2 Statistical uncertainties

The statistical uncertainty on the cross section accounts for the number of data and

MC events. The uncertainty on the number of data events (∆Ndata) was calculated

using Poisson statistics if the number of data events was below 100, otherwise

Gaussian statistics were used (∆Ndata =√

Ndata).

The uncertainty on the number of NC DIS MC events and PHP MC events was

137

determined from the weights applied to each MC event (wi) for the normalisation

to the data integrated luminosity and the longitudinal vertex reweighting using

∆NMC =√

∑

i w2i . The uncertainty on the number of MC events was generally

insignificant.

The total statistical uncertainty (∆σstat) in a certain bin was then calculated

using

(

∆σstat

σ

)2

=

√

∆N2data + ∆N2

bg

Ndata − Nbg

2

+

(

∆N recMC

N recMC

)2

. (9.4)

The uncertainty on the number of data events for the reduced cross section bins

is shown in Fig.( 9.4). The statistical error is ∼ 1% (∼ 10, 000 events) in the lowest

Q2 bins, and grows to at most 15% (∼ 50 events) in the very high x and high Q2

bins.

138

x-310 -210 -110 1

)2 (

GeV

2Q

310

410

Stat. error<1%<2%<3%<4%<5%<6%<7%<8%<9%<10%<15%<20%

<1%<2%<3%<4%<5%<6%<7%<8%<9%<10%<15%<20%

Figure 9.4: Statistical error in the reduced cross section bins.

9.3 Systematic uncertainties

Unlike statistical uncertainties, which depend solely on the number of events taken,

the systematic uncertainties require a thorough understanding of the detector and

possible error sources. These errors could depend on the selection criteria, models

used to reconstruct variables, and also inputs to MC simulations.

A number of changes were made to the selection criteria and the reconstruction

methods to quantify the systematic uncertainty in the cross section. These changes

were made to reflect the resolution of the detector or the suitability of a certain

139

reconstruction procedure (for example, an alternative parameterisation to reject

backsplash from the HFS). The particular variation to an individual selection cut

was determined from studies based on the resolution and effectiveness of the cut.

For example, the resolution on the projection of the hadronic angle onto the FCAL

is approximately 3 cm, so the RFCALh cut is varied by ±3 cm. Also, the changes

in the ye cut (ye < 0.95 to 0.9) and E − pz cut interval (varied by ±4 GeV) are

expected to alter the background contamination by approximately 10% [70].

The change in the cross section due to these individual alterations are added

in quadrature separately for the positive and negative deviations from the nom-

inal cross section value to obtain the total systematic uncertainty. Systematic

uncertainties which involve just one change, such as switching to a different elec-

tron finder algorithm, are symmetrised such that they contribute a positive and

negative deviation to the nominal cross section. The systematic uncertainties in

the single-differential cross sections and the reduced cross sections are shown in

Figs. (9.5 - 9.9) and are described in the following sections.

9.3.1 Background rejection

• Varying the E − Pz cut:

The cut interval 38 GeV < E−PZ < 65 GeV is changed by ±4 GeV to vary the

level of background contamination. This systematic error is typically within

140

1% growing to at most 3% in the highest Q2 bin in σ.

• Varying the PT /√

ET cut:

The cut PT/√

ET < 4 GeV is altered by ±1 GeV and contributes negligibly

to the systematic uncertainty.

• Varying the ye cut:

The high ye region contains PHP background events, so this cut is tightened

from ye < 0.95 to ye < 0.9 to improve the purity of DIS events. The uncer-

tainty on the cross sections is small apart from the highest y bin in dσ/dy,

where it reaches 5%.

• Varying the normalisation of the background PHP MC:

A normalisation factor of ±40% is applied to the PHP MC, determined from

MC comparisons with a PHP enriched data sample [50]. This causes at most

a 2% effect in dσ/dy at the highest y bin.

9.3.2 Electron purity and hadronic final state

• Varying the distance of closest approach cut:

The reliability of track matching is increased by tightening this cut from

DCA < 10 cm to 8 cm. The systematic uncertainty is typically within a

percent over the entire kinematic region considered.

141

• Varying the electron track momentum cut:

The cut P etrk > 3 GeV is varied by ±1 GeV, and typically changes the cross

sections by less than 1% over the whole kinematic region.

• Varying the electron isolation cut:

The isolation of the scattered electron is investigated by varying the cut

Econenot electron < 5 GeV by ±2 GeV. This systematic error is small in all kine-

matic regions except at high Q2 in dσ/dQ2 where it grows to at most 9%. The

reason for this uncertainty being large at very high Q2 is that in this kine-

matic region the electron is scattered in the forward direction (in the proton

direction) and so will be found close to the HFS.

• Varying the γh projection onto the FCAL cut:

The cut RFCALh > 20 cm is varied by ±3 cm. This variation is most relevant

to high x events where the current jet is very forward and detected close to

the FCAL beam-pipe. This leads to uncertainties growing at high x, reaching

5% in the highest x bin in dσ/dx. The reduced cross sections also show

uncertainties reaching 9% in the high x bins.

• Backsplash γmax parameter:

As discussed in Chapter 7, the γmax backsplash parameter derived using MC

events is used to determine the systematic uncertainty. The backsplash cut

142

is most sensitive to events at low γh, where the HFS is very forward, so this

systematic is largest at high x in dσ/dx and σ, reaching 5%.

• Changing electron finders (EM → SINISTRA):

The SINISTRA electron finder, described in Section 6.3, is used as an alter-

native to the EM electron finder. This systematic is generally the dominant

uncertainty in most kinematic regions, particularly at high y in dσ/dy grow-

ing to almost 20%. The SINISTRA electron finder tends to increase the

cross section value. Variables such as electron energy and electron scattering

angle are generally described well when using either EM or SINISTRA, so

this large systematic error is presently not well understood. An investigation

into the differences between the two electron finder algorithms is shown in

Appendix C.

9.3.3 Calorimeter energy and alignment

• Varying the hadronic energy scale:

The MC hadronic energy (Eh) is varied by ±1%. This variation in the

hadronic energy scale was determined from measurements of pT,h/pT,DA shown

in Fig. (6.4), and typically contributes less than one percent to the systematic

uncertainty.

143

• Varying the electron energy scale:

The MC electron energy (E ′e) is varied by ±3%, as determined from measure-

ments of E ′e/EDA [50]. The high y region is populated with events with an

electron energy close to the 10 GeV cut threshold, so a change in the elec-

tron energy scale generally effects only the high y region. It is the dominant

systematic error in dσ/dy (Q2 > 185 GeV2) at high y, growing to at most 6%.

• Varying the electron energy resolution:

The MC electron energy resolution is changed by ±3% and contributes a

negligible uncertainty over the entire kinematic region.

• Varying the electron polar angle:

The electron polar angle (θe) is varied by ±1 mrad to reflect the uncertainty

in the spatial alignment of the CAL [50]. This causes a negligible effect on

the cross sections.

144

)2 (GeV2Q

310 410

sys

. err

or

%2

/dQ

σd

-20

-15

-10

-5

0

5

10

15

20DCAe- isolation

ZE - P)

T/sqrt(ETP

trke- P

hFCALR

ey

e- finder (Sini.)Backsplash

scaleeE resol.eE

eθ scalehadE

PHP norm.Total sys. errorData stat. error

y < 0.9

Figure 9.5: Systematic uncertainties in dσ/dQ2. The icons represent individual

systematic uncertainties, the red line shows the total systematic uncertainty and

the shaded band is the statistical uncertainty. Note that systematic changes which

are altered in just one way, such as switching to a different electron finder algo-

rithm, are symmetrised such that they contribute a positive and negative systematic

uncertainty.

145

x

-210 -110

/dx

sys.

err

or

%σd

-20

-15

-10

-5

0

5

10

15

20DCAe- isolation

ZE - P)

T/sqrt(ETP

trke- P

hFCALR

ey


scaleeE resol.eE

eθ scalehadE


, y < 0.92 > 185 GeV2Q

x

-210 -110

/dx

sys.

err

or

%σd

-20

-15

-10

-5

0

5

10

15

20DCAe- isolation

ZE - P)

T/sqrt(ETP

trke- P

hFCALR

ey


scaleeE resol.eE

eθ scalehadE


, y < 0.92 > 3000 GeV2Q

Figure 9.6: Systematic uncertainties in dσ/dx measured at y < 0.9 and Q2 >

185 GeV2 (top) or Q2 > 3000 GeV2 (bottom).

146

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/dy

sys.

err

or

%σd

-20

-15

-10

-5

0

5

10

15

20DCAe- isolation

ZE - P)

T/sqrt(ETP

trke- P

hFCALR

ey


scaleeE resol.eE

eθ scalehadE


2 > 185 GeV2Q

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/dy

sys.

err

or

%σd

-20

-15

-10

-5

0

5

10

15

20DCAe- isolation

ZE - P)

T/sqrt(ETP

trke- P

hFCALR

ey


scaleeE resol.eE

eθ scalehadE


2 > 3000 GeV2Q

Figure 9.7: Systematic uncertainties in dσ/dy measured at Q2 > 185 GeV2 (top)

and Q2 > 3000 GeV2 (bottom).

147

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

MAXγBacksplash

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

8cm→DCA > 10 σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

2GeV± < 5 not e-coneEσ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

4GeV± width ZE-P

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

2%± scale eE

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

1%± smeared eE

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

1mrad± eθσ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

1%± scale hE

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

40%±PHP bg. σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

1GeV± < 4 TE/TPσ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

1GeV± > 3 trkePσ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

3cm± > 20 hFCALRσ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

e- finder (Sini.)σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

0.9→ < 0.95 e

y

σ∼in

x-310 -210 -110

)2 (

GeV

2Q

310

410

> 1% > 2% > 3%

Total sys. errorσ∼in

Figure 9.8: Individual systematic uncertainties in σ shown on the x − Q2 plane.

The magnitude of the uncertainties are shown explicitly in Fig. (9.9).

148

bin number2x-Q0 10 20 30 40 50 60 70 80 90

syst

emat

ic e

rro

r (%

)

-20

-15

-10

-5

0

5

10

15

20~ σ

DCAe- isolation

ZE-P)

T/sqrt(ETP

trke- P

hFCALR

ey


scaleeE resol.eE

eθ scalehadE

PHP norm.

Total sys. error

Data stat. error

x-310 -210 -110

)2 (

GeV

2Q

310

410

bin number scheme2x-Q

1 2 3 4 5 6 7 89 10 11 12 13 14 1516 17 18 19 20 21 2223 24 25 26 27 28 29 30

31 32 33 34 35 36 3738 39 40 41 42 43 4445 46 47 48 49 50 51 52

53 54 55 56 57 58 59 6061 62 63 64 65 66 67

68 69 70 71 72 73

75 76 77 78 79

80 81 82 83

85 86 87

88 89

90

74

84

Figure 9.9: The upper plot shows the systematic uncertainties in σ in terms of

x − Q2 bin number. The icons represent individual systematic uncertainties, and

the dashed lines show Q2 bin boundaries. The bottom plot shows the x − Q2 bin

numbering scheme (numbers 1-8 correspond to the horizontal band at lowest Q2).

Note that spikes occur in the highest x bins due to the statistical uncertainty.

149

10 Results and discussion

The main results are presented in this chapter (tabulated in Appendix E), and are

compared with the SM prediction obtained using the ZEUS-JETS PDFs. The SM

prediction is produced by extrapolating the PDFs in Q2 and combining them with

the appropriate electroweak couplings, kinematic factors, and polarisation values.

The ZEUS-JETS PDFs and the NC DIS cross section are discussed in Sections 2.2.4

and 2.4, and the details of obtaining the SM prediction can be found in [9].

10.1 Single-differential cross sections

The measurements of the single differential cross sections dσ/dQ2, dσ/dx, and

dσ/dy using the entire 2005-06 e−p data set with a residual polarisation Pe = −0.04

are shown in Fig. (10.1). The measurement of dσ/dQ2 is beautifully described by

the SM as it falls by six orders of magnitude. The precision of this measurement is

apparent by comparing with the previous results from HERA shown in Fig. (2.10).

The measurements of dσ/dx and dσ/dy are also well described by the SM, and span

150

the kinematic range of 0.00794 < x < 0.794 and 0.075 < y < 0.875.

ZEUS

)2 (GeV2Q

310 410

)2

(p

b/G

eV2

/dQ

σd

-610

-510

-410

-310

-210

-1101

10 , y < 0.92 > 185 GeV2Q

)-1p (177.2 pb-05-06 e

SM (ZEUS-JETS)

= -0.04eP

x-210 -110

/dx

(pb

)σd

310

410

510

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

/dy

(pb

)σd

310

410

x-110

/dx

(pb

)σd

0

50

100

150

200

250

300

350

2 > 3000 GeV2Q

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/dy

(pb

)σd

0

20

40

60

80

2 > 3000 GeV2Q

Figure 10.1: Measurements of dσ/dQ2, dσ/dx, and dσ/dy using the entire 2005-06

e−p data set overlayed with the SM prediction calculated using ZEUS-JETS PDFs.

The inner error bars show the statistical uncertainty, while the outer bars show the

statistical and systematic uncertainties added in quadrature.

151

The ratio of the measured single differential cross sections to the SM predic-

tions are shown in Figs. (10.2) and (10.3) for the entire data set, and the neg-

atively/positively polarised data separately. The uncertainty in the SM predic-

tion is typically 1 − 2% in the kinematic region probed, and is shown in detail in

Fig. (10.11). The SM agrees with the dσ/dQ2, dσ/dx and dσ/dy measurements

typically within 5%. The fluctuations in dσ/dQ2 are generally within statistical

and systematic uncertainties, whereas the discrepancies in dσ/dx and dσ/dy at

Q2 > 185 GeV2 suggest a certain trend. The dσ/dx measurement at Q2 > 185 GeV2

tends to dip below the SM prediction by 5% in the middle x region (x ∼ 0.03),

which is also seen in the low y region in dσ/dy measured at Q2 > 185 GeV2. The

cross sections are extracted using the Double Angle (DA) method described in

Chapter 5, so the cross sections are most sensitive to the angles of the electron

and hadronic system (θe and γh). To test whether the discrepancy between the

measurements and the SM prediction is due to a bias in reconstruction of γh, the

cross sections were re-calculated using only information from the electron via the

Electron reconstruction method. The results are presented in Appendix D, and

show that the differences between the measured cross sections and the SM predic-

tion using the Electron method are of a similar shape and magnitude to the DA

method.

152

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=-0.04)e

, P-1p (177.2 pb-05-06 e

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=+0.30)e

, P-1p (71.8 pb-05-06 e

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=-0.27)e

, P-1p (105.4 pb-05-06 e

Figure 10.2: Ratio of dσ/dQ2 to the SM prediction. Measurement using all data,

positively polarised data and negatively polarised data are shown on the left, top

right, and bottom right, respectively. The inner error bars show the statistical

uncertainty, while the outer bars show the statistical and systematic uncertainties

added in quadrature.

153

x-210 -110

/dx

rati

o (

dat

a/S

M)

σd 0.80.850.9

0.951

1.051.1

1.151.2

, y < 0.92 > 185 GeV2Q

= -0.04e

, P-1L=177.2pb = -0.27

e, P-1L=105.4pb

= +0.30e

, P-1L=71.8pb

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

/dy

rati

o (

dat

a/S

M)

σd 0.80.850.9

0.951

1.051.1

1.151.2

2 > 185 GeV2Q

x-110 1

/dx

rati

o (

dat

a/S

M)

σd 0.50.60.70.80.9

11.11.21.31.41.5

, y < 0.92 > 3000 GeV2Q

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

/dy

rati

o (

dat

a/S

M)

σd 0.50.60.70.80.9

11.11.21.31.41.5

2 > 3000 GeV2Q

Figure 10.3: Ratio of dσ/dx and dσ/dy to the SM shown on the left and right,

respectively. Measurements using all data, negatively polarised data and positively

polarised data are shown as black squares, red dots and empty blue circles, respec-

tively. The inner error bars show the statistical uncertainty, while the outer bars

show the statistical and systematic uncertainties added in quadrature.

The measurement of dσ/dQ2 for positively polarised electrons, negatively po-

larised electrons, and a ratio of the two cross sections are shown in Fig. (10.4) and

compared with the SM prediction calculated using ZEUS-JETS PDFs. The cross

sections are described well by the SM, as shown previously in Fig. (10.2), and the

ratio of the positively and negatively polarised cross sections demonstrates parity

violation, as the value deviates from unity as Q2 increases.

154

ZEUS

)2 (GeV2Q310 410

)2

(p

b/G

eV2

/dQ

σd

-610

-510

-410

-310

-210

-110

110

y < 0.9

)-1p (71.8 pb-

05-06 eSM (ZEUS-JETS)

= +0.30eP

)2 (GeV2Q310 410

)2 (

pb

/GeV

2/d

Qσ

d

-610

-510

-410

-310

-210

-110

110

)-1p (105.4 pb-


= -0.27eP

)2 (GeV2Q310 410

=-0.

27)

e(Pσ

=+0.

30)

/ e

(Pσ 0.4

0.6

0.8

1

1.2

p-


= -0.27e = +0.30 / PeP

Figure 10.4: Measurements of dσ/dQ2 versus Q2 for (top) positively and (middle)

negatively longitudinally polarised electrons. The bottom plot is a ratio of the two

measurements, shown with statistical uncertainties. The SM prediction is overlayed.

155

Parity violation is also clearly observed in the polarisation asymmetry (A−)

measurement shown in Fig. (10.5), where the asymmetry is defined by inserting the

appropriate dσ/dQ2 measurements into Eqn. (2.27). Note that the Q2 bin widths

were increased to lower the statistical uncertainties on each measured point. The

level of agreement between A− and the predicted value can be quantified via a χ2

test, defined using [71]

χ2 =∑

bins

(

measured value − expected value

uncertainty on measurement

)2

. (10.1)

The expected values for the asymmetry measurement were chosen to be either the

SM prediction or zero (in the case of no parity violation). The χ2 value divided

by the number of degrees of freedom (ndf) is shown in Fig. (10.6) versus the Q2

threshold. At Q2 > 1000 GeV2, χ2/ndf = 4.2 for the asymmetry = 0 case, and

χ2/ndf = 1.1 when using the SM prediction. The expected value of χ2 is the

ndf , so the measurements support the SM prediction of parity violation. This is

quantified further by using the probability of the χ2 distribution [71]

Pndf(χ2 > c), (10.2)

where the probability Pndf is for χ2 to be above a certain value (c) for a given ndf .

This probability is shown in Fig. (10.6) versus the Q2 threshold. The probability

for the asymmetry = 0 case at Q2 > 1000 GeV2 is 2 × 10−4, which supports the

evidence of parity violation.

156

ZEUS

)2 (GeV2Q310 410

Asy

mm

etry

-0.4

-0.2

0

0.2

)-1p (177.2 pb-ZEUS NC, e

SM (ZEUS-JETS)

Figure 10.5: Measurement of the polarisation asymmetry (A−) versus Q2 shown

with statistical uncertainties. The red line indicates the SM prediction.

157

)2 threshold (GeV2Q310 410

/ n

df

2 χ

0

2

4

6

8

10

A = 0 case

A = SM case

)2 threshold (GeV2Q310 410

Pro

bab

ility

-1110

-910

-710

-510

-310

-110

A = 0 case

A = SM case

Figure 10.6: A χ2 test of the polarisation asymmetry measurement using the case

A− = 0 or A− as predicted by the SM. On the left shows χ2/ndf using the polar-

isation asymmetry values measured at a Q2 greater or equal to the Q2 threshold

value. On the right shows the probability that for a given ndf the value of χ2 could

be larger.

The single differential cross sections dσ/dx and dσ/dy are shown in Figs. (10.7)

and (10.8), measured separately for positively and negatively polarised electrons,

and a ratio between them. The ratio of the polarised cross sections are predicted

by the SM to be approximately flat versus x and y, which is reasonably supported

by the measurements, although the data seem to show a decreasing trend in dσ/dx

versus x for Q2 > 185 GeV2. To quantify the level of agreement between data

and the SM, a χ2 test was performed for the ratio of the polarised cross sections

shown in Figs. (10.7 - 10.8), with the results displayed in Table 10.1. As mentioned

previously, the expected value of χ2 is the ndf , so the measurements support the

158

SM prediction rather than the case of no parity violation.

ZEUS

x-210 -110

/dx

(pb

)σd

310

410

510, y < 0.92 > 185 GeV2Q

)-1p (71.8 pb-05-06 eSM (ZEUS-JETS)

= +0.30eP

x-110

/dx

(pb

)σd

0

50

100

150

200

250

300

350, y < 0.92 > 3000 GeV2Q


= +0.30eP

x-210 -110

/dx

(pb

)σd

310

410

510

)-1p (105.4 pb-05-06 eSM (ZEUS-JETS)

= -0.27eP

x-110

/dx

(pb

)σd

0

50

100

150

200

250

300

350

)-1p (105.4 pb-05-06 eSM (ZEUS-JETS)

= -0.27eP

x-210 -110

=-0.

27)

e(P

σ=+

0.30

) /

e(P

σ 0.92

0.94

0.96

0.98

1

1.02

p-05-06 eSM (ZEUS-JETS)

= -0.27e = +0.30 / PeP

x-110

=-0.

27)

e(P

σ=+

0.30

) /

e(P

σ 0.5

1

1.5

2

2.5


= -0.27e = +0.30 / PeP

Figure 10.7: Measurement of dσ/dx versus x for positively (top) and negatively

(middle) longitudinally polarised electrons. The bottom plot is a ratio of the

measurements with statistical uncertainties shown. The left (right) column is for

Q2 > 185 GeV2 (Q2 > 3000 GeV2). The red line indicates the SM prediction.

159

ZEUS

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

/dy

(pb

)σd

310

4102 > 185 GeV2Q


= +0.30eP

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/dy

(pb

)σd

0

20

40

60

80

2 > 3000 GeV2Q


= +0.30eP

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

/dy

(pb

)σd

310

410 )-1p (105.4 pb-05-06 eSM (ZEUS-JETS)

= -0.27eP

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/dy

(pb

)σd

0

20

40

60

80

)-1p (105.4 pb-05-06 eSM (ZEUS-JETS)

= -0.27eP

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

=-0.

27)

e(P

σ=+

0.30

) /

e(P

σ 0.85

0.9

0.95

1

1.05


= -0.27e = +0.30 / PeP

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

=-0.

27)

e(P

σ=+

0.30

) /

e(P

σ 0.6

0.8

1

1.2

1.4 p-05-06 eSM (ZEUS-JETS)

= -0.27e = +0.30 / PeP

Figure 10.8: Measurement of dσ/dy versus y for positively (top) and negatively

(middle) longitudinally polarised electrons. The bottom plot is a ratio of the

measurements with statistical uncertainties shown. The left (right) column is for

Q2 > 185 GeV2 (Q2 > 3000 GeV2). The red line indicates the SM prediction.

160

Measurement Q2 cut χ2/number of degrees of freedom

(ratio of polarised cross sections) ( GeV2) SM prediction Unity

dσ/dx 185 13.5 / 8 61.7 / 8

3000 5.1 / 7 17.2 / 7

dσ/dy 185 26.3 / 15 62.9 / 15

3000 14.2 / 17 30.5 / 17

Table 10.1: A χ2 test of the ratio of the polarised dσ/dx and dσ/dy cross sections

for Q2 > 185 GeV2 and Q2 > 3000 GeV2 (lower plots in Figs. (10.7 - 10.8)). The

expected value was taken as the SM prediction or unity (in the case of no parity

violation).

10.2 Reduced cross sections

The reduced cross section is defined as the double differential cross section with

respect to Q2 and x divided by kinematic terms, as shown in Eqn. (2.23), such that

the contributions of the structure functions is apparent:

σe±p = F2(x, Q2) ∓ Y−

Y+

xF3(x, Q2) − y2

Y+

FL(x, Q2). (10.3)

The reduced cross section measured using negatively and positively polarised elec-

tron data is shown in Fig. (10.9) versus x in fixed bins of Q2. The measurements are

161

well described by the SM over two orders of magnitude in Q2 and in x. At low Q2

(Q2 . 1000 GeV2), the reduced cross section is dominated by the structure function

F2, which is proportional to the sum of the quark and anti-quark PDFs. Note the

similarities between the measurement of σ and the PDFs shown in Fig. (2.8). The

small shoulder in σ noticeable at x ∼ 0.2 and Q2 . 800 GeV2 is due to the valence

quark distribution, and the increase of σ at low x is due to the sea quarks.

The reduced cross section measured using the entire 2005-06 e−p data set is

shown in Fig. (10.10) compared with previously published ZEUS e+p measure-

ments4 [69]. The residual polarisation of Pe = −0.04 in the total e−p data set was

corrected to zero using theoretical predictions. This correction was at most 1% in

the highest Q2 bin. The difference between σ(e−p) and σ(e+p) is due to parity

violation, and is particularly noticeable at high Q2 values. The charge asymmetry

is contained within σ via the xF3 structure function, as shown in Eqn. (10.3).

The ratio of the σ measurements to the SM prediction is shown in Fig. (10.11).

The measurements agree reasonably with the SM prediction. The dip of ∼ 7% in

the ratio data/SM at low Q2 and middle x is the same effect seen in the dσ/dx

measurement shown in Fig. (10.3).

4New e+p data from HERA II was still being collected while this analysis was ongoing. There-fore, previously published measurements from HERA I were used to extract xF3.

162

ZEUS

0.20.40.60.8

11.2 2 = 200 GeV2Q

0.20.40.60.8

11.2 2 = 650 GeV2Q

0.20.40.60.8

11.2 2 = 2000 GeV2Q

-210 -1100

0.20.40.60.8

11.2 2 = 12000 GeV2Q

2 = 250 GeV2Q

2 = 800 GeV2Q

2 = 3000 GeV2Q

-210 -110

2 = 20000 GeV2Q

2 = 350 GeV2Q

2 = 1200 GeV2Q

2 = 5000 GeV2Q

-210 -110

2 = 30000 GeV2Q

x

2 = 450 GeV2Q

2 = 1500 GeV2Q

2 = 8000 GeV2Q

ZEUS NC

)-1p (105.4 pb- 05-06 e SM (ZEUS-JETS)

= -0.27e P

ZEUS NC)-1p (71.8 pb- 05-06 e

SM (ZEUS-JETS) = +0.30e P

p)- (

eσ~

Figure 10.9: The NC e−p DIS reduced cross sections versus x in fixed bins of Q2 for

positively and negatively polarised electrons are shown as empty circles and filled

circles. The red and blue lines indicate the SM prediction evaluated at Pe = +0.30

and Pe = −0.27.

163

ZEUS

0.20.40.60.8

11.2 2 = 200 GeV2Q

0.20.40.60.8

11.2 2 = 650 GeV2Q

0.20.40.60.8

11.2 2 = 2000 GeV2Q

-210 -1100

0.20.40.60.8

11.2 2 = 12000 GeV2Q

2 = 250 GeV2Q

2 = 800 GeV2Q

2 = 3000 GeV2Q

-210 -110

2 = 20000 GeV2Q

2 = 350 GeV2Q

2 = 1200 GeV2Q

2 = 5000 GeV2Q

-210 -110

2 = 30000 GeV2Q

x

2 = 450 GeV2Q

2 = 1500 GeV2Q

2 = 8000 GeV2Q

ZEUS NC

)-1p (177.2 pb- 05-06 e SM (ZEUS-JETS)

= 0e P

ZEUS NC)-1p (63.2 pb+ 99-00 e

SM (ZEUS-JETS) = 0e P

p)± (

eσ~

Figure 10.10: The unpolarised NC e±p DIS reduced cross sections versus x in

fixed bins of Q2 for the total e−p data set (filled circles) compared with previously

published NC e+p cross sections (empty circles). The red and blue lines indicate

the SM prediction for e+p and e−p scattering.

164

0.8

1

1.2

1.4 2 = 200 GeV2Q

p) /

SM-

(e

σ~ 0.8

1

1.2

1.4

0.8

1

1.2

1.4 2 = 650 GeV2Q

0.8

1

1.2

1.4

0.6

0.8

1

1.2

1.4 2 = 2000 GeV2Q

0.6

0.8

1

1.2

1.4

-210 -1100.6

0.8

1

1.2

1.4 2 = 12000 GeV2Q

-210 -1100.6

0.8

1

1.2

1.4

2 = 250 GeV2Q

2 = 800 GeV2Q

2 = 3000 GeV2Q

-210 -110

2 = 20000 GeV2Q

-210 -110

2 = 350 GeV2Q

2 = 1200 GeV2Q

2 = 5000 GeV2Q

-210 -110

2 = 30000 GeV2Q

x-210 -110

2 = 450 GeV2Q

2 = 1500 GeV2Q

2 = 8000 GeV2Q

)-1p (177.2 pb- 05-06 e

= 0e P

)-1p (105.4 pb- 05-06 e

= -0.27e P

)-1p (71.8 pb- 05-06 e

= +0.30e P

SM uncertainty

Figure 10.11: Reduced cross sections divided by the SM prediction as a function

of x in fixed bins of Q2. Measurements using all data, negatively polarised data

and positively polarised data are shown as black squares, red dots and empty blue

circles, respectively. The shaded band corresponds to the uncertainty on the SM

prediction generated using ZEUS-JETS PDFs.

165

10.3 The structure functions xF3 and xF γZ3

The structure function xF3 is extracted by taking the difference of the σ(e−p) and

σ(e+p) measurements, as shown in Eqn. (2.29):

xF3(x, Q2) =Y+

2Y−(σe−p − σe+p).

Approximately 10 times more e−p integrated luminosity is available for this mea-

surement compared with the previous xF3 measurement at ZEUS [72], making this

the most precise measurement of xF3 in e−p DIS to date.

The structure function xF3 is shown in Fig. (10.12) versus x in fixed bins of Q2

and compared with the SM prediction. The xF3 structure function is proportional

to the valence quark content of the proton and grows with Q2 at fixed x. The

valence quark density versus x is expected to peak at x ∼ 0.2 and tend to zero at

low and high x. The data and SM prediction agree reasonably well.

166

ZEUS 3

xF

-0.1

0

0.1

0.2

2 = 3000 GeV2Q

-110 1

-0.1

0

0.1

0.2

2 = 12000 GeV2Q

2 = 5000 GeV2Q

-110 1

2 = 20000 GeV2Q

2 = 8000 GeV2Q

-110 1

2 = 30000 GeV2Q

ZEUS NC)-1p (240.4 pb± e

SM (ZEUS-JETS)

xFigure 10.12: The structure function xF3 versus x in fixed bins of Q2. The inner

error bars show the statistical uncertainty, while the outer bars show the statisti-

cal and systematic uncertainties added in quadrature. The line indicates the SM

prediction.

167

The interference structure function xF γZ3 can be extracted using Eqn. (2.30):

xF γZ3 = xF3/(−aek), (10.4)

by ignoring the small contribution from the term associated with xF Z3 . The previous

measurement of xF γZ3 (also known as xG3) taken by the ZEUS collaboration and in

fixed target muon carbon scattering by the BCDMS collaboration [73] is shown in

Fig. (10.13), evaluated at Q2 = 1500 GeV2 and Q2 = 100 GeV2. Note that the value

of xF γZ3 measured by BCDMS is the average structure function for the proton and

neutron.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 x

xG3

x

xG3

x

xG3

ZEUS

ZEUS e±p 96−99BCDMS µ±N 40 < Q2 < 180 GeV2

e±p ZEUS-S Q2 = 1500 GeV2

µ±N ZEUS-S Q2 = 100 GeV2

Figure 10.13: Previous measurements of xF γZ3 (also known as xG3) made by the

ZEUS collaboration (solid points) and the BCDMS collaboration (open squares).

The solid and dashed lines are the SM predictions using the ZEUS-S PDFs. Plot

taken from [72].

168

-1

-0.5

0

0.5

1

2 = 1500 GeV2Q

Zγ 3xF

-210 -1100

0.1

0.2

0.3

0.4

0.5

0.6

2 = 8000 GeV2Q

2 = 2000 GeV2Q

-210 -110

2 = 12000 GeV2Q

2 = 3000 GeV2Q

-210 -110

2 = 20000 GeV2Q

2 = 5000 GeV2Q

-210 -110

2 = 30000 GeV2Q

ZEUS NC)-1p (240.4 pb± e

SM (ZEUS-JETS)

x

Figure 10.14: The interference structure function xF γZ3 versus x in fixed bins of Q2.

The inner error bars show the statistical uncertainty, while the outer bars show the

statistical and systematic uncertainties added in quadrature. The line indicates the

SM prediction.

The new measurement of the structure function xF γZ3 using 2005-06 e−p data

and 1999 e+p data is shown in Fig. (10.14) as a function of x in fixed bins of

Q2. The SM curves in Fig. (10.14) indicate that xF γZ3 is predicted to be weakly

169

dependent on Q2 (note the change of scale on the axes). Therefore, the measure-

ments can be safely extrapolated to a single bin in Q2 using theoretical predictions,

and then averaged in x. This procedure was used to present xF γZ3 with the best

possible statistical precision. The data shown in Fig. (10.14) was extrapolated to

Q2 = 5000 GeV2, using factors generally within 5%, and is shown in Fig. (10.15).

The value of Q2 = 5000 GeV2 was chosen as it minimised the amount of Q2 extrap-

olation. The structure function xF γZ3 describes the valence quark distribution, and

can be directly compared with the valence quark PDFs shown in Fig. (2.8). The

statistical precision of this measurement is unprecedented, and can be compared

with previous measurements of xF γZ3 taken by the ZEUS and BCDMS collabora-

tion shown in Fig. (10.13). The new measurement of xF γZ3 extends the range of x

values down to 0.021. At the time of writing, new HERA II e+p data with an in-

tegrated luminosity of ∼ 120 pb−1 had been collected, but not fully analysed. This

additional data is projected to reduce the statistical error in the xF γZ3 measurement

presented by ∼ 8% at lowest x.

The sum rule shown in Eqn. (2.32) predicts∫ 1

0dxx

xF γZ3 = 5

3, by counting the

number of valence quarks inside the proton. However, the measurement of xF γZ3

is limited in the x range due to the acceptance of the detector. The integral of the

xF γZ3 measurement was obtained as

∫ 0.65

0.021

dx

xxF γZ

3 = 1.2 ± 0.1(stat) ± 0.1(sys), (10.5)

170

and is consistent with the ZEUS-JETS PDF prediction of 1.06 ± 0.02 within the

same x range.

ZEUS

x-210 -110 1

Zγ 3xF

0

0.2

0.4

0.6

0.8

1

2 = 5000 GeV2Q)-1p (240.4 pb±ZEUS NC, e

SM (ZEUS-JETS)

Figure 10.15: The interference structure function xF γZ3 versus x, extrapolated to

Q2 = 5000 GeV2. The inner error bars show the statistical uncertainty, while the

outer bars show the statistical and systematic uncertainties added in quadrature.

171

11 Summary and outlook

Neutral current e−p DIS cross sections measured at the ZEUS detector have been

presented. The HERA collider has provided an electron beam energy of 27.5 GeV

and a proton beam energy of 920 GeV yielding a centre-of-mass energy of√

s =

318 GeV. The data analysed was collected from 2005-06 and corresponds to an

integrated luminosity of 177.2 pb−1. The data set was split between negatively

polarised electrons (L = 105.4 pb−1, Pe = −0.27) and positively polarised electrons

(L = 71.8 pb−1, Pe = +0.30).

The single differential cross sections dσ/dx, dσ/dy, and dσ/dQ2 have been mea-

sured at y < 0.9 and Q2 > 185 GeV2 (and also Q2 > 3000 GeV2) and are well

described by the SM. The measurement of dσ/dQ2 in bin-centres ranging between

195 GeV2 < Q2 < 36, 200 GeV2 using negatively and positively polarised data has

been used to calculate the polarisation asymmetry (A−). This measurement is the

first observation of parity violation in NC e−p DIS at distances down to 10−18 m.

The e−p reduced cross section has been measured in the bin-centre ranges of

172

200 GeV2 < Q2 < 30, 000 GeV2 and 0.005 < x < 0.65. These measurements have

been compared with previously published e+p reduced cross sections to extract the

proton structure function xF3, which contains the parity violating part of the re-

duced cross section. The interference structure function xF γZ3 , which describes the

valence quark distribution inside the proton, has been extracted. The integral of

the measured xF γZ3 distribution versus x is consistent with the SM. The measure-

ments of the structure functions xF3 and xF γZ3 presented in this thesis are the most

precise to date.

The cross section measurements presented in this thesis will have a direct impact

on PDF fits. The ZEUS collaboration has released PDF uncertainties using the

preliminary results from this thesis and from HERA II e−p CC data, shown in

Fig. (11.1). The addition of these new measurements has improved the precision of

the high x PDF distributions, particularly for the u valence quark. The constraint

of the PDF uncertainties is of great importance, as a precise knowledge of the PDFs

provided by HERA will be essential for future studies at the Large Hadron Collider.

Efforts have begun to combine measurements from both the ZEUS and H1

detectors for a greater statistical impact. Figure (11.2) shows a combined polarisa-

tion asymmetry measurement (A±) from the H1 and ZEUS collaborations, which

includes preliminary measurements of A− from this thesis. This combined measure-

ment is based on an integrated luminosity of ∼ 290 pb−1 between the experiments,

173

and the shape and magnitude of A± as a function of Q2 is well described by the

SM. The ZEUS and H1 experiments have now collected a total of ∼ 900 pb−1 of

positively and negatively polarised e±p data. The analysis of this total data set

will yield the final word on electroweak measurements at HERA.

-1

-0.5

0

0.5

1vxu

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

2 = 10000 GeV2Q

-1

-0.5

0

0.5

1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2vxd

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1

-0.5

0

0.5

1xS

-410 -310 -210 -110

-410 -310 -210 -110

ZEUS-JETS

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1xg

-410 -310 -210 -110

-410 -310 -210 -110

ZEUS-pol (prel.)

-1

-0.5

0

0.5

1

ZEUS

x

frac

tion

al u

ncer

tain

ty

Figure 11.1: Fractional uncertainty of the ZEUS-JETS PDFs compared with the

ZEUS-Pol PDFs [74] (which include preliminary measurements from this thesis).

The uncertainties at Q2 = 10, 000 GeV2 are shown, with an improvement seen at

high x, particularly for the u valence quark.

174

Figure 11.2: Measurements of the polarisation asymmetry A± by the ZEUS and

H1 collaborations combined to achieve the greatest statistical impact [16]. Data

collected with an integrated luminosity of ∼ 290 pb−1 has been used.

175

A Acronyms

BCAL - Barrel Calorimeter

CAL - Calorimeter

CC - Charged Current

CFLT - Calorimeter First Level Trigger

CTD - Central Tracking Detector

CTEQ - Coordinated Theoretical-Experimental Project on QCD

DESY - Deutsches Elektronen Synchrotron (a research centre)

DIS - Deep Inelastic Scattering

EMC - Electromagnetic Calorimeter

FCAL - Forward Calorimeter

FLT - First Level Trigger

FSR - Final State Radiation

H1 - A general purpose particle detector at HERA

HAC - Hadronic Calorimeter

176

HERA - Hadron Elektron Ring Anlage (an e±p accelerator)

HFS - Hadronic Final State

ISR - Initial State Radiation

LHC - Large Hadron Collider

LO - Leading Order

MC - Monte Carlo

MVD - Micro-vertex Detector

NC - Neutral Current

PDF - Parton Density Function

PHP - Photoproduction

PMT - Photomultiplier Tube

QED - Quantum Electrodynamics

QCD - Quantum Chromodynamics

QPM - Quark-Parton Model

RCAL - Rear Calorimeter

SLT - Second Level Trigger

SM - Standard Model

TLT - Third Level Trigger

ZEUS - A general purpose particle detector at HERA

177

B Trigger slots

B.1 First Level Trigger

The energy sums of importance to this analysis are detailed in Fig. B.1. Further

variables are listed below:

• EREMC,th: Energy deposited in the entire RCAL EMC, only including cells

with an energy above 625 MeV

• ET,all: Total transverse energy including all towers

• R/B/FIsoE: An isolated EMC deposit (IsoE) in the RCAL, BCAL, or FCAL,

respectively

• RIsoE - 3q: An isolated REMC deposit found, excluding the third quadrant.

The RCAL is made up of 4 quadrants defined by the sign of the coordinates

in the x − y plane; (+x, +y), (+x,−y), (−x, +y), and (−x,−y). The third

quadrant (−x, +y) suffers from background events arising from low energy

electrons in the incoming beam that are deflected into the RCAL surface.

178

• Track: A vertex fitted track found at the CTD-FLT

The following FLT slots were used, taking a logical OR between all slots:

• Isolated Electron slots

– FLT 30: RIsoE and (EREMC ≥ 4 GeV or EREMC,th ≥ 15 GeV)

– FLT 46: RIsoE - 3q and (EREMC ≥ 2 GeV or EREMC,th ≥ 3.8 GeV) and

Track

– FLT 39: BIsoE and EBEMC ≥ 3.4 GeV and Track

– FLT 28: FIsoE or ( BIsoE and Track) and ET,all > 20 GeV

• Inclusive slots

– FLT 40: EEMC ≥ 20 GeV

– FLT 41: ET ≥ 30 GeV

– FLT 43: ET ≥ 15 GeV and Track

– FLT 44: (EBEMC ≥ 4.8 GeV or EREMC ≥ 3.4 GeV) and Track

The purpose of this FLT chain is to trigger on isolated electromagnetic clusters and

use the inclusive slots to trigger on the highest Q2 events. The ‘Track’ bit is used

where appropriate to allow looser energy cuts.

179

FCAL BCAL RCAL

e p

(b) CFLT: EMC

(c) CFLT: BEMC (d) CFLT: REMC

(a) CFLT: ET

3 rings

1 ring

1 ring

1 ring

Figure B.1: A sketch of the energy sums used at the CFLT, showing the CAL

centred around the beam-pipe (denoted by a dashed line). The yellow areas corre-

spond to the CAL regions used in the energy sums of (a) ET , the total transverse

energy, (b) EMC, the CAL sections used for electromagnetic deposits, (c) BEMC,

the barrel EMC, and (d) REMC, the rear EMC. Inner rings of CAL towers at the

FCAL or RCAL are excluded from the energy sums to avoid the proton remnant

or beam-gas interactions.

180

B.2 Second Level Trigger

The following slots were used at the SLT, taking a logical OR between all slots:

• DIS slot with good electron candidate

– SLT DIS07

∗ (EREMC or EBEMC > 2.5 GeV) or (EFEMC or EFHAC > 10 GeV),

where FHAC refers to the forward HAC section

∗ At least one FLT slot indicating a DIS event

∗ (E −Pz) + 2×ELumi−γ > 29 GeV, where ELumi−γ is the energy of a

radiated photon detected in the luminosity monitor

∗ An electron candidate with an energy above 5 GeV

• High transverse energy slots

– SLT EXO1

∗ ET > 35 GeV

– SLT EXO2

∗ (ET > 15 GeV and FLT 28) OR

∗ (ET > 25 GeV and E − PZ > 15 GeV)

– SLT EXO3

181

∗ ET > 16 GeV and E − PZ > 34 GeV

The purpose of this combination of triggers was to use the DIS slot for the main

bulk of the NC DIS events, and to use the high ET slots for the highest Q2 events.

Note that the ET sum avoids most of the proton remnant by excluding the FCAL

inner ring of towers.

182

C Comparisons between electron finders

The EM electron finder is the default algorithm used in this thesis, and the SINIS-

TRA electron finder is used to determine a contribution to the systematic uncer-

tainty in the cross sections. This systematic error generally dominates the other

uncertainties discussed in Section 9.3.2, as shown in Figs. (9.5-9.9).

To investigate the cause of this large systematic uncertainty, a number of data

to MC comparisons were made for the variables used in the event selection. A few

of these checks are shown in Fig. (C.1). The electron polar angle (θe) and electron

energy (E ′e) are consistent between the two electron finders, but a noticeable dif-

ference was seen in the distributions of the electron track momentum (P trke ) and

distance of closest approach (DCA) between the energy cluster and endpoint of

the extrapolated track. However, these discrepancies do not affect the measured

cross sections significantly (below 1%), as the differences occur away from the cut

thresholds (P trke > 3 GeV and DCA < 10 cm).

A further check of the electron finders involved determining the amount of

183

PHP contamination in each cross section bin. The percentage amount of PHP

events in the NC e−p DIS single differential cross sections and reduced cross section

(corresponding to the measurements shown in Fig. (10.1) for Q2 > 185 GeV2 and

Fig. (10.10)) is shown in Fig. (C.2). Both electron finders let through approximately

equal amounts of PHP events, with differences of up to 1.5% at high Q2 where the

statistical error is large.

Figure C.1: Data/MC distributions for certain variables involved in the event selec-

tion of NC DIS events, compared between the EM and SINISTRA electron finders

(black and red dots, respectively). The distributions of the electron energy (E ′e),

electron polar angle (θe), electron track momentum (P trke ), and distance of closest

approach (DCA) are shown. An account of these variables is given in Section 8.5.

184

)2 (GeV2Q310 410

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

(y < 0.9)2/dQσdEMSINISTRAData stat. error

)2 (GeV2Q310 410

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

x-210 -110

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

, y < 0.9)2 > 185 GeV2/dx (QσdEMSINISTRAData stat. error

x-210 -110

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

)2 > 185 GeV2/dy (QσdEMSINISTRAData stat. error

y0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

x-Q2 bin number0 10 20 30 40 50 60 70 80 90

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

Reduced cross sectionEMSINISTRAData stat. error

x-Q2 bin number0 10 20 30 40 50 60 70 80 90

PH

P C

on

ten

t (%

)

00.5

11.5

22.5

33.5

44.5

5

Figure C.2: Percentage amount of PHP events in the single differential cross sections

and reduced cross section for the combined 2005/06 e−p data set, compared between

the EM and SINISTRA electron finders (shown in black and red, respectively).

The shaded band corresponds to the statistical uncertainty of the data. The bin

numbering scheme of the reduced cross section is described in Fig. (9.9).

185

D Extracting cross sections using the Electron

method

The Double Angle (DA) reconstruction method was chosen to calculate cross sec-

tions, as discussed in Chapter 5. Therefore, the cross section binning relies on

the angles of the electron and hadronic system. A comparison with the Electron

reconstruction method is useful as it relies entirely on measurements of the scat-

tered electron. The single differential cross sections and the reduced cross section

measured using the Electron method divided by the SM prediction are shown in

Figs. (D.1 - D.3). The differences between the measurements and the SM prediction

are of a similar shape and magnitude to the nominal cross sections calculated using

the DA method (shown in Chapter 10).

186

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=-0.04)e

, P-1p (177.2 pb-05-06 e

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=+0.30)e

, P-1p (71.8 pb-05-06 e

)2 (GeV2Q310 410

/ S

M2

/dQ

σd

0.7

0.8

0.9

1

1.1

1.2

1.3

=-0.27)e

, P-1p (105.4 pb-05-06 e

Figure D.1: Ratio of dσ/dQ2 reconstructed using the Electron method to the SM

prediction. Measurement using all data, and positively or negatively polarised

electrons is shown on the left, top right, and bottom right, respectively. The inner

error bars show the statistical uncertainty, while the outer bars show the statistical

and systematic uncertainties added in quadrature.

187

x-210 -110

/dx

rati

o (

dat

a/S

M)

σd 0.80.850.9

0.951

1.051.1

1.151.2

, y < 0.92 > 185 GeV2Q

= -0.04e

, P-1L=177.2pb = -0.27

e, P-1L=105.4pb

= +0.30e

, P-1L=71.8pb

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

/dy

rati

o (

dat

a/S

M)

σd 0.80.850.9

0.951

1.051.1

1.151.2

2 > 185 GeV2Q

x-110 1

/dx

rati

o (

dat

a/S

M)

σd 0.50.60.70.80.9

11.11.21.31.41.5

, y < 0.92 > 3000 GeV2Q

y0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

/dy

rati

o (

dat

a/S

M)

σd 0.50.60.70.80.9

11.11.21.31.41.5

2 > 3000 GeV2Q

Figure D.2: dσ/dx and dσ/dy reconstructed using the Electron method divided

by the SM prediction is shown on the left and right. Measurements using all

data, negatively polarised data, and positively polarised data are shown as black

squares, red dots, and empty blue circles, respectively. The inner error bars show

the statistical uncertainty, while the outer bars show the statistical and systematic

uncertainties added in quadrature.

188

0.8

1

1.2

1.4 2 = 200 GeV2Q

p) /

SM-

(e

σ~ 0.8

1

1.2

1.4

0.8

1

1.2

1.4 2 = 650 GeV2Q

0.8

1

1.2

1.4

0.6

0.8

1

1.2

1.4 2 = 2000 GeV2Q

0.6

0.8

1

1.2

1.4

-210 -1100.6

0.8

1

1.2

1.4 2 = 12000 GeV2Q

-210 -1100.6

0.8

1

1.2

1.4

2 = 250 GeV2Q

2 = 800 GeV2Q

2 = 3000 GeV2Q

-210 -110

2 = 20000 GeV2Q

-210 -110

2 = 350 GeV2Q

2 = 1200 GeV2Q

2 = 5000 GeV2Q

-210 -110

2 = 30000 GeV2Q

x-210 -110

2 = 450 GeV2Q

2 = 1500 GeV2Q

2 = 8000 GeV2Q

)-1p (177.2 pb- 05-06 e

= 0e P

)-1p (105.4 pb- 05-06 e

= -0.27e P

)-1p (71.8 pb- 05-06 e

= +0.30e P

SM uncertainty

Figure D.3: Reduced cross sections reconstructed using the Electron method di-

vided by the SM prediction. Measurements using all data, negatively polarised data,

and positively polarised data are shown as black squares, red dots, and empty blue

circles, respectively. The inner error bars show the statistical uncertainty, while the

outer bars show the statistical and systematic uncertainties added in quadrature.

The shaded band corresponds to the uncertainty on the SM prediction.

189

E Tables of Results

The single-differential cross sections, polarisation asymmetry, reduced cross sec-

tions, and structure functions are tabulated in the following pages.

190

x range xc dσ/dx ( pb) Ndata NMC Nbg

Measured SM

0.0063 - 0.01 0.00794 (8.94 ± 0.04 +0.18−0.16 )·104 8.70 ·104 42010 42018 110

0.01 - 0.016 0.0126 (5.90 ± 0.03 +0.10−0.10 )·104 5.92 ·104 51117 51458 103

0.016 - 0.025 0.02 (3.59 ± 0.02 +0.06−0.05 )·104 3.69 ·104 51564 52920 77

0.025 - 0.04 0.0316 (2.09 ± 0.01 +0.03−0.03 )·104 2.21 ·104 52723 55383 46

0.04 - 0.063 0.0501 (1.25 ± 0.01 +0.02−0.01 )·104 1.27 ·104 43641 44588 15

0.063 - 0.1 0.0794 (7.11 ± 0.04 +0.10−0.09 )·103 7.18 ·103 39572 40216 7

0.1 - 0.16 0.126 (4.00 ± 0.02 +0.08−0.08 )·103 3.96 ·103 36022 35746 2

0.16 - 0.25 0.2 (2.07 ± 0.01 +0.06−0.05 )·103 2.07 ·103 20020 19903 2

Table E.1: The single differential cross section dσ/dx for for Q2 > 185 GeV2 measured using the combined 05-06e−p data set (L = 177.2 pb−1, Pe = −0.04). The first (second) error on the measured cross section refers tothe statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFsare given. The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg

respectively. The subscript c indicates the bin centre.

191


Measured SM

0.0063 - 0.01 0.00794 (8.94 ± 0.06 +0.18−0.16 )·104 8.75 ·104 24976 24980 65

0.01 - 0.016 0.0126 (5.91 ± 0.03 +0.10−0.10 )·104 5.96 ·104 30469 30592 61

0.016 - 0.025 0.02 (3.61 ± 0.02 +0.06−0.05 )·104 3.72 ·104 30814 31460 46

0.025 - 0.04 0.0316 (2.11 ± 0.01 +0.03−0.03 )·104 2.22 ·104 31652 32926 27

0.04 - 0.063 0.0501 (1.26 ± 0.01 +0.02−0.01 )·104 1.28 ·104 26267 26509 9

0.063 - 0.1 0.0794 (7.21 ± 0.05 +0.10−0.09 )·103 7.24 ·103 23864 23903 4

0.1 - 0.16 0.126 (4.07 ± 0.03 +0.08−0.08 )·103 4.00 ·103 21732 21243 1

0.16 - 0.25 0.2 (2.11 ± 0.02 +0.06−0.05 )·103 2.09 ·103 12173 11839 1

Table E.2: The single differential cross section dσ/dx for for Q2 > 185 GeV2 measured using the negativelypolarised 05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27). The first (second) error on the measured crosssection refers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM usingZEUS-JETS PDFs are given. The number of observed data, MC and PHP background events are given as Ndata,NMC and Nbg respectively. The subscript c indicates the bin centre.

192


Measured SM

0.0063 - 0.01 0.00794 (8.93 ± 0.07 +0.18−0.16 )·104 8.62 ·104 17034 17042 45

0.01 - 0.016 0.0126 (5.87 ± 0.04 +0.10−0.10 )·104 5.86 ·104 20648 20870 42

0.016 - 0.025 0.02 (3.56 ± 0.02 +0.06−0.05 )·104 3.65 ·104 20750 21464 31

0.025 - 0.04 0.0316 (2.06 ± 0.01 +0.03−0.03 )·104 2.18 ·104 21071 22461 19

0.04 - 0.063 0.0501 (1.22 ± 0.01 +0.02−0.01 )·104 1.26 ·104 17374 18082 6

0.063 - 0.1 0.0794 (6.96 ± 0.06 +0.09−0.09 )·103 7.08 ·103 15708 16315 3

0.1 - 0.16 0.126 (3.92 ± 0.03 +0.07−0.07 )·103 3.91 ·103 14290 14504 1

0.16 - 0.25 0.2 (2.00 ± 0.02 +0.06−0.04 )·103 2.04 ·103 7847 8067 1

Table E.3: The single differential cross section dσ/dx for for Q2 > 185 GeV2 measured using the positivelypolarised 05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross sectionrefers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETSPDFs are given. The number of observed data, MC and PHP background events are given as Ndata, NMC andNbg respectively. The subscript c indicates the bin centre.

193


Measured SM

0.04 - 0.063 0.0501 (1.97 ± 0.08 +0.15−0.15 )·102 2.05 ·102 680 726 6

0.063 - 0.1 0.0794 (2.14 ± 0.06 +0.07−0.06 )·102 2.14 ·102 1270 1290 3

0.1 - 0.16 0.126 (1.64 ± 0.04 +0.03−0.03 )·102 1.59 ·102 1619 1582 0

0.16 - 0.25 0.2 (9.56 ± 0.26 +0.13−0.13 )·10 9.56 ·10 1385 1380 2

0.25 - 0.4 0.316 (4.29 ± 0.14 +0.05−0.06 )·10 4.39 ·10 998 1000 2

0.4 - 0.63 0.501 (1.05 ± 0.05 +0.04−0.03 )·10 1.07 ·10 372 363 0

0.63 - 1 0.794 (2.29 +0.50−0.42

+0.17−0.12 )·10−1 2.75 ·10−1 30 32 0

Table E.4: The single differential cross section dσ/dx for for Q2 > 3000 GeV2 measured using the combined 05-06e−p data set (L = 177.2 pb−1, Pe = −0.04). The first (second) error on the measured cross section refers tothe statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFsare given. The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg


194


Measured SM

0.04 - 0.063 0.0501 (2.08 ± 0.10 +0.16−0.16 )·102 2.14 ·102 427 432 4

0.063 - 0.1 0.0794 (2.23 ± 0.08 +0.07−0.06 )·102 2.24 ·102 784 767 2

0.1 - 0.16 0.126 (1.72 ± 0.05 +0.03−0.03 )·102 1.66 ·102 1011 941 0

0.16 - 0.25 0.2 (9.90 ± 0.34 +0.14−0.14 )·10 10.02 ·10 852 821 1

0.25 - 0.4 0.316 (4.32 ± 0.18 +0.05−0.06 )·10 4.60 ·10 597 594 1

0.4 - 0.63 0.501 (1.06 ± 0.07 +0.04−0.03 )·10 1.12 ·10 222 216 0

0.63 - 1 0.794 (1.80 +0.62−0.48

+0.13−0.10 )·10−1 2.87 ·10−1 14 19 0

Table E.5: The single differential cross section dσ/dx for for Q2 > 3000 GeV2 measured using the negativelypolarised 05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27). The first (second) error on the measured crosssection refers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM usingZEUS-JETS PDFs are given. The number of observed data, MC and PHP background events are given as Ndata,NMC and Nbg respectively. The subscript c indicates the bin centre.

195


Measured SM

0.04 - 0.063 0.0501 (1.80 ± 0.11 +0.14−0.14 )·102 1.92 ·102 253 294 2

0.063 - 0.1 0.0794 (2.02 ± 0.09 +0.06−0.06 )·102 2.00 ·102 486 523 1

0.1 - 0.16 0.126 (1.51 ± 0.06 +0.03−0.03 )·102 1.48 ·102 608 642 0

0.16 - 0.25 0.2 (9.08 ± 0.39 +0.12−0.12 )·10 8.90 ·10 533 560 1

0.25 - 0.4 0.316 (4.25 ± 0.21 +0.05−0.06 )·10 4.09 ·10 401 405 1

0.4 - 0.63 0.501 (1.05 ± 0.09 +0.04−0.03 )·10 1.00 ·10 150 147 0

0.63 - 1 0.794 (3.01 +0.95−0.74

+0.22−0.16 )·10−1 2.57 ·10−1 16 13 0

Table E.6: The single differential cross section dσ/dx for for Q2 > 3000 GeV2 measured using the positivelypolarised 05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross sectionrefers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETSPDFs are given. The number of observed data, MC and PHP background events are given as Ndata, NMC andNbg respectively. The subscript c indicates the bin centre.

196

y range yc dσ/dy ( pb) Ndata NMC Nbg

Measured SM

0 - 0.05 0.025 (1.64 ± 0.01 +0.04−0.03 )·104 1.64 ·104 81352 81263 0

0.05 - 0.1 0.075 (8.03 ± 0.03 +0.11−0.10 )·103 8.35 ·103 66579 69198 9

0.1 - 0.15 0.125 (5.60 ± 0.03 +0.08−0.07 )·103 5.80 ·103 46442 47990 7

0.15 - 0.2 0.175 (4.35 ± 0.02 +0.06−0.05 )·103 4.47 ·103 34213 35042 17

0.2 - 0.25 0.225 (3.58 ± 0.02 +0.05−0.05 )·103 3.63 ·103 26799 27236 17

0.25 - 0.3 0.275 (3.03 ± 0.02 +0.04−0.04 )·103 3.04 ·103 21779 21995 22

0.3 - 0.35 0.325 (2.65 ± 0.02 +0.05−0.05 )·103 2.60 ·103 18436 18361 18

0.35 - 0.4 0.375 (2.30 ± 0.02 +0.04−0.04 )·103 2.26 ·103 15478 15473 18

0.4 - 0.45 0.425 (2.03 ± 0.02 +0.04−0.04 )·103 1.99 ·103 13032 13061 16

0.45 - 0.5 0.475 (1.82 ± 0.02 +0.03−0.03 )·103 1.77 ·103 11501 11541 28

0.5 - 0.55 0.525 (1.63 ± 0.02 +0.04−0.04 )·103 1.59 ·103 10136 10237 33

0.55 - 0.6 0.575 (1.51 ± 0.02 +0.04−0.03 )·103 1.43 ·103 9045 8915 47

0.6 - 0.65 0.625 (1.37 ± 0.02 +0.05−0.04 )·103 1.30 ·103 7654 7673 57

0.65 - 0.7 0.675 (1.28 ± 0.02 +0.07−0.05 )·103 1.19 ·103 6247 6197 42

0.7 - 0.75 0.725 (1.16 ± 0.02 +0.10−0.09 )·103 1.10 ·103 4618 4695 39

Table E.7: The single differential cross section dσ/dy for for Q2 > 185 GeV2 measured using the combined 05-06e−p data set (L = 177.2 pb−1, Pe = −0.04). The first (second) error on the measured cross section refers tothe statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFsare given. The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg


197


Measured SM

0 - 0.05 0.025 (1.66 ± 0.01 +0.04−0.03 )·104 1.65 ·104 48952 48311 0

0.05 - 0.1 0.075 (8.14 ± 0.04 +0.11−0.10 )·103 8.41 ·103 40131 41144 5

0.1 - 0.15 0.125 (5.62 ± 0.03 +0.08−0.07 )·103 5.84 ·103 27702 28530 4

0.15 - 0.2 0.175 (4.41 ± 0.03 +0.06−0.05 )·103 4.51 ·103 20597 20833 10

0.2 - 0.25 0.225 (3.56 ± 0.03 +0.05−0.05 )·103 3.66 ·103 15855 16192 10

0.25 - 0.3 0.275 (3.04 ± 0.03 +0.04−0.04 )·103 3.06 ·103 13009 13075 13

0.3 - 0.35 0.325 (2.66 ± 0.03 +0.05−0.05 )·103 2.62 ·103 10991 10915 11

0.35 - 0.4 0.375 (2.31 ± 0.02 +0.04−0.04 )·103 2.28 ·103 9240 9198 11

0.4 - 0.45 0.425 (2.05 ± 0.02 +0.04−0.04 )·103 2.01 ·103 7831 7765 10

0.45 - 0.5 0.475 (1.82 ± 0.02 +0.03−0.03 )·103 1.79 ·103 6836 6861 16

0.5 - 0.55 0.525 (1.65 ± 0.02 +0.04−0.04 )·103 1.60 ·103 6072 6086 19

0.55 - 0.6 0.575 (1.53 ± 0.02 +0.04−0.03 )·103 1.45 ·103 5432 5299 28

0.6 - 0.65 0.625 (1.40 ± 0.02 +0.05−0.04 )·103 1.31 ·103 4670 4561 34

0.65 - 0.7 0.675 (1.28 ± 0.02 +0.07−0.05 )·103 1.20 ·103 3729 3683 25

0.7 - 0.75 0.725 (1.17 ± 0.02 +0.10−0.09 )·103 1.11 ·103 2766 2790 23

Table E.8: The single differential cross section dσ/dy for for Q2 > 185 GeV2 measured using the negativelypolarised 05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27). The first (second) error on the measured crosssection refers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM usingZEUS-JETS PDFs are given. The number of observed data, MC and PHP background events are given as Ndata,NMC and Nbg respectively. The subscript c indicates the bin centre.

198


Measured SM

0 - 0.05 0.025 (1.61 ± 0.01 +0.04−0.03 )·104 1.63 ·104 32400 32958 0

0.05 - 0.1 0.075 (7.86 ± 0.05 +0.11−0.10 )·103 8.27 ·103 26448 28060 4

0.1 - 0.15 0.125 (5.57 ± 0.04 +0.08−0.07 )·103 5.74 ·103 18740 19464 3

0.15 - 0.2 0.175 (4.27 ± 0.04 +0.06−0.05 )·103 4.42 ·103 13616 14212 7

0.2 - 0.25 0.225 (3.60 ± 0.03 +0.05−0.05 )·103 3.58 ·103 10944 11046 7

0.25 - 0.3 0.275 (3.01 ± 0.03 +0.04−0.04 )·103 3.00 ·103 8770 8922 9

0.3 - 0.35 0.325 (2.64 ± 0.03 +0.05−0.05 )·103 2.57 ·103 7445 7448 7

0.35 - 0.4 0.375 (2.29 ± 0.03 +0.04−0.04 )·103 2.23 ·103 6238 6276 7

0.4 - 0.45 0.425 (2.00 ± 0.03 +0.04−0.04 )·103 1.97 ·103 5201 5298 7

0.45 - 0.5 0.475 (1.82 ± 0.03 +0.03−0.03 )·103 1.75 ·103 4665 4681 11

0.5 - 0.55 0.525 (1.61 ± 0.03 +0.04−0.04 )·103 1.57 ·103 4064 4152 13

0.55 - 0.6 0.575 (1.49 ± 0.02 +0.03−0.03 )·103 1.41 ·103 3613 3616 19

0.6 - 0.65 0.625 (1.31 ± 0.02 +0.05−0.04 )·103 1.28 ·103 2984 3112 23

0.65 - 0.7 0.675 (1.27 ± 0.03 +0.07−0.05 )·103 1.17 ·103 2518 2514 17

0.7 - 0.75 0.725 (1.15 ± 0.03 +0.10−0.09 )·103 1.08 ·103 1852 1905 16

Table E.9: The single differential cross section dσ/dy for for Q2 > 185 GeV2 measured using the positivelypolarised 05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross sectionrefers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETSPDFs are given. The number of observed data, MC and PHP background events are given as Ndata, NMC andNbg respectively. The subscript c indicates the bin centre.

199


Measured SM

0.05 - 0.1 0.075 (3.47 ± 0.22 +0.07−0.05 )·10 3.40 ·10 255 240 0

0.1 - 0.15 0.125 (6.19 ± 0.28 +0.17−0.16 )·10 6.48 ·10 481 490 2

0.15 - 0.2 0.175 (6.67 ± 0.29 +0.06−0.06 )·10 7.06 ·10 528 552 0

0.2 - 0.25 0.225 (6.40 ± 0.28 +0.06−0.08 )·10 6.85 ·10 539 571 0

0.25 - 0.3 0.275 (6.39 ± 0.27 +0.11−0.11 )·10 6.42 ·10 552 552 0

0.3 - 0.35 0.325 (6.10 ± 0.27 +0.06−0.06 )·10 5.95 ·10 525 512 0

0.35 - 0.4 0.375 (5.20 ± 0.25 +0.23−0.23 )·10 5.50 ·10 443 470 0

0.4 - 0.45 0.425 (5.38 ± 0.25 +0.08−0.07 )·10 5.09 ·10 464 439 0

0.45 - 0.5 0.475 (5.24 ± 0.25 +0.13−0.14 )·10 4.72 ·10 442 400 0

0.5 - 0.55 0.525 (4.31 ± 0.23 +0.08−0.08 )·10 4.39 ·10 359 369 0

0.55 - 0.6 0.575 (4.29 ± 0.23 +0.10−0.10 )·10 4.09 ·10 347 336 0

0.6 - 0.65 0.625 (3.90 ± 0.22 +0.12−0.12 )·10 3.83 ·10 312 310 0

0.65 - 0.7 0.675 (4.01 ± 0.23 +0.13−0.09 )·10 3.59 ·10 313 285 1

0.7 - 0.75 0.725 (3.08 ± 0.20 +0.27−0.26 )·10 3.39 ·10 235 265 0

0.75 - 0.8 0.775 (3.22 ± 0.21 +0.39−0.39 )·10 3.20 ·10 236 242 0

0.8 - 0.85 0.825 (3.00 ± 0.21 +0.56−0.56 )·10 3.04 ·10 212 221 2

0.85 - 0.9 0.875 (2.73 ± 0.21 +0.27−0.26 )·10 2.89 ·10 183 194 7

Table E.10: The single differential cross section dσ/dy for for Q2 > 3000 GeV2 measured using the combined05-06 e−p data set (L = 177.2 pb−1, Pe = −0.04). The first (second) error on the measured cross section refersto the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFsare given. The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg


200


Measured SM

0.05 - 0.1 0.075 (3.73 ± 0.29 +0.08−0.06 )·10 3.51 ·10 163 142 0

0.1 - 0.15 0.125 (5.78 ± 0.35 +0.16−0.15 )·10 6.72 ·10 267 291 1

0.15 - 0.2 0.175 (6.92 ± 0.38 +0.06−0.06 )·10 7.35 ·10 326 328 0

0.2 - 0.25 0.225 (6.67 ± 0.37 +0.06−0.08 )·10 7.14 ·10 334 340 0

0.25 - 0.3 0.275 (6.68 ± 0.36 +0.11−0.12 )·10 6.71 ·10 343 328 0

0.3 - 0.35 0.325 (6.25 ± 0.35 +0.07−0.06 )·10 6.22 ·10 320 304 0

0.35 - 0.4 0.375 (5.02 ± 0.31 +0.22−0.22 )·10 5.76 ·10 254 279 0

0.4 - 0.45 0.425 (5.87 ± 0.34 +0.08−0.08 )·10 5.33 ·10 301 261 0

0.45 - 0.5 0.475 (5.46 ± 0.33 +0.13−0.14 )·10 4.95 ·10 274 238 0

0.5 - 0.55 0.525 (4.48 ± 0.30 +0.08−0.09 )·10 4.60 ·10 222 220 0

0.55 - 0.6 0.575 (4.64 ± 0.31 +0.10−0.11 )·10 4.29 ·10 223 200 0

0.6 - 0.65 0.625 (4.10 ± 0.29 +0.13−0.13 )·10 4.02 ·10 195 184 0

0.65 - 0.7 0.675 (4.22 ± 0.30 +0.14−0.10 )·10 3.77 ·10 196 169 1

0.7 - 0.75 0.725 (3.17 ± 0.26 +0.27−0.27 )·10 3.56 ·10 144 157 0

0.75 - 0.8 0.775 (3.49 ± 0.28 +0.42−0.42 )·10 3.36 ·10 152 144 0

0.8 - 0.85 0.825 (3.05 ± 0.27 +0.56−0.57 )·10 3.19 ·10 128 131 1

0.85 - 0.9 0.875 (2.73 ± 0.27 +0.27−0.26 )·10 3.04 ·10 109 115 4

Table E.11: The single differential cross section dσ/dy for for Q2 > 3000 GeV2 measured using the negativelypolarised 05-06 e−p data set (L = 105.4 pb−1, Pe = −0.27). The first (second) error on the measured cross sectionrefers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETSPDFs are given. The number of observed data, MC and PHP background events are given as Ndata, NMC andNbg respectively. The subscript c indicates the bin centre.

201


Measured SM

0.05 - 0.1 0.075 (3.08 +0.36−0.32

+0.07−0.05 )·10 3.23 ·10 92 97 0

0.1 - 0.15 0.125 (6.79 ± 0.47 +0.19−0.18 )·10 6.11 ·10 214 199 1

0.15 - 0.2 0.175 (6.29 ± 0.44 +0.06−0.06 )·10 6.64 ·10 202 224 0

0.2 - 0.25 0.225 (6.01 ± 0.42 +0.06−0.07 )·10 6.42 ·10 205 232 0

0.25 - 0.3 0.275 (5.96 ± 0.41 +0.10−0.11 )·10 6.00 ·10 209 224 0

0.3 - 0.35 0.325 (5.87 ± 0.41 +0.06−0.05 )·10 5.55 ·10 205 207 0

0.35 - 0.4 0.375 (5.47 ± 0.40 +0.24−0.24 )·10 5.12 ·10 189 191 0

0.4 - 0.45 0.425 (4.66 ± 0.37 +0.07−0.06 )·10 4.73 ·10 163 178 0

0.45 - 0.5 0.475 (4.91 ± 0.38 +0.12−0.13 )·10 4.38 ·10 168 162 0

0.5 - 0.55 0.525 (4.05 ± 0.35 +0.07−0.08 )·10 4.07 ·10 137 150 0

0.55 - 0.6 0.575 (3.78 ± 0.34 +0.09−0.09 )·10 3.79 ·10 124 136 0

0.6 - 0.65 0.625 (3.60 ± 0.33 +0.11−0.11 )·10 3.55 ·10 117 126 0

0.65 - 0.7 0.675 (3.69 ± 0.34 +0.12−0.08 )·10 3.33 ·10 117 116 1

0.7 - 0.75 0.725 (2.94 +0.34−0.31

+0.25−0.25 )·10 3.13 ·10 91 107 0

0.75 - 0.8 0.775 (2.82 +0.34−0.31

+0.34−0.34 )·10 2.96 ·10 84 98 0

0.8 - 0.85 0.825 (2.93 +0.36−0.32

+0.54−0.55 )·10 2.81 ·10 84 90 1

0.85 - 0.9 0.875 (2.72 +0.37−0.33

+0.27−0.26 )·10 2.67 ·10 74 79 3

Table E.12: The single differential cross section dσ/dy for for Q2 > 3000 GeV2 measured using the positivelypolarised 05-06 e−p data set (L = 71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross sectionrefers to the statistical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETSPDFs are given. The number of observed data, MC and PHP background events are given as Ndata, NMC andNbg respectively. The subscript c indicates the bin centre.

202

Q2 range Q2c dσ/dQ2 ( pb/ GeV2) Ndata NMC Nbg

( GeV2) ( GeV2) Measured SM

185 - 210 195 19.74 ± 0.08 +0.30−0.27 19.65 61789 62560 35

210 - 240 220 14.84 ± 0.06 +0.22−0.20 14.78 54392 55088 31

240 - 270 255 10.24 ± 0.05 +0.18−0.16 10.42 39689 40947 35

270 - 300 285 8.01 ± 0.05 +0.14−0.13 8.00 30991 31422 27

300 - 340 320 6.00 ± 0.03 +0.11−0.09 6.06 30985 31658 32

340 - 380 360 4.57 ± 0.03 +0.08−0.07 4.57 23493 23773 24

380 - 430 400 3.54 ± 0.02 +0.06−0.05 3.54 22125 22430 23

430 - 480 450 2.66 ± 0.02 +0.05−0.04 2.66 16268 16481 21

480 - 540 510 1.94 ± 0.02 +0.04−0.04 1.96 14060 14356 23

540 - 600 570 1.47 ± 0.01 +0.03−0.03 1.49 9785 10070 13

600 - 670 630 1.17 ± 0.01 +0.02−0.02 1.17 8848 8926 20

670 - 740 700 (9.03 ± 0.10 +0.13−0.12 )·10−1 9.01 ·10−1 7884 7962 13

740 - 820 780 (6.94 ± 0.08 +0.09−0.08 )·10−1 6.89 ·10−1 7990 7990 27

820 - 900 860 (5.41 ± 0.07 +0.08−0.07 )·10−1 5.40 ·10−1 6598 6643 10

900 - 990 940 (4.29 ± 0.06 +0.06−0.06 )·10−1 4.35 ·10−1 5980 6070 14

990 - 1080 1030 (3.49 ± 0.05 +0.05−0.05 )·10−1 3.45 ·10−1 4886 4853 21

1080 - 1200 1130 (2.78 ± 0.04 +0.05−0.04 )·10−1 2.73 ·10−1 5198 5147 27

Table E.13: The single differential cross section dσ/dQ2 measured using the combined 05-06 e−p data set(L = 177.2 pb−1, Pe = −0.04). The first (second) error on the measured cross section refers to the statisti-cal (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given.The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg respectively.The subscript c indicates the bin centre. This table is continued in Table E.14.

203



1200 - 1350 1270 (2.06 ± 0.03 +0.03−0.03 )·10−1 2.04 ·10−1 4896 4879 13

1350 - 1500 1420 (1.52 ± 0.03 +0.03−0.02 )·10−1 1.54 ·10−1 3680 3733 11

1500 - 1700 1590 (1.14 ± 0.02 +0.01−0.01 )·10−1 1.15 ·10−1 3642 3693 12

1700 - 1900 1790 (8.51 ± 0.16 +0.15−0.15 )·10−2 8.54 ·10−2 2737 2755 15

1900 - 2100 1990 (6.30 ± 0.14 +0.09−0.08 )·10−2 6.51 ·10−2 2051 2124 9

2100 - 2600 2300 (4.41 ± 0.08 +0.09−0.09 )·10−2 4.50 ·10−2 3467 3545 17

2600 - 3200 2800 (2.72 ± 0.05 +0.06−0.06 )·10−2 2.70 ·10−2 2476 2481 5

3200 - 3900 3500 (1.49 ± 0.04 +0.04−0.04 )·10−2 1.52 ·10−2 1674 1714 5

3900 - 4700 4200 (9.46 ± 0.28 +0.23−0.22 )·10−3 9.50 ·10−3 1179 1182 3

4700 - 5600 5100 (5.18 ± 0.19 +0.13−0.12 )·10−3 5.72 ·10−3 749 825 0

5600 - 6600 6050 (3.87 ± 0.16 +0.08−0.08 )·10−3 3.60 ·10−3 619 577 2

6600 - 7800 7100 (2.35 ± 0.11 +0.07−0.07 )·10−3 2.33 ·10−3 438 436 1

7800 - 9200 8400 (1.62 ± 0.09 +0.05−0.05 )·10−3 1.47 ·10−3 349 318 0

9200 - 12800 10800 (7.11 ± 0.36 +0.20−0.20 )·10−4 7.16 ·10−4 390 392 0

12800 - 18100 15200 (2.49 ± 0.18 +0.15−0.15 )·10−4 2.47 ·10−4 201 199 0

18100 - 25600 21500 (0.85 ± 0.08 +0.07−0.07 )·10−4 0.71 ·10−4 104 87 2

25600 - 51200 36200 (0.69 +0.13−0.11

+0.07−0.04 )·10−5 0.63 ·10−5 39 36 0

Table E.14: Continuation of Table E.13.

204



185 - 210 195 19.77 ± 0.10 +0.30−0.27 19.71 36795 37196 21

210 - 240 220 14.87 ± 0.08 +0.22−0.20 14.84 32417 32756 19

240 - 270 255 10.28 ± 0.07 +0.18−0.16 10.47 23682 24344 21

270 - 300 285 8.07 ± 0.06 +0.15−0.14 8.03 18582 18683 16

300 - 340 320 6.05 ± 0.04 +0.11−0.10 6.09 18560 18821 19

340 - 380 360 4.61 ± 0.04 +0.08−0.07 4.59 14076 14133 14

380 - 430 400 3.53 ± 0.03 +0.06−0.05 3.56 13127 13337 14

430 - 480 450 2.70 ± 0.03 +0.05−0.04 2.68 9813 9800 12

480 - 540 510 1.98 ± 0.02 +0.04−0.04 1.98 8534 8538 13

540 - 600 570 1.47 ± 0.02 +0.03−0.03 1.51 5852 5991 8

600 - 670 630 1.18 ± 0.02 +0.02−0.02 1.18 5285 5305 12

670 - 740 700 (9.23 ± 0.13 +0.13−0.12 )·10−1 9.11 ·10−1 4781 4723 8

740 - 820 780 (7.16 ± 0.10 +0.09−0.08 )·10−1 6.97 ·10−1 4894 4741 16

820 - 900 860 (5.53 ± 0.09 +0.08−0.07 )·10−1 5.47 ·10−1 4008 3946 6

900 - 990 940 (4.41 ± 0.07 +0.07−0.06 )·10−1 4.41 ·10−1 3647 3608 8

990 - 1080 1030 (3.57 ± 0.07 +0.05−0.05 )·10−1 3.50 ·10−1 2974 2885 12

1080 - 1200 1130 (2.84 ± 0.05 +0.05−0.04 )·10−1 2.78 ·10−1 3159 3060 16

Table E.15: The single differential cross section dσ/dQ2 measured using the negatively polarised 05-06 e−p dataset (L = 105.4 pb−1, Pe = −0.27). The first (second) error on the measured cross section refers to the statistical(systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given. Thenumber of observed data, MC and PHP background events are given as Ndata, NMC and Nbg respectively. Thesubscript c indicates the bin centre. This table is continued in Table E.16.

205



1200 - 1350 1270 (2.10 ± 0.04 +0.03−0.03 )·10−1 2.08 ·10−1 2969 2901 8

1350 - 1500 1420 (1.54 ± 0.03 +0.03−0.02 )·10−1 1.57 ·10−1 2211 2220 6

1500 - 1700 1590 (1.17 ± 0.02 +0.01−0.01 )·10−1 1.18 ·10−1 2225 2196 7

1700 - 1900 1790 (8.55 ± 0.21 +0.15−0.15 )·10−2 8.74 ·10−2 1636 1638 9

1900 - 2100 1990 (6.32 ± 0.18 +0.09−0.08 )·10−2 6.68 ·10−2 1224 1263 5

2100 - 2600 2300 (4.47 ± 0.10 +0.09−0.09 )·10−2 4.63 ·10−2 2093 2108 10

2600 - 3200 2800 (2.79 ± 0.07 +0.06−0.06 )·10−2 2.79 ·10−2 1510 1475 3

3200 - 3900 3500 (1.52 ± 0.05 +0.04−0.04 )·10−2 1.58 ·10−2 1018 1019 3

3900 - 4700 4200 (9.76 ± 0.36 +0.24−0.22 )·10−3 9.90 ·10−3 723 703 2

4700 - 5600 5100 (5.45 ± 0.25 +0.13−0.13 )·10−3 5.99 ·10−3 469 491 0

5600 - 6600 6050 (4.00 ± 0.21 +0.08−0.09 )·10−3 3.78 ·10−3 381 343 1

6600 - 7800 7100 (2.41 ± 0.15 +0.07−0.07 )·10−3 2.46 ·10−3 267 259 1

7800 - 9200 8400 (1.67 ± 0.11 +0.05−0.05 )·10−3 1.55 ·10−3 214 189 0

9200 - 12800 10800 (7.51 ± 0.48 +0.21−0.21 )·10−4 7.60 ·10−4 245 233 0

12800 - 18100 15200 (2.38 ± 0.22 +0.14−0.15 )·10−4 2.64 ·10−4 114 118 0

18100 - 25600 21500 (0.91 +0.13−0.11

+0.07−0.07 )·10−4 0.76 ·10−4 66 51 1

25600 - 51200 36200 (0.77 +0.18−0.15

+0.08−0.04 )·10−5 0.67 ·10−5 26 22 0


206



185 - 210 195 19.69 ± 0.12 +0.30−0.27 19.55 24994 25369 14

210 - 240 220 14.78 ± 0.10 +0.22−0.20 14.70 21975 22337 13

240 - 270 255 10.18 ± 0.08 +0.18−0.16 10.35 16007 16606 14

270 - 300 285 7.90 ± 0.07 +0.14−0.13 7.94 12409 12742 11

300 - 340 320 5.94 ± 0.05 +0.11−0.09 6.01 12425 12840 13

340 - 380 360 4.52 ± 0.05 +0.08−0.07 4.53 9417 9643 10

380 - 430 400 3.55 ± 0.04 +0.06−0.05 3.51 8998 9096 9

430 - 480 450 2.60 ± 0.03 +0.05−0.04 2.63 6455 6683 8

480 - 540 510 1.88 ± 0.03 +0.04−0.04 1.94 5526 5820 9

540 - 600 570 1.45 ± 0.02 +0.03−0.03 1.47 3933 4080 5

600 - 670 630 1.16 ± 0.02 +0.02−0.02 1.15 3563 3622 8

670 - 740 700 (8.73 ± 0.16 +0.12−0.11 )·10−1 8.86 ·10−1 3103 3238 5

740 - 820 780 (6.61 ± 0.12 +0.09−0.07 )·10−1 6.77 ·10−1 3096 3248 11

820 - 900 860 (5.23 ± 0.10 +0.08−0.07 )·10−1 5.29 ·10−1 2590 2697 4

900 - 990 940 (4.13 ± 0.09 +0.06−0.06 )·10−1 4.25 ·10−1 2333 2463 6

990 - 1080 1030 (3.36 ± 0.08 +0.05−0.04 )·10−1 3.37 ·10−1 1912 1969 8

1080 - 1200 1130 (2.68 ± 0.06 +0.05−0.04 )·10−1 2.67 ·10−1 2039 2088 11

Table E.17: The single differential cross section dσ/dQ2 measured using the positively polarised 05-06 e−p dataset (L = 71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross section refers to the statistical(systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given. Thenumber of observed data, MC and PHP background events are given as Ndata, NMC and Nbg respectively. Thesubscript c indicates the bin centre. This table is continued in Table E.18.

207



1200 - 1350 1270 (2.00 ± 0.05 +0.03−0.03 )·10−1 1.98 ·10−1 1927 1979 6

1350 - 1500 1420 (1.50 ± 0.04 +0.02−0.02 )·10−1 1.49 ·10−1 1469 1514 4

1500 - 1700 1590 (1.10 ± 0.03 +0.01−0.01 )·10−1 1.12 ·10−1 1417 1497 5

1700 - 1900 1790 (8.44 ± 0.26 +0.15−0.15 )·10−2 8.23 ·10−2 1101 1117 6

1900 - 2100 1990 (6.26 ± 0.22 +0.09−0.08 )·10−2 6.26 ·10−2 827 862 4

2100 - 2600 2300 (4.31 ± 0.12 +0.09−0.09 )·10−2 4.31 ·10−2 1374 1438 7

2600 - 3200 2800 (2.61 ± 0.08 +0.06−0.06 )·10−2 2.57 ·10−2 966 1006 2

3200 - 3900 3500 (1.44 ± 0.06 +0.04−0.04 )·10−2 1.44 ·10−2 656 695 2

3900 - 4700 4200 (9.02 ± 0.42 +0.22−0.21 )·10−3 8.91 ·10−3 456 479 1

4700 - 5600 5100 (4.77 ± 0.29 +0.12−0.11 )·10−3 5.33 ·10−3 280 335 0

5600 - 6600 6050 (3.67 ± 0.24 +0.08−0.08 )·10−3 3.34 ·10−3 238 234 1

6600 - 7800 7100 (2.26 ± 0.17 +0.07−0.07 )·10−3 2.15 ·10−3 171 177 1

7800 - 9200 8400 (1.54 ± 0.13 +0.05−0.05 )·10−3 1.34 ·10−3 135 129 0

9200 - 12800 10800 (6.51 ± 0.54 +0.18−0.18 )·10−4 6.50 ·10−4 145 159 0

12800 - 18100 15200 (2.66 +0.32−0.28

+0.16−0.16 )·10−4 2.23 ·10−4 87 81 0

18100 - 25600 21500 (0.77 +0.15−0.13

+0.06−0.06 )·10−4 0.64 ·10−4 38 35 1

25600 - 51200 36200 (0.56 +0.20−0.15

+0.06−0.03 )·10−5 0.55 ·10−5 13 15 0


208

Q2 range Q2c Polarisation asymmetry


185 - 300 250 (-1.49 ± 0.83 )·10−2 -1.84 ·10−2

300 - 400 350 (-2.46 ± 1.41 )·10−2 -2.53 ·10−2

400 - 475.7 440 (-3.60 ± 2.16 )·10−2 -3.14 ·10−2

475.7 - 565.7 520 (-8.22 ± 2.54 )·10−2 -3.66 ·10−2

565.7 - 672.7 620 (-0.52 ± 2.99 )·10−2 -4.30 ·10−2

672.7 - 800 730 (-12.09 ± 3.07 )·10−2 -4.98 ·10−2

800 - 1050 900 (-10.36 ± 2.68 )·10−2 -5.99 ·10−2

1050 - 1460 1230 (-9.71 ± 2.99 )·10−2 -7.83 ·10−2

1460 - 2080 1730 (-6.16 ± 3.75 )·10−2 -10.33 ·10−2

2080 - 3120 2500 (-8.78 ± 4.69 )·10−2 -13.55 ·10−2

3120 - 5220 3900 (-1.55 ± 0.60 )·10−1 -1.78 ·10−1

5220 - 12500 7000 (-1.24 ± 0.79 )·10−1 -2.34 ·10−1

12500 - 51200 22400 (0.23 ± 1.87 )·10−1 -3.08 ·10−1

Table E.19: The polarisation asymmetry measured using negatively and positively polarised 05-06 e−p data(L = 105.4 pb−1, Pe = −0.27 and L = 71.8 pb−1, Pe = +0.30 respectively). The total error on the measurementcorresponds to the statistical uncertainties. The asymmetry predicted by the SM using ZEUS-JETS PDFs isgiven. The subscript c indicates the bin centre.

209

Q2 range Q2c x range xc σ Ndata NMC Nbg

(GeV2) (GeV2) Measured SM

185 - 240 200 0.0037 - 0.006 0.005 1.13 ± 0.01 +0.02−0.02 1.09 14823 14770 27

0.006 - 0.01 0.008 (9.50 ± 0.07 +0.14−0.13 )·10−1 9.37 ·10−1 17245 17194 17

0.01 - 0.017 0.013 (7.86 ± 0.06 +0.13−0.12 )·10−1 8.03 ·10−1 18542 18872 8

0.017 - 0.025 0.021 (6.43 ± 0.06 +0.09−0.08 )·10−1 6.82 ·10−1 13221 13933 1

0.025 - 0.037 0.032 (5.56 ± 0.05 +0.10−0.09 )·10−1 5.92 ·10−1 12560 13317 0

0.037 - 0.06 0.05 (5.08 ± 0.05 +0.06−0.05 )·10−1 5.11 ·10−1 11626 11726 0

0.06 - 0.12 0.08 (4.44 ± 0.04 +0.10−0.10 )·10−1 4.38 ·10−1 14997 14915 0

0.12 - 0.25 0.18 (3.41 ± 0.04 +0.12−0.11 )·10−1 3.29 ·10−1 7756 7467 0

240 - 310 250 0.006 - 0.01 0.008 (9.67 ± 0.09 +0.17−0.15 )·10−1 9.56 ·10−1 11963 12007 14

0.01 - 0.017 0.013 (8.03 ± 0.07 +0.14−0.13 )·10−1 8.18 ·10−1 13283 13500 6

0.017 - 0.025 0.021 (6.57 ± 0.07 +0.10−0.09 )·10−1 6.93 ·10−1 9393 9861 3

0.025 - 0.037 0.032 (5.60 ± 0.06 +0.07−0.07 )·10−1 5.99 ·10−1 9227 9836 4

0.037 - 0.06 0.05 (5.04 ± 0.05 +0.07−0.07 )·10−1 5.15 ·10−1 8979 9190 2

0.06 - 0.12 0.08 (4.32 ± 0.04 +0.10−0.10 )·10−1 4.40 ·10−1 10915 11197 0

0.12 - 0.25 0.18 (3.32 ± 0.04 +0.09−0.07 )·10−1 3.27 ·10−1 7357 7220 0

310 - 410 350 0.006 - 0.01 0.008 1.01 ± 0.01 +0.02−0.02 0.98 7295 7259 24

0.01 - 0.017 0.013 (8.32 ± 0.08 +0.18−0.17 )·10−1 8.40 ·10−1 9988 10109 8

0.017 - 0.025 0.021 (6.97 ± 0.08 +0.10−0.10 )·10−1 7.09 ·10−1 7683 7790 0

0.025 - 0.037 0.032 (5.90 ± 0.07 +0.10−0.09 )·10−1 6.10 ·10−1 7441 7668 0

0.037 - 0.06 0.05 (5.06 ± 0.06 +0.14−0.13 )·10−1 5.22 ·10−1 7913 8172 1

0.06 - 0.12 0.08 (4.42 ± 0.05 +0.07−0.07 )·10−1 4.43 ·10−1 8875 8947 1

0.12 - 0.25 0.18 (3.22 ± 0.04 +0.11−0.10 )·10−1 3.24 ·10−1 6946 6964 0

Table E.20: The reduced cross section σ measured using the combined 05-06 e−p data set (L =177.2 pb−1, Pe corrected to zero). The first (second) error on the measured cross section refers to the statis-tical (systematic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given.The number of observed data, MC and PHP background events are given as Ndata, NMC and Nbg respectively.The subscript c indicates the bin centre. This table is continued in Tables E.21 -E.23.

210



410 - 530 450 0.006 - 0.01 0.008 1.03 ± 0.01 +0.03−0.03 0.99 5614 5625 34

0.01 - 0.017 0.013 (8.82 ± 0.13 +0.12−0.13 )·10−1 8.54 ·10−1 4967 4846 8

0.017 - 0.025 0.021 (6.92 ± 0.11 +0.12−0.10 )·10−1 7.20 ·10−1 3859 4012 0

0.025 - 0.037 0.032 (5.81 ± 0.09 +0.11−0.11 )·10−1 6.18 ·10−1 4383 4645 3

0.037 - 0.06 0.05 (5.10 ± 0.07 +0.10−0.10 )·10−1 5.27 ·10−1 5489 5674 0

0.06 - 0.1 0.08 (4.37 ± 0.07 +0.07−0.06 )·10−1 4.45 ·10−1 4455 4562 0

0.1 - 0.17 0.13 (3.62 ± 0.06 +0.08−0.07 )·10−1 3.72 ·10−1 3917 4039 0

0.17 - 0.3 0.25 (2.63 ± 0.05 +0.08−0.08 )·10−1 2.62 ·10−1 2960 2912 0

530 - 710 650 0.01 - 0.017 0.013 (9.06 ± 0.12 +0.18−0.16 )·10−1 8.70 ·10−1 5635 5529 15

0.017 - 0.025 0.021 (7.58 ± 0.12 +0.12−0.12 )·10−1 7.36 ·10−1 3745 3645 7

0.025 - 0.037 0.032 (5.95 ± 0.11 +0.10−0.08 )·10−1 6.30 ·10−1 2883 3053 0

0.037 - 0.06 0.05 (5.08 ± 0.09 +0.05−0.04 )·10−1 5.34 ·10−1 3057 3221 0

0.06 - 0.1 0.08 (4.25 ± 0.08 +0.10−0.10 )·10−1 4.48 ·10−1 2539 2685 1

0.1 - 0.17 0.13 (3.64 ± 0.08 +0.06−0.06 )·10−1 3.72 ·10−1 2331 2382 0

0.17 - 0.3 0.25 (2.55 ± 0.06 +0.07−0.07 )·10−1 2.58 ·10−1 1997 1993 0

710 - 900 800 0.009 - 0.017 0.013 (8.82 ± 0.15 +0.22−0.20 )·10−1 8.75 ·10−1 3517 3604 30

0.017 - 0.025 0.021 (7.40 ± 0.15 +0.16−0.14 )·10−1 7.45 ·10−1 2475 2514 1

0.025 - 0.037 0.032 (6.33 ± 0.12 +0.07−0.06 )·10−1 6.38 ·10−1 2602 2615 6

0.037 - 0.06 0.05 (5.16 ± 0.10 +0.07−0.07 )·10−1 5.39 ·10−1 2831 2963 0

0.06 - 0.1 0.08 (4.54 ± 0.09 +0.05−0.05 )·10−1 4.51 ·10−1 2449 2441 0

0.1 - 0.17 0.13 (3.81 ± 0.09 +0.04−0.04 )·10−1 3.72 ·10−1 1992 1946 0

0.17 - 0.3 0.25 (2.59 ± 0.07 +0.07−0.06 )·10−1 2.57 ·10−1 1475 1441 0


211



900 - 1300 1200 0.01 - 0.017 0.014 (9.18 ± 0.19 +0.42−0.41 )·10−1 8.47 ·10−1 2317 2275 50

0.017 - 0.025 0.021 (8.11 ± 0.16 +0.17−0.16 )·10−1 7.63 ·10−1 2693 2580 15

0.025 - 0.037 0.032 (6.15 ± 0.12 +0.09−0.08 )·10−1 6.57 ·10−1 2612 2793 3

0.037 - 0.06 0.05 (5.51 ± 0.09 +0.05−0.05 )·10−1 5.53 ·10−1 3382 3388 1

0.06 - 0.1 0.08 (4.57 ± 0.08 +0.04−0.03 )·10−1 4.59 ·10−1 3192 3208 1

0.1 - 0.17 0.13 (3.76 ± 0.07 +0.03−0.02 )·10−1 3.75 ·10−1 2578 2563 0

0.17 - 0.3 0.25 (2.52 ± 0.06 +0.03−0.03 )·10−1 2.54 ·10−1 1988 1971 0

0.3 - 0.53 0.4 (1.25 ± 0.05 +0.10−0.03 )·10−1 1.36 ·10−1 675 704 0

1300 - 1800 1500 0.017 - 0.025 0.021 (8.11 ± 0.23 +0.25−0.25 )·10−1 7.67 ·10−1 1339 1302 22

0.025 - 0.037 0.032 (6.42 ± 0.17 +0.15−0.14 )·10−1 6.66 ·10−1 1477 1545 4

0.037 - 0.06 0.05 (5.26 ± 0.12 +0.06−0.05 )·10−1 5.61 ·10−1 1848 1977 0

0.06 - 0.1 0.08 (4.72 ± 0.11 +0.05−0.05 )·10−1 4.63 ·10−1 1985 1955 0

0.1 - 0.15 0.13 (3.83 ± 0.11 +0.05−0.04 )·10−1 3.77 ·10−1 1271 1249 0

0.15 - 0.23 0.18 (3.16 ± 0.10 +0.04−0.03 )·10−1 3.20 ·10−1 1080 1084 0

0.23 - 0.35 0.25 (2.65 ± 0.10 +0.09−0.08 )·10−1 2.53 ·10−1 766 720 0

0.35 - 0.53 0.4 (1.32 ± 0.07 +0.12−0.07 )·10−1 1.34 ·10−1 339 332 0

1800 - 2500 2000 0.023 - 0.037 0.032 (6.56 ± 0.21 +0.40−0.39 )·10−1 6.83 ·10−1 1037 1083 23

0.037 - 0.06 0.05 (5.62 ± 0.16 +0.12−0.11 )·10−1 5.77 ·10−1 1281 1321 3

0.06 - 0.1 0.08 (4.58 ± 0.13 +0.03−0.03 )·10−1 4.75 ·10−1 1305 1357 1

0.1 - 0.15 0.13 (3.75 ± 0.12 +0.05−0.05 )·10−1 3.83 ·10−1 927 946 0

0.15 - 0.23 0.18 (3.11 ± 0.11 +0.04−0.06 )·10−1 3.23 ·10−1 753 775 0

0.23 - 0.35 0.25 (2.51 ± 0.11 +0.03−0.02 )·10−1 2.54 ·10−1 524 522 0

0.35 - 0.53 0.4 (1.21 ± 0.08 +0.03−0.04 )·10−1 1.33 ·10−1 250 265 0


212



2500 - 3500 3000 0.037 - 0.06 0.05 (6.04 ± 0.21 +0.33−0.32 )·10−1 6.12 ·10−1 821 847 3

0.06 - 0.1 0.08 (5.06 ± 0.16 +0.04−0.04 )·10−1 5.01 ·10−1 947 946 0

0.1 - 0.15 0.13 (3.79 ± 0.15 +0.05−0.05 )·10−1 3.99 ·10−1 656 689 2

0.15 - 0.23 0.18 (3.26 ± 0.14 +0.02−0.03 )·10−1 3.32 ·10−1 558 565 0

0.23 - 0.35 0.25 (2.86 ± 0.14 +0.14−0.13 )·10−1 2.58 ·10−1 441 392 0

0.35 - 0.53 0.4 (1.38 ± 0.10 +0.08−0.08 )·10−1 1.32 ·10−1 198 184 0

0.53 - 1 0.65 (1.66 +0.23−0.20

+0.11−0.10 )·10−2 2.08 ·10−2 65 76 0

3500 - 5600 5000 0.04 - 0.1 0.08 (5.37 ± 0.17 +0.27−0.26 )·10−1 5.65 ·10−1 1051 1121 6

0.1 - 0.15 0.13 (4.59 ± 0.18 +0.06−0.06 )·10−1 4.42 ·10−1 640 619 0

0.15 - 0.23 0.18 (3.49 ± 0.15 +0.04−0.02 )·10−1 3.60 ·10−1 535 550 0

0.23 - 0.35 0.25 (2.49 ± 0.14 +0.05−0.05 )·10−1 2.74 ·10−1 339 366 2

0.35 - 0.53 0.4 (1.38 ± 0.10 +0.04−0.03 )·10−1 1.36 ·10−1 184 175 0

5600 - 9000 8000 0.07 - 0.15 0.13 (5.82 ± 0.23 +0.17−0.19 )·10−1 5.16 ·10−1 625 559 1

0.15 - 0.23 0.18 (4.35 ± 0.23 +0.10−0.11 )·10−1 4.12 ·10−1 363 344 0

0.23 - 0.35 0.25 (3.17 ± 0.20 +0.03−0.05 )·10−1 3.04 ·10−1 250 237 0

0.35 - 0.53 0.4 (1.16 +0.13−0.12

+0.02−0.03 )·10−1 1.45 ·10−1 93 112 0

0.53 - 1 0.65 (1.76 +0.35−0.30

+0.10−0.09 )·10−2 2.08 ·10−2 35 39 0

9000 - 15000 12000 0.09 - 0.23 0.18 (4.89 ± 0.28 +0.20−0.19 )·10−1 4.85 ·10−1 298 298 0

0.23 - 0.35 0.25 (3.51 ± 0.28 +0.07−0.08 )·10−1 3.50 ·10−1 154 153 0

0.35 - 0.53 0.4 (1.56 +0.20−0.18

+0.07−0.07 )·10−1 1.59 ·10−1 75 74 0

15000 - 25000 20000 0.15 - 0.35 0.25 (4.69 ± 0.41 +0.40−0.41 )·10−1 4.32 ·10−1 132 121 2

0.35 - 1 0.4 (1.88 +0.30−0.26

+0.20−0.20 )·10−1 1.89 ·10−1 51 50 0

25000 - 50000 30000 0.25 - 1 0.4 (2.52 +0.43−0.37

+0.24−0.14 )·10−1 2.22 ·10−1 46 40 0


213



185 - 240 200 0.0037 - 0.006 0.005 1.13 ± 0.01 +0.03−0.05 1.09 8814 8782 16

0.006 - 0.01 0.008 (9.45 ± 0.09 +0.23−0.30 )·10−1 9.41 ·10−1 10192 10223 10

0.01 - 0.017 0.013 (7.86 ± 0.07 +0.15−0.22 )·10−1 8.06 ·10−1 11013 11221 5

0.017 - 0.025 0.021 (6.39 ± 0.07 +0.23−0.20 )·10−1 6.85 ·10−1 7800 8284 1

0.025 - 0.037 0.032 (5.59 ± 0.06 +0.12−0.14 )·10−1 5.94 ·10−1 7506 7919 0

0.037 - 0.06 0.05 (5.09 ± 0.06 +0.08−0.11 )·10−1 5.13 ·10−1 6930 6972 0

0.06 - 0.12 0.08 (4.50 ± 0.05 +0.13−0.14 )·10−1 4.40 ·10−1 9017 8865 0

0.12 - 0.25 0.18 (3.48 ± 0.05 +0.07−0.07 )·10−1 3.30 ·10−1 4707 4443 0

240 - 310 250 0.006 - 0.01 0.008 (9.81 ± 0.12 +0.48−0.54 )·10−1 9.61 ·10−1 7210 7140 8

0.01 - 0.017 0.013 (8.08 ± 0.09 +0.12−0.29 )·10−1 8.22 ·10−1 7935 8026 4

0.017 - 0.025 0.021 (6.61 ± 0.09 +0.09−0.16 )·10−1 6.96 ·10−1 5618 5863 2

0.025 - 0.037 0.032 (5.65 ± 0.08 +0.04−0.07 )·10−1 6.02 ·10−1 5532 5847 3

0.037 - 0.06 0.05 (5.15 ± 0.07 +0.02−0.07 )·10−1 5.18 ·10−1 5452 5466 1

0.06 - 0.12 0.08 (4.32 ± 0.05 +0.03−0.04 )·10−1 4.42 ·10−1 6479 6654 0

0.12 - 0.25 0.18 (3.38 ± 0.05 +0.04−0.05 )·10−1 3.28 ·10−1 4445 4293 0

310 - 410 350 0.006 - 0.01 0.008 1.01 ± 0.02 +0.04−0.05 0.99 4346 4317 14

0.01 - 0.017 0.013 (8.29 ± 0.11 +0.42−0.44 )·10−1 8.46 ·10−1 5915 6011 4

0.017 - 0.025 0.021 (7.00 ± 0.10 +0.23−0.26 )·10−1 7.14 ·10−1 4584 4631 0

0.025 - 0.037 0.032 (5.94 ± 0.09 +0.06−0.09 )·10−1 6.15 ·10−1 4451 4559 0

0.037 - 0.06 0.05 (5.10 ± 0.07 +0.04−0.07 )·10−1 5.25 ·10−1 4736 4859 1

0.06 - 0.12 0.08 (4.44 ± 0.06 +0.03−0.08 )·10−1 4.46 ·10−1 5299 5317 1

0.12 - 0.25 0.18 (3.28 ± 0.05 +0.05−0.06 )·10−1 3.26 ·10−1 4200 4141 0

Table E.24: The reduced cross section σ measured using the negatively polarised 05-06 e−p data set (L =105.4 pb−1, Pe = −0.27). The first (second) error on the measured cross section refers to the statistical (system-atic) uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given. The numberof observed data, MC and PHP background events are given as Ndata, NMC and Nbg respectively. The subscriptc indicates the bin centre. This table is continued in Tables E.25 -E.27.

214



410 - 530 450 0.006 - 0.01 0.008 1.02 ± 0.02 +0.05−0.06 1.00 3305 3341 20

0.01 - 0.017 0.013 (8.93 ± 0.16 +0.13−0.17 )·10−1 8.62 ·10−1 2985 2879 5

0.017 - 0.025 0.021 (6.95 ± 0.14 +0.16−0.14 )·10−1 7.27 ·10−1 2305 2390 0

0.025 - 0.037 0.032 (5.96 ± 0.12 +0.04−0.06 )·10−1 6.24 ·10−1 2671 2764 2

0.037 - 0.06 0.05 (5.21 ± 0.09 +0.06−0.06 )·10−1 5.31 ·10−1 3333 3375 0

0.06 - 0.1 0.08 (4.51 ± 0.09 +0.02−0.02 )·10−1 4.48 ·10−1 2733 2713 0

0.1 - 0.17 0.13 (3.64 ± 0.08 +0.04−0.05 )·10−1 3.75 ·10−1 2344 2401 0

0.17 - 0.3 0.25 (2.71 ± 0.06 +0.04−0.04 )·10−1 2.64 ·10−1 1813 1732 0

530 - 710 650 0.01 - 0.017 0.013 (9.10 ± 0.16 +0.42−0.46 )·10−1 8.82 ·10−1 3357 3284 9

0.017 - 0.025 0.021 (7.58 ± 0.16 +0.03−0.18 )·10−1 7.46 ·10−1 2215 2161 4

0.025 - 0.037 0.032 (5.98 ± 0.14 +0.07−0.11 )·10−1 6.38 ·10−1 1716 1811 0

0.037 - 0.06 0.05 (5.19 ± 0.12 +0.13−0.14 )·10−1 5.41 ·10−1 1855 1915 0

0.06 - 0.1 0.08 (4.31 ± 0.11 +0.03−0.03 )·10−1 4.53 ·10−1 1530 1599 1

0.1 - 0.17 0.13 (3.73 ± 0.10 +0.03−0.03 )·10−1 3.76 ·10−1 1419 1419 0

0.17 - 0.3 0.25 (2.56 ± 0.07 +0.01−0.02 )·10−1 2.61 ·10−1 1194 1187 0

710 - 900 800 0.009 - 0.017 0.013 (9.07 ± 0.20 +0.18−0.27 )·10−1 8.88 ·10−1 2151 2143 18

0.017 - 0.025 0.021 (7.76 ± 0.20 +0.03−0.17 )·10−1 7.57 ·10−1 1539 1494 1

0.025 - 0.037 0.032 (6.52 ± 0.16 +0.18−0.18 )·10−1 6.48 ·10−1 1588 1554 3

0.037 - 0.06 0.05 (5.32 ± 0.13 +0.14−0.14 )·10−1 5.47 ·10−1 1730 1758 0

0.06 - 0.1 0.08 (4.60 ± 0.12 +0.09−0.09 )·10−1 4.57 ·10−1 1467 1447 0

0.1 - 0.17 0.13 (3.84 ± 0.11 +0.03−0.04 )·10−1 3.77 ·10−1 1186 1153 0

0.17 - 0.3 0.25 (2.72 ± 0.09 +0.03−0.04 )·10−1 2.60 ·10−1 915 853 0


215



900 - 1300 1200 0.01 - 0.017 0.014 (9.29 ± 0.25 +0.43−0.52 )·10−1 8.67 ·10−1 1389 1353 30

0.017 - 0.025 0.021 (8.45 ± 0.21 +0.13−0.25 )·10−1 7.80 ·10−1 1662 1534 9

0.025 - 0.037 0.032 (6.30 ± 0.16 +0.27−0.28 )·10−1 6.72 ·10−1 1584 1660 2

0.037 - 0.06 0.05 (5.52 ± 0.12 +0.08−0.08 )·10−1 5.65 ·10−1 2007 2014 1

0.06 - 0.1 0.08 (4.73 ± 0.11 +0.08−0.08 )·10−1 4.68 ·10−1 1957 1907 1

0.1 - 0.17 0.13 (3.87 ± 0.10 +0.04−0.05 )·10−1 3.83 ·10−1 1568 1523 0

0.17 - 0.3 0.25 (2.69 ± 0.08 +0.01−0.01 )·10−1 2.59 ·10−1 1255 1171 0

0.3 - 0.53 0.4 (1.29 ± 0.06 +0.01−0.01 )·10−1 1.38 ·10−1 411 419 0

1300 - 1800 1500 0.017 - 0.025 0.021 (8.20 ± 0.29 +0.27−0.28 )·10−1 7.88 ·10−1 802 774 13

0.025 - 0.037 0.032 (6.54 ± 0.22 +0.15−0.16 )·10−1 6.84 ·10−1 890 918 3

0.037 - 0.06 0.05 (5.16 ± 0.16 +0.15−0.15 )·10−1 5.75 ·10−1 1074 1176 0

0.06 - 0.1 0.08 (4.91 ± 0.14 +0.07−0.09 )·10−1 4.75 ·10−1 1223 1162 0

0.1 - 0.15 0.13 (3.93 ± 0.14 +0.03−0.03 )·10−1 3.86 ·10−1 772 743 0

0.15 - 0.23 0.18 (3.28 ± 0.13 +0.06−0.06 )·10−1 3.27 ·10−1 664 645 0

0.23 - 0.35 0.25 (2.68 ± 0.13 +0.03−0.05 )·10−1 2.59 ·10−1 459 428 0

0.35 - 0.53 0.4 (1.38 ± 0.10 +0.01−0.01 )·10−1 1.37 ·10−1 211 198 0

1800 - 2500 2000 0.023 - 0.037 0.032 (6.68 ± 0.27 +0.15−0.23 )·10−1 7.06 ·10−1 624 644 13

0.037 - 0.06 0.05 (5.89 ± 0.21 +0.15−0.20 )·10−1 5.96 ·10−1 793 785 2

0.06 - 0.1 0.08 (4.73 ± 0.17 +0.03−0.06 )·10−1 4.89 ·10−1 798 807 1

0.1 - 0.15 0.13 (3.50 ± 0.15 +0.01−0.03 )·10−1 3.95 ·10−1 512 562 0

0.15 - 0.23 0.18 (3.21 ± 0.15 +0.03−0.04 )·10−1 3.32 ·10−1 459 461 0

0.23 - 0.35 0.25 (2.65 ± 0.15 +0.04−0.04 )·10−1 2.61 ·10−1 327 310 0

0.35 - 0.53 0.4 (1.20 ± 0.10 +0.00−0.00 )·10−1 1.36 ·10−1 147 157 0


216



2500 - 3500 3000 0.037 - 0.06 0.05 (6.24 ± 0.28 +0.10−0.09 )·10−1 6.39 ·10−1 501 503 2

0.06 - 0.1 0.08 (5.09 ± 0.21 +0.11−0.09 )·10−1 5.23 ·10−1 563 563 0

0.1 - 0.15 0.13 (3.80 ± 0.19 +0.03−0.02 )·10−1 4.15 ·10−1 389 410 1

0.15 - 0.23 0.18 (3.51 ± 0.19 +0.05−0.05 )·10−1 3.45 ·10−1 355 336 0

0.23 - 0.35 0.25 (2.71 ± 0.17 +0.02−0.03 )·10−1 2.68 ·10−1 247 233 0

0.35 - 0.53 0.4 (1.60 ± 0.14 +0.01−0.01 )·10−1 1.37 ·10−1 136 109 0

0.53 - 1 0.65 (1.81 +0.32−0.28

+0.00−0.00 )·10−2 2.15 ·10−2 42 45 0

3500 - 5600 5000 0.04 - 0.1 0.08 (5.80 ± 0.23 +0.07−0.09 )·10−1 5.98 ·10−1 668 666 4

0.1 - 0.15 0.13 (4.86 ± 0.24 +0.05−0.06 )·10−1 4.66 ·10−1 400 368 0

0.15 - 0.23 0.18 (3.68 ± 0.20 +0.03−0.02 )·10−1 3.79 ·10−1 333 327 0

0.23 - 0.35 0.25 (2.43 ± 0.17 +0.03−0.03 )·10−1 2.88 ·10−1 195 218 1

0.35 - 0.53 0.4 (1.31 ± 0.13 +0.00−0.00 )·10−1 1.43 ·10−1 103 104 0

5600 - 9000 8000 0.07 - 0.15 0.13 (6.12 ± 0.31 +0.07−0.09 )·10−1 5.51 ·10−1 387 333 1

0.15 - 0.23 0.18 (4.44 ± 0.30 +0.06−0.06 )·10−1 4.39 ·10−1 218 205 0

0.23 - 0.35 0.25 (3.34 ± 0.27 +0.07−0.08 )·10−1 3.24 ·10−1 155 141 0

0.35 - 0.53 0.4 (1.17 +0.18−0.16

+0.02−0.02 )·10−1 1.54 ·10−1 55 67 0

0.53 - 1 0.65 (1.71 +0.47−0.38

+0.00−0.00 )·10−2 2.20 ·10−2 20 23 0

9000 - 15000 12000 0.09 - 0.23 0.18 (5.42 ± 0.39 +0.10−0.11 )·10−1 5.21 ·10−1 194 177 0

0.23 - 0.35 0.25 (3.48 +0.41−0.37

+0.01−0.02 )·10−1 3.76 ·10−1 90 91 0

0.35 - 0.53 0.4 (1.49 +0.27−0.23

+0.01−0.01 )·10−1 1.70 ·10−1 42 44 0

15000 - 25000 20000 0.15 - 0.35 0.25 (4.84 +0.61−0.55

+0.06−0.13 )·10−1 4.68 ·10−1 80 72 1

0.35 - 1 0.4 (2.01 +0.42−0.35

+0.03−0.04 )·10−1 2.04 ·10−1 32 30 0

25000 - 50000 30000 0.25 - 1 0.4 (2.80 +0.61−0.51

+0.08−0.06 )·10−1 2.41 ·10−1 30 24 0


217



185 - 240 200 0.0037 - 0.006 0.005 1.13 ± 0.01 +0.02−0.03 1.08 6009 5989 11

0.006 - 0.01 0.008 (9.58 ± 0.11 +0.21−0.38 )·10−1 9.32 ·10−1 7053 6973 7

0.01 - 0.017 0.013 (7.87 ± 0.09 +0.18−0.18 )·10−1 7.99 ·10−1 7529 7652 3

0.017 - 0.025 0.021 (6.51 ± 0.09 +0.24−0.22 )·10−1 6.79 ·10−1 5421 5650 1

0.025 - 0.037 0.032 (5.52 ± 0.08 +0.12−0.14 )·10−1 5.89 ·10−1 5054 5399 0

0.037 - 0.06 0.05 (5.06 ± 0.07 +0.08−0.10 )·10−1 5.08 ·10−1 4696 4755 0

0.06 - 0.12 0.08 (4.37 ± 0.06 +0.13−0.12 )·10−1 4.36 ·10−1 5980 6051 0

0.12 - 0.25 0.18 (3.31 ± 0.06 +0.06−0.07 )·10−1 3.27 ·10−1 3049 3026 0

240 - 310 250 0.006 - 0.01 0.008 (9.48 ± 0.14 +0.47−0.56 )·10−1 9.50 ·10−1 4753 4869 6

0.01 - 0.017 0.013 (7.98 ± 0.11 +0.14−0.24 )·10−1 8.13 ·10−1 5348 5475 2

0.017 - 0.025 0.021 (6.51 ± 0.11 +0.09−0.14 )·10−1 6.89 ·10−1 3775 3999 1

0.025 - 0.037 0.032 (5.53 ± 0.09 +0.04−0.06 )·10−1 5.96 ·10−1 3695 3989 2

0.037 - 0.06 0.05 (4.89 ± 0.08 +0.02−0.03 )·10−1 5.12 ·10−1 3527 3725 1

0.06 - 0.12 0.08 (4.33 ± 0.07 +0.03−0.04 )·10−1 4.38 ·10−1 4436 4544 0

0.12 - 0.25 0.18 (3.24 ± 0.06 +0.04−0.05 )·10−1 3.25 ·10−1 2912 2927 0

310 - 410 350 0.006 - 0.01 0.008 1.01 ± 0.02 +0.04−0.04 0.97 2949 2943 10

0.01 - 0.017 0.013 (8.37 ± 0.13 +0.41−0.44 )·10−1 8.33 ·10−1 4073 4098 3

0.017 - 0.025 0.021 (6.94 ± 0.12 +0.23−0.25 )·10−1 7.03 ·10−1 3099 3160 0

0.025 - 0.037 0.032 (5.85 ± 0.11 +0.05−0.05 )·10−1 6.06 ·10−1 2990 3111 0

0.037 - 0.06 0.05 (5.01 ± 0.09 +0.05−0.08 )·10−1 5.18 ·10−1 3177 3314 1

0.06 - 0.12 0.08 (4.39 ± 0.07 +0.03−0.06 )·10−1 4.39 ·10−1 3576 3630 1

0.12 - 0.25 0.18 (3.14 ± 0.06 +0.05−0.06 )·10−1 3.22 ·10−1 2746 2824 0

Table E.28: The reduced cross section σ measured using the positively polarised 05-06 e−p data set (L =71.8 pb−1, Pe = +0.30). The first (second) error on the measured cross section refers to the statistical (systematic)uncertainties. The cross sections as predicted by the SM using ZEUS-JETS PDFs are given. The number ofobserved data, MC and PHP background events are given as Ndata, NMC and Nbg respectively. The subscript cindicates the bin centre. This table is continued in Tables E.29 -E.31.

218



410 - 530 450 0.006 - 0.01 0.008 1.04 ± 0.02 +0.06−0.07 0.98 2309 2285 14

0.01 - 0.017 0.013 (8.68 ± 0.20 +0.11−0.19 )·10−1 8.46 ·10−1 1982 1966 3

0.017 - 0.025 0.021 (6.90 ± 0.17 +0.16−0.14 )·10−1 7.13 ·10−1 1554 1623 0

0.025 - 0.037 0.032 (5.61 ± 0.14 +0.04−0.09 )·10−1 6.12 ·10−1 1712 1881 1

0.037 - 0.06 0.05 (4.95 ± 0.11 +0.05−0.05 )·10−1 5.21 ·10−1 2156 2300 0

0.06 - 0.1 0.08 (4.17 ± 0.10 +0.03−0.05 )·10−1 4.41 ·10−1 1722 1850 0

0.1 - 0.17 0.13 (3.58 ± 0.09 +0.04−0.05 )·10−1 3.69 ·10−1 1573 1638 0

0.17 - 0.3 0.25 (2.51 ± 0.07 +0.03−0.04 )·10−1 2.60 ·10−1 1147 1180 0

530 - 710 650 0.01 - 0.017 0.013 (9.03 ± 0.19 +0.43−0.52 )·10−1 8.58 ·10−1 2278 2245 6

0.017 - 0.025 0.021 (7.62 ± 0.20 +0.04−0.14 )·10−1 7.26 ·10−1 1530 1483 3

0.025 - 0.037 0.032 (5.93 ± 0.17 +0.07−0.11 )·10−1 6.22 ·10−1 1167 1241 0

0.037 - 0.06 0.05 (4.93 ± 0.14 +0.12−0.12 )·10−1 5.27 ·10−1 1202 1306 0

0.06 - 0.1 0.08 (4.19 ± 0.13 +0.04−0.03 )·10−1 4.42 ·10−1 1009 1087 1

0.1 - 0.17 0.13 (3.53 ± 0.12 +0.03−0.04 )·10−1 3.67 ·10−1 912 964 0

0.17 - 0.3 0.25 (2.54 ± 0.09 +0.01−0.02 )·10−1 2.55 ·10−1 803 806 0

710 - 900 800 0.009 - 0.017 0.013 (8.44 ± 0.23 +0.16−0.35 )·10−1 8.59 ·10−1 1366 1462 12

0.017 - 0.025 0.021 (6.91 ± 0.23 +0.03−0.17 )·10−1 7.33 ·10−1 936 1020 1

0.025 - 0.037 0.032 (6.09 ± 0.19 +0.18−0.19 )·10−1 6.27 ·10−1 1014 1062 2

0.037 - 0.06 0.05 (4.95 ± 0.15 +0.12−0.14 )·10−1 5.30 ·10−1 1101 1204 0

0.06 - 0.1 0.08 (4.48 ± 0.14 +0.08−0.07 )·10−1 4.43 ·10−1 982 994 0

0.1 - 0.17 0.13 (3.79 ± 0.13 +0.03−0.04 )·10−1 3.67 ·10−1 806 793 0

0.17 - 0.3 0.25 (2.41 ± 0.10 +0.03−0.03 )·10−1 2.53 ·10−1 560 587 0


219



900 - 1300 1200 0.01 - 0.017 0.014 (9.10 ± 0.31 +0.41−0.51 )·10−1 8.25 ·10−1 928 923 20

0.017 - 0.025 0.021 (7.68 ± 0.24 +0.14−0.23 )·10−1 7.43 ·10−1 1031 1046 6

0.025 - 0.037 0.032 (5.99 ± 0.19 +0.25−0.25 )·10−1 6.40 ·10−1 1028 1133 1

0.037 - 0.06 0.05 (5.54 ± 0.15 +0.09−0.08 )·10−1 5.39 ·10−1 1375 1374 1

0.06 - 0.1 0.08 (4.37 ± 0.12 +0.07−0.08 )·10−1 4.48 ·10−1 1235 1301 1

0.1 - 0.17 0.13 (3.64 ± 0.11 +0.04−0.05 )·10−1 3.67 ·10−1 1010 1040 0

0.17 - 0.3 0.25 (2.30 ± 0.08 +0.01−0.02 )·10−1 2.48 ·10−1 733 800 0

0.3 - 0.53 0.4 (1.21 ± 0.07 +0.01−0.01 )·10−1 1.33 ·10−1 264 286 0

1300 - 1800 1500 0.017 - 0.025 0.021 (8.05 ± 0.35 +0.26−0.32 )·10−1 7.44 ·10−1 537 528 9

0.025 - 0.037 0.032 (6.32 ± 0.26 +0.14−0.25 )·10−1 6.47 ·10−1 587 627 2

0.037 - 0.06 0.05 (5.45 ± 0.20 +0.16−0.17 )·10−1 5.45 ·10−1 774 802 0

0.06 - 0.1 0.08 (4.49 ± 0.16 +0.07−0.06 )·10−1 4.51 ·10−1 762 793 0

0.1 - 0.15 0.13 (3.73 ± 0.17 +0.02−0.05 )·10−1 3.67 ·10−1 499 507 0

0.15 - 0.23 0.18 (3.01 ± 0.15 +0.05−0.05 )·10−1 3.12 ·10−1 416 440 0

0.23 - 0.35 0.25 (2.63 ± 0.15 +0.03−0.05 )·10−1 2.47 ·10−1 307 292 0

0.35 - 0.53 0.4 (1.23 ± 0.11 +0.01−0.01 )·10−1 1.31 ·10−1 128 135 0

1800 - 2500 2000 0.023 - 0.037 0.032 (6.48 ± 0.33 +0.18−0.17 )·10−1 6.58 ·10−1 413 439 9

0.037 - 0.06 0.05 (5.31 ± 0.24 +0.12−0.14 )·10−1 5.56 ·10−1 488 536 1

0.06 - 0.1 0.08 (4.41 ± 0.20 +0.05−0.03 )·10−1 4.58 ·10−1 507 550 1

0.1 - 0.15 0.13 (4.16 ± 0.20 +0.03−0.02 )·10−1 3.70 ·10−1 415 383 0

0.15 - 0.23 0.18 (3.01 ± 0.18 +0.04−0.03 )·10−1 3.12 ·10−1 294 314 0

0.23 - 0.35 0.25 (2.34 ± 0.17 +0.04−0.03 )·10−1 2.46 ·10−1 197 212 0

0.35 - 0.53 0.4 (1.23 ± 0.12 +0.01−0.01 )·10−1 1.29 ·10−1 103 107 0


220



2500 - 3500 3000 0.037 - 0.06 0.05 (5.84 ± 0.33 +0.08−0.12 )·10−1 5.83 ·10−1 320 343 1

0.06 - 0.1 0.08 (5.09 ± 0.26 +0.11−0.09 )·10−1 4.78 ·10−1 384 384 0

0.1 - 0.15 0.13 (3.83 ± 0.23 +0.02−0.05 )·10−1 3.81 ·10−1 267 280 1

0.15 - 0.23 0.18 (2.95 ± 0.21 +0.03−0.04 )·10−1 3.18 ·10−1 203 229 0

0.23 - 0.35 0.25 (3.12 ± 0.22 +0.03−0.03 )·10−1 2.47 ·10−1 194 159 0

0.35 - 0.53 0.4 (1.07 +0.15−0.14

+0.00−0.00 )·10−1 1.27 ·10−1 62 75 0

0.53 - 1 0.65 (1.45 +0.37−0.30

+0.00−0.00 )·10−2 2.00 ·10−2 23 31 0

3500 - 5600 5000 0.04 - 0.1 0.08 (4.87 ± 0.25 +0.05−0.06 )·10−1 5.30 ·10−1 383 454 2

0.1 - 0.15 0.13 (4.28 ± 0.28 +0.03−0.06 )·10−1 4.15 ·10−1 240 251 0

0.15 - 0.23 0.18 (3.27 ± 0.23 +0.01−0.03 )·10−1 3.39 ·10−1 202 223 0

0.23 - 0.35 0.25 (2.63 ± 0.22 +0.04−0.05 )·10−1 2.58 ·10−1 144 149 1

0.35 - 0.53 0.4 (1.51 +0.19−0.17

+0.01−0.00 )·10−1 1.28 ·10−1 81 71 0

5600 - 9000 8000 0.07 - 0.15 0.13 (5.52 ± 0.36 +0.07−0.01 )·10−1 4.77 ·10−1 238 227 1

0.15 - 0.23 0.18 (4.32 ± 0.36 +0.06−0.04 )·10−1 3.82 ·10−1 145 140 0

0.23 - 0.35 0.25 (3.00 +0.34−0.31

+0.07−0.06 )·10−1 2.82 ·10−1 95 96 0

0.35 - 0.53 0.4 (1.18 +0.22−0.19

+0.02−0.02 )·10−1 1.35 ·10−1 38 46 0

0.53 - 1 0.65 (1.87 +0.62−0.48

+0.00−0.00 )·10−2 1.94 ·10−2 15 16 0

9000 - 15000 12000 0.09 - 0.23 0.18 (4.26 ± 0.42 +0.11−0.07 )·10−1 4.44 ·10−1 104 121 0

0.23 - 0.35 0.25 (3.63 +0.51−0.45

+0.00−0.13 )·10−1 3.21 ·10−1 64 62 0

0.35 - 0.53 0.4 (1.71 +0.35−0.30

+0.01−0.01 )·10−1 1.46 ·10−1 33 30 0

15000 - 25000 20000 0.15 - 0.35 0.25 (4.61 +0.74−0.65

+0.07−0.07 )·10−1 3.93 ·10−1 52 49 1

0.35 - 1 0.4 (1.75 +0.50−0.40

+0.03−0.02 )·10−1 1.72 ·10−1 19 20 0

25000 - 50000 30000 0.25 - 1 0.4 (2.19 +0.69−0.54

+0.06−0.03 )·10−1 2.01 ·10−1 16 16 0


221

Q2 range Q2c x range xc xF3


2500 - 3500 3000 0.037 - 0.06 0.05 (4.21 ± 2.74 +2.36−2.33 )·10−2 6.75 ·10−2

0.06 - 0.1 0.08 (1.08 ± 0.34 +0.08−0.10 )·10−1 0.77 ·10−1

0.1 - 0.15 0.13 (5.73 ± 5.55 +3.10−1.24 )·10−2 8.12 ·10−2

0.15 - 0.23 0.18 (2.66 ± 7.18 +1.43−3.10 )·10−2 7.79 ·10−2

0.23 - 0.35 0.25 (2.25 ± 0.94 +0.56−0.68 )·10−1 0.67 ·10−1

0.35 - 0.53 0.4 (1.52 ± 11.67 +6.31−6.16 )·10−2 3.69 ·10−2

0.53 - 1 0.65 (-3.89 +4.53−4.38

+2.76−1.72 )·10−2 0.59 ·10−2

3500 - 5600 5000 0.04 - 0.1 0.08 (8.06 ± 1.95 +1.93−1.82 )·10−2 10.95 ·10−2

0.1 - 0.15 0.13 (1.10 ± 0.36 +0.08−0.09 )·10−1 1.15 ·10−1

0.15 - 0.23 0.18 (1.26 ± 0.42 +0.09−0.13 )·10−1 1.09 ·10−1

0.23 - 0.35 0.25 (7.39 ± 5.39 +1.82−1.85 )·10−2 9.30 ·10−2

0.35 - 0.53 0.4 (9.89 ± 6.60 +2.20−1.41 )·10−2 5.05 ·10−2

5600 - 9000 8000 0.07 - 0.15 0.13 (1.88 ± 0.25 +0.13−0.14 )·10−1 1.50 ·10−1

0.15 - 0.23 0.18 (1.55 ± 0.35 +0.10−0.12 )·10−1 1.42 ·10−1

0.23 - 0.35 0.25 (1.61 ± 0.43 +0.11−0.09 )·10−1 1.20 ·10−1

0.35 - 0.53 0.4 (4.50 +4.90−4.72

+1.21−1.03 )·10−2 6.41 ·10−2

0.53 - 1 0.65 (1.88 +2.40−1.87

+0.47−0.51 )·10−2 0.97 ·10−2

9000 - 15000 12000 0.09 - 0.23 0.18 (1.07 ± 0.31 +0.14−0.18 )·10−1 1.70 ·10−1

0.23 - 0.35 0.25 (1.34 ± 0.43 +0.07−0.14 )·10−1 1.42 ·10−1

0.35 - 0.53 0.4 (9.75 +4.50−4.29

+1.40−1.61 )·10−2 7.55 ·10−2

15000 - 25000 20000 0.15 - 0.35 0.25 (2.08 ± 0.26 +0.22−0.23 )·10−1 1.68 ·10−1

0.35 - 1 0.4 (1.05 +0.41−0.31

+0.19−0.19 )·10−1 0.88 ·10−1

25000 - 50000 30000 0.25 - 1 0.4 (1.13 +0.32−0.25

+0.14−0.15 )·10−1 0.95 ·10−1

Table E.32: The structure function xF3 extracted using the combined 05-06 e−p data set (L =177.2 pb−1, Pe corrected to zero) and previously published NC e+p DIS results (L = 63.2 pb−1, Pe = 0). Thefirst (second) error on the measurement refers to the statistical (systematic) uncertainties. The SM prediction iscalculated using ZEUS-JETS PDFs. The subscript c indicates the bin centre.

222

xc xF γZ3

Measured SM

0.021 (7.46 ± 2.21 ±2.12 )·10−1 2.54 ·10−1

0.032 (1.05 ± 1.57 ±1.20 )·10−1 3.03 ·10−1

0.05 (1.13 ± 1.16 ±0.72 )·10−1 3.55 ·10−1

0.08 (3.57 ± 0.64 ±0.35 )·10−1 4.03 ·10−1

0.13 (4.80 ± 0.60 ±0.23 )·10−1 4.22 ·10−1

0.18 (3.33 ± 0.54 ±0.20 )·10−1 4.02 ·10−1

0.25 (4.01 ± 0.43 ±0.17 )·10−1 3.42 ·10−1

0.4 (2.19 ± 0.39 ±0.16 )·10−1 1.86 ·10−1

0.65 (3.95 ± 6.08 ±1.44 )·10−2 2.87 ·10−2

Table E.33: The interference structure function xF γZ3 at Q2 = 5000 GeV2. The first (second) error on the

measurement refers to the statistical (systematic) uncertainties. The SM prediction is calculated using ZEUS-JETS PDFs. The subscript c indicates the bin centre.

223

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