Charm Production and F2cc Measurements in Deep ... - Zeus - Desy

CHARM PRODUCTION AND F cc
2 MEASUREMENTS
IN DEEP INELASTIC SCATTERING AT HERA II
Jerome I. Whyte
A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATE
STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF
DOCTOR OF PHILOSOPHY
GRADUATE PROGRAM IN PHYSICS AND ASTRONOMY
YORK UNIVERSITY
TORONTO, ONTARIO
September, 2008

Abstract
This thesis examines charm production in electron-proton Deep Inelastic Scattering
at HERA II, measured with the ZEUS detector. HERA II collides protons and
electrons at a center-of-mass energy of √ s = 318 GeV. The ZEUS detector, which
is nearly hermetic, is used to reconstruct the momenta and energies of the particles
created in the electron-proton interactions.
The charm contribution F2 cc(x,Q2
) to the proton structure function F 2 (x,Q 2 ) is extracted
and compared to Next-To-Leading Order Quantum Chromodynamics predictions.
This charm contribution to the proton structure is shown to be as high as
30%.
Single differential D ∗± cross sections for the kinematic region of 5 < Q 2 < 1000
GeV 2 , 0.02 < y < 0.7, and requiring 1.5 < P T (D ∗± ) < 15.0 GeV and −1.5 <
η(D ∗± ) < 1.8, are presented.
The efficiencies for reconstructing the decay products of D ∗± mesons, since the
introduction of the ZEUS micro vertex detector, are examined.

Acknowledgments
In the process of completing for my Ph.D I have had opportunities and experiences
that have permanently influenced my life.
I would like to first thank my supervisor Scott Menary for his guidance in the
direction of my thesis. I would also like to thank Sampa Bhadra, Marlene Caplan,
Wendy Taylor, and Vladka Soltesz, who have assisted me greatly.
L. O’Brien, H. Freedhoff, J. Darewych, A. Palmer, and T. Yavin, are some people
at York that I appreciate.
I would like to thank the ZEUS Heavy Flavour group in particular; R. H. Wilton, J.
Loizides, L. Gladilin, M. Wing, J. Ferrando, A. Geiser, F. Karstens, and B. Dunne.
The York University office: J. Standage, Y. Cui, and especially S. U. Noor.
As time passed during my time in Germany, my German associates eventually became
my German friends and eventually just friends. These people at ZEUS and
DESY helped me adjust to a different way of life, and hopefully I influenced them: E.
Ron, M. Soares, M. Jimenez, C. Uribe-Estrada, T. Koop, N. Coppola, S. Fourletov,
H. Stadie, R. Walsh, R. Mankel, R. Hori, Y. Yamazaki, R. Yoshida, A. Pellegrino,
G. Grigorescu, M. Bindi, J. Carter, S. Boogert, and E. Olabisi.
I made some good friends in Germany who showed me around their city and country:
The Ballers: Kandindima Oyeleye, Dennis Babikir, Andy, Arne, Jeff, Eddy, and
Elinor Merchant aka Fischers Parc ballers.
I can never forget the ladies of Aurel and Reh Bar: Janine Buschmeyer, Katharina
Marioth, and Su Jin Lee. As well as Magnus and Carsten Darnedde.
I’d like to mention a few other people; A. Montanari first time I saw you thought
this was one serious guy, M. Wlasenko never will forget how you showed me around
Amsterdam, Ramona Fikru-Johannes vroom vrooom! see you in NYC, T. Danielson
a friend and SC addict, G. S. Gomes the sweetest heart I ever met, Avraam
Keramidas can’t stand when you away or around, W. Dunne funniest guy I ever
met and a good person, A. Yagues a true friend and a shoulder when I needed it,
the Lawson Clan especially D-Bunz aka VodaFone aka TTB aka D. Lawson the
world cup belonged to us girl, T. Namsoo aka The Naminator a.k.a. B double S E
Y, J. Loizides aka Yohnny you helped more than I can count and are a friend for
life!, again I have to mention U. Noor a great friend and at indoor kick-soccer I am
leading 1,000,000-1.
While away I want to thank the friends that kept me up to date: T. Rakocevic, G.
Kyei, P. Romeo, V. Murray, C. Patterson, V. Passels, Pastromi, I. K. Harnarine, Dr.
President, J. Taffe, W. Dwyer, D. Warner, N. Balaskas, J. Heliopolous, K. Barnes
(and the rest of the Barnes’s), S. Watson, T. Henry, O. Barrett, N. Adjei and Jesse
Barfield.
My family: N. Nicholson (I love you so much!), W. Whyte (my best friend), N.
Whyte (you my heart boy, stand on my shoulders and reach high), J. Whyte (Sr.),
Grandma, Dimples, Semone Myrie, N. Ramage, Mr. O, V. McGregor, M. Campbell,
v

C. Newton, L. Sutherland, all my uncles and aunts and cousins all over.
vi

Contribution to the ZEUS Experiment
As a member of the Canadian group at ZEUS I have had the opportunity to work
at a collaboration with approximately 400 physicists in Hamburg, Germany. For
almost three years I was based in Hamburg where I had a variety of duties related
to the ZEUS experiment and to my analysis.
For two years I was the ZEUS code manager responsible for maintaining the present
software at ZEUS, and for aiding in the implementation of new software packages.
As code manager I wrote applications that simplified the job and set up webpages
detailing events.
During the almost three years in Hamburg I took regular 8 shifts overlooking the
ZEUS detector.
As a member of the Heavy Flavour group at ZEUS I made presentations regarding my
analyses, and collaboration presentations discussing the state of all group analyses.
During my time at York I was the system administrator responsible for updating
and upgrading operating systems, adding desired applications, and solving computer
issues.
I presented at the 42 nd Les Recontres de Physique de la Valle d’Aoste on behalf or
ZEUS and the H1 collaborations. The topic of the presentation was heavy flavour
production at HERA.
vii

Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Contribution to ZEUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
1 Introduction 1
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Perturbative Quantum Chromodynamics . . . . . . . . . . . . . . . . 8
1.3.1 Running Coupling Constant . . . . . . . . . . . . . . . . . . . 9
2 Charm in the Proton 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Deep Inelastic Scattering Kinematics . . . . . . . . . . . . . . . . . . 12
2.2.1 DIS Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Quark Parton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 QPM Structure Functions . . . . . . . . . . . . . . . . . . . . 15
2.4 Improved Quark Parton Model . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 DGLAP Evolution . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.3 Parton Density Function . . . . . . . . . . . . . . . . . . . . . 24
2.5 Charm Contribution F2 cc to the Proton Structure Functions F 2 . . . 26
2.6 Fragmentation Functions . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6.1 Lund String Fragmentation . . . . . . . . . . . . . . . . . . . 28
2.6.2 Peterson Fragmentation . . . . . . . . . . . . . . . . . . . . . 29
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Monte Carlo Simulation 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Parton Shower . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Cross-Section Generators . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 RAPGAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 HERWIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
viii

3.3 Cross-Section Integrators . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 HVQDIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 HERA II and the ZEUS Detector 37
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 HERA II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 HERA II Beam Parameters and Luminosity . . . . . . . . . . 40
4.3 The ZEUS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 ZEUS Co-ordinate System . . . . . . . . . . . . . . . . . . . . 42
4.4 Calorimeter (CAL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.2 CAL Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.3 CAL Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.4 CAL Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.5 CAL Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Small angle Rear Tracking Detector (SRTD) . . . . . . . . . . . . . . 51
4.6 Central Tracking Detector (CTD) . . . . . . . . . . . . . . . . . . . . 52
4.6.1 Drift Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6.2 CTD Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6.3 CTD Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6.4 CTD Superlayer . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.7 Micro Vertex Detector (MVD) . . . . . . . . . . . . . . . . . . . . . 58
4.7.1 Silicon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.7.2 MVD Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.8 Straw Tube Tracker (STT) . . . . . . . . . . . . . . . . . . . . . . . 64
4.9 An Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Charged Particle Tracking at ZEUS 68
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 Fit Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.2 Pattern Recognition Fit . . . . . . . . . . . . . . . . . . . . . 72
5.2.3 Trajectory Fit . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 Tracking Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4 D ∗ Tracking and Resolutions . . . . . . . . . . . . . . . . . . . . . . 78
5.4.1 Tracking Resolution Parameters . . . . . . . . . . . . . . . . 78
5.4.2 Tracking Resolution Method . . . . . . . . . . . . . . . . . . 81
5.4.3 Resolution Results . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4.4 Delving Deeper into Resolutions . . . . . . . . . . . . . . . . 88
5.5 D ∗ Track Loss Probability . . . . . . . . . . . . . . . . . . . . . . . . 92
ix

6 Reconstruction of Event Variables 98
6.1 Reconstructed Variables . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2 CAL Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Electron Finders and Reconstruction . . . . . . . . . . . . . . . . . . 99
6.4 Hadronic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.4.1 E − P z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.4.2 Hadronic Angle γ h . . . . . . . . . . . . . . . . . . . . . . . . 101
6.5 Energy Flow Object (EFO) Reconstruction . . . . . . . . . . . . . . 102
6.6 Event Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.6.1 Electron Method . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.6.2 Jacquet-Blondel Method . . . . . . . . . . . . . . . . . . . . . 105
6.6.3 Double Angle Method . . . . . . . . . . . . . . . . . . . . . . 105
7 Event Selection and Triggering 107
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.1 FLT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.2.2 SLT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.2.3 TLT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.2.4 Global Tracking Trigger . . . . . . . . . . . . . . . . . . . . . 112
7.2.5 DST bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3 Trigger Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3.1 FLT Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.3.2 TLT Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.3.3 DST Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.4 Electron Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.5 Box Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.6 E − P z Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.7 Z Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.8 y Cleaning Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8 D ∗ Production at HERA II 118
8.1 D ∗ Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.1.1 ∆M Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.1.2 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.1.3 Wrong Charge Subtraction Method . . . . . . . . . . . . . . . 122
8.1.4 Fit Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.1.5 Number of D ∗ Candidates . . . . . . . . . . . . . . . . . . . . 126
8.1.6 Number of D ∗ Candidates Using Fit . . . . . . . . . . . . . . 130
8.2 Acceptances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
8.3 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.3.1 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . 135
8.3.2 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . 136
x

8.4 Purities and Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.5 Control Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.6 Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.7 Cross Section Results . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.7.1 Corrections to MC . . . . . . . . . . . . . . . . . . . . . . . . 155
8.7.2 Systematic Checks . . . . . . . . . . . . . . . . . . . . . . . . 157
8.7.3 HVQDIS Prediction . . . . . . . . . . . . . . . . . . . . . . . 162
8.8 D ∗ Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.9 Extending Forward in η . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.10 Numbers During 2006 and 2007 . . . . . . . . . . . . . . . . . . . . . 171
8.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9 F2 cc at HERA II 173
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.1.1 y Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.1.2 Acceptances, Purities, and Efficiencies . . . . . . . . . . . . . 177
9.1.3 Number of D ∗ Candidates . . . . . . . . . . . . . . . . . . . . 181
9.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9.2.1 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9.3 F2 cc Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
10 Conclusions 188
A Charm Tagging via P 2,Rel
T
of Jets 190
A.1 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.1.1 k T Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.3 P 2,Rel
T
Distribution in RAPGAP . . . . . . . . . . . . . . . . . . . . 195
A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
B D ∗+ and D ∗− Production Rates 202
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
B.1.1 Wrong Charge Subtraction Revisited . . . . . . . . . . . . . . 202
B.2 D ∗± Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
B.2.1 D ∗± Number Of Candidates . . . . . . . . . . . . . . . . . . . 203
B.2.2 D ∗± Difference in D ∗+ - D ∗− . . . . . . . . . . . . . . . . . . 204
B.2.3 D ∗± Acceptances . . . . . . . . . . . . . . . . . . . . . . . . . 205
B.2.4 D ∗± Differential Cross Sections . . . . . . . . . . . . . . . . . 206
B.2.5 D ∗+ to D ∗− Asymmetry . . . . . . . . . . . . . . . . . . . . . 207
B.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
C Tracking Resolutions 209
xi

D Supplementary D ∗ Plots 217
D.1 Single Differential Related Plots . . . . . . . . . . . . . . . . . . . . . 217
D.1.1 ∆M Distributions . . . . . . . . . . . . . . . . . . . . . . . . 218
D.1.2 Systematic Uncertainties of Differential Cross Sections . . . . 221
D.1.3 Consistency Check Differential Cross Sections . . . . . . . . . 231
D.1.4 HVQDIS Theoretical Uncertainties . . . . . . . . . . . . . . . 233
D.2 F2 cc Related Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
D.2.1 Q 2 − y ∆M Distributions . . . . . . . . . . . . . . . . . . . . 236
D.2.2 F2 cc Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . 237
D.2.3 F2 cc Theoretical Systematics . . . . . . . . . . . . . . . . . . . 245
Index 253
Bibliography 259
xii

List of Figures
1.1 Particle and Gauge Boson . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Coupling Constants in QED and QCD as a function of 1/Q 2 . . . . 7
2.1 The Full D ∗ Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 DIS Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 F 2 Proton Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Improved Resolution with Q 2 . . . . . . . . . . . . . . . . . . . . . . 20
2.5 QPM and LO QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Boson-Gluon Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Proton Momentum in BGF . . . . . . . . . . . . . . . . . . . . . . . 23
2.8 Altarelli-Parisi Splitting Functions . . . . . . . . . . . . . . . . . . . 24
2.9 Higher Order Splitting Function . . . . . . . . . . . . . . . . . . . . 25
2.10 Parton Distributions at Q 2 = 10 GeV 2 . . . . . . . . . . . . . . . . . 26
2.11 String Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Showering and Hadronization . . . . . . . . . . . . . . . . . . . . . . 33
4.1 Overview of the HERA Accelerator . . . . . . . . . . . . . . . . . . . 38
4.2 HERA Accelerator Layout . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Delivered and Gated Integrated Luminosities . . . . . . . . . . . . . 41
4.4 Schematic of the ZEUS Detector . . . . . . . . . . . . . . . . . . . . . 42
4.5 ZEUS Co-ordinates System . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Shower Profiles for Different Particles . . . . . . . . . . . . . . . . . 45
4.7 Schematics of a Tower . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.8 Schematics of an FCAL Module . . . . . . . . . . . . . . . . . . . . . 50
4.9 Layout of the SRTD . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.10 X − Y Layout of CTD Cell . . . . . . . . . . . . . . . . . . . . . . . 54
4.11 CTD Octant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.12 CTD Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.13 Schematic View a of Silicon Strips Sensors . . . . . . . . . . . . . . . 59
4.14 X − Y View of MVD . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.15 Side view of MVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.16 Barrel Module and Forward Sectors . . . . . . . . . . . . . . . . . . 63
xiii

4.17 STT Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.18 STT Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.19 Event with ZEUS Detector . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1 Track Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Plane X − Y Pattern Fit . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3 Coulomb Multiple Scattering in Dead Material . . . . . . . . . . . . 80
5.4 ∆P T Distributions in regions of P T for π with Gaussian Fit Superimposed
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.5 ∆P T Distributions in regions of P T for K with Gaussian Fit Superimposed
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.6 ∆P T Distributions in regions of P T for π s with Gaussian Fit Superimposed
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.7 D ∗ σ(P T ) Tracking Resolution as a function of P T with Fit Superimposed
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.8 D ∗ σ(|P|) Tracking Resolution as a function of |P| with Fit Superimposed
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.9 Primary Vertexed D ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.10 σ(η) Tracking Resolution as a function of P T with Fit Superimposed 90
5.11 σ(φ) Tracking Resolution as a function of P T with Fit Superimposed 90
5.12 P T (π s ) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 93
5.13 η(π s ) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.14 P T (π) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 94
5.15 η(π) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.16 P T (K) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 95
5.17 η(K) Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1 Energy Flow Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2 NC DIS Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.1 Data flow through the ZEUS trigger . . . . . . . . . . . . . . . . . . . 109
8.1 ∆M Signal at ZEUS . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.2 RC and WC Distributions . . . . . . . . . . . . . . . . . . . . . . . . 123
8.3 ∆M Distributions for Q 2 . . . . . . . . . . . . . . . . . . . . . . . . 127
8.4 Number of D ∗ Candidates with respect to P T (D ∗ ) . . . . . . . . . . 128
8.5 Number of D ∗ Candidates with respect to η(D ∗ ) . . . . . . . . . . . 129
8.6 Number of D ∗ Candidates with respect to Q 2 . . . . . . . . . . . . . 129
8.7 Number of D ∗ Candidates with respect to x . . . . . . . . . . . . . . 130
8.8 Number of D ∗ Candidates using Fit . . . . . . . . . . . . . . . . . . 131
8.9 P T (D ∗ ) Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.10 η(D ∗ ) Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.11 Q 2 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
xiv

8.12 x Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.13 P T (D ∗ ) Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.14 η(D ∗ ) Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.15 Q 2 Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.16 x Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.17 P T (D ∗ ) Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.18 η(D ∗ ) Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.19 Q 2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.20 x Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.21 DIS Control Plots 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.22 DIS Control Plots 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.23 DIS Control Plots 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.24 P T Control Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.25 η Control Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.26 φ Control Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.27 DIS Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.28 P T of the D ∗ Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.29 η of the D ∗ Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.30 Q 2 DA
Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.31 Q 2 e Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.32 Q 2 JB Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.33 X DA Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.34 P T (D ∗ ) Control Plot Before and After P T (π s ) Re-Weighting . . . . . 156
8.35 Systematic Check: No Electron Smearing . . . . . . . . . . . . . . . 159
8.36 Track Loss Probability Systematic Check . . . . . . . . . . . . . . . 160
8.37 No P T Re-Weight Systematic Check . . . . . . . . . . . . . . . . . . 161
8.38 P T (π s ) Cut Systematic Check . . . . . . . . . . . . . . . . . . . . . . 162
8.39 P T (D ∗ ) Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . 164
8.40 P T (D ∗ ) Differential Cross Section . . . . . . . . . . . . . . . . . . . . 165
8.41 η(D ∗ ) Differential Cross Section . . . . . . . . . . . . . . . . . . . . . 166
8.42 Q 2 Differential Differential Cross Section . . . . . . . . . . . . . . . . 167
8.43 x Differential Cross Section . . . . . . . . . . . . . . . . . . . . . . . 168
8.44 Extending η, Number of D ∗ Candidates . . . . . . . . . . . . . . . . 169
8.45 Extending η, Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.46 Extending η, Differential Cross Section . . . . . . . . . . . . . . . . . 171
9.1 Y DA Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.2 Y e Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.3 Y JB Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.4 Y DA Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.5 Y DA Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
9.6 Y DA Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
xv

9.7 Number of D ∗ Candidates . . . . . . . . . . . . . . . . . . . . . . . . 181
9.8 Y DA Cross Sections at values of Q 2 . . . . . . . . . . . . . . . . . . . 182
9.9 F2 cc vs. x at Different Q 2 . . . . . . . . . . . . . . . . . . . . . . . . 184
9.10 F2 cc vs. Q 2 at Different x . . . . . . . . . . . . . . . . . . . . . . . . 185
9.11 The F2 cc to F 2 Ratio, for increasing Q 2 . . . . . . . . . . . . . . . . . 186
A.1 Hadronization and Two Body Decay . . . . . . . . . . . . . . . . . . 190
A.2 P 2,Rel
T
of π s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
A.3 Correlation P T of generated π s and D ∗ . . . . . . . . . . . . . . . . . 198
A.4 Correlation P T , η and φ of the generated D ∗ and D ∗ Jet . . . . . . . 199
A.5 Correlation P T of Reconstructed D ∗ Jet and Generated D ∗ Jet . . . 200
B.1 Number of D ∗± Candidates . . . . . . . . . . . . . . . . . . . . . . . 203
B.2 D ∗+ - D ∗− Difference . . . . . . . . . . . . . . . . . . . . . . . . . . 204
B.3 Acceptances of D ∗± Candidates . . . . . . . . . . . . . . . . . . . . . 205
B.4 D ∗+ Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . 206
B.5 D ∗− Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . 207
B.6 D ∗± Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
C.1 σ(η) with respect to P T Tracking Resolution . . . . . . . . . . . . . . 209
C.2 σ(φ) with respect to P T Tracking Resolution . . . . . . . . . . . . . 210
C.3 σ(|P|) with respect to P T Tracking Resolution . . . . . . . . . . . . 210
C.4 σ(P T ) with respect to η Tracking Resolution . . . . . . . . . . . . . . 211
C.5 σ(η) with respect to η Tracking Resolution . . . . . . . . . . . . . . 211
C.6 σ(φ) with respect to η Tracking Resolution . . . . . . . . . . . . . . 212
C.7 σ(|P|) with respect to η Tracking Resolution . . . . . . . . . . . . . 212
C.8 σ(P T ) with respect to φ Tracking Resolution . . . . . . . . . . . . . 213
C.9 σ(η) with respect to φ Tracking Resolution . . . . . . . . . . . . . . 213
C.10 σ(φ) with respect to φ Tracking Resolution . . . . . . . . . . . . . . 214
C.11 σ(|P|) with respect to φ Tracking Resolution . . . . . . . . . . . . . 214
C.12 σ(P T ) with respect to |P| Tracking Resolution . . . . . . . . . . . . 215
C.13 σ(η) with respect to |P| Tracking Resolution . . . . . . . . . . . . . 215
C.14 σ(φ) with respect to |P| Tracking Resolution . . . . . . . . . . . . . 216
C.15 σ(|P|) with respect to |P| Tracking Resolution . . . . . . . . . . . . 216
D.1 ∆M Distributions for P T . . . . . . . . . . . . . . . . . . . . . . . . 218
D.2 ∆M Distributions for η . . . . . . . . . . . . . . . . . . . . . . . . . 219
D.3 P T ∆M Distributions for x . . . . . . . . . . . . . . . . . . . . . . . 220
D.4 Systematic Check 1: No Electron Smearing . . . . . . . . . . . . . . 221
D.5 Systematic Check 2: E e Scaled ±1% in MC . . . . . . . . . . . . . . 222
D.6 Systematic Check 3: E HAD Scaled ±3% in MC . . . . . . . . . . . . 222
D.7 Systematic Check 4: E e Cut Increased to 11 GeV in MC . . . . . . . 223
D.8 Systematic Check 5: Box Cut increased by 1 cm . . . . . . . . . . . 223
xvi

D.9 Systematic Check 6: Z vtx Decreased by 3 cm . . . . . . . . . . . . . 224
D.10 Systematic Check 7: Y e Cleaning Cut . . . . . . . . . . . . . . . . . 224
D.11 Systematic Check 8: Y JB Cleaning Cut . . . . . . . . . . . . . . . . 225
D.12 Systematic Check 9: δ h Window Widened . . . . . . . . . . . . . . . 225
D.13 Systematic Check 10: M(D 0 ) Window Widened and Narrowed . . . 226
D.14 Systematic Check 11: ∆M Window Widened and Narrowed . . . . . 226
D.15 Systematic Check 12: No P T (π s ) Re-weighting . . . . . . . . . . . . 227
D.16 Systematic Check 13: Track Loss Probability ±20% . . . . . . . . . 227
D.17 Systematic Check 14a: P T (K,π) Cut changed ±0.02 GeV . . . . . . 228
D.18 Systematic Check 14b: P T (π s ) Cut changed ±0.02 GeV . . . . . . . 228
D.19 Systematic Check 15: Doubled Beauty . . . . . . . . . . . . . . . . . 229
D.20 Consistency Check 16: Fit . . . . . . . . . . . . . . . . . . . . . . . . 229
D.21 Consistency Check 17: HERWIG . . . . . . . . . . . . . . . . . . . . 230
D.22 Consistency Check Using a Fit for Number of D ∗ Candidates . . . . 231
D.23 Consistency Check Using HERWIG instead of RAPGAP . . . . . . . 232
D.24 η(D ∗ ) Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . 233
D.25 Q 2 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . 234
D.26 X Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . 235
D.27 ∆M Distributions used for F2 cc . . . . . . . . . . . . . . . . . . . . . 236
D.28 Q 2 = 5.5 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 237
D.29 Q 2 = 6.8 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 238
D.30 Q 2 = 11 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 239
D.31 Q 2 = 18 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 240
D.32 Q 2 = 31 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 241
D.33 Q 2 = 61 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 242
D.34 Q 2 = 131 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 243
D.35 Q 2 = 510 GeV 2 Systematics . . . . . . . . . . . . . . . . . . . . . . . 244
D.36 F2 cc Theoretical Uncertainties Q 2 = 5.5 GeV 2 . . . . . . . . . . . . . 245
D.37 F2 cc Theoretical Uncertainties Q 2 = 6.8 GeV 2 . . . . . . . . . . . . . 246
D.38 F2 cc Theoretical Uncertainties Q 2 = 11 GeV 2 . . . . . . . . . . . . . 247
D.39 F2 cc Theoretical Uncertainties Q 2 = 19 GeV 2 . . . . . . . . . . . . . 248
D.40 F2 cc Theoretical Uncertainties Q 2 = 31 GeV 2 . . . . . . . . . . . . . 249
D.41 F2 cc Theoretical Uncertainties Q 2 = 61 GeV 2 . . . . . . . . . . . . . 250
D.42 F2 cc Theoretical Uncertainties Q 2 = 133 GeV 2 . . . . . . . . . . . . . 251
D.43 F2 cc Theoretical Uncertainties Q 2 = 510 GeV 2 . . . . . . . . . . . . . 252
xvii

List of Tables
1.1 Quark and Lepton Properties . . . . . . . . . . . . . . . . . . . . . . 4
1.2 The Gauge Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Decay Modes Populated in MC . . . . . . . . . . . . . . . . . . . . . 34
4.1 HERA II Beam Information . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 CAL Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 CTD Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 MVD Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5 STT Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1 REG vs ZTT tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Efficiency Reconstruction Statistics . . . . . . . . . . . . . . . . . . . 97
8.1 Systematic Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9.1 Q 2 − y Regions for F cc
2 Measurements . . . . . . . . . . . . . . . . . 174
xviii

Chapter 1
Introduction
A desire to understand the elementary particles making up our universe has been
around for quite some time. In the 6 th century BC Greek philosophers such as
Leucippus and Democritus proposed that matter was made up of smaller elementary
units. In the 19 th century, the English chemist John Dalton believed that each
element was composed of individual units which he called atoms after the Greek
word atomos, meaning indivisible.
British physicist Joseph John Thomson made the discovery that the electron is
a part of the atom. Later in the early 20 th century, he proposed that the atom
was something like plum pudding. The atom had electrons suspended in a soup of
positive charge equal to and balancing the negative charge of the electrons.
Soon after New Zealand born physicist Ernest Rutherford disproved the plum pudding
model using the famous Gold Foil Experiment. From the experiment Rutherford
concluded that the atom was composed mostly of empty space. The atom has a
massive positively charged center, called the nucleus, and orbiting electrons, similar
to how planets orbit the sun. Later he proposed that the nucleus was made up of
both positive and neutral particles called protons and neutrons, respectively.
1

In the early 20 th century, it was believed that electrons, protons, and neutrons
were the fundamental particles in the universe. Presently it is known that at least
the proton and neutron are not fundamental particles, but have structure and are
composed of partons, later to be identified as quarks.
To better understand the structure of matter, particle accelerators are constructed.
These accelerators either collide a beam onto a fixed target, or collide two beams.
The underlying principle behind using particle accelerators to probe the structure
of matter is based on the de Broglie relation. This states that as the momentum (p)
of a particle increases, the wavelength (λ) at which it resolves structure decreases:
λ = h/p, (1.1)
where h is Plank’s constant 1 . This means that higher momentum particles are able
to probe shorter distances.
The results presented in this thesis are obtained by the ZEUS collaboration at the
HERA machine located at the DESY laboratory in Hamburg Germany. DESY, the
Deutsches Elektronen-Synchrotron, is a research laboratory founded in 1959 and
(primarily) located in Hamburg, Germany, and is the home to many accelerators
and experiments including HERA, and ZEUS. HERA, the Hadron Elektron Ring
Anlage, is an electron-proton 2 (ep) colliding-beam ring accelerator. There are four
experiments located on the HERA ring, two of which are at ep interaction points.
Each beam crossing at an interaction point is called an event. The term event is more
generally used for a beam crossing with one or more interactions of interest. ZEUS
is an international collaboration with a detector located at one of the ep interaction
1 Throughout this thesis natural units are used. Natural units are when = c = 1, thus the
units of mass and momentum [GeV/c 2 ] and [GeV/c] respectively now have units of energy [GeV].
2 Unless otherwise specified the word electron will refer to both electrons and positrons.
2

sites. H1 is another collaboration with a detector centered at the other ep site.
1.1 The Standard Model
The Standard Model is a theory that attempts to describe matter and how it interacts.
Three of the four known interactions are included in this model: the electromagnetic,
weak, and strong interactions, the gravitational interaction is not included.
The gravitational interaction is much weaker than the other three interactions
at the masses concerned, thus can be safely ignored. In the Standard Model
the fundamental particles making up matter are spin 1/2 particles, called fermions.
These are organized into three generations of quarks and leptons, where both quarks
and leptons have six different flavours. Tab. 1.1 shows the electric charges in units of
the electron charge e, and masses of the fundamental particles. Quarks and leptons
are considered point-like (i.e., have no sub-structure). Each elementary particle has
a corresponding antiparticle that is identical in all intrinsic properties except for
charge, magnetic moment, lepton or baryon number.
3

Charge [e] Generation I Generation II Generation III
+2/3 up (u) charm (c) top (t)
1 → 3 MeV 1.25 ± 0.09 GeV 174.2 ± 3.3 GeV
-1/3 down (d) strange (s) bottom (b)
3 → 7 MeV 95 ± 25 MeV 4.20 ± 0.07 GeV
-1 electron (e) muon (µ) tau (τ)
510.99892 ± 4 × 10 −4 eV 105.658369 ± 9 × 10 −6 MeV 1776.99 +0.29
−0.26 MeV
0 electron neutrino (ν e) muon neutrino (ν µ) tau neutrino (ν τ)
< 2 eV < 0.19 MeV < 18.2 MeV
Table 1.1: Quark and lepton charges, masses, for the different generations. (The first two
rows refer to quarks, and the last two refer to leptons.) The masses shown in
Tab. 1.1 and 1.2 are obtained from [1].
Interaction Boson Charge [e] Mass [GeV]
electromagnetic photon (γ) 0 0
strong gluon (g) 0 0
weak W ± ±1 80.403 ± 0.029
weak Z 0 0 91.1876 ± 0.0021
Table 1.2: The gauge bosons, the interaction they mediate, and their masses are indicated.
Note that although the gluon has no electromagnetic charge, each gluon carries
a colour and anti-colour charge. The colour charge comes in three states red,
green, blue, and opposites anti-red, anti-green, anti-blue.
In the Standard Model each force has a corresponding gauge boson, which acts as the
mediator for the force between particles. Information about the interaction and the
mediating gauge boson is seen in Tab. 1.2. These gauge bosons are either emitted
or absorbed by interacting particles. The emission (or, equivalently, absorption) of a
gauge boson is seen in Fig. 1.1. The strength of a general interaction, which we call
B, can be understood as how strongly the mediating gauge boson Ω couples to the
interacting particle. This is given as the coupling constant, α B , of the interaction.
The mediating boson has 4-momentum q = k − k ′ and can be used to probe the
structure of matter. The distance that can be resolved decreases as the momentum
4

k
√ αB
k ′
Ω
Figure 1.1: The coupling of a gauge boson (Ω), mediating an interaction (B), to a particle
with initial and final 4-momentum k and k ′ , respectively. The strength of the
interaction is given by the coupling constant, α B .
transfer squared, Q 2 = −q 2 = −(k − k ′ ) 2 , increases, i.e., λ ∼ √ 1 .
Q 2
Particles made up of quarks are called hadrons and are found in two groups: baryons
and mesons. The baryon is a bound state with three quarks (the anti-baryon has
three anti-quarks). The meson is a bound state made up of a quark and anti-quark.
The quark constituents of hadrons as described are the valence quarks and will be
discussed in the following chapter.
The Standard Model is built up from two theories: the electroweak theory that
combines the electromagnetic and the weak interactions, and Quantum Chromodynamics
(QCD) encompassing the strong interaction. Some aspects of QCD are
discussed in the following section.
1.2 Quantum Chromodynamics
Quantum Chromodynamics is a SU(3) symmetry field theory used to describe the
strong interaction. Before the development of QCD, baryons introduced a paradox
into quantum theory because three quarks of the same flavour form a particle and yet
all appear to have the same quantum numbers. This violates the Pauli Exclusion
Principle. The principle states that no two fermions in a bound state can have
identical quantum numbers. The solution was to introduce a new quantum number
carried by the quarks, given the name colour. Now the three quarks of the baryon
5

have different quantum colours and no longer violate the Pauli exclusion principle.
The colour charge in QCD is analogous to the electric charge in Quantum Electrodynamics
(QED) but the former has three states compared to the latter’s one.
These states are given the name red, green, and blue, and have opposites, anti-red,
anti-green, and anti-blue, similar to the positive and negative nature of the electric
charge. An aspect of the QCD field theory not shared by QED is that the gauge boson
mediating the QCD strong interaction, the gluon, is itself colour-charged, unlike
the photon in QED, which is electrically neutral. The gluon is in fact bi-coloured,
carrying both a colour and an anti-colour charge.
Two important features arising from QCD theory are confinement and asymptotic
freedom. Confinement is the reason that isolated quarks have never been observed.
The strength of the strong force between quarks increases with their separation, so
any attempt to isolate a single quark snaps quark and anti-quark pairs (qq) out of
the vacuum, leading to the creation of hadrons in colourless states. The word colour
used to describe the new charge was chosen because in nature when red, green,
and blue light overlap, the result is white light, which is colourless. Extending the
analogy to quarks, bound three quark states will have one quark of each colour
to remain colourless (three anti-quarks will have have an anti-quark of each anticolour).
The mesons remain colourless because the quark and anti-quark are of
the same colour and anti-colour, for example, red and anti-red. The colour and
anti-colour cancel, leaving the meson colour neutral, i.e., white.
Asymptotic freedom refers to the phenomenon that at close distances (or equivalently,
at high momentum transfers, Q 2 ) the strength of the force between quarks is
very weak, allowing them to be considered non-interacting or free. This is very useful
6

ecause it allows perturbative techniques to be used to understand the interaction
between quarks at small distances.
Understanding the QCD coupling constant, α s , sheds light onto confinement and
asymptotic freedom. Consider two scenarios in which a high-momentum particle
probes a target: an EM charged target in one case, and a colour charged target in
the other.
Proton radius ≈ 1 fm
α
αs
Confinement barrier
α = 1
137
Distance from EM Charge Distance from Colour Charge
or 1/Q 2 or 1/Q 2
Figure 1.2: The QED and QCD coupling constants as a function of 1/Q 2 .
In QED, a charged target can emit a photon that is reabsorbed or that splits into
electron-positron pairs. The electron, migrates towards the positively charged QED
particle and the positron migrates away from it (the pair migrate in opposite directions
if the target is negatively charged). The photon emission leads to the creation
of a surrounding cloud of virtual particles. This cloud screens the true charge of
the target such that the probe at large distances observes an effective charge less
than the target’s actual charge. At shorter distances within this cloud, the probe
observes a charge that asymptotically increases.
Analogous to the QED case, colour-charged targets in QCD emit gluons, which are
reabsorbed or split into a quark anti-quark pair that screens the target’s true colour
7

charge. However, unlike QED, the emitted gluon can also split to a gluon-gluon
pair! Gluons carry twice the colour charge of quarks or, more accurately, carry
both a colour charge and an anti-colour charge. Gluon-gluon effects from the cloud
dominate and spread out the effective colour charge of the QCD target. A probe
at long distances (small momentum transfers) observes a large colour charge from
the QCD target, while at short distances (large momentum transfers), it observes
a vanishing colour charge. This observation is know as anti-screening. Fig. 1.2
illustrates how the QED and QCD coupling constants change with distance. The
QED coupling constant is named the fine structure constant and asymptotically
approaches α QED = e 2 /4π ≈ 1/137, where e is the electron charge. The QCD
coupling constant is analogously defined as α s = g 2 /4π, where g is the colour charge
of the quarks and gluons. As the distance increases, α s asymptotically rises. A
cut-off occurs at approximately 1 fm, which is the radius of the proton.
1.3 Perturbative Quantum Chromodynamics
Perturbative techniques are used in field theories to find approximate solutions to
problems. Typically, similar problems with known solutions are modified by a small
perturbing influence to approximate the desired problem. The solution to the perturbed
problem is not exact and is expressed in terms of a power series expanded
about a small parameter. The desired level of accuracy of the solution is determined
by the number of terms evaluated in the series. In perturbative Quantum
Chromodynamics (pQCD), cross sections involving particles of 4-momenta (p) at
momentum transfer (Q 2 ) can be expressed as an expansion about a parameter, g
∞∑
σ(p,Q 2 ) = A n (p,Q 2 )g 2n = A 0 (p,Q 2 ) + A 1 (p,Q 2 )g 2 + A 2 (p,Q 2 )g 4 + · · · . (1.2)
n=0
8

The coefficients, A n , are calculated from Feynman diagrams, each successive term
representing a higher order process. The parameter g is the previously mentioned
colour charge and at short distances is small, allowing the expansion to converge
(see Fig. 1.2) provided that the coefficients A n also remain “small”. Although not
explicitly indicated, g is a function of Q 2 , thus g = g(Q 2 ).
Renormalization Scheme
The purpose of a renormalization scheme in field theory is to systematically replace
divergent integrals appearing in Feynman calculations by finite expressions. The
renormalization process introduces a parameter called the renormalization scale, µ,
into the calculation, where the value of µ depends on the scheme used. The renormalization
scale is chosen such that divergent integrals vanish. Two approaches, the
momentum subtraction and the minimal subtraction schemes, are commonly used
and explained in [2].
1.3.1 Running Coupling Constant
The value of α s is not constant but rather a function of Q 2 , and for this reason α s is
referred to as the running coupling constant. The introduction of a renormalization
scale into the theory should not alter any physical observable. This principle leads
to the differential form of the QCD colour charge g [2]:
Q 2dg(Q2 )
dQ 2 = β(g(Q 2 )) (1.3)
(recall g(Q 2 ) = √ 4πα s (Q 2 )). The beta function, β, is a series expanded about α s
with coefficients β i , where i = 1,2, · · ·:
(
αs
β(g) = −g
4π β 1 +
9
( αs
) 2
β2 + · · ·)
. (1.4)
4π

To first order the beta function is calculated to have the value [2]:
β 1 = 11 − 2n f /3 = (11N c − 2n f )/3, (1.5)
where n f is the number of active quark flavours and N c is the number of colour
charges in the theory (in this case three). Active quark flavours refers to the different
quark flavours visible in the proton at a particular value of Q 2 (this is explained in
greater detail in the following chapter). Using equations 1.3, 1.4, and 1.5, the strong
coupling constant to first order is
α s (Q 2 ) =
4π
β 1 ln(Q 2 /Λ 2 ) . (1.6)
The energy scale at which α s becomes infinite is given the symbol Λ QCD :
( ) −2π
Λ QCD = µ exp
β 1 α s (µ 2 , (1.7)
)
where µ is the renormalization scale resulting from the renormalization scheme.
Typically, Λ QCD has a value in the range of 100 → 500 MeV. For values of Q 2
much greater than Λ 2 QCD , the coupling constant α s is small such that perturbative
QCD calculations are valid. When Q 2 is of the order Λ 2 QCD
then pQCD can no
longer be used. Thus, Λ QCD sets a scale at which quarks and gluons can be treated
as interacting very weakly or when they arrange themselves in hadrons preventing
pQCD from being used.
10

Chapter 2
Charm in the Proton
2.1 Introduction
The focus of the analyses presented in this thesis is the charm content in the proton.
This is interesting considering that the charm quark mass, m c ≈ 1.5 GeV, is greater
than the mass of the proton, m p ≈ 1 GeV. This means one of the constituents of
the proton is more massive than the proton itself!
Up until now the quark content of the proton was described as three quarks, which is
true but not the entire picture. In addition to these three quarks, called the valence
quarks, there are virtual qq pairs and gluons making up what is called the sea of the
proton. (Valence quarks and the proton sea are discussed in §2.3.) So the charm
content in the proton is actually the charm content of the proton sea. To “see”
the charm in the proton an electron probe is used to “knock” a charm quark out
of the proton, creating a charmed hadron. Charm measurements are made in this
thesis by reconstructing the charmed meson state, D ∗± , which has a quark content
cd (cd). At ZEUS, the D ∗± meson is reconstructed by looking for three tracks that
are the potential daughters of the D ∗± decay via D ∗+ → (D 0 )π + → (K − π + )π + (or
11

charge conjugate 1 ) (see Fig. 2.1).
This chapter outlines some of the theoretical framework used in this thesis, along
with some useful Lorentz-invariant variables used to describe the interaction between
protons and electrons, with a discussion of the concept of charm in the proton.
e −
γ
c
c
d
d
d
π + s
p +
d
u
u
g
c
u
D 0
u
D ∗+ K −
π +
c
W +
s
u
u
d
Figure 2.1: An ep interaction creating a D ∗+ meson. The D ∗+ strongly decays to a D 0 and
π + s , the D0 weakly decays to a K − and π + .
2.2 Deep Inelastic Scattering Kinematics
Neutral Current Deep Inelastic Scattering, NCDIS, is the process describing the
scattering of a lepton off a hadron that is mediated by the exchange of a neutral
virtual boson. At HERA this process is the scattering of an electron, with initial
and final 4-momenta k and k ′ , respectively, off of a proton with initial 4-momentum
1 In future unless otherwise specified D ∗ represents both the D ∗+ and D ∗− mesons.
12

P. The interaction has the form
e(k) + p(P) → e(k ′ ) + X, (2.1)
where X refers to all final state particles created in the interaction, excluding the
scattered electron. The term neutral current indicates that the mediating gauge
boson emitted by the electron is electrically neutral. This boson can either be a
photon (γ) or Z 0 boson. In the Q 2 region used in this thesis, the exchange of
a Z 0 boson can be safely ignored because the large mass of the Z 0 suppresses its
production at low momentum transfers. A similar interaction involving the exchange
of a charged virtual boson, the W + or the W − , is called Charged Current DIS and
in this exchange the charged electron becomes a neutral neutrino. Unless otherwise
specified, DIS will refer specifically to the neutral current case, since charged current
DIS results are outside the scope of this thesis.
In the acronym DIS, deep refers to the probing power of the boson. The greater the
momentum transfer, the finer the distances that can be resolved or the “deeper”
the proton is probed. Inelastic scattering refers to the quark being “knocked” out
of the proton and as a result the proton is broken up. Fig. 2.2 illustrates a DIS
process where key variables used in describing the interaction are indicated.
13

e(k)
p(P)
x · P
y e(k ′ )
γ/Z 0 (q 2 )
x = −q2 , x ∈ [0,1] (2.3)
2P · q
Q 2 y = P · q , y ∈ [0,1] (2.4)
P · k
Q 2 = −q 2 = −(k − k ′ ) 2 , Q 2 ∈ [0,s] (2.2)
s = (k + P) 2 ≈ 4E p · E e (2.5)
W
W 2 = (P + q) 2 , W ∈ [m 2 p,s] (2.6)
Figure 2.2: Neutral current deep inelastic scattering kinematics.
The virtuality, Q 2 , is the 4-momentum transfer squared of the exchanged photon.
The scattering of a virtual photon and a quark in DIS is called the hard scattering
process. The terms hard and soft have the following meaning: regions of large
momentum transfers allowing processes to be treated perturbatively is called hard,
and small momentum transfers where pQCD is not valid is called soft.
The Bjorken scaling variable, x, can be interpreted as the fraction of the proton’s
incoming 4-momentum carried by the struck parton. The inelasticity, y, in the
proton’s rest frame, is a measure of the amount of energy transferred between the
electron and the proton. The center-of-mass energy squared of the initial electronproton
system is s. At HERA II the beam energies yield √ s = 318 GeV. The
center-of-mass energy squared of the final hadronic system is W 2 . The Lorentzinvariant
variables Q 2 , x, and y are not completely independent: they are related
by
Q 2 = sxy, (2.7)
and because s is fixed, only two of the three variables are independent.
14

2.2.1 DIS Cross Sections
The electron-proton inclusive cross section, σ, has components arising from the
kinematics of the hard scatter, ̂σ i , and from the structure of the proton, q i :
σ(P,Q 2 ) ∝ ∑ i
∫ 1
0
dx · ̂σ i (xP,Q 2 ) ⊗ q i (x). (2.8)
The partonic cross section, ̂σ i , accounts for the hard scatter of the virtual photon
(sometimes indicated by γ ∗ ), of virtuality Q 2 , with parton i, carrying a fraction x
of the proton’s momentum, P. Feynman diagrams determine ̂σ i . The probability
density of finding parton i in the proton with momentum xP is q i (x). q i (x) is called
the parton density function, PDF. Ultimately, the PDF describes the structure of
the proton at a specific Q 2 .
2.3 Quark Parton Model
The Quark Parton Model, QPM, was developed by Feynman and Bjorken (see [3]
and [4]) to explain a feature, observed in SLAC’s DIS data, named scaling (see
below). In this model the partons are the point-like particles making up the proton.
2.3.1 QPM Structure Functions
The neutral current DIS double differential cross section can be expressed in terms
of structure functions:
d 2 σ ep
dxdQ 2 = 2πα2
xQ 4 (
2xy 2 F 1 (x) + 2(1 − y)F 2 (x) − (2y − y 2 )xF 3 (x) ) . (2.9)
The three structure functions F 1 , F 2 , and xF 3 are not explicitly calculated but must
be determined by experiment and are described shortly. (There exist alternate but
equivalent parametrizations of the double differential cross sections using different
15

structure functions.) The term scaling is used to describe the feature that in the
quark parton model the structure functions at high Q 2 are no longer dependent on
Q 2 , but only on the Bjorken scaling variable x. Probing deeper into the proton
shows no additional structure therefore, the structure functions remain constant:
F a (x,Q 2 ) → F a (x) when Q 2 → ∞ for a = 1,2,3. Thus, scaling is a consequence
of the partons being the only point-like constituents in the proton. The F 1 and F 2
structure functions are not independent. The Callan-Gross relation [5] is
2xF 1 (x) = F 2 (x), (2.10)
and arises from partons being spin 1 2
particles. The cross section can now be simplified
to
d 2 σ ep
dxdQ 2 = 2πα2
xQ 4 [(1 + (1 − y)2 )F 2 (x) − (2y + y 2 )xF 3 (x)]. (2.11)
In the QPM the F 1 and F 2 structure functions can be interpreted as the sum of the
quark density in the proton:
2xF 1 (x) = F 2 (x) = ∑ i
F i 2(x) = x ∑ i
e 2 i q i (x), (2.12)
where e i is the electric charge of quark i. The structure function xF 3 describes
the parity violating contribution to the double differential cross section. The parity
violation in NCDIS does not occur through the exchange of a photon but through
the exchange of a Z 0 boson. In the kinematic region of interest for this thesis,
5 < Q 2 < 1000 GeV 2 , the xF 3 structure function can be ignored because the mass
of the Z 0 boson, m 2 Z
≈ 8300 GeV 2 , is greater than the Q 2 limit of this thesis.
0
(A negligible xF 3 contribution occurs from the exchange of the γ − Z 0 interference
boson at the higher Q 2 values of this thesis). Neglecting xF 3 allows the double
16

differential cross section to further simplify:
d 2 σ ep
dxdQ 2 = 2πα2
xQ 4 (1 + (1 − y)2 )F 2 (x). (2.13)
If the partons making up the proton are only three quarks then summing the fractional
momenta x of the three quarks should yield:
∑
∫ 1
i 0
dx · x · q i (x) = ∑ i
∫ 1
0
F i 2 (x)
e 2 i
≡ 1. (2.14)
However, results show that the quarks carry closer to 50% of the proton’s momentum
[6]. As it turns out, the quarks carry fractions u = 0.36 and d = 0.18 of the proton’s
momentum, where u(x) is the probability density of finding the u quark carrying
fraction x of the proton’s momentum (u(x) = q i (x) where i = u). A similar definition
holds for the other quark flavours. The missing fractional momentum not carried by
the three quarks means that there exists neutral constituents to the proton carrying
the remaining half of its momentum. The following Fig. 2.3 shows the expected
proton structure F 2 for different proton models.
17

The Proton Structure:
F 2 (x)
a) 3 non-inteacting
valence quarks
1/3
x
b) 3 bound valence
quarks
1/3 x
Sea
Valence
c) 3 bound
valence
quarks plus
sea quarks
1/3 x
Figure 2.3: The F 2 structure function vs. x if the proton is:
a) three non interacting valence quarks, then a single peak at x = 1/3 with each
quark carrying 1/3 of the protons momentum is observed.
b) three interacting valence quarks, then the peak at x = 1/3 is smeared because
quarks redistribute their momentum amongst themselves.
c) three interacting valence quarks with gluons and gluons splitting to qq pairs,
the distribution no longer falls off at low x, sea quarks carry a significant fraction
of protons momentum.
The word valence, where only an atoms outer shell electrons are discussed instead of
all its electrons, is borrowed from atomic theory to describe the constituent quarks
of a hadron. The constituent quarks of a hadron are in a state of constant emission
and absorption of gluons, and these gluons in turn can split to virtual qq pairs or
into gluon pairs. These virtual quark and gluon pairs are referred to as the proton
18

sea and carry a large fraction of the proton’s momentum. The F 2 data supports the
description of the proton as a collection of valence quarks, gluons, and sea quarks,
as seen in Fig 2.3c).
2.4 Improved Quark Parton Model
In the improved quark parton model, the proton is no longer a static system of three
quarks but a dynamic system made up of quarks and gluons. The F 2 structure
function is no longer only dependent on x at high Q 2 but dependent on Q 2 as
well! Scaling violations occur in the improved QPM because at higher Q 2 ’s the F 2
structure function is sensitive to the gluons. F 2 is now a function of the quark and
anti-quark densities in the proton:
F 2 (x,Q 2 ) = x ∑ i
e 2 i
(
qi (x,Q 2 ) + q i (x,Q 2 ) ) , (2.15)
where q i is the probability density of finding anti-quark i at fractional momentum x
and momentum transfer Q 2 . The structure of the proton becomes more complicated
with increasing Q 2 because the finer resolution allows for softer qq pairs with smaller
values of x to be observed; this is depicted in Fig. 2.4. The DIS cross section in
the QPM is purely QED in nature and does not involve QCD. DIS in the QPM
involves the scattering of a virtual photon and a valence quarks of the proton in
the hard process; this is seen in Fig. 2.5a). The improved QPM allows for hard
scattering processes involving the sea quarks of the proton. Boson-gluon fusion and
QCD Compton Scattering now contribute to the DIS cross section in the improved
QPM; see Fig. 2.5b) and c).
19

γ
γ
Q 2 0
Q 2 ≫ Q 2 0
Improved
Resolution
p
x
Resolution p
a) b)
x
Figure 2.4: The virtual photon probing the proton “sees” a different quark distribution as
Q 2 increases. At higher values of Q 2 softer quarks are resolvable.
e ′ e ′ e ′
e
e
e
√ α
√ αs
√ αs
√ α
√ α
p p p
a) QPM b) LO QCD BGF
c) LO QCD Compton Scattering
Figure 2.5: a) Quark parton model flavour excitation, scattering off valence quark, no QCD
involved b) LO QCD, boson-gluon fusion scattering off sea quark c) LO QCD
Compton Scattering along with BGF, is the lowest order charm production
mechanism at HERA.
2.4.1 Factorization
Factorization separates the short distance from the long distance contributions to the
DIS cross section. A new energy scale called the factorization scale, µ f , is introduced
to set the point of separation of the two effects. An assumption is made that the
short distance and long distance contributions are independent of one another. The
proton’s F 2 structure function for the DIS process involving the exchange of a vector
20

gauge photon at virtuality Q 2 and momentum transfer x is
F (γp)
2 (x,Q 2 ) = ∑
i=f,f,G
∫ 1
0
dξ · ̂σ (γ) (
i x/ξ,Q 2 /µ 2 ,µ 2 f /µ2 ,α s (µ 2 ) ) × φ p,i (ξ,µ f ,µ 2 ).
(2.16)
The summation i is summed over all flavours of quark f, anti-quark f, and gluon
G. The new term, φ p,i , represents the quark, anti-quark, and gluon densities in
the proton and replaces q(x,Q 2 ) and q(x,Q 2 ). The integration over all fractional
momenta, ξ, is from 0 to 1.
e(k ′ )
e(k)
γ/Z 0
Q
Jet
p(P)
Hard Scatter
g
Q
D ∗
Proton Structure
Fragmentation
Figure 2.6: Photon-gluon fusion, PGF, (a specific case of the more general boson-gluon
fusion, BGF) involves the hard scatter of a photon and quark from a qq pair
produced by a gluon in the proton. Indicated in the figure is the hard scatter, the
proton structure, and fragmentation leading to the production of heavy charmed
hadrons.
Short distances are within the regime where α s is small and allow for perturbation
theory to be used. These effects are on the partonic level and are encompassed by the
hard scattering function, ̂σ (γ)
i
, calculated with Feynman diagrams. For a specific DIS
process (for example photon-gluon fusion, PGF, see Fig. 2.6) the hard scattering
21

function, ̂σ (γ)
i
, involving virtual photon γ and parton i is always the same! This
means that in all lepton-hadron interactions the PGF hard scattering function will
be the same! In fact, even in hadron-hadron interactions the hard scattering function
from photon-gluon fusion is the same! The hard scattering function depends on the
following: the fractional momentum x, virtuality Q 2 , the renormalization scale µ,
the factorization scale µ f , and the strong coupling constant α s (at Q 2 = µ 2 ).
The long distance contribution to the DIS cross section can not be treated perturbatively
due to the large coupling constant between partons. This contribution is
encompassed by the parton density function φ p,i . The long distance contribution
depends on: ξ, µ f , and µ 2 and is independent of Q 2 ! The long distance contribution
φ p,i to the DIS cross section is independent of the hard scattering process and is universal.
Once φ p,i is measured then it is known and is the same for all protons. The
φ p,i are not directly calculable but are determined by comparing the cross section
from Eq. 2.13 (with the F 2 structure function Eq. 2.16) for a specific hard scatter
̂σ (γp) to experiment.
2.4.2 DGLAP Evolution
The measurement of the parton distribution function (PDF) at one energy scale
Q 2 = µ 2 allows for its distribution to be predicted at other energy scales Q 2 = µ 2 0
provided that both coupling constants α s (µ 2 ) and α s (µ 2 0 ) are small. The ability
to predict the PDF at a new energy scale is known as the evolution of the parton
density functions, and when the renormalization scale is set to µ 2 R = Q2 the PDF
evolves according to
Q 2 d
dQ 2φ p,i(x,µ,Q 2 ) = ∑
j=f,f,G
∫ 1
x
(
dξ x
ξ P ij
ξ ;α s(Q ))
2 φ p,i (ξ,µ,Q 2 ). (2.17)
22

This important equation is called the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
(DGLAP) evolution equation [7, 8]. The DGLAP evolution equation introduces
the splitting functions P ij . The splitting function P ij (z) is proportional to the probability
of parton j to emit i carrying fraction z of parton j’s momentum (from Fig.
2.7 where z = x/ξ).
k ′
k
q
(q − xP)
P
xP
ξP
(ξ − x)P
(1 − ξ)P
Figure 2.7: Momentum transfers in BGF.
The splitting functions are perturbative expansions about α s :
P ij (z) = P (1)
ij (z) + α s
2π P (2)
ij (z) + α2 s
4π
(3)
2P ij
(z) + · · · , (2.18)
with the higher order terms involving an additional split. The parton involved in
the hard scattering interaction may have been radiated from a valence parton or
radiated from a parton that was radiated from a valence parton, etc. The splitting
functions encompass these parton radiation possibilities into the evolution of the
PDF. The effect of the splitting functions is to increase the density of low x partons
in the proton. The first-order splitting functions are seen in Fig. 2.8 and evaluated
below:
P (1)
qq (z) = 4 3
( ) 1 + z
2
1 − z
(2.19)
23

q
q(z)
q
g(z)
g
q(z)
g
g(z)
g(1-z)
P qq (z)
q(1-z)
P gq (z)
q(1-z)
P qg (z)
g(1-z)
P gg (z)
Figure 2.8: Feynman representation of the Altarelli-Parisi splitting functions.
P (1)
gq (z) = 4 3
P (1)
qg (z) = 1 2
P (1)
gg (z) = 6
( (1 − z) 2 )
+ 1
z
(2.20)
(
(1 − z) 2 + z 2) (2.21)
( z
1 − z + 1 − z ) ( 11
+ z(1 − z) +
z
2 − n )
f
δ(1 − z).
3
(2.22)
The specific quark-to-quark splitting function P (1)
qq (z) can be interpreted in two
equivalent ways: the splitting of a quark into a quark-gluon (qg) pair, or the emission
of a gluon by a quark. In both cases the quark ends up with fraction z of the initial
quark’s momentum.
Higher order splitting functions account for additional emissions between parton j
splitting to parton i. Fig. 2.9 depicts the two possible contributions to the secondorder
splitting function in the quark to quark case P (2)
qq (z).
The ability of the DGLAP equation to predict the quark and gluon distributions in
hadrons at new energy scales from a measurement at Q 2 0
makes it one of the most
powerful tools in pQCD.
2.4.3 Parton Density Function
Parton density functions are not calculable but are determined from experiment
at a value Q 2 0 , and evolved using DGLAP to extrapolate the parton densities at
other values of Q 2 . Two common schemes for the treatment of the heavy quark
24

q(z)
q(z)
q
q
a) b)
P (2)
qq (z)
Figure 2.9: The higher order P (2)
qq (z) splitting function. a) Quark splits to a qg pair followed
by the gluon splitting to a qq pair with one quark with fraction z of the
initial quark’s momentum b) Quark emits two successive gluons reducing its
momentum to fraction z.
distributions in the PDFs are as follows: a Fixed Flavour Number scheme, FFN,
and a Zero Mass Variable Flavour Number scheme, ZMVFN [9].
FFN schemes treat the quarks in the proton as massive, however the heavy quarks
c, b, and t are not active flavours in the proton PDF. Heavy flavours are produced
in the hard scatter, i.e., from γg → QQ. FFN schemes provide a useful description
of the proton PDF at low Q 2 when p T ∼ m Q .
In ZMVFN schemes all quark flavours are massless and active in the proton PDF.
Heavy quark Q begins to populate the PDF when Q 2 ≥ 4m 2 Q
. Heavy quark production
occurs through the hard scatter and additionally is produced via gq → gq
processes in the proton. This approach is valid when Q 2 ≫ m Q .
The analyses presented use the ZEUS-S PDF, a fixed flavour number scheme populated
with light quarks u, d, and s. The ZEUS-S PDF is obtained through a fit to
ZEUS data. Some other choices in PDFs include CTEQ6 [10], TRVFN [11, 12], and
MRST2001 [13].
The parton distributions shown in Fig. 2.10 are a result of fits to ZEUS data.
Indicated in the figure are the sea, gluon, and valence quark densities at fractional
25

momenta x.
Care must be given when using PDFs such that the order of the splitting functions
used is consistent with the order in perturbation theory of the hard scattering process
involved. Thus higher order processes must use higher order PDFs.
xf
0.8
0.7
0.6
(a)
ZEUS
ZEUS NLO QCD fit
α s
(M 2 Z
) = 0.118
Q 2 =10 GeV 2
xu v
tot. error
0.5
uncorr. error
0.4
xg(× 0.05)
xd v
0.3
0.2
xS(× 0.05)
0.1
0
10 -3 10 -2 10 -1 1
x
Figure 2.10: The gluon, sea, and u and d valence distributions extracted from the ZEUS-S
fit at Q 2 = 10 GeV 2 [14]. Notice at a fractional momentum x ≈ 0.3 the up
valence quark density is twice that of the down quarks, indicating the proton
is made up of 2 u and 1 d quark. At low x the gluons and the sea dominate
the fractional momentum of the proton.
2.5 Charm Contribution F cc
2 to the Proton Structure
Functions F 2
The charm content in the proton arises from the virtual quarks in the proton sea.
The sea produces quarks of all flavours. This thesis specifically measures the charm
26

contribution F cc
2 to the proton structure function F 2. The hard scatter of a charmed
sea quark, shown in the BGF diagram Fig 2.6, knocks the charm quark out of the
proton. This quark hadronizes, creating a charmed hadron. The double differential
cross section for charm production is
dσ cc (x,Q 2 )
dxdQ 2
= 2πα2
xQ 4 (
1 + (1 + y)
2 ) F cc
2 (x,Q 2 ). (2.23)
Measuring charmed hadron production in DIS events at HERA allows one to determine
the charm contribution to the proton, with the underlying assumption that the
charm in the measured charmed hadron has origins in the proton sea. Measurements
of the charmed meson D ∗ are used to determine F cc
2 .
Three regions of interest are indicated in the boson-gluon fusion diagram of Fig. 2.6:
the hard scatter, the proton structure, and finally fragmentation, which involves
charm quarks hadronizing to D ∗ mesons.
During the ep collision, Lorentz contractions and time dilation allow the electron to
see essentially a static distribution of partons in the proton. The hard scatter occurs
quickly and is unaffected by the interactions between partons. Hadronization follows
the hard scatter and is the process of quarks and gluons coalescing into colourless
particles. The three regions involved in a DIS event are assumed to be independent,
thus not influencing one another. The exclusive case of finding a D ∗ with momentum
h is
dσ D ∗(h) ∝ ∑ i
∫ 1
0
dz · ̂σ i (h/z) ⊗ φ p,i (z) ⊗ f D ∗ ,i(z), (2.24)
where f D ∗ ,i(z) is the fragmentation function that describes the probability of parton
i with momentum h/z to produce a D ∗ with momentum h.
27

2.6 Fragmentation Functions
Fragmentation Functions are used to model soft processes that are not perturbatively
calculable. Specifically, fragmentation functions model the process of quarks
becoming hadrons. The models used to describe fragmentation are phenomenological,
and the model’s parameters are tuned, i.e., set to ideal values, to describe the
data. Monte Carlo generators (see §3.1.1) use fragmentation functions to hadronize
partons to colourless objects. Two models, the Lund String and Peterson Fragmentation
functions, are discussed.
2.6.1 Lund String Fragmentation
The Lund String Fragmentation model [15] has the form
f(z) ∝
(1 − z)a
z
exp
(− bm2
z
)
, (2.25)
where z is the fractional longitudinal momentum carried by the hadron relative to
its parent parton. The parameters a and b are obtained from fits to data with values
of 0.11 and 0.52 GeV −2 , respectively, and m is the mass of qq system. Much like
in the QED case where opposite EM charged particles form dipoles, the QCD case
has an equivalent colour dipole amongst oppositely coloured qq pairs. Linear colour
fields, represented by strings, connect the qq pairs, as seen in Fig. 2.11. As the
qq pair separates the colour string stretches to the point where the energy stored
within the string is sufficient to produce a new qq pair. At this point the string will
snap. The process continues until the energy within the strings is too low to form
additional qq pairs. The Lund string fragmentation function combines the string
fragments to form hadrons.
28

Seperation
q
q
Mesons
Time
Figure 2.11: The separation of a quark and anti-quark with time. As qq pairs separate the
energy within the colour string increases. Eventually the energy is sufficient to
produce new qq pairs.
2.6.2 Peterson Fragmentation
An alternate model, the Peterson Fragmentation Function [16], describes the fragmentation
of heavy quarks to heavy hadrons. The analyses presented involve the
charm quark fragmenting to a D ∗± meson, i.e., c → cd. Peterson fragmentation has
the form
f Q (z) = 1 z
(
1 − 1 z − ǫ ) −2
Q
, (2.26)
1 − z
where ǫ Q is the Peterson fragmentation parameter and is determined from experiment.
The value of ǫ C = 0.035 for the charm fragmentation parameter is used at
ZEUS. In a fashion analogous to the DGLAP evolution of the parton density functions
(see Eq. 2.17), the fragmentation functions also evolve with Q 2 . The evolution
of the fragmentation function f Q (z) with Q 2 is
df q (x,Q 2 )
d ln Q 2 /Λ 2 = α ∫ 1
s dξ [
fq (ξ,Q 2 )P qq (x/ξ) + f g (ξ,Q 2 )P gq (x/ξ) ] , (2.27)
2π x ξ
29

df g (x,Q 2 )
d lnQ 2 /Λ 2 = α ∫ 1
s dξ
[∑
fq (ξ,Q 2 )P qg (x/ξ) + f g (ξ,Q 2 )P gg (x/ξ)]
. (2.28)
2π x ξ
2.7 Summary
The theoretical framework to understand charm production from ep interactions is
now developed. This thesis examines charm production at HERA by specifically
selecting events that include D ∗± mesons. These mesons are measured using the
ZEUS detector. Cross sections, the probability of an interaction occurring, are determined
and used to calculate the charm contribution F cc
2 to the proton structure
function F 2 .
30

Chapter 3
Monte Carlo Simulation
3.1 Introduction
Simulations are used to predict and understand many aspects of a high energy
physics experiment. At ZEUS simulations are used to model the physics processes
involved during an ep interaction and in the ZEUS detector’s response. Simulations
utilize Monte Carlo integration [17]. Monte Carlo integration uses random numbers
to evaluate numerical solutions to integrals. Random numbers are used at high
energy physics experiments because both ep events and particle interactions with
matter are explained by probabilities. Using random number integration for simulations
at high energy physics experiments falls under the umbrella term Monte
Carlo (MC).
For a process of interest two methods to predict cross sections are used: cross-section
generators and cross-section integrators [18].
3.1.1 Parton Shower
A MC generator will simulate the hard scattering process using information from the
proton’s parton distribution function and the kinematics of the event. The outgoing
partons pull quark anti-quark pairs from the vacuum, which in turn can pull more
31

particles from the vacuum in a process known as parton showering. Different MC
generators have differing treatments of how the partons shower. MC generators
typically involve the following: an evolution variable t, for example, the Q 2 of the
event, a cut-off term t 0 under which showering halts, a momentum fraction z carried
by the emitted parton relative to its parent, and the DGLAP splitting functions (see
§2.4.2) governing the creation of quarks and gluons during the showering process.
3.2 Cross-Section Generators
Consider a cross section of the form σ = ∫ f(θ,φ)dcos θdφ. To sample the phase
space 1 of this cross section means to randomly generate the variables θ ∈ [−π,π]
and φ ∈ [0,2π] uniformly. The generated variables, in this case {θ,φ}, form what is
called a candidate event. The differential cross section, dσ, for a specific candidate
event {θ 0 ,φ 0 } is called an event weight and is related to the probability for this
particular event to occur. The average of many event weights is an approximation
of ∫ dσ and eventually converges to the theoretical cross section.
The parameters of an event are generated with a frequency corresponding to a
theoretical prediction. Ideally, the generated event is indistinguishable from what
the actual detector might observe, i.e., the number, charge, and 4-momentum of
particles created during the interaction. Cross-section generators have a structure
depicted in Fig. 3.1. Five key aspects to generating an event are indicated.
Two MC Cross-Section generators, RAPGAP and HERWIG, are used in this thesis
and are discussed below.
1 The phase space is the multi-dimensional hypercube spanning all the degrees of freedom of an
interaction.
32

Decay
Hadronization
Parton
Shower
Hard Scatter
e ′
Time
Parton
Distribution
φ(x, Q 2 )
p
e
Figure 3.1: The basic structure of an event generator.
1) the parton distribution function of the proton
2) the specific hard scattering process involved
3) the parton showering after the hard scatter
4) hadronization of the partons after showering
5) decay of the unstable hadrons to daughter particles
3.2.1 RAPGAP
RAPGAP, a leading order (LO) MC event generator, is used to determine resolutions,
acceptances, efficiencies, and purities in the analyses presented in this thesis.
Key aspects to RAPGAP are as follows [17]:
• main source of charm production: BGF
• fragmentation: LUND string model implemented through PYTHIA, an event
generator [19]
• proton PDF: GRV94, a low x proton PDF [20]
• parton showering: interface to PYTHIA using colour dipole
33

The RAPGAP sample that is used is a DIS charm-enriched sample. Specifically,
each event has Q 2 > 1.5 GeV 2 and a charmed hadron with a specific decay mode.
Eight charmed hadron decay modes are populated in RAPGAP allowing for a robust
study of charm production to be performed at ZEUS.
1) D ∗ → D 0 (→ Kπ)π s 2) D ∗ → D 0 (→ K s ππ)π s
3) D ∗ → D 0 (→ Kπππ)π s 4) D 0 → Kπ
5) D s → φ(→ KK)π 6) D + → φ(→ KK)π
7) D + → Kππ 8) Λ c → Kpπ
Table 3.1: The eight charmed hadron decay modes populated in both the RAPGAP and
HERWIG MC samples.
Each decay mode occurs approximately once in every eight events. The background
in the sample includes alternate decay modes for the charmed hadrons. Charm
tagging, i.e., techniques to measure charmed hadrons, are performed with this MC
sample.
3.2.2 HERWIG
HERWIG [18] is another LO MC event generator with the following features:
• 2 → 2 (gγ → qq) scattering for heavy flavours (via BGF)
• fragmentation: Peterson fragmentation
• proton PDF: GRV94
• parton showering: angular ordering algorithm
• hadronization: cluster hadronization
34

3.3 Cross-Section Integrators
Cross-section integrators are used to create theoretical distributions of variables, for
example, the Q 2 distribution of ep collisions. The event weights, dσ, described above,
are used to create these distributions from a large number of candidate events. In
the limit of an infinite number of candidate events, the distributions, obtained from
cross-section integrators, approximate the theoretical predictions. The HVQDIS
program is a cross-section integrator and is discussed.
3.3.1 HVQDIS
HVQDIS [21] is a Heavy Quark DIS next-to-leading-order (NLO) cross-section integrator.
HVQDIS is used as the theoretical prediction for heavy quark production
for the e + p → Q + Q + X interactions at HERA. For this thesis, the PDFs used
by HVQDIS is a FFN scheme and is populated by the light quarks. The Peterson
fragmentation function transforms the heavy quarks into heavy hadrons. Many
parameters can be set when running the HVQDIS program including
• the fragmentation parameter ǫ Q ,
• the heavy quark mass,
• the proton PDF,
• the renormalization and factorization scales.
HVQDIS creates cross sections for specific heavy flavour hadrons. For the presented
analyses, HVQDIS integrates cross sections for the D ∗ meson.
35

3.4 Detector Simulation
The ZEUS detector is simulated using the GEANT3 program [22]. GEANT3 creates
a description of the detector components including dimensions, position, materials,
etc. The result of an event generator is a list of particles created during the interaction
of defined type and 4-momentum. The list of particles from the simulation
should represent what might be produced during a DIS ep interaction. ZEUS developed
a program called MOZART that takes as input the generated particle list and
simulates the following:
• the detector’s response to particle interactions with its components
• the response of the triggers (see §7.2)
• probabilities that particles go undetected
• dead times of components, i.e., the time after an interaction where the components
cannot make further measurements.
The output from MOZART has the same form as the raw data collected from the
detector. MOZART allows an identical analysis to be done on MC data in the same
way that is done for real data.
The detector simulations determine the acceptances (§8.2), purities and efficiencies
(§8.4), and tracking/energy resolutions. These four quantities are defined later but
are all related to how well the detector (and relevant software) reconstructs generated
quantities.
36

Chapter 4
HERA II and the ZEUS Detector
4.1 Introduction
ZEUS is a multi-component detector at one of the ep interaction points on the HERA
ring. The ZEUS detector measures the energies and momentum of particles created
during the collisions of the electron and proton beams. In 2000-01, HERA shut
down and underwent upgrades to better focus the ep beams and to increase the
delivered luminosity [23]. The upgraded HERA machine is referred to as HERA
II. The HERA II run period is divided into two energy configurations: high energy
runs (HER), which are relevant to this thesis, and a set of low (and medium) energy
runs (LER).
This chapter will briefly discuss HERA and the components of the ZEUS detector
relevant to this thesis.
4.2 HERA II
The Hadron Elektron Ring Anlage (HERA) was constructed in Hamburg, Germany
from May 1984 until November 1990 and commissioned in 1991. (HERA and the
beam energies are described in detail in [24].) HERA is a lepton-hadron collider.
37

Figure 4.1: Overhead photograph of the HERA and PETRA accelerator rings. The location
of the ZEUS detector is indicated by the number 1 on the photo.
Specifically, it collides an electron beam of 27.5 GeV with a proton beam of 920 GeV.
The HERA tunnel is 6.3 km in circumference and lies 10 to 25 m below ground level
(see Fig. 4.2). The tunnel contains two independent storage rings, one accelerating
electrons the other protons.
The electrons are first pre-accelerated in the linear accelerator, LINAC II, to 450
MeV, then passed to the synchrotron, DESY II, where they are accelerated to 7.5
GeV. They are then transferred to and accelerated in the PETRA storage ring to an
energy of 14 GeV and finally injected into HERA where they achieve a final energy
of 27.5 GeV.
The protons start off as negative hydrogen ions, H − , accelerated by the proton
38

Figure 4.2: The HERA ring and the location of the different experiments that lie on it. The
directions of the electron and proton beams are indicated. The ZEUS detector
is located in the southern hall.
LINAC to 50 MeV. They are passed to the proton synchrotron DESY III where
they are stripped of their electrons and accelerated to 7.5 GeV. From there the
protons are transferred to PETRA where they are injected into the HERA storage
ring after reaching an energy of 40 GeV. In the HERA ring the protons are finally
accelerated to an energy of 920 GeV.
Four experiments lie along the HERA ring. ZEUS is one them and has a multipurpose
detector at one of the ep interaction points. H1 is an experiment at another
interaction point along the HERA ring making similar measurements. HERMES and
39

HERA B are the other two experiments on HERA. As of 2007 HERA shutdown.
4.2.1 HERA II Beam Parameters and Luminosity
Within their respective storage rings, the electron and proton beams are not continuous
streams but rather collected into bunches that cross once every 96 ns. The
HERA machine collides these beams onto each other at a center of mass energy of
√ s = 318 GeV. Tab. 4.1 summarizes information on the HERA II machine.
HERA II Beam Parameters Proton Electron
Beam Current [mA] 58 140
Beam Energy [GeV] 920 27.5
Center of Mass Energy [GeV] 318
Number of Bunches 200
Colliding Bunches 174
Number per bunch (n) 4.0 · 10 10 10.3 · 10 10
Luminosity [cm 2 s −1 ] 1.82 · 10 30
Time between Crossings [ns] 96
Size of proton Beam at Crossing σ x [µm] 112 112
Size of proton Beam at Crossing σ y [µm] 30 30
Size of proton Beam at Crossing σ z [mm] 191 10.3
Circumference [m] 6336
Table 4.1: HERA II beam information after the 2000-01 upgrade [25].
The (specific) luminosity delivered by the HERA machine is calculated from Eq.
4.1 [26]:
L = f n en p
4πσ x σ y
, (4.1)
where f is the frequency of beam crossings. The luminosity delivered by HERA
is not the same as the luminosity gated by ZEUS. Downtime for detector repairs,
calibrations, trigger dead-times, and poor beam conditions are a few of the reasons
why the delivered and gated luminosities differ. Fig. 4.3 shows the integrated
luminosities delivered and gated over days running. The different years and lepton
40

Integrated Luminosity (pb -1 )
225
200
175
150
125
100
75
HERA Luminosity 2002 - 2007
Integrated Luminosity (pb -1 )
160
140
120
100
80
60
ZEUS Luminosity 2002 - 2007
50
40
25
20
0
0 50 100 150 200 250 300 350
Days of running
0
0 50 100 150 200 250 300 350
Days of running
Figure 4.3: HERA delivered integrated luminosity (left), and ZEUS gated integrated luminosity
(right) during HERA II run period. Different colours indicate different
years and types of lepton beams.
beam types are indicated. During the HERA II HER ZEUS gated an integrated
luminosity of 370.5 pb −1 .
4.3 The ZEUS Detector
The ZEUS detector shown schematically in Fig. 4.4, is built of many components
used to record tracking and energy information from an ep interaction.
41

FCAL
BCAL
SOLENOID
RCAL
Beam Pipe
← p
e →
CTD
MVD
STT
Figure 4.4: Schematic of the ZEUS detector. Some of the main components are labeled.
The ZEUS detector is designed such that the components responsible for tracking
and vertexing information are closest to the interaction point. The solenoid creates
a magnetic field of 1.43 T that aids in tracking and charge identification of particles.
All the tracking components except for the STT (see §4.8) lie within the solenoid.
The CAL completely surrounds the solenoid and the tracking detectors (see §4.4),
and measures the angle and energy deposited by charged and neutral particles.
4.3.1 ZEUS Co-ordinate System
The ZEUS co-ordinate system defines the origin as the nominal point of interaction
between the electron/proton beams. The detector is ‘centered’ on this position. By
convention the positive z-axis is defined in the direction of the proton beam, the
42

positive x-axis points towards the center of the HERA ring, and the positive y−axis
is defined such that ŷ = ẑ × ˆx (thus points upwards). The typical spherical polar
co-ordinate system is also used at ZEUS, with radius r, polar angle θ, and azimuthal
angle φ (see Fig. 4.5). The rapidity has the form y = 1 2 ln (
E+PL
E−P L
), where E and
P L are the energy and the longitudinal momentum, respectively, of a particle. The
rapidity is a Lorentz-additive, meaning that for two successive Lorentz boosts along
the same axis the rapidities add. Frequently the pseudorapidity, η, is used in place
of the polar angle θ. Defined as
(
η = − ln tan θ )
, (4.2)
2
the pseudorapidity approximates the rapidity y when particles are massless. The
forward direction, defined as η > 0, has a maximum value of η = +∞, corresponding
to the proton beam direction. The rear direction, η < 0, has a maximum of η = −∞
in the electron beam direction.
43

y
r
p
η
θ
φ
z
x
e
Figure 4.5: The ZEUS co-ordinate system centered at the interaction point of ep collisions.
Euclidean and spherical polar co-ordinates are indicated. The x-axis points to
the center of the HERA ring.
4.4 Calorimeter (CAL)
4.4.1 Calorimetry
The calorimeter in a high energy physics experiment measures energy deposits from
the outgoing particles created in the interaction. Ideally, a calorimeter stops all
particles traversing it and measures the total energy deposited by each particle.
One radiation length, X o , is the distance at which the probability that a high energy
electron has lost all but 1/e of its energy (note that in this case e is the base of the
natural logarithm). A related quantity, the absorption length, λ, is the distance
in a medium at which the probability a particle has been absorbed is 1 − e −1 .
Calorimeters are designed to be multiple radiation lengths (absorption lengths) in
depth to ensure that most of the energy of a particle traversing it is absorbed. Some
particles are not measured by calorimeters for a variety of reasons. Some particles
44

go undetected due to the geometry of the experiment (particles going down the
beam pipe). Others, like neutrinos, interact very weakly and thus travel through
calorimeters unaffected. Fig. 4.6 shows how electrons, hadrons, and muons traverse
and deposit energy in a sampling calorimeter. These are called shower profiles.
hadron electron muon
Figure 4.6: The different incoming particles shower differently in the CAL.
Electrons of energies greater than 100 MeV lose almost all their energy in Bremsstrahlung
radiation [26] (radiation created from accelerating charges). Photons of
comparable energies interact with matter mostly via pair production. Each subsequent
photon or electron-positron pair has less energy than its parent. Thus a
high energy electron traversing a calorimeter will create an electromagnetic shower
of electrons, positrons, and photons.
High energy hadrons shower differently from electrons. Secondaries, are the particles
created by the initial (primary) hadron, tend to have high transverse momenta with
respect to the primary. Showers from hadrons tend to be broad and spread out
45

laterally more so than electron showers. About half of the hadron’s energy is passed
on to high energy secondaries. The remainder of the energy is used in multi-particle
creation of particles such as pions. Many particles created in hadron showers are
neutral pions, π 0 . These pions decay immediately into two photons, which shower
electromagnetically, thus a hadronic shower can have an electromagnetic component.
Muons tend to go largely undetected by the CAL. Muon like electrons, both Bremsstrahlung
radiate, however, the larger mass of the muon strongly suppresses this
process.
To provide spatial information a calorimeter is segmented into smaller units. Each
unit measures a fraction of the deposited energy and is provided with its own readout.
Read-out systems usually consist of scintillators and photomultiplier tubes
(PMTs). A fraction of the energy lost by a charged particle excites atoms of the
scintillator, which de-excite, producing light at a specific wavelength. PMTs are
built from photoelectric cathodes, meaning electrons are ejected when light impinges
upon the cathode. This feature allows electrical signals to be produced and amplifies
them. Calorimeters made from layers of absorber and detector are called sampling
calorimeters because only a fraction (sample) of the deposited energy is converted
into a signal. A compensating calorimeter is a sampling calorimeter designed to
have an equal response for electrons and hadrons of the same energies.
4.4.2 CAL Overview
The ZEUS calorimeter was designed to meet the following criteria:
• hermetic
• jet energy measurements with resolutions of σ(E)/E = 35%/ √ E ⊕ 2% (E in
46

[GeV])
• calibration of energy scale to 1%
• angular resolution of jets better than 10 mrad and good jet separation
• hadron-electron separation for both isolated electrons and electrons in jets
ZEUS uses a Uranium Calorimeter (CAL) to achieve these aims. The CAL is divided
into three sections: the forward (FCAL), the barrel (BCAL), and the rear (RCAL)
calorimeter, covering 99.8% of the solid angle in the forward hemisphere and 99.5%
in the rear hemisphere. The smallest unit of the CAL is called a cell or section.
Cells are organized into two groups, electromagnetic (EMC) and hadronic (HAC),
and when put together form a tower. Each cell is readout via channels. This gives
position information for energy deposits. Towers are aligned in columns forming
modules (see Fig. 4.8). The radioactive nature of the uranium calorimeter is used
as a stable long-term calibration signal.
4.4.3 CAL Cells
The cells of the CAL are made from a sandwich of alternating depleted uranium
( 238 U) plates for absorbers and polystyrene scintillator plates [27]. The thickness
of the plates, 3.3 mm of uranium and 2.6 mm of scintillator, is chosen such that
electrons and hadrons have an equal response for the same energies in the CAL.
The absorber thickness of 3.3 mm corresponds to one radiation length.
The innermost cells of the CAL (i.e., cells closest to the interaction point) are EMC
cells. The CAL energy resolution for electrons scales as 18%/ √ E GeV.
HAC cells lie outside EMC cells and measure the hadronic showers. The energy
resolution for hadrons scales as 35%/ √ E GeV. The depth in radiation lengths of
47

the CAL, specifically, of the HAC cells, was designed to contain more than 95% of
the energy for 90% of the jets in all parts of the CAL. Two photomultiplier tubes
are attached to each cell and are responsible for calculating the amount of energy
deposited in the cell.
4.4.4 CAL Towers
At HERA the ep system is boosted in the positive z direction. So more particles are
expected to be found in the forward direction. For this reason the ZEUS detector,
including the CAL, is asymmetric. The proton, which has an initial energy of 920
GeV, or its remnant also move in the forward direction after the ep interaction. For
the proton’s energy to be absorbed, larger cells are needed in the FCAL with respect
to the RCAL. For these two reasons, each tower of the FCAL and BCAL have four
EMC cells and two HAC cells, thus can absorb higher energies and with improved
EMC (angular) resolution.
Beyond the electron, not too many particles are expected in the RCAL. For this
reason the angular energy resolution in the RCAL was not designed to be as high
as the FCAL and BCAL, thus the RCAL has only two EMC cells. In addition the
depth of the HAC cells in the RCAL is less than those of the BCAL, which in turn
is less than those of the FCAL (recall the initial electron energy is 27.5 GeV).
The towers of the BCAL are radially projective (wedge-shaped), thus not orthorectangular
like the towers of the FCAL and RCAL (Fig. 4.7). This arrangement
allows for a uniform angular energy resolution for the BCAL in the φ direction. The
inner radius of the BCAL is r I = 122 cm and outer r O = 290 cm, thus having a
depth of ∆r = 168 cm.
48

φ
r
patricle from IP
EMC
HAC1
HAC2
1λ
25X o
21 cm
2λ
2λ
Figure 4.7: Diagram of a BCAL tower with four EMC cells, and two HAC cells. Towers of
the BCAL are radially projective from the IP.
4.4.5 CAL Modules
Towers are grouped together in modules as seen in Fig. 4.8. A summary of the
FCAL, BCAL, and RCAL is provided in Tab. 4.2.
49

ZEUS FCAL MODULE
EMC HAC 1 HAC 2
4.6 m
PARTICLES
PMT
SCI PLATE
U PLATE
TOWER
2 m
Figure 4.8: An FCAL module composed of cells, and towers. The FCAL has one EMC cell
and two HAC cells.
50

CAL Info. FCAL BCAL RCAL
Polar Angle θ 2.2 → 39.9 ◦ 36.7 → 129.1 ◦ 128.1 → 176.5 ◦
Pseudorapidity η 3.95 → 1.01 1.10 → −0.74 −0.72 → −3.49
Number of Cells 2172 2592 1154
Towers per Module 11-23 14 11-23
Number of Modules 24 32 24
Total Radiation Length X o 194.3 127.6 108.5
Total Absorption Length λ 7.14 4.92 3.99
Face EMC Cell Dim. [cm 2 ] 5 × 20 5 × 20 20 × 20
Face HAC Cell Dim. [cm 2 ] 20 × 20 20 × 20 20 × 20
Position along z [cm] 452 > z > 222 205 > z > −125 −148 > z > −309
Total Mass [t] 240.3 310 156.6
Table 4.2: Parameters for the FCAL, BCAL, and RCAL.
4.5 Small angle Rear Tracking Detector (SRTD)
The Small angle Rear Tracking Detector (SRTD) is designed to measure the energy
and position of electrons scattered at small angles, and therefore is useful in DIS
analyses. Small angle refers to small deflections with respect to the electron beam.
These are in fact large polar angles (see §4.3.1). The SRTD lies on the inner face
of the RCAL, and consists of two layers of scintillator silicon strips (see Fig. 4.9).
One layer of 68 by 68 cm 2 silicon strips is aligned vertically, the other horizontally.
51

68
45
44
Plane 1 − Horizontal strips
2
1
68
Plane 2 − Vertical strips
3
4
25
24
01
2203
01
01
1044
24 25
68
Figure 4.9: Layout of the SRTD. The SRTD is made up of two layers of silicon strips aligned
orthogonally to each other.
The position resolution of the SRTD is 3 mm, which is better than that of the CAL
(1 cm). In addition to tracking and energy information, the SRTD also aids in
triggering, see §7.2.
4.6 Central Tracking Detector (CTD)
4.6.1 Drift Chambers
In order to operate, a drift chamber must have the following: a gas medium capable
of ionization, an electric field followed by electrons and positive ions (in opposite directions),
and a read-out system, usually wires kept at a positive potential (anode).
Unlike calorimeters, which are designed to stop incoming particles, drift chambers
make position measurements while negligibly affecting the ionizing particle’s momentum.
Conceptually, a charged particle traversing the drift chamber ionizes the
gas medium along its path. The positive ions migrate to the cathodes while the
52

electrons drift at a much greater speed towards the nearest anodes, thus creating a
measurable signal. Neutral particles traverse drift chambers undetected. Within a
(preferably uniform) magnetic field, drift chambers can determine the charge and
momentum of the ionizing agent traversing it. Charged particles moving through
a magnetic field experience the Lorentz force. The direction of the Lorentz force
experienced by a particle depends upon its charge ±q. Positively and negatively
charged particles bend in opposite directions within a magnetic field, allowing the
sign of a charged particle to be identified.
4.6.2 CTD Overview
The Central Tracking Detector (CTD) is a large single cylindrical drift chamber
situated about the ep interaction point. The CTD performs high precision tracking/momentum
measurements, and distinguishes charge ambiguity, with the help of
the 1.43 T solenoid within which it lies.
The active length of the CTD spans along the z-axis from z = −100 to z = +105
cm, with (active) inner and outer radii r I = 18.2 cm and r O = 79.4 cm, respectively.
The CTD is made up of 576 cells, 4608 sense wires (anodes), 19 584 field wires
(cathodes) for a total of 24 192 wires.
The smallest unit of the CTD is the cell. The layout of a cell is shown in Fig. 4.10.
Each cell is an identical pattern. This pattern is rotated in φ and repeated, creating
a superlayer. The cells for all superlayers are identical in design. The CTD is made
up of nine numbered superlayers with superlayer one being the innermost, and nine
the outermost. The CTD end plate is shown in Fig. 4.12 and is divided into 16
sectors, which are primarily identified for read-out and high-voltage purposes.
The gas medium of the CTD is a mixture of argon, carbon dioxide, and ethane at
53

a ratio of Ar/CO 2 /C 2 H 6 : 85/13/2. The gain, drift velocity, and ability to quench
sparking are among some of the reasons this mixture is chosen.
4.6.3 CTD Cell
The CTD cell shown in Fig. 4.10 has eight sense wires per cell, each individually
sensitive to electrons created by an ionizing particle. All the sense wires of one
superlayer are kept at the same potential (approximately +1.5 kV).
ko
field wire
shaper wire
guard wire
ground wire ko
sense wire
Figure 4.10: X − Y layout of a CTD cell. The line joining the first and last sense wire of
each cell is tilted by 45 ◦ with respect to the radial axis r. The blue (red) arrow
indicates the path of a positively (negatively) charged ionizing agent traversing
the cell creating positive ions and free electrons in its path. The green arrows
indicate the path the free electrons follow on the way to the sense wire. The
green circles are sense wires with electrons collected.
Field wires are maintained at potentials varying from superlayer to superlayer, but
kept in a range of -2.4 to -3.8 kV. The field wires are oriented to create a potential
such that the electron’s drift is radially transverse to the r − φ plane (see field lines
in Fig. 4.10). To achieve this drift direction, the electric field of the CTD cells is
54

oriented at a 45 ◦ angle with respect to r, the radial axis.
The ground wires (kept at 0 V), guard wires, and shaper wires are used to maintain
the desired electric field (and uniformity) in and on the outer ends of a cell.
Due to the geometry of the cell, polarity of the potentials, and the direction of the
magnetic field, positively charged ionizing agents, which bend counter clockwise with
respect to the magnetic field, are reconstructed better than negatively charged ionizing
agents, which bend clockwise. Roughly the same number of free electrons are
created within the gas medium by positively and negatively charged ionizing agents
traversing the CTD cell, however these electrons are collected by fewer sense wires
for positively charged ionizing agents; as illustrated in Fig. 4.10. A particle creating
free electrons collected over many sense wires can result in a lost signal. However,
if these free electrons are collected over only a few sense wires then the signal may
be detected. For this reason positively charged tracks are better reconstructed than
negatively charged tracks.
4.6.4 CTD Superlayer
The CTD is made up of nine superlayers organized into two groups: axial and stereo
layers. The odd layers (1, 3, 5, 7 and 9), have wires parallel to the chamber axis,
i.e., along the z-axis, are called the axial layers. The wires of the even layers are
stereo wires with an angle of ∼ 5 ◦ with respect to the chamber axis. Some CTD
parameters are listed in Tab. 4.3.
55

1 2
Superlayer
4 5 6 7 8 9
0.00
+4.98
0.00
−5.31
0.00
y
Stereo Angle
−5.51
0.00
x
z Out of Page
+5.62 0.00
Figure 4.11: Track traversing a CTD octant. Ghost hits for the track are shown in red.
The stereo angle is chosen such that the angular resolutions in θ and φ are approximately
equal. The axial layers are used to give the z − by − timing coordinate of
the tracks. This is done by using the time difference between the signals reaching
the two ends of the wire. The z position can be determined by the stereo layers
(z −by −stereo) from a method of parallax. The stereo superlayers break the tracking
symmetry of the axial superlayers, which helps to identify ghost tracks (see Fig.
4.11).
56

Figure 4.12: End view of the CTD from x − y plane. The nine superlayers are shown, with
their sectors and cells numbered.
Superlayer No. of Cells Stereo Angle [ ◦ ] Center Radius [cm] θ Range [ ◦ ]
1 32 0 20.97 11.3 → 168.2
2 40 4.98 27.23 14.3 → 164.8
3 48 0 35.00 18.4 → 160.7
4 56 -5.31 41.30 21.5 → 157.3
5 64 0 48.73 24.9 → 154.0
6 72 -5.51 55.52 27.9 → 151.0
7 80 0 62.74 30.9 → 147.9
8 88 5.62 69.46 33.5 → 145.2
9 96 0 76.54 36.1 → 142.6
Table 4.3: Parameters for the CTD: the number of cells per superlayer, the mean stereo
angle, the center radius of the superlayer, and the polar angle θ range.
The CTD tracking resolution with respect to the transverse momentum is quoted
57

as [28]
σ(P T )/P T = 0.0058P T ⊕ 0.0065 ⊕ 0.0014/P T , (4.3)
where P T is measured in GeV. However this value was determined before the MVD
was introduced. In Ch. 5 a new value for the P T resolution that includes the effect
of the MVD is presented.
4.7 Micro Vertex Detector (MVD)
4.7.1 Silicon Detectors
The chemical element silicon is a semiconductor that has four valence electrons.
Silicon can be negatively doped (n-type), i.e., impurities added with more that four
valence electrons, or positively doped (p-type), i.e., impurities added with fewer valence
electrons than Si. Pure Si has a high resistance, but becomes more conductive
when its temperature is increased. Doped Si is much more conductive than pure
Si and its conductivity mildly improves with temperature increases. Electrons are
responsible for conduction in n-type, and holes, the lack of an electron, in p-type.
When brought into physical contact, the n and p type semiconductors form a pn
junction, commonly used in diodes.
58

Charged particle
External amplifier
Aluminum strips
Silicon dioxide layer
20 µm
300 µm
electron
p-type implanted strips
hole
n-type silicon
N +
Aluminum
Figure 4.13: Schematic view of a silicon detector. An incoming particle traverses the silicon
and in the process creates electron-hole pairs.
Silicon detectors are built up of many pn junctions, typically with one side of the
diode segmented into strips and implanted into the other side (see Fig. 4.13). These
segmented diodes are usually paired such that their strips are perpendicular to each
other, creating an x − y grid. Silicon detectors act like solid drift chambers. A
charged particle traversing it dislodges electrons along its path, creating electronhole
pairs that eventually recombine. When placed within an electric field these
electron-hole pairs migrate (in the process, creating more electron-hole pairs), and
collect at electrodes, producing a measurable signal when amplified. Per unit length
traversed, incoming particles create much more charge carriers in Si than produced
in drift chambers. Electron hole pairs created in the silicon move much faster in
the electric field than electrons and ions in drift chambers. These two features give
silicon detectors a few advantages over drift chambers: thinner detectors can be
59

used, larger signals for incoming particles are obtained and much shorter collection
times are needed, leading to fast signals of ∼ 10 ns. Thus silicon detectors can be
designed to measure very small spatial resolutions.
4.7.2 MVD Overview
The Micro Vertex Detector (MVD) is the ZEUS silicon detector responsible for
vertexing and aids in tracking. The MVD was installed during the HERA II upgrade
and lies between the CTD and the beampipe. Before the introduction of the MVD,
the CTD required primary and secondary vertices to be separated by at least 0.5
-1.0 cm to be distinguishable [29]. The decay lengths of charmed hadrons are of the
order ∼ 100−300 µm. This means the separation of primary and secondary vertices
is too small to measure using the CTD. The MVD was built to meet the following
specifications:
• two track separation of 200 µm
• polar angle coverage of 10 → 170 ◦ (η of 2.44 → −2.44)
• three space points along each track
• impact parameter resolution of 100 µm for tracks with θ = 90 ◦ .
The addition of the MVD allows heavy flavour tagging methods to be used that
were previously not possible with the CTD alone, improves some track reconstruction
by adding MVD information to the CTD information, and provides vertexing
information.
The MVD sensors are made up of p-type silicon strips segmented as seen in Fig.
4.13. These p-type strips are embedded in an n-type substrate forming multiple pn
60

junctions. The width of a strip is 12 µm with a separation between adjacent strips
of 20 µm [30]. After every fifth strip (i.e., every 120 µm) there is a read-out strip.
The MVD is organized into two parts: the barrel (BMVD) seen in Fig. 4.14 and
4.15, and the forward (FMVD) seen in Fig. 4.15. The barrel MVD is made up of
three cylinders and the forward MVD is organized in four wheels.
Figure 4.14: X − Y view of the BMVD. Ladders, composed of many sensors, make up the
three cylinders.
61

Figure 4.15: Side view of the four wheels and three cylinders of the MVD.
BMVD
Sensors are paired perpendicular to each other forming half modules seen in Fig.
4.16a). Half modules mirrored onto each other form a module. Five modules are
glued to a ladder. There are a total of thirty ladders that form the three cylinders
making up the BMVD, with four ladders making up the first cylinder, ten making up
the second, and 16 making up the third. The ladders are not completely symmetric
about the beampipe because the MVD is not exactly centered on the beam pipe and
the x − y cross section of the beampipe is an ellipse. For this reason, the innermost
cylinder of the MVD is left incomplete; see Fig. 4.14. BMVD sensors provide z and
r − φ co-ordinates of tracks.
62

a) b)
Figure 4.16: a) Diagram of two half modules forming a barrel module. b) An MVD wheel
comprising severed sectors.
FMVD
The sensors are organized differently in the FMVD than in the barrel. Forward
sensors are paired back-to-back, creating the inner and outer sensor, called a sector;
seen in Fig. 4.16b). Each wheel is made up of 14 sectors that are rotated with
respect to one another. In total there are four wheels made up of a total 56 sectors.
Table 4.4 summarizes some of the MVD parameters.
MVD Info Barrel Wheel
Num. Of Strips Per Sensor 512 480
Strip Width [µm] 12 12
Strip Separation [µm] 20 20
Num. Of Sensors 600 112
Strip Length [mm] 62.2 5.6 → 73.3
Sensor Area [cm 2 ] 41.2 34.9 (25.7)
Total Num. Of Strips 307k 54k
Table 4.4: MVD parameters.
63

4.8 Straw Tube Tracker (STT)
In addition to the installation of the MVD during the HERA II shutdown, ZEUS
added the Straw Tube Tracker (STT). The STT is located in the forward region
of the detector, and was designed to measure the most forward tracks missed by
the CTD. The STT ranges in polar angle from 5 < θ < 25 ◦ , (3.13 < η < 1.51).
Conceptually the STT is a drift chamber, or better stated, many drift chambers.
Each straw of the STT is its own drift chamber. A sensor wire threading the straw is
kept at a potential of 1850 V. In total there are 10 944 sensor wires [31]. Similar to
the CTD, electrons created by the incoming particle drift to the sensor wire, while
the ions migrate to the outer straw.
Straw Ground
Anode 1850 V
Figure 4.17: Straws making up an STT sector. The anode wires are kept at 1850 V, while
the straw itself is maintained at ground.
STT straws are organized into layers, each successive straw in a layer longer than
the one before; as seen in Fig. 4.17. Three layers of straws are stacked on one
another, forming wedges (also called sectors). In total there are 48 wedges. There
64

are two types of wedges, STT1 and STT2, the difference between the two being the
number of straws. Six STT wedges are rotated with respect to one another forming
the eight superlayers (seen in Fig. 4.18). A module is formed when two superlayers
are combined. In total there are four modules. A well-measured track will traverse
24 layers of STT straws.
Figure 4.18: Overview of the STT. The STT comprises four modules, two of which are made
up of STT1 wedges and two of STT2 wedges.
Tab. 4.5 summarizes some STT information.
65

STT Info STT1 STT2
Num. Of Straws 11040 65 + 64 + 65 89 + 88 + 89
Radius from Beampipe [cm] 14.402 → 63.938 14.488 → 82.213
Straw Length [cm] 20.0 → 80.1 20.7 → 101.9
Straw Diameter [mm] 7.495
Straw Tube Thickness [mm] 0.123
Separation Between Straws [mm] 7.740
Table 4.5: STT parameters [32].
4.9 An Event
During the reconstruction phase of an event, ZEUS utilizes a program ZEVIS (ZEUS
Event VISualisation) that highlights, using a graphical program, the different ZEUS
components involved in reconstructing the event. The event displayed in Fig. 4.9
θ = 36, 7 ◦ θ = 90 ◦
θ = 129.1 ◦
η = 1.1
η = 0 η = −0.743
π
K
π
K
πs
θ = 0 ◦
η → ∞
πs
θ = 180 ◦
η → −∞
a) xy View
b) zr View
Figure 4.19: The ZEUS detector using the ZEVIS display program shows the result of an
ep collision. The detector is shown from xy and zr planes. This event has a
potential D ∗ candidate. Notice that two tracks in the xy plane bend in the
same direction indicating they have the same charge, while a third charge bends
in the opposite direction. These 3 tracks are the potential K, π, π s daughters
of the D ∗ .
66

may be a D ∗ event and indicates the following:
• tracks traversing both the MVD and CTD
• very forward tracks traversing the STT
• energy deposits in the forward and barrel regions of the CAL.
67

Chapter 5
Charged Particle Tracking at ZEUS
5.1 Introduction
Only the charged particles traversing the ZEUS detector have their tracks reconstructed.
At ZEUS a particle’s track is its trajectory as it traverses the detector.
The most relevant aspect of a track is its momentum reconstructed at the interaction
point (or vertex at which it was created). Tracking is done primarily through
the CTD with the aid of the MVD, STT and SRTD (described in sections §4.6, §4.7,
§4.8, §4.5, respectively). The MVD and STT were introduced during the HERA II
shutdown to improve forward tracking and vertex reconstruction. Depending on the
information available different components are used to reconstruct tracks.
The ZEUS tracking detectors attempt to convert hits/measurements from the tracking
components into tracks using reconstruction algorithms. This chapter provides
a brief introduction to ZEUS tracking, highlight two different ZEUS tracking modes
and examines the D ∗ tracking resolutions along with the D ∗ track loss probabilities.
68

5.2 Track Reconstruction
The reconstruction of tracks at ZEUS is a two phase process described in detail in
[33]:
1. Pattern Recognition Phase: hit positions in the detector components are used
to create a five parameter helix that creates a rough representation of the path
the charged particle travels within the magnetic field
2. Trajectory Fit Phase: this refining phase takes as input the five parameter
helix and makes improvements to the trajectory on a step-by-step basis.
The output is a set of parameters for each track organised in a table (named VC-
TRHL). Information on charged particle tracking by detectors is found in [34, 35].
The trajectory of a charged particle within a constant magnetic field can be described
by a helix parametrization a i , and covariance matrix c ij . Each element
in the covariance matrix, for example c 23 , loosely speaking provides a measure of
the strength of the correlation between parameters a 2 and a 3 . For a particle with
charge Q, helix radius R in the x − y plane, and reference point (X 0 ,Y 0 ,Z 0 ) on the
trajectory, ZEUS uses the five parameters:
1. a 1 = φ 0 (angle tangent to the helix in the x − y plane)
2. a 2 = Q/R
3. a 3 = QD 0 (vector to reference point on helix from origin)
4. a 4 = Z 0
5. a 5 = cot θ (= tan λ) where λ = π/2 − θ (dip with respect to the x − y plane)
69

Fig. 5.1 shows the trajectory of a particle in both the x − y and y − z planes, the
five parameters are indicated. The function s(φ) is used to describe any point on
the helix as a function of the trajectory’s outbound path length in the x − y plane:
s(φ) = −QR(φ − φ 0 ). (5.1)
s
φ 1
y
s
y
φ 0
Q
R
D 0
z = Z 0
θ
s = 0
θ 0
z
(0,0)
D 0
x
s = 0
Figure 5.1: The trajectory of a particle viewed from the x − y and y − z planes.
Rearranged, the parameters give the coordinates and momentum of a particle at
s = 0:
X = X 0 + QR(− sin φ + sin φ 0 ) (5.2)
Y = Y 0 + QR(+ cos φ − cos φ 0 ) (5.3)
Z = Z 0 + s(φ)cot θ (5.4)
p = QBR (5.5)
(p x ,p y ,p z ) = (p cos φsin θ,psinφsin θ,pcos θ). (5.6)
70

5.2.1 Fit Formalism
Fits are made by minimizing a Chi Squared, χ 2 ; the general form for the χ 2 is
χ 2 (a + δa) =
N∑
m
(
Fm − f(m;a + δa)
σ m
) 2
. (5.7)
F m is the m th measurement of N with an associated error σ m , modeled by the
function f(m;a). An expansion about a leads to
f(m;a + δa) = f(m;a) +
n∑
i=1
δa i
d
da i
f(m;a). (5.8)
The χ 2 is minimized with respect to δa by differentiating and setting to zero
dχ 2 /da i = 0 for i = 1,n, yielding the minimum δa i . The minimum δa and minimized
χ 2 in terms of fit sums, are given by
δa = U −1 B, (5.9)
χ 2 (a + δa) = S − δaB. (5.10)
The fit sums: U, an n × n matrix, B, an n dimensional array, and S, a scalar, have
the form
U ij =
B i =
S =
N∑
m
N∑
m
d
da i
f(m;a) d
da j
f(m;a)/σ 2 m , (5.11)
d
da i
f(m;a)(F m − f(m;a))/σ 2 m , (5.12)
N∑
(F m − f(m;a)) 2 /σm 2 . (5.13)
m
Thus, to minimize χ 2 the fits sums are determined, then δa is solved (Eq. 5.9), and
substituted into Eq. 5.10.
The problem of fitting data to a pattern now amounts to defining
71

• the measurement F m and its error σ m
• the fitting function f(m;a)
• the parameters a ν (ν = 1,n).
5.2.2 Pattern Recognition Fit
The full 3D pattern recognition is a two fit process using least-squares fitting. The
first fit pattern is a circle in the x − y plane, that determines a 1 and a 2 of the helix
parameters. The second fit pattern is a line in the s − Z plane, z = a 4 + sa 5 .
Plane Fit X − Y
The pattern that the measurements are fit to in the X − Y plane is a circle. For
the 2D plane fit, the trajectory is pinned to the reference point, thus setting a 3 = 0,
forcing the reference point (X 0 ,Y 0 ,Z 0 ) to lie on the circle. The objective at this
stage is to minimize the χ 2 of the form
χ 2 = ∑ m
( QDm
σ m
) 2
. (5.14)
The term QD m is the signed perpendicular distance, where D m is the distance from
the m th measurement to the circle, measured along the axis connecting the m th
measurement and the circle’s center, as seen in Fig. 5.2. The error on the m th
measurement is σ m .
72

(x m , y m )
a 1 = φ 0
D m (x 0 , y 0 )
Q = +1
y
x
R
(x c , y c )
a 2 = Q/R
Figure 5.2: X − Y plane pattern recognition fit. Measurements are fit to a circle of radius
R by minimizing D m .
At the end of this fit the parameters a 1 and a 2 are determined.
Plane Fit s − Z
The s − Z plane fit requires the a 1 and a 2 parameters obtained from the X − Y
plane fit. The Z value of the m th measurement is z m . The plane fit minimizes the
χ 2 in the s − Z plane that is the distance between z m and the line
g m = q 1 + s m q 2 . (5.15)
The parameter q 1 is the Z value at the reference point q 1 = a 4 = Z 0 , and q 2 is the
tangent of the helix dip q 2 = a 5 = cot θ. The term s m is the 2D path length (recall
Eq. 5.1) and is measured from the reference point s 0 :
s m = s(φ m ) = −(φ m − a 1 )/a 2 + s 0 . (5.16)
The χ 2 of the form
χ 2 = ∑ m
(
zm − ∑ 2
ν=1 q ν dgm
dq ν
σ m
) 2
(5.17)
73

is minimized using fit sums obtaining the remainder of the helix parameters.
Different track seeds are used depending upon which components obtained information
during the event. The CTD and MVD information is used for the X − Y
pattern fit. The s − Z fit uses information from the CTD with additional information
coming from the SRTD and STT. Not all hits are necessarily added to the fit
sums some quality filters must be passed.
5.2.3 Trajectory Fit
The axial helix from the pattern recognition phase does not have the accuracy
required for ZEUS tracking. Corrections, due to the inhomogeneous magnetic field
and from kinks arising from particles entering different detector components, are
made during the trajectory fit. Kinks are the changes in the trajectory’s outbound
slope: a 2D kink in the X − Y plane arises from the CTD-MVD junction, and a 3D
kink comes from the CTD-SRTD and CTD-STT junctions.
The trajectory fit models an outgoing particle’s path by a series of linked local
trajectories. Two types of local trajectories are used:
• local helix parameters: a local
ν
in the vicinity of the CTD and MVD,
• z-reference coordinates: q ν = (x,y,dx/dz,dy/dz,Q/|p|) in the vicinity of the
SRTD and STT (at the z value of the component) .
Only one of the linked local trajectories is treated as independent, usually the innermost
a I µ . The remaining local trajectories aj µ are dependent upon it. Each local
trajectory is swum out, while accounting for the magnetic field and kinks, to the
next measurement.
74

The trajectory fit estimates the changes δa i with respect to the initial estimates a i
found in the pattern recognition phase. A new χ 2 test is performed:
χ 2 =
N∑
m
(
dm − d(m;a)
σ m
) 2
, (5.18)
where d m is the m th measurement in the CTD (or MVD) and d(m;a) is the helixparametrised
trajectory.
During the trajectory fit, vertexing can be performed. Vertexing is the process of
determining a common position from which more than one track originates. The
primary vertex is the interaction point of the ep beams. Particles created in the
interaction originate here. Some of these decay into daughter particles creating
secondary vertices.
5.3 Tracking Modes
ZEUS employs a variety of tracking modes differing in which components are used
and on how tracks are reconstructed. The previous track reconstruction section §5.2
describes the regular (REG) tracking mode, which unless otherwise indicated is the
tracking mode used in the analyses presented. REG was developed during HERA
I and was modified in HERA II, replacing the vertexing detector 1 with the MVD,
and the forward detectors with the STT. In REG tracking the CTD is the main
component responsible for tracking; the SRTD, STT, and MVD can aid in tracking
but are not solely used.
During HERA II another tracking mode ZTT was developed. Details on ZTT
tracking can be found in [29, 31]. The ZTT tracking mode uses a Kalman filter [36]
to reconstruct tracks. The Kalman filter estimates the state of a dynamic system
1 The vertexing detector VXD was removed during the HERA I run period.
75

(trajectory) distorted by noise sources (errors on hit positions). The extension of
the Kalman filter for use in reconstructing tracks is explained in [37].
Kalman Filter
The Kalman filter requires some starting information about the track. At ZEUS the
starting information is the output from REG tracking. The track fit is a three step
process:
1. A prediction step that uses the present state k (hits already used to determine
the present trajectory) to predict the position of the next k + 1 hit on the
next measurement plane. (The plane may be the next wire for the CTD or
the next silicon sensor for the MVD.)
2. A filter step that estimates the state using the predicted k + 1 position from
step one and the k + 1 measurement and covariance obtained from the next
measurement plane.
3. A smoothing step that updates the previous k−1 step using the current filtered
state k.
The Kalman filter evaluates the measurements (hits) separately while the leastsquares
fit estimates all hits simultaneously. As the number of hits increase, the
fit sum matrices become large, resulting in an increase in the computation time for
least-squares fitting. Removing wrong hits from the least-squares fitting requires
all fits to be recalculated from the start. The effect of multiple scattering on the
trajectory is easier to incorporate into the fit when using a Kalman filter.
Tab. 5.1 provides information on REG and ZTT tracking.
76

REG
uses least-squares fitting
always uses CTD information
ZTT
uses Kalman filter
input uses output from REG tracks
uses a combined track pattern
recognition of MVD and CTD not merely
an extension of CTD tracks into the MVD
incorporates multiple scattering
and ionization loss
Table 5.1: Properties of REG and ZTT tracking.
77

5.4 D ∗ Tracking and Resolutions
5.4.1 Tracking Resolution Parameters
The tracking resolution with respect to the transverse momentum P T is parametrized
as follows:
σ(P T )/P T = a 1 P T ⊕ a 2 ⊕ a 3 /P T . (5.19)
The first term a 1 P T arises from the error on the track radius of curvature R. The
following equations show the relationship between the momentum, transverse momentum,
and radius.
P T = |P| · sin θ (5.20)
m|v| 2
R
= |qv × B| (5.21)
|P | = |qB|R (5.22)
∴ P T ∝ R. (5.23)
The error on the curvature k = 1/R due to measurement errors is [38]
σ(k) = ǫC LN . (5.24)
ZEUS quotes the RMS 2 measurement error ǫ as 200 µm [33]. The coefficient C LN
is dependent on both the number of hits N and the projected track length L. The
relationship between the uncertainties in both R and k is σ(k) = 1 R 2 σ(R). Therefore
σ(P T ) ∝ σ(R) ∝ ǫR 2 ∝ ǫP 2 T . (5.25)
Thus the first term is
σ(P T )/P T = a 1 P T . (5.26)
q
2 P
1
The Root Mean Square, RMS, error has the form ǫ RMS = n
n i=1 ǫ2 i .
78

The next two terms are of decreasing powers of P T and account for the multiple
scattering that occurs within the CTD, a 2 , and before entering the CTD, a 3 . The
tracking resolution assumes that multiple scattering affects the momentum only by
altering the track’s direction, leaving the magnitude of the momentum unaffected.
The uncertainty of the transverse momentum is thus obtained from Eq. 5.20:
σ(P T ) = |P|cos θσ(θ) (5.27)
(the minus sign in front is dropped). The a 2 term arises because within the CTD
the uncertainty in P T due to the smearing effect of multiple scattering is expected
to have a component that is linear with P [39], i.e., σ(P T ) ∝ P T . Therefore,
σ(P T )/P T = a 2 . (5.28)
The third term in the tracking resolution arises from the dead material a particle
traverses before reaching the CTD. This dead material includes the beampipe, the
MVD and the CTD inner wall. In Fig. 5.3 a particle from the vertex traverses
the dead material with a thickness in radiation lengths of L 0 at polar angle θ. The
amount of material that the particle actually traverses is L 0 /sin θ.
79

σ(θ)
L 0
θ
x = L /
0
sin θ
Figure 5.3: A particle from the interaction vertex traverses L 0 / sin θ radiation lengths of
dead material before entering the CTD. The particle’s polar angle is altered by
σ(θ).
The smearing of θ is given by [1]
σ(θ) = 0.0136
|P|
Using Eq. 5.27 the tracking resolution is
[GeV] √
L0 /sin θ(1 + 0.038ln √ L 0 /sin θ). (5.29)
[GeV]
σ(P T )
P T
= 0.0136
P T
cos θ √ L 0
√
sin θ
(1 + 0.038ln √ L 0 /sin θ) = a 3
P T
. (5.30)
Smaller parameters mean a better tracking resolution. The three terms are expected
to be uncorrelated so they are added in quadrature.
During the HERA I operating period the D ∗ transverse momentum tracking resolution
was measured to be [28] 3
σ(P T )/P T = 0.0058P T ⊕ 0.0065 ⊕ 0.0014/P T , (5.31)
with P T measured in units of GeV. Tracking resolutions have yet to be determined
since the addition of the micro vertex detector during the HERA II shutdown. The
MVD should aid in vertexing and in tracking but also acts as dead material, thereby
3 The symbol ⊕ indicates the terms are added in quadrature. The uncertainty on P T is σ(P T).
80

worsening the tracking resolution due to multiple scattering. A new D ∗ tracking
resolution is obtained following and improving on the method used for HERA I. The
following sections discuss the origin of the tracking resolution terms, the method
used to calculate the tracking resolution, and finally the results for the new tracking
resolution.
5.4.2 Tracking Resolution Method
Resolutions and residuals of quantities are determined by comparing the value of
that quantity generated (also called true or hadronic level) to its reconstructed value
(also called detector level) in the Monte Carlo. A charm-enriched RAPGAP sample
of 632 pb −1 is used for this study. The kinematic region and selection criteria are
as follows:
• P T (Dgen ∗ ) > 1.5 GeV
• |η(Dgen ∗ )| < 1.5
• P T (π s,gen ) > 0.150 GeV
• P T (π gen ,K gen ) > 0.400
GeV
• REG tracks
• primary vertexed tracks
• tracks traversing CTD superlayer 1 and superlayer
3 (or greater)
(The subscript gen refers to generator level.) Four quantities are examined: the
transverse momentum P T , the absolute value of the momentum |P|, the pseudorapidity
η (measured from [-1.5, 1.5]), and the azimuthal angle φ (from [−π, π]). The
resolution is defined as (for example, P T )
∆P T = P T,gen − P T,rec
P T,gen
. (5.32)
A subtle distinction is made between tracking resolution and resolution: the latter
refers to Eq. 5.32, and the former to Eq. 5.19, describing a distribution made from
81

esolutions. The residual is defined as (for example, η)
δη = η gen − η rec . (5.33)
(The residual is used for η and φ whose values contain zero, thus the residual avoids
division by zero.) The tracking resolution in terms of one of the variables is obtained
by plotting its resolution (or residual) in different bins of one of the variables. For
example, the resolution ∆P T can be determined for many different bins of η and
plotted, thereby giving the P T tracking resolution with respect to η.
The purpose of this approach is to understand the D ∗ tracking resolution using
the ZEUS detector. In this thesis the number of D ∗ candidates is obtained with
the wrong charge subtraction method (see §8.1.3). The approach involves matching
reconstructed tracks to their generated tracks using the ZEUS routine VMCU [40].
Care is taken to make sure the reconstructed kaons and pions from the primary
vertex are matched to a generated kaon and pion of the same charge, and the
generated parent is a D ∗ .
Once the resolution (or residual) is obtained, it is fit to a three parameter Gaussian
of the form
G(x) = N exp
(− (x − x 0) 2 )
2σ 2 , (5.34)
where the N parameter is the height of the Gaussian, and the Gaussian is centered
on x 0 with a width of σ. The width of the Gaussian in a kinematic region is that
region’s tracking resolution. The distribution of Gaussian widths is fit to Eq. 5.19:
√
( )
σ(P T )
2 a3
= (a 1 P T )
P 2 + (a 2 ) 2 + , (5.35)
T P T
giving the P T tracking resolution. The tracking resolutions of the kaon, pion, and
the slow pion from D ∗ candidates are presented.
82

5.4.3 Resolution Results
The P T distribution of the π, K, and π s in bins of P T are shown in Figs. 5.4, 5.5,
and 5.6.
1800
1600
1400
Entries
1200
1000
800
600
N = 1568.3
Mean = 0.0039
σ = 0.0140
400
200
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.40, 1.00]
T T
∈
2500
Entries
2000
1500
1000
500
N = 2252.3
Mean = 0.0005
σ = 0.0145
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [1.00, 2.00]
T T
∈
Entries
900 N = 930.9
800
Mean = −0.0001
700
σ = 0.0159
600
500
400
300
200
100
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [2.00, 3.00]
T T
∈
Entries
300
250
200
150
100
50
N = 268.4
Mean = −0.0020
σ = 0.0184
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [3.00, 4.00]
T T
∈
Entries
90
80
70
60
50
40
30
20
10
N = 80.2
Mean = −0.0009
σ = 0.0229
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [4.00, 5.00]
T T
∈
Entries
40
35
30
25
20
15
10
5
N = 32.4
Mean = −0.0011
σ = 0.0230
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [5.00, 6.00]
T T
∈
Entries
14 N = 11.4
12
Mean = 0.0045
10
σ = 0.0316
8
6
4
2
Entries
7
6
5
4
3
2
1
N = 4.8
Mean = −0.0101
σ = 0.0331
Entries
5
4
3
2
1
N = 3.4
Mean = 0.0002
σ = 0.0300
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [6.00, 7.00]
T T
∈
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [7.00, 8.00]
T T
∈
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [8.00, 9.00]
T T
∈
Entries
2
N = 1.2
1.8
Mean = 0.0227
1.6
1.4
σ = 0.0461
1.2
1
0.8
0.6
0.4
0.2
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P ∈ [9.00, 10.00]
T T
Figure 5.4: ∆P T distributions in regions of P T for π with Gaussian fit superimposed.
83

Entries
1000 N = 1031.4
Mean = 0.0058
800
σ = 0.0177
600
400
200
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.40, 1.00]
T T
∈
Entries
2200 N = 2120.2
2000
1800
1600
1400
1200
Mean = 0.0004
σ = 0.0155
1000
800
600
400
200
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [1.00, 2.00]
T T
∈
Entries
1000 N = 1015.1
800
Mean = −0.0004
σ = 0.0167
600
400
200
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [2.00, 3.00]
T T
∈
Entries
300 N = 302.8
250
Mean = −0.0011
200
σ = 0.0190
150
100
50
Entries
100
80
60
40
20
N = 91.8
Mean = 0.0005
σ = 0.0226
Entries
50 N = 39.4
40
Mean = −0.0014
σ = 0.0216
30
20
10
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [3.00, 4.00]
T T
∈
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [4.00, 5.00]
T T
∈
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [5.00, 6.00]
T T
∈
Entries
22
20
18
16
14
12
10
N = 17.3
Mean = −0.0001
σ = 0.0261
8
6
4
2
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [6.00, 7.00]
T T
∈
Entries
10
8
6
4
2
N = 7.1
Mean = −0.0022
σ = 0.0303
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [7.00, 8.00]
T T
∈
Entries
6
5
4
3
2
1
N = 3.5
Mean = −0.0018
σ = 0.0352
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [8.00, 9.00]
T T
∈
Entries
7
6
5
4
3
2
1
N = 4.1
Mean = −0.0085
σ = 0.0159
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P ∈ [9.00, 10.00]
T T
Figure 5.5: ∆P T distributions in regions of P T for K with Gaussian fits superimposed.
84

Entries
900 N = 876.3
800
700
600
500
400
300
200
Mean = 0.0187
σ = 0.0313
100
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.15, 0.20]
T T
∈
Entries
1000 N = 1041.7
Mean = 0.0172
800
σ = 0.0212
600
400
200
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.20, 0.25]
T T
∈
Entries
800
700
600
500
400
300
200
100
N = 789.6
Mean = 0.0127
σ = 0.0170
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.25, 0.30]
T T
∈
Entries
600
500
400
300
200
100
N = 557.2
Mean = 0.0102
σ = 0.0146
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.30, 0.35]
T T
∈
Entries
400
350
300
250
200
150
100
50
N = 375.9
Mean = 0.0081
σ = 0.0136
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.35, 0.40]
T T
∈
Entries
250
200
150
100
50
N = 227.3
Mean = 0.0058
σ = 0.0140
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.40, 0.45]
T T
∈
Entries
160
140
120
100
80
60
40
20
N = 148.8
Mean = 0.0061
σ = 0.0141
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.45, 0.50]
T T
∈
Entries
90 N = 92.1
80
70
60
50
Mean = 0.0037
σ = 0.0151
40
30
20
10
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.50, 0.55]
T T
∈
Entries
70 N = 65.9
60
Mean = 0.0023
50
σ = 0.0129
40
30
20
10
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
∆P ; P [0.55, 0.60]
T T
∈
Entries
45 N = 39.0
40
Mean = 0.0031
35
σ = 0.0153
30
25
20
15
10
5
0
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
P [0.60, 0.65]
∆P ; ∈
T T
Figure 5.6: ∆P T distributions in regions of P T for π s with Gaussian fits superimposed.
The P T tracking resolution, seen in Fig. 5.7, is fit to the three parameter tracking
resolution of Eq. 5.19 [41]. Since three distributions are present in the plot, two of
which cover the same region (the kaon and pion), it was chosen that the pion and
the slow pion will be used for the fit (thus excluding the kaon from the fit whose
distribution is similar to that of the pions). From the fit the three parameters
including their errors are found to be
a 1 = 0.00395 ± 0.00001,
a 2 = 0.01387 ± 0.00001,
a 3 = 0.003866 ± 0.000003. (5.36)
85

Thus, the P T tracking resolution is fit to the π s and π distributions (see Fig. 5.7):
σ(P T )/P T = 0.00395P T ⊕ 0.0139 ⊕ 0.00387/P T . (5.37)
T
)/P
T
σ(P
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
σ (P )/P = 0.00395P T
⊕ 0.01387 ⊕ 0.00387/P
T T
T
1 10
[GeV/c]
P T
π S
K
π
Figure 5.7: The σ(P T ) tracking resolution of the D ∗ as a function of P T with fit superimposed.
The quality of the P T fit will be discussed shortly but first the transverse momentum
tracking resolution is shown (see Fig. 5.8). This uses an identical fit as in Eq. 5.19,
except instead of P T the magnitude of the momentum, |P|, is used. In HERA I the
absolute momentum tracking resolution was [28]:
σ(|P|)/|P| = 0.0056|P| ⊕ 0.0074 ⊕ 0.00/|P|. (5.38)
The fit yields
σ(|P|)/|P| = 0.00398|P| ⊕ 0.013 ⊕ 0.00464/|P|. (5.39)
86

σ(|P|)/|P|
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
σ (|P|)/|P| = 0.00398|P| ⊕ 0.01300 ⊕ 0.00464/|P|
π S
K
π
1 10
|P| [GeV/c]
Figure 5.8: The σ(|P|) tracking resolution of the D ∗ as a function of |P| with fit superimposed.
The first term, a 1 |P|, in the D ∗ |P| tracking resolution is less than previously quoted.
The ZEUS tracking is an evolving system with improvements constantly being made.
A possible reason for the improvement is that the RMS measurement error has
decreased.
The second term, a 2 , arising from multiple scattering occurring within the CTD
has increased. The CTD is constantly monitored and repaired, and on occasions
wires have been lost. Over time these have contributed to the deterioration of the
resolution. In addition the potential on the CTD wires has been reduced to decrease
the number of wires burning out. The effect of this reduced potential is to decrease
the sensitivity of the CTD.
The last term, a 3 /|P|, accounts for multiple scattering occurring before the CTD,
and has increased from HERA I as expected. This increase is due to the addition
87

of the MVD, which acts as dead material.
5.4.4 Delving Deeper into Resolutions
The tracking resolutions are obtained from tracks originating from the primary vertex.
Selecting only primary vertexed tracks creates a cleaner D ∗ signal by removing
the tracks of particles with long-lived parents. Requiring the slow pion to originate
from the primary vertex is a safe approximation because the D ∗ decays quickly, thus
near to the primary vertex. However, requiring the other pion and kaon to originate
from the primary vertex artificially diminishes their tracking resolutions. Fig. 5.9
illustrates a D ∗ decaying at the primary vertex to a D 0 and slow pion. The D 0 with
its longer lifetime travels some distance before decaying to a kaon and pion.
K +
φ g,K
π −
D ∗− D 0
z-axis
Out of Page
φ r,πs
πs
−
x-axis
Figure 5.9: Requiring the tracks making up a D ∗ to be from the primary vertex has the
effect of diminishing the φ and η tracking resolution of the K and the π. The r
and g subscripts indicated reconstructed and generated quantities respectively.
The momenta p = (p x ,p y ,p z ) of the three tracks are determined by the bend of
their trajectories in the magnetic field. The azimuthal angle φ and η for each track
is calculated from its momentum p:
p = |p| =
√
p 2 x + p2 y + p2 z , (5.40)
88

( )
θ = cos −1 pz
, (5.41)
p
(
η = − ln tan θ )
, (5.42)
2
( )
φ = tan −1 py
, (5.43)
p x
where tan −1 is defined to take the correct quadrant of (p x ,p y ) into account. The
azimuthal angle φ of the slow pion is well reconstructed, however the other pion and
the kaon azimuthal angles are not. The reconstructed φ of the kaon does not reflect
its true φ at its point of creation, because the kaon is (incorrectly) reconstructed
back at the primary vertex! In fact, for particles not originating from the primary
vertex, the definition of φ and η is somewhat ambiguous because these quantities
are described from the ep interaction point.
The φ and η Tracking Resolutions with respect to P T
The σ(φ) and σ(η) distributions with respect to P T are seen in Figs. 5.10 and
5.11 and display the expected discontinuity. The tracking resolution of the primary
vertexed π s does not overlap with the tracking resolution of the secondary vertexed
π and K at a common P T .
The σ(η) and σ(φ) resolutions with respect to P T are fit to Eq. 5.44:
σ(X) = a 1 ⊕ a 2 /P T , (5.44)
where X = η or φ. The fit only spans the P T region of the slow pion because of the
discontinuity of the tracking resolution.
89

σ(η)
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
σ (η ) = 0.00067 ⊕ 0.00089/P
T
π S
K
π
1 10
P T
[GeV/c]
Figure 5.10: The σ(η) tracking resolution of the D ∗ as a function of P T with fit superimposed.
σ(φ)
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
σ (φ ) = 0.00000 ⊕ 0.00101/P
T
1 10
[GeV/c]
P T
π S
K
π
Figure 5.11: The σ(φ) tracking resolution of the D ∗ as a function of P T with fit superimposed.
90

The previous σ(η) and σ(φ) resolutions at ZEUS are quoted as [28]
σ(η) = 0.0015 ⊕ 0.0017/P T , (5.45)
σ(φ) = 0.0006 ⊕ 0.002/P T . (5.46)
The same resolutions since the addition of the MVD in HERA II are
σ(η) = 0.00067 ⊕ 0.00089/P T , (5.47)
σ(φ) = 0.000 ⊕ 0.001/P T . (5.48)
The η and φ tracking resolutions with respect to P T have improved for primary
vertexed tracks. The remaining distributions are found in App. C.
P T Tracking Resolution
The P T tracking resolution is clearly not as good as the |P| tracking resolution (see
Fig. 5.7 and 5.8, respectively). Both are better than the η and φ distributions. The
discontinuity apparent in η and φ is also seen in the P T tracking resolution, but to a
much smaller degree. This is because the P T resolution incorporates both a |P| and
θ component since P T = |P|sin θ. The θ component is the reason for the poor fit
of the P T distribution and causes the observable discontinuity where the slow pion
distribution stops and the other pion distribution begins.
91

5.5 D ∗ Track Loss Probability
The method used to determine the number of D ∗ candidates requires all three tracks
of the D ∗ ’s daughters to be reconstructed. The slow pion typically has a smaller
momentum (and thus transverse momentum) than the kaon and other pion. Some
slow pions fail to reach the CTD and instead spiral down the beampipe undetected.
This is because of their small P T . The addition of the MVD for HERA II, which
also acts as dead material, causes the π s to lose energy whilst traversing it.
The D ∗ track loss probability is a study that is used in systematics to quantify the
rate that D ∗ ’s are lost due to non-reconstructed π s . The study was done for the
HERA I ZEUS detector simulation in [42] and is reproduced here for the HERA II
detector simulation. The D ∗ track-finding efficiency is defined as a “ratio of the
number of D ∗± mesons with all three daughter tracks reconstructed to the number
of D ∗± mesons with at least both D 0 daughter tracks reconstructed”. In more
general terms, the ratio when all three D ∗ tracks are found to when at least two
tracks are found is the track-finding efficiency. The procedure involves matching
generator level tracks (gen) to reconstructed tracks (rec) in Monte Carlo. This allows
the three D ∗ daughter tracks to be clearly identified as a π, K, or π s , when
reconstructed, or, if not, indicates which tracks were lost. Two P T distributions
are made for the generated slow pion, one where the K and π are found regardless
of whether the π s is found, the other distribution made when the K, π and π s are
found. The track-finding efficiency is the ratio of the two distributions. As an extension
to when the slow pion is lost, the tracking efficiency of the kaon and other pion
are also determined. The study uses the same charm-enriched RAPGAP MC sample
of 632 pb −1 . The kinematic region of interest and selection criteria are as follows:
92

• 5 < Q 2 < 1000 GeV 2
• 0.02 < y < 0.70
• tracks traverse CTD superlayers 1
and 3 or greater
• primary vertexed tracks
• 1.5 < P T (D ∗ ) < 15.0 GeV
• |η(D ∗ )| < 1.5
• P T (π,K) > 0.400 GeV
The results of the D ∗ track loss probability study are shown in Figs. 5.12 to 5.17.
P T
(π s ) Efficiency
1.2
1
0.8
0.6
0.4
0.2
π s
0
0.2 0.4 0.6 0.8 1
P T
[GeV]
Figure 5.12: The tracking efficiency in MC of the slow pion as a function of P T .
93

) Efficiency
s
η(π
0.7
0.6
0.5
0.4
0.3
0.2
0.1
π s
0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
η
Figure 5.13: The tracking efficiency in MC of the slow pion as a function of η.
P T
(π) Efficiency
1.2
1
0.8
0.6
0.4
0.2
π
0
0 1 2 3 4 5 6 7 8 9 10
P T
[GeV]
Figure 5.14: The tracking efficiency in MC of the pion as a function of P T .
94

η(π) Efficiency
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
π
0.1
0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
η
Figure 5.15: The tracking efficiency in MC of the pion as a function of η.
P T
(K) Efficiency
1.4
1.2
1
0.8
0.6
0.4
0.2
K
0
0 1 2 3 4 5 6 7 8 9 10
P T
[GeV]
Figure 5.16: The tracking efficiency in MC of the kaon as a function of P T .
95

η(K) Efficiency
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
K
0.1
0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
η
Figure 5.17: The tracking efficiency in MC of the kaon as a function of η.
The figures show that the slow pion is the particle that limits the reconstruction of
the D ∗ . With efficiencies peaking at approximately 80% in P T and 70% in η, the
slow pion’s reconstruction rate is the lowest of the D ∗ daughters. The efficiency is
low at small transverse momentum and increases with P T and somewhat plateaus.
The efficiency drops significantly at low and high values for the pseudorapidity.
These efficiencies are significantly less than found in HERA I. In HERA I the P T
and η efficiencies were ≈ 98% and 96%, respectively. A potential source for this loss
in efficiency is due to the presence of the MVD, which for low momentum particles
acts as dead material. The general shapes of the π s distributions are the same as in
HERA I, however the dip occurring around η ∼ 0 is somewhat more pronounced in
HERA II.
The other pion and kaon have similar P T and η distributions to one another. These
P T and η distributions peak at about 90%.
96

The total number of D ∗ s generated in the specified kinematic region decaying via
D ∗ → (D 0 )π s → (Kπ)π s is 64 086. From these, all daughters are reconstructed 44%
of the time (28 361). Tab. 5.2 summarizes some of the findings.
π s K π
Other trks. found (particle irrelevant) 43 261 67.5% 33 573 52.4% 32 742 51.1%
Only trk. found 1259 2% 3125 4.9% 3830 6%
Trk. found, regardless of other trks. 39 213 61.2% 50 767 79.2% 52 303 81.6%
Table 5.2: Reconstruction statistics from the RAPGAP MC sample studied. (Trk. refers to
the track of a pion or kaon).
97

Chapter 6
Reconstruction of Event Variables
6.1 Reconstructed Variables
This chapter will discuss the reconstruction of some key components and variables,
including the CAL, scattered electrons, some hadronic variables, and methods to
measure the kinematic variables Q, y, and x, relevant to presented analysis.
6.2 CAL Reconstruction
The CAL is segmented, allowing both position and energy information to be gathered.
As mentioned in §4.4.2, electrons and hadrons shower differently within the
CAL, thus allowing a level of hadron-electron distinction. CAL information is reconstructed
from the outside inwards, i.e., HAC2 cells to HAC1 cells to EMC cells;
see Fig. 4.7. Clustering begins by merging HAC2 cells with other HAC2 cells,
HAC1 cells with other HAC1 cells, and EMC cells with other EMC cells. Merging
continues by connecting cells with their highest energy neighbors. A cone island is
formed when CAL cells from HAC2 to HAC1 to the EMC are connected.
During energy reconstruction the natural radioactivity of the CAL cells are used for
calibration. Noisy cells are identified and removed from the energy reconstruction
98

step.
The MC simulation of the electron energy measured in the CAL differs from the
energy in the real CAL. To correct for this the reconstructed MC electron energy
is adjusted by -2% and smeared by 3%; see [43] for details. Specifically, the reconstructed
electron energies are multiplied by 0.98, and smeared by multiplying this
energy by a Gaussian random number generator centered on 1 of width (σ) 0.03.
6.3 Electron Finders and Reconstruction
The identification of an electron is one of the key signals used to determine a neutral
current DIS event. ZEUS has developed a variety of electron finders during the
operation period [44]. The analyses presented use SINISTRA, which is a neuralnetwork
based finder [45].
The objective of the electron finder is to identify the scattered electron in an event.
This is a three step process:
1. Identify the electron candidates using typical signatures.
2. Assign a value, ranging from zero to one, to the quality of each candidate,
E prob . A value of E prob = 0 is not an electron candidate while a value of
E prob = 1 is the scattered electron.
3. The best amongst all electron candidates is identified, and the candidate is
accepted or rejected as the scattered electron depending upon the value of
E prob .
The electron finders use CAL and tracking information to identify electrons. The
scattered electron should deposit most of its energy in the EMC cells of the CAL.
99

These energy deposits are grouped into energy islands, where each island is an
electron candidate. Tracks are matched to islands if P T > 0.1 GeV, the angular
distance between the track and island in the θ − φ plane is less than 45 ◦ , and the
distance of closest approach is less than 50 cm. When more than one track exists
the best matching track is chosen. The neural network assigns a quality for each
island between zero for hadron-like and one for electron-like. Some of the criteria
used to determine the electron quality are the candidate with the highest energy,
and the candidate with the highest P T .
6.4 Hadronic Variables
The hadronic variables are primarily determined by summing energy deposits within
the CAL. The energy of the scattered electron is omitted from the summing process.
Two hadronic variables, ‘E − P z ’, δ h , and the hadronic angle, γ h , are used for the
reconstruction of the event kinematics and are described below.
6.4.1 E − P z
The ‘E − P z ’ or the δ h variable is useful in selecting neutral current DIS events. In
DIS events δ h should be a conserved quantity, meaning δ h,i = δ h,f . This is because
in DIS events the proton initially has all of its momentum longitudinal along the
+z direction (note P L = P z ). After colliding with the electron, the proton remnant
has very little transverse momentum, thus most of the remnant goes down the beam
pipe. The quantity δ h has the form
δ h ≡ E − P z = ∑ j (E j − P z,j ) = ∑ j E j(1 − cos θ j )
≈ ∑ √
j
PT,j 2 + P z,j 2 − ∑ j P z,j, (6.1)
100

where j is summed over all final state particles (rest masses are neglected). This
is easily calculated by summing over all energy deposits in the calorimeter (care is
taken to avoid the scattered electron). So δ h,i has a value
E − P z = (E p + E e ) − (P zp + P ze )
≈ (E p + E e ) − (E p −E e ) = 2E e = 55 GeV. (6.2)
Many particles j that go undetected by the CAL are lost down the beam pipe and
therefore must have a small P T,j . A charged current DIS event, where the scattered
electron is not found, will typically have δ h less than 30 GeV [46]. A nice feature of
δ h is that when one requires an event’s ‘E − P z ’ to be tightly centered 1 on 55 GeV,
then NCDIS events are selected.
6.4.2 Hadronic Angle γ h
The deflection angle of the struck quark is the hadronic angle, γ h , and is determined
through
cos γ h = P2 T − δ2 h
PT 2 + . (6.3)
δ2 h
The variable, P T , is the total hadronic transverse momentum of the event measured
by summing over CAL cells:
P 2 T = ∑ i
(
P
2
x,i + Py,i
2 )
. (6.4)
P T is measured poorly when the event is not fully contained, i.e., when particles
enter the beampipe.
1 The δ h resolution is σ(δ h ) = 3.00 GeV see §8.6.
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6.5 Energy Flow Object (EFO) Reconstruction
Tracking, using the tracking detectors, and energy, using the CAL, information can
be combined to give a particle’s trajectory and energy. Energy Flow Objects, EFO,
is the name ZEUS uses for the 4-momentum vectors representing these particles [47].
EMC
HAC
1
Charged
Particle
4
5
2
Neutral
Particle
3
Unmatched
Track
Figure 6.1: Energy flow objects can be made up solely of tracks, or energy deposits in CAL,
or a combination of both.
EFOs can be made from tracks, energy deposits, or both. EFOs include lowmomentum
particles failing to reach the CAL, neutral particles undetected by the
tracking detectors, and charged particles with tracks and energy deposits. In total
there are four types of EFOs:
1. one-to-one track-to-island,
2. island with no matching track,
3. a track unmatched to an island,
4. multiple track to multiple island matches.
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For one to one track to island EFOs the 4-momentum will be based on tracking
information instead of the CAL information when
σ(P)
P
E CAL
P
< σ(E CAL)
E CAL
and
< 1.0 + 1.2 · σ
(
ECAL
P
)
, (6.5)
where σ represents the uncertainty of the bracketed variable. In addition, tracking
information was favored when
E CAL < 5 GeV
or
E CAL
P < 0.25 or P T < 30 GeV. (6.6)
Otherwise CAL information was used.
Tracks unassociated with any islands were counted as charged energy. The energy
was determined from the track momentum where the mass is set to the pion mass.
Islands unassociated with any tracks are counted as neutral energy, and CAL information
was used. The magnitude of the 3 momentum is set to the CAL energy.
Multiple tracks to multiple islands are treated in a similar fashion as one to one
tracks to islands. The following replacements are made:
• E CAL → ∑ i E i,CAL,
• P → ∑ i P i,
• σ(E CAL ) → √∑ i (σ(E i,CAL)) 2 ,
• σ(P) → √∑ i (σ(P i)) 2 ,
with the same logic used to determine whether tracking or CAL information is used
to construct the EFO.
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6.6 Event Kinematics
Depending on a variety of reasons including the kinematic region, and the information
available, different approaches are used to extract the kinematic variables
Q 2 , x and y. When any two are known then the third can be determined using
the equality Q 2 = sxy, where s, the center of mass energy of the electron-proton
system squared, is s = (k + p) 2 ≈ 4E e E p . Some of the variables of interest: the
initial electron energy E e , its final energy E e, ′ the scattering angle θ e , and the initial
proton energy E p are shown in Fig. 6.2.
e
E e
E ′ e e ′
θ e
q
p
E p
γ h
Figure 6.2: Neutral current DIS kinematics. The quantities such as the angle of the scattered
electron, its initial and final 4-momentum and energy, γ h , protons initial 4-
momentum and energy are indicated.
6.6.1 Electron Method
The electron method [48] primarily uses the electron information to reconstruct Q 2
, x, and y. The scattered electron’s final energy E ′ e and angle θ e are required as
104

indicated in the following:
x e
y e
= E e E ′ e
(
)
1 − cos θ e
2E p E e − E p E e ′(1 − cos θ , (6.7)
e)
= 1 − E′ e
2E e
(1 − cos θ e ), (6.8)
Q 2 e = 2E e E ′ e(1 + cos θ e ). (6.9)
6.6.2 Jacquet-Blondel Method
The Jacquet-Blondel [49] method uses the hadronic information of the event, measured
using the CAL. Both δ h and P T are required. This method provides a good
measure of low y. However, Q 2 JB (and as a result x JB) is not measured very well
because the transverse hadronic energy is reconstructed poorly when particles are
lost down the beampipe. The relevant equations are
x JB =
Q 2
s · y JB
, (6.10)
y JB = δ h
2E e
, (6.11)
Q 2 JB =
P 2 T
1 − y JB
. (6.12)
6.6.3 Double Angle Method
The double angle method [50] uses the angles θ e and γ h to reconstruct the event, as
follows:
x DA = E e sin γ h + sin θ e + sin(θ e + γ h )
E e sin γ h + sin θ e − sin(θ e + γ h ) , (6.13)
y DA =
sin θ e (1 − cos γ h )
sin γ h + sinθ e − sin(θ e + γ h ) , (6.14)
Q 2 DA = 4E 2 e sin γ h (1 + cos γ h )
sin γ h + sinθ e − sin(θ e + γ h ) . (6.15)
The nature of an analysis will determine which of the above methods are used to
determine the event kinematics. At very high Q 2 , Q 2 1000 GeV 2 , the electron
105

method is expected to outperform the other methods. At low y, Jacquet-Blondel
should be the best. The double-angle method is expected to be the best in the
kinematic region of the analyses presented in this thesis.
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Chapter 7
Event Selection and Triggering
7.1 Introduction
As mentioned in §4.2, the HERA machine collides an electron and proton beam
every 96 ns, thus beam crossings occur at a frequency of ∼ 10 MHz. Of these beam
crossings ZEUS selects the interesting events from the background, recording both
charged- and neutral-current processes. The words trigger, filter and cut are used to
describe the choice of selecting or rejecting an event based on some criteria. Triggers
reduce the overall data to a subset of itself. Some examples of cuts include requiring
a scattered electron to be found, or Q 2 of an event to be greater than some value
Q 2 0 . The aim of the ZEUS trigger is to limit the good events written to tape to a few
Hz. These analyses look at neutral current deep inelastic scattering events, which
are identified as Q 2 > 1 GeV events where the scattered electron is found.
7.2 Triggers
ZEUS employs a three level trigger system to reduce the trigger rate from 10 MHz to
a few Hz. The first level trigger (FLT) reduces the trigger rate to ∼ 1 kHz. The FLT
comprises local processors that are combined into a global first level trigger (GFLT).
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The second level trigger (SLT) analyzes the data of the components, combining the
results into a global second level trigger (GSLT). If the event is kept then all the
data is sent to a third level trigger (TLT), which again reduces the trigger rate. The
flow of data through the ZEUS trigger system that is ultimately written to tape is
shown in Fig. 7.1.
ZEUS triggers 1 on charged and neutral current events of interest, photoproduction
events of interest, and events that may produce new particles. The analyses in this
thesis focus on deep inelastic scattering events, which include
• high Q 2 events: threshold cuts on energy or E T ,
• NC events: high energy isolated electrons (E < 30 GeV), found in the RCAL
or BCAL, balanced in P T by a jet,
• low-x NC events: lower energy isolated electron at large angle, P T balance.
1 The word trigger is used as both an noun and as a verb.
108

Rate
10 7 Hz
CTD
Front End
CAL
Front End
CTD
FLT
Other
Components
CAL
FLT
200 Hz
5 µs Pipeline
Global First
Level Trigger
Fast
Clear
Accept/Abort
Accept/Reject
5 µs Pipeline
Event Builder
CTD
SLT
Other
Components
Global Second
Level Trigger
CAL
SLT
Event Builder
35 Hz
Accept/Reject
CTD ... CAL ...
Event Builder
Third Level Trigger
cpu
cpu
cpu
cpu
cpu
cpu
5 Hz
Offline Tape
Figure 7.1: Data flow through the ZEUS trigger.
109

7.2.1 FLT
The goal of the FLT is to reduce the amount data stored by eliminating most of
the background events while maintaining a high acceptance of the “interesting”
physics events. Two common background processes are beam-gas and beam-halo
events. Events when the electron or proton beams interact with residual gas in
the beampipe or with the actual beampipe are called beam-gas events. Beam-gas
interactions create pions that subsequently decay to muons. These muons follow the
proton beam and will interact with the detector, causing false signals to measured.
These are referred to as beam-halo processes.
Every 96 ns there is a beam crossing and all the data is stored in a pipeline for 5 µs
while the FLT information is being processed. Each detector component has its own
local processor that computes trigger information and passes this to the GFLT ∼
2.5 µs after the bunch crossing, with GFLT calculations taking an additional ∼ 1.9
µs (20 bunch crossings). The GFLT makes a decision ∼ 4.4 µs (46 bunch crossings)
after the original event. If the GFLT decision is to not proceed for the event, then
the data from the components is discarded.
7.2.2 SLT
If an event passes the GFLT then all the component data is transferred to buffers for
processing by the SLT. The SLT processors function as a series of parallel processors,
with decisions made in the order of events received. The SLT has access to a large
fraction of the information from the event allowing for more complicated calculations
to be completed. The SLT primarily reduces beam-gas events using a variety of
signals. A typical signal of a beam-gas event is that these events are out of time
110

with respect to the ep collision. So, timing information in addition to the CAL FLT
is used to reject beam-gas events. The angle at which energy is deposited in the
CAL cells with respect to the beam axis can be used to further reject beam-gas
events because beam-gas events tend to have small angles (150 mrad). Events when
the beam-gas interacts with the walls of the beampipe are rejected using vertex
information. The aim of the SLT is to reduce the trigger rate from 1 kHz to 100 Hz.
Event Builder
Data from each component passing the GSLT are sent to the EVent Builder (EVB).
The EVB stores completed events, including FLT and SLT information until the
TLT is ready to process them.
7.2.3 TLT
The data passing the GSLT is sent to the TLT, which is composed of a farm of
computers. The TLT algorithms include more elaborate vertex fitting and track
finding than is possible at the SLT. In addition the kinematic variables E T , Q 2 , x,
and y are calculated and used in the decision process. The TLT runs a reduced
version of the offline analysis code on the component’s data with an output rate of
3-5 Hz.
Trigger Access using Words
For each event the three levels of trigger information are stored in words built up of
unsigned integers. An integer is made of four bytes (32 bits). An example of a third
level trigger word is TLTW(15) [51] made of 15 integers. This one word contains all
the different values for the many TLT triggers. A specific trigger within the word is
either off or on. This means the bit corresponding to that trigger has a value of 0
111

or 1, respectively. As an example the TLT trigger HFL02 information is stored at
“TLTW(10), 2”, meaning at the 2 nd bit of the 10 th word.
7.2.4 Global Tracking Trigger
During the HERA II upgrade the MVD was added to the ZEUS detector. The MVD
allows for improved vertexing and tracking information when used in addition to
the CTD and STT. For these reasons a new Global Tracking Trigger (GTT) was
introduced to be used at the SLT level. The GTT can calculate the invariant mass
of tracks and can use this information to select D mesons while maintaining a low
trigger rate.
7.2.5 DST bits
Following the TLT, data is processed with offline reconstruction software that reconstructs
the kinematics of an event, implements calibration constants, etc. The
events are passed through an additional filter that sorts events according to physics
criteria. The events sorted by this filter are given a code called a Data Storage Tape
(DST) bit. DST bits provide easy access to specific physics events.
7.3 Trigger Logic
This section briefly discusses the triggers and the DST bits used in these analyses.
The logical and group operators
• A ∩ B for a logical AND of A and B,
• A ∪ B for a logical OR of A and B,
• A ⊂ B for A is a SUBSET of B,
112

are used throughout the description.
7.3.1 FLT Triggers
The following first level trigger chain is used: FLT30 ∪FLT34 ∪FLT36 ∪FLT44 ∪
FLT46. To understand the trigger logic the following explanations are needed:
TRACK means a good CTD track was found; SRTD means a good SRTD track was
found; ISOE means an isolated electron was found; EMC, REMC, BEMC,FEMC,
is the EMC energy in the total, rear, barrel, and forward calorimeter; CAL, RCAL,
BCAL, FCAL, is the complete energy found in the total, rear, barrel, and forward
calorimeter.
The specific criteria for each trigger term are given below.
FLT30
FLT34
(RCAL ISOE ) ∩ ((RCAL + EMC ≥ 4.0 GeV) ∪ (REMC ≥ 15 GeV)) (7.1)
FLT36
(RCAL ISOE ) ∩ (RCAL + EMC ≥ 4.0 GeV) ∪
(REMC ≥ 5 GeV)) ∩ (TRACK) ∩ (CAL ≥ 0.01 GeV) (7.2)
FLT44
(RCAL ISOE ) ∩ ((RCAL + EMC ≥ 4.0 GeV) ∪ (REMC ≥ 5.0 GeV)) (7.3)
((BCAL ≥ 4.8 GeV) ∪ (RCAL + EMC ≥ 3.4 GeV)) (7.4)
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FLT46
(RCAL ISOE ) ∩
((RCAL + EMC ≥ 2.0 GeV) ∪ (REMC ≥ 3.8 GeV)) ∩
(TRACK) (7.5)
7.3.2 TLT Triggers
The TLT trigger chain SPP02∪SPP09∪DIS03∪HFL02 is used in these analyses.
The specific criteria for each trigger term are given below.
SPP02
Inclusive Low Q2 DIS
SLT SPP01 ∩
30 < E − P z < 100 GeV ∩
Box Cut |x|, |y| > 12 cm ∩
E e > 4 GeV (7.6)
SPP09
Inclusive (a bit less) Low Q2 DIS
SLT SPP01 ∩
30 < E − P z < 100 GeV ∩
Box Cut |x|, |y| > 15 cm ∩
E e > 4 GeV (7.7)
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DIS03
Inclusive medium Q2 DIS
30 < E − P z < 100 GeV ∩ (7.8)
Box Cut |x|, |y| > 35 cm ∩ (7.9)
E e > 4 GeV (7.10)
7.3.3 DST Selection
The DST chain DST9 ∪ DST10 ∪ DST11 is used.
DST9
Diffractive low x:
DST10
((E e > 4) ∪ (Zvtx)) ∩
(electron found with one of 4 electron finders). (7.11)
Vertex found:
V C ∪ TC vertex (7.12)
two routines to find vertices.
DST11
Diffractive low x, Nominal neutral current:
NC − TLT ∩ (E − P z + 2E γ ) ∪ (Z > 30 GeV) (7.13)
E γ is the energy of a radiated photon detected.
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7.4 Electron Selection
The electron selection uses the SINISTRA candidate (see §6.3) with the highest
probability as the scattered electron:
7.5 Box Cut
(Prob e > 0.9) ∩ (E e > 10 GeV). (7.14)
The x − y position of the scattered electron measured using the SRTD (see §4.5)
is used to select events. To remove events in which the electron passed through a
poorly described region of the RCAL (§4.4.2), i.e., striking the RCAL from under
the beampipe a box cut is used:
7.6 E − P z Cut
(x e > 15cm) ∪ (y e > 15cm). (7.15)
The δ h cut is useful to select NCDIS events. For these analyses
7.7 Z Vertex
40 < δ h < 60 GeV. (7.16)
The Z vert is used to select events whose interaction point lies well within the MVD
and CTD. Both the scattered electron angle, θ e , and the hadronic angle, γ h , use the
Z vert :
30 < Z vert < 30 cm. (7.17)
116

7.8 y Cleaning Cuts
Two cleaning cuts involving y JB and y e are used to select events:
y JB > 0.02,
y e < 0.95. (7.18)
117

Chapter 8
D ∗ Production at HERA II
8.1 D ∗ Reconstruction
The method used to measure D ∗± production at HERA II with the ZEUS detector
is discussed in this section. (Another approach to measure D ∗± is examined in App.
A.) The specific decay chain that is used to reconstruct a D ∗± meson is 1 :
D ∗+ → (D 0 )π + s → (K− π + )π + s
D ∗− → (D 0 )π − s → (K + π − )π − s . (8.1)
This is in fact two decays with their own branching fractions [1]:
Γ D ∗ →D 0 π s
/Γ = (67.7 ± 0.5)% (8.2)
Γ D 0 →Kπ/Γ = (3.80 ± 0.07)%. (8.3)
The D ∗ decays along three major modes. Eq. 8.2 is the mode with the largest
branching fraction and produces a well-defined signal that will be discussed shortly.
The D 0 decay mode in Eq. 8.3 produces two charged daughters. Charged particles
are important because the ZEUS detector is better at reconstructing them compared
1 For clarity Eq. 8.1 was written explicitly for both D ∗ charges, in future the charges will be
omitted unless relevant thus D ∗ → (D 0 π)π s → (Kπ)π s.
118

to neutral particles. The combined branching fraction of D ∗ → (D 0 π)π s → (Kπ)π s
is (2.57 ± 0.02)%.
One nice feature of the decay mode in Eq. 8.1 is that the combined mass of the
daughter particles is almost equal to the mass of the D ∗ :
M(D ∗ ) = 2010.0 MeV
M(D 0 ) = 1864.5 MeV
M(π s ) = 139.57 MeV
M(D ∗ ) − M(D 0 ) − M(π s ) = 5.93 MeV. (8.4)
The mass of daughters subtracted from the mass of the parent is referred to as the
Q value. Eq. 8.4 is the Q value for the D ∗ decay. With very little energy left over,
the D 0 and the π s daughters have very little momentum with respect to the parent
D ∗ . This is the reason for the subscript s on one of the pions. This pion is moving
relatively slowly. The distribution
∆M = M Kππs − M Kπ (8.5)
is expected to have a sharp peak at 145 MeV because the small Q value of the decay
strongly limits the energy of the daughters.
8.1.1 ∆M Distribution
After selecting events that pass the trigger and event cuts described in Ch. 7,
particle 4-momenta are used to calculate an invariant mass. The invariant 2-mass
of two particles is determined from:
m 2 12 = E 2 12 − P 2 12
119

= (E 1 + E 2 ) 2 − (P 1 + P 2 ) 2 = · · ·
)
= m 2 1 + m2 2
(√m + 2 2 1 + P2 1
√m 2 2 + P2 2 − P 1 · P 2 . (8.6)
The tracking detectors do not measure particle masses and for this reason each
track is assigned a kaon or pion mass when determining the invariant mass. A
similar calculation yields the invariant 3-mass:
m 2 123 = m2 1 + m2 2 + m2 3 − 2(P 1 · P 2 + P 2 · P 3 + P 3 · P 1 )
+2(√
(m
2
1 + P 2 1 )(m2 2 + P2 2 )
+ √ (m 2 2 + P2 2 )(m2 3 + P2 3 ) + √ (m 2 3 + P2 3 )(m2 1 + P2 1 ) )
. (8.7)
The procedure to make a ∆M distribution involves looping over all tracks in an
event. For every combination of three tracks, ABC, the invariant 3-mass m ABC
is determined and subtracted by the invariant 2-mass three times, once for each
2-mass possibility, i.e., m ABC −m AB , m ABC −m BC , and m ABC −m AC . (In fact the
subtraction only occurs twice for charge conservation reasons discussed shortly).
This creates a high combinatorial distribution. Charge information reduces the
combinations in the ∆M distribution by requiring that the invariant masses are
determined using possible charge combinations. Thus the invariant 3-mass that
represents the D ∗ cannot have all three particles with the same charge (the D ∗ has
charge ±1 not ±3). Similar logic dictates that the particles in the invariant 2-mass
representing the D 0 must have opposite charges. A typical ∆M signal measured
with the ZEUS detector is seen in Fig. 8.1.
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Combinations per 0.0005 GeV
2000
-1
1800
HERA II Data, L = 175.4 pb
Wrong Charge Distribution
1600
Fit
1400
1200
1000
800
600
400
200
0.135 0
0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Figure 8.1: The ∆M signal obtained at HERA using the ZEUS detector, with a luminosity
of L = 175.4 pb −1 . The data, normalized wrong charge, and fit are indicated.
8.1.2 Selection Criteria
The following D ∗ cuts are made on the candidates included in the ∆M distribution:
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Kinematic Region:
• 5 < Q 2 < 1000 GeV 2
• 0.02 < y < 0.70
Trigger and DST selection:
D ∗ Kinematics:
• 1.5 < P T (D ∗ ) < 15.0 GeV
• |η(D ∗ )| < 1.5
D ∗ Selection:
• FLT: FLT30 ∪ FLT34 ∪ FLT36 ∪
FLT44 ∪ FLT46
• TLT: SPP02 ∪ SPP09 ∪ DIS03 ∪
HFL02
• DST: DST9 ∪ DST10 ∪ DST11
Data Selection:
• 5 < Q 2 DA
< 1000
• |η(D ∗ )| < 1.5
GeV2
• y DA < 0.70 ∩ y JB > 0.02 ∩ y e < 0.95
D ∗ Track Cuts:
• 40 < δ h < 60 GeV
• |Z vtx | < 30 cm
• E corr > 10 GeV
• P T (K,π) > 0.400 GeV
• P T (π s ) > 0.120 GeV
• 1.80 < M D 0 < 1.92 GeV
• 0.143 < ∆M < 0.148 GeV
• 1.5 < P T (D ∗ ) < 15.0 GeV
• REG tracking used unless otherwise
indicated
• tracks traverse superlayers 1 to at
least 3
• box cut: x ele > 15 cm∪y ele > 15 cm
• tracks are primary vertexed
8.1.3 Wrong Charge Subtraction Method
The wrong charge subtraction method is an approach used to measure the number of
D ∗ candidates. This involves making two ∆M distributions, one of which is identical
to the distribution described in §8.1.1 and is called the right charge combination
(RC). The other ∆M distribution is made with particle charge combinations that
are impossible to be a D ∗ , i.e., (K,π,π s ) = (+,+,-) or (-,-,+), because the two pions
must be of like charge. (Again subtracted from the invariant 3-mass of this D ∗ is the
invariant 2-mass of the two like-charged tracks that make up the D 0 , again charge
impossible.) This is called the wrong-charge combination (WC). Fig. 8.2 shows the
RC and WC ∆M distributions and indicates four regions of interest.
122

Number of Events
1800
1600
1400
1200
1000
800
600
400
200
A
B
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17
∆ M
Number of Events
700
600
500
400
300
200
100
C
D
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17
∆ M
Figure 8.2: The right charge and wrong charge ∆M distributions are shown. Key regions
of interest are highlighted.
• Region A: the entries in the RC distribution lying between 0.143 < ∆M <
0.148 GeV. This is where the D ∗ signal is visible.
• Region B: the entries in the RC distribution between 0.150 < ∆M < 0.165
GeV (the background).
• Region C: the entries in the WC distribution between 0.143 < ∆M < 0.148
GeV.
• Region D: the entries in the WC distribution between 0.150 < ∆M < 0.165
GeV.
123

The purpose of the WC distribution is to estimate the shape of the background
such that the background can be removed from the signal. Ideally the number of D ∗
candidates N D ∗ would be A−C. However, to be conservative the WC distribution is
normalized before it is subtracted from the RC distribution. The WC is normalized
by multiplying the distribution by a weight such that B = D.
Once this is done the number of D ∗ candidates is
N D ∗ = A − B C. (8.8)
D
The error associated to a region of a histogram such as A, B, C and D has the form
[52]
δA = √ A. (8.9)
Using standard error propagation the uncertainty in the number of D ∗ candidates
δN D ∗
is
δN D ∗ =
√
A + BC (BD + CD + CB). (8.10)
D3 Thus, the number of D ∗ candidates can be determined using the wrong charge
subtraction method.
8.1.4 Fit Method
An alternate method uses a fit to determine the number of D ∗ candidates. The
fit method requires the same right-charge ∆M distribution seen in Fig. 8.1. To
obtain the number of D ∗ candidates the distribution is fit to a two-part function: a
modified Gaussian for the signal and a power term for the background. The modified
Gaussian is a three parameter function of the form
)
˜G = p 0 · exp
(−0.5 · x 1+ 1
1+0.5·x , (8.11)
124

where x is x = |∆M−p 1|
p 2
. The background has the form:
B = p 3 · (∆M − m π ) p 4
, (8.12)
where m π is the pion mass. So, the RC ∆M distribution is fit to the function
F = ˜G
)
+ B = p 0 · exp
(−0.5 · x 1+ 1
1+0.5·x + p 3 · (∆M − m π ) p 4
(8.13)
to determine the five parameters. The modified Gaussian is used instead of the
normal Gaussian because “it gave a better χ 2 value than a conventional Gaussian
form” [53]. The five parameters of the fit can be interpreted as follows:
• p 0 is the height of the Gaussian
• p 1 the energy difference M D ∗ − M D 0
• p 2 width of the Gaussian
• p 3 the height of the background
• p 4 power of the background.
The number of D ∗ candidates is determined by integrating ˜G(∆M;p 0 ,p 1 ,p 3 ) within
the signal region:
N D ∗ =
=
(∫ 0.148
0.143
(∫ 0.148
0.143
)
˜G(∆M;p 0 ,p 1 ,p 3 )d(∆M) /∆X
) )
p 0 · exp
(−0.5 · x 1+ 1
1+0.5·x d(∆M) /∆X. (8.14)
The ∆X term in Eq. 8.14 is the bin width of the entries in the RC distribution.
The fit method is used as a consistency check for the D ∗ candidates determined
using the wrong charge subtraction method.
125

8.1.5 Number of D ∗ Candidates
For differential cross sections (discussed in §8.3.2) the D ∗ candidates are determined
in bins of P T (D ∗ ), η(D ∗ ), Q 2 , and x. The binning goes as follows:
• P T (D ∗ ): 1.5 → 2.4 → 3.1 → 4.0 → 6.0 → 15 GeV (using REG tracking)
• η(D ∗ ): −1.5 → −0.8 → −0.35 → 0.0 → 0.4 → 0.8 → 1.5 (using REG
tracking)
• Q 2 : 5 → 10 → 20 → 40 → 80 → 200 → 1000 GeV 2 (using Q 2 DA )
• x: 0.00008 → 0.0004 → 0.0016 → 0.005 → 0.01 → 0.1 (using x DA )
The ∆M right charge and wrong charge distributions for Q 2 , along with the fits are
shown in Fig 8.3 for the Q 2 binning range. The remaining ∆M distributions can be
found in App. D.
126

Combinations per 0.0005 GeV
400
350
300
250
200
150
2
5.0 < Q < 10.0
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
600
500
400
300
200
100
2
10.0 < Q < 20.0
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
450
2
400
20.0 < Q < 40.0
350
300
250
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
300
250
200
150
100
50
2
40.0 < Q < 80.0
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
200
180
2
80.0 < Q < 200.0
160
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
100
90
2
200.0 < Q < 1000.0
80
70
60
50
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
127
Figure 8.3: ∆M distributions in Q 2 bins, in red are the fits.

Using the wrong-charge subtraction method the number of D ∗ candidates in P T , η,
Q 2 , and x bins is obtained.
Num. of Cand.
1600
1400
1200
1000
800
600
400
200
0
2 3 4 5 6 7 8 9 10*
P T
(D ) [GeV]
Figure 8.4: The number of D ∗ candidates with respect to P T (D ∗ ).
At ZEUS fewer D ∗ candidates are reconstructed at low and high P T than in the
central P T region.
128

Num. of Cand.
1400
1200
1000
800
600
400
200
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.5: The number of D ∗ candidates with respect to η(D ∗ ).
The number of D ∗ candidates is relatively flat in the central η region.
Num. of Cand.
2000
1800
1600
1400
1200
1000
800
600
400
200
0
10
2
10
2 2
Q [GeV ]
Figure 8.6: The number of D ∗ candidates with respect to Q 2 .
129

Except for the first bin, the number of D ∗ candidates has a downwards trend with
respect to Q 2 . In HERA II the lowest Q 2 bin does not have the most candidates.
This is different from the HERA I results. A possible reason is that Q 2 ∝ P T , and
since the addition of the MVD the rate that low P T tracks are lost has increased,
therefore leading to fewer low Q 2 D ∗ candidates.
Num. of Cand.
3000
2500
2000
1500
1000
500
0
10
-4
-3
10
-2
10
10
x
-1
Figure 8.7: The number of D ∗ candidates with respect to x.
The number of D ∗ candidates decreases with x.
The wrong charge subtraction method yields a total number of D ∗ candidates of
5789 ± 142, over the HERA II data of L = 175.4 pb −1 .
8.1.6 Number of D ∗ Candidates Using Fit
As a cross check the number of D ∗ candidates using the fit method are compared
to the wrong charge subtraction method, as shown in Fig. 8.8. The fit method
consistently yields a greater number of D ∗ candidates in both data and MC. This
130

Num. of Cand.
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Fit
Wrong Charge Subtraction
2 3 4 5 6 7 8 9 10*
P T
(D ) [GeV]
Num. of Cand.
1600
1400
1200
1000
800
600
400
200
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D )
Num. of Cand.
2500
2000
1500
1000
500
Num. of Cand.
3500
3000
2500
2000
1500
1000
500
0
10
2
10
2 2
Q [GeV ]
0
10
-4
-3
10
-2
10
-1
10
x
Figure 8.8: The number of D ∗ candidates using fit in black, and wrong charge subtraction
in red.
is not a source of large systematic uncertainties as long as the same method is used
consistently in both data and in MC.
8.2 Acceptances
The acceptance is a measure of how well the generated variables are reconstructed.
Two pieces of information are required to measure the D ∗ acceptance: the number
of D ∗ candidates in MC (ND MC ∗ ), determined with exactly the same method as was
done for the data, and the number of generated D ∗ ’s (ND GEN ∗ ). Not all generated
D ∗ ’s are counted; N GEN
D ∗
is the number of generated D∗ ’s that decay along the mode
D ∗ → (D 0 )π s → (Kπ)π s . Another requirement is that the D ∗ ’s are generated in the
kinematic region of interest, i.e., the Q 2 , x, η(D ∗ ), and P T (D ∗ ) regions are the same
131

for data, reconstructed MC, and generator level. Even if the reconstruction method
was 100% efficient, only 2.57% of the D ∗ ’s created during ep interactions would be
reconstructed because of the branching fractions involved in the decay chain. The
acceptance for the number of D ∗ candidates is determined using a charm enriched
RAPGAP Monte Carlo sample of L = 632 pb −1 ; see §3.2.1. The acceptance is
defined as
δA = A ·
A = NMC D ∗
ND GEN . (8.15)
∗
Using standard error propagation the error on the acceptance is
√ (δN
MC
D ∗
= A ·
N MC
D ∗ ) 2
+
√ (δN
MC
) 2
D ∗
ND MC + 1
∗
( δN
GEN
) 2
D ∗
ND GEN ∗
N GEN
D ∗ . (8.16)
This is not the whole story as N MC
D ∗
is a subset of NGEN; Eq. 8.16 is conservative
D ∗
and ignores these correlations.
The acceptances are seen below.
132

Acceptance
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
2 3 4 5 6 7 8 9 10*
P T
(D ) [GeV]
Figure 8.9: The P T (D ∗ ) acceptance. The acceptance rises with P T and peaks at 45%.
Acceptance
0.35
0.3
0.25
0.2
0.15
0.1
0.05
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.10: The η(D ∗ ) acceptance. The acceptance is best in the central part of the detector
peaking at 30%, the acceptance in the forward and rear parts of the
detector drops off.
133

Acceptance
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
10
2
10
2 2
Q [GeV ]
Figure 8.11: The Q 2 acceptance. The acceptance rises with Q 2 and peaks at 37%.
Acceptance
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
10
-4
-3
10
-2
10
10
x
-1
Figure 8.12: The x acceptance. Peaks at 35%.
134

8.3 Cross Sections
A Cross Section is the rate at which a process of interest occurs, for instance the
creation of a D ∗ . Cross sections are useful because they can be directly compared to
and understood by other experiments, whereas the number of D ∗ candidates will be
different because different experiments will have differing luminosities, acceptances,
etc. This allows predictions to be compared to data.
The cross section for D ∗ production at HERA II is the rate at which D ∗ mesons are
created by ep collisions at a center of mass energy of √ s = 318 GeV, per pb −1 of
luminosity in the kinematic region of interest:
σ(D ∗ ) =
N D ∗ →(Kπ)π s
A · Br D ∗ →(Kπ)π s · L . (8.17)
Here Br = Γ D ∗ →(D 0 )π s
× Γ D 0 →Kπ is the branching ratio equal to 2.57%. The error
on the cross section is:
δσ(D ∗ ) = σ(D ∗ ) ·
√ (δND
∗
N D ∗
) 2 ( ) δA 2
+ . (8.18)
A
The errors on the cross section due to luminosity and branching ratios are quoted
separately. The errors thus far encountered are all statistical in nature. The other
form of uncertainty on the cross section are the systematic errors.
8.3.1 Systematic Errors
Systematic uncertainties arise from the sensitivity of a cross section to a cut, or to a
reconstruction method, or even to the choice of MC. Ideally, this choice should have
little impact on the cross section, however in practice this is not always the case.
Typically uncertainties are estimated by varying cuts and measuring the effect on
the cross section. For example, the variation may be to alter a cut by ±1σ of its
135

esolution. Determining the overall uncertainty involves measuring the change in
the cross section for each variation.
Let’s assume that there is a default cross section σ that is made with the best
choice of cuts, MC, and reconstruction techniques. Let’s also assume that there
are N checks that may lead to systematic uncertainties, and let’s examine the i th
check, for example, tightening of the signal region 0.143 < ∆M < 0.148 GeV. The
difference between the cross sections ∆σ i = σ − σ i can be either positive ∆σ + i
or
negative ∆σ − i
. To determine the total systematic uncertainty the positive differences
are all summed in quadrature:
∑
∆σ + = √ N (∆σ
i + )2 (8.19)
i
∑
∆σ − = √ N (∆σi − )2 . (8.20)
i
The same is done with the negative difference allowing them to be quoted separately
as the systematic error on the cross section. When the effect of a systematic error
such as tightening and loosening the signal region, which are related, causes the cross
section to change in the same direction, then only the greater of the two effects is
added to the overall systematic uncertainty.
8.3.2 Differential Cross Sections
It is useful to see how the D ∗ cross section changes with respect to some variable.
This analysis examines the cross section with respect to P T (D ∗ ), η(D ∗ ), Q 2 , and x.
When measuring differential cross sections, the data is measured in bins. The size
of the bins are chosen to be small such that they approximate infinitesimal changes,
yet are large enough to avoid bin migrations.
136

Each bin of a differential cross section requires the number of D ∗ candidates to be
obtained using the wrong-charge subtraction method.
Before showing the results, the purities, efficiencies, control plots, and resolutions
are shown.
8.4 Purities and Efficiencies
The purities P and efficiency E in a bin i are quantities closely related to the
acceptance
A i = E i
P i
. (8.21)
The D ∗ purity can be understood as the probability that the D ∗ that was reconstructed
in bin i and also generated in bin i. A sample with a poor purity would
mean that massive bin migrations occur in the reconstruction phase. The fact that
a D ∗ was reconstructed in bin i would not mean with high certainty that it was
actually created in bin i. The purity in bin i is defined as
P i = NGEN i
∩ N REC
i
Ni
REC
. (8.22)
The numerator in Eq. 8.22 uses the logical AND meaning that each D ∗ must be
both generated and reconstructed in bin i for it to be counted. The efficiency is
similar to an acceptance except that it requires that the D ∗ was generated AND
reconstructed in the same bin, therefore having no bin migrations. The efficiency in
bin i is:
E i = NGEN i
∩ N REC
i
Ni
GEN
. (8.23)
The conservative uncorrelated uncertainty on the purities and efficiencies are
√
1
δP i = P i
Ni
GEN ∩ Ni
REC + 1
Ni
REC ,
137

δE i = E i
√
N GEN
i
1
∩ Ni
REC
+ 1
Ni
GEN . (8.24)
The following plots show the purities and efficiencies for P T (D ∗ ), η(D ∗ ), Q 2 , and x.
Purity
1
0.8
0.6
0.4
0.2
0
2 3 4 5 6 7 8 9 10*
P T
(D ) [GeV]
Figure 8.13: The D ∗ purity as a function of P T (D ∗ ).
138

Purity
1
0.8
0.6
0.4
0.2
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.14: The D ∗ purity as a function of η(D ∗ ).
Purity
1
0.8
0.6
0.4
0.2
0
10
2
10
2 2
Q [GeV ]
Figure 8.15: The D ∗ purity as a function of Q 2 .
139

Purity
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
-4
-3
10
-2
10
x
Figure 8.16: The D ∗ purity as a function of x.
The RAPGAP MC sample is a very pure D ∗ sample. Purities peak at ≈ 100% and
fall as low as 73%. The efficiencies are now shown.
140

Efficiency
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
2 3 4 5 6 7 8 9 10*
P T
(D ) [GeV]
Figure 8.17: The D ∗ efficiency as a function of P T (D ∗ ).
Efficiency
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.18: The D ∗ efficiency as a function of η(D ∗ ).
141

Efficiency
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
10
2
10
2 2
Q [GeV ]
Figure 8.19: The D ∗ efficiency as a function of Q 2 .
Efficiency
0.3
0.25
0.2
0.15
0.1
0.05
0
10
-4
-3
10
-2
10
x
Figure 8.20: The D ∗ efficiency as a function of x.
The efficiencies very much mirror the acceptances shown earlier (see Figs. 8.9 to
142

8.12). This is due to the high purity, that is A = E/P ≈ E as P → 1.
8.5 Control Plots
Control plots compare reconstructed variables in data to their reconstructed value
in MC. The reconstructed MC distributions are area normalized such that they are
equal in area to the data distributions. Discrepancies in control plots can indicate
a variety of problems. Generator level problems could indicate that the underlying
physics of an event are not well described. MC reconstruction problems could
indicate that the detector is not well described during the FUNNEL stage (see §3.4).
The following are DIS event control plots of variables shown or cut on for these
analyses. The green histograms are the MC while the points are the data. The MC
uses the already discussed charm-enriched RAPGAP sample corresponding to 632
pb −1 . The data is 175.4 pb −1 from the HERA II run time.
143

dN/dZ
600
500
400
300
200
100
dN/dY DA
1000
800
600
400
200
-40
0
-30 -20 -10 0 10 20 30 40
Z Vertex [cm]
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y DA
dN/dY JB
1000
800
600
400
200
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dN/dY e
900
800
700
600
500
400
300
200
100
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y JB
Y e
Figure 8.21: DIS control plots. The Z vtx , Y DA , Y JB , and Y e are shown.
144

dN/dX DA
3
10
2
10
dN/dX e
3
10
2
10
10
10
1
1
-1
10 0 0.0020.0040.0060.008 0.01 0.0120.0140.0160.018 0.02
-1
10 0 0.0020.0040.0060.008 0.01 0.0120.0140.0160.018 0.02
X DA
X e
dN/dE prob
4
10
3
10
2
10
dN/dE e,corr
350
300
250
200
10
1
150
100
50
-1
10
0.9 0.92 0.94 0.96 0.98 1
E prob
0
5 10 15 20 25 30 35 40
E e,corr [GeV]
Figure 8.22: DIS control plots. The X DA , X e , E prob , and E corr the corrected electron energy
are shown.
145

dN/dδ h
1600
1400
1200
1000
800
600
400
200
0
30 35 40 45 50 55 60 65 70
δ h
[GeV]
dN/dθ e
6000
5000
4000
3000
2000
1000
1 1.5 2 2.5 3
θ e
[°]
2
DA
dN/dQ
3
10
2
10
2
e
dN/dQ
3
10
2
10
10
10
1
1
-1
10 0 50 100 150 200 250 300 350 400 450 500
2 2
Q [GeV ]
DA
-1
10 0 50 100 150 200 250 300 350 400 450 500
2 2
Q [GeV ]
e
Figure 8.23: DIS control plots. The δ h , θ e , Q 2 DA , and Q2 e
are shown.
Some D ∗ control plots with respect to P T , η, Q 2 , and x are shown below.
146

dN/dP T
1400
1200
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10
P T
(π)[GeV]
dN/dP T
1400
1200
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10
P T
(K)[GeV]
dN/dP T
1600
1400
1200
1000
800
600
400
200
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P T
(π S
)[GeV]
dN/dP T
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10
*
P T
(D )[GeV]
Figure 8.24: P T control plots of the pion, kaon, slow pion, and D ∗ .
147

dN/dη
1200
1000
dN/dη
1200
1000
800
800
600
600
400
400
200
200
-1.5
0
-1 -0.5 0 0.5 1 1.5
η(π)
-1.5
0
-1 -0.5 0 0.5 1 1.5
η(K)
dN/dη
1200
1000
dN/dη
1200
1000
800
800
600
600
400
400
200
200
-1.5
0
-1 -0.5 0 0.5 1 1.5
η(π )
S
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.25: η control plots of the pion, kaon, slow pion, and D ∗ .
148

dN/dφ
800
700
600
500
400
300
200
100
0
0 1 2 3 4 5 6
φ(π)
dN/dφ
800
700
600
500
400
300
200
100
0
0 1 2 3 4 5 6
φ(K)
dN/dφ
800
700
600
500
400
300
200
100
0
0 1 2 3 4 5 6
φ(π_s)
dN/dφ
800
700
600
500
400
300
200
100
0
0 1 2 3 4 5 6
*
φ(D )
Figure 8.26: φ control plots of the pion, kaon, slow pion, and D ∗ .
The most alarming discrepancy is for the P T of the slow pion and hence of the
D ∗ . As a result the P T distribution of the slow pion of the MC was re-weighted
such that it matched that of the data. The resulting P T of the D ∗ control plot is
shown. For one of the systematic checks on the cross section the unweighted slow
pion distribution is used.
8.6 Resolutions
The resolution indicates how well a reconstructed variable, X REC , matches its generated
variable, X GEN . The distribution of ∆X = X GEN − X REC is made in MC
and fit to a Gaussian of the form shown in Eq. 5.34. The width of the Gaussian,
σ(X), is the resolution of the variable X. The resolutions presented below show
149

that within the regions of interest σ is less than the bin widths. This is an important
consideration when choosing the size of the bins. The bin width should
always be larger than the resolution within the bin, otherwise large migrations can
be expected.
Entries
2000 N = 1838.076
1800
Mean = −0.00042
1600
σ = 0.010130
1400
1200
1000
800
600
400
200
0
−0.04 −0.02 0 0.02 0.04
∆Z VTX
[cm]
Entries
3500 N = 3429.055
Mean = 0.66604
3000
σ = 1.158573
2500
2000
1500
1000
500
0
−10 −5 0 5 10
∆E corr
[GeV]
Entries
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
N = 2252.505
Mean = 1.51076
σ = 2.730390
−10 0 10
∆δ h
[GeV]
Entries
4500 N = 4727.663
Mean = −0.00045
4000
σ = 0.002506
3500
3000
2500
2000
1500
1000
500
0
−0.02 0 0.02
∆θ e
[°]
Figure 8.27: DIS resolutions. The Z vtx , E corr , δ h , and θ e are shown.
The event variables in Fig. 8.27 are cut on during the analyses.
150

Entries
700
600
500
400
300
200
100
0
N = 646.812
Mean = 0.01143
σ = 0.024891
−0.2 −0.1 0 0.1 0.2
∆P T
[GeV]; P ∈ [1.5, 2.4]
T
Entries
600 N = 575.047
Mean = 0.01302
500
σ = 0.029667
400
300
200
100
0
−0.2 −0.1 0 0.1 0.2
∆P T
[GeV]; P ∈ [2.4, 3.1]
T
Entries
900
800
700
N = 828.084
Mean = 0.01043
σ = 0.044752
600
500
400
300
200
100
0
−0.4 −0.2 0 0.2 0.4
∆P T
[GeV]; P ∈[3.1, 4.0]
T
Entries
700
600
500
400
300
200
100
0
N = 713.174
Mean = 0.01100
σ = 0.066807
−0.4 −0.2 0 0.2 0.4
∆P T
[GeV]; P ∈ [4.0, 6.0]
T
400 N = 362.302
350
Mean = 0.01649
300
σ = 0.110587
250
200
150
100
50
0
−1 −0.5 0 0.5 1
∆P T
[GeV]; P ∈[6.0, 15.0]
T
Entries
Figure 8.28: The P T resolution of the D ∗ within the bins used in this analysis are shown.
The resolution gets worse, i.e., σ increases, with P T .
Entries
400
300
200
100
0
N = 394.332
Mean = 0.00020
σ = 0.003419
−0.02 −0.01 0 0.01 0.02
∆η; η ∈ [−1.5, −0.8]
Entries
600
500
400
300
200
100
0
N = 600.902
Mean = 0.00025
σ = 0.002753
−0.02 −0.01 0 0.01 0.02
∆η; η ∈ [−0.8, −0.35]
Entries
600 N = 559.500
Mean = 0.00022
500
σ = 0.002360
400
300
200
100
0
−0.02 −0.01 0 0.01 0.02
∆η; η ∈ [−0.35, 0.0]
Entries
600 N = 569.608
Mean = −0.00012
500
σ = 0.002891
400
300
200
100
0
−0.02 −0.01 0 0.01 0.02
∆η; η ∈ [0.0, 0.4]
Entries
600
500
400
300
200
100
0
N = 533.564
Mean = −0.00027
σ = 0.002791
−100
−0.02 −0.01 0 0.01 0.02
∆η; η ∈ [0.4, 0.8]
Entries
500
400
300
200
100
0
N = 512.851
Mean = −0.00004
σ = 0.002737
−0.02 −0.01 0 0.01 0.02
∆η; η ∈[0.8, 1.5]
Figure 8.29: η of the D ∗ resolution.
151

The P T and η resolutions seen in Fig. 8.28 and 8.29 are clearly smaller than the bin
widths.
Entries
700
600
500
400
300
200
100
0
−10 −5 0 5 10
2 2 2
∆Q [GeV ]; Q ∈ [5.0, 10.0]
DA
DA
N = 705.797
Mean = −0.22861
σ = 0.930797
Entries
1400 N = 1418.710
1200
Mean = −0.16521
σ = 1.147582
1000
800
600
400
200
0
−10 0 10
2 2 2
∆Q [GeV ]; Q ∈ [10.0, 20.0]
DA
DA
Entries
800 N = 834.236
Mean = −0.03862
700
σ = 1.493250
600
500
400
300
200
100
0
−10 0 10
2
∆Q
2 2
[GeV ]; Q ∈ [20.0, 40.0]
DA
DA
Entries
600
500
400
300
200
100
0
−20 0 20
2 2 2
∆Q [GeV ]; Q ∈[40.0, 80.0]
DA
DA
N = 630.206
Mean = 0.17392
σ = 2.542478
Entries
300 N = 294.527
Mean = 0.13858
250
σ = 4.084231
200
150
100
50
−40
0
−20 0 20 40
2 2 2
∆Q [GeV ]; Q ∈ [80.0, 200.0]
DA
DA
Entries
80
60
40
20
0
2
∆QDA
−50 0 50
2 2
[GeV ]; Q ∈ [200.0, 1000.0]
DA
N = 75.815
Mean = 0.79299
σ = 9.259882
Figure 8.30: The Q 2 resolution using the double-angle method.
152

Entries
500
400
300
200
100
0
−4 −2 0 2 4
2 2 2
∆Q [GeV ]; Q ∈ [5.0, 10.0]
e
e
N = 506.899
Mean = 0.11225
σ = 0.562316
Entries
1400 N = 1373.284
Mean = 0.23429
1200
σ = 0.823872
1000
800
600
400
200
0
−10 −5 0 5 10
2 2 2
∆Q [GeV ]; Q ∈ [10.0, 20.0]
e
e
Entries
700 N = 668.029
600
Mean = 0.46727
σ = 1.366814
500
400
300
200
100
0
−10 −5 0 5 10
2 2 2
∆Q [GeV ]; Q ∈ [20.0, 40.0]
e
e
Entries
450 N = 445.877
Mean = 0.59769
400
σ = 2.653348
350
300
250
200
150
100
50
−20
0
−10 0 10 20
2 2 2
∆Q [GeV ]; Q ∈[40.0, 80.0]
e
e
Entries
220 N = 203.251
200
180
160
140
120
100
80
60
40
20
0
−20 0 20
2 2 2
∆Q [GeV ]; Q ∈ [80.0, 200.0]
e
e
Mean = 1.93373
σ = 5.021936
Entries
60
50
40
30
20
10
0
−50 0 50
2 2 2
∆Q [GeV ]; Q ∈ [200.0, 1000.0]
e
e
N = 46.215
Mean = 11.44380
σ = 17.136636
Figure 8.31: The Q 2 resolution using the electron-method.
240
220
N = 214.672
Mean = 1.24268
200
σ = 3.659087
180
160
140
120
100
80
60
40
20
0
−20 −10 0 10 20 30
2 2 2
∆Q [GeV ]; Q ∈ [5.0, 10.0]
Entries
JB
JB
Entries
400 N = 386.593
Mean = −2.96553
350
σ = 5.742598
300
250
200
150
100
50
0
−20 0 20
2
∆Q
2 2
[GeV ]; Q ∈ [10.0, 20.0]
JB
JB
Entries
400
350
300
250
200
150
100
50
0
−40 −20 0 20
2 2 2
∆Q [GeV ]; Q ∈ [20.0, 40.0]
JB
JB
N = 367.511
Mean = −11.76775
σ = 8.765013
Entries
300 N = 257.548
Mean = −21.05368
250
σ = 18.739691
200
150
100
50
0
−50 0
2 2 2
∆Q [GeV ]; Q ∈[40.0, 80.0]
JB
JB
200 N = 167.902
180
Mean = −33.96515
160
σ = 37.431271
140
120
100
80
60
40
20
−150
0
−100 −50 0 50
2
∆Q
2 2
[GeV ]; Q ∈ [80.0, 200.0]
Entries
JB
JB
Entries
45 N = 34.634
40
Mean = −61.68425
35
σ = 79.945416
30
25
20
15
10
5
−200
0
−100 0 100
2
∆Q
2 2
[GeV ]; Q ∈ [200.0, 1000.0]
JB
JB
Figure 8.32: Q 2 JB resolution. The Jacquet-Blondel method to reconstruct Q2 has resolution
whose mean becomes more negative with Q 2 .
153

The analyses presented use the double-angle method to reconstruct Q 2 , however
the three Figs. 8.30, 8.31, and 8.32, show the resolution using the double-angle,
electron, and Jacquet-Blondel method. The double-angle and electron methods
have comparable resolutions, however the double-angle method out performs the
electron method when it comes to the mean. The mean on the double-angle method
is centered closer to zero than that of the electron method. The Jacquet-Blondel
method clearly is the worst in the binning used in the analyses presented; not only
the mean but the resolution is poor.
Entries
350
300
250
200
150
100
50
0
N = 289.919
Mean = −0.00001
σ = 0.000115
−3
×10
−0.5 0 0.5
∆X DA
; X ∈ [0.00008, 0.0004]
DA
Entries
1400
1200
1000
800
600
400
200
N = 1328.267
Mean = −0.00009
σ = 0.000262
0
−0.002 −0.001 0 0.001 0.002
∆X DA
; X ∈ [0.0004, 0.0016]
DA
Entries
1000 N = 985.671
Mean = −0.00013
σ = 0.000579
800
600
400
200
0
−0.004−0.002 0 0.002 0.004
∆X DA
; X ∈ [0.0016, 0.005]
DA
Entries
300 N = 280.509
Mean = −0.00009
250
σ = 0.001084
200
150
100
50
−0.01
0
−0.005 0 0.005 0.01
∆X DA
; X ∈ [0.005, 0.01]
DA
Entries
120
100
80
60
40
20
0
N = 105.509
Mean = −0.00005
σ = 0.001291
−0.01 0 0.01
∆X DA
; X ∈[0.01, 0.1]
DA
Figure 8.33: X DA resolution within bins presented in these analyses.
The x resolution seen in Fig. 8.33 increases with x, but remains smaller than the
bin width in the chosen binning range.
154

8.7 Cross Section Results
Before the differential cross sections are determined, corrections to the MC are made,
systematic uncertainties are measured, and theoretical uncertainties are calculated.
8.7.1 Corrections to MC
Four corrections, two of which affect the electron energy and two corrections due to
the description of the slow pion, are implemented on the MC.
Electron Energy Scaled
A discrepancy exists between the reconstruction of the electron energy in MC and
data. As a result, the electron energy in MC is scaled down by 2% [53]. Terms
dependent on the electron energy are scaled accordingly. As a systematic check on
the differential cross sections, the unscaled electron energy is used.
Electron Energy Smeared
In addition to the scaling of the electron energy, the electron energy is also smeared
in MC by 3%. The smearing procedure multiplies the electron energy by a random
Gaussian, G, centered on zero with a width of one. The electron energy is smeared
by
E e ′ = E e × (1 + 0.03 · G). (8.25)
Re-weighting of the Transverse Momentum of the Slow Pion
The P T of the π s in data and MC are different, as seen in the π s control plot in Fig.
8.24. As a result, the MC P T distribution was multiplied by a weight W(P T (π s ))
such that bin by bin the P T distribution of the π s in data and MC are be equal:
P ′ T(π s ) = W(P T (π s )) ∗ P T (π s ). (8.26)
155

The effect on the P T (D ∗ ) distribution is seen in Fig. 8.34; the MC now describes
the distribution better.
dN/dP T
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10
*
P T
(D )[GeV]
a)
dN/dP T
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10
*
P T
(D )[GeV]
b)
Figure 8.34: P T (D ∗ ) control plot before a) and after b) P T (π s ) re-weighting in MC.
The unweighted distribution is another of the systematic checks.
156

Re-weight Events due to Slow Pion Track Loss Probability
The track loss probability of the slow pion discussed in §5.5 is used as one of the
systematic checks. The efficiency as a function of P T for the kaon, pion, and slow
pion are ǫ K , ǫ π , and ǫ πs , respectively. The overall efficiency of finding a D ∗ is the
product of the three; ǫ = ǫ K · ǫ π · ǫ πs . The inefficiency is then ξ = 1 − ǫ. Events are
weighted according to the track loss inefficiency:
W =
1 − ξ × (1.0 ± 0.20)
. (8.27)
1 − ξ
The affect of reweighting the event by a -20% (+20%) W is to increase (decrease)
the acceptance, this reduces (increases) the cross section because σ ∝ 1/A.
8.7.2 Systematic Checks
The following systematic checks are made:
157

ID
Description
1. E e NOT smeared
2. Scaled E e by ±1% in MC
3. Scaled E Had by ±3% in MC
4. E e cut increased to 11 GeV
5. Box cut increase by 1.0 cm
6. Z vtx cut decreased by 3 cm
7. Y e cleaning cut reduced to 0.90
8. Y JB cleaning cut increased to 0.03
9. δ h window to 42 < E − P z < 57 GeV
10. M(D 0 ) widened and narrowed by ±0.01 GeV
11. ∆M widened and narrowed by ±0.001 GeV
12. P T (π s ) distribution NOT re-weighted
∗13. Track loss probability changed by ±20 %
14. Changed P T (K,π,π s ) cut by ±0.02 GeV
15. Doubled beauty content in MC
∗16. Fit instead of wrong charge subtraction
∗17. HERWIG instead of RAPGAP in MC
Table 8.1: The systematic checks. The IDs with stars indicate consistency checks and are
not used when determining the systematic uncertainty.
The first two systematic checks account for the uncertainty in the energy reconstruction
in the CAL of the electron in MC. Check #3 accounts for the uncertainty
of the hadronic energy reconstruction in the CAL in MC. Systematic checks #4 to
11 check how sensitive the cross sections are to choice of the values that are cut on.
Check #12 shows the effect of the re-weighting of the π s distribution in MC. Check
#13 accounts for the track loss inefficiency, but is not used when determining the
systematic uncertainty. The uncertainty in the reconstruction of the momentum by
the tracking detectors is accounted for by the 14 th systematic. Beauty is produced
at HERA and a large fraction decay to D ∗ . To account for this, a beauty enriched
MC is used in the analysis. The effect of doubling this beauty contribution is the
15 th systematic. The final two, checks #16 and 17, are consistency checks and are
158

not used as systematic checks.
The fractional systematic uncertainties of not smearing the electron energy is shown
for the η, P T , Q 2 , and x distributions in Fig. 8.35. The green line, mirrored in the
x−axis is the fractional statistical error for the distribution. The points are the
fractional systematic uncertainty of the check.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
No Smearing of the Electron Energy
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure 8.35: Systematic Check: No Electron Smearing. The green line is mirrored on the
negative y axis and indicates the fractional statistical error, the points are the
systematic errors.
The remaining checks are in App. D.1.2. Most of the systematic checks have effects
less that 3%. The exceptions are the three checks that involve the description of the
transverse momentum of the slow pion.
159

Track Loss Probability
The effect of decreasing the track loss efficiency is as high as 35%. The fractional
difference decreases as P T (D ∗ ) increases, and decreases with Q 2 because Q 2 is proportional
to P T . In fact, the fractional difference decreases with x as well; recall
Q 2 = sxy.
Frac. Diff.
0.3
0.2
0.1
MC EVT RWT w/(K, π, π s
) Trk Loss Prb. −20%
0
0
Frac. Diff.
0.3
0.2
0.1
−0.1
−0.1
−0.2
MC EVT RWT w/(K, π, π s
) Trk Loss Prb. +20%
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T (D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure 8.36: Track loss probability systematic check.
No P T Re-Weight
The result of not re-weighting the slow pion’s P T distribution in MC is the next
largest effect, which is as high as 35% in some bins. Again it is noticed that the
effect decreases as P T and as a result Q 2 (and x) increases.
160

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
No Reweighting of P (π s ) Distribution
T
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T (D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure 8.37: No P T re-weight systematic check.
P T (π s ) Cut
Tightening and loosening the minimum P T cut on the slow pion is the last large
systematic effect examined. The tightening and loosening effects appear to mirror
each other, where the largest effect of 60% is noticed is in the lowest P T (D ∗ ) bin.
Outside of that bin, the effect’s maximum is under 20%.
161

Frac. Diff.
0.3
0.2
0.1
Loosen Cut On Mimimum P T
(π s )
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Cut On Mimimum P (π s )
T
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T (D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure 8.38: P T (π s ) cut systematic check.
The trend of the fractional difference lessening as P T , Q 2 , and x increase is observed
in all three of these systematic checks. This is a further indication that the cross
sections are most sensitive to the P T description of the π s .
Using a modified Gaussian for a fit to obtain the number of D ∗ candidates, and
using HERWIG as the MC to determine the acceptances, both represent consistency
checks and yield similar cross sections. These are shown in App. D.1.3, and are in
good agreement with theory.
8.7.3 HVQDIS Prediction
The next-to-leading-order neutral current DIS MC program HVQDIS is used to
predict the theoretical differential D ∗ cross sections. HVQDIS was discussed in
§3.3.1. In addition to the differential cross sections, HVQDIS is used to predict the
theoretical uncertainties, by varying the input parameters. The default parameters
162

for the HVQDIS program are
• the PDF ZEUS-S [54],
• charm quark mass m c = 1.5 GeV,
• Peterson charm fragmentation parameter ǫ c = 0.035,
• renormalization and factorization scale µ 2 R,F = √ Q 2 + 4m 2 c .
The theoretical uncertainty in the cross section was obtained by varying the following:
• charm quark mass ∆m c ± 0.15 GeV,
• Peterson fragmentation parameter ∆ǫ c ± 0.015,
• changing renormalization and factorization scales used:
– doubled default scale µ 2 R,F = 4√ Q 2 + 4m 2 c ,
– halved default scale µ 2 R,F = 1/4√ Q 2 + 4m 2 c,
– used µ 2 R,F = 2m c as scale,
– used µ 2 R,F = MAX(√ Q 2 /4 + m 2 c,2m c ) as scale,
Note that the appropriate ZEUS PDFs must be used when the renormalization and
factorization scales are charged.
163

Frac. Diff.
0.25
0.2
0.15
0.1
Decreased m c
Frac. Diff.
0.25
0.2
0.15
0.1
Increased m c
Frac. Diff.
0.25
0.2
0.15
0.1
Decreased Peterson ∈
0.05
0.05
0.05
0
0
0
-0.05
-0.05
-0.05
-0.1
P 10
T [GeV]
-0.1
P 10
T
[GeV]
-0.1
P 10
T
[GeV]
Frac. Diff.
0.25
0.2
0.15
0.1
Increased Peterson ∈
Frac. Diff.
0.25
0.2
0.15
0.1
µ = 2m c
R,F
Frac. Diff.
0.25
0.2
0.15
0.1
Doubled µ
R,F
0.05
0
0.05
0
0.05
0
-0.05
-0.05
-0.05
-0.1
P 10
T
[GeV]
-0.1
P 10
T
[GeV]
-0.1
P 10
T
[GeV]
Frac. Diff.
0.25
0.2
0.15
0.1
Halved µ
R,F
Frac. Diff.
0.25
0.2
0.15
0.1
2 2
µ = MAX( Q /4 + m , 2m )
R,F
c c
0.05
0.05
0
0
-0.05
-0.05
-0.1
P 10
T
[GeV]
-0.1
P 10
T
[GeV]
Figure 8.39: The fractional difference between the default HVQDIS prediction of the P T
of the D ∗ cross section, the theoretical uncertainties are shown in blue. The
theoretical uncertainties are indicated.
The theoretical uncertainty is determined in the same manner as the systematic
uncertainty of the cross section in §8.3.1. The difference in the theory value from
each variation is summed in quadrature.
The fractional difference between the default and the theoretical uncertainty in the
HVQDIS prediction of the transverse momentum of the D ∗ is shown in Fig. 8.39.
164

The remaining uncertainties for η, Q 2 , and x are seen in Appendix D.1.4.
8.8 D ∗ Results
The differential cross sections including the HVQDIS NLO predictions are shown in
Fig. 8.40 to 8.43. The points represent the data, the central value of the theory is the
blue line, and the theoretical uncertainty is the solid yellow band. The symmetric
error bars on the data points show the statistical error, the extension of the error
bars are the systematic errors.
The Differential D ∗ Cross Section with respect to P T
[nb/GeV]
dσ/dP T
10
1
−1
−1
HERA II Data, L = 175.4 pb
HVQDIS Central Value
Theoretical Uncertainty
10
−2
2 3 4 5 6 7 8 9 10
*
P T (D
) [GeV]
Figure 8.40: The differential D ∗ cross section with respect to P T .
The D ∗ meson is produced at a higher rate at the lower P T region in Fig. 8.40. As
P T increases the rate of D ∗ production decreases. The theory is in agreement with
165

the HERA II data.
The Differential D ∗ Cross Section with respect to η
dσ/dη [nb]
2.5
2
1.5
1
0.5
0
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D
)
Figure 8.41: The differential D ∗ cross section with respect to η.
The production rate of D ∗ mesons in the η region examined in Fig. 8.41 is relatively
flat. The theory is in agreement with the HERA II data.
166

10
2
10
The Differential D ∗ Cross Section with respect to Q 2 ]
[nb/GeV
2
2
]
dσ/dQ
10
10
10
−1
−2
−3
10
−4
10
−5
Q
2
3
10
2
[GeV ]
Figure 8.42: The differential D ∗ cross section with respect to Q 2 .
The production rate of D ∗ mesons in the Q 2 region examined in Fig. 8.42 falls off
with Q 2 . The theory is in agreement with the HERA II data.
167

The Differential D ∗ Cross Section with respect to x
dσ/dx [nb]
4
10
3
10
2
10
10
1
10
−1
10
−4
10
−3
10
−2
10
x
−1
Figure 8.43: The differential D ∗ cross section with respect to x.
The production rate of D ∗ mesons in the x region examined in Fig. 8.42 falls off
with x, similar to both the P T and Q 2 cross sections. The theory is in agreement
with the HERA II data.
8.9 Extending Forward in η
The addition of the STT and tracking improvements have allowed for tracks that
are more forward in η to be used. The following differential cross section is obtained
using ZTT tracking (§5.3), and extends the range from η(D ∗ ) ∈ [−1.5,1.5]
to η(D ∗ ) ∈ [−1.5,1.8]. The following plots show the number of D ∗ candidates, the
acceptance using ZTT tracking, and finally the cross section including the NLO
168

prediction in the most forward η bin.
Num. of Cand.
1200
1000
800
600
400
200
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.44: The number of D ∗ candidates in the extended η region.
169

Acceptance
0.35
0.3
0.25
0.2
0.15
0.1
0.05
-1.5
0
-1 -0.5 0 0.5 1 1.5
*
η(D )
Figure 8.45: The D ∗ acceptance in the extended η region using ZTT tracking. The acceptance
of the most forward η point is low ≈ 5%.
170

dσ/dη [nb]
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D
)
Figure 8.46: The D ∗ differential cross section with respect to η in the extended η region.
The statistical significance of the extended η point is limited, however this serves as
a test of using the ZTT tracking package. The statistical error on the last point is
large. However, adding data from the HERA II run period of 2006 to 2007 should
improve this measurement.
8.10 Numbers During 2006 and 2007
Thus far D ∗ results from the HERA II data-taking period of 2003 to 2005, using an
integrated luminosity of 175.4 pb −1 , have been shown. However, the high energy
runs (see §4.1) data-taking period ended in 2007, with a HERA II shutdown at
the end of 2005. During this shutdown ZEUS made repairs to and moved detector
components. The Monte Carlo used to describe the ZEUS detector and determine
171

acceptances for the D ∗ data has yet to be updated 2 , posing a problem due to altered
detector conditions. The data-taking period of 2006 and 2007 has an integrated
luminosity of 195.0 pb −1 . When combined with the remainder of the HERA II data
this could potentially more than double the number of D ∗ candidates, and reduce
the statistical errors by 1/ √ 2.
8.11 Summary
The number of D ∗ candidates is determined using the wrong charge subtraction
method. The acceptances are found using a charm enriched RAPGAP sample, and
range from 15 to 45%. The MC sample very D ∗ pure, with efficiencies of 15 to
45%. The control plots indicate that the MC describes the data reasonably well
except for the P T description of the slow pion. The bin size of the differential cross
sections is acceptable and can in fact be safely reduced because it falls well short
of the resolution in the bins. The size of the bins are chosen such that the results
are directly comparable to the HERA I data. The theoretical cross sections within
errors are in good agreement with the HERA II data.
2 At this time there is potentially a MC sample that may accurately describe the ZEUS detector
and the D ∗ data for the HER of 2006 and 2007, further investigation is required.
172

Chapter 9
F cc
2 at HERA II
9.1 Introduction
This chapter explores the extraction of the charm contribution F cc
2 (x,Q2 ) to the
proton structure function F 2 (x,Q 2 ) using DIS charm cross sections made in Q 2 − y
bins. Many of the tools used in the extraction of F cc
2
chapter and the results are presented here.
were developed in the previous
The binning to measure F cc
2 in the HERA II data is shown in Tab. 9.1, and was
chosen such that it closely matches the binning of the HERA I data [53]. Each y
bin is represented by a single y value. The center of gravity of the bin, i.e., the
value at which there are an equal number of entries above and below in that bin, is
used as the value for the y point. The y value is converted to a value of x using the
relation Q 2 = sxy or x = Q 2 /sy where √ s = 318 GeV 2 . Similarly, each Q 2 region
is represented by a Q 2 value equal to the center of gravity of the bin.
For each y bin a ∆M distribution is made for both the right and wrong charge
combinations. The number of D ∗ candidates and the acceptance are determined
using the wrong charge subtraction method described in §8.1.3 and §8.2.
173

Q 2 GeV 2 ID y Bins Value of x
5.0 → 6.5 1) 0.02 → 0.08 0.00100
2) 0.08 → 0.18 0.00035
3) 0.18 → 0.33 0.00018
Q 2 ≃ 5.5 GeV 2 4) 0.33 → 0.70 0.00007
6.5 → 9.0 5) 0.02 → 0.08 0.00150
6) 0.08 → 0.25 0.00060
Q 2 ≃ 6.8 GeV 2 7) 0.25 → 0.70 0.00018
9.0 → 14.0 8) 0.02 → 0.08 0.00300
9) 0.08 → 0.20 0.00100
10) 0.20 → 0.35 0.00035
Q 2 ≃ 11 GeV 2 11) 0.35 → 0.70 0.00018
14.0 → 22.0 12) 0.02 → 0.08 0.00300
13) 0.08 → 0.20 0.00150
14) 0.20 → 0.35 0.00060
Q 2 ≃ 19 GeV 2 15) 0.37 → 0.70 0.00035
22.0 → 44.0 16) 0.02 → 0.08 0.00600
17) 0.08 → 0.22 0.00150
18) 0.22 → 0.35 0.00100
Q 2 ≃ 31 GeV 2 19) 0.35 → 0.70 0.00060
44.0 → 90.0 20) 0.02 → 0.14 0.01200
21) 0.14 → 0.28 0.00300
Q 2 ≃ 61 GeV 2 22) 0.28 → 0.70 0.00150
90.0 → 200.0 23) 0.02 → 0.14 0.03000
24) 0.14 → 0.28 0.00600
Q 2 ≃ 133 GeV 2 25) 0.28 → 0.70 0.00300
200.0 → 1000.0 26) 0.02 → 0.23 0.03000
Q 2 ≃ 510 GeV 2 27) 0.23 → 0.70 0.01200
Table 9.1: Shown in this table are Q 2 regions divided into bins of y. An ID number is
indicated for further reference. The x value corresponding to the y bin is shown.
The selection criteria are identical to the selection used for the previous D ∗ crosssection
measurements (see §8.1.2) with the added requirement that y is determined
using the double-angle method y DA . The y resolutions, acceptances, purities and
efficiencies are calculated using the same 632 pb −1 charm-enriched RAPGAP MC
sample that was used to determine the previous differential D ∗ cross sections.
174

9.1.1 y Resolution
The y resolution using three different reconstruction techniques is shown for each
y bin in Fig. 9.1 to 9.3. All three reconstruction methods; double-angle, electron,
and Jacquet-Blondel, have resolutions σ(y) smaller than the width of the bins ∆y.
Entries
300 N = 285.024
Mean = 0.00262
250
σ = 0.014396
200
150
100
50
Entries
1000 N = 958.046
Mean = −0.00013
σ = 0.030356
800
600
400
200
0
−0.1 −0.05 0 0.05 0.1
∆Y DA ;Y ∈ [0.02, 0.08]
DA
0
−0.2 −0.1 0 0.1 0.2
∆Y DA ;Y ∈ [0.08, 0.20]
DA
Entries
800
700
600
500
400
300
200
100
0
N = 779.318
Mean = 0.00105
σ = 0.057048
−0.4 −0.2 0 0.2 0.4
∆Y DA ;Y ∈ [0.20, 0.35]
DA
Entries
800 N = 757.008
700
600
500
400
300
200
100
0
Mean = −0.00948
σ = 0.084551
−0.5 0 0.5
∆Y DA ;Y ∈ [0.35, 0.70]
DA
Figure 9.1: Y DA resolutions in regions of y indicated in the figure. The resolutions, σ, are
less than the bin widths.
175

Entries
160 N = 130.265
140
Mean = 0.00904
σ = 0.023921
120
100
80
60
40
20
0
−0.1 −0.05 0 0.05 0.1
∆Y e ;Y ∈ [0.02, 0.08]
e
Entries
900 N = 840.323
800
700
600
500
400
300
200
100
0
Mean = −0.01360
σ = 0.031965
−0.2 −0.1 0 0.1 0.2
∆Y e ;Y ∈ [0.08, 0.20]
e
Entries
1200 N = 1224.870
Mean = −0.01949
1000
σ = 0.034080
800
600
400
Entries
1200
1000
800
600
400
N = 1238.257
Mean = −0.01510
σ = 0.031508
200
200
−0.4
0
−0.2 0 0.2
∆Y e ;Y e ∈ [0.20, 0.35]
−0.4
0
−0.2 0 0.2 0.4
∆Y e ;Y e ∈ [0.35, 0.70]
Figure 9.2: Y e resolutions in regions of y indicated in the figure. The resolutions, σ, are less
than the bin widths.
Entries
350 N = 311.078
300
Mean = −0.00506
σ = 0.010283
250
200
150
100
50
0
−0.1 −0.05 0 0.05 0.1
∆Y JB ;Y ∈ [0.02, 0.08]
JB
Entries
1200 N = 1173.317
Mean = −0.01123
1000
σ = 0.019459
800
600
400
200
0
−0.1 0 0.1
JB
∆Y JB ;Y ∈ [0.08, 0.20]
Entries
1200 N = 1151.979
Mean = −0.01346
1000
σ = 0.032108
Entries
1000
800
N = 941.977
Mean = −0.01819
σ = 0.049944
800
600
400
200
600
400
200
0
−0.2 0 0.2
JB
∆Y JB ;Y ∈ [0.20, 0.35]
0
−0.4 −0.2 0 0.2 0.4
∆Y JB ;Y ∈ [0.35, 0.70]
JB
Figure 9.3: Y JB resolutions in regions of y indicated in the figure. The resolutions, σ, are
less than the bin widths.
176

The electron method has the worst resolution in the lowest y bin, however, it improves
as y increases. The double-angle and Jacquet-Blondel methods are comparable
for each bin of y, but recall Figs. 8.32 and 8.30, which show their Q 2 resolutions;
the Jacquet-Blondel method poorly reconstructs high Q 2 events relative to
the double-angle method as Q 2 increases.
9.1.2 Acceptances, Purities, and Efficiencies
As shown in the following figures, the y acceptance for each Q 2 region peaks at ≈
47%. The sample is quite pure, however, some bins dip as low as 45%. The efficiency
mirrors the acceptances ranging from 5 to 40%.
177

Acceptance
0.1
0.08
0.06
0.04
0.02
2
2
5 < Q < 6.5 GeV
DA
Acceptance
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
2
2
6.5 < Q < 9 GeV
DA
0
-2
2×10
-1
10
-1
2×10
Y DA
0
-2
2×10
-1
10
-1
2×10
Y DA
Acceptance
0.3
0.25
Acceptance
0.35
0.3
0.2
0.25
0.15
0.2
0.1
0.05
2
2
9 < Q < 14 GeV
DA
0.15
0.1
0.05
2
2
14 < Q < 22 GeV
DA
0
-2
2×10
-1
10
-1
2×10
Y DA
0
-2
2×10
-1
10
-1
2×10
Y DA
Acceptance
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
2
2
22 < Q < 44 GeV
DA
Acceptance
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
2
2
44 < Q < 90 GeV
DA
0
-2
2×10
-1
10
-1
2×10
Y DA
0
-2
2×10
-1
10
-1
2×10
Y DA
Acceptance
0.5
0.4
Acceptance
0.5
0.4
0.3
0.3
0.2
0.2
0.1
2
2
90 < Q < 200 GeV
DA
0.1
2
2
200 < Q < 1000 GeV
DA
0
-2
2×10
-1
10
-1
2×10
Y DA
0
-2
2×10
-1
10
-1
2×10
Y DA
178
Figure 9.4: Y DA acceptance in regions of Q 2 .

Purity
0.8
0.7
0.6
0.5
0.4
Purity
0.8
0.7
0.6
0.5
0.4
0.3
0.3
0.2
0.1
2
5 < Q
DA
2
< 6.5 GeV
0.2
0.1
2
6.5 < Q
DA
2
< 9 GeV
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Purity
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
9 < Q
DA
2
< 14 GeV
Purity
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
14 < Q
DA
2
< 22 GeV
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Purity
1
0.9
Purity
1
0.8
0.7
0.8
0.6
0.5
0.6
0.4
0.3
0.4
0.2
0.1
2
22 < Q
DA
2
< 44 GeV
0.2
2
44 < Q
DA
2
< 90 GeV
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Purity
1
0.8
0.6
Purity
1.2
1
0.8
0.6
0.4
0.4
0.2
2
90 < Q
DA
2
< 200 GeV
0.2
200 < Q
2
DA
2
< 1000 GeV
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Figure 9.5: Y DA purity in regions of Q 2 .
179

Efficiency
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
2
5 < Q
DA
2
< 6.5 GeV
Efficiency
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
2
6.5 < Q
DA
2
< 9 GeV
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Efficiency
0.25
0.2
Efficiency
0.35
0.3
0.25
0.15
0.2
0.1
0.15
0.1
0.05
2
9 < Q
DA
2
< 14 GeV
0.05
2
14 < Q
DA
2
< 22 GeV
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Efficiency
0.4
0.35
0.3
0.25
Efficiency
0.5
0.45
0.4
0.35
0.3
0.2
0.25
0.15
0.1
0.05
2
22 < Q
DA
2
< 44 GeV
0.2
0.15
0.1
0.05
2
44 < Q
DA
2
< 90 GeV
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0 -2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Efficiency
0.5
0.45
0.4
Efficiency
0.5
0.45
0.4
0.35
0.35
0.3
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.05
2
90 < Q
DA
2
< 200 GeV
0.1
0.05
200 < Q
2
DA
2
< 1000 GeV
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
0
-2
2×10
-2
3×10
-1
10
-1
2×10
-1
3×10
Y DA
Figure 9.6: Y DA efficiency in regions of Q 2 .
180

9.1.3 Number of D ∗ Candidates
The number of D ∗ candidates in each Q 2 region divided in bins of y is shown in Fig.
9.7.
Num. Of Cand.
160
140
120
100
Num. Of Cand.
400
350
300
250
80
200
60
150
40
20
2
5 < Q
DA
2
< 6.5 GeV
100
50
2
6.5 < Q
DA
2
< 9 GeV
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
Num. Of Cand.
600
500
400
Num. Of Cand.
500
400
300
300
200
200
100
2
9 < Q
DA
2
< 14 GeV
100
2
14 < Q
DA
2
< 22 GeV
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
Num. Of Cand.
700
600
500
400
Num. Of Cand.
400
350
300
250
200
300
150
200
100
2
22 < Q
DA
2
< 44 GeV
100
50
2
44 < Q
DA
2
< 90 GeV
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
Num. Of Cand.
200
180
160
140
120
Num. Of Cand.
120
100
80
100
60
80
60
40
40
20
2
90 < Q
DA
2
< 200 GeV
20
2
200 < Q
DA
2
< 1000 GeV
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Y DA
Figure 9.7: Number of D ∗ candidates in regions of Q 2 . The ∆M distribution used to obtain
these numbers are shown in App. D.2.
181

9.2 Results
9.2.1 Cross Sections
The cross sections in regions of Q 2 divided in bins of y are shown.
[nb]
σ
0.7
0.6
0.5
2
2
Q = 5.5 GeV
−1
HERA II Data, L = 175.4 pb
[nb]
σ
0.7
0.6
0.5
2
2
Q = 6.8 GeV
0.4
HVQDIS NLO Central Value
Theoretical Uncertainty
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
−2
2×10
−1
10
−1
2×10
0
−2
2×10
−1
10
−1
2×10
Y DA
Y DA
σ [nb]
0.7
0.6
0.5
2
2
Q = 11 GeV
σ [nb]
0.7
0.6
0.5
2
2
Q = 19 GeV
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
−2
2×10
−1
10
−1
2×10
0
−2
2×10
−1
10
−1
2×10
Y DA
Y DA
[nb]
σ
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
−2
2×10
2
2
Q = 31 GeV
−1
10
−1
2×10
[nb]
σ
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
−2
2×10
2
2
Q = 61 GeV
−1
10
−1
2×10
Y DA
Y DA
[nb]
σ
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−2
2×10
2
2
Q = 133 GeV
−1
10
−1
2×10
[nb]
σ
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
−2
2×10
2
2
Q = 510 GeV
−1
10
−1
2×10
Y DA
Y DA
Figure 9.8: The HERA II data points have both statistical and systematic uncertainties.
The blue histogram is the theoretical prediction. The theoretical uncertainty is
the yellow band. The theoretical predictions are in agreement with the HERA
II data.
182

9.3 F cc
2 Extraction
The double differential charm cross section has the form (recall Eq. 2.23)
dσ cc (x,Q 2 )
dxdQ 2
= 2πα2
xQ 4 [(
1 + (1 + y)
2 ) F cc
2 (x,Q 2 ) ] . (9.1)
A ratio of the cross section in data relative to the theoretical value is used to extract
F2 cc:
F2,DATA(x,Q cc 2 ) = σcc DATA (x,Q2 )
σTHEO cc (x,Q2 ) F 2,THEO(x,Q cc 2 ). (9.2)
Thus, the ratios of the measured to theory cross sections (from Fig. 9.8) at their
corresponding x values (found in Tab. 9.1) are multiplied by the theory value of
F cc
2 ,THEO(x,Q 2 ) to obtain F cc
2 ,DATA(x,Q 2 ).
Both the theory cross sections, obtained using HVQDIS, and the charmed structure
function F cc
2 are determined with a NLO FFN scheme PDF (see §3.3.1).
The F cc
2 results along with the theory curves with respect to x for increasing Q 2 ’s
are shown in Fig. 9.9.
The data and theory curves are reorganised to show F cc
2 vs. Q2 for bands of common
x in Fig. 9.10. For clarity the data and theory curves are multiplied by a constant
indicated in the plot.
The final plot, Fig. 9.11, shows the ration of the charm contribution F cc
2
F 2 proton structure function.
to the total
183

c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 5.5 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 6.8 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 11 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 19 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 31 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 61 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 133 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
c c
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−5
10 2×10
−5
−4
10 2×10
−4
2
2
Q = 510 GeV
−3
10 2×10
−3
−2
10 2×10
−2
10
x
−1
Figure 9.9: F2 cc vs. x at different Q 2 . The points are the F2 cc data, while the blue curve
represents the theoretical upper and lower bounds for F cc
2 .
184

)
2
(x, Q
cc
2
F
10
5
9
x = 0.00008 (× 4 )
8
x = 0.00018 (× 4 )
4
10
7
x = 0.00035 (× 4 )
6
x = 0.00060 (× 4 )
3
10
2
10
5
x = 0.00100 (× 4 )
4
x = 0.00150 (× 4 )
3
x = 0.00300 (× 4 )
10
1
2
x = 0.00600 (× 4 )
1
x = 0.01300 (× 4 )
−1
10
0
x = 0.03000 (× 4 )
−2
10
10
2
10
3
10
2 2
Q [GeV ]
Figure 9.10: F2 cc vs. Q 2 at different x. The blue curve is the HVQDIS NLO prediction, the
points are the HERA II data. The theory curves and HERA II F2 cc values are
multiplied by a constant indicated in the plot.
185

2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
10
−5
−4
10
−3
10
2
2
Q = 5.5 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 6.8 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 11 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 19 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 31 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 61 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
−5
−4
10
−3
10
2
2
Q = 133 GeV
−2
10
10
x
−1
2
/F
cc
F 2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
10
−5
−4
10
−3
10
2
2
Q = 510 GeV
−2
10
10
x
−1
Figure 9.11: The ratio of the charm contribution F2 cc to total F 2 proton structure function
is shown for increasing values of Q 2 . F2 cc is measured while F 2 is the theoretical
prediction [53]. The charm contribution falls with increasing x and rises with
increasing Q 2 . The charm contribution to the proton is as high as 40% at the
smaller values of x.
186

9.4 Summary
The charm contribution to the proton structure function, F 2 , falls of with increasing
x in all regions of Q 2 ; see Fig. 9.9. At low fractional momenta the charm density
in the proton increases. This is expected in this region because the proton’s parton
distribution function (PDF) is dominated by the sea quarks. At higher fractional
momenta the charm contribution falls off and the valence quarks begin to dominate
the PDF.
The charm contribution to the photon PDF increases with Q 2 , as seen in Fig. 9.10.
At higher virtualities the proton probe has an increasing probability of striking
a sea quark. The F cc
2 contribution to the proton structure function appears to
increases without leveling off. In the simple quark parton model, scaling is expected
to show that at high Q 2 the structure functions no longer depend on Q 2 , i.e., become
flat. Thus scaling violations are observed and indicate that the proton is more
complicated than only the three valence quarks.
187

Chapter 10
Conclusions
An overview of the HERA accelerator and the ZEUS detector is presented. Attention
to the tracking and the energy reconstruction components is given.
The simulation of the physics processes at HERA and of the ZEUS detector is discussed
in the Monte Carlo chapter. The specific MC generators and cross section
predictors, used in the thesis, are described.
The tracking of charged particles using the ZEUS detector, specifically the daughters
of the D ∗ meson, is discussed. The D ∗ tracking resolution and its track loss probability
are made for the first time since the addition of the micro vertex detector in
this thesis.
This thesis describes how events are reconstructed and selected. Some quantities in
an event can be reconstructed in more than one way. Specifically, the reconstruction
of the Lorentz invariant quantities Q 2 , x, and y are described. Triggers and cuts are
used to select charmed events out of the many events at HERA.
The theoretical framework used to understand charm production at HERA is developed.
The development describes that the DIS charm production cross sections can
be factorized into three independent parts, the hard scattering process, the proton
188

structure, and fragmentation. For charm production, the dominant hard scattering
process is photon gluon fusion. The proton structure is described by parton distribution
functions, which are evolved using the DGLAP equations. The hadronization
of charm quarks is modeled by the Peterson fragmentation function.
How charm production is measured at HERA is described. The wrong charge subtraction
method is used to determine the number of D ∗ candidates. Differential
cross sections of the P T , η, Q 2 , and x of the D ∗ are made and compared to theory.
By adding information from the straw tube tracker component, more forward tracks
in η are included into the data. New differential cross sections with η extended, are
made and presented.
Finally the charm contribution to the proton structure function is measured. Charm
in the proton is seen to increase with Q 2 and with decreasing x.
189

Appendix A
Charm Tagging via P 2,Rel
T
of Jets
An alternate approach to tag charmed events inspired by [55, 56] is to examine the
squared relative transverse momentum, P 2,Rel
T
, distribution of all objects in a jet
relative to the jet axis. The two underlying concepts to this approach are that the
jet axis approximates the direction of the charm quark in the hard scatter and that
charm quark hadronizes to a D ∗ decaying along the mode D ∗ → D 0 π s ; see Fig.
A.1. This D ∗ decay mode is significant because the daughters are produced very
PT
Rel
PT
Rel
PT
Rel
Jet Axis
D 0
p D 0, m D 0
P, M D
D ∗ ∗
p πs
, m πs
Hadronization
π s
a)
c
b)
Figure A.1: a) In the hard scatter the charm quark hadronizes in the process creating a jet
whose axis closely approximates its initial direction. The transverse momentum
of the particles with the jet are measure with respect to the jet axis. b) The
two body decay of the D ∗ to a D 0 and π s .
190

close to the kinematic limit (M D ∗ ≈ M D 0 +M 1 πs ). As a result they have very little
momentum relative to the parent D ∗ .
The energies of the daughters in the D ∗ rest frame are found in Eq. A.1 and A.2.
This is a two body decay, therefore, the daughters must have the same absolute
momentum in the parent’s rest frame (see Eq. A.3). Thus, the maximum possible
transverse momentum squared relative to the D ∗ is given by Eq. A.4. This occurs
when the slow pion and D 0 decay in a direction perpendicular to the D ∗ axis.
E D 0 = M2 D ∗ − m2 π s
+ m 2 D 0
2M D ∗
(A.1)
The P 2,Rel
T
P 2,Rel
T
E πs = M2 D ∗ − m2 D 0 + m 2 π s
2M D ∗
|p D 0| = |p πs |
[(
M
2
D ∗ − (m D 0 + m πs ) 2) ( MD 2 ∗ − (m D 0 − m π s
) 2)] 1/2
=
2M D ∗
(A.2)
(A.3)
P 2,Rel
T
≤ |p D 0| 2 ≈ 0.001568 GeV 2 (A.4)
distribution of particles within a jet should have an observable signal at
< 0.0016 GeV 2 for D ∗ events relative to events without D ∗ mesons.
An advantage of using this approach to tag D ∗ candidates over the wrong charge
subtraction method is that the subsequent D 0 → Kπ decay does not need to be
reconstructed. The D 0 reconstruction mode has a branching fraction of Γ D 0 →Kπ =
(3.80 ± 0.07) %. Requiring the specific D 0 decay reduces the potential number of
tagged D ∗ events by 96% 2 . For this reason the P 2,Rel
T
approach can have a large
gain in statistics over the wrong-charge subtraction method.
The following sections will discuss jets and how they are reconstructed, and show
1 The masses are M D ∗ = 2.0100 ± 0.0004 GeV, M D 0 = 1.8645 ± 0.0004 GeV, and M πs =
0.13957018 ± 0.00000035 GeV [1].
2 Including reconstruction inefficiencies further reduces the number of tagged D ∗ .
191

Monte Carlo results for a charm-enriched RAPGAP sample.
A.1 Jet Reconstruction
A jet can be defined as “a large amount of hadronic energy in a small angular
region” [57]. During the hard scatter quarks, while hadronizing, can initiate jet
production. Reasons to use jets to measure heavy quark production are that the
effects from fragmentation are reduced, and jets are a good approximation of the
outgoing partons from the hard scatter. Neutral hadrons created in the jet will go
undetected by the tracking detectors but will deposit energy in the calorimeter. For
this reason jets can reconstruct the total energy along with the direction of the hard
scatter.
Two commonly used jet reconstruction algorithms are a cone-type algorithm [58],
which maximizes the amount of energy that can be covered by cones of a fixed size,
and a clustering algorithm [59], which iteratively assigns particles to a jet when an
energy angle variable y ij exceeds a resolution parameter y cut . ZEUS uses the k T -
clustering algorithm for jet reconstruction because it handles multi-jet events better
[59].
A.1.1 k T Clustering
The k T -clustering algorithm typically runs over energy deposits in the calorimeter,
however energy flow objects, called EFO (see §6.5), are used at ZEUS. EFOs include
CAL information and tracks that may not correspond to energy deposits but also
represent hadronic energy. Clustering EFOs into a jet requires a test variable d kl
that specifies whether hadrons h k and h l belong to the same cluster, and a recombination
procedure that relates cluster resolution variables to the hadrons belonging
192

to them. The clustering algorithm uses the ZEUS coordinate system discussed in
§4.3.1, boosted into the center-of-mass system of the ep collision. The following
definitions are required for clustering:
• energy of hadron h k , E k ,
• angle between hadrons h k and h l , θ kl ,
• angle between hadron h k and incoming proton momentum, θ kB .
The jet test variables are
d kl = 2min(E 2 k ,E2 l )(1 − cos θ kl), (A.5)
d kB = 2E 2 k (1 − cos θ kB), (A.6)
where “min” refers to the lesser of the two hadron energies. The generalized radius
R 2 kl is R 2 kl = (η k − η l ) 2 + (φ k − φ l ) 2 . (A.7)
Clustering into jets is a two step process: a pre-clustering stage, which separates
beam jets (jets associated to the proton remnant) from hard final-state jets, and
resolving hard final-state jets into sub-jets.
Pre-Clustering of Hadrons
Pre-clustering is a three step process:
1. For every hadron h k the values d kl and d kB are determined.
2. If d kl is the smaller of {d kl ,d kB } then h k and h l are merged into a pseudoparticle
with momentum p (kl) according to a recombination scheme described
shortly. If d kB is smaller then hadron h k is included in the beam jet.
193

3. The procedure is repeated for all particles and pseudoparticles until all objects
have d kl or d kB larger than a cut-off value d cut .
The stopping parameter d cut defines the hard scale of the process, i.e., the boundary
between the low transverse momentum k t scattering and the hard scattering
subprocesses. Hadron candidates are now factorized into hard final-state (related
to the hard scattering process) jets and beam jets (low k t ).
Resolving Sub-Jets
The beam jets determined above are removed from the event. Sub-jets are resolved
from final-state jets according to the following process:
1. Define a resolution parameter y cut = Q 2 0 /d cut < 1, where Q 2 0 is the fragmentation
scale of the jets. Soft hadrons, produced from the fragmentation of the
hard partons (involved in the hard scatter), are merged into the hard parton
jet according to this scale.
2. For any hadron in a hard final-state jet, determine the rescaled resolution
variable y kl = d kl /d cut .
3. For y ij , the smallest y kl in a hard final-state jet, if y ij < y cut then combine p i
and p j into a single pseudoparticle p ij according to recombination scheme.
4. Steps 2 and 3 are repeated for all pairs of particles and pseudoparticles with
y kl < y cut . The remaining objects in the hard final-state jet are the sub-jets.
Recombination Scheme
When particles or pseudoparticles h i and h j pass y ij < y cut they are merged into
a single pseudoparticle with 4-momentum, pseudorapidity, and azimuthal angle ac-
194

cording to the p t weighted recombination scheme:
p t(ij) = p ti + p tj ,
(A.8)
η (ij) = p tiη i + p tj η j
p t(ij)
, (A.9)
φ (ij) = p tiφ i + p tj φ j
p t(ij)
. (A.10)
The result of the k t -clustering algorithm is to have jets whose momentum approximates
the momentum of the partons involved in the hard scattering process.
A.2 Event Selection
The charm-enriched RAPGAP sample of 343 pb −1 mentioned in §3.2.1 is used for
this analysis. The following are requirements that the events must pass:
• Q 2 > 1.5 GeV 2 (intrinsic to the MC sample),
• an electron found,
• E e > 10 GeV,
• 40 < δ h < 60 GeV,
• |Z vtx | < 30 cm,
• y jb > 0.02 ∩ y e < 0.95,
• a generated D ∗ decaying along D ∗ → D 0 π s .
A.3 P 2,Rel
T
Distribution in RAPGAP
As a feasibility test the slow pion P 2,Rel
T
distribution in MC is made. The slow
pion is identified by a routine that matches reconstructed tracks (R) to their generated
tracks (G) with the requirement that the generated track is a pion, which is
195

the daughter of a D ∗ decaying along D ∗ → D 0 π s . The k T -clustering algorithm is
run over both the generated final-state particles and the reconstructed particles to
identify the jets in the event. In addition the algorithm can identify in which jet
a particle ends up. With this information the slow pion is uniquely identified in a
manner impossible to do in data. The P 2,Rel
T
distribution of the slow pion in MC
should provide a signal much cleaner than can be accomplished in data.
The P 2,Rel
T
’s of the generated π s with respect to the generated D ∗ axis and the
generated D ∗ jet axis are shown below.
196

Entries
250
200
a) P
2,Rel
T
*
wrt D of π s
Axis
150
100
50
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
2,Rel
2
(π s,G
) [GeV ]
P T
Entries
50
40
b) P
2,Rel
T
*
wrt D of π s
Jet Axis
30
20
10
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
2,Rel
2
(π s,G
) [GeV ]
P T
Figure A.2: a) P 2,Rel
T
b) P 2,Rel
T
of π s with respect to the D ∗ axis.
of π s with respect to the D ∗ jet axis.
The D ∗ jet is the jet to which the slow pion is associated.
The kinematic limit of P 2,Rel
T
< 0.0016 GeV 2 is clearly seen as expected in Fig.
A.2a). The same distribution is made in Fig. A.2b) with the P 2,Rel
T
197
of the π s with

espect to the D ∗ jet axis. However, no observable signal is present. This is alarming
considering the P 2,Rel
T
particles in the D ∗ jet.
distribution is of only the slow pion in the D ∗ jet and not all
To check if particles are identified correctly a correlation of the generated P T of the
slow pion and the generated P T of the D ∗ is made Fig. A.3.
P T
(π s,G
) [GeV]
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 2 4 6 8 10 12 14 16 18 20
*
P T
(D ) [GeV]
G
Figure A.3: The P T correlation between the generated π s and D ∗ .
Kinematic constraints limit the P T of the π s relative to its parent D ∗ . A clear
boundary is seen, which indicates particles are identified correctly.
To check if the generated D ∗ approximates the D ∗ jet axis and in fact to test if the
D ∗ is correctly placed into a jet, the correlation between the generated D ∗ and the
198

*
*
*
generated D ∗ jet is made for P T , η, and φ in the following Fig. A.4.
Jet)
P T
(D
G
30
25
Jet)
η(D
G
2.5
2
1.5
20
15
10
5
0
0 5 10 15 20 25 30 *
P T
(D )
G
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 *
η(D )
G
Jet)
φ(D
G
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3 *
φ(D )
G
Figure A.4: The P T , η, and φ correlation between the generated D ∗ and D ∗ jet.
The generated D ∗ and D ∗ jet axis appear to be correlated as is seen in the three
figures. However, the correlation in P T looks the weakest. It appears that this level
of correlation between the D ∗ and the D ∗ jet is not strong enough for this study to
work at ZEUS.
An additional potential problem occurs when looking at the P T correlation between
199

the highest generated and reconstructed P T jets, as seen in Fig. A.5.
) [GeV]
P T
(Jet
R
40
35
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40
P T
(Jet ) [GeV]
G
Figure A.5: The P T correlation between the reconstructed D ∗ jet and generated D ∗ jet.
From this plot a generated jet can be reconstructed with a transverse momentum
difference of as much as 5 GeV. Considering that the bulk of the jets have P T that
lie within 2 to 15 GeV, this 5 GeV variation is significant.
A.4 Summary
The P 2,Rel
T
approach was done on a charm-enriched RAPGAP sample and showed
no observable signal at the generator level. The likelihood of observing the signal in
data is small. This version of RAPGAP produces a D ∗ decaying via D ∗ → D 0 π s once
in every 8 events, far higher than at HERA. The slow pion and D ∗ at the generator
level can be uniquely identified. This means the jet the π s winds up in is known
200

and yet on a generator level no signal is observed. In data the π s is impossible to
uniquely identify. In addition many slow pions are lost in the reconstruction phase.
The feasibility of such a study over the data seems small.
201

Appendix B
D ∗+ and D ∗− Production Rates
B.1 Introduction
The D ∗+ and D ∗− production rates are explored in this appendix. These rates
should be the same at HERA considering that the main source of D ∗ production
is via boson gluon fusion. The actual reconstruction rate is not symmetric; D ∗+
are better reconstructed than D ∗− because positively charged tracks are better reconstructed
by the CTD than the negatively charged tracks; see §4.6.3. The D ∗+ ,
which decays via D ∗+ → (D 0 )π s + → (K − π + )π s + , has three charged tracks, two of
which are positive, compared to the D ∗− , D ∗− → (D 0 )πs − → (K + π − )πs − with only
one of its three tracks positively charged.
B.1.1 Wrong Charge Subtraction Revisited
The number of D ∗ candidates is determined using the wrong-charge subtraction
method described in §8.1.3. For the D ∗+ the ∆M right charge distribution is made
up of three charged tracks two of which are positive with the requirement that the
two like charged tracks are assigned the pion mass, while the oppositely charged
track is assigned the kaon mass (the reverse is true for the D ∗− ). The wrong-charge
∆M distribution for the D ∗+ is made up of three tracks: the tracks associated
202

to the D 0 daughters, the kaon and pion, are (incorrectly) both positively charged,
and the track assigned the slow pion mass is (incorrectly) negatively charged, i.e.,
(K,π,π s ) = (+,+, −). Similarly, the wrong-charge ∆M distribution for the D ∗−
has (K,π,π s ) = (−, −,+). Once the RC and WC distributions are obtained the
number of D ∗+ and D ∗− candidates is determined in the same fashion as before.
B.2 D ∗± Results
The tools to obtain the number of D ∗ candidates are developed already and the
results are shown below.
B.2.1 D ∗± Number Of Candidates
Cand.
*±
Num. Of D
700
600
500
400
Cand.
*±
Num. Of D
800
700
600
500
400
300
300
200
100
*+
D
*-
D
200
100
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D )
0
2 3 4 5 6 7 8 9 10 *
P T (D ) [GeV]
Cand.
1000
Cand.
1400
*±
Num. Of D
800
*±
Num. Of D
1200
1000
600
800
400
600
200
400
200
0
10
2
10
3
10
2 2
Q [GeV ]
0
-4
10
-3
10
-2
10
-1
10
x
Figure B.1: Number of D ∗± candidates.
203

B.2.2 D ∗± Difference in D ∗+ - D ∗−
)
*-
) - Num(D
*+
Num(D
200
150
100
)
*-
) - Num(D
*+
Num(D
500
400
300
200
50
100
0
0
-100
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D )
2 3 4 5 6 7 8 9 10 *
P T (D ) [GeV]
)
*-
) - Num(D
*+
300
250
)
*-
) - Num(D
*+
500
400
Num(D
200
Num(D
300
150
200
100
50
100
0
0
-50
10
2
10
3
10
2 2
Q [GeV ]
-100
-4
10
-3
10
-2
10
-1
10
x
Figure B.2: Difference in the number of D ∗+ - D ∗− candidates.
204

B.2.3 D ∗± Acceptances
Acceptance
*±
D
0.3
0.25
Acceptance
*±
D
0.45
0.4
0.35
0.2
0.3
0.15
0.25
0.2
0.1
0.05
*+
D
*-
D
0.15
0.1
0.05
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D )
0
2 3 4 5 6 7 8 9 10 *
P T (D ) [GeV]
Acceptance
*±
D
0.4
0.35
0.3
Acceptance
*±
D
0.35
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
10
2
10
3
10
2 2
Q [GeV ]
0
-4
10
-3
10
-2
10
-1
10
x
Figure B.3: Acceptances of D ∗± candidates.
205

2
2
]
B.2.4 D ∗± Differential Cross Sections
dσ/dη [nb]
*+
D
1.2
1
0.8
dσ/dP T
[nb/GeV]
*+
D
1
0.6
-1
10
0.4
0.2
-2
10
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D
)
2 3 4 5 6 7 8 9 10
*
P T (D
) [GeV]
[nb/GeV
-1
10
dσ/dx[nb]
3
10
*+
dσ/dQ
*+
D
-2
10
D
2
10
-3
10
10
-4
10
1
-5
10
10
2
10
3
10
2
2
Q
[GeV
]
-1
10
-4
10
-3
10
-2
10
-1
10
x
Figure B.4: D ∗+ differential cross sections. The blue points are data, blue histogram is the
HVQDIS prediction, yellow band is the theoretical uncertainties.
206

dσ/dη [nb]
*-
D
1
0.8
dσ/dP T
[nb/GeV]
*-
1
D
2
2
]
0.6
-1
10
0.4
0.2
-2
10
0
-1.5 -1 -0.5 0 0.5 1 1.5
*
η(D
)
*
P 10
(D
T ) [GeV]
[nb/GeV
-1
10
dσ/dx[nb]
dσ/dQ
*-
D
-2
10
*-
3
10
D
2
10
-3
10
10
-4
10
1
-5
10
10
2
10
3
10
2
2
Q
[GeV
]
-1
10
-4
10
-3
10
-2
10
-1
10
x
Figure B.5: D ∗− differential cross sections. The red points are data, green histogram is the
HVQDIS prediction, yellow band is the theoretical uncertainties.
B.2.5 D ∗+ to D ∗− Asymmetry
Using the differential cross sections an asymmetry in the production rate is determined:
A i = σ i(D ∗+ ) − σ i (D ∗− )
σ i (D ∗+ ) + σ i (D ∗− ) .
(B.1)
The errors associated with the asymmetry have the form
δA i = A i
( δσi (D ∗+ ) + δσ i (D ∗− )
σ i (D ∗+ ) − σ i (D ∗− )
The asymmetries are calculated and shown in Fig. B.6.
+ δσ i(D ∗± )
)
σ i (D ∗± . (B.2)
)
207

Asymmetry
1
0.8
0.6
Asymmetry
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1.5
-1
-1 -0.5 0 0.5 1 1.5
η
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
2 3 4 5 6 7 8 9 10
P_T [GeV]
Asymmetry
1
0.8
0.6
Asymmetry
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10
2
10
3
10
2 2
Q [GeV ]
-1
-4
10
-3
10
-2
10
-1
10
X
Figure B.6: D ∗± asymmetry with respect to η, P T , Q 2 , and x.
B.3 Summary
The results indicate no evidence of an asymmetry between the D ∗+ and D ∗− production
rates during the HERA II running period.
208

Appendix C
Tracking Resolutions
The remainder of the tracking resolutions developed in §5.4 are shown here.
σ(η) with respect to P T
σ(η)
0.006
0.005
0.004
0.003
π S
K
π
0.002
0.001
0
1 10
[GeV]
P T
Figure C.1: σ(η) with respect to P T tracking resolution.
209

σ(φ) with respect to P T
σ(φ)
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
1 10
[GeV]
P T
Figure C.2: σ(φ) with respect to P T tracking resolution.
σ(|P|) with respect to P T
σ(|P|)/|P|
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
1 10
[GeV]
P T
Figure C.3: σ(|P|) with respect to P T tracking resolution.
210

σ(P T ) with respect to η
T
)/P
T
σ(P
0.05
0.04
0.03
0.02
0.01
0
−1.5 −1 −0.5 0 0.5 1 1.5
η
Figure C.4: σ(P T ) with respect to η tracking resolution.
σ(η) with respect to η
σ(η)
0.006
0.005
0.004
0.003
0.002
0.001
0
−1.5 −1 −0.5 0 0.5 1 1.5
η
Figure C.5: σ(η) with respect to η tracking resolution.
211

σ(φ) with respect to η
σ(φ)
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
−1.5 −1 −0.5 0 0.5 1 1.5
η
Figure C.6: σ(φ) with respect to η tracking resolution.
σ(|P|) with respect to η
σ(|P|)/|P|
0.05
0.04
0.03
0.02
0.01
0
−1.5 −1 −0.5 0 0.5 1 1.5
η
Figure C.7: σ(|P|) with respect to η tracking resolution.
212

σ(P T ) with respect to φ
T
)/P
T
σ(P
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
−3 −2 −1 0 1 2 3
φ
Figure C.8: σ(P T ) with respect to φ tracking resolution.
σ(η) with respect to φ
σ(η)
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
−3 −2 −1 0 1 2 3
φ
Figure C.9: σ(η) with respect to φ tracking resolution.
213

σ(φ) with respect to φ
σ(φ)
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
−3 −2 −1 0 1 2 3
φ
Figure C.10: σ(φ) with respect to φ tracking resolution.
σ(|P|) with respect to φ
σ(|P|)/|P|
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
−3 −2 −1 0 1 2 3
φ
Figure C.11: σ(|P|) with respect to φ tracking resolution.
214

σ(P T ) with respect to |P|
T
)/P
T
σ(P
0.05
0.04
0.03
0.02
0.01
0
1 10
|P| [GeV]
Figure C.12: σ(P T ) with respect to |P| tracking resolution.
σ(η) with respect to |P|
σ(η)
0.006
0.005
0.004
0.003
0.002
0.001
0
1 10
|P| [GeV]
Figure C.13: σ(η) with respect to |P| tracking resolution.
215

σ(φ) with respect to |P|
σ(φ)
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
1 10
|P| [GeV]
Figure C.14: σ(φ) with respect to |P| tracking resolution.
σ(|P|) with respect to |P|
σ(|P|)/|P|
0.06
0.05
0.04
0.03
0.02
0.01
0
1 10
|P| [GeV]
Figure C.15: σ(|P|) with respect to |P| tracking resolution.
216

Appendix D
Supplementary D ∗ Plots
D.1 Single Differential Related Plots
The following plots are from Ch. 8.
217

D.1.1 ∆M Distributions
Combinations per 0.0005 GeV
800
700
600
500
400
300
200
100
HERA II Data
Wrong Charge Distribution
Fit
1.5 < P T
< 2.4
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
450
400
2.4 < P T
< 3.1
350
300
250
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
400
350
300
250
200
150
100
50
< 4.0
3.1 < P T
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
450
400
4.0 < P T
< 6.0
350
300
250
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
180
160
6.0 < P T
< 15.0
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Figure D.1: ∆M distributions in P T bins with fits.
218

Combinations per 0.0005 GeV
250
-1.5 < η < -0.8
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
350
300
250
200
150
100
-0.8 < η < -0.35
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
300
-0.35 < η < 0.0
250
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
350
300
250
200
150
100
0.0 < η < 0.4
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
400
350
0.4 < η < 0.8
300
250
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
400
350
300
250
200
150
100
0.8 < η < 1.5
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Figure D.2: ∆M distributions in η bins with fits.
219

Combinations per 0.0005 GeV
700
600
0.00008 < X < 0.0004
500
400
300
200
100
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
1400
1200
1000
800
600
400
200
0.0004 < X < 0.0016
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
1000
0.0016 < X < 0.005
800
600
400
200
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
300
250
200
150
100
0.005 < X < 0.01
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Combinations per 0.0005 GeV
140
120
100
80
60
0.01 < X < 0.1
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
Figure D.3: ∆M distributions in x bins with fits.
220

D.1.2 Systematic Uncertainties of Differential Cross Sections
The fractional change, discussed in §8.7.2, due to the systematic checks in η, P T ,
Q 2 , and x are shown.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
No Smearing of the Electron Energy
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.4: Systematic Check 1: No Electron Smearing. The green line is mirrored on the
negative y axis and indicates the statistical error, the points are the systematic
errors.
221

Frac. Diff.
0.3
0.2
0.1
Scale Electron Energy by −1%
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Scale Electron Energy by +1%
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.5: Systematic Check 2: E e Scaled ±1% in MC.
Frac. Diff.
0.3
0.2
0.1
Scale Hadron Energy in CAL by −3%
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Scale Hadron Energy in CAL by +3%
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.6: Systematic Check 3: E HAD Scaled ±3% in MC.
222

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Increase Electron Energy Cut
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.7: Systematic Check 4: E e Cut Increased to 11 GeV in MC.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Box Cut
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.8: Systematic Check 5: Box Cut increased by 1 cm.
223

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Z Cut
vertex
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.9: Systematic Check 6: Z vtx Decreased by 3 cm.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Loosen Y E
Cleaning Cut
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.10: Systematic Check 7: Y e Cleaning Cut.
224

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Y
Cleaning Cut
JB
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.11: Systematic Check 8: Y JB Cleaning Cut.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Decrease δ (E − p z
) Window
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.12: Systematic Check 9: δ h Window Widened.
225

Frac. Diff.
0.3
0.2
0.1
0
Decrease D Mass Window
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
0
Increase D Mass Window
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.13: Systematic Check 10: M(D 0 ) Window Widened and Narrowed.
Frac. Diff.
0.3
0.2
0.1
Decrease ∆M Window
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Increase ∆M Window
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.14: Systematic Check 11: ∆M Window Widened and Narrowed.
226

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
No Reweighting of P (π s ) Distribution
T
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.15: Systematic Check 12: No P T (π s ) Re-weighting.
Frac. Diff.
0.3
0.2
0.1
MC EVT RWT w/(K, π, π s
) Trk Loss Prb. −20%
Frac. Diff.
0.3
0.2
0.1
0
−0.1
0
−0.1
−0.2
MC EVT RWT w/(K, π, π s
) Trk Loss Prb. +20%
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.16: Systematic Check 13: Track Loss Probability ±20%.
227

Frac. Diff.
0.3
0.2
0.1
Loosen Cut On Mimimum P T
(K, π)
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Cut On Mimimum P (K, π)
T
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.17: Systematic Check 14a: P T (K, π) Cut changed ±0.02 GeV.
Frac. Diff.
0.3
0.2
0.1
Loosen Cut On Mimimum P T
(π s )
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Tighten Cut On Mimimum P (π s )
T
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.18: Systematic Check 14b: P T (π s ) Cut changed ±0.02 GeV.
228

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Doubling Beauty Contribution
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.19: Systematic Check 15: Doubled Beauty.
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Numbers Obtained via Fit
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.20: Consistency Check 16: Fit.
229

Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
Use HERWIG MC. instead of RAPGAP
−0.3
−1.5 −1 −0.5 0 0.5 1 1.5
*
η(D )
−0.2
−0.3
2 4 6 8 10 12 14
*
P T
(D ) [GeV]
Frac. Diff.
0.3
0.2
0.1
Frac. Diff.
0.3
0.2
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
100 200 300 400 500 600 700 800 900 1000
2 2
Q [GeV ]
−0.3
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x
Figure D.21: Consistency Check 17: HERWIG.
230

2
]
T
D.1.3 Consistency Check Differential Cross Sections
The following two differential cross sections are shown as consistency checks: using
fits instead of the wrong charge subtraction method to obtain the number of D ∗
candidates, and using HERWIG instead of RAPGAP as the MC that determines
the acceptances.
[nb/GeV]
dσ/dP
1
dσ/dη [nb]
3
2.5
2
-1
10
1.5
1
0.5
-2
10
2 3 4 5 6 7 8 9 10
*
P T (D
) [GeV]
-1.5 0
-1 -0.5 0 0.5 1 1.5
*
η(D
)
-2
[nb/GeV
1
-1
10
dσ/dX [nb]
3
10
dσ/dQ
-2
10
2
10
-3
10
10
-4
10
1
-5
10
10
2
10
2
2
Q
[GeV
]
-4
10
-3
10
-2
10
-1
10
X
Figure D.22: Cross sections obtained using a fit for the number of D ∗ candidates.
231

2
]
[nb/GeV]
T
dσ/dP
1
dσ/dη [nb]
3
2.5
2
-1
10
1.5
1
0.5
-2
10
2 3 4 5 6 7 8 9 10
*
P T (D
) [GeV]
-1.5 0
-1 -0.5 0 0.5 1 1.5
*
η(D
)
-2
[nb/GeV
1
-1
10
dσ/dX [nb]
3
10
dσ/dQ
-2
10
2
10
-3
10
10
-4
10
1
-5
10
10
2
10
2
2
Q
[GeV
]
-4
10
-3
10
-2
10
-1
10
X
Figure D.23: Cross sections obtained using HERWIG for the MC.
232

D.1.4 HVQDIS Theoretical Uncertainties
The HVQDIS theoretical uncertainties.
0.25
0.2 Decreased m c
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
0.25
0.2 Increased m c
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
0.25
0.2 Decreased Peterson ∈
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
Frac. Diff.
0.25
0.2
0.15
Increased Peterson ∈
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
0.25
0.2
0.15
µ = 2m c
R,F
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
0.25
0.2
0.15
Doubled µ
R,F
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
0.25
0.2 Halved µ
R,F
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
0.25
2 2
0.2 µ = MAX( Q /4 + m , 2m )
R,F
c c
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-1.5 -1 -0.5 0 0.5 1 1.5
η
Frac. Diff.
Figure D.24: The fractional difference between the default HVQDIS prediction of the η of
the D ∗ cross section, the theoretical uncertainties are shown in blue. The
theoretical uncertainties are indicated.
233

Frac. Diff.
0.2
0.15
0.1
Decreased m c
Frac. Diff.
0.2
0.15
0.1
Increased m c
Frac. Diff.
0.2
0.15
0.1
Decreased Peterson ∈
0.05
0.05
0.05
0
0
0
-0.05
-0.05
-0.05
-0.1
10
2
10
2
Q [GeV]
-0.1
10
2
10
2
Q [GeV]
-0.1
10
2
10
2
Q [GeV]
Frac. Diff.
0.2
0.15
0.1
Increased Peterson ∈
Frac. Diff.
0.2
0.15
0.1
µ = 2m c
R,F
Frac. Diff.
0.2
0.15
0.1
Doubled µ
R,F
0.05
0.05
0.05
0
0
0
-0.05
-0.05
-0.05
-0.1
10
2
10
2
Q [GeV]
-0.1
10
2
10
2
Q [GeV]
-0.1
10
2
10
2
Q [GeV]
Frac. Diff.
0.2
0.15
0.1
Halved µ
R,F
Frac. Diff.
0.2
0.15
0.1
2 2
µ = MAX( Q /4 + m , 2m )
R,F
c c
0.05
0.05
0
0
-0.05
-0.05
-0.1
10
2
10
2
Q [GeV]
-0.1
10
2
10
2
Q [GeV]
Figure D.25: The fractional difference between the default HVQDIS prediction of the Q 2
cross section.
234

Frac. Diff.
0.15
0.1
0.05
Decreased m c
Frac. Diff.
0.15
0.1
0.05
Increased m c
Frac. Diff.
0.15
0.1
0.05
Decreased Peterson ∈
0
0
0
-0.05
-0.05
-0.05
-0.1
10
-4
-3
10
-2
10
X
-0.1
10
-4
-3
10
-2
10
X
-0.1
10
-4
-3
10
-2
10
X
Frac. Diff.
0.15
0.1
0.05
Increased Peterson ∈
Frac. Diff.
0.15
0.1
0.05
µ = 2m c
R,F
Frac. Diff.
0.15
0.1
0.05
Doubled µ
R,F
0
0
0
-0.05
-0.05
-0.05
-0.1
10
-4
-3
10
-2
10
X
-0.1
10
-4
-3
10
-2
10
X
-0.1
10
-4
-3
10
-2
10
X
Frac. Diff.
0.15
0.1
0.05
Halved µ
R,F
Frac. Diff.
0.15
0.1
0.05
2 2
µ = MAX( Q /4 + m , 2m )
R,F
c c
0
0
-0.05
-0.05
-0.1
10
-4
-3
10
-2
10
X
-0.1
10
-4
-3
10
-2
10
X
Figure D.26: The fractional difference between the default HVQDIS prediction of the X
cross section.
235

D.2 F cc
2 Related Plots
D.2.1 Q 2 − y ∆M Distributions
The following plot shows the ∆M distribution for the Q 2 − y bins, see Tab. 9.1 for
the key.
Comb. per 0.001 GeV
18
16
1)
14
12
10
8
6
4
2
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
40
35
30
25
2)
20
15
10
5
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
70
60
50
3)
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
90
80
4)
70
60
50
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
60
50
40
5)
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
240
220
200
180
160
140
120
100
80
60
40
6)
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
180
160
7)
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
140
120
100
8)
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
250
200
9)
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
250
200
10)
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
140
120
100
11)
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
120
100
80
12)
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
250
200
13)
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
200
180
14)
160
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
120
100
80
15)
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
100
90
16)
80
70
60
50
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
350
300
250
17)
200
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
200
180
18)
160
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
180
160
19)
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
140
120
100
20)
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
250
200
21)
150
100
50
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
200
180
22)
160
140
120
100
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
80
70
60
50
23)
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
120
100
80
24)
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
140
120
100
25)
80
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
∆M [GeV]
Comb. per 0.001 GeV
100
90
26)
80
70
60
50
40
30
20
10
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
Comb. per 0.001 GeV
120
100
80
27)
60
40
20
0
0.135 0.14 0.145 0.15 0.155 0.16 0.165
∆M [GeV]
∆M [GeV]
Figure D.27: ∆M distributions used for F cc
2 , see Tab. 9.1. The points are the right charge
combinations, the green histogram is the wrong charge combination, and the
red line is wrong charge subtracted distribution.
236

2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
D.2.2 F cc
2 Systematics
The systematic checks for each Q 2 region are shown in the following plots.
c c
Frac. Diff. on F
0.8
0.6
0.4
0.2
0
−0.8
0
Increase D
Mass Window
2
2
Q = 5.5 GeV
−0.2
−0.4
0
Decrease D Mass Window
−0.6
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
Decrease δ (E − p) Window
z
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Increase ∆M Window
0.4
0.2
0
−0.2
−0.4
Decrease ∆M Window
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Increase Electron Energy Cut
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Use HERWIG MC. instead of RAPGAP
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Tighten Cut On Mimimum P (K, π)
T
0.4
0.2
0
−0.2
−0.4
Loosen Cut On Mimimum P
−0.6
T (K, π)
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6
0.4
0.2
0
−0.2
Tighten Cut On Mimimum P (π s )
T
−0.4
Loosen Cut On Mimimum P
−0.6
T (π s )
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Loosen Y E Cleaning Cut
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6
0.4
0.2
0
−0.2
−0.4
Tighten Y
JB
Cleaning Cut
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Scale Electron Energy by +1%
0.4
0.2
0
−0.2
−0.4
Scale Electron Energy by −1%
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Scale Hadron Energy in CAL by +3%
0.4
0.2
0
−0.2
−0.4
Scale Hadron Energy in CAL by −3%
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 No Reweighting of P (π s ) Distribution
T
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
MC EVT RWT w/(K, π, π
) Trk Loss Prb. +20%
s
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Tighten Box Cut
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Tighten Z Cut
vertex
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Numbers Obtained via Fit
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 Doubling Beauty Contribution
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
c c
Frac. Diff. on F
0.8
0.6 No Smearing of the Electron Energy
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
x
Figure D.28: Q 2 = 5.5 GeV 2 systematics.
237

2
c c
2
2
2
2
2
2
2
2
2
2
2
2
2
Frac. Diff. on F
2
2
2
2
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0
Increase D
0
Decrease D
Mass Window
2
2
Q = 6.8 GeV
Mass Window
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Decrease δ (E − p) Window
z
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4 Increase ∆M Window
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Decrease ∆M Window
−0.4
−0.5
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Increase Electron Energy Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Use HERWIG MC. instead of RAPGAP
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Cut On Mimimum P (K, π)
T
Loosen Cut On Mimimum P T (K, π)
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Cut On Mimimum P (π s )
T
Loosen Cut On Mimimum P T (π s )
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Loosen Y E Cleaning Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Y
JB
Cleaning Cut
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Scale Electron Energy by +1%
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Scale Electron Energy by −1%
−0.4
−0.5
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Scale Hadron Energy in CAL by +3%
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Scale Hadron Energy in CAL by −3%
−0.4
−0.5
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
No Reweighting of P (π s ) Distribution
T
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
MC EVT RWT w/(K, π, π
) Trk Loss Prb. +20%
s
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Tighten Box Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Z
vertex
Cut
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Numbers Obtained via Fit
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
c c
Frac. Diff. on F
0.5
0.4 Doubling Beauty Contribution
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.00080.0010.00120.00140.00160.0018 0.002
x
c c
Frac. Diff. on F
0.5
0.4 No Smearing of the Electron Energy
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.00020.00040.00060.0008 0.0010.00120.00140.00160.00180.002
x
Figure D.29: Q 2 = 6.8 GeV 2 systematics.
238

c c
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Frac. Diff. on F
2
2
2
2
0.2
0.1
0
−0.1
−0.2
0
Increase D Mass Window
2
2
Q = 11 GeV
0
Decrease D
Mass Window
c c
Frac. Diff. on F
0.2 Decrease δ (E − p) Window
z
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.2 Increase ∆M Window
0.1
0
−0.1
Decrease ∆M Window
−0.2
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.2 Increase Electron Energy Cut
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.2 Use HERWIG MC. instead of RAPGAP
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.2 Tighten Cut On Mimimum P (K, π)
T
0.1
0
−0.1
Loosen Cut On Mimimum P −0.2
T (K, π)
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.2 Tighten Cut On Mimimum P T
(π s )
0.1
0
−0.1
−0.2 Loosen Cut On Mimimum P T (π s )
c c
Frac. Diff. on F
0.2 Loosen Y E Cleaning Cut
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.2 Tighten Y Cleaning Cut
JB
0.1
0
−0.1
−0.2
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.2 Scale Electron Energy by +1%
0.1
0
−0.1
Scale Electron Energy by −1%
−0.2
c c
Frac. Diff. on F
0.2 Scale Hadron Energy in CAL by +3%
0.1
0
−0.1
Scale Hadron Energy in CAL by −3%
−0.2
c c
Frac. Diff. on F
0.2 No Reweighting of P T
(π s ) Distribution
0.1
0
−0.1
−0.2
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.2 MC EVT RWT w/(K, π, π ) Trk Loss Prb. +20%
s
0.1
0
−0.1
−0.2
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
c c
Frac. Diff. on F
0.2 Tighten Box Cut
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.2 Tighten Z Cut
vertex
0.1
0
−0.1
−0.2
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.2 Numbers Obtained via Fit
0.1
0
−0.1
c c
Frac. Diff. on F
0.2 Doubling Beauty Contribution
0.1
0
−0.1
c c
Frac. Diff. on F
0.2 No Smearing of the Electron Energy
0.1
0
−0.1
−0.2
−0.2
−0.2
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
Figure D.30: Q 2 = 11 GeV 2 systematics.
239

c c
Frac. Diff. on F
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.3
0.2
0.1
0
−0.1
−0.2
0
Increase D Mass Window
2
2
Q = 19 GeV
0
Decrease D
Mass Window
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
−0.2
Decrease δ (E − p) Window
z
c c
Frac. Diff. on F
0.3
Increase ∆M Window
0.2
0.1
0
−0.1
−0.2 Decrease ∆M Window
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
Increase Electron Energy Cut
0.2
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.3
Use HERWIG MC. instead of RAPGAP
0.2
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Tighten Cut On Mimimum P (K, π)
T
−0.1
−0.2 Loosen Cut On Mimimum P T (K, π)
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Tighten Cut On Mimimum P (π s )
T
−0.1
−0.2 Loosen Cut On Mimimum P T (π s )
c c
Frac. Diff. on F
0.3
Loosen Y
0.2
E Cleaning Cut
0.1
0
−0.1
−0.2
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
−0.2
Tighten Y
JB
Cleaning Cut
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
Scale Electron Energy by +1%
0.2
0.1
0
−0.1
−0.2 Scale Electron Energy by −1%
c c
Frac. Diff. on F
0.3
Scale Hadron Energy in CAL by +3%
0.2
0.1
0
−0.1
−0.2 Scale Hadron Energy in CAL by −3%
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
−0.2
No Reweighting of P (π s ) Distribution
T
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
MC EVT RWT w/(K, π, π ) Trk Loss Prb. +20%
0.2
s
0.1
0
−0.1
−0.2
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
Tighten Box Cut
0.2
0.1
0
−0.1
−0.2
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
−0.2
Tighten Z
vertex
Cut
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
Numbers Obtained via Fit
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
Doubling Beauty Contribution
c c
Frac. Diff. on F
0.3
No Smearing of the Electron Energy
0.2
0.1
0
−0.1
−0.2
−0.2
−0.2
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
−0.3
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
x
Figure D.31: Q 2 = 19 GeV 2 systematics.
240

2
c c
2
2
2
2
2
2
2
2
2
2
2
2
2
Frac. Diff. on F
2
2
2
2
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0
Increase D
0
Decrease D
Mass Window
2
2
Q = 31 GeV
Mass Window
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Decrease δ (E − p) Window
z
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Increase ∆M Window
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Decrease ∆M Window
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Increase Electron Energy Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Use HERWIG MC. instead of RAPGAP
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Cut On Mimimum P (K, π)
T
Loosen Cut On Mimimum P T (K, π)
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Cut On Mimimum P (π s )
T
Loosen Cut On Mimimum P T (π s )
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Loosen Y E Cleaning Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Y
JB
Cleaning Cut
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Scale Electron Energy by +1%
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Scale Electron Energy by −1%
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Scale Hadron Energy in CAL by +3%
0.3
0.2
0.1
0
−0.1
−0.2
−0.3 Scale Hadron Energy in CAL by −3%
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
No Reweighting of P (π s ) Distribution
T
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
MC EVT RWT w/(K, π, π
) Trk Loss Prb. +20%
s
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Tighten Box Cut
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
Tighten Z
vertex
Cut
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Numbers Obtained via Fit
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 Doubling Beauty Contribution
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
c c
Frac. Diff. on F
0.5
0.4 No Smearing of the Electron Energy
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
x
Figure D.32: Q 2 = 31 GeV 2 systematics.
241

2
2
2
2
2
2
c c
Frac. Diff. on F
2
2
2
2
2
2
2
2
2
2
2
2
0.3
0.2
0.1
0
0
Increase D Mass Window
2
2
Q = 61 GeV
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Decrease δ (E − p) Window
z
c c
Frac. Diff. on F
0.3
Increase ∆M Window
0.2
0.1
0
−0.1
−0.2
0
Decrease D
Mass Window
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
Decrease ∆M Window
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Increase Electron Energy Cut
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Use HERWIG MC. instead of RAPGAP
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Tighten Cut On Mimimum P (K, π)
T
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
Loosen Cut On Mimimum P T (K, π)
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Tighten Cut On Mimimum P (π s )
T
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Loosen Y E Cleaning Cut
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Tighten Y
JB
Cleaning Cut
−0.1
Loosen Cut On Mimimum P T (π s )
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Scale Electron Energy by +1%
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Scale Hadron Energy in CAL by +3%
c c
Frac. Diff. on F
0.3
0.2
0.1
0
No Reweighting of P (π s ) Distribution
T
−0.1
Scale Electron Energy by −1%
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
Scale Hadron Energy in CAL by −3%
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
MC EVT RWT w/(K, π, π ) Trk Loss Prb. +20%
0.2
s
0.1
0
−0.1
−0.2
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
Tighten Box Cut
0.2
0.1
0
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
−0.1
−0.2
Tighten Z
vertex
Cut
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Numbers Obtained via Fit
c c
Frac. Diff. on F
0.3
0.2
0.1
0
Doubling Beauty Contribution
c c
Frac. Diff. on F
0.3
No Smearing of the Electron Energy
0.2
0.1
0
−0.1
−0.1
−0.1
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
−0.2
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
x
Figure D.33: Q 2 = 61 GeV 2 systematics.
242

2
c c
2
2
2
2
2
2
2
2
2
2
2
2
2
Frac. Diff. on F
2
2
2
2
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
Increase D
0
Decrease D
Mass Window
2
2
Q = 133 GeV
Mass Window
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Decrease δ (E − p) Window
z
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Increase ∆M Window
0.6
0.4
0.2
0
−0.2
−0.4
−0.6 Decrease ∆M Window
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Increase Electron Energy Cut
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Use HERWIG MC. instead of RAPGAP
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Tighten Cut On Mimimum P (K, π)
T
Loosen Cut On Mimimum P T (K, π)
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Tighten Cut On Mimimum P (π s )
T
Loosen Cut On Mimimum P T (π s )
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
Loosen Y E Cleaning Cut
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Tighten Y
JB
Cleaning Cut
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Scale Electron Energy by +1%
0.6
0.4
0.2
0
−0.2
−0.4
−0.6 Scale Electron Energy by −1%
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Scale Hadron Energy in CAL by +3%
0.6
0.4
0.2
0
−0.2
−0.4
−0.6 Scale Hadron Energy in CAL by −3%
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
No Reweighting of P (π s ) Distribution
T
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
MC EVT RWT w/(K, π, π
) Trk Loss Prb. +20%
s
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Tighten Box Cut
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Tighten Z
vertex
Cut
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Numbers Obtained via Fit
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 Doubling Beauty Contribution
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
c c
Frac. Diff. on F
1
0.8 No Smearing of the Electron Energy
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
x
Figure D.34: Q 2 = 131 GeV 2 systematics.
243

c c
2
2
2
2
2
2
Frac. Diff. on F
2
2
2
2
2
2
2
2
2
2
2
2
2
1.5
1
0.5
0
0
Increase D
Mass Window
2
2
Q = 510 GeV
−0.5
−1
0
Decrease D Mass Window
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
Decrease δ (E − p) Window
z
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 Increase ∆M Window
1
0.5
0
−0.5
−1
Decrease ∆M Window
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
Increase Electron Energy Cut
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
Use HERWIG MC. instead of RAPGAP
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
Tighten Cut On Mimimum P (K, π)
T
−1
Loosen Cut On Mimimum P
−1.5
T (K, π)
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
Tighten Cut On Mimimum P (π s )
T
−1
Loosen Cut On Mimimum P
−1.5
T (π s )
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 Loosen Y E Cleaning Cut
1
0.5
0
−0.5
−1
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
Tighten Y
JB
Cleaning Cut
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
Scale Electron Energy by +1%
−0.5
−1
Scale Electron Energy by −1%
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
Scale Hadron Energy in CAL by +3%
−0.5
−1
Scale Hadron Energy in CAL by −3%
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 No Reweighting of P (π s ) Distribution
T
1
0.5
0
−0.5
−1
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
MC EVT RWT w/(K, π, π
) Trk Loss Prb. +20%
s
MC EVT RWT w/(K, π, π ) Trk Loss Prb. −20%
s
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
Tighten Box Cut
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5
1
0.5
0
−0.5
−1
−1.5
Tighten Z
vertex
Cut
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 Numbers Obtained via Fit
1
0.5
0
−0.5
−1
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 Doubling Beauty Contribution
1
0.5
0
−0.5
−1
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
c c
Frac. Diff. on F
2
1.5 No Smearing of the Electron Energy
1
0.5
0
−0.5
−1
−1.5
−2
0.01 0.015 0.02 0.025 0.03 0.035
x
Figure D.35: Q 2 = 510 GeV 2 systematics.
244

D.2.3 F cc
2 Theoretical Systematics
Theoretical systematics in regions of Q 2 indicated.
0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.36: F cc
2 Theoretical Uncertainties Q 2 = 5.5 GeV 2
245

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.37: F cc
2 Theoretical Uncertainties Q 2 = 6.8 GeV 2
246

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.38: F cc
2 Theoretical Uncertainties Q 2 = 11 GeV 2
247

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.39: F cc
2 Theoretical Uncertainties Q 2 = 19 GeV 2
248

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.40: F cc
2 Theoretical Uncertainties Q 2 = 31 GeV 2
249

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.41: F cc
2 Theoretical Uncertainties Q 2 = 61 GeV 2
250

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.42: F cc
2 Theoretical Uncertainties Q 2 = 133 GeV 2
251

0.3
0.2
Decreased m c
0.3
0.2
Increased m c
0.3
0.2
Decreased Peterson ∈
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Increased Peterson ∈
0.3
0.2
µ = 2m c
R,F
0.3
0.2
Doubled µ
R,F
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.3
0.2
Halved µ
R,F
0.3
0.2
2 2
µ = MAX( Q /4 + mc , 2m )
R,F
c
0.1
0.1
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure D.43: F cc
2 Theoretical Uncertainties Q 2 = 510 GeV 2
252

Index
δ h , 106
γ h , 107
absorption length, 53
anti-screening, 19
antiparticle, 15
asymptotic freedom, 18
baryon, 17
BCAL
barrel calorimeter, 56
BGF, 31
Bjorken variable, 26
branching ratio, 138
Bremsstrahlung radiation, 54
CAL
Calorimeter, 53
cell, 56
electron energy resolution, 56
hadron energy resolution, 56
tower, 56
Callan-Gross relation, 27
CCDIS
charge current deep inelastic scattering,
25
Chi Squared, 78
colliding beam experiment, 14
colour, 17
cone island, 104
confinement, 18
covariance, 77
covariance matrix, 77
cross section generators, 41
cross section integrators, 41
CTD, 117
cell, 63
Central Tracking Detector, 61
axial, 64
module, 56
stereo, 64
superlayer, 64
253

cut, 112
de Broglie relation, 14
Democritus, 13
DESY
Deutsches Elektronen-Synchrotron, 14
DESY II, 48
DESY III, 48
DGLAP, 40
Dokshitzer-Gribov-Lipatov-Altarelli-
Parisi, 33
diode, 67
DIS, 25, 112
Deep Inelastic Scattering, 23
DST, 126
data storage tape, 117
DST10, 120
DST11, 120
DST9, 120
selection, 120
EFO, 187
energy flow object, 107
electron finders, 105
Ernest Rutherford, 13
event, 14
event builder, 116
factorization, 31
factorization scale, 31
FCAL
forward calorimeter, 56
fermions, 15
FFN
fixed flavour number, 35
filter, 112
fit sums, 79
fixed target experiment, 14
FLT, 115
FLT30, 118
FLT34, 118
FLT36, 118
FLT44, 118
FLT46, 118
triggers used, 117
first level trigger, 112
fragmentation, 38
fragmentation functions, 38
FUNNEL, 43, 145
gauge bosons, 16
GEANT, 43
254

generalized radius, 188
GFLT
global first level trigger, 112
gluon, 18
Gold Foil Experiment, 13
GSLT
global second level trigger, 112
GTT
global tracking trigger, 117
H1, 14
hadron, 17
hadronization, 38
Hamburg Germany, 47
hard process, 25
HEP
high energy physics, 53
HER, 50
high energy runs, 47
HERA
Hadron Elektron Ring Anlage, 14, 47
HERA II, 47
beam parameters, 49
HVQDIS, 161
Index, 246
inelasticity, 26
invariant mass, 123
IP
interaction point, 52
jet, 185
clustering algorithm, 187
cone algorithm, 187
John Dalton, 13
Joseph John Thomson, 13
Kalman filter, 83
least-squares fitting, 79
LER
low energy runs, 47
Leucippus, 13
LINAC, 48
LINAC II, 48
Lorentz Force, 62
Lund String Fragmentation, 39
meson, 17
minimal subtraction, 21
momentum subtraction, 21
Monte Carlo, 38, 41
MVD, 117
255

Micro Vertex Detector, 67
cylinders, 69
ladder, 71
sector, 71
sensor, 69
wheels, 69
natural units, 14
NCDIS
neutral current deep inelastic scattering,
24
neural network, 105
neutral current, 24
pair production, 54
parton density function, 26
parton shower, 43
partons, 14
Pauli exclusion principle, 17
Peterson Fragmentation, 40, 45
PETRA, 48
PGF
photon-gluon fusion, 32
photoelectric effect, 55
PMT
photomultiplier tube, 55
pn junction, 67
polystyrene, 56
pQCD
perturbative Quantum Chromodynamics,
20
pseudoparticle, 188
pseudorapidity, 52
Q value, 123
QCD
Quantum Chromodynamics, 17
QCD Compton Scattering, 31
QED
Quantum Electrodynamics, 17
QPM
quark parton model, 26
quarks, 14
radiation length, 53, 56
radiation lengths, 87
RAPGAP, 87, 136, 186
RCAL, 60
rear calorimeter, 56
regular tracking, 82
renormalization scale, 21
residual, 87
256

esolution, 87
right charge combination
RC, 126
scaling, 26, 27
scaling violation, 30
scintillators, 55
sea, 23, 29
silicon detector, 67
SLT, 115
second level trigger, 112
soft process, 25
solenoid, 62
spherical polar, 52
splitting functions, 33
SRTD
Small angle Rear Tracking Detector,
60
Standard Model, 15
structure function, 1, 27
STT, 117
Straw Tube Tracker, 72
sector, 73
wedge, 73
superlayer, 62
tagging, 45
TLT, 116
DIS03, 119
SPP02, 119
SPP09, 119
third level trigger, 113
tower, 56
tracks, 76
trigger, 112, 126
logic, 117
TRVFN
Thorne Roberts variable flavour number,
36
valence, 23, 29
VCTRHL, 77
VXD, 82
words, 116
wrong charge combination
WC, 126
wrong charge subtraction, 88, 126
ZEUS, 14
co-ordinates, 52
Detector, 50
257

ZMVFN
zero mass variable flavour number,
35
ZTT, 83, 167
258

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