Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS docx

Measurements of Event Shapes in Deep Inelastic
Scattering at HERA with ZEUS
by
Adam A. Everett
A dissertation submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
(Physics)
at the
University of Wisconsin – Madison
2006
c
 Copyright by Adam A. Everett 2006
All Rights Reserved
Measurements of Event Shapes in Deep
Inelastic Scattering at HERA with ZEUS
Adam A. Everett
Under the supervision of Professor Wesley H. Smith
At the University of Wisconsin — Madison
Mean values and differential distributions of event-shape variables have been
studied in neutral current deep inelastic scattering using an integrated luminosity
of 82.2 inverse pico-barns collected with the ZEUS detector at HERA. The kinematic
range was Q-squared from 80 to 20480 GeV-squared and Bjorken-x from 0.0024 to 0.6,
where Q-squared is the virtuality of the exchanged boson. The Q-dependence is com-
pared with a model based a combination of next-to-leading-order QCD calculations
with next-to-lead-logarithm corrections and the Dokshitzer-Webber non-perturbative
power corrections.
4
i
Abstract
Mean values and differential distributions of event-shape variables have been

studied in neutral current deep inelastic scattering using an integrated luminosity of
82.2 pb
−1
collected with the ZEUS detector at HERA. The kinematic range was 80 <
Q
2
< 20480 GeV
2
and 0.0024 < x < 0.6, where Q
2
is the virtuality of the exchanged
boson and x is the Bjørken variable. The Q-dependence is compared with a model
based a combination of next-to-leading-order QCD calculations with next-to-lead-
logarithm corrections and the Dokshitzer-Webber non-perturbative power corrections.
ii
Acknowledgements I would like to thank the High Energy Physics de-
partment at the University of Wisconsin for the opportunity to perform research with
an outstanding group of physicists at an outstanding university. I would especially like
to acknowledge and thank Wesley Smith and Don Reeder for their guidance, support,
and superb dedication.
I would also like to thank the members of the ZEUS Collaboration who made data
taking possible, and who gave me great advice on all of the details of an analysis.
A very special thanks are due to my colleagues from the University of Glasgow, Ian
Skillicorn and Steven Hanlon, who very patiently taught me the ropes of an event
shape analysis, and shared so much of their knowledge and experience with me. And,
of course, I thank Alexandre Savin and Dorian K¸cira for being my ”advisors away
from home.”
Thank you to the friends who were always willing to play cards, watch movies, and
play when we were in danger of doing too much work.
I give special thanks to my parents and family for their support and teasing. And I

offer a huge thank you to my wife, Jayda, for putting up with me and following me
around the globe. I will never be able to thank you enough for all you have done for
me during this adventure.
iii
Contents
Abstract i
Acknowledgements ii
1 Introduction 1
1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.4 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Perturbative Quantum Chromodynamics . . . . . . . . . . . . . 12
2 Event Shapes in Deep Inelastic Scattering 15
2.1 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.1 Kinematic description . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 DIS Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.3 QCD Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
iv
2.2 Introduction to Event Shapes in Deep Inelastic Scattering . . . . . . . 26
2.2.1 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 Power Corrections . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.3 Mean Non-Perturbative Calculations . . . . . . . . . . . . . . . 30
2.2.4 Differential Non-Perturbative Calculations . . . . . . . . . . . . 31
2.3 Definition of the Event Shapes . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 The Breit Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Experimental Setup 39
3.1 Detection of Particle Interactions . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.2 Basic Experimental Design . . . . . . . . . . . . . . . . . . . . . 44
3.2 Deutsches Elektronen Synchrotronen . . . . . . . . . . . . . . . . . . . 48
3.3 Hadron-Elektron Ring Anlage . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.1 HERA Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.2 HERA Experiment Halls . . . . . . . . . . . . . . . . . . . . . . 53
3.3.3 HERA Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4 The ZEUS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.1 The Tracking Detectors . . . . . . . . . . . . . . . . . . . . . . 59
3.4.2 The Uranium Calorimeter and Plastic Scintillator . . . . . . . . 63
3.4.3 Background Rejection . . . . . . . . . . . . . . . . . . . . . . . 67
3.5 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . 69
4 Event Simulation 73
4.1 Monte Carlo Event Generation . . . . . . . . . . . . . . . . . . . . . . 74
v
4.1.1 Monte Carlo Input: Parton Distribution Functions and Parton
Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.2 Hard Process and Higher Order Effects . . . . . . . . . . . . . . 76
4.1.3 Soft Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Monte Carlo Programs in HEP . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Hadronic Final States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 NLO Calculations 83
5.1 The Running Coupling Constant . . . . . . . . . . . . . . . . . . . . . 83
5.2 NLO Integration Techniques . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3 NLO Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 Differential Distributions . . . . . . . . . . . . . . . . . . . . . . 87
5.4 DISENT, DISASTER, DISPATCH, and DISRESUM Programs . . . . . 88
5.4.1 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.4.2 Differential Distributions . . . . . . . . . . . . . . . . . . . . . . 89
6 Event Reconstruction 95
6.1 Particle Track and Vertex Reconstruction . . . . . . . . . . . . . . . . . 95
6.2 Calorimeter Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.1 Calorimeter Cell Removal . . . . . . . . . . . . . . . . . . . . . 98
6.2.2 Calorimeter Energy Corrections . . . . . . . . . . . . . . . . . . 98
6.3 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.4 Hadronic System Reconstruction . . . . . . . . . . . . . . . . . . . . . 102
vi
6.5 Event Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.5.1 The Electron Method . . . . . . . . . . . . . . . . . . . . . . . . 105
6.5.2 The Jacquet-Blondel Method . . . . . . . . . . . . . . . . . . . 107
6.5.3 The Double-Angle Method . . . . . . . . . . . . . . . . . . . . . 107
6.6 Calorimeter Cells and Energy Flow Objects (EFOs) . . . . . . . . . . . 108
6.7 Boosting to the Breit Frame . . . . . . . . . . . . . . . . . . . . . . . . 110
6.8 Reconstruction Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7 Event Selection 113
7.1 Online Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.1 First Level Trigger (FLT) . . . . . . . . . . . . . . . . . . . . . 115
7.1.2 Second Level Trigger (SLT) . . . . . . . . . . . . . . . . . . . . 116
7.1.3 Third Level Trigger (TLT) . . . . . . . . . . . . . . . . . . . . . 116
7.2 Offline Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.1 Trigger Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.2 Electron Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.2.3 Background Rejection . . . . . . . . . . . . . . . . . . . . . . . 119
7.2.4 Kinematic Selection and Phase Space Definition . . . . . . . . . 120
7.2.5 Particle Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8 Analysis Method 125
8.1 Monte Carlo Description of the Data . . . . . . . . . . . . . . . . . . . 126
8.2 Data Corrected to the Hadron Level . . . . . . . . . . . . . . . . . . . 133

8.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 137
vii
9 Fit Method 191
9.1 Fits to the Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
9.1.1 Fit Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
9.1.2 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . 193
9.2 Fits to the Differential Distributions . . . . . . . . . . . . . . . . . . . 195
9.2.1 Fit Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
9.2.2 Fit Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.3.1 Mean values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.3.2 Differential distributions . . . . . . . . . . . . . . . . . . . . . . 205
9.3.3 Y
2
and K
OUT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
10 Conclusions 223
10.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
10.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
A Treatment of Statistical Uncertainties 227
A.1 Differential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 227
A.2 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
B Data Tables 233
viii
ix
List of Tables
3.1 The integrated luminosity delivered by HERA I and HERA II and gated
by ZEUS for each year of running. . . . . . . . . . . . . . . . . . . . . . 55
3.2 Active and inactive dimensions of the CTD . . . . . . . . . . . . . . . . 60

3.3 Radiation length and interaction length of some common materials . . 65
8.1 List of systematic checks performed . . . . . . . . . . . . . . . . . . . . 141
8.2 Efficiencies, purities, and correction factors for mean event shapes. . . . 150
9.1 Kinematic bins used in this analysis. . . . . . . . . . . . . . . . . . . . 209
9.2 Fit ranges used for fits to differential data . . . . . . . . . . . . . . . . 209
9.3 Results from the Hessian fit to means for α
s
(M
Z
) . . . . . . . . . . . . 210
9.4 Results from Hessian fit to means for α
0
. . . . . . . . . . . . . . . . . 210
9.5 Effect of matching methods on extraction of α
s
(M
Z
) from differential
distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
9.6 Effect of matching methods on extraction of α
0
from differential distri-
butions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
9.7 Results from the Hessian fit to distributions for α
s
(M
Z
) . . . . . . . . . 212
9.8 Results from the Hessian fit to distributions for α
0

. . . . . . . . . . . . 221
x
B.1 Mean data and uncertainties for Q, x, T
T
, B
T
, and C. . . . . . . . . . . 234
B.2 Mean data and uncertainties for T
γ
, B
T γ
, M
2
, y
2
and K
OU T /Q
. . . . . . 235
B.3 Differential tables for C . . . . . . . . . . . . . . . . . . . . . . . . . . 236
B.4 Data tables for M
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
B.5 Data tables for T
T
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
B.6 Data tables for B
T
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
B.7 Data tables for T
γ

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
B.8 Data tables for B
γ
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
B.9 Data tables for K
OU T
/Q . . . . . . . . . . . . . . . . . . . . . . . . . . 242
B.10 Data tables for K
OU T
/Q . . . . . . . . . . . . . . . . . . . . . . . . . . 243
B.11 Data tables for y
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
B.12 Data tables for y
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
xi
List of Figures
1.1 Different concepts of the atom . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 The generations of matter . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Forces and Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Generations of matter and forces . . . . . . . . . . . . . . . . . . . . . 7
1.5 Diagrams of generic LO, NLO, and NNLO processes in which one initial
particle undergoes one split. . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 Generic DIS diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Picture of a DIS event . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Probe resolution as a function of Q
2
. . . . . . . . . . . . . . . . . . . . 19
2.4 Probe resolution of the proton . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Illustration of a simple scattering cross section . . . . . . . . . . . . . . 22
2.6 Diagrams of higher order DIS interactions. . . . . . . . . . . . . . . . . 24
2.7 Evolution from a hard process to final state hadrons . . . . . . . . . . . 27
2.8 Diagram of the Breit Frame . . . . . . . . . . . . . . . . . . . . . . . . 35
2.9 Current hemisphere in the Breit frame compared to e
+
e
i
annihilation . 36
xii
3.1 A cross sectional view of a generic detector and the passage of various
particles through this detector. . . . . . . . . . . . . . . . . . . . . . . 44
3.2 An aerial view of HERA and PETRA. . . . . . . . . . . . . . . . . . . 49
3.3 HERA injection system. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 HERA tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 The integrated luminosity delivered by HERA I and HERA II for each
year of running. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6 A 3D cutout of the ZEUS detector. . . . . . . . . . . . . . . . . . . . . 57
3.7 A 2D x-y cross sectional view of the ZEUS detector. . . . . . . . . . . . 58
3.8 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.9 An x-y view of the CTD. . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.10 An x-y view of the UCAL. . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.11 Diagram of a BCAL tower. . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.12 The timing of various events in the ZEUS detector. . . . . . . . . . . . 69
3.13 The ZEUS trigger and DAQ systems. . . . . . . . . . . . . . . . . . . . 72
4.1 Event generating dice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Event generator stages . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3 Diagrams of simple QED radiation . . . . . . . . . . . . . . . . . . . . 77
4.4 Diagrams of models used in event simulation. . . . . . . . . . . . . . . 79
5.1 Fit parameters for mean NLO event shapes . . . . . . . . . . . . . . . . 90

5.2 Fit parameters for mean NLO event shapes . . . . . . . . . . . . . . . . 91
6.1 Helix fit for the CTD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
xiii
6.2 Clustering cells into islands . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 ZEUS kinematic plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4 Matching tracks to islands: EFOs . . . . . . . . . . . . . . . . . . . . . 109
7.1 Event chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.2 Kinematic bins used in this analysis . . . . . . . . . . . . . . . . . . . . 124
8.1 Ariadne description of z
vtx
and E − p
z
. . . . . . . . . . . . . . . . . 128
8.2 Ariadne description of electron scattering angle. . . . . . . . . . . . . 129
8.3 Ariadne description of E

e
and E

t
. . . . . . . . . . . . . . . . . . . . 130
8.4 Ariadne description of x
DA
and Q
2
DA
. . . . . . . . . . . . . . . . . . . 131
8.5 Ariadne description of y
EL
and y

JB
. . . . . . . . . . . . . . . . . . . . 132
8.6 Mean reconstructed MC event shapes compared to data . . . . . . . . . 140
8.7 Measured distributions of T
T
compared to reconstructed MC . . . . . . 142
8.8 Measured distributions of B
T
compared to reconstructed MC . . . . . . 143
8.9 Measured distributions of M
2
compared to reconstructed MC . . . . . 144
8.10 Measured distributions of C compared to reconstructed MC . . . . . . 145
8.11 Measured distributions of T
γ
compared to reconstructed MC . . . . . . 146
8.12 Measured distributions of B
γ
compared to reconstructed MC . . . . . . 147
8.13 Measured distributions of y
2
compared to reconstructed MC . . . . . . 148
8.14 Measured distributions of K
out
/Q compared to reconstructed MC . . . 149
8.15 Efficiencies according to Ariadne for T
T
. . . . . . . . . . . . . . . . . 151
8.16 Efficiencies according to Ariadne for B
T

. . . . . . . . . . . . . . . . . 152
8.17 Efficiencies according to Ariadne for M
2
. . . . . . . . . . . . . . . . 153
8.18 Efficiencies according to Ariadne for C. . . . . . . . . . . . . . . . . 154
xiv
8.19 Efficiencies according to Ariadne for T
γ
. . . . . . . . . . . . . . . . . 155
8.20 Efficiencies according to Ariadne for B
γ
. . . . . . . . . . . . . . . . . 156
8.21 Efficiencies according to Ariadne for y
2
. . . . . . . . . . . . . . . . . 157
8.22 Efficiencies according to Ariadne for K
out
/Q. . . . . . . . . . . . . . 158
8.23 Purities according to Ariadne for T
T
. . . . . . . . . . . . . . . . . . . 159
8.24 Purities according to Ariadne for B
T
. . . . . . . . . . . . . . . . . . . 160
8.25 Purities according to Ariadne for M
2
. . . . . . . . . . . . . . . . . . . 161
8.26 Purities according to Ariadne for C. . . . . . . . . . . . . . . . . . . . 162
8.27 Purities according to Ariadne for T
γ

. . . . . . . . . . . . . . . . . . . 163
8.28 Purities according to Ariadne for B
γ
. . . . . . . . . . . . . . . . . . . 164
8.29 Purities according to Ariadne for y
2,kt
. . . . . . . . . . . . . . . . . . 165
8.30 Purities according to Ariadne for K
out
/Q. . . . . . . . . . . . . . . . . 166
8.31 Correction Factors according to Ariadne for T
T
. . . . . . . . . . . . . 167
8.32 Correction Factors according to Ariadne for B
T
. . . . . . . . . . . . . 168
8.33 Correction Factors according to Ariadne for M
2
. . . . . . . . . . . . . 169
8.34 Correction Factors according to Ariadne for C. . . . . . . . . . . . . . 170
8.35 Correction Factors according to Ariadne for T
γ
. . . . . . . . . . . . . 171
8.36 Correction Factors according to Ariadne for B
γ
. . . . . . . . . . . . . 172
8.37 Corrected data compared with hadron level MC for mean event shapes. 173
8.38 Corrected data compared to hadron level MC for T
T
. . . . . . . . . . . 174

8.39 Corrected data compared to hadron level MC for B
T
. . . . . . . . . . . 175
8.40 Corrected data compared to hadron level MC for M
2
. . . . . . . . . . . 176
8.41 Corrected data compared to hadron level MC for C. . . . . . . . . . . . 177
xv
8.42 Corrected data compared to hadron level MC for T
γ
. . . . . . . . . . . 178
8.43 Corrected data compared to hadron level MC for B
γ
. . . . . . . . . . . 179
8.44 Corrected data compared to hadron level MC for y
2,kt
. . . . . . . . . . 180
8.45 Corrected data compared to hadron level MC for K
out
/Q. . . . . . . . . 181
8.46 Fractional systematic error for mean T
T
. . . . . . . . . . . . . . . . . . 182
8.47 Fractional systematic error for mean B
T
. . . . . . . . . . . . . . . . . 183
8.48 Fractional systematic error for mean M
2
. . . . . . . . . . . . . . . . . 184
8.49 Fractional systematic error for mean C . . . . . . . . . . . . . . . . . . 185

8.50 Fractional systematic error for mean T
γ
. . . . . . . . . . . . . . . . . . 186
8.51 Fractional systematic error for mean B
γ
. . . . . . . . . . . . . . . . . 187
8.52 Fractional systematic error for mean y
2
. . . . . . . . . . . . . . . . . . 188
8.53 Fractional systematic error for mean K
OU T
/Q . . . . . . . . . . . . . . 189
9.1 Ratio of (NLO+NLL+PC) to (NLO+NLL) . . . . . . . . . . . . . . . . 199
9.2 Mean corrected data compared to MC . . . . . . . . . . . . . . . . . . 200
9.3 Mean corrected data fit to NLO + PC . . . . . . . . . . . . . . . . . . 201
9.4 Extraction of (α
s
, α
0
) from event shape means . . . . . . . . . . . . . . 202
9.5 Effects of high Bjørken x kinematic bins and statistical uncertainties
only in extracting (α
s
(M
Z
), α
0
) values from event shape means. . . . . 203
9.6 Differential data compared to Ariadne for M
2

, C, T
T
. . . . . . . . . 213
9.7 Differential data compared to Ariadne for T
γ
and B
γ
. . . . . . . . . 214
9.8 Differential data fit to NLO+NLL+PC for M
2
, C, and T
T
. . . . . . . 215
9.9 Differential data fit to NLO+NLL+PC for T
γ
and B
γ
. . . . . . . . . . 216
xvi
9.10 Extraction of α
s
and α
0
, from distributions, using different matching
schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
9.11 Study of differential extraction dependence on Q
2
. . . . . . . . . . . . 218
9.12 Measurements of y
2

compared to NLO and MC . . . . . . . . . . . . . 219
9.13 Measurements of K
OU T
/Q compared to MC . . . . . . . . . . . . . . . 220
10.1 Future of Event Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
1
Chapter 1
Introduction
1
Science is the observation, identification, description, and explanation of phenomena.
In short, science is mankind’s methodical attempt to understand the physical universe.
Physics is the branch of science that studies matter, energy, and their interactions;
and particle physics is the branch of physics which investigates the basic elements of
matter as well as the fundamental laws that control them. From the early philosophers
such as Democritus and Aristotle to the more modern scientists such as Galileo and
Newton, the study of the universe has progressed from a philosophical basis to a base
of empirical observations merged with mathematical descriptions. As understanding
of the macroscopic universe increased, scientists attempted to organize the universe
into fundamental constituents: atomic elements. Mendeleev’s organization in 1869
of all known elements according to their atomic mass lead to the realization that the
elements could be grouped according to similar chemical properties: the Periodic Table
of Elements. The large number of elements and the periodic structure of properties
suggested a more fundamental substructure within the atom.
The first advance in the study of the structure of the atom came with the 1898
1
Reference [1] was useful in compiling this chapter.
2
discovery by Joseph Thompson of the electron. About a decade later, Ernest Ruther-
ford demonstrated that atoms have a small, dense, positively charged nucleus. Ernest
Rutherford found the first evidence of the proton in 1919, and James Chadwick dis-

covered the neutron in 1931. The discoveries of the electron and proton helped to lead
to Max Born’s declaration that “Physics as we know it will be over in six months.”
Figure 1.1: Conceptual views reflecting our understanding of the atom at different times in
history. Atoms were once thought to be the smallest constituent of matter, but the ability to
probe the atom at higher energies has led to a deeper understanding of its internal structure.
Image courtesy of [2].
Physics, however, was not over in six months. There were still a few questions
remaining such as: what holds the protons and neutrons together? Similar to scatter-
ing experiments used to probe the structure within the atom, accelerator experiments
probed the nucleus and the interactions between the neutrons and the protons. The
result of these studies the 1950s showed a “particle explosion” in which physicists dis-
covered many new particles similar to protons and neutrons: baryons, and a new class
of particles: mesons. Then in 1964, Murray Gell-Mann and George Zweig proposed
3
to explain the structure of the hundred or so baryons and mesons with just a few
more-fundamental particles: quarks.
1.1 Standard Model
The quark theory of Gell-Mann and Zweig has evolved into the Standard Model
of Fundamental Particles and Interactions. Despite a few shortcomings, the Standard
Model is now the most consistent theory that explains particles and their complex
interactions, or forces. In the Standard Model there are three types of elementary
particles: leptons, quarks, and the force mediators, which are bosons.
1.1.1 Leptons
Leptons are a class of spin-
1
2
point particles which do not form composite objects.
Three of the leptons have an electrical charge of −1, and their only observable differ-
ence is their mass quantum number. These leptons are the electron, muon, and tau.
These three leptons each have a corresponding neutrino (also a lepton) which have

no charge and very little mass. These six leptons are divided into three generations
of leptons: the lepton and its corresponding neutrino. Each of these six leptons also
have a corresponding antimatter antilepton, so that there are a total of 12 leptons.
1.1.2 Quarks
Quarks are a class of spin-
1
2
particles which form composite objects, but are
never observed independently. Whereas, leptons have integer electrical charge, quarks
have fractional electrical charge of 2/3 or −1/3. Each quark has a quantum number
known as flavor which identifies the quark according to its electroweak transformation
4
properties. So like leptons, quarks are organized into three generations of two quark
flavors with each generation having progressively higher mass. Also like leptons, each
of the quarks have a corresponding antiquark.
Figure 1.2: The quarks and leptons organized into their families (generations) in order of
increasing mass. Image courtesy of [2].
Quarks carry an additional charge called color. The color charges are red, blue,
and green. The corresponding anti-colors are anti-red, anti-blue, and anti-green. With
each quark and antiquark that can come in three colors, there are a total of 36 quarks.
Quarks combine to form composite particles called hadrons which have an integer
net electrical charge and have no net color. Hadrons are divided into two classes:
baryons made of three quarks, and mesons made of one quark and one antiquark, and
their anitparticles.
5
1.1.3 Bosons
The above mentioned basic particles can interact with each other. These in-
teractions include attraction, repulsion, annihilation, and decay; and the force and
quantum number exchange are carried by the spin-1 force carrier particles, bosons. A
particular boson can only be produced or absorbed by a particle which is affected by

that particular force. For example, only particles that carry electric charge (such as
the electron or proton) can produce or absorb the electromagnetic force carrier par-
ticle, whereas particles that carry no electrical charge (neutrinos) cannot produce or
absorb the electromagnetic force carrier.
Electromagnetic Interaction The electromagnetic force carrier is the photon,
which is massless and carries no electric charge.
Weak Interaction Another type of interaction is the weak interaction. The weak
interaction mediator is the W
±
or the Z
0
. The Standard Model unifies the weak and
the electromagnetic interactions into the electroweak interaction.
Strong Interaction The interaction which binds quarks together to form hadrons
is the strong force which is mediated by the gluon. The gluon mediates forces between
the color charged quarks. Gluons, however, also have color charge so that gluons
can interact with gluons. When two quarks are close to one another, they exchange
gluons such that quarks continually change their color charge. Because gluon exchange
changes color and since color is conserved, the gluons carry a color and anti-color
charge. The three colors and three anti-colors mean that there are eight combinations