Measurement of the Top Quark Mass, Cross Section and Anomalous ...

Measurement of the Top Quark Mass, Cross Section and
Anomalous Couplings at the International Linear
Collider
Erik Devetak
Brasenose College, Oxford
Thesis submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy at the University of Oxford
Trinity Term, 2009

Abstract
A feasibility study to measure the proprieties of the top quark at the International Linear
Collider is presented. The study is performed in the fully hadronic channel e + e − → t¯t →
b¯bq¯qq¯q and employs the Silicon Detector (SiD) concept to establish the precision achievable
when measuring the cross section (∼ 1.3 fb), the top mass (∼ 49 MeV) and the forward
backward asymmetry of the top quark (∼ 0.008) as well as of the b quark originating from
the top decay (∼ 0.008).
The software developed for the tagging of heavy flavour jets and for reconstructing the
charge of the quark from which they originate is also described. The jet tagging software has
been developed within the International Linear Detector framework; but tested also within
SiD. The performance has been benchmarked using dijet samples at 91.2 GeV centre of mass
energy. The achievable purity of b quark identification is of the order of 90% when a 70%
efficiency is required. In the case of charge reconstruction a purity of up to 80% is achievable
with an efficiency lower than 60% when the charges of well identified b quarks are being
reconstructed. The charge reconstruction has been tested on a b¯bq¯qq¯q sample with 500 GeV
centre of mass energy. Both algorithms are a fundamental component of the presented top
study.
A hardware study analysing the capacitance of the CPC2 sensor, a proposed technology
for the SiD vertex detector, has also been performed. The analysis aims at minimizing the
clock current needed to operate the sensor. It has been found that the the major component
of the pixel capacitance comes from the inter-gate capacitance (2.7pF/cm of gate overlap).
A series of different possible designs of this region have been studied with the help of finite
element modelling and of test structures.
An experimental set up for the running and testing of the CPC2 sensor has been devised.
The noise of the sensor has been measured as 70 e − .

Dedicated to my family
i

“Poets say science takes away from the beauty of the stars - mere globs of gas atoms. I too
can see the stars on a desert night and feel them. But do I see less or more?”
- Richard P. Feynman
ii

Acknowledgements
My past four years spent as a D.Phil. student in Oxford have been altogether thoroughly
enjoyable and fulfilling. Although Oxford is a very pretty medieval town it has been the
presence of some wonderful people around me that have made my stay particularly pleasant.
Firstly I would like to thank my supervisor Andrei Nomerotski. His help and patience
over the past four years have been invaluable. Without his guidance the completion of this
thesis would have been a much harder task and a substantially less enjoyable endeavour.
I would like to extend my gratitude also to the rest of the LCFI collaboration and the
SiD benchmarking group, who were always ready to share their expertise and to help me
with my rather continuous questions and problems.
Thanks also to the fellow D.Phil. students who often lightened my days. A particular
mention is due to all those whose pursuit of idiosyncratic office activities made the daily
routine ever so pleasant. As it is often the case a lot of problems were solved outside the
office premises; thanks therefore to all the people who over lunch or in the pub have helped
me with ideas and comments.
During my D.Phil. I also had the opportunity to spend a few months at SLAC. A
wonderful experience that has been made even more enjoyable because of the warm welcome
I received from the whole SLAC SiD group. The welcome of the STFC student contingent
in Palo Alto has also been very much appreciated.
Without the generous founding provided by STFC, formerly PPARC, I would have never
been able to pursue my D.Phil. studies; I am indeed very grateful for the opportunity they
have given me.
I am also very grateful to all the Oxford support staff who often helped me with organisational
and administrative problems that seemed more insurmountable than others.
Last but not least I would like to thank my friends and family whose persistent support
has been a source of lasting and invaluable encouragement. It has been truly wonderful to
know that I can always rely on them.
iii

Preface
This thesis is the result of four years of the author’s work as a member of the LCFI and
SiD collaborations. As it is often the case in particle physics a lot of the work presented has
been performed in conjunction with other collaborators. It is therefore important to clearly
define the contribution of the author.
The presented thesis can be subdivided in four areas of approximately equal lengths:
• Chapters 1, 2 and 3 are the introductory chapters describing: the basis of the used
particle physics theory; the accelerator and the detector; the used simulation and
reconstruction software. The author’s contribution in these chapters is minimal with
the exception of chapter 3 where he has helped with the testing and running of the
software.
• Chapter 4 presents the hardware work performed by the author: section 1 describes the
characterization of the CPC2 capacitance, section 2 describes the capacitance analysis
on CPC2 test structures (work performed partially with the help of Oxford M.Phys.
student Philip Coulter), section 3 describes the set-up for the testing of the CPC2
sensor and the CPC2 sensor noise analysis (work performed with the help of Oxford
D.Phil. students Ben Jeffery and Yambazi Banda). The overwhelming majority of the
work described in this chapter has been performed by the thesis author.
• Chapter 5 presents the LCFI Vertex software. The software has been developed by the
author together with Ben Jeffery and Mark Grimes (Ph.D. Bristol). Small contributions
have been received also from some members of the LCFI collaboration. Section
1 describes the track selection procedures, section 2 describes the ZVTOP vertexing;
section 3 describes the flavour tagging discriminating variables, section 4 describes the
used neural network, sections 5 and 6 describe the performances in the ILD and SiD
concepts. The author has been responsible for sections 3 and 6. It has also had major
contributions in sections 1 and 5, with minor contributions towards sections 2 and 4.
• Chapters 6 and 7 present the performed physics analysis aimed to measure the proprieties
of the top quark at the ILC. Both chapters present exclusively the work of the
author, including section 1 of chapter 7 which is part of the LCFI Vertex software.
Finally throughout the thesis the help of Dr. Andrei Nomerotski has been heavily exploited.
iv

Contents
1 Physics of the Top Quark: Theoretical Introduction 1
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 The Top Quark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Effective Field Theories . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 The ILC and the SiD Detector Concept 14
2.1 The ILC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Silicon Detector Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Vertex Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Silicon Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Muon Identification System . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.5 Forward Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 The International Large Detector . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Simulation and Reconstruction 30
3.1 Monte Carlo Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 Particle Flow Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.3 Jet Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 The Software Framework . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 The Column Parallel CCD as an ILC Vertex Detector Technology 39
4.1 CPC2 Capacitance Characterization . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.1 Substrate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.2 Intergate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.3 Finite Element Model of CPC2 Capacitance . . . . . . . . . . . . . . 47
4.2 CPC2 Capacitance Test Structures . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 CPC2 Readout and Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
v

5 The LCFI Vertex Flavour Tagging Software 66
5.1 Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 The ZVRES Vertex Finding Algorithm . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 ZVRES Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3 Flavour Discriminating Variables . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3.1 Variables for Jets without Secondary Vertices . . . . . . . . . . . . . 77
5.3.2 Variables for Jets with Secondary Vertices . . . . . . . . . . . . . . . 83
5.4 Neural Network Combination . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 Performance of Flavour Tagging . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.6 Flavour Tagging in the SiD Detector Concept . . . . . . . . . . . . . . . . . 99
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 The Top Quark Mass and the t¯t Cross Section 101
6.1 Preliminary Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Kinematic Fitter and W Identification . . . . . . . . . . . . . . . . . . . . . 105
6.3 b Tagging Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.4 Top Quark Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4.1 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4.2 Template Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5 Cross Section of the b¯bq¯qq¯q Process . . . . . . . . . . . . . . . . . . . . . . . 121
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7 Quark Charge and Forward Backward Asymmetries 124
7.1 Vertex Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 Momentum Weighted Vertex and Jet Charge . . . . . . . . . . . . . . . . . . 126
7.3 Combined Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4 Bottom Quark Forward Backward Asymmetry . . . . . . . . . . . . . . . . . 133
7.5 Top Quark Forward Backward Asymmetry . . . . . . . . . . . . . . . . . . . 138
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8 Conclusion 142
A CPC2 Bias Voltages 144
B LCFI Vertex Flavour Tagging Software Parameters 145
Bibliography 146
vi

List of Figures
1.1 Standard Model Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Constraints to Higgs Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Feynman Diagrams of Signal and Background Events . . . . . . . . . . . . . 11
2.1 The International Linear Collider . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 The SiD Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 The SiD Subdetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 The Vertex Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 The Tracking Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Tracking Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7 PFA Visual Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8 Calorimeter Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.9 SiD Calorimeter Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.10 The Forward Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1 Tracking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Charged Coupled Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 CCD vs. CPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Graphical Representation of CCD Depletion Regions . . . . . . . . . . . . . 43
4.4 CPC2 Capacitance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 Substrate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 CPC2 One Pixel Geometry for Finite Element Analysis . . . . . . . . . . . . 47
4.7 Modelled Substrate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.8 Intergate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.9 Sketch of Realistic Intergate Region . . . . . . . . . . . . . . . . . . . . . . . 50
4.10 Intergate Capacitance FEEM Study . . . . . . . . . . . . . . . . . . . . . . . 51
4.11 Picture of a Test Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.12 Test Structures Schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.13 Test Structure Parasitic Capacitance . . . . . . . . . . . . . . . . . . . . . . 54
4.14 Test Structures Substrate Capacitance . . . . . . . . . . . . . . . . . . . . . 54
4.15 Test Structures Substrate Capacitance for Different Polysilicon Layers . . . . 55
4.16 Test Structures Intergate Capacitance . . . . . . . . . . . . . . . . . . . . . . 57
4.17 Noise Analysis Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . 58
4.18 Oscilloscope Picture of the CPC2 Readout . . . . . . . . . . . . . . . . . . . 59
4.19 ADC Readout User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.20 CPC2 Noise for Different Power Supplies . . . . . . . . . . . . . . . . . . . . 61
vii

4.21 Correlated Double Sampling User Interface . . . . . . . . . . . . . . . . . . . 63
4.22 CPC2 Noise with New Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 Schematic of Displaced Vertices in B Meson Decays . . . . . . . . . . . . . . 67
5.2 ZVRES Graphical Representation . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 ZVRES Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 ZVRES Vertexing Performance . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 Flavour Discriminating Variables - 1 Vertex Reconstructed . . . . . . . . . . 79
5.6 Joint Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.7 Impact Parameter Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.8 Track Attachment Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.9 Flavour Discriminating Variables - 2 Vertices Reconstructed . . . . . . . . . 88
5.10 Charm Tagging Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.11 Charm tag vs. Bottom tag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.12 Flavour Tagging Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.13 Flavour Tagging Leakage Rates . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.14 Flavour Tagging Performance with K s , Λ and Conversion Tagger . . . . . . . 96
5.15 Flavour Tagging Performance in SiD . . . . . . . . . . . . . . . . . . . . . . 100
6.1 Kinematic and Topological Event Selections . . . . . . . . . . . . . . . . . . 105
6.2 Kinematic Fit of the W bosons . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3 b Tagging in a Six Jet Environment . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 b − tag sum Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.5 b Tagging Single Jet Event Selection . . . . . . . . . . . . . . . . . . . . . . 110
6.6 Top Quark Kinematic Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.7 Top Quark Kinematic Fit Event Selection . . . . . . . . . . . . . . . . . . . 112
6.8 Top Quark Mass - Curve Fitting Technique . . . . . . . . . . . . . . . . . . . 114
6.9 Template Fitting Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.10 Template Fitting χ 2 Minimization . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1 LCFI Vertex Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.2 Momentum Weighted Vertex Charge . . . . . . . . . . . . . . . . . . . . . . 127
7.3 Momentum Weighted Jet Charge . . . . . . . . . . . . . . . . . . . . . . . . 128
7.4 Momentum Weighted Vertex and Jet Charge: B + /B − and ¯B 0 /B 0 . . . . . . 129
7.5 f¯b
i (x i )/fi b (x i ) for Momentum Weighted Vertex Charge and Jet Charge . . . . 131
7.6 Combined Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.7 Combined Charge b jet-1 × Combined Charge b jet-2 . . . . . . . . . . . . . 134
7.8 Events for the Calculation of the b Quark A fb . . . . . . . . . . . . . . . . . 135
7.9 Resolution of b Quark Angle θ . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.10 Events for the Calculation of the t Quark A fb . . . . . . . . . . . . . . . . . 139
7.11 Resolution of t Quark Angle θ . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.1 Schematic of the CPC2 Bias Voltages . . . . . . . . . . . . . . . . . . . . . . 144
viii

List of Tables
1.1 Bosons in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Fermions in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 ILC Beam Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 PFA Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1 Measured Intergate Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.1 Track Selection Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 ZVRES Track Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3 Joint Probability Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4 Importance of Discriminating Variables Z Mass Resonance - 1 Vertex Found 97
5.5 Importance of Discriminating Variables Z Mass Resonance - 2 Vertices Found 97
5.6 Importance of Discriminating Variables Z Mass Resonance - 3+ Vertices Found 97
5.7 Importance of Discriminating Variables 500GeV - 1 Vertex Found . . . . . . 98
5.8 Importance of Discriminating Variables 500GeV - 2 Vertices Found . . . . . 98
5.9 Importance of Discriminating Variables 500GeV - 3+ Vertices Found . . . . 98
6.1 Kinematic and Topological Event Selections . . . . . . . . . . . . . . . . . . 104
6.2 Top Kinematic Fitting Constraints . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Top Quark Mass - Curve Fitting Technique . . . . . . . . . . . . . . . . . . . 115
6.4 Template Fitting Results - Renormalized Cross Section . . . . . . . . . . . . 119
6.5 Template Fitting Results - MC Cross Section . . . . . . . . . . . . . . . . . 120
6.6 b¯bq¯qq¯q Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.1 LCFI Vertex Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2 Reconstructed A fb for the b Quark . . . . . . . . . . . . . . . . . . . . . . . 136
7.3 Anomalous W tb Coupling Theoretical Predictions for b Quark A fb . . . . . . 137
7.4 Reconstructed A fb for the t Quark . . . . . . . . . . . . . . . . . . . . . . . 140
B.1 LCFI Vertex Default Parameters . . . . . . . . . . . . . . . . . . . . . . . . 145
ix

Chapter 1
Physics of the Top Quark: Theoretical
Introduction
Ideally the complex objects and phenomena that we observe every day can all be described
with just a handful of basic constituents and a matching set of laws describing their interactions.
Hence the inherit aim of particle physics is to comprehensively and self-consistently describe
the most fundamental constituents of matter in the simplest form possible. Throughout
the past century a new level of precision in measurements and new analytical techniques
allowed human kind to explore deeper into matter. Scientists therefore observed what are
now believed to be the discrete units of matter and tried to describe their interactions. First
came the theory of Quantum Electro Dynamics (QED), which is essentially the quantised
version of electromagnetic interactions. Far from being complete the theory left a lot unexplained,
not least the β decay of nuclei. It was to explain such phenomena that the weak
force was postulated and subsequently encompassed in the Electro-Weak theory. This successfully
incorporated QED and also provided a description for the weak force by introducing
the exchange of massive force carrying particles. Still a complete picture could not be built.
The theory does not predict a stable atomic nucleus; furthermore, it has been discovered,
that both the proton and the neutron exhibit a substructure. It is only with the introduction
of the strong force and therefore the field theory of Quantum Chromo Dynamics (QCD),
1

1.1 The Standard Model 2
that it is possible to understand this substructure and at the same time predict a stable
behaviour of the nucleus.
1.1 The Standard Model
The Standard Model (SM) is currently the most widely accepted approximation to a comprehensive
and self-consistent theory of the fundamental constituents of matter and their
interactions. It consists of three Quantum Field Theories: Quantum Electro Dynamics,
Electro-Weak theory and Quantum Chromo Dynamics theories. It is the aim of this section
to give a synthetic, experimentally backed overview of the principles of the SM.
In any quantum field theory a complex n-dimensional wave function ψ(x) represents one
or more particles, where |ψ(x)| 2 is the probability of finding the system in the physical state
x. The amplitude of the function is hence a measurable quantity, while the phase is not. The
phase of the system cannot be restricted from physical observations and hence an arbitrary
phase can be assigned. Clearly the theory should not be dependent on this arbitrary decision
and therefore it should be invariant under local gauge transformations:
ψ(x) → e iθ(x) ψ(x). (1.1)
The gauge requirement has a few far reaching consequences. It can be immediately seen
that the classical derivative ∂ µ is not gauge invariant. The covariant derivative must hence
be used, leading to the automatic introduction of the force carrying particle as a gauge
field of the covariant derivative. In the QED formalism this is easily shown. The covariant
derivative is:
D µ = ∂ µ + ieA µ (1.2)
where e is the electric charge of the considered particle. Additionally the gauge field A µ is
required to transform as:
A µ → A µ + ∂ µ θ(x). (1.3)

1.1 The Standard Model 3
Taking then, as an example, the simple Lagrangian of the particle in a electromagnetic field:
L = i ¯ψγ µ ∂ µ ψ − e ¯ψγ µ A µ ψ − m ¯ψψ − 1 4 F µνF µν (1.4)
where γ µ are the Dirac gamma matrices and m is the mass of the particle. The field F µν is
then defined as:
F µν = ∂ µ A ν − ∂ ν A µ . (1.5)
By then using the Euler-Lagrange equation on the initial particle field ψ and on the gauge
field A µ one derives:
iγ µ ∂ µ ψ − mψ = eγ µ A µ ψ (1.6)
∂ ν F µν = e ¯ψγ µ ψ (1.7)
Noticeably the left hand side (LHS) of (1.6) is the well known Dirac equation. Differently
the right hand side (RHS) of the equation, which derives directly from the covariant derivative,
and hence from the gauge invariance postulate, represents the particle’s interaction with
the electromagnetic field. The field A µ can now be interpreted as a force mediating particle.
In fact its behaviour is not at all dissimilar from the original field ψ(x). The behaviour of
the electromagnetic field tensor can be instead seen in (1.7).
This is however not the only important result that can be derived from the axiom of gauge
invariance. Noether’s theorem in fact postulates that for every differentiable symmetry there
must be a corresponding conservation law. In the present case it can be shown that gauge
invariance directly implies the conservation of charged currents. Charge itself must therefore
be conserved. It is hence clear that the importance of gauge invariance in particle physics
cannot be underestimated[1, 2].
The figure illustrated here deals only with the QED theory, which is mathematically a
Unitary Group of order one (U(1) EM ). It therefore has only one generator and hence only
one charge and one force carrying vector boson. Not at all dissimilar are the considerations
for the weak and strong force which can be mathematically represented by the non-abelian

1.1 The Standard Model 4
SU(2) and SU(3) groups. Given that SU(3) has 8 generators it also has the corresponding
eight gluons and three conserved “colour charges“. Intuitively the same will apply for the
weak SU(2) theory. The Electro-Weak description is however slightly more complex. In
SU(2) L ×U(1) Y two charged bosonic particles derive from the original weak fields as naively
expected and therefore are responsible for the W + and W − particles. Differently the neutral
fields derive from the mixing of the U(1) Y field and the neutral SU(2) L field. The strength
of the mixing is encoded in terms of the weak mixing angle (θ w )[3, 4, 5]. After the mixing the
theory describes both the Electro-Magnetic field and the neutral weak field and is therefore
responsible for the γ and Z 0 particles.
In order to present a more detailed picture of Electro-Weak theory the field must be
broken into its right and left handed components.
ψ R = 1 2 (1 + γ 5)ψ (1.8)
ψ L = 1 2 (1 − γ 5)ψ (1.9)
By construction the 1±γ 5 operators decompose the field into the right handed and left
handed chiral states. In the approximation where the particle is massless this is always
equivalent to the spin parallel and anti-parallel components with respect to the momentum
of the particle. This assumption breaks down for a massive particle, as by definition a
frame of reference exists where the particle appears to be travelling in the opposite direction
to the one initially postulated. Chien-Shiung Wu et al. discovered that the weak force
interacts only with the chiral left handed component of the SU(2) group[6]. In terms of
a mathematical representation this can be interpreted as a weak isodoublet for chiral left
handed fermions interacting with the weak force and an isosinglet for their right handed
counterparts. A synthetic summary of the present theory describing the interaction of matter
at the most fundamental level has been now described (table 1.1, fig. 1.1). All matter and
its interaction is however still represented by massless constituents, something that has been
clearly disproved by numerous experiments and our everyday life.

1.1 The Standard Model 5
It is only with the introduction of the Higgs mechanism that the theoretical problem has
been solved. The mechanism introduces four new scalar fields. Three are massless Goldsone
bosons and are responsible via their interaction terms for the transverse polarization and
therefore the masses of the W and Z bosons. Hence the Higgs mechanism elegantly predicts
the masses of the W and Z bosons from their observed couplings (or vice versa) and as a
consequence explains the broken Electro-Weak symmetry. In fact it can be now proven that
the masses of the Z and W bosons depend on the mixing angle of the electromagnetic and
the neutral weak field: cos(θ w )=M W /M Z . The remaining scalar field manifests itself as a
massive particles. The interaction of the massless fermionic fields with this last scalar field,
the Higgs field, gives all remaining constituents of matter their masses [7]. Although there
is some indirect evidence for the Higgs mechanism from the masses of the W and Z boson a
conclusive experimental proof in terms of the direct observation of the Higgs boson has not
yet been achieved.
Standard Model Bosons
Coupling Particle Charge (e) Spin Mass (Gev/c 2 )
Z 0 0 1 91.2
Weak W + +1 1 80.4
W − −1 1 80.4
EM γ 0 1 0
Strong 8 Gluons 0 1 0
H 0 0 0 > 114.4
Table 1.1: Boson spectrum of the Standard Model.
What still needs to be described are the fundamental constituents that perform these
interactions. At present there are no tested theoretical models that will predict the existence
of matter constituents from axiomatic principles, all information derives from experimental
evidence. It has been so found that matter can be divided in two separate groups: quarks and
leptons, both with spins of 1/2. The difference between the two is that quarks can interact
also via the strong force while leptons cannot. Additionally the neutrinos, representing
the members of the left-handed isodoublets interacting with the weak force have no charge
and hence cannot interact with the photon. Three different generations of leptons have
been found and all interaction observed conserve the generation number, with the exception

1.1 The Standard Model 6
being the oscillation of neutrinos, an area however not universally regarded as the Standard
Model and that will not be discussed in this thesis. Similarly also three generation of quarks
have been found. Mixing between the quark generations is allowed only via a charged weak
interaction. In such case the interaction with generation conserving particles is still the most
likely process. The precise quantitative value of each mixing is derived experimentally and
is encoded in the Cabibbo-Kobayashi-Maskawa matrix[8].
Standard Model Fermions
Group Particles Charge (e) Spin Interaction Weak eigenstates
Leptons
ν e ν µ ν τ 0 1/2 Weak L
e µ τ −1 1/2 EM, Weak L, R
Quarks
d i s i b i −1/3 1/2 Strong, EM, Weak L, R
u i c i t i +2/3 1/2 Strong, EM, Weak L, R
Table 1.2: Fermion spectrum of the Standard Model. The index, i, on each quark runs from
0 to 2 and represents its colour.
The aim of a synthetic description of all matter and its interaction has been achieved by
means of the above described framework (table 1.2, table 1.1, fig. 1.1). The existence of antimatter
has however been theoretically predicted by Paul Dirac in the late nineteen-twenties
and successfully discovered by Anderson shortly thereafter. In a first order approximation
the laws of physics for matter and antimatter should be equivalent once also a parity conjugation
has been performed. The Charge conjugation operator effectively inverts the charge
of the particle while the parity operator inverts, one or more, spacial axes of the coordinate
system. Hence the parity operator transforms a physical coordinate system into its mirror
image; the SU(2) L group therefore transforms into SU(2) R . Clearly this raises the problem
of over abundance of matter in the known universe, with respect to antimatter. A mechanism
that violates the charge and parity symmetry must therefore exist. In fact such mechanism
was experimentally discovered in 1964 by James Cronin, Val Fitch and collaborators in a experiment
observing the decay of neutral kaons [9]. Since then other CP-Violation effects have
been observed in many different reactions and the mechanism has been successfully incorporated
in the Cabibbo-Kobayashi-Maskawa matrix as a complex phase. However the rate of
asymmetry predicted by the SM is substantially too small to explain the present universe.

1.2 The Top Quark 7
The over-abundace of matter in the universe is therefore still an unresolved question.
Figure 1.1: Map of all interactions allowed by the Standard Model
1.2 The Top Quark
The top quark is substantially more massive than the rest of the observed quarks and leptons.
It is therefore the logical starting point for any physical mechanism that describes the mass
difference between all fermionic matter; a mechanism often referred to as Flavour Symmetry
Breaking (FSB). If the Standard Model postulates that mass is acquired via the Yukawa
coupling [2] the reason behind the vast variety of such couplings from particle to particle
and generation to generation is a completely speculative area of theoretical research. Many
models exists and in most, if not all, the top quark plays a central role. As an added benefit
many of the discussed theories not only address Flavour Symmetry Breaking but also address
the hierarchy between different forces.
Chronologically one of the first families of such theories is Technicolor. This postulates a
new strong gauge interaction in the TeV scale region that effectively performs the symmetry
breaking role of the now absent Higgs boson. From an experimental point of view the theory
manifest itself as resonances decaying, usually preferentially, into t and ¯t quarks. In the more
specific Topcolor and Topcolor assisted Techincolor models the gauge boson is nothing else
than a t¯t bound state or a ’top gluon’. These again decay almost exclusively into top and
anti-top quarks[10].

1.2 The Top Quark 8
Theories based on extra dimensions are similar to Technicolour; while the origin of the
gauge boson is different, the observable phenomenology is exactly the same. The symmetry
breaking mechanism is a boson that propagates only in the hypothesized extra dimension
and that couples to the fields on the Standard Model brane. In most scenarios the gauge
boson has preferential couplings to heavier generations and hence to the top quark[11].
The top quark is of great experimental importance also for the theory of Super-Symmetry
(SUSY). This theory predicts a new global space-time symmetry in which a bosonic superpartner
is assigned to every fermion present in the Standard Model and vice versa. Direct
searches at LEP and at Tevatron have set lower limits on masses of various SUSY particles.
All the limits are substantially above the mass of the bottom quark, but the possibility of a
top quark decaying into a SUSY particle is not as of yet excluded and it is an active area of
research [11, 12].
Figure 1.2: Indirect Electro-Weak constraints to the Higgs Mass derived from the mass
measurements of the W ± boson and the top quark. The region below 114.4 GeV/c 2 is
excluded from direct LEP searches.[13]
Not to be forgotten is also the role of the top quark in constraining the searches for the
Higgs boson. Because of the large Yukawa coupling the mass of the top quark is one of the
main theoretical constraints on the allowed mass of the Higgs boson, the other constraint
being the mass of the W. As it can be seen from fig. 1.2 these constraints point to a SM

1.2 The Top Quark 9
Higgs with mass of around or below 114 GeV or a light Higgs. A scenario clearly excluded
by direct LEP searches [13]. Such constraints are therefore useful not only for restricting the
phase space of the searches but also for interpreting the experimental results and therefore
discriminating between, for example, a SM and a SUSY Higgs. It is clear that if a Higgs
like particle is found at 300 GeV of mass this is incompatible with a purely SM description
and the presently measured top mass of 171.2 ± 2.1 GeV [14]. An explanation of this result
would therefore need to come from a different theory.
The aforementioned theories are not in any way the only ones that benefit from a detailed
and precise study of the characteristics of the top quark. The list presented is not meant to
be exhaustive but aims to give an idea of the central role that the top quark plays in the
Standard Model and most Beyond the Standard Model theories. They must be therefore
viewed as a motivation of the work presented in the following chapters.
1.2.1 Effective Field Theories
It is also important to mention the widespread use of effective field theories that are generally
independent of wider theoretical models. Such theories look only at the detail of a particular
coupling and infer all possible extensions to the Lagrangian given specific postulates. The
obvious and most universally used postulate is the conservation of local gauge invariance.
In the present thesis all effective field theories will use this axiom as well as Charge-Parity
conservation. Additionally the Lagrangian will be restricted to operators of dimension six
or lower and all higher order terms will be omitted. Under this assumption one can write
any interaction between any two fermions and a vector gauge boson as [15]:
L V f i f j
= ¯fj γ µ (A L P L + A R P R ) f i V µ
+ ¯f j iσ µν q ν (B L P L + B R P R )f i V µ + H.O. (1.10)
where V µ is the gauge field of the boson, q ν is the four momentum of the boson f and ¯f are
the fermionic fields, A L,V and B L,V are the form factors, P L,V are the left and right handed

1.2 The Top Quark 10
chiral projection operators, σ µν = i/2(γ µ γ ν − γ ν γ µ ) and H.O. are the higher order terms.
Using this parametrization it is then possible to derive the vertices that are relevant to this
analysis. Firstly the decay vertex Wtb [15][16]:
L W tb = − g √
2¯bγ µ (A L P L + A R P R )tW − µ
− g √ 2¯biσ µν q ν
M W
(B WL P L + B WR P R ) tW − µ (1.11)
where the t and ¯b fermions replace the fermionic fields f of the previous equation and the
W µ boson replaces the gauge field V µ , M W is the mass of the gauge boson. According to the
Cabibbo mixing in the Standard Model the top quark decays to a b quark via the emission
of a W boson in 99.8% of the cases. For all practical purposes of this analysis the Wtb vertex
will be considered as the only top quark decay mode. Experimentally the ratio of the top
quark decay into the b quark divided by the top quark decays into any negatively charged
quark has been measured to be 0.97 +0.09
−0.08 [8]. A value that is consistent with the Standard
model prediction. This also predicts a value of 1 for A L and 0 for all the remaining form
factors.
Additionally also the production vertices γt¯t and Zt¯t will be used in the analysis[15]:
L γ t¯t =
L Z t¯t =
−eQ t¯tγ µ tAµ − e¯t iσµν q ν
(B γL P L + B γR P R )tA µ
m t − g ¯tγ ( ) µ X L P L + X R P R − 2s 2
2c
wQ t tZµ
w
− g
2c w
¯t iσµν q ν
m Z
(B ZL P L + B ZR P R )tZ µ (1.12)
where e is the electron charge, Q t is the electric charge of the top quark, A µ and Z µ are the
bosonic gauge fields, m t and m Z are the masses of the top quark and the Z boson, c w and s w
are the cosine and sine of the Weinberg angle respectively. The slightly different format of
the form factors aims to highlight explicitly the Electro-Weak symmetry breaking and the
resulting Weinberg angle. Therefore in the SM X L = 2T 3 (t L ) = 1, where T 3 denotes the

1.2 The Top Quark 11
third isospin component of SU(2) L . Similarly X R = 2T 3 (t R ) = 0, because the Weak force
interacts only with the chiral left handed component. All the remaining, higher order form
factors (B γL , B γR , B ZL , B ZR ), are also predicted to have a value of 0 in the Standard Model.
1.2.2 Observables
Having presented the theories that will be considered in this thesis it is now important to
define a narrow set of observables that will be analysed. As the International Linear Collider
(ILC) and the Silicon Detector (SiD) are in the design stages this choice has been driven
not only by the underlying physics but also by the need for optimization of the proposed
detector and the related algorithms.
With such considerations in mind it has been chosen not to pursue any analysis where
the top decays leptonically. It has also been chosen to analyse only the top pair production
channel and disregard the single top channel. Therefore for the purposes of this analysis
the process e + e − → t¯t → b¯bq¯qq¯q (representing ≈ 45% of all e + e − → t¯t) is considered as the
signal and all remaining Standard Model processes are considered background; the signal
process and the top mediated background processes can be seen in fig. 1.3. The reasoning
behind this decision is two fold. The decision to pursue the pair production channel is
based on considerations about the sample and background statistics. The pair production
channel has a higher number of events produced than the single top case (at a centre-of-mass
energy of 500 GeV). Additionally there are significantly less background processes that have
a topology similar to the top pair production as more particles are produced in this process.
(a) (b) (c)
Figure 1.3: Feynman diagrams of a) signal events, b) and c) top mediated background events.

1.2 The Top Quark 12
The hadronic decay has instead been considered as more challenging for all the detector
components; a quark undergoes hadronisation and fragmentation before reaching the detector
in the form of a jet, a much more complex object than any lepton. The possible exception
being the τ lepton, but a top decays via the tau channel in only ≈ 11% of the events. Because
of jet multiplicity and the lack of missing energy it is believed that the hadronic process is
the best benchmarking process for many detector components and reconstruction techniques
described in the next chapters. It is also a test for any quark charge identification technique,
which is not needed in any other of the top decay channels as it can be reconstructed by
the charge of the detected lepton. These are in return very stringent benchmarks for the
tracking and vertexing as the loss of even the softest track can result in a mis-reconstruction.
The underlying idea behind the presented channel selection is therefore to test the detector
and reconstruction as thoroughly as possible, but keep the analysis methods simple.
The analysis also focuses on four specific observables: the cross section, the mass of the
top, the forward backward asymmetry of the top quark and the forward backward asymmetry
of the b quark resulting from the top decay. In the precedent sections the importance of the
mass as a constraint to the SM Higgs mass has already been discussed. Also other models
of Electro-Weak symmetry breaking have phenomenologies that are highly dependent on
the mass of the top quark with the obvious example of a SUSY Higgs[12]. The paramount
importance of this observable is therefore clear; hence the inclusion in this analysis. Similarly
straightforward is the justification of the cross section observable. Any discrepancy between
the theoretically predicted cross section and the measured one would indicate the presence
of an unknown production mechanism.
A bit more convoluted is the interpretation of the forward-backward asymmetry observables:
A fb = σ(θ < 90◦ ) − σ(θ > 90 ◦ )
σ(θ < 90 ◦ ) + σ(θ > 90 ◦ )
(1.13)
where σ(θ < 90 ◦ ) is the cross section of the events where the quark (t or b) has a polar
angle of less than 90 ◦ in the centre of mass frame of reference. These two parameters can be
interpreted as a test of the Electro-Weak theory couplings. By considering equations 1.12 it

1.2 The Top Quark 13
is possible to see how any deviation from the Electro-Weak predictions will alter the relation
between the number of spin parallel and spin anti-parallel top quarks produced. This in
turn will alter the stated forward backward asymmetry, which comes as a direct result of
the left handedness of the SU(2) L and spin conservation. By measuring the asymmetry one
therefore constrains the relationship between the form factors presented in these equations.
For the case of equation 1.11 it must be noted that the A fb for the bottom quark in the
centre of mass frame is really a convolution of the production t quark asymmetry and the
A fb of the b quark in the top quark rest frame. In order to deconvolute the two process
and therefore be able to set the constraints on the W tb vertex one must either measure and
therefore constrain the t quark asymmetry or perform the whole measurement in the top
quark rest frame. This analysis follows the first method and therefore simply measures A fb
of both quarks in the centre of mass frame.
Finally a centre of mass energy has to be chosen. The choice for this analysis is to use
the highest energy that will be available at the ILC as it is clear that this is where most
of the runs will be performed. Although this is probably not the best method to measure
the top mass (a threshold scan of the limit where top pair production becomes accessible
probably is [17]), it is a belief of the writer that for the more wide and generic physics and
benchmarking purposes of this analysis the 500 GeV centre-of-mass energy is optimal. Not
only this is the energy where the highest top quark statistics will be available; it is also the
energy where new particles and phenomena are most likely to be observed.

Chapter 2
The ILC and the SiD Detector
Concept
In order to probe deeper and deeper into the matter surrounding us higher and higher
energies need to be reached. The scales of the constituents of nature that we are probing are
in fact, to a first order approximation, inversely proportional to the energies at which they
collide. Bigger energies imply, assuming no paradigm shift in the technology, ever larger sizes
for accelerators and detectors. Particle physics has therefore moved from using cyclotrons
that fit into a small room to modern synchrotrons with circumferences comparable to those
of medium sized cities. Historically two main types of colliders exist: hadron colliders
(proton-proton and proton-antiproton) and lepton colliders (electron-positron). The first
ones generally reach higher energies, but suffer from a less clean environment. The proton
is in fact composed of quarks and the sought for interactions occur only between these
constituents, resulting in a large amount of proton remnant and a large spread of possible
interaction energies. Differently, lepton colliders produce a much cleaner environment and
a well defined interaction. However, as the mass of electrons is quite small when compared
to the proton mass, circular e + e − colliders suffer extensively from synchrotron radiation and
reaching higher energy in a circular accelerator becomes more and more expensive. Above
certain energies a linear collider becomes the economically most viable options. It is because
14

2.1 The ILC 15
of such reasoning that the next high energy collider is expected to be a linear e + e − collider.
This will complement the results from the current Large Hadron Collider with precision
measurements.
2.1 The ILC
The International Linear Collider (ILC) is a proposed electron-positron collider operating
in the centre of mass energy range √ s = 200 GeV - 500 GeV, with possible calibration
runs at the Z mass energy. An upgrade to the centre of mass energy of 1 TeV is also
envisaged. The basic layout of the ILC, which can be seen in Fig. 2.1, consists of two
almost identical arms; one being the electron accelerator, the other the positron one. The
electron source, a laser illuminating a photocatode in a DC gun, is located in the positron
arm and generates 76 MeV electrons. These are afterwards accelerated to 5 GeV as they
are transported into the damping ring. The role of the damping ring is to accumulate the
beam and squeeze the electrons into the required bunch structure. As the bunches circulate
in the damping rings they loose energy via synchrotron radiation and are re-accelerated by
an RF cavity. The synchrotron radiation decreases the motion in any direction, while the
cavity acceleration is directional; as a result the beam emittance is significantly reduced.
After this has been performed the electrons are ready to be injected into the main linac for
acceleration, which is performed from ≈ 280 RF cavities having an accelerating gradient of
31.5 MV/m. Some bunches continue straight through to the interaction point, other instead
reach the energy of 150 GeV and are then diverted into the undulator. This acts as a source
of high energy photons that are later converted into electron positron pairs. The positrons
that are separated from the rest of the beam (photons and electrons) are accelerated to 5
GeV and transported into the damping ring. From here on they follow a path through the
linac which is identical to the one previously described for the electrons; until the interaction
point (IP) [18]. Here the electrons and positrons collide with a crossinf angle of 14mrad.
Because of its size and complexity the design of the ILC pushes the limits of many

2.1 The ILC 16
Figure 2.1: The Proposed International Linear Collider
accelerator technologies. One of the most challenging tasks is reaching and maintaining
the required beam emittance. This poses constraints on the size and the technology of
the damping rings. In particular it is difficult to control the electron cloud effect that is
generated by squeezing the positrons together and the fast ion instabilities that are intrinsic
in the electron beam [18]. Even if these sources of emittance are kept under control and
the beam reaches the desired parameters when exiting the damping rings, one must also
make sure to maintain the emittance as low as possible while transporting the beam to the
interaction point.
It is the emittance requirements at the IP, combined with the small beam size of 640×
5.7 nm, that allows the ILC to reach the high design luminosity of 2 × 10 34 cm −2 s −1 ; but
to achieve these goals the alignment of the machine must be extremely precise. The required
precision is of 200 µm over a distance of 200m for the main accelerator components
and slightly lower for the damping rings (150 µm over 100 m) [19]. Additionally the machine
components have a rotational tolerance of only 20 µrad. At the present moment the
technological feasibility of these targets is in the process of being proven.
To deliver any significant luminosity, one must make sure that the beams hit precisely
head on. For this purpose an on line beam alignment system will have to be developed. It
will consist of a electronic feedback system that will use the first few bunches of the train
to adjust the alignment of the remaining bunches. This can be achieved with the usage of
a a stripline kicker [20]. The problem is complicated by the structure of the ILC beam,
composed from a series of trains with very tightly squeezed bunches. In the nominal beam
configuration there are 2625 bunches separated by only 369 ns giving a total active train

2.1 The ILC 17
time of 0.97 ms followed by a dead time of approximately 199 ms [19]. A description of
the main beam parameters of the ILC can be seen in table 2.1. If the aim is to attempt a
realignment in between each bunch crossing, then, by using the fastest of modern processors,
only a few mathematical operations can be performed in the available time. The transport
of information also introduces a delay that needs to be taken into account. Ideally therefore
a process that will require very few calculations and allow for a hardware system that can
be located close to the interaction point needs to be developed. The same beam structure,
imposed by the choice of a cold superconducting technology for the RF cavities, is clearly
challenging also for the vertex and tracking detectors.
ILC Beam Parameters
Parameter
Unit
Bunch Population 2 × 10 10
Number of Bunches 2625
Linac Bunch interval ns 369
Horizontal Beam size at IP nm 640
Vertical Beam size at IP nm 5.7
Normalized horizontal emittance at IP mm x mrad 10
Normalized vertical emittance at IP mm x mrad 0.04
Table 2.1: Main beam parameters for the ILC.
Technological challenges exist in other areas of the ILC project as well. In order to
contain the main accelerator in a reasonable length of 31 km the RF cavities must have
an average acceleration gradient of at least 31.5 MV/m. Presently tested RF cavities have
achieved gradients of up to 50 MV/m. While this is routinely achieved with only a single
accelerating cell the result is not easily scalable. Only recently a first succesful attempt of
adjacent cavities reaching the required acceleration has been performed [21]. Additionally
the production yield of RF cavities with gradients that meet or exceed these targets are
very low and will have to rise substantially in order to make the ILC a viable project. The
currently achieved production yield is in the region of ≈ 50% [22], while the aim is to increase
it to 80% [19].
As a broad generalization regarding the whole ILC R&D program it is safe to say that,
although not all the ILC parameters can be met at the present time, all the technologies

2.2 The Silicon Detector Concept 18
have been proven and all the R&D targets appear to be within sight. It is therefore expected
that the goals will be met in the coming years and given the right scientific and political will
the building of the ILC could then start.
2.2 The Silicon Detector Concept
The Silicon Detector concept (SiD) is a general purpose linear detector concept designed
to perform precision measurements and at the same time be sensitive to a wide range of
possible new phenomena. The distinguishing features, with respect to the other proposed
detectors, are the combination of silicon-only tracking and highly granular calorimetry optimized
for particle flow algorithms. SiD is composed of many separate subdetectors; in
order of the radial distance from the interaction point these are the pixel vertex detector,
the silicon strip tracker, the electromagnetic calorimeter, the hadronic calorimeter and the
muon identification system. With the exclusion of the muon system all the barrel region
subdetectors are encompassed by a 5 Tesla solenoid. An iron flux return after the solenoid
acts as the absorbing material for the muon identification system and also helps with the
radiation shielding. The picture is completed with the presence at very small polar angles
of a Luminosity Calorimeter (LumiCal) and a Beam Calorimeter (BeamCal) which is actually
mounted inside the accelerator’s final focusing magnetic system QD0[23]. An artistic
drawing and schematic model of the SiD detector can be seen in fig. 2.2 and 2.2
Before continuing with the detailed description of the subdetectors present in the SiD
design it is important to define the coordinate scheme that will be used. Given the physical
shape of the detector it is natural to use a set of cylindrical coordinates. As it is common in
e + e − colliders the z direction is defined as p⃗
e − −p⃗
e +, which given the very small beam crossing
angle of 14 mrad envisaged at the ILC can be approximated to the direction of the electron
beam. The origin is then defined at the interaction point. The radius of the cylinder r is
defined as the distance to the z-axis. Finally the angle φ is defined as the angle of rotation
around the z-axis, with the 0 being defined as parallel to the ground. Additionally the angle

2.2 The Silicon Detector Concept 19
Figure 2.2: An artist’s impression of the SiD detector
θ is defined from the relationship: θ = arctan(r/z).
2.2.1 Vertex Detector
The vertex detector is the innermost subdetector and its first layer is only a few millimetres
away from the beampipe. As the name itself suggests the primary aim of the detector is
to enable the precise reconstruction of vertices. As such it must be able to pinpoint the
coordinates of the tracked particle as precisely as possible. SiD proposes a silicon based
pixel detector composed of five cylindric silicon layers in the barrel region and four disks in
each forward region. An additional three outer pixel disks at larger |z| are envisaged in each
forward region to provide a uniform coverage in the transition between the vertex and the
tracking detector. The barrel layers are 125 mm long and are distributed at radii between
14 mm and 60 mm. The inner endcaps are located at distances between 76 mm and 180
mm from the interaction point and have an outer radius of 75 mm. The outer radius of
all the outer disks is 166 mm and their distances from the IP vary between 211 mm and

2.2 The Silicon Detector Concept 20
Figure 2.3: Subdetectors’ disposition in a quadrant of the SiD detector.
834 mm. The inner radius of all the endcap disks is determined from the conical shape of
the beampipe at the interaction region and spans between 15 mm for the closest disk up to
118 mm for the furthest one (fig. 2.4). The ultimate aim of the disposition is to achieve a
hermeticity in the polar region of | cos θ| ≤ 0.984 [23].
Figure 2.4: R-z view of the vertex detector. The right hand side has been drawn without
the support structures.
At present a clear technology for the vertex detector has not been selected; although the
need for a pixel detector has been established. Most of the present designs base themselves
on CCD, CMOS or DEPFET technologies [23, 24]. A lot of research is also being performed
on the possibility of using vertically integrated “3D” technologies [24]. A more detailed

2.2 The Silicon Detector Concept 21
description of one of the proposed CCD technologies the Column Parallel CCD will be
presented in the fourth chapter. For the purposes of the simulation a generic 20 × 20 µm 2
pixel is assumed, with a 3.5 µm expected point resolution of each layer for the barrel and
the inner endcap disks. The resolution of the outer disks is instead modelled as 7 µm. It is
expected that such a detector, when combined with the tracking detector, will allow for an
impact parameter resolution of better than σ rφ = σ rz = 5 ⊕ 10/(p × sin 2/3 (θ))[µm] for high
momentum tracks. The final aim of having such a small impact parameter resolution is to
permit a very precise determination of the IP vertex. The impact parameter of a track is
defined as the distance between the track’s point of closest approach to the IP and the IP
in the selected projection.
Lastly a word must be spent on the material budget and therefore also the mechanical
support of the detector. In the detector model used in this thesis the silicon sensors are
113 µm thick of which only the outer 20 µm, the epitaxial layer, are sensitive. Each barrel
and endcap layer is then supported by a 260 µm thick carbon fibre with a 25% coverage.
The combined thickness of the ladder is therefore approximately 0.15% of a radiation length
(X 0 ). Different designs also exist with an all silicon support structure, these allow X 0 0.1%
and therefore an even further reduced effect from multiple scattering [25].
2.2.2 Silicon Tracker
The aim of the silicon tracker is to provide precision track measurements in the intermediate
radial region and hence contribute to the measurement of the momentum and the vertex
reconstruction. The proposed design achieves the goal by using 300 µm thick strip sensors.
Each strip however gives only a one dimensional measurement in the sensor plane. Hence,
in order to pinpoint a precise 3D location, two layers of strips tilted at an angle with respect
to each other are needed for each module of the detector. The third dimension for the
barrel region, as in the case of the vertex detector, is given from the radial location of the
layer itself. Similarly for the endcap region the third dimension is determined by the layer’s
displacement on the z axis.

2.2 The Silicon Detector Concept 22
In the currently proposed SiD configuration the strips are 10 cm long and have a strip
pitch of 25 µm; however only every second strip is read out and hence the readout pitch is
50 µm. The resulting modelled resolution is of 7µm in the direction of the strip axis of each
layer. The stereo angle between the layers is 12 ◦ , a value chosen in order to maximize the
precision of the resolution in both angular directions while minimizing the reconstruction
confusion in the matching of the hits in the two layers. The resulting resolution in the z
direction is 7µm/ sin(12 ◦ ) or ≈ 34 µm.
In terms of geometry the detector will consist of 5 barrel modules and 4 endcap modules.
Each module consists of two layers of strip sensors attached back to back in order to allow
for a 3 dimensional measurement. The barrel modules located at radii between 22 cm and
122 cm. The length of the modules is between 111.6 cm and 304.5 cm. A schematic view of
the tracker can be seen in fig. 2.5.
Figure 2.5: R-z view of the whole tracking system.
The total material budget of the combined tracking and vertexing detectors is 8% X 0 in
the transverse region, rising to approximately 20% in the transition between the barell and
endcaps at θ = 40 ◦ and then diminishing again to 12% in the central endcap region [23, 25].
Such construction should allow for a distance of closest approach (DCA) resolution of just
below 5 µm for tracks with momentum higher than 10 GeV located in the transverse region;

2.2 The Silicon Detector Concept 23
clearly in agreement with the stated design aims. The results deteriorates significantly for
angles lower than 20 ◦ and momenta lower than a few GeV. The performance of the tracker
can be seen in fig. 2.6(a) and fig. 2.6(b).
(a)
(b)
Figure 2.6: Tracking Resolution: a) momentum resolution with respect to the energy of the
track plotted for different detector regions, b) Equivalent plot for the impact parameter,
Distance of Closest Approach (DCA).
2.2.3 Calorimetry
The SiD design uses a Particle Flow Algorithm (PFA) based approach to Calorimetry. This
algorithm takes advantage of precise momentum measurements of charged particles in the
tracker. In practical terms this implies the possibility of: associating the energy deposited
in the calorimeter to a specific neutral or charged particle; associating the energy deposited
in the electromagnetic calorimeter to a specific track and separating electrons from charged
hadron tracks. In order to perform these tasks efficiently the calorimeter is required to have
excellent segmentation [23, 26].
The resulting PFA reconstructed particles will therefore be represented, when the particles
are charged, by a track and a calorimeter cluster; if the particles are not charged by the
calorimeter cluster only. A visual representation of the calorimeter and the particle flow algorithm
can be seen in 2.2.3. Algorithms attempting to perform such functions have already
been applied in existing detectors: ALEPH and ZEUS are just two examples and have re-

2.2 The Silicon Detector Concept 24
sulted in a significant improvement in the energy resolution. However, unlike these detectors,
the SiD is being designed in order to make full usage of the PFA capabilities and therefore
the improvement in the performance is expected to be even greater[23]. More specifically the
SiD detector calorimeters should have imaging capabilities and hence be highly segmented in
the longitudinal and transverse directions. The calorimeters should also be placed inside the
solenoid in order to minimize the amount of energy that is deposited in the passive material
and maximize the successful cluster to particle assignment.
Figure 2.7: Simulated ρ → π + π 0 decay in the SiD Detector, demonstrating the concept of
Particle Flow
Electromagnetic Calorimeter
In order to be able to confine the jet clusters in the calorimeter one not only needs to have a
very finely segmented calorimeter, but also needs to prevent the overlap of the electromagnetic
showers. The showers should therefore be confined to the smallest volume possible and
the lateral spread should be minimized. It is therefore essential to choose a design and a
material that has a small Moliere radius.
The SiD Electromagnetic Calorimeter (ECAL) has alternating layers of tungsten and
silicon pixel detectors. In both the barrel and the endcap regions the inner 20 layers of
tungsten are 2.5 mm thick, while the next 10 layers are 5 mm thick; the silicon layers are

2.2 The Silicon Detector Concept 25
always 1.25 mm thick. The resulting detector has a depth of 26 radiation lengths (X 0 ) and
a Moliere radius of 13.5 mm. Importantly the configuration allows for a track resolution of
∼ 1mm from the calorimeter and it can therefore be used as a final point in any track reconstruction
algorithm. Apart from the obvious advantage in the performance of the tracking
this also helps immensely with the association of the track to a specific calorimeter cluster.
This method of calorimetry assisted tracking is particularly well suited for reconstructing
tracks that have originated outside the vertex detector as sometimes occurs with Λ and K S
decays [23].
The specific technology of the silicon layers has not yet been chosen and two main options
are under consideration. The baseline option is to use commonly available off the shelf large
pixel sensors. Each of these would be segmented in 1024 13 mm 2 pixels. All readout would
be concentrated in a single chip (KPiX) bump bonded in the centre of the wafer (fig. 2.8(a)).
An alternative option is to use CMOS Monolithic Active Pixel Sensors with pixel sizes of
50 µm × 50 µm [23]. In this case digital electromagnetic calorimetry would be performed
and the ECAL would effectively serve as a particle counter. The advantages of the design
are an excellent imaging resolution of the calorimeter and a simple design of the pixels; they
effectively act only as counters of minimum ionizing particles (MIPs). The problem however
lies in the enormous number of channels: 1,000,000 for each 5 cm × 5 cm sensor. The stated
aims for both technologies are an efficient (95%) reconstruction of photons in jets and an
EM energy resolution of 18%/ √ E [23]. The possibility of obtaining such results has already
been proven with the use of full simulation using the GEANT4 software[27].
(a)
(b)
Figure 2.8: The active layer technologies used as a baseline design in the a) ECAL: the pixel
silicon sensor using the KPiX readout b) HCAL: an RPC cell

2.2 The Silicon Detector Concept 26
Hadronic Calorimeter
Facing very similar challenges to the ECAL is the hadronic calorimeter (HCAL), which is
located just after the ECAL (r=142 cm), but still inside the solenoid magnet(r=258 cm). The
geometry presented here applies to the barrel region, but it is conceptually the same also for
the forward region where the HCAL outer radius is delimited from the Muon Identification
System rather than the solenoid. Its size, dictated by the nuclear interaction length, needs
to be substantially bigger than the one of the ECAL.
Ideally the HCAL would have a very similar segmentation to the one just presented for
the ECAL; however in order to maintain reasonable complexity and costs a much coarser
readout is foreseen for this subdetector. In fact it is composed of 40 layers of 2 cm thick
stainless steel, acting as absorber plates, separated by 8 mm of Resistive Plate Chambers
(RPCs), acting as active detector elements (fig. 2.8(b)). RPCs are gaseous detectors limited
by two resistive plates, typically either glass or Bakelite. The outer surface of the plates is
then coated with a layer of resistive paint to which a high voltage is applied. In the presented
detector a potential of approximately 6.3kV is envisaged. In this operational mode a charged
particle crossing the the gaseous region (composed mainly of Freon R134A) will initiate an
avalanche of electrically charged particles; generating a potential difference across the RPC
that can be detected. The size of each RPC sensor is 1 cm 2 . Such a detector should be able
to give good imaging quality, because of the small sizes of each RPC element, and an energy
resolution of 65%/ √ E for neutral hadrons [23]. Again the result has been validated by a
simulation using the GEANT4 software [27]. The results of a small calorimeter prototype in
a test-beam can be seen in fig. 2.2.3.
It has to be stressed that the described technology is the one that at presents constitutes
the baseline scenario, but it is by no means the only possibility being considered. For the
active detector elements there is a wide variety of different proposals; all of which are still in
the R&D and testing stages. These vary from scintillators with Silicon photomultipliers to
Gas Electron Multiplies (GEMs) or MICRO MEsh GAseous Structures (MICROMEGAS)
[23].

2.2 The Silicon Detector Concept 27
Figure 2.9: Response of a small prototype hadronic calorimeter to positrons with energies of
1, 2, 4, 8, 16 GeV. The data points are presented in black, with a gaussian fit performed on
them, the red histograms are the GEANT4 Simulations. The yellow histograms represent
the same data on a different scale. As the axis is in this case common to all the energies, it
is possible to directly compare the performance of the calorimeter for the different energies.
2.2.4 Muon Identification System
The Muon Identification System starts outside the calorimeters and the 5 T magnet solenoid
system at a radius of 3.40 m. The system is expected to consist of eleven 20 cm thick stainless
steel absorber plates in the barrel and the endcap regions. These also act as a flux return
structure for the solenoid magnet. In between the steel plates, in gaps of 4 cm, RPC active
detector layers are inserted. An additional layer of RPC is present between the magnetic
solenoid and the first barrel layer. The RPCs will use a strip detector geometry with a pitch
of 3 cm and a maximum area covered by each strip of 300 cm 2 . In this way an occupancy
from background hits of less than 1% is expected. In each detector layer there will be two
strips placed orthogonally to each other allowing for a precise two dimensional measurement.
Currently investigations are in progress to determine whether smaller sensors are needed in
the layers closest to the beampipe. The system is expected to identify more than 96% of the
muons with energies above 4 GeV and have extremely high purity. Hadron punch-through
is the most problematic background [23].

2.2 The Silicon Detector Concept 28
2.2.5 Forward Detector
The so called Forward Detector represents the region with | cos θ| ≥ 0.99. Here one can find
two separate subdetectors: the Beam Calorimeter (BeamCal) and the Luminosity Calorimeter
(LumiCal). Their main aim is to extend the hermeticity of the calorimeter into very
small angles. This is essential for a lot of new physics searches since many of these reactions
are expected to have a substantial component of missing energy. At the same time these detectors
can help monitor the luminosity produced by the ILC. More specifically the LumiCal
is designed to monitor the integrated luminosity by using the small angle Bhabha scattering
and the e + e − → W + W − interaction. The goal is to measure the luminosity with an
accuracy better than 10 −3 . The aim of the Beamcal is instead to evaluate the instantaneous
luminosity by using Bremsstrahlung pairs.
In terms of design the LumiCal uses the same technology as the one used for the ECAL
and it extends from 158 cm to 173 cm in the direction of the beampipe which it surrounds.
The inner radius is 6 cm and the outer radius is 20 cm. The energy resolution of the
LumiCal for electrons with 1 GeV energy is 15%/ √ E and it rises to 20%/ √ E for the most
energetic events envisaged at the ILC. The BeamCal is instead composed of 50 layers of 2.5
cm tungsten intercalated with an active silicon layer. The detector is located at 295 cm from
the interaction point and spans between 2 cm and 13.5 cm in radius as it can be seen in fig.
2.10 [23, 25].
Figure 2.10: Forward Region

2.2 The Silicon Detector Concept 29
2.3 The International Large Detector
The International Large Detector (ILD) is another proposed multi-purpose detector for the
ILC [28]. Its general features are similar to the ones just presented for the SiD. The main
differences lie in the presence of a Time Projection Chamber that replaces part of the silicon
strip tracker, in the use of a lower magnetic field parameter (3.5 T instead of 5 T) and in
the consequently resulting larger overall dimensions. The choice of magnetic field also forces
the beampipe to be slightly larger than in SiD (1.45 cm) in order to filter out most of the
pair production background.
Although the presented analysis has been ultimately performed on a model of the SiD
Detector a lot of the software tools have been developed and tested for the ILD and its
extremely similar predecessor the Large Detector Concept (LDC). In particular the flavour
tagging package that is presented in this thesis has been widely tested on the LDC detector
and only afterwards used for SiD.

Chapter 3
Simulation and Reconstruction
Given the size, complexity and the financial commitment that modern detectors require they
need to be simulated and their performance analysed in a virtual environment before their
construction is started. The purpose of such an exercise is to optimize the detector design,
implement the needed algorithms and test the physics capabilities of the project. This
process can be separated into three distinctive stages: Monte Carlo generation, detector
simulation and event reconstruction. In a running experiment these simulations would be
compared to the collected data.
3.1 Monte Carlo Generation
The first step of the process is to reproduce our understanding of the Standard Model. The
Feynman diagrams of the desired events are hence generated and run through the hadronization,
fragmentation and showering processes. It is possible at this stage to simplify the modelling
by omitting any of the Initial State Radiation (ISR) or Final State Radiation processes
(FSR). This is usually done in the initial stage of an analysis in order to gain an intuitive
understanding of the event by concentrating solely on the underlying physics. Although all
the results here presented incorporate these effects many algorithms and techniques were
initially studied with a simplified sample. Additionally one should also model the back-
30

Chapter 3. Simulation and Reconstruction 31
ground generated from the beam-beam interactions which is a source of underlying e + e −
pairs. These however have not been included in the present study because of the substantial
increase of computational resources required. A small study has instead been performed
that shows the very limited effect that beam-beam background has on the b quark tagging
efficiencies. For this specific study the GUINEA PIG [29] software has been used. The
programs used for the Feynman diagrams generation were: Whizard Monte Carlo [30, 31]
for all the analysis presented except for the ILD/LDC flavour identification sections where
PYTHIA was used. All the remaining processes were modelled in PYTHIA[32]. The output
of the program is a list of stable and decayed particles with their points of origin, points of
decay (if applicable), energy and momenta.
3.2 Detector Simulation
The detector simulation is the subsequent step of the process. In fact, since the ILC and the
SiD are still in the design stages it is clear that no physical detector exists and any detector
description such as the one that has been just performed in the previous chapter, is the
result of a computational simulation of a plausible detector. Also in quite a few areas of the
detector many technologies are still under investigation. In such occurrences the modelling
has been performed by using as generic a technology as possible and a series of details and
technicalities were omitted. In this process the interaction of the generated particles with
the detector material is reproduced. The product is a list of simulated detector hits which
contain the location where the particles have interacted with the detector and the energy
deposited by the particle at each specific location. However the information is available only
for the material that has been labelled as active in the detector description.
As most of the presently produced particle physics analyses based on simulation also this
one uses the GEANT4 framework [27]. However, given its immense complexity the code
is usually accessed via a simplified interface. The SiD detector concept uses the SLIC [33]
software as its wrapper of choice. The ILD collaboration uses the Mokka package [34, 35].

Chapter 3. Simulation and Reconstruction 32
Digitization is the next step; the simulated hits are smeared according to the actual
detector resolution capabilities. The aim is to model the physical properties of the detector
(such as pixel sizes or strip pitches) and hence smear the position and the energy of the
simulated hits as a real detector would.
3.3 Reconstruction
Finally the reconstruction stage is performed. It is now assumed that all the data that
would be produced from a real detector has been effectively simulated. The remaining
reconstruction algorithms should therefore be the same as for the case of real data. Their aim
is to reconstruct the event by using only the data that the detector would provide. Clearly
in simulated data much more information is available, this information however must not be
used for the physics analysis but only for the purpose of algorithm benchmarking. In the
following subsection we will describe the tracking, the PFA and the jet finding algorithms.
The flavour tagging and the quark charge reconstruction algorithms which are more vital to
this analysis will be described in more detail in separate chapters.
3.3.1 Tracking
The aim of the tracking algorithm is to transform a series of tracker hits into a set of tracks
with the highest possible reconstruction efficiency and the lowest possible number of fake
tracks. Apart from describing the path taken by the particle through the vertex and tracking
detector the track object must also contain the relevant error matrix on the reconstructed
path and a track momentum estimation. In the SiD detector the tracking is separated into
two stages and therefore algorithms[23, 36].
In the first algorithm track finding is controlled by a set of strategies. A strategy consist
of the list of detector layers to be used and the role of each layer, requirements on the
number of hits, kinematic constraints (momentum and impact parameters) and the χ 2 cut

Chapter 3. Simulation and Reconstruction 33
to be applied. The layers’ roles can be of three types: seed, confirm and extend. Given a
strategy the tracking algorithm proceeds in four steps:
1. Three seed layers are expected in each strategy; all the hits found in these three layers
are used to perform all possible helix fits given the kinematic constraints. If helixes
can be formed that are consistent with the constraints and the χ 2 then the helixes are
considered as track candidates, otherwise they are rejected.
2. The algorithm then proceeds to consider the confirmation layer(s). Each track candidate
must have a suitable hit that will allow a helix refit without exceeding the required
χ 2 in each of the confirmation layers, else the track is rejected. Generally it has been
found that strategies with only one confirmation layer work best.
3. Then the hits of the extension layers are considered. If a hit is consistent with any of
the tracks that passed the previous stages it is assigned to this track, else the hit is
ignored. Regardless whether there has been a sucessful match in any of the extension
layers the track is kept.
4. In the final stage all track candidates that do not meet the required number of hits are
rejected. Additionally all ambiguities deriving from different tracks sharing hits are
resolved.
A complete tracking algorithm consists of multiple strategies which are designed to be exhaustive
so that all possible hit combinations are considered. Any possible conflict between
strategies are resolved so that all tracks can share a maximum of one hit. All the strategies
used in this thesis require 1 confirmation hit, a minimum of 7 hits (6 in the barrel region),
p t > 200 MeV, xy and z distances of closest approach to the IP < 10 mm.
The second algorithm aims to perform calorimeter assisted tracking and it is run subsequently
to the one just described. All the tracks that are initially found are propagated into
the ECAL. Clusters of calorimeter hits that match the track trajectory are then associated
to the found tracks. All other clusters that contain hits in the inner layers of the ECAL

Chapter 3. Simulation and Reconstruction 34
and that are consistent with the hypothesis of being produced by a MIP are considered as
candidate track hits and are used as seeds. The seeds, which contain both the position and
the direction of the track at the entry point in the ECAL, are then propagated back into
the tracker. In this process they can pick up any unassigned track hits. After checking for
the quality of the track and resolving ambiguities a further list of tracks is provided. This
method is particularly powerful for reconstructing tracks from long lived particles that decay
outside the vertex detector [23, 36].
The final performance of the combined tracking algorithms can be seen in fig. 3.1(a) and
3.1(b).
(a)
(b)
Figure 3.1: Tracking Efficiency: a) efficiency vs. cos(θ) where the gap between the barrel
and the forward regions at values of ≈ cos(θ) = 0.7 can be clearly seen , b) efficiency vs.
the momentum of the track that is being reconstructed, where the excellent efficiency of
the reconstruction above 0.2 GeV can be seen. The tracks from the t¯t sample described in
chapter 5 were used as the sample.
3.3.2 Particle Flow Algorithm
The idea behind the PFA algorithm is to separate the calorimeter energy deposits of each
individual particle allowing therefore the measurement of the energy of the particle in the
optimal subsystem: the ECAL for the photon, the tracker for charged particles and both
calorimeters for neutral hadrons. In order to achieve the goal the PFA takes as inputs the
energy deposits in the calorimeters and the muon systems and the tracks derived from the
tracking algorithm. The algorithm can be described as observing the following steps [26, 23]:
1. Validation of the Input: all calorimeter hits that are not-physical or unmeasurable are

Chapter 3. Simulation and Reconstruction 35
discarded. Generally these are hits below an energy threshold or occurring later than
100 ns from the primary interaction.
2. Electron, Muon and Photon Reconstruction: muons are identified by extrapolating
tracks through the ECAL and HCAL and requiring them to connect to a MIP stub in
the muon ID system. Electrons and photons leave a distinctive shower in the ECAL
which are reconstructed via a clustering algorithm. If a cluster momentum and position
matches the parameters of one of the tracks it is declared as an electron cluster else it
is defined as a photon.
3. Charged Hadrons Identification: the first step is to identify the MIP stubs that derive
from charged hadrons travelling through the detector, but not showering. In the process
the tracking information is once again used as non-leptonic tracks are propagated into
the detector and nearby MIP hits are considered being part of the stubs. At this point
all the remaining hits are expected to derive from hadronic showers. A set of algorithms
is then used to separate the shower into distinctive clusters. The tracking information
is used again; for each track that has not been identified as a muon or electron a seed
ECAL cluster is found. The track can also be associated first to a MIP stub and then
to a cluster. Clusters are then iteratively added to the seed by considering the point
of closest approach of the track and other discriminating variables. The algorithm
stops when either there are no more clusters that would pass our predetermined cuts
or when the energy of the cluster becomes too large with respect to the energy of the
track. The same procedure is repeated for every non-leptonic track. A whole list of
ambiguities are then resolved. For example if the energy of the track is substantially
higher than the energy of the cluster the association criteria are relaxed and nearby
cluster are added.
4. Neutral Hadrons Identification: a similar algorithm is applied to the one previously
described for the charged hadrons. However given that there are no tracks associated
with neutral hadrons the tracking information cannot be used and clusters are merged
only by their calorimetry signatures.

Chapter 3. Simulation and Reconstruction 36
5. Production of Reconstructed Particles: finally all the information is collected in a set
of unambiguously reconstructed particles that are ready to be used in any physics
analysis. The energies of the particles are established from the optimal subsystem.
The performance of this algorithm at different energies can be seen in table 3.1 [26]. It
can bee noted that the performance deteriorates with the increase in the jet energy. This
is because the leakage out of the back of the calorimeter becomes an important effect and
because the separation of the clusters becomes more difficult.
PFA Performance
Resolution
Process Barrel Endcap
e + e − → q¯q, √ s = 100GeV 3.7% 3.8%
e + e − → q¯q, √ s = 200GeV 3.0% 3.2%
e + e − → q¯q, √ s = 360GeV 2.7% 2.7%
e + e − → q¯q, √ s = 500GeV 3.5% 3.3%
e + e − → Z(¯q)Z(ν¯ν), 4.7% 3.9%
Table 3.1: PFA performance for SiD02. For the e + e → q¯q processes, the rms90 of the energy
sum is quoted as a fraction of √ s, and for the e + e → ZZ process the rms90 of the dijet
mass is quoted as a fraction of m Z . The term rms90 is defined as the root mean square of
the contiguous block of 90% of events with smallest root mean square values.
3.3.3 Jet Finding
It is well known that a quark cannot remain free and it hence undergoes hadronization and
fragmentation into a number of colourless hadronic particles. Assuming that the momenta of
the particles are substantially higher than their masses the relativistic boost will ensure that
the direction of motion will be similar for all resulting particles. Typically the directions
of the newly created particles form a cone around the direction of motion of the original
parton. The main purpose of any jet finding algorithm is to combine these particles into
a new entity called a jet. It is clear from the definition that the concept of a jet is very
variable. For example a hadronically decaying top will generate three jets if decaying at rest
and only one if it is highly boosted. Never-the-less the concept is extremely powerful as it
enables us to study the original jet-producing particle.

Chapter 3. Simulation and Reconstruction 37
The jet algorithm used in this analysis is the y-cut algorithm with a fixed number of jets.
More specifically in the flavour tagging section the number of jets is fixed to two and in the
hadronic t¯t analysis is fixed to 6. The reason is the topology of the events. In the flavour
tagging section e + e − → Z/γ → q¯q events are considered, which naturally produce 2 jets. A
hadronic t¯t event at 500 GeV is instead expected to have 6 separate jets. The following is a
brief description of the algorithm [37]:
1. The discriminating quantity y is calculated for each pair of reconstructed particles:
y ij = 2min(E2 i ,E 2 j )(1 − cos(θ ij ))
E 2 vis
(3.1)
where E i (E j ) is the energy of the reconstructed particle i (j), θ ij is the angle between
the two particles and E vis is the total visible energy defined as E vis = Σ i E i .
2. If the number of particles is more than the desired one combine the two entities that
produce the lowest y ij value into a new pseudo-particle where ⃗p = ⃗p i + ⃗p j and repeat
step one, else quit algorithm.
Additionally to the list of jets the algorithm also outputs the value of y for the last
pseudo-particle association made and the value of y for the next association that could have
been made. The first value (y 56 ) represents the jet separation between an event with five
and an event with six jet topology. The second value (y 67 ) is the six and seven jet topology
separation. These values are used in the presented analysis.
3.3.4 The Software Framework
Although it is not an algorithm it is important to mention the framework in which the
analysis has been reconstructed. Two separate frameworks were used: the SiD developed
org.lcsim package [36] and the ILD Marlin plus Marlin Reco package [38]. The tracking and
the PFA have always been done within the recommended package, so org.lcsim [36] for the
analysis events and Marlin for the flavour tagging events. Jet clustering and flavour tagging

Chapter 3. Simulation and Reconstruction 38
have however always been performed in the Marlin environment [38, 39]. Also the physics
analysis software has been developed and run within the Marlin framework. As we can see
for all the events produced in SiD the software framework has been switched in the middle
of the reconstruction process. The procedure has been facilitated by the shared data storage
software LCIO [40] and by the almost complete lack of dependence on the detector geometry
of the flavour tagging and analysis software. Although the transition has been smooth this
analysis has been the first one to perform it and it has helped to understand and resolve any
remaining incompatibility.

Chapter 4
The Column Parallel CCD as an ILC
Vertex Detector Technology
The simplest form of a Charged Coupled Device (CCD) invented in 1969 [41] is essentially
an array of Metal Oxide Semiconductor (MOS) capacitors. By applying different voltages to
nearby gates a potential well can be created under a specific gate and charge can therefore
be stored. In order to accumulate the charge in a constrained space, but also to prevent the
charge from being located on the sensor’s surface, all modern imaging CCDs add a buried
channel structure. The CCD can therefore be interpreted as a MOS capacitor with a p-n
junction structure beneath it as seen in fig. 4.1(a).
If the potential of the gates is then altered it is possible to transfer charge from one pixel
to another. The charge can be transferred in the desired direction either by the use of three
different clock voltages (three phase CCD) or by using only two clock voltages in combination
with an inbuilt barrier in the form of altered ion implantation under part of the pixel (two
phase CCD). The CCD technology studied by the LCFI collaboration is of the latter type.
In a traditional CCD a single readout is used for a whole matrix of pixels; charge is therefore
transported first in one direction and then perpendicularly. In the proposed Column Parallel
CCD (CPC) an amplifier is instead attached at the end of each column. The number of clock
cycles needed to read the whole array is hence reduced by a factor equal to the width of the
39

Chapter 4. The Column Parallel CCD as an ILC Vertex Detector Technology40
(a)
(b)
Figure 4.1: Representation of Charged Coupled Devices: a) Cross section and physical
concept behind charge storage. The line below the diagram represents the potential well
below every gate. The plot is shown when gate one is in accumulation state. Q1, Q2 and
Q3 are the charges that have been accumulated due to the interaction of three Minimum
Ionizing Particles (MIP), with the silicon and the subsequent creation of electron-hole pairs.
b) Photograph of the 2 nd generation Column Parallel CCD by LCFI, CPC2-10
sensor expressed in number of pixels. The two different concepts are illustrated in fig. 4.2(a)
and fig. 4.2(b). The charge is prevented from spreading in the not desired directions by the
usage of doped ion implants and channel stops underneath the gates.
CCDs have numerous proprieties that make them suitable for the ILC Vertex detector
[42, 43]. Their pixels can be very small; in the proposed CPC the size is 20 µm × 20 µm, but
much smaller sizes have been achieved. They can also be made very thin since the sensitive
epitaxial layer can be as small as 20 µm, which allows for a very low material budget. In
fact the CCDs can be thinned so that only the epitaxial layer is left. Finally although they
usually collect only about 80 e − for each MIP per micrometer of track (so about 1600 e − for
a 20 µm path in silicon), they also have extremely low readout noise, as low as 10 electron
equivalent, and a very high charge transfer efficiency.
As a downside CCDs are vulnerable to radiation damage which tends to generate charge
traps and reduce the charge transfer efficiency. Additionally electrical connections of a CCD
can be problematic due to the difficulty to drive the large gate capacitance of the imaging
area [44]. This leads to the need to supply large enough clock currents to the detector. The
need to have large storage capacitors nearby to support the peak current may substantially

Chapter 4. The Column Parallel CCD as an ILC Vertex Detector Technology41
(a)
(b)
Figure 4.2: Readout of a) standard CCD; readout time = N × M/f b) LCFI CPC; readout
time = N/f, where f is the clock frequency. The factor of two derives from the fact that
two phase CCDs are considered each pixel is hence composed of 2 separate gates.
increase the material budget. Since the CCDs are operated at low temperatures (-10/-50 ◦ C)
in order to minimize dark current and to improve charge transfer after radiation damage,
an efficient cooling system is also required. It is therefore essential to understand the clock
distribution and to attempt to optimize it. The power stored in the form of capacitance
(and subsequently dissipated by the resistive components in the form of heat) in a two phase
CCD imaging area is [41]:
P = 2C PIX ∆V 2
IGf c N PIX (4.1)
where C PIX is the total capacitance of each pixel, ∆V IG is the clock voltage amplitude, f c
is the clock frequency and N PIX is the number of pixels present. Most of these parameters
are however constrained by the requirements of the SiD and the ILC design. The size and
hence the number of pixels is defined by the required resolution. The frequency of the clock
is defined by the beam structure and the inner layer occupancy requirement. The ocupancy
of each layer of the vertex detector should in fact be small, in this case a value of < 1%
is required in the innermost layer. This is done in order to ensure that track finding is
not compromised. A fast readout is therefore needed; simulation have shown that the clock
frequency required to drive the CPC is 50 MHz. A lot of effort has therefore been put in

4.1 CPC2 Capacitance Characterization 42
reducing the driving clock voltage and the capacitance of the CPC to minimize the stored
power P. As a consequence the clock amplitude was reduced to less than 2 V; substantially
less than the standard 10-15 V used while operating a conventional CCD. Never the less
given the size of ≈ 10 cm 2 for each sensor, a total capacitance of the sensor of 50 nF and a
clock voltage of 2 V the total required power per sensor is still ≈ 20 Watts; corresponding
to a clock current of 10 A. It was therefore reputed important to try to understand and
minimize the capacitance [45].
In all the further sections the analysis have been performed on a second generation CPC
sensor, CPC2, produced at e2V [5]. The CPC2 pixel size is 20 µm square with 750 pixels per
row. Several length variations are available achieved by a stitching process. The used sensor,
CPC2-40, has an overall imaging area of 1.5 cm × 5.28 cm. The pixel is two-phase clocked
with the active lengths of the barrier and storage parts of each phase being correspondingly
3.5 µm/6.5 µm. The inter-column isolation region is 6.0 µm wide. The silicon wafers used
for CPC2 production are 500 µm thick and have a p-type epitaxial layer of about 20 µm.
4.1 CPC2 Capacitance Characterization
It is in this light that a characterization of the CPC2 capacitances was undertaken. The first
step towards the measurement of the capacitance is to create a simple model of the CCD
and therefore also distinguish all the capacitances embedded in the C PIX term (equation
4.1). For this purpose we need to understand the behaviour of the CCD when a gate (V G )
and/or a reference voltage (V Ref ) are applied. V Ref and V G are defined as voltage across
the p-n junction and a voltage differential between the gate and the substrate. In particular
there is a need of understanding the behaviour of the depletion regions and therefore of the
capacitances associated. From theoretical considerations we expect that an increase of the
reference voltage will increase the junction depletion. The application of a reference voltage
effectively reverse biases the p-n junction. Similarly an increase in the gate voltage will
increase the gate depletion region and shift the depletion of the p-n junction away from the

4.1 CPC2 Capacitance Characterization 43
gate region. Because of this shift the total depletion distance will be larger at saturation
when V G is larger. A graphical representation of this effect can be seen in fig.4.3. Saturation
is considered as the state where the gate and the p-n junction depletion regions merge; hence
the buried channel is completely depleted and any increase of the reference voltage will have
no further effect[41].
Figure 4.3: Graphical representation of a CCD, in particular interesting for the purpose
of this analysis are the p-n junction depletion regions and the gate depletion regions. The
picture presents a CCD with both a V Ref and a V G being applied. Note that the gate
depletion region is different between the gates labelled OTG and OSW. This is due to an
intergate voltage differential being applied as when the CCD is being run.
Finally it must be remarked that in order for a potential well to be created under the CCD
gates the device must be in a saturated regime. It is now necessary to make a capacitance
model of each pixel 4.4(a) and of the whole device 4.4(b).
4.1.1 Substrate Capacitance
The simplest measurement that can be performed is the determinations of the substrate
capacitance for different V Ref and V G . By shorting points A and B and then applying a
potential with respect to point C all the C S are in parallel and each pixel can be hence
treated independently; see fig. 4.4(b). The results of this measurement can be seen in fig.
4.5. All the results presented in this section have been retrieved by using the Hewlett-

4.1 CPC2 Capacitance Characterization 44
V−A
G1
C−IG
G2
V−A
V−B
G1 C−IG G2 C−IG G3 C−IG G4 C−IG G5
V−B
C−S
C−S
C−S
C−S
C−S
C−S
C−S
V−C
V−C
(a)
(b)
Figure 4.4: Circuit model of a) one pixel, b) series of interconnected pixels or the CCD
imaging area. GN is the gate number N, C-IG is the intergate capacitance, C-S is the
substrate capacitance, V is the the potential at different points in the circuit.
Packard LCR 4284A. Various different frequencies and amplitudes for the AC current have
been used in the capacitance measurement, no substantial dependence on either of these
parameters was found. The AC frequency at which the measurement is performed has been
varied between 5 kHz and 80 kHz and the measurement sinusoidal voltage has been varied
between RMS of 0.2 V and 1 V. In this and the following sections all V Ref and V G are to be
interpreted as a DC voltage.
1/Csub (1/nF)
0.11
0.10
0.09
0.08
0V Vgate
1V Vgate
2V Vgate
3V Vgate
4V Vgate
5V Vgate
6V Vgate
7V Vgate
8V Vgate
9V Vgate
10V Vgate
11V Vgate
12V Vgate
13V Vgate
14V Vgate
15V Vgate
0.07
6 8 10 12 14 16
Vref (V)
Figure 4.5: Total substrate capacitance C Sub = N PIX × 2 × C S plotted as 1/C Sub (since this
is a value proportional to the depletion region x d ) of the CPC2 for different values of V Ref
and V G . The graph is presented without uncertainties for clarity purposes. However all C Sub
measurements should be interpreted as having an uncertainty of ± 0.5 nF
The results are consistent with the expectations regarding the behaviour of the depletion
presented in the previous paragraphs. In fact under the assumption that the C Sub is an
infinite plate capacitor the depletion distance is inversely proportional to C Sub . It is also
possible to conclude that the minimum reference voltage at which the CPC2 can be operated

4.1 CPC2 Capacitance Characterization 45
is larger than 10 V. It is only at this potential that the buried channel is fully depleted as
seen in fig. 4.5. The V Ref value at which the depletion occurs has only a weak dependence
on V G unless this potential is comparable to V Ref where the dependence is accentuated. The
relationship can be interpreted as the previously described shift of the p-n junction depletion
region. The capacitance dependence on the V G once the buried channel is depleted is clearly
visible, in particular for larger V G . Before moving to the next topic it must be noted that
this is not the regime in which the CPC2 is expected to be operated. The running of the
CPC2 is performed with a substantially lower gate potential, about 2 V, and the buried
channel completely depleted.
By assuming that the substrate capacitance behaves as a uniform infinite plate capacitor
the thickness of the depletion region can also be evaluated: x d = ǫ r ǫ 0 A/C Sub , where A is the
imaging area and ǫ r is the dielectric constant of silicon. It can be therefore seen that when
V G =0 V x d ≈ 6 µm while by applying a gate voltage of V G =10 V due to the extension of the
depletion region x d changes to 8 µm, rising up to 9 µm at higher gate voltages. This value
is substantially below the stated thickness of the epitaxial layer of ≈ 20 µm which would
imply that not all the epitaxial layer is depleted. A different interpretation of the result
can also be made. In fact almost half of the area of the CPC has implants serving either
as channel stops or as barriers enabling the two-phase operation. Because of the different
doping concentration this areas will not deplete as quickly, if at all, as the remaining part
of the CPC. The estimation of the capacitance of these elements is difficult as it depends
strongly on their geometry and on assumptions on whether they are floating or grounded.
However it is reasonably expected that C Sub will be at least partially (if not largely) driven
by these areas. As a consequence the other regions may have an x d that is substantially
larger than 9 µm.
4.1.2 Intergate Capacitance
Once the substrate capacitance has been understood also the intergate capacitance has to
be measured. This is however a more challenging task as each single pixel cannot be treated

4.1 CPC2 Capacitance Characterization 46
independently. It is now important to reason in terms of voltages. Considering an infinite
number of pixels, see fig. 4.4(b), a fair assumption given the considerable size of the CPC2,
the AC voltage amplitude between points A and C is half of the amplitude between the
points A and B: ∆V A−C = ∆V B−C = 1/2∆V A−B . The total energy of the circuit is therefore:
{
E T = 1 2 ∆V A−BC 2 Mes = N PIX × ∆VA−BC 2 IG +
(
∆VA−B
2
) 2
C S
}
(4.2)
This allows the evaluation of the intergate capacitance as:
C Mes = N PIX ×
(
2 × C IG + 1 )
2 C S
(4.3)
Which is exactly equivalent to considering the CPC as being simply composed of N independent
pixels, fig. 4.4(a), but with a doubled intergate capacitance component. This is
due to the fact that between each pixel there is an additional gate and hence an additional
C IG in parallel. In terms of measurable quantities the total contribution of the intergate
capacitance C IG,Tot to the CPC2 is:
C IG,Tot = C Mes − 1 4 C Sub (4.4)
where C Mes was measured by applying a sinusoidal potential with RMS Voltage of 1V between
V A and V B ; the V Ref was instead varied, but always kept above 10V where the buried
channel is completely depleted. In this region there should be almost no dependence of C Mes
on V Ref . In fact to first order C IG does not depend on V Ref ; any dependence derives only
from the edge effect caused by the change in the depletion distance below the gates, which
at V Ref = 10 is essentially fixed. The measurements performed are summarized in table 4.1;
all measurements having an error of 0.5nF.
Intergate Capacitance
V Ref 11 V 12 V 13 V 14 V 15 V
C Mes 25.7 nF 24.9 nF 24.7 nF 24.6 nF 24.5 nF
Table 4.1: Measured intergate capacitance at different V Ref levels.

4.1 CPC2 Capacitance Characterization 47
A graph of the capacitance measurements after they have been renormalized with respect
to the gate overlap length can be seen in in fig. 4.8. Clearly some dependence on V Ref can
be seen, but this is of the order of a percent once the 11V point is discounted.
4.1.3 Finite Element Model of CPC2 Capacitance
In order to confirm that we correctly understand the capacitance of the CPC2 imaging area
a finite element model of a single pixel was generated (see fig. 4.6) inside the Finite Element
Method Magnetics (FEMM) software [46]. The C IG and C S capacitances have then been
estimated and compared to the ones previously measured.
Figure 4.6: Geometrical model used in the FEMM software to represent a single CPC2 pixel.
The presented structure is for the C IG calculations. In the calculations for C S the potential
is applied across the depleted region and both gates are at the same voltage.
To a first approximation the modelling of the intergate capacitance is simple; all one
needs to know is the specifics of the CPC2 geometry and assume that it is operated in a
regime where the buried channel is fully depleted. Differently certain assumptions must be
made for the C S modelling. It is in fact impossible to know the depletion depths under
the gates directly. One measurement point has therefore been used to determine the total
depletion depth at saturation; under the assumption of an infinite parallel plate capacitor.
Subsequently all the non saturated depletion depths have been calculated by using the relationship
x d ∝ √ V Ref ,where x d is the depleted depth. In order to compare the results both
the measured and the modelled values have been converted into units of nF/cm 2 instead of
being expressed as capacitances of the whole sensor. As previously mentioned the imaging
area of the CPC2-40 sensor is 1.5 cm × 5.28 cm; so all that this conversion implies for the

4.1 CPC2 Capacitance Characterization 48
measured data is the division by the constant value of 7.92 cm 2 . If one would then like to
quote the capacitance in terms of the length of the gate overlaps one needs to know that
there are 10 m of gate overlap in each square centimetre of imaging area.
Csub(nF/cm^2)
3.4 FEMM Model
3.2
Data
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 2 4 6 8 10 12 14 16
Vref (V)
Figure 4.7: Modelled (red curve) and measured (black data points) substrate capacitance
normalized to an area of 1 cm 2 plotted vs. the applied V Ref .
It can be immediately seen in fig. 4.7 that the modelled and measured C S agree very well;
the only exception being at V Ref < 3V . Because of the small depletion region this area is the
most vulnerable to idiosyncratic features of the CPC2 that have not been included in the
simple geometrical model. It therefore seems to validate the previously explained theory that
the actual depletion depth is deeper than the one calculated and that a partial capacitance
contribution does derive from the fixed capacitance to these un-modelled features. The
regime at V Ref < 3 V is the most difficult to model. On the other hand it is also the one
least interesting for the running of the CPC2.
Slightly different is the situation for the intergate capacitance. Although the model and
the data agree in predicting an essentially flat capacitance in the depleted buried channel
regime, the only one here analysed, there is a 20%-25% disagreement in the actual value (fig.
4.8). The model predicts a capacitance of 2.24 nF/cm 2 while the calculated C IG is of 2.74
± 0.08 nF/cm 2 .
It is then possible to decompose the C PIX capacitance as presented in equation 4.1. Since
the voltage is driven across the gates, C PIX will follow the same circuit diagram described

4.1 CPC2 Capacitance Characterization 49
3.0
FEMM Model
Data
2.5
2.0
Cig(nF/cm^2)
1.5
1.0
0.5
0.0
11 12 13 14 15
Vref (V)
Figure 4.8: Comparison of the modelled (red curve) and measured (black data points) intergate
capacitance normalized to an area of 1 cm 2 plotted vs. the applied V Ref .
in fig. 4.4(b). Hence for the purposes of driving the CPC2 C PIX is equal to C Mes (once
both have been normalized to the same area) as defined in equation 4.1 and equation 4.2
respectively. Additionally C IG as expressed in eq. 4.3 can be decomposed into the part
modelled with the FEMM software and a part that we hypothesize being due to the presence
of additional CPC2 features. Once this is done it is easy to see how C PIX = 3.11 ± 0.05
nF/cm 2 of which 0.39 ± 0.02 nF/cm 2 derives from the C S , 2.24 ± 0.08 nF/cm 2 derives from
C IG and was modelled in FEMM, 0.48 ± 0.09 nF/cm 2 is the C IG contribution not modelled
by FEMM and most likely associated to the coupling of the gate to other elements of the
CPC that have not been modelled. These are the channel stops that occupy roughly a third
of the area and the ion implants needed for the two phase running, but also the shape of
the intergate region. In fact while we have modelled the gates as regular parallelepipeds, in
reality they always have irregular edges that are often substantially higher than the rest of
the gate. A more realistic model can be seen in 4.9. No attempt was performed to model
this effect because the precise geometry of both gates would have to be known.
The effect of channel stops and ion implants is not easily evaluated. Their presence
reduces the edge effect of the intergate capacitance and hence has a, relatively small, negative
effect on the intergate capacitance. However their coupling to each other might also add an
additional capacitance in parallel to the intergate capacitance and hence add to the total
measured capacitance. The effect due to the presence of irregular gate edges, expected to

4.2 CPC2 Capacitance Test Structures 50
Figure 4.9: Sketch of realistic intergate region: pink is polysilicon, light pink is depleted
silicon, red is silicon oxide and yellow is nitride.
be significantly larger, would instead increase the area and therefore proportionally increase
the intergate capacitance. Already a height variation of ≈ 0.1 µ would explain the seen
discrepancy. The discrepancy can also depend on the way that the C PIX was modelled or
on external parasitic capacitances.
In any event the most important conclusion of this study is that the capacitance is
mainly driven by the intergate contribution. Any effort to substantially decrease the power
consumption of the CPC will therefore start by addressing this area. The FEMM software
was used to do just that. Three separate parameters to which the C IG is expected to be
most sensitive have been identified and the behaviour of the capacitance while their values
are varied was analysed. It has therefore been seen that the thickness of the nitride layer
has only a small influence on the capacitance (fig. 4.10(c)). A bit more significant is the
capacitance relation with the thickness of the oxide (fig. 4.10(b)). Ultimately however the
C IG depends strongly only on the gap between subsequent gates; fig. 4.10(a).
4.2 CPC2 Capacitance Test Structures
Once the FEMM modelling results have been analysed it was decided to produce small test
structures, as seen in fig. 4.11, in order to study further the dependence of the intergate

4.2 CPC2 Capacitance Test Structures 51
Cig(nF/cm^2)
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Gap between neighbouring gates ( m)
FEMM Model
Currently used value
Cig(nF/cm^2)
2.35
2.30
2.25
2.20
2.15
2.10
FEMM Model
Currently used value
2.05
0.00 0.05 0.10 0.15 0.20 0.25
Thickness of oxide layer ( m)
(a)
(b)
2.27
FEMM Model
Currently used value
2.26
Cig(nF/cm^2)
2.25
2.24
2.23
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Thickness of nitride layer ( m)
(c)
Figure 4.10: Study of the intergate capacitance a) FEMM study of C IG vs. gap between two
adjacent gates. b) FEMM study of C IG vs. thickness of the oxide layer present under the
gates. c) FEMM study of C IG vs. thickness of the nitride layer present under the gates. In
all figures the currently used parameter values are highlighted by a black data point.
capacitance on the gap/overlap between the gates. Ideally these test structures should
reproduce the CPC2 as closely as possible and therefore have a buried channel. However due
to some production issues at e2V this has not been the case. The delivered test structures
are in fact an array of gates on field oxide and highly doped p + silicon. The substrate
therefore cannot be depleted. Therefore in all of the following measurements the edge effect
of the intergate capacitance was underestimated since there was no layer of depleted silicon
present underneath the gates. Never the less there is a lot of useful information that can
be deduced from studying the test structures. The test structures that have been produced
have 4 different polysilicon layers, P0, P1, P2 and P3 acting as conducting material. In
the production process flow first the P0 layer will be placed on the oxide, followed by a

4.2 CPC2 Capacitance Test Structures 52
layer of oxide, and then P1 will be placed followed by a layer of oxide, and so on. This
means that different polysilicon layers are separated by different thicknesses of oxide. It
also means that upper and lower gates, as in fig. 4.12, are produced from different layers
of polysilicon. A thin layer of oxide is applied not only below but also around the gates
produced with the lowest layer of polysilicon (the overlapped gates). This oxide layer was
estimated to be approximately 0.5 µm. In all the future work the capacitance structures
will be labelled according to the gate overlap (a negative value representing a gap) as in fig.
4.12(a), fig.4.12(b) and the layers of polysilicon used for creating the gates.
Figure 4.11: Picture of a test structure taken while a measurement is being performed on
the probe station.
(a)
(b)
Figure 4.12: Schematic representation of the test structures for: a) negative overlap values;
b) positive overlap values.
In the first instance the intergate capacitance was to be analysed. The same mathematical
and circuit considerations as the ones presented in the previous sections were used. It has
to be however noted that the approximation that the substrate capacitances are the same

4.2 CPC2 Capacitance Test Structures 53
under both gates has been dropped. The assumption that the CPC2 can be modelled as
N independent pixels with double intergate capacity has however still been used, as it was
explained when interpreting eq. 4.2. The measurement performed and the equation relating
them to the individual capacitance components are therefore:
C A−B = N PIX ×
C A−C = N PIX ×
C B−C = N PIX ×
(
(
(
2 × C IG +
C S1 +
C S2 +
)
1
1
C S1
+ 1
C S2
)
1
1
2×C IG
+ 1
C S2
)
1
1
2×C IG
+ 1
C S1
(4.5)
where C A−B is the measurement between voltage points A and B in fig. 4.4(a) and C S1
and C S2 are the substrate capacitance below gates one and two. While using this method it
was discovered that by placing the test structure directly onto the probe station the results
for C IG become negative due to the parasitic coupling to the metal probe base which has
not been included in the model. In order to confirm this different thicknesses of insulating
material have been inserted between the test structure and the base of the probe station.
Given the formula: C = ǫ r ǫ 0 A/d this should substantially decrease the parasitic capacitance
as confirmed by fig. 4.13. The effect of the coupling is negligible for large separations
between the base and the test structure; corresponding to small values of ǫ r /d. All further
measurements have been conducted using a large enough separation.
In order to understand further the capacitance behaviour of the test structures the substrate
capacitance was analysed (fig. 4.14). As it is clear from the results the lower and
upper gates have a significantly different substrate capacitance. It has subsequently been
found that the reason is due to different gate areas. With the increase or decrease of the
overlap the gate area of the lower gates is kept constant while the gate area of the upper
gates is increased/decreased. It is hence expected that, as it can be seen in the graph, the
upper gates will have lower capacitances at negative overlaps. Because of the increase in
oxide thickness in between the gates one would expect that even at similar gate areas the
upper gates should still have slightly lower capacitances. This effect is however obscured by

4.2 CPC2 Capacitance Test Structures 54
0
Cig
-2
-4
Cig (pF)
-6
-8
-10
-12
0.1 1 10
epsilon/distance(1/mm)
Figure 4.13: The dependence of the C IG capacitance measurement on the insulation from
the test probe stand.
16
15
14
Csub (pF)
13
12
Total substrate capacitance lower gates
Total substrate capacitance upper gates
11
-2 -1 0 1 2 3
Overlap ( m)
Figure 4.14: The substrate capacitances ot the lower gates and upper gates for the p3onp0
structures.
the fact that the oxide layer between the gates counts towards the area of the lower gates;
hence at nominally equal areas the lower gates are actually slightly smaller. Assuming no effect
from the different oxide thickness it is now possible to roughly calculate the thickness of
the oxide coating of the lower gates. This is, to a rough approximation, the point where the
curves of the lower and the upper gates intersect. The thickness has hence been estimated
to be approximately 0.5 µm in agreement with the factory data sheet.
In order to better understand the influence of different layer selections on the substrate
capacitance the value for each polysilicon combination and for each overlap was plotted for
the lower gates in fig. 4.15(a) and for the upper gates in fig. 4.15(b).

4.2 CPC2 Capacitance Test Structures 55
18
17
16
P3onP0
P2onP1
P2onP0
P3onP1
P3onP2
18
17
16
P3onP0
P2onP1
P2onP0
P3onP1
P3onP2
15
15
Csub (pF)
14
13
Csub (pF)
14
13
12
12
11
11
10
-2 0 2 4
Overlap ( m)
10
-2 0 2 4
Overlap ( m)
(a)
(b)
Figure 4.15: The total calculated substrate capacitances for the lower gates a) and upper
gates b) in all the available test structures. All data points have uncertainties of 0.3 pF.
Although the differences between the various manufacturing processes are small, between
0.1 and 1.1pF, many are still significant when compared to our experimental error of 0.3 pF
and an analysis is therefore possible. Starting from the lower gate (fig. 4.15(a)) it can
immediately be seen how the bigger the difference between polysilicon layer numbers the
smaller is the substrate capacitance. Hence the P3onP0 sample is the one with the smallest
capacitance. Differently the largest capacitance is obtained from the P3onP2 layer. These
results suggest that the increased oxide thickness of the different production methods are
only present in between the polysilicon layers. In the areas where the polysilicon is not
present no additional layer of oxide seems to be added. If this was not the case C S,Lower
should be minimal when the value of the lower gate is maximal.
Interesting enough for the upper gates, described in fig. 4.15(a), the pattern is reversed
with P3onP0 now having the highest capacitance and P3onP2 the lowest. Once again the
results suggest that the additional layer of oxides are deposited only in between polysilicon
layers. If this were not the case the capacitance should be minimized when the value of the
upper gate is greatest. Given the extremely small differences between the C S of different
manufacturing methods it is difficult to pinpoint the precise reason behind them. Tiny
variations of the area or the shape of the gate can indeed account for the seen results.

4.2 CPC2 Capacitance Test Structures 56
Finally if one considers the sum of the capacitiance of the upper and lower gates one
reaches a rather unsurprising conclusion: the different manufacturing processes do not substantially
change the total substrate capacitances. If a pattern can be inferred it is very
minimal. In fact if the capacitances of both gates are added together all the points with
overlap values of 0 or above are within 0.4 pF or 3% from each other which is actually
also our experimental error. Therefore the total substrate capacitance of the test structures
seems to depend almost exclusively on the total area in contact with the oxide layer present
below the gates.
It is now possible to perform the main task of the analysis and measure C IG . This was
done with two methods: the one already presented and by shorting the substrate voltage
to the virtual ground of the Hewlett-Packard LCR 4284A. In this case the capacitance
across the gates, C IG , is directly measured and there is no model dependence in the final
results. The results of the exercise can be seen in fig. 4.16(a), which shows that the two
methods yield similar yet slightly different capacitance values. In general the method that
does not ground the substrate underestimates the total capacitance by 0.6 pF. This shift
is constant and independent on the overlap. Incidentally the consistency of the results also
validates the method used in performing the measurements on the actual CPC2. The most
probable reason hypothesized for this shift is in fact the presence of some residual parasitic
capacitance. Because of the symmetry of the substrate calculation in eq. 4.5 we expect
a similar constant shift to be present also for the previously presented substrate results.
A similar correction to the absolute values of the measured capacitance should therefore
be applied. This is however not the aim of the analysis, which is focused on the study
of intergate capacitance and aims to understand the substrate capacitance only as a tool
for understanding the intergate component. The substrate capacitance is in fact a smaller
component of the total load capacitance which determines the clock driving conditions.
Fig. 4.16(b) presents the final results of this analysis as it shows the C IG dependence
on the gate production method and on the gate overlap with the shorted substrate method
being used. Both are shown to behave as expected; in fact the capacitance increases with the

4.2 CPC2 Capacitance Test Structures 57
Capacitance (pF)
10
8
6
4
2
0
Cig - With Shorted Substrate
Cig - Using Calculation Method
-2 -1 0 1 2
Overlap ( m)
Capacitance / Overlap (pF/cm)
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
p3onp0
p3onp2
p2onp0
p3onp1
p2onp1
-2 -1 0 1 2 3
Overlap ( m)
(a)
(b)
Figure 4.16: The intergate capacitance of the test structures: a) for the p3onp0 test structures
by using both the shorted substrate and the calculated method; b) only the shorted
substrate method is used but the results are presented in the form of pF/cm of overlap for
all the test structures. The errors in plot b) are 0.05 pF/cm for all the data points.
overlap and decreases with the gap between the polysilicon layers used. Also as expected the
difference between the different polysilicon arrangements is minimal at small gate overlaps
and it becomes substantial once they become positive. Ideally one would like to compare
these values to the ones measured and simulated in the previous sections and because of this
reason the results are quoted in pF per centimetre of gate overlap; there are 4.8706 cm of
overlap in each test structure. It can be immediately seen that all the test structures predict
a significantly smaller C IG for similar overlap values. The capacitance measured in the test
structures is in the region of 1 pF/cm of gate overlap while in the actual CPC2 sensor
the comparable value is 2.7pF/cm of gate overlap. This is not very surprizing given the
previously mentioned observation that the test structure geometry is substantially different
from the imaging area of the CPC2. The explanation comes mainly from the mentioned
reduced edge effect due to the lack of depleted substrate, which is very significant when the
depletion region is very small or as in this case non existent. In fact by using the FEMM
software one finds out that the C IG of the CPC2 without any depletion is 0.9 pF/cm of gate
overlap. A result consistent with the one measured in the test capacitance structures. We
have therefore been able to characterized the relative behaviour of the CPC2 capacitance
when the gate overlap and the used polysilicon layers are varied.

4.3 CPC2 Readout and Noise Analysis 58
4.3 CPC2 Readout and Noise Analysis
In addition to the CPC2 capacitance characterization a separate analysis has been performed
in order to determine the noise performance of the sensor. The aim of this project was to
develop an experimental set-up together with the associated software for the use of future
studies and to concurrently analyse the noise sources. The initial hardware set-up used is
described in fig. 4.17.
Figure 4.17: Schematic representation of the experimental set-up used in the following noise
analysis
In this configurations the two power supplies provide the necessary bias voltages for the
CPC2 to run; a schematic of the role of these voltages as well as their values can be found in
Appendix A. The function generator acts as an input to the BVM2 module which produces
all the clock and trigger timing sequences for the CPC2 and when the ADC is in an external
triggering mode also for the ADC (not drawn). A separate pulse generator is used for the
Reset Gate (RG) in order to provide a fast signal with a well defined timing. The RG resets
the output node to the default state after every readout and has a large influence on the
achievable noise performance. The output signal of the CPC2 is diverted via a low-pass
filter and an amplifier before reaching the ADC. The ADC is triggered and clocked from
the BVM2 and it can record amplitudes for up to four columns in parallel with a maximum

4.3 CPC2 Readout and Noise Analysis 59
frequency of 100 MHz. In order to visually monitor the output the channels can also be
directed to an oscilloscope. An example of the oscilloscope display can be seen in fig. 4.18.
In order to prove that the sensor is capable of acting as a particle detector and also for
the calibration of the ADC output units a radioactive source ( 55 Fe) was used. The iron
isotope decays to manganese via the absorption of an electron in the innermost K shell. In
this process an electron from the outer shells L or M falls inwards to replace the absorbed
electrons and emits a photon of 5.89 keV (L shell-K α ) or 6.49 keV (M shell-K β ). The X-rays
can then travel through the silicon detector and can interact through a photoelectric process.
If this happens the signal is generated via the production of electron-hole pairs. Charge is
therefore collected in the well structure of the gate potential. Given that in silicon it takes
3.6 eV for each created electron-positron pair the signal is equivalent to 1620 electrons for
K α decays and to 1778 electrons for the seven times less frequent K β decays [41]. X-rays of
different energies are also possible, but much less likely. Assuming that the two peaks cannot
be resolved the average iron radioactive decay is expected to produce a signal of 1640 e − in
the potential wells of the CPC2. By detecting the peak of the iron decay it is hence possible
to calibrate the detector and to estimate the noise of the detector in terms of electrons.
Figure 4.18: Oscilloscope picture of the CPC2 readout showing a series of pixels. The picture
displayed shows the status of the pixels intgrated over time, each pixel is hence sampled
multiple times. The wide bands are hence the noise of the sensor. The lines directly below
them are instead the signal from the 55 Fe.
Having discussed the hardware set-up it is important to briefly comment on the readout

4.3 CPC2 Readout and Noise Analysis 60
sequencing and software. It should be mentioned that the CPC2 is not read out constantly,
instead an integration time t int is allowed between the sequences to accumulate events with
55 Fe interactions or to integrate some leakage current. In the active readout period the CPC2
is clocked at the desired frequency and the output node is reset at the beginning of every
clock cycle. The control software for the BVM2 Module, the biases, the low pass filter and
the amplifier was developed. Additionally an on-line monitoring tool that is an integral part
of the ADC control program has been coded. The user interface can be seen in fig. 4.19.
At the bottom of the screen the raw data collected in the current run is displayed. Here
the noise peak (on the left) and the 55 Fe calibration peak (on the right) can be clearly seen.
Both peaks are then automatically fitted with a Gaussian. The parameters of both Gaussian
fit are shown at the top left. These parameters are then used to calculate the noise in terms
of electrons which is displayed on the top right graph.
Figure 4.19: The user interface of the on-line noise monitoring tool.
The first measurements performed were aimed at analysing the dependence of the noise
on the time over which the 55 Fe signal is integrated between readouts and on the clock
frequency. If the noise is dominated by dark current due to production of electron-hole pairs

4.3 CPC2 Readout and Noise Analysis 61
from thermal excitation, then a clear dependence on the integration time should be seen:
σ ≈ √ N = √ I × t int /e (4.6)
where N is the number of electron collected during the integration time t int , e is the electron
charge and I is the dark current. If instead the noise is dominated by a clock feed-through
effect then the noise should increase with the increase of the clock frequency. The effect in
fact arises from the capacitive coupling of the clock distributive network with the imaging
area. The higher the clock frequency the larger is the current passing through the clock and
the sharper is the clock rising time, resulting in a higher noise from the feed-through effect.
The clock network capacitative coupling can change substantially the charge stored in the
immaging area and therefore alter the signal. A fixed pattern noise term can derive from
the different strenght of the coupling to different pixels, due to the topology of the clock
network. A higher frequencies slight time variations in the clock periods, clock jitter, also
induce a significant source of noise due to the clock capacitative coupling. However the noise
was found to be ≈ 280 electrons at room temperature and independent of the integration
time or the clock frequency, disproving both hypotheses (fig. 4.20). It was decided to check
the experimental set-up external to the chip and motherboard for possible noise sources.
300
Noise (e - )
280
260
240
220
Original (34C)
Original (-13C)
Keithley (-13C)
Agilent (-13C)
Agilent (34C)
200
180
0 100 200 300 400 500
Integration Time (ms)
Figure 4.20: The calculated noise of the CPC2 is presented for different power supplies at
different temperatures and integration times. All data points to be regarded as having an
error of ± 3 electrons.
It has been hence discovered that the power supply used was delivering an unstable

4.3 CPC2 Readout and Noise Analysis 62
voltage and was therefore a major source of noise. In order to eliminate this effect and start
studying the intrinsic noise of the CPC2 a new power supply was used; the Oxford designed
ad-hoc supply was replaced with the Agilent N6700B. Fig. 4.20 shows the result of the
study performed regarding the effect of different power supplies on the measured CPC noise.
In this way the noise was reduced to ≈ 180 electrons. However a clear dependence on the
integration time still cannot be seen.
It was found that the noise was in fact dominated by its reset component. Since the
output node is reset after every cycle the reference level varies slightly for each pixel which
translates into a source of noise. The common way of dispensing with the reset noise is to
implement a correlated double sampling algorithm. In such algorithm, instead of reading
out the absolute value of the signal, the voltage difference between the reference level, before
the charge has been transferred to the output node, and the signal level, after the charge
has been transferred to the output node, is taken. Since the node is not reset in between the
two measurements the two levels should have exactly the same contribution from the reset
noise. The noise is hence cancelled by the algorithm. Fig. 4.21 shows the user interface of
the implemented correlated double sampling algorithm. On the top right the full readout
of the CPC is presented. On the bottom a zoom of only two clock cycles is shown. On
each cycle the reset signal can be seen (the high spike). The reference level is then the
following plateau, the signal level is the lower flat plateau. In the implemented correlated
double sampling the value of the signal between the blue square and the yellow square is
averaged and subtracted from the average value between the red and the green box. The
exact location of the squares can be determined by using the controls on the top left of the
user interface.
The noise performance was greatly improved after these amendments to the set up and
therefore the dependence of the noise on the integration time and the temperature has been
re-examined. While the behaviour of the dark current with respect to the integration time
has already been explained, the behaviour with respect to the temperature still needs to
be addressed. The theory states that with a higher temperature the number of electron-

4.3 CPC2 Readout and Noise Analysis 63
Figure 4.21: The user interface of the correlated double sampling program. The program
calculates the average between a number of user defined points in the reference and the
signal levels and then calculates the difference between these two averages. On the picture
the points between which the averaging is performed are graphically represented by the red
and green dots for the reference level and the blue and yellow dots for the signal level.
hole pairs present at thermal equilibrium increases and with it the resulting dark current
generated noise. More specifically the dark current relationship is [41]:
I ∝ T 3/2 e −Eg/kT (4.7)
where I is the dark current expressed in electrons per second, T is the temperature, E g is
the silicon band gap and k is the Boltzmann constant. Fig. 4.22 shows the results of a study
of the noise dependence on the temperature and the integration time.
It can be immediately seen that above the temperature of 0 ◦ C the noise increases with
the temperature and with the integration time. This is a good indication that most external
noise sources have been eliminated and that the main source of noise is the dark current. The
best level of measured noise, achieved at room temperature and with very short integration

4.3 CPC2 Readout and Noise Analysis 64
Noise (e - )
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
3ms
12ms
24ms
48ms
-10 0 10 20 30 40
Temperature C
Figure 4.22: The CPC noise is displayed for the new improved set-up. The noise is displayed
vs. the temperature of the motherboard and for different integration times. It has to be
noted that the temperature of the motherboard is only a rough indication of the temperature
of the CCD. All the data is taken with a clock frequency of 0.375 MHz.
times, decreased to 70 ± 3 e − , from the previously presented ≈ 280e − . Incidentally this level
of noise can be also achieved by decreasing the temperature and prolonging the integration
time. The similarity with the result of ∼ 65 e − noise that has been achieved at the Rutherford
Laboratory with a different set-up, but using the same sensor, also seems to confirm that all
major sources of external noise deriving from the hardware and software set-up have been
eliminated [47]. Of course some element of set-up noise is inevitable. The remaining noise is
therefore constant and mainly intrinsic in the CPC2 design. This is expected to be deriving
primarily from the ultimately unavoidable thermal (kTC) noise generated by the thermal
agitation of the charge carriers. This is in particular significant in the readout stages; in
the first stage of internal amplification in the CPC2 (of the order of a few tens of electrons)
and also from the motherboard on which the CPC2 is placed. Both of these have been
investigated later in different studies and the noise was further reduced to ∼ 50 e − . The set
up of the software and hardware for future experiment and its debugging by the use of the
simple noise study has hence been successfully completed. In fact the experimental set up
has since been used for many different measurements and also for different applications [48].

4.4 Summary 65
4.4 Summary
The first part of this chapter described a study of the CPC2 sensor capacitance, the final
aim being the minimization of the clock current needed to operate the sensor; currently 10 A
for a 10 cm 2 sensor. The sensor capacitance has been found to be 3.11 ± 0.05 nF/cm 2 . The
main contribution has been found to come from the intergate capacitance which accounts
for 87% of the total pixel capacitance. Subsequently a series of different designs have been
investigated with the help of finite element modelling and of test structures.
The chapter also described the experimental set-up developed for the testing of the CPC2
sensor. A brief description has been given of the the hardware set-up as well as of the software
data aquisition. Finally a short study of the CPC2 noise has been performed. The noise of
the sensor has been measured as 70 e − .

Chapter 5
The LCFI Vertex Flavour Tagging
Software
As has been already mentioned the role of the vertex detector is to facilitate the finding
of vertices and therefore also to provide crucial information for tagging the flavour of the
original quarks that initiated the reconstructed jets. However, as is the case with any
tracking particle detector, all it actually outputs is the location of the interaction with a
candidate particle. It is up to the software to reconstruct the event. The first task, for the
tracking software, is to produce a list of tracks. Tracks are then merged into jets by the jet
clustering. These jets are the inputs to the vertexing software, which tries to determine if
and how many displaced vertices are present in the reconstructed jets. A primary vertex,
deriving from the e + e − interaction is always present in any event and is event specific, this
is where all jets originate. All further reconstructed vertices are jet specific; these vertices
are called secondary. There are a series of possible reasons behind the creation of secondary
vertices. They can originate from the material interaction of the particles passing through
the detector, they can originate from γ → e + e − processes, they can originate from τ leptons,
they can originate from decaying K S /Λ or they can originate from decaying heavy b and
c quarks, fig. 5. The aim of the flavour tagging software is to identify the later two cases.
It therefore aims to separate jets originated from b quarks from jets created from c quarks
66

5.1 Track Selection 67
from all other light jets. The issue of the contamination from the τ originated jets has not
been directly dealt with in the present software.
Figure 5.1: Schematic showing the creation of secondary and tertiary displaced vertices in
the case of a B meson decay.
In general the software described below deals with separating the c and b quarks from the
uds quarks; c and uds quarks are therefore considered as a background when the b tagging
is performed, while b and uds quarks are used as a background when c tagging is performed.
A separate algorithm that aims at eliminating the tracks from all the K S /Λ and photon
conversions a priori has also been implemented. All the plots presented in this chapter have
been tested on the LDC/ILD framework and use the LDCPrime 02Sc detector model. The
data sample used is 10000 e + e − → Z/γ → q¯q events and unless differently stated they are
at a center of mass energy of 91.2 GeV. An equivalent sample with a centre of mass energy
of 500 GeV has also been used. In both cases the final quark states represent the natural
production at the corresponding energies. The events have been processed as described in
the simulation chapter and forced into a dijet topology at jet clustering level.
Please note that this chapter is derived from a paper published by the LCFI Collaboration
[49], to which the author of the thesis has made major contributions.
5.1 Track Selection
The first step in the process is to remove all the spurious tracks and all tracks deriving from
photon conversions and from K S /Λ decays. Initially all two-track combinations present in

5.1 Track Selection 68
the whole event are considered. The two track combination is considered as a K S /Λ decay
or photon conversion if it passes all of the following criteria:
• The tracks must have opposite charge sign.
• The distance of closest approach between the two track helices must not exceed 1 mm.
• The distance between the point of closest approach and the interaction point (IP) must
be larger than 1 mm in order to reduce the risk of fake tags consisting of combinations
of primary vertex tracks.
• The invariant mass of the two track combination has to be compatible with that of the
K S ,Λ or the photon.
To check the mass compatibility, the rest mass of the combination is calculated using
three mass hypotheses, choosing the masses of the decay products accordingly: both tracks
are assumed to be electrons in the case of conversions, or pions for the K S hypothesis; for the
Λ hypothesis the track with larger momentum is assigned the proton mass and the other the
pion mass. The resulting rest mass of the combination is considered to be compatible with
the hypothesis if it differs from the PDG value [8] by not more than 5 MeV for conversions
and kaons and by not more than 2 MeV for Lambdas. The efficiencies of the devised
procedure are 25%, 72% and 70% for the photon conversion, the K S and Λ respectively. The
equivalent fake rates are 4%, 33% and 38%. The increased performance from the usage of
this additional preliminary track selection algorithm will be analysed in the result section at
the end of this chapter.
All objects that are not identified as stemming from the above sources are passed on
to the track selection processor preceding the subsequent steps such as vertex finding and
flavour tagging. In order to eliminate the presence of spurious tracks a set of cuts has also
been developed. These tracks can be tuned independently for the various sections of the
flavour tagging software. It is therefore possible to implement a set of cuts while fitting the
interaction point, a completely different set when searching for secondary vertices and yet a

5.2 The ZVRES Vertex Finding Algorithm 69
different one when calculating the flavour discriminating variables. In order to calculate the
optimal cut values an extensive optimization analysis has been performed. Different values
for cut parameters have been implemented and compared by looking at their flavour tagging
performance; cross correlation between parameters has however not been considered in order
to reduce the number of required iterations. The values used in the presented analysis are
shown in table 5.1. Please note that this table only presents the track selection parameters.
A detailed list of all remaining parameters of the LCFI Vertex software can be found in
Appendix B.
Track Selection Parameters
Parameter ≷ IP Fit Vertexing Flavour Tagging
χ 2 / ndf of track fit < 5 4 -
R − φ impact parameter d 0 (mm) < 20 2 20
R − z impact parameter z 0 (mm) < 20 5 20
d 0 uncertainty (mm) < - 0.007 -
z 0 uncertainty (mm) < - 0.025 -
track p T (GeV) > 0.1 0.2 0.1
Table 5.1: Track selection parameters for all the LCFI Vertex algorithms. Please note that
in the case of flavour tagging the presented track selections are only the ones applied to the
whole process. Additional track selection procedures can apply for specific discriminatory
variables.
5.2 The ZVRES Vertex Finding Algorithm
The ZVTOP vertex finder, developed at the SLD experiment [50], provides two complementary
algorithms which use topological information to identify track combinations that are
likely to have their origin at a common vertex. The first of these, the ZVRES algorithm, can
be used to find multi-pronged secondary vertices with an arbitrary geometrical distribution
and hence is most generally applicable, provided the detector system has a sufficiently high
spatial resolution. The second algorithm, ZVKIN, has a more specialistic function and aims
to address the case of one prong vertices originating from decays with only one charged track.
Both algorithms have been completely re-coded and re-developed inside the ILC software
framework by the LCFI collaboration [49].

5.2 The ZVRES Vertex Finding Algorithm 70
Since only the ZVRES algorithm has been used throughout the presented thesis this is
the only one described here. A description of the ZVKIN algorithm can be found in [49, 51].
The central idea of the ZVRES algorithm is to describe each track i by a probability density
function f i (⃗r) in three-dimensional space and to use these to define a vertex function V (⃗r)
that yields higher values in the vicinity of true vertex locations and lower values elsewhere,
as well as providing a criterion for when two vertex candidates are resolved from each other.
The track functions have a Gaussian profile in the plane normal to the trajectory. With
⃗p the point of closest approach of the track i to the space point ⃗r, the track function f i (⃗r) is
defined as:
{
f i (⃗r) = exp − 1 }
(⃗r − ⃗p)V−1 i (⃗r − ⃗p) T
2
(5.1)
where V −1
i
is the inverse of the position covariance matrix of track ⃗p. A graphical representation
of the track functions can be seen in 5.2(a). The vertex function, in its most basic
form, is defined as:
V (⃗r) =
N∑
∑ N
i=1
f i (⃗r) −
f2 i (⃗r)
∑ N
i=1 f i(⃗r)
i=1
(5.2)
with the second term ensuring that V (⃗r) approaches zero in spatial regions in which only
one track contributes significantly to the first term and where hence no vertex should be
found. A graphical representation of the track functions can be seen in 5.2(b).
(a)
(b)
Figure 5.2: A graphical representation of the ZVRES algorithm. In a) the track function
stage can be seen, in b) the vertex function stage is displayed.
Optionally, further knowledge on where vertices are more likely to be found can be used

5.2 The ZVRES Vertex Finding Algorithm 71
to weight the vertex function, thereby suppressing fake vertices and increasing the purity of
the vertices found (i.e. the fraction of correctly assigned tracks). The knowledge of the IP
position can be used to suppress fake vertices from tracks passing close to each other in the
vicinity of the IP. This is accomplished by representing the IP by a contribution:
{
f 0 (⃗r) = exp − 1 }
(⃗r − ⃗p)V−1
IP
2 (⃗r − ⃗p)T
(5.3)
where ⃗p is now the position of the IP and V IP is its covariance matrix. With this inclusion
the vertex function becomes:
V (⃗r) = w IP f 0 (⃗r) +
N∑
i=1
f i (⃗r) − w0 IP f 0(⃗r) + ∑ N
i=1 f2 i (⃗r)
w IP f 0 (⃗r) + ∑ N
i=1 f i(⃗r)
(5.4)
where w IP is a weighting factor. Values of w IP > (

5.2 The ZVRES Vertex Finding Algorithm 72
than at large angle from it, which is taken into account by weighting the vertex function
outside a cylinder of radius 50 µm by:
V ′ (⃗r) = V (⃗r) exp(−kE Jet α 2 ) (5.5)
where k is a user defined parameter and α is the angle formed between the location r and
the edge of this cylinder. Once the vertex function has been calculated it is still important
to define the parameters that will resolve the vertices. In order for two vertices at different
positions to be declared resolved they must satisfy the following condition:
min{V ′ (⃗r) : ⃗r ∈ ⃗r 1 + α(⃗r 2 − ⃗r 1 ), 0 ≤ α ≤ 1}
min{V ′ (⃗r 1 ),V ′ (⃗r 2 )}
< R 0 (5.6)
where V ′ (⃗r 1 ),V ′ (⃗r 2 ) are the values of the vertex function at its local maxima; min{V ′ (⃗r 1 ),V (⃗r 2 )}
is therefore the lower of the two maxima. min{V (⃗r) : ⃗r ∈ ⃗r 1 + α(⃗r 2 − ⃗r 1 ), 0 ≤ α ≤ 1} is the
minimum of the vertex function on the straight line connecting the maxima V ′ (⃗r 1 ),V ′ (⃗r 2 ); R 0
is instead an externally defined parameter. Having defined the mathematical functionality
of ZVRES we can now describe the process algorithmically:
• Initially all track-track and track-IP combinations are fitted. Only fits with χ 2 < χ 0
and that satisfy a minimum value of the vertex function are kept. χ 0 and the minimum
value of the vertex function are user defined parameters.
• Tracks that are associated with two or more vertices are removed from all the vertices
that have V ′ (⃗r V ert ) < V ′ (⃗r MAX ). Where V ′ (⃗r MAX ) is the maximum vertex function of
all the vertices that the track is associated with.
• All the resulting V ′ vertex functions are ordered from the highest to the lowest. The
resolution criterion, equation 5.6, is used to attempt in combining vertices starting
from the one with the highest V ij . The process stops when all remaining vertices are
considered as being resolved.
• Tracks with a high χ 2 contribution are removed from the resulting candidate vertices:

5.2 The ZVRES Vertex Finding Algorithm 73
iteratively, the track with the highest χ 2 contribution is removed if its contribution to
χ 2 is above a threshold χ 2 TRIM . The vertex is then refit.
• If a track is still associated with more than two vertices the ambiguity is solved by
removing it from the vertex with the lowest vertex function maximum.
Throughout this process the vertices that are not associated with at least two tracks (or that
do not represent the IP) are removed. The default parameters of the ZVRES algorithm are
given in Appendix B.
5.2.1 ZVRES Performance
For the purposes of benchmarking a pure e + e − → Z/γ → b¯b sample produced at the centre
of mass energy of 91.2 GeV has been used. The energy has been selected to allow for direct
comparison with earlier studies and because the ILC calibration run will be operated at
this energy. First of all the efficiency of secondary vertex finding has been analysed in fig.
5.3. It can be immediately seen that the vertex finding efficiency is approximately constant
∈(sec. vertex)
1
0.8
0.6
0.4
0.2
0
0 2 4 6 8 10 12 14
Monte Carlo B decay length/mm
Figure 5.3: Efficiency for finding a secondary vertex, for a pure sample of B mesons
for all vertices that are displaced by more than 1 mm at MC level. In total 89% of the
vertices that are displaced by more than 1 mm at MC level are found by the algorithm. It
is clear that at very small decay lengths is it very difficult, if not impossible, to distinguish
the secondary vertex from the IP, hence the visible drop of efficiency. This result can be
compared with the performance of previous detectors and implementations of the ZVRES

5.2 The ZVRES Vertex Finding Algorithm 74
algorithm. In the case of the SLD-VDX3 detector the efficiency was 80% and the plateau of
constant efficiency started only at 2 mm [53]; the vertex finding efficiency for the ILC vertex
detector model is clearly improved. The improvement is mostly due to the larger angular
coverage, better impact parameter resolution and reduced material budget of the proposed
ILC vertex detectors.
Using the same sub-sample of b¯b jets, the reconstructed decay lengths of the B and D
mesons were compared to the corresponding MC decay lengths on a jet-by-jet basis. In
fig. 5.4(a), the B decay length comparison is shown for jets in which at least two vertices
(the primary, or IP vertex, plus at least one secondary vertex) were found. This class of
jets includes cases in which the D meson decayed so close to the B decay vertex that the
D meson generated vertex could not be resolved. For these cases the reconstructed decay
length is shifted to larger values, if compared to the MC B decay length. Short B decay
lengths, where the B meson secondary vertex cannot be resolved, but the D meson generated
one can, also result in reconstructed secondary vertex decay length that are larger than the
MC truth value. In fig. 5.4(b), the decay length of the D meson is compared to the MC
value for jets in which exactly three vertices were reconstructed by ZVRES. As expected for
this category of jets, the correlation between reconstructed and MC values is better. The
efficiencies for the finding of the tertiary vertex is 73%; 972 vertices are reconstructed of the
1331 present at MC level.
In addition to the precision with which the decay lengths can be reconstructed, clearly an
important parameter for many physics studies, also the track content of the reconstructed
vertices has been investigated. For each type of reconstructed vertex: the primary, the secondary
and, if available, the tertiary vertex, the average percentage of tracks that originated
from the corresponding MC decay vertex was determined, yielding the purity of the track
content of each type of vertex. Table 5.2 gives the purities for b jets at centre of mass energies
of 91.2 GeV and, most importantly for this analysis, at 500 GeV. These purities are particularly
important for the following determination of the flavour of the jet and of the charge
of the vertex. The tracks associated to the vertex are widely used for these determinations

5.2 The ZVRES Vertex Finding Algorithm 75
rec. sec. vertex decay length / mm
20
18
16
14
12
10
8
6
4
2
at least 2 ZVTOP vertices found
rec. ter. - sec. vertex decay length / mm
20
18
16
14
12
10
8
6
4
2
exactly 3 ZVTOP vertices found
0
0 2 4 6 8 10 12 14 16 18 20
Monte Carlo B decay length / mm
0
0 2 4 6 8 10 12 14 16 18 20
Monte Carlo D decay length / mm
(a)
(b)
Figure 5.4: Reconstructed decay length vs. MC decay length for: a) B meson decays in b
jets in which at least two vertices have been found, b) D meson decays in b jets with three
vertices. The secondary vertex is defined as the non-primary vertex with the shortest decay
length, distance to the IP, the tertiary vertex is instead the vertex with the second shortest
distance to the IP. The secondary is therefore associated with the B meson decay and the
tertiary is associated with the D meson decay. The case where more than two vertices are
present in the same jet is very rare.
and the mis-association of even a single track can vary the output of the algorithms.
The best assignment of tracks to vertices, corresponding to the highest purities, was
obtained for b jets with three reconstructed vertices. This is understandable given the fact
that if both the bottom and the subsequent charm decay result in multi-prong vertices, the
result is a cleaner topology that can be more easily reconstructed. If a smaller number of
vertices is found in b jets, this can indicate either that one of the decay vertices is onepronged
and thus cannot be found by ZVRES, or that the decay length of one of the heavy
flavour hadrons is so short that its decay vertex cannot be resolved from the preceding vertex
in the decay chain, and that, for example, the secondary vertex found by ZVRES contains
some tracks that actually originated from the D decay and some from the B decay. Both
effects can result in a mis-assignment of tracks by ZVRES and hence to a reduced purity
for vertices in this category. While comparing the results at 91.2GeV and 500GeV one must
bear in mind that the increase of the centre of mass energy results in an increased collimation
of jets as well as in the increased multiplicity of the tracks originated from the IP. As a result

5.3 Flavour Discriminating Variables 76
Monte Carlo Reconstructed track-vertex association
track origin Two vertex case Three vertex case
pri sec iso pri sec ter iso
91.2GeV Primary 91.5 1.4 36.2 95.2 3.1 1.9 49.9
B Decay 6.7 46.7 29.6 3.1 75.3 10.6 22.8
D Decay 1.8 51.9 34.2 1.7 21.6 87.5 27.2
500 GeV Primary 93.7 2.6 35.3 97.4 4.9 4.0 48.5
B Decay 4.6 47.3 29.8 1.8 72.3 13.5 24.5
D Decay 1.7 50.1 34.9 0.8 22.9 82.5 27.0
Table 5.2: Percentages of tracks assigned to the reconstructed primary, secondary and tertiary
vertex and of tracks not associated to any vertex (labelled iso) which originate from
the IP, the B or the D decay at MC level, for b jets.
vertex finding is more challenging. This effect is at least partially counterbalanced by the
increased decay lengths of the hadronic particles due to the increased boost. As it can be
seen the net result is a slightly lower purity in the track assignments when trying to separate
between the secondary and the tertiary vertex.
At last it has to be pointed out that the number of tracks not assigned to any vertex in
the present configuration of the algorithm is very low. For the case of b quark jets in the 91.2
GeV centre of mass simulation this is only 8.0% if the tertiary vertex is reconstructed and
13.9% if only the secondary is reconstructed. For c quark jets these numbers are 7.0% and
7.6% respectively. In the case of the 500 GeV simulation the numbers rise by a percentage
point or two.
5.3 Flavour Discriminating Variables
Once the vertices of the jet have been found it is important to attempt to distinguish between
the jets originated from b, c and light quarks. In order to perform this procedure a series of
discriminating parameters based on the quark proprieties as well as kinematic and topological
considerations are used. The variables presented in this analysis have been used in a previous
study done on the TESLA experiment [54]. Most if not all of them have however been
developed and tested in previous experiments such as ALEPH, OPAL, SLD and DELPHI
[55, 56, 57, 58]. Many of the variables most sensitive to the jet flavour are only defined for

5.3 Flavour Discriminating Variables 77
jets in which non-IP vertices have been found, different procedures are therefore used for jets
containing one vertex and jets containing more than one vertex. This process is ideal also
because the number of vertices already provides a very good indication of the original quark.
In fact in the events where two or more secondary vertices are found at reconstruction level
91.7% of events have been found to be from b quark jets at MC level, 7.7% from c jets at
MC level and the remaining from light jets at MC level. If one secondary vertex has been
found 54.3% of events are from b quarks, 34.4% from c quarks and 11.3% from uds quarks.
In the case that only the primary vertex is found these values are 6.4%, 13.2% and 80.4%.
As usual this study has been done on the 91.2 GeV sample.
It must be also noted that, as the ZVTOP calculation, the flavour algorithm is done on
a jet by jet basis, no information from other jets is therefore used for the determination of
the jet flavour.
5.3.1 Variables for Jets without Secondary Vertices
In the case that only one vertex, the IP vertex, has been found, the input jet is searched
for the two tracks of highest impact parameter significance in the R-φ plane. These are
referred to as the most significant and the second-most significant track in what follows.
For finding these two tracks, separate minimum momentum cuts p trk,NL ,min and p trk,NL −1,min
are applied for tracks with hits on all N L vertex detector layers or with hits on only N L -
1 layers. The momenta |p trk | and the impact parameter significances of these tracks in the
R-φ plane and the R-z plane are used as flavour discriminating variables. A single track of
high impact parameter significance may indicate that the jet under consideration is a charm
jet with the leading D ± having decayed to a single charged track (one-prong decay), which
is expected for ≈ 40% of all D ± decays. The observables obtained from the second most
significant track help distinguish between c and b jets, for which it is more likely that two
tracks of high impact parameter significance are found, typically with one resulting from the
decay of the leading hadron and one from the decay of the charmed hadron produced in that
decay. Fig. 5.5 shows the distributions of the inputs, used for the flavour tagging, for the

5.3 Flavour Discriminating Variables 78
most significant and second-most significant tracks, separately for b, c and light flavour jets.
Please note that the distributions plotted are cumulative; hence the b distribution includes
the plotted c and uds events and the c distribution includes the plotted uds events. The
sample used for the distribution is 10000 e + e − → Z/γ → q¯q events, with natural branching
ratios at 91.2 GeV centre of mass energy.

5.3 Flavour Discriminating Variables 79
N jets
4
10
N jets
4
10
3
10
3
10
2
10
2
10
10
10
1
1
-10 -5 0 5 10 15 20
most signif. trk, d
/σ(d
)
0
0
-10 -5 0 5 10 15 20
2nd most signif. trk, d
/σ(d
)
0
0
(a)
(b)
N jets
N jets
3
10
3
10
2
10
2
10
10
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
most signif. trk, z
/σ(z
)
0
0
1
-10 -8 -6 -4 -2 0 2 4 6 8 10
2nd most signif. trk, z
/σ(z
)
0
0
(c)
(d)
N jets
1000
800
600
N jets
800
700
600
500
b-jets
c-jets
u,d,s-jets
400
400
300
200
200
100
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
most signif. trk, log|p
(e)
trk
| / GeV
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2nd most signif. trk, log|p
(f)
trk
| / GeV
Figure 5.5: Flavour discriminating variables used when only the IP vertex is reconstructed;
based on the most [plots a), c), e)] and second-most [plots b), d), f)] significant track in the
jet. Shown are the impact parameter significance in R-φ in a), b), the impact parameter
significance in R-z in c), d) and the track momentum in e), f).

5.3 Flavour Discriminating Variables 80
Further information is contained in the joint probability for all tracks to originate from
the primary vertex, as introduced by ALEPH [55]. Two joint probability variables are
calculated from the impact parameter significances in R-φ and in R-z of all the tracks in
the jet that pass the specific selection criteria. The distribution f(x) of unsigned impact
parameter significances for tracks originating from the IP is assumed to be known; it can
be determined from the data, as described in the next subsection. The probability of an IP
track having an impact parameter significance of b/σ b or larger is then given by:
P i =
∫ ∞
b/σ b
f(x)dx
∫ ∞
0
f(x)dx . (5.7)
For a set of N tracks the probability,P J , that all N tracks originate from the IP is:
N−1
∑
P J = y
k=0
−ln(y) k
k!
y = Π N−1
i=0 P i (5.8)
y is the product of the N individual track probabilities and P J is the probability that the
product of N random numbers uniformly distributed from 0 to 1 is y or smaller. The joint
probability observable, P J , is calculated for the set of tracks that pass the track selection
cuts described in table 5.1 as well as an upper cut on the impact parameter of 5 mm and
on the impact parameter significance of 200. As mentioned it is calculated separately for
the R-φ and the R-z impact parameter significances. It can be seen from the resulting P J
distributions shown in fig. 5.6(a) and fig. 5.6(b) that light quark jets tend to have values of
P J closer to 1, while the distributions for b and c jets peak at zero.
It can be noted that, given the above definition, the joint probability distribution of all
uds jet should be flat. However this is only true under the condition that the track selection
used for calculating the impact parameter significance distribution and the track selection
used when calculating the joint probability are equivalent. This has not been the case in this
study. The track selections applied are in fact complex and still in the process of being fully
optimized, with the consequence of time consuming recalculation of the impact parameter
distribution being needed every time any parameter has been changed. Instead the impact

5.3 Flavour Discriminating Variables 81
parameter significance distribution has been calculated prior to the track selections and
prior to the K S , Λ and photon conversions. Additionally, for similar reasons, the default IP
value has been used when calculating the impact parameter significance distributions. The
observed distribution is therefore not flat and, as it can be seen in fig. 5.6(a) and fig. 5.6(b),
the probability of quarks originating from the IP is shifted to slightly higher values. However
it is clear from the plotted distributions that the discriminating power of this method is still
present.
N jets
N jets
b-jets
3
10
3
10
c-jets
u,d,s-jets
2
10
2
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
joint probability, R-φ
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
joint probability, R-z
(b)
Figure 5.6: Joint probability for all tracks in the jet passing the track selection cuts to
originate from the primary vertex. This probability is calculated separately from a) the R-φ
impact parameter significances and b) the impact parameter significances in R-z. Please note
that the distributions plotted are cumulative; hence the b distribution includes the plotted c
and uds events and the c distribution includes the plotted uds events. The sample used for
the distribution is 10000 e + e − → Z/γ → q¯q events, with natural branching ratios, at 91.2
GeV centre of mass energy.
Impact Parameter Significance Distribution
It follows from the definition of the joint probability P J , that it depends heavily on the
distribution of impact parameter significances of IP tracks. The function f(x) that approximates
this distribution is determined from the data as follows: for IP tracks, the impact
parameter significance distributions are symmetric. The shape of the distribution of positive
impact parameters, used to find P J , can therefore be determined by fitting the distribution

5.3 Flavour Discriminating Variables 82
of absolute values for tracks with negative impact parameter, corresponding to a very pure
IP track sample. A negative impact parameter is defined as an impact parameter that is in
the opposite hemisphere with respect to the jet direction. The distribution is approximated
by fitting the sum of a Gaussian and two exponentials, i.e. by finding parameters p f0 , . . .,
p f6 such that:
f(x) = p f0 × exp(−0.5( x − p f1
p f2
) 2 ) + p f4 exp(p f3 x) + p f6 exp(p f5 x) (5.9)
best describes the measured distribution. Within this model the integral ∫ ∞
b/σ b
f(x)dx can be
written as:
∫ ∞
b/σ b
f(x)dx ≈
(∫
2
∞
∫ ∞
)
√ × exp (−r 2 )dr −
exp (−r 2 )dr
π (b/σ b )/( √ 2p I0 )
(b/σ b ) √ cut/( 2p I0 )
+(p I1 exp (−p I2 )(b/σ b ) − p I1 exp (−p I2 )(b/σ b ) cut )
+(p I3 exp (−p I4 )(b/σ b ) − p I1 exp (−p I4 )(b/σ b ) cut ) (5.10)
where the integral over the Gaussian and the exponential functions is cut off at (b/σ b ) cut .
These are also the user definable significance cuts that have been mentioned in the previous
section. When defining the parameters the following substitutions are used:
p I0 = p f2
p I1 = − 2 √ π
× p f3 /(p f0 p f2 p f4 )
p I2 = −p f4
p I3 = − 2 √ π
× p f5 /(p f0 p f2 p f6 )
p I4 = −p f6 (5.11)
As it can be seen in these equations the parameter p f1 disappears. The assumption that
the mean of the Gaussian is equal to zero has been applied. This should be a fair assumption
for tracks that originate from the IP. The values calculated for the detector geometry
LDCPrime 02Sc which has been used in this chapter are displayed in table 5.3.

5.3 Flavour Discriminating Variables 83
Joint Probability Resolution Parameters
Parameter R-φ projection R-z projection
p I0 0.843 0.911
p I1 0.365 0.306
p I2 0.620 0.423
p I3 0.150 0.139
p I4 0.029 0.028
Table 5.3: Parameters used in the calculation of the joint probability in R-φ and in R-z,
respectively, obtained from a fit of negative impact parameter distributions.
Fig. 5.7 instead displays the automatically generated visual output that is shown from the
program that calculates the parameters of the impact parameter significance distributions.
The impact parameter distribution can be seen, as well as the Gaussian component of the
fit, for both the d 0 and the z 0 impact parameters. The fit is a preliminary fit, using only a
simple Gaussian, that is used to seed the parameters for the final fit.
(a)
(b)
Figure 5.7: Graphical output of the program fitting the impact parameter distributions.
Both the distribution and the preliminary Gaussian fit can be seen for the: a) d 0 impact
parameter significance and b) z 0 impact parameter significance.
5.3.2 Variables for Jets with Secondary Vertices
In the case that more than one vertex is found, observables derived from these additional
vertices provide more powerful means to distinguish between b, c and light quark jets. The

5.3 Flavour Discriminating Variables 84
following set of eight variables is used in such cases:
• The decay length and decay length significance of the vertex with the largest decay
length significance in three dimensions with respect to the IP;
• The total momentum |p| of the set of tracks assigned to the non-primary vertices after
the track attachment has been performed (see below);
• The p T corrected vertex mass, calculated as described below;
• The number N trk,vtx of tracks in all non-primary vertices;
• The secondary vertex probability of the tracks assigned to the non primary vertices
after the track attachment has been performed: a new vertex fit is performed using
these tracks and the probability that they all originate from the same secondary vertex
is calculated from the fit’s χ 2 ;
• The already described joint probability variables.
In addition to the general track selection used for the calculation of the flavour tag variables,
a special track selection is applied for the variables M PT
, |p| and the secondary vertex
probability. The seed vertex, i.e. the vertex furthest away from the IP, is used to define
the distances D between this vertex and the IP, and L as shown in fig. 5.8 The vertex
axis is the straight line connecting the seed vertex with the IP. For each track, the point of
closest approach to the vertex axis is projected onto the vertex axis and L defined as the
distance of the resulting point on the vertex axis from the IP. Tracks with 0.18 < L/D <
2.5 and a transverse distance T of the point of closest approach from the vertex axis below
1.0 mm are attached to the decay chain. The real purpose of this process is to include
tracks from possible one prong tertiary vertices and hence increase the precision of the mass
calculation. A choice now has to be made with respect to whether the tracks from the
secondary vertices are automatically included. If they are included then we automatically
select all tracks originating from the B and the subsequent D meson decay. Clearly this
is the ideal case assuming perfect track assignment and that there are no fake vertices or

5.3 Flavour Discriminating Variables 85
vertices deriving from other decays. These however should already have been rejected by the
conversion tagger. Therefore in the presented algorithm all tracks from secondary vertices
have been included regardless on whether the tracks have or have not passed the additional
selection criteria. In the code the possibility not to automatically include them also exists.
The difference in the result between these two selection processes is however minimal.
Track
Vertex Axis
Secondary
T
L
D
IP
Beam Axis
Figure 5.8: Schematic diagram showing the definition of distances L, D and T used in the
track attachment algorithm.
The momentum |p| is the modulus of the vector sum of all decay chain track momenta.
The secondary vertex probability is found by fitting a common vertex to these tracks and
calculating the probability from the χ 2 value of this fit in the same way as for the ZVKIN
vertex finder, see Section 3.2. For the secondary vertex probability the number of tracks in
the decay chain is required to exceed the value N trks,min and the normalized χ 2 is required to
be below a user-settable value. For jets that do not meet these requirements, the probability
is set to 0, to lower the risk of such jets leaking into the heavy flavour samples. For the
calculation of the p T corrected vertex mass M Pt , first the vertex mass before correction M V tx ,

5.3 Flavour Discriminating Variables 86
is obtained from the decay chain tracks, assigning a pion mass to each track. With θ V tx the
angle between the seed vertex axis as given by the vertex position and the vertex momentum
with respect to the IP, it is required that p 2 V tx (1−cos2 θ V tx ) ≤ w PT ,maxMV 2 tx , where the factor
w PT ,max is a user-defined LCFI Vertex parameter of default value 3. This cut ensures that
cases in which both θ V tx and |p| are large are excluded from the correction procedure to
reduce the risk of fake vertices being assigned a large correction and subsequently affecting
the flavour tag. Jets failing this cut are assigned an M Pt value of 0. A conservative estimate
of the transverse momentum p V tx
T
corresponding to θ V tx and taking the error matrices of the
seed axis and the IP into account, is obtained by iteratively minimizing the correction term
p V tx
T
and recalculating the seed axis direction. For this minimization, the parameter N σ,max
determines the permitted extent of the seed axis correction in units of its uncertainty. The
p T corrected vertex mass M Pt is then defined as:
M Pt =
√
M 2 V tx
tx
+ |pV
T
| 2 + |p V T tx |. (5.12)
Finally, it is required that the correction does not exceed the uncorrected value by a large
factor, M Pt ≤ w corr,max × M V tx , where w corr,max is a code parameter.
Figure 5.9 shows the flavour tag input variables used for jets for which more than one
vertex was found, for b, c and light quark jets separately. Please note that the distributions
plotted are cumulative; hence the b distribution includes the plotted c and uds events and
the c distribution includes the plotted uds events. The sample used for the distribution is
10000 e + e − → Z/γ → q¯q events, with natural branching ratios, at 91.2 GeV centre of mass
energy. Some of these variables, such as M Pt , already provide a very good separation of the
different jet flavours on their own, with the correlations between the observables, exploited
by the neural network approach, further improving the tagging performance.
Finally please note that, as the momenta of the most and second-most significant track
(presented in the previous section), the decay length significance and the seed vertex momentum
depend on the energy of the input jet, in order to be able to use the neural networks
that are trained with jets from the e + e → Z/γ → q¯q events at the Z resonance for arbitrary

5.3 Flavour Discriminating Variables 87
energy, these observables are normalized to the jet energy before being fed into the neural
networks described in the next section.

5.3 Flavour Discriminating Variables 88
N jets
300
N jets
3
10
250
200
2
10
150
100
10
50
0
0 1 2 3 4 5 6 7 8 9 10
1
0 20 40 60 80 100 120 140 160 180 200
decay length / mm
decay length significance
(a)
(b)
N jets
500
N jets
400
400
350
300
300
250
200
200
150
100
100
50
0
0 5 10 15 20 25 30 35 40 45 50
0
0 1 2 3 4 5 6 7
raw momentum |p| / GeV
M Pt
/ GeV
(c)
(d)
N jets
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0 5 10 15 20
N jets
3
10
b-jets
2
10
c-jets
u,d,s-jets
10
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
number of non-prim. vtx tracks
log secondary vertex probability
(e)
(f)
Figure 5.9: Flavour discriminating variables used when two or more vertices have been
reconstructed: a) the decay length of the seed vertex, b) the decay length significance, c) the
momentum of the seed vertex, d) the transverse momentum corrected vertex mass, e) the
number of tracks found in all secondary vertices, f) the probability that all tracks present in
secondary vertices originate from the same secondary vertex.

5.4 Neural Network Combination 89
5.4 Neural Network Combination
For heavy flavour tagging, that is the identification of bottom and charm jets, neural networks
are trained such that the target output provided in the training phase is 1 for signal jets and
0 for background. The output value of a trained network will be the closer to 1 the more
signal-like the values of the input observables. By default, each of the networks has 8 input
nodes, one hidden layer of 14 tan-sigmoid nodes and one output node and is trained using
the conjugate gradient backpropagation algorithm. As explained in the previous section, the
flavour tag is based on different observables for jets with one and for jets with two or more
found vertices. Furthermore, for a given jet flavour, the distributions of sensitive variables
are significantly different for jets with two and jets with three or more vertices, so the ability
to distinguish between b and c jets is enhanced by treating these two cases separately. For
each of these categories of one, two or at least three vertices, three networks are trained, so
a complete set consists of nine networks altogether. For b nets, the signal provided in the
training phase consists of b jets while c and light flavour jets form the background. The c
nets are trained with c jets as signal and b and light flavour jets as background. As for some
physics processes the background for the identification of c jets is known to consist almost
exclusively of b jets, and charm jets are easier to distinguish from these than from light
flavour jets, dedicated networks are provided for these cases. The networks are therefore
only presented with b jets as background in the training run.
It has to be noted that the LCFI Vertex software is very flexible, permitting the use of
different input variables, network architectures, node types, transfer functions and training
algorithms. In fact we will see in the next sections how this flexibility has been used in order
to adapt the LCFI Vertex software to the needs of the SiD detector.

5.4 Neural Network Combination 90
N jets , 1 vertex
3
10
2
10
N jets , 2 vertices
3
10
b-jets
2
10
c-jets
u,d,s-jets
10
10
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
c-tag neural net output
c-tag neural net output
(a)
(b)
N jets , >= 3 vertices
3
10
2
10
N jets
3
10
10
2
10
1
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
c-tag neural net output
c-tag neural net output
(c)
(d)
Figure 5.10: Output of the neural networks used for charm tagging. The plots show the
outputs for the three separate networks used in case a) one, b) two and c) three or more
vertices are found in the input jet. In d), the resulting combined distribution for arbitrary
number of vertices is shown. Please note that the distributions plotted are cumulative; hence
the b distribution includes the plotted c and uds events and the c distribution includes the
plotted uds events.

5.4 Neural Network Combination 91
Fig. 5.10 shows the distribution of the output variables of neural networks used for
tagging charm jets (c nets) separately for the cases of one, two and at least three vertices, and
the combined distribution for an arbitrary number of vertices. The calculation is performed
on a dijet sample at √ s = 91.2 GeV. The most straightforward way of using the charm
tag (i.e. c net output) in an analysis is to require one or more jets in an event to have
a charm tag exceeding a certain cut value, chosen as appropriate for the specific analysis.
The resulting performance on a jet by jet basis is discussed in the next section. In some
occasions event selection can also be improved by using information from both the charm
and the bottom tags. This can, for example, be achieved by plotting charm versus bottom
tag, as shown in fig. 5.11 for bottom (fig. 5.11(a)), charm (fig. 5.11(b)) and light flavour
(fig. 5.11(c)) jets from the two jet Z peak sample, and placing a cut on the resulting two
dimensional distribution. Note that in the two-dimensional distribution for c jets, the peak
near (b-tag = 0, c-tag = 0) stems mainly from jets in which only the primary vertex was
reconstructed, while the peaks near (0, 1) is usually due to jets in which secondary vertices
were also found.

5.4 Neural Network Combination 92
b-jets
c-jets
N jets
1600
1400
1200
1000
800
600
400
200
0
1
0.8
0.6
0.4
0.2
c-tag neural net output
0 0
0.2
0.4
0.6
0.8
1
b-tag neural net output
N jets
120
100
80
60
40
20
0
1
0.8
0.6
0.4
0.2
c-tag neural net output
0 0
0.2
0.4
0.6
0.8
1
b-tag neural net output
(a)
(b)
uds-jets
N jets
1200
1000
800
600
400
200
0
1
0.8
0.6
0.4
0.2
c-tag neural net output
0 0
0.2
0.4
0.6
0.8
1
b-tag neural net output
(c)
Figure 5.11: Charm tag vs. bottom tag for input samples consisting purely of a) bottom
jets, b) charm jets and c) light quark jets.

5.5 Performance of Flavour Tagging 93
5.5 Performance of Flavour Tagging
As a measure of the flavour-tagging performance, the purity of selecting bottom and charm
jets is studied as function of the efficiency. Fig. 5.12 shows purity vs. efficiency for the
three tags provided by the LCFI Vertex package, for the two jet sample at √ s = 91.2 GeV
and at √ s = 500 GeV. A flavour composition of approximately 22% (15%) of bottom, 17%
(25%) of charm and about 61% (60%) of light flavour jets at √ s = 91.2 GeV (500 GeV) is
assumed. The plot is obtained by varying a simple cut on the neural net output variable and
calculating purity and efficiency at each cut value. At the Z resonance, for the b-tag a very
pure sample, containing 92% b jets, can be selected at an efficiency of 70%. In comparison,
high c-tag purities can only be achieved at lower efficiencies, mainly because light flavour jets
leak into the sample. Because of these reasons the c-tag with all backgrounds included has
been found to be the most sensitive of the tags whenever changing the conditions used in the
study, such as using different tracking algorithms, code parameters and detector geometries.
At 500 GeV, the b-tag performance is degraded with respect to that at the Z resonance,
while c-tag purity is very similar at both energies and the purity of the c-tag with only b
background is slightly improved at the higher energy. However it is clear that part of the
difference in the performance is explained from the different quark compositon of the sample.
The decrease of the performance in tagging b jets is therefore at least partially driven from
the lower number of b quarks (signal) and the higher number of light quarks (background)
in the sample composition.
A way of studying tagging performance that is independent of the sample composition
is to look at the efficiency of selecting each of the wrong flavours when cutting on one of the
tagging variables, i.e. the wrong flavour efficiencies or mistags. Figures 5.13(a) and 5.13(b)
show the c and light quark jet efficiencies as a function of the b-tag efficiency and the b
and light flavour jet efficiencies vs. the c-tag efficiency. It is clearly seen that the main
background to the b-tag is due to c jets. For the c-tag the main background, at efficiencies
above about 75%, is due to light flavour jets, while at lower efficiencies it is dominated by
misidentified b jets, as it would be expected from the comparison of the purities for c-tag

5.5 Performance of Flavour Tagging 94
purity
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
b c bc
MARLIN, LDCPrime_02Sc, 90 GeV
MARLIN, LDCPrime_02Sc, 500 GeV
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
efficiency
Figure 5.12: Comparison of tagging performance at the Z resonance and at √ s = 500 GeV.
Tagging purity is plotted as function of efficiency for b jets and c jets. Performance for c
jets assuming only b background (labelled bc) is also shown.
and c-tag with b background only.
By using the same methods it is also possible to analyse the effect of the K s , Λ and
conversion tagger on the flavour tagging performance. The analysis displayed in Fig. 5.14
does just that. The plot shows how the performance of the b quark tagging can be improved
only minimally by using the implemented track removal algorithm or as a matter of fact any
other similar algorithm. In fact given a certain efficiency the algorithm performs at worst
a few percentage points worse in terms of purity than if all the reconstructable Ks, Λ and
conversion tracks are removed by using MC information. The same consideration applies
also for the c quark tagging when only the b quark background is present. Differently a
substantial improvement can be seen by using the conversion tagger on the c quark.
It is at this point also interesting to study the relative importance of the input variables
on the flavour tag results. The different contribution to every neural network has been
determined using an estimator from the Toolkit for Multivariate Data Analysis with ROOT

5.5 Performance of Flavour Tagging 95
wrong flavour efficiency
1
-1
10
-2
10
wrong flavour efficiency
1
-1
10
-2
10
c jet leakage
u,d,s jet leakage
-3
10
b jet leakage
u,d,s jet leakage
-3
10
-4
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
c-tag efficiency
(a)
-4
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b-tag efficiency
(b)
Figure 5.13: Efficiencies for selecting jets with the wrong flavour when tagging a) bottom
jets and b) charm jets.
(TMVA) [59]. Following this approach, the input importance of a variable i is defined as:
I i = ¯x 2 i
∑n h
j=1
(w ij ) j = 1,...,n var (5.13)
where ¯x i is the average of the values of variable i in the input sample and the sum extends
over the weights w ij corresponding to the connections of the neural network node of variable
i with the n h nodes in the adjacent network layer. The calculation was implemented as part
of the neural network code provided with LCFI Vertex. Tables 5.4, 5.5, 5.6 and 5.7, 5.8, 5.9
summaries the results obtained at the Z resonance and at 500 GeV, respectively, where for
each neural network, the values I i are normalized to the maximum value I max .
Some quite significant differences can be seen in the importance of the inputs for the
91.2 GeV and the 500 GeV case. In particular, as expected due to the increased boost of
the particles, the decay length of the vertices gains in importance. In the case that only
the primary vertex is found the most striking difference is the increased importance of the
impact parameter significances, at the expense of the joint probability. This can derive from
an increased discriminatory power of these variable due to an increase boost of the jets. This
seems however unlikely because the track significances are also inputs to the joint probability.

5.5 Performance of Flavour Tagging 96
purity
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
b c bc
no V0 finding in vertex detector
ConversionTagger V0 finding
Cheater: all reconstructable V0s masked
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
efficiency
Figure 5.14: Comparison of tagging with and without K s , Λ and conversion tagging and
performance obtained when using MC information at √ s=91.2 GeV
Alternatively it can derive from decreased performance of the joint probability. This seems
much more likely as the negative impact parameter distribution has been calculated only for
91.2 GeV jets. If this is the case an energy renormalization of these parameters should be
designed and the performance of the tagging at 500 GeV can therefore be improved.

5.5 Performance of Flavour Tagging 97
Z mass resonance - 1 vertex found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
most signif. track d 0 /σ(d 0 ) 0.002 ± 0.004 0.005 ± 0.008 0.000 ± 0.000
2 nd -most signif. track d 0 /σ(d 0 ) 0.058 ± 0.016 0.009 ± 0.007 0.026 ± 0.010
most signif. track z 0 /σ(z 0 ) 0.001 ± 0.001 0.003 ± 0.003 0.002 ± 0.001
2 nd -most signif. track z 0 /σ(z 0 ) 0.115 ± 0.030 0.005 ± 0.001 0.066 ± 0.017
most signif. track |p trk | 0.113 ± 0.275 0.003 ± 0.015 0.043 ± 0.002
2 nd -most signif. track |p trk | 0.062 ± 0.003 0.068 ± 0.006 0.048 ± 0.003
joint probability R-φ 1 0.676 ± 0.031 0.887 ± 0.041
joint probability z 0.922 ± 0.037 1 1
Table 5.4: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at the Z resonance in the case only the IP vertex has been found.
Z mass resonance - 2 vertices found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
M Pt 1 1 1
|p| 0.098 ± 0.007 0.404 ± 0.029 0.114 ± 0.008
decay length 0.182 ± 0.013 0.990 ± 0.072 0.139 ± 0.010
decay length significance 0.070 ± 0.008 0.187 ± 0.022 0.115 ± 0.013
N trk,vtx 0.063 ± 0.004 0.162 ± 0.009 0.081 ± 0.004
secondary vertex probability 0.230 ± 0.017 0.212 ± 0.016 0.124 ± 0.010
joint probability R-φ 0.040 ± 0.004 0.071 ± 0.007 0.052 ± 0.005
joint probability z 0.061 ± 0.008 0.159 ± 0.021 0.052 ± 0.007
Table 5.5: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at the Z resonance in the case only one secondary vertex has been found.
Z mass resonance - 3 or more vertices found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
M Pt 1 1 1
|p| 0.490 ± 0.076 0.960 ± 0.148 0.580 ± 0.089
decay length 0.550 ± 0.119 0.338 ± 0.072 0.370 ± 0.080
decay length significance 0.810 ± 0.018 0.106 ± 0.023 0.078 ± 0.017
N trk,vtx 0.665 ± 0.089 0.811 ± 0.108 0.829 ± 0.111
secondary vertex probability 0.087 ± 0.045 0.112 ± 0.057 0.066 ± 0.034
joint probability R-φ 0.006 ± 0.002 0.012 ± 0.005 0.007 ± 0.003
joint probability z 0.007 ± 0.003 0.017 ± 0.007 0.009 ± 0.003
Table 5.6: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at the Z resonance in the case two or more secondary vertices have been found.

5.5 Performance of Flavour Tagging 98
500GeV - 1 vertex found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
most signif. track d 0 /σ(d 0 ) 0.363 ± 0.084 1 0.063 ± 0.014
2 nd -most signif. track d 0 /σ(d 0 ) 0.499 ± 0.079 0.072 ± 0.020 0.429 ± 0.067
most signif. track z 0 /σ(z 0 ) 0.036 ± 0.008 0.166 ± 0.053 0.148 ± 0.033
2 nd -most signif. track z 0 /σ(z 0 ) 1 0.057 ± 0.016 1
most signif. track |p trk | 0.019 ± 0.004 0.057 ± 0.019 0.013 ± 0.003
2 nd -most signif. track |p trk | 0.009 ± 0.002 0.013 ± 0.005 0.012 ± 0.003
joint probability R-φ 0.364 ± 0.066 0.304 ± 0.091 0.564 ± 0.102
joint probability z 0.363 ± 0.061 0.487 ± 0.142 0.688 ± 0.116
Table 5.7: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at 500 GeV in the case only the IP vertex has been found.
500GeV - 2 vertices found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
M Pt 1 0.438 ± 0.116 1
|p| 0.071 ± 0.021 0.128 ± 0.034 0.082 ± 0.024
decay length 0.420 ± 0.119 1 0.320 ± 0.091
decay length significance 0.011 ± 0.006 0.013 ± 0.007 0.019 ± 0.011
N trk,vtx 0.054 ± 0.014 0.061 ± 0.013 0.070 ± 0.018
secondary vertex probability 0.262 ± 0.078 0.106 ± 0.028 0.141 ± 0.042
joint probability R-φ 0.083 ± 0.026 0.064 ± 0.018 0.108 ± 0.034
joint probability z 0.147 ± 0.057 0.168 ± 0.061 0.125 ± 0.049
Table 5.8: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at 500GeV in the case only one secondary vertex has been found.
500GeV - 3 or more vertices found by ZVTOP
variable b-tag c-tag c-tag(b bgd.)
M Pt 0.500 ± 0.268 0.814 ± 0.435 0.745 ± 0.398
|p| 0.173 ± 0.096 0.553 ± 0.307 0.306 ± 0.169
decay length 1 1 1
decay length significance 0.013 ± 0.010 0.028 ± 0.021 0.019 ± 0.014
N trk,vtx 0.418 ± 0.172 0.829 ± 0.341 0.775 ± 0.318
secondary vertex probability 0.349 ± 0.504 0.731 ± 1.050 0.394 ± 0.569
joint probability R-φ 0.015 ± 0.011 0.048 ± 0.036 0.028 ± 0.021
joint probability z 0.035 ± 0.033 0.127 ± 0.123 0.062 ± 0.061
Table 5.9: Relative importance I i /I max of variables used as inputs for flavour tag neural
nets at 500GeV in the case two or more secondary vertices have been found.

5.6 Flavour Tagging in the SiD Detector Concept 99
At the Z resonance, in case only the primary vertex is found by ZVRES, the joint probability
variables in R-φ and R-z provide the best handle for distinguishing between different
jet flavours. This is to be expected given that these variables combine information from all
the tracks in the jet, rather than resulting from only one of them (as is the case for the
other six inputs). For the c tag provided for the case that all backgrounds are present, the
momentum of the most significant track in the jet also contributes significantly to the flavour
tag result. The other variables contribute to a much lesser extent. At 500 GeV, the joint
probability variables are still important, but the impact parameter significances of the most
and second most significant track in the jet play a similarly important role in jet flavour
identification.
If at least two vertices are found in a jet, the p t corrected vertex mass provides the clearest
indication of the jet flavour. Other important variables are the seed vertex decay length and
the number of tracks in the seed vertex, especially if three or more vertices are found, as well
as the vertex momentum |p| and the secondary vertex probability. As can be expected, the
relative importance of the decay length increases with increasing jet energy, and surpasses
that of the M Pt variable for the three vertex case at 500 GeV.
5.6 Flavour Tagging in the SiD Detector Concept
Although the presented algorithm has been mainly studied in the ILD/LDC framework it
has been extensively used also with the SiD detector geometry. In order to validate the
software also in this framework the performance of the flavour tagging has been analysed.
The analysis has been attempted in two separate stages. In the first stage the networks
have not been retrained and the same networks have been used as the ones presented in the
ILD/LDC analysis. As it can be seen in fig. 5.15 this resulted in a substantial deterioration
of the flavour tagging performance. In order to improve the performance the networks
have been retrained. However in order to simplify the process instead of using 9 different
neural networks only 3 have been used. Each neural network, b tag, c tag and c tag with b

5.7 Summary 100
background therefore used all sixteen described discriminating variables plus an additional
two: the jet energy and the number of vertices reconstructed in the jet. As it can be seen
in fig. 5.15 the retraining of the neural network substantially improved the performance to
a level comparable with the one seen in the LDCPrime 02Sc detector model.
Figure 5.15: Comparison of tagging performance at √ s = 500 GeV. Tagging purity is plotted
as function of efficiency for b jets (red) and c jets (green). Performance for c jets assuming
only b background is also shown (blue). The dashed lines represent the performance using
the LDC trained neural networks, while the solid lines represent the performance using the
SiD trained neural networks.
5.7 Summary
In this chapter the vertexing and flavour tagging algorithms for the ILD detector concept
are described in detail. The performance of both algorithms is investigated in detail using
a dijet sample with 91.2 GeV centre of mass energy. It has been found that b jets can be
selected with a ∼ 90% purity for an efficiency of ∼ 70%. When using 500 GeV centre of
mass energy dijet events, assuming the same efficiency, the purity decreases to ∼ 80%.
The algorithms have also been tested within the SiD detector concept.

Chapter 6
The Top Quark Mass and the t¯t Cross
Section
Having set the stage and described all the hardware and software tools that are needed
it is now possible to perform the chosen analysis. This chapter focuses on two specific
observables: the mass of the top quark and the t¯t cross section. Given the early stages of the
ILC project the main interest is directed at understanding the limits and uncertainties that
one would be able to extract from the ILC data. More specifically, as all early feasibility
studies, this analysis focuses on the understanding of the statistical uncertainties of a wide
range of observables. At this early stage it is difficult to account for all systematic errors,
particularly considering the limited resources.
Additionally it is important to understand the performance of the detector in the most
challenging environments. Because of this reason all the presented studies are being performed
in the hadronic channel e + e − → t¯t → b¯bq¯qq¯q, which can be described as an excellent
testing ground for the performance of the reconstruction in very busy events [60].
In order to perform the analysis five separate samples have been used:
1. A Standard Model background sample. This is a weighted sample composed of ∼ 7
× 10 6 events. As the name suggests it includes all the background Standard Model
101

Chapter 6. The Top Quark Mass and the t¯t Cross Section 102
processes. Each event is weighted in such a way that the integrated luminosity of
the sample is 500 fb −1 , although the total number of generated events is substantially
lower. In such manner the event generation becomes substantially less CPU intensive.
This sample includes all SM final states with the exclusion of the b¯bf ¯ff ¯f events which
have been stripped out.
2. A b¯bf ¯ff ¯f sample generated with a top quark mass of 174.0 GeV. The sample is
composed of ∼ 0.25 × 10 6 unweighted events. These events can be further separated
into the signal events b¯bq¯qq¯q and the remaining background events. It has to be noted
that e + e − → t¯t → b¯bq¯qq¯q is not the only process contributing to the production of
the b¯bq¯qq¯q signature, but is by far the dominant contribution. More specifically it has
been calculated by using the Whizard Monte Carlo generator [30, 31] that the top
mediated events are responsible for 90% ± 3% of the produced events. In this sample
it is impossible to separate the top mediated and the non top mediated events. The
full b¯bq¯qq¯q sample has therefore been used as signal and from here onwards is referred
to as the hadronic t¯t.
3. Three b¯bf ¯ff ¯f template samples with top quark masses of 173.5 GeV, 174.0 GeV and
174.5 GeV. All three samples are composed of ∼ 1.1 × 10 6 events with a weight of 0.25.
These events can be further separated into the signal events b¯bq¯qq¯q and the remaining
background events.
In all the following sections, unless differently stated, all number of events are considered
as multiplied by their weights so that the samples are normalized to the same integrated
luminosity of 500 fb −1 . All the samples used in the process have undergone full reconstruction
in the SiD detector as described in the Simulation and Reconstruction chapter. The samples
are representative of an ILC total integrated luminosity of 500fb −1 of which 250fb −1 taken
with an electron polarization of -80% and a positron polarization of +30% and the remaining
250fb −1 with an electron polarization of +80% and a positron polarization of -30%.

6.1 Preliminary Event Selection 103
6.1 Preliminary Event Selection
As it is very often the case the first step of the presented analysis is to perform a process
of event selection. The main aim of this process is to separate the signal events from the
background events in the best way feasible. It is clear that ultimately one aims at rejecting
as many background events as possible while retaining the majority of the signal events.
However the optimal balancing point between the loss of efficiency and the increased purity
of the signal sample after the selection process is often dependent on the specific details
of the measurement that one ultimately aims to perform. In the case of a cross section
measurement the optimal selection process can be argued, from simple error considerations,
to be the one that maximizes the ratio S/ √ S + B, where S and B are respectively the
number of signal and background events. More difficult is the case of an invariant mass or
asymmetry measurement in which the uncertainty will depend not only on the number of
background and signal events left in the final sample, but also on their particular distributions
and the fitting procedures. Since the presented analysis has a very wide scope, as it ultimately
aims to perform four separate measurements, it is difficult to define a single optimized event
selection process. The difficulty is further amplified by the cross correlation of the variables.
The alternative of defining separate event selections for each process is instead not feasible
in a preliminary study.
The approach of the author has therefore been to attempt to define a set of common
selection criteria that generically define the e + e − → t¯t → b¯bq¯qq¯q process and aim to reject
most of the non-top SM background, leptonic top decays and poorly reconstructed hadronic
top decays. The algorithm has been separated into three stages: lepton event selection,
event selection using kinematic and topological variables and particle ID event selection.
Initially the algorithm looks at isolated leptons, defined as a jet containing only one
reconstructed particle which is either an electron or a muon, and rejects all events where
one or more isolated leptons have been found. No such jet should in fact be present in
a e + e − → t¯t → b¯bq¯qq¯q event, if the jets have been well reconstructed. The all inclusive
Standard Model background instead has an abundance of events where an isolated lepton is

6.1 Preliminary Event Selection 104
expected. This process eliminates ∼ 75× 10 6 background events, or 0.6% of all background,
without the loss of a single signal event.
Subsequently a set of kinematic and topological discriminating variables has been identified.
These are the total energy of the event, the jet finder y 56 parameter (the y cut separation
between the 5 and 6 jet hypothesis, as explained in chapter 3), the number of particles in
the event and the number of tracks in the event. The number of particles in the event is
defined as the number of reconstructed particles that the Particle Flow Algorithm (PFA)
identifies. In particular, the y 56 variable is a good indicator that an event is topologically
consistent with a six jet hypothesis. For example, if physically there are only five jets in
the event one jet of the event will have to be separated into two reconstructed jets, due to
the six jet requirement. This will result in the substantially lower y 56 value and therefore
the rejection of the event. It also ensures that the jets are well reconstructed and discards
events where two jets from a six jets events are overlapping. Events with jets outside of the
acceptance will have a total energy that is substantially lower than 500 GeV, and will be
rejected by the total energy requirement. Similar considerations apply to events in which
neutrinos represent a substantial fraction of the total energy, such events will also be rejected
by the same requirement. Fig. 6.1 illustrates the discriminatory power of each variable when
these are considered independently. Table 6.1 instead presents the full list of kinematic event
selections.
Kinematic and Topological Event Selection
Variable Barrel Value
E tot > 400 GeV
log(y 56 ) > -8.5
number of particles in event > 80
number of tracks in event > 30
Table 6.1: List of the kinematic and topological event selection procedures.
After this process has been performed all but 492 × 10 3 background events have been
rejected. This compares to the initial number of 12.5 × 10 9 events and corresponds to a
99.996% rejection factor. The selection process comes to the expense of an efficiency loss of
9.7% of the initial 143 × 10 3 signal events. Although the performance of these preliminary

NumberOFparticlesnocutsTOPHARD
Entries
132410
Mean 119.1
RMS 18.66
YCutMinnocutsTOPHARD
Entries
132410
Mean −6.007
RMS 0.9707
TotalEnergynocutsWRONG
Entries 7020944
Mean 429.1
RMS 64.75
NumberOFtracksnocutsWRONG
Entries 7020944
Mean 2.601
RMS 0.976
6.2 Kinematic Fitter and W Identification 105
log(y_56) − Hadronic ttbar
Total Energy − Hadronic ttbar
Events
7
10
Events
6
10
6
10
log(y_56) − Hadronic ttbar
5
10
5
10
log(y_56) − SM Background
4
10
4
10
3
10
3
10
2
10
2
10
Total Energy − SM Background
10
10
Total Energy − Hadronic ttbar
Events
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
−11 −10 −9 −8 −7 −6 −5 −4 −3
log(y_56)
10
(a)
Number of Particles − Hadronic ttbar
Number of Particles − Hadronic ttbar
Number of Particles − SM Background
1
40 60 80 100 120 140 160 180 200 220
# of Particles
(c)
Events
10
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
300 320 340 360 380 400 420 440 460 480 500
Total Energy (GeV)
10
(b)
Number of Tracks − Hadronic ttbar
Number of Tracks − Hadronic ttbar
Number of Tracks − SM Background
1
0 20 40 60 80 100 120
# of Tracks
(d)
Figure 6.1: Kinematic and Topological Event Selections a) y 56 , b) total energy, c) number
of particles in the event, d) number of tracks in the event.
cuts is already significant it is clear that one should be able to improve it by means of particle
identification processes. One would therefore aim at identifying the b quarks by using the
described LCFI Vertex algorithm and at identifying the W bosons by its significant invariant
mass.
6.2 Kinematic Fitter and W Identification
In order to identify the invariant mass of the reconstructed candidate W bosons the KinFit
[61, 62] kinematic fitting algorithm has been used. This section therefore briefly describes the
algorithm used for identifying the W bosons and, subsequently, for calculating the top quark
mass. The idea behind kinematic fitting is to use kinematic constraints of a given physical
process to improve the precision of the parameters of interest. The desired parameters are

6.2 Kinematic Fitter and W Identification 106
fitted using a least squares technique and the physical constraints are incorporated into the
fit using Lagrange multipliers [61, 62], forcing the fit to fulfil these constraints. In more
mathematical terms this can be expressed as the following χ 2 minimization:
χ 2 Tot(⃗η,⃗ε, ⃗ λ) = (⃗y − ⃗η) T · V −1 · (⃗y − ⃗η) + 2 ⃗ λ T · ⃗f(⃗η,⃗ε) (6.1)
where ⃗y are the measured quantities, ⃗η are the measured parameters to be optimized, ⃗ε are
the unmeasured parameters to be optimized, V −1 is the inverse of the uncertainty matrix
on the measurements, here assumed to be a diagonal matrix, ⃗ f are the constraint function
and ⃗ λ are the Lagrange multipliers. ⃗ε,⃗η, ⃗ λ are the unknown values. The χ 2 Tot
is therefore
composed of a conventional χ 2 term and of a constraint term. It can now be shown that the
following equations must be solved:
⃗0 =
⃗0 =
V −1 · (⃗y − ⃗η) + F T η · ⃗λ
F T ε · ⃗λ
⃗0 = ⃗ f(⃗η,⃗ε) (6.2)
where the matrices F T η and F T ε are defined as:
F T η = (F T η ) kn = ∂f k
∂η n
F T ε = (F T ε ) kj = ∂f k
∂ε j
(6.3)
and k, n and j are respectively the number of constraints, the number of measured and
unmeasured parameters. The third equation of 6.2 ensures that the hard constraints are met.
Additionally it is clear from equation 6.1 that in order to perform the fit the uncertainties
on the measured quantities must be determined. More specifically in the presented analysis
the jet energy and angle uncertainties need to be known. The parameters used have been
50%/ √ E for the jet energy expressed in GeV and 30 mrad for the angle. Such values have
been found to model well the performance of the SiD detector. [63]

Entries 128574
Mean 77.37
RMS 16.62
FourOnlyWDiffMassFitnocutsTOPHARD
Entries 129080
Mean 76.46
RMS 14.67
Entries 121414
Mean 72.96
RMS 21.24
Entries 129080
Mean 77.29
RMS 15.12
6.2 Kinematic Fitter and W Identification 107
In the case of W boson identification the only set constraint is that the masses of the two
candidate W bosons present in the event should be equal. This is of course an approximation
since the W bosons are not physically forced to decay on the mass shell and therefore they
are not forced to have the same mass. However this method has been shown to produce
slightly better results when compared to the possibility of not applying any constraints.
Another problem presented while trying to identify the W bosons is the choice of the right
combination of jets. One can either consider all six jets present in the event or only the
four least b-like jets. As it is expected, given the good performance of the LCFI Vertex b
tagging and the resulting reduced number of combinatorial possibilities, the second method
is substantially superior (shown in fig. 6.2). Such method has therefore been used.
W bosons Mass − Hadronic ttbar
Events
4000
3500
3000
Four Jet Mass
Four of Six Jet Mass
Events
W bosons Mass − Hadronic ttbar
4500
4000
3500
Kinematic Fit
No Kinematic Fit
2500
2000
1500
1000
500
3000
2500
2000
1500
1000
500
40 50 60 70 80 90 100 110 120
Mass (GeV)
(a)
40 50 60 70 80 90 100 110 120
Mass (GeV)
(b)
Events
5000
W bosons Mass − Hadronic ttbar
Known W Mass
Events
W bosons Mass− SM Background
6000
4000
Unknown W Mass
5000
3000
4000
2000
1000
3000
2000
1000
W mass known with fit
W mass known no fit
W mass unknown
40 50 60 70 80 90 100 110 120
Mass (GeV)
(c)
0
40 50 60 70 80 90 100 110 120
Mass (GeV)
(d)
Figure 6.2: Different methods of reconstructing the W bosons: a) the methods using only
the four least b-like jets in the kinematic fit (black line) is compared to the method where all
jets are used (light line), b) the results are shown before (black line) and after the kinematic
fit (light line), c) the methods where the mass of the W boson is known (black line) is
compared to the method where the mass is unknown (light line), in d) the effect of the
various procedures on the background sample is displayed. All variables are plotted after
the kinematic event selection.

6.3 b Tagging Event Selection 108
Even after considering only four jets three possible jet combinations are still left. A
way of determining the best combination must therefore be defined. Two possibilities have
been considered: the chosen combination is either the one that best fulfils the equal mass
constraint or the one that minimizes the quantity ∆M = √ (M w1 − M w ) 2 + (M w2 − M w ) 2 ,
where M w1 and M w2 are the masses of the W boson candidates before kinematic fitting; M w
is the world average for the W boson mass.
The second method has been shown to perform better and has hence been utilized for the
event selection. As it can be noticed (fig. 6.2) the introduction of a constrain improves only
minimally the result, but it substantially simplifies the logic behind the process since both
bosons are forced to have the same mass. A further event selection was therefore performed
on the calculated mass after the kinematic fitting process. More specifically the events that
have calculated masses for the W boson candidates of less than 50GeV or more than 110GeV
are rejected as background events.
6.3 b Tagging Event Selection
The final step of the event selection process is the rejection of events in which two b quarks
have not been clearly identified, done by means of the already presented LCFI algorithm.
However the method has been originally tested only on a dijet sample. It has been therefore
deemed necessary to check the performance in the case of more complex topologies, as the
one presented by the hadronic top. The satisfactory results of such test can be seen in fig.
6.3. In numerical terms, if a b quark tagging efficiency of 45.0% is required, then one will
incur a 2.6% c quark mistagging efficiency and 0.8% uds quark mistagging efficiency. As we
can infer from fig. 5.13(b), comparable mistagging efficiencies for the same tagging efficiency
in the LDC dijet study at 91.2 GeV are 0.8% and 0.07%. Only part of this degradation can
be however attributed to the increased complexity of the event. The unoptimized SiD neural
networks, as seen in fig. 5.15 have in fact been used in this study. The optimized ones were
not available in time to be included into this analysis.

neural net of uds
Entries
1.956656e+07
Mean 0.04469
RMS 0.1023
6.3 b Tagging Event Selection 109
NN output for b,c,uds jets at MC level
Jets
7
10
NN output for ’MC−uds jets
NN output for ’MC−c jets’
6
10
NN output for ’MC−b jets’
5
10
4
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b−tag NN output
Figure 6.3: Performance of the b tagging algorithm when used on a b¯bq¯qq¯q sample.
In a first instance the variable b − tag sum , the sum of the b-tag neural net outputs for
all six jets is calculated (as seen in fig. 6.4(a)) and used for the selection procedure. Given
that this is at the same time the most complex and the most powerful of the used variables
an optimization has been attempted. Fig. 6.4(b) shows the S/ √ S + B quantity assuming
the selection is performed at different values of the summed neural net output. The value of
S/ √ S + B that fig. 6.4(b) suggests to use for the event selection is one. S/ √ S + B however
decreases only minimally if a slightly higher requirement is imposed. The importance that
the b tagging has in the kinematic fitting of the W boson, as already seen, and of the top
quark is however not expressed in the simplicity of this graph. It has therefore been decided
that a slightly higher requirement would be beneficial to the remainder of the analysis;
particularly because the kinematic fitting methods described require the presence of not
one, but two well identified b quarks. All events below the b − tag sum value of 1.5 have
therefore been rejected as background while all events with values above 1.5 are considered
signal.
As mentioned one would also like to ensure that at least two recognizable b jets are
present in the event. Events whose most b-like jet has a neural net b-tag output of less than
0.9 (fig. 6.5(a)) or whose second most b-like jet has a neural net b-tag output of less than
0.4 are also rejected (fig. 6.5(b)).

BsumTOPHARDEYPTcut
Entries
129080
Mean 1.787
RMS 0.6173
HighestBtagTOPHARDEYPTcut
Entries
129080
Mean 0.9229
RMS 0.1601
SecondBtagWRONGEYPTcut
Entries
121414
Mean 0.1871
RMS 0.2788
6.3 b Tagging Event Selection 110
Events
5
10
4
10
3
10
2
10
10
Sum of b−tag NN output
Hadronic ttbar
SM Background
1
0 1 2 3 4 5 6
Sum b−tag NN output
(a)
Signal/sqrt(Signal + Background)
b−tag Event Selection Optimization
240
220
200
180
160
140
120
100
80
60
40
20
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Sum b−tag NN output
(b)
Figure 6.4: The variable b − tag sum is plotted for the signal and background events in a). In
b) one can see the resulting S/ √ S + B quantity used for the event selection optimization.
All variables are plotted after the kinematic event selection.
Jets
3
×10
120
100
Most b−quark like jet in the event
Hadronic ttbar
Jets
250
3
×10
Second most b−quark like jet in the event
Hadronic ttbar
80
SM Background
200
SM Background
60
150
40
100
20
50
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
NN output b−tag
(a)
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
NN output b−tag
(b)
Figure 6.5: The neural net output for the most b-like jet , in a), and second most b-like jet,
in b), are displayed for both the signal and the background sample. All variables are plotted
after the kinematic event selection.
After both particle identification procedures have been applied the signal selection efficiency
is 51.5%, this implies that approximately 74 thousand b¯bq¯qq¯q events have passed all
event selection procedures. Of the background samples 33.5 thousand events have passed
the selection. The purity of the resulting sample is therefore 68.8%. Of the remaining background
events 8.5 thousands, or 25%, are b¯bqlνq¯q events. It is also expected that a significant
proportion of the remaining background derives from the e + e − → W + W − → q¯qq¯q process,
with a smaller contribution from e + e − → ZZ → q¯qq¯q.

6.4 Top Quark Mass 111
6.4 Top Quark Mass
The next step of the analysis is the calculation of the top mass. Once again a kinematic
fitter was employed to reduce the combinatorial background of the six-jet environment and
to take advantage of the existing kinematic constraints of top decays. Table 6.2 illustrates
the full list of constraints used for this analysis. Similarly to what was previously described
the two most b-like jets were considered to be originating from b-quarks and therefore were
not used in the reconstruction of the two W bosons. Additionally the masses of such b-jets
were forced to be 5.8 GeV, which is roughly the mass of B mesons.
Top Kinematic Fitting Constraints
Mass(top1) = Mass(top2)
Mass(W1) = 80.4 GeV
Mass(W2) = 80.4 GeV
Mass(b Jet1 ) = 5.8 GeV
Mass(b Jet2 ) = 5.8 GeV
E Total = 500 GeV
p x ;p y ;p z = 0
Table 6.2: List of kinematic fitting constraints used for the calculation of the top mass.
It is clear that, in setting the constraints of table 6.2, a whole set of approximations is
made. Similarly to the already discussed W boson example the masses of the two top quarks
are set to be equal; the W boson mass is now constrained even further to its on-shell values.
The beam bremsstrahlung process is also ignored and the ideal momentum and energy values
of the beam are therefore used as constraints.
The software calculates the best kinematic configuration for each of the six possible
combinations. Of these six configurations the one with the lowest χ 2 , as presented in equation
6.1, is chosen. The impact of this procedure on the reconstructed top mass distribution can
be seen in 6.6(a). In order to interpret the result it must be noted that while before the
kinematic fitting the top and the antitop quarks produced in each event can be used as
two statistically independent measures of the top mass, after the fitting the mass of the
top and antitop quarks are equal and therefore represent only one statistically independent

Six2bNoFitMasswithbmassEYPTBcutTOPHARD
Entries
145058
Mean 179.3
RMS 33.61
Six2bFitMasswithbmassEYPTBcutTOPHARD
Entries
72529
Mean 189.8
RMS 24.31
Six2bNoFitMasswithbmassEYPTBcutTOPHARD
Entries
23690
Mean 188.1
RMS 43.26
Six2bFitMasswithbmassEYPTBcutTOPHARD
Entries 11845
Mean 192.5
RMS 33.28
6.4 Top Quark Mass 112
measurement. The kinematic fitting procedure can therefore be seen as an alternative, and
arguably better, use of the same information. In fact, as it can be seen in 6.6(a) it improves
the resolution of the mass distribution and also betters the jet energy scale on a per event
basis.
Top quarks/Events
Top Quark Mass − Hadronic ttbar
1400
1200
1000
800
600
400
Kinematic Fit
No Kinematic Fit
Top quarks/Events
Top Quark Mass − SM Background
300
Kinematic Fit
250
No Kinematic Fit
200
150
100
200
0
120 140 160 180 200 220 240 260 280 300
Mass (GeV)
(a)
50
0
120 140 160 180 200 220 240 260 280 300
Mass (GeV)
(b)
Figure 6.6: Top quark kinematic fit: the effect of the kinematic fit on the invariant mass
distribution of the signal sample, in a), and on the background sample, in b), can be seen.
It is also possible to convert the χ 2 of the fit into a probability and to select events whose
probability of satisfying the required constraints is higher than a certain minimum. The
effect of setting such event selection has been studied and can be seen in fig. 6.7.
Events
Top Quark Mass − Hadronic ttbar
1200
1000
800
600
400
200
0
All Fitted Events
Probability > 1%
Probability > 30%
140 160 180 200 220 240 260
Mass (GeV)
(a)
Events
240
220
200
180
160
140
120
100
80
60
40
20
0
Top Quark Mass − SM Background
All Fitted Events
Probability > 1%
Probability > 30%
140 160 180 200 220 240 260
Mass (GeV)
(b)
Figure 6.7: Top quark kinematic fit event selection; the results of performing an event
selection on the basis of the probability that the event satisfies the kinematic fit constraints
are displayed: in a) for the signal, in b) for the background events.
It is clear that rejecting the events with probability lower than 1% has a significant
influence on the number of signal and background events as well as on the shape of the

6.4 Top Quark Mass 113
mass distribution. Differently any further rejection seems to have only a very small effect.
This result suggests that the best mass resolution will be achieved with the 1% probability
selection procedure. As any tighter cut performs similarly with respect to the mass resolution
and background rejection, but has slightly lower signal efficiencies.
Having reached the goal of plotting the top quark mass distribution a method needs to
be implemented in order to estimate the top mass and its relative error. Two techniques
were used for this: the curve fitting and the template fitting. Both techniques are described
below.
6.4.1 Curve Fitting
The first method used in this analysis is a simple curve fitting technique. In this process the
calculated top quark distribution is modelled with a Breit-Wigner distribution, representing
the natural width of the top quark convoluted with an ad-hoc determined resolution function:
∫
S(t) = N
BW(x) × RES(t − x)dx (6.4)
where N is a normalization factor and the Breit-Wigner is defined as:
BW(x) =
Γ
2π[(x − M) 2 + Γ 2 /4]
(6.5)
the used resolution function is an asymmetric double gaussian:
⎧
⎪⎨ l × exp
RES(x) =
⎪⎩ l × exp
(− (x−M)2
2σ1
(− 2 (x−M)2
2σ 2 1
)
+ (1 − l) × exp
)
+ (1 − l) × exp
(− (x−M)2
2σ2
(− 2 (x−M)2
2σ 2 3
)
, x > M
)
, x < M
(6.6)
In equation 6.5 Γ is the Breit-Wigner width and M is the mass of the top quark. In equation
6.6 l is a weight parameter and σ 1,2,3 are the standard deviation of the fitted Gaussians; as
before M is the mass of the top quark. Additionally the SM background has been modelled
with a second order polynomial.

BWconvGaussplustanh
Entries 57396
Mean 177.3
RMS 7.92
χ 2
/ ndf
157.8 / −10
p1 174
±
0.1
6.4 Top Quark Mass 114
The first step of the process is to fit the statistically independent MC generated signal
events with the function displayed in equation 6.4. Please note that these are not the same
events as the ones on which the final, mass determining, fit is performed. In this process
the parameters Γ and M are fixed to the ones specified at the generator level. The aim of
the fit is therefore to extract the resolution function parameters: w and σ 1,2,3 . In a separate
process the background events are fitted with the second order polynomial. Ideally one would
fit a statistically independent background sample; but, given the lack of such sample, the
background data sample has been fit as an approximation. Given the relatively low statistics
of the background with respect to the signal (

6.4 Top Quark Mass 115
Top Quark Mass
Event Selection Fit Range (GeV) χ 2 /NDF Mass (GeV) σ(GeV)
Kinematic fit 165-200 308/68 173.937 0.054
Kinematic fit 165-185 130/38 173.565 0.051
Probability > 1% 165-200 858/68 173.902 0.056
Probability > 1% 165-185 157/38 173.965 0.051
Probability > 30% 165-200 945/68 174.153 0.045
Probability > 30% 165-185 160/38 173.884 0.045
Table 6.3: Top quark mass - curve fitting technique: the full list of results obtained from
the curve fitting techniques using different event selection and fit ranges is displayed
which explains the fat tails at high masses, not present before the kinematic fit (fig. 6.6(a)).
This derives from the forcing of the events reconstructed with masses higher than 250GeV
to a lower value, compatible with the set constraints. Other major unmodelled sources of
discrepancy are the combinatorial background and the approximation of t¯t → b¯bq¯qq¯q as the
signal sample. It is clear that with a choice of different and substantially more complex
functions all the above described events could be accounted for, this is however not the path
chosen by this analysis. In fact a different and more reliable method for determining the top
quark mass, a template fitting method, has subsequently been implemented and is described
in the next section.
Finally also the background events are weighted and this poses a choice on what shall
be considered as the background uncertainty. For example, if the weights of events w i are
larger than one, then by considering the uncertainty of a bin as √ ∑i w2 i the modelled error
is clearly overstated with respect to the physically expected one. The effect of considering
the error as √ ∑i w i, as it has been done in this analysis, is instead more subtle. In this case
the uncertainty seems to imply a much smoother distribution than the presented one, as the
error of each bin is statistically understated. A curve fitted on such events will therefore
tend to result in a larger χ 2 /NDF value. This might also explain partially the seemingly
large values obtained in the presented fits. Although this can be a major effect, it is present
only in the background events and hence probably not very dramatic in this analysis. It
has therefore been preferred to the possible alternative. Incidentally while dealing with
a template sample, because one is not trying to model the actually collected data but to

6.4 Top Quark Mass 116
reproduce our theoretical model the uncertainty should always be calculated as √ ∑i w2 i , as
it has also been.
Because of the combination of all these reasons the fit had to be restricted only to a
narrow window encompassing the peak of the distribution. This is in fact the region where
the distribution is most sensitive to the signal, least sensitive to the background and to
most of the described limitations. It is clear from table 6.3 that widening the fit region
further decreases the reliability of the fit. Interestingly enough no major effect is seen by
selecting events only above a certain kinematic fit probability; only a small improvement in
the uncertainty can be seen.
As a result of this procedure one can conclude that the obtainable statistical uncertainty
on the top mass at the ILC will be around 50 MeV. Given the limitations of the method it
seems sensible to quote this only as an approximate value. As already stated a method, which
we consider more reliable, has also been implemented. The next section in fact describes the
template fitting method. The result of this section should therefore be considered mainly as
a check of such method, rather than the final result of the top mass analysis.
6.4.2 Template Fitting
In the template method the data signal sample is compared to several MC signal templates
which have been generated using different values of the top mass (173.5GeV, 174.0GeV and
174.5GeV). The χ 2 between the distributions can then be calculated as:
χ 2 =
N∑
bins
i=1
(t i − y i + δ i ) 2
(σ 2 t,i + σ2 y,i + σ2 SM,i ) (6.7)
where N bins are the number of bins in the top mass histogram considered in the calculation, t i ,
y i are the number of events in the i th bin for the the template sample and the signal sample,
σ t,i , σ y,i , σ SM,i are the uncertainties on the i th bin for the template sample, the signal sample
and the SM background. δ i is instead a Gaussian smearing term. This term accounts for
the SM model background in a statistically independent way. It is a value randomly picked

6.4 Top Quark Mass 117
from a Gaussian distribution of mean zero and standard deviation equal to σ SM,i . In fig. 6.9
one can see a graphical representation of the algorithm. Please note that the uncertainties
presented in the plot are the sum under quadrature of the data sample uncertainties and the
template sample uncertainties. The plotted values and their uncertainties do not however
include any SM background component.
Top Mass: template − data
Events template − Events data
600
400
200
0
−200
Template 173.5GeV
Template 174.5GeV
−400
−600
150 160 170 180 190 200 210
Top Mass (GeV)
Figure 6.9: Graphical representation of the template fitting technique. The curves show the
difference in the number of events in each bin between the template sample and the data
sample
Once the χ 2 of the data sample with all the three template samples is calculated a
parabola is fit on the three mass points and the minimum of the parabola, χ 2 min, is determined.
The mass value corresponding to χ 2 min represents the reconstructed mass of the top
quark. The uncertainty of the data sample is then defined as the mass point for which
the following relationship is satisfied: χ 2 = χ 2 min + 1 [61]. Fig. 6.10 displays a graphical
illustration of the above described χ 2 minimization and uncertainty estimation. It has to
be noted that ideally more than three template samples should be used for the presented
minimization. However the generation of millions of MC events is very CPU intensive. Given
the small amount of available resources it has been decided to limit the number of template

6.4 Top Quark Mass 118
samples to the bare minimum of three.
Figure 6.10: Graphical representation of the template fitting minimization. The red crosses
represent them measured χ 2 values (please note that in the case of this analysis only three
such points are calculated).
This method clearly does not suffer from most of the issues described in the previous
section. In fact the problems of ’kinematic reflection’, combinatorial background and of the
t¯t = b¯bq¯qq¯q approximation are automatically taken care of. The precise shape of the curve
does not in fact need to be known, but only the difference between the two curves; as both
curves incorporate these effects they will not influence the final results of the algorithm.
Additionally given that the algorithm works on a bin by bin basis the inconsistency derived
from the weighting of events is substantially reduced. The only assumption that the method
uses is that the χ 2 distribution can be approximated, near its minimum, as a parabolic
function.
Before analysing the results from the template fitting one must be aware that two different
ways of renormalizing the template samples can be applied. One can renormalize the number
of events to the observed number (the number of signal events present in the data sample) in
which case only the shape of the distribution is used in determining the mass and its error.
Alternatively one can consider also the fact that, at different top masses, the cross sections
will be different and therefore use this information. Of course the later result will further

6.4 Top Quark Mass 119
Top Quark Mass
Event Selection Fit Range (GeV) χ 2 min /NDF Mass (GeV) σ (GeV)
No Kinematic fit 120-200 148/159 174.135 0.090
No Kinematic fit 140-180 83/79 174.173 0.097
Kinematic fit 150-200 94/99 174.033 0.053
Kinematic fit 165-200 63/69 173.991 0.056
Kinematic fit 165-185 42/39 173.990 0.058
Probability > 1% 150-200 101/99 174.018 0.049
Probability > 1% 165-200 61/69 174.013 0.049
Probability > 1% 165-185 41/39 174.010 0.053
Probability > 5% 150-200 97/99 174.024 0.050
Probability > 5% 165-200 61/69 174.017 0.050
Probability > 5% 165-185 38/39 174.17 0.053
Probability > 10% 150-200 100/99 174.012 0.050
Probability > 10% 165-200 68/69 174.012 0.051
Probability > 10% 165-185 40/39 174.14 0.052
Probability > 20% 150-200 91/99 174.013 0.049
Probability > 20% 165-200 68/69 174.010 0.050
Probability > 20% 165-185 39/39 174.022 0.052
Probability > 30% 150-200 98/99 174.021 0.049
Probability > 30% 165-200 68/69 174.020 0.050
Probability > 30% 165-185 47/39 174.027 0.052
Table 6.4: The template fitting results using the renormalized cross sections are displayed
for different event selections and different fit ranges.
depend on the accuracy of the cross section calculation.
Table 6.4 shows the result obtained by using the first method. It can be immediately
seen that the estimated statistical uncertainty is of the order of 50 MeV it can also be noted
that while applying the kinematic fitting and the rejecting the events that have probabilities
of matching the constraints smaller than 1% is beneficial to the final result, but any tighter
selection does not improve the performance. Given fig. 6.7 this is an expected effect; also
increasing the fit width beyond the 165 GeV-185 GeV region does not substantially improve
the result, as is to be expected from fig. 6.9.
Table 6.5 instead presents the kinematic fitting results when the cross sections from
the MC generator are used. Note that in the presented calculation the MC cross sections
are assumed to have no uncertainty. As more information is used for the template fit a
slightly better mass resolution is expected. In fact this can be clearly seen and the statistical

6.4 Top Quark Mass 120
Top Quark Mass
Event Selection Fit Range (GeV) χ 2 min /NDF Mass (GeV) σ (GeV)
No Kinematic fit 120-200 151/159 174.198 0.062
No Kinematic fit 140-180 83/79 174.192 0.079
Kinematic fit 150-200 94/99 174.033 0.049
Kinematic fit 165-200 66/69 174.035 0.050
Kinematic fit 165-185 42/39 174.010 0.056
Probability > 1% 150-200 101/99 174.046 0.046
Probability > 1% 165-200 62/69 174.048 0.045
Probability > 1% 165-185 41/39 174.025 0.051
Probability > 5% 150-200 96/99 174.049 0.047
Probability > 5% 165-200 62/69 174.049 0.047
Probability > 5% 165-185 38/39 174.030 0.051
Probability > 10% 150-200 99/99 174.033 0.047
Probability > 10% 165-200 68/69 174.039 0.047
Probability > 10% 165-185 41/39 174.23 0.051
Probability > 20% 150-200 89/99 174.013 0.047
Probability > 20% 165-200 63/69 174.031 0.050
Probability > 20% 165-185 39/39 174.031 0.051
Probability > 30% 150-200 97/99 174.035 0.047
Probability > 30% 165-200 73/69 174.040 0.047
Probability > 30% 165-185 46/39 174.035 0.051
Table 6.5: The template fitting results using the MC cross sections are displayed for different
event selections and different fit ranges.
resolution achievable is now lower at 45 MeV.
It is now important to determine the stability and reliability of the template fitting
method. A few simple tests can be devised. Theoretically the value of χ 2 min/NDF should
be ≈ 1 in all presented cases. Looking at table 6.4 and table 6.5 it is clear that this is
the case. Additionally, if the measurements are statistically independent, they should form
a Gaussian distribution around the central value. Given that the samples used are always
the same the measurements are clearly not independent, never the less the fact that in
most of the cases the measurements fall inside one σ is reassuring. The accuracy of the
measurement also performs as expected when the fit ranges or event selections are varied.
Finally the measurement should also not be dependent on the way it is displayed, for example
the variation of bin sizes should not change the final result. This has been also tested and
indeed the results have been found stable. In order to further test the stability and reliability
of the used template fitting method a toy MC study has also been performed. In this study

6.5 Cross Section of the b¯bq¯qq¯q Process 121
the template method has been compared to the curve fitting method for a series of known
distributions. The results between the two methods have been found to be always consistent.
A final word has to be said on the interpretation of the template fitting result. By
considering equation 6.7 one can immediately see that the result is dependent on the error
of the template. Given that the template sample is four times larger than the signal data
sample the relative uncertainty is: σ t,i ≈ 1/2σ y,i . Similarly since the purity of the data
sample is 75%-80% also σ SM,i ≈ 1/2σ y,i . It is then possible to make a back of the envelope
estimation of the uncertainty achievable with this method in the limit where σ t,i

6.6 Summary 122
b¯bq¯qq¯q Cross Section
Event Selection Efficiency Purity Cross Section (fb) σ (fb) σ (%)
No kinematic fit 51.5% 68.7% 287.4 1.3 0.45%
Kinematic fit 48.6% 74.8% 287.2 1.3 0.45%
Probability > 1% 35.4% 83.6% 287.2 1.7 0.59%
Probability > 5% 31.9% 85.0% 288.5 1.5 0.52%
Probability > 10% 30.0% 85.8% 287.3 1.6 0.56%
Probability > 20% 27.3% 86.8% 287.5 1.6 0.56%
Probability > 30% 25.3% 87.4% 287.2 1.6 0.55%
Table 6.6: The b¯bq¯qq¯q cross section as calculated using different event selections. The event
selection is based on the probability that the events match the kinematic fitting constraints.
deteriorate if any further event selection is applied due to the reduced statistics. One can
now compare the obtained result with the actual cross section at MC level (285.8fb) and
notice their statistical agreement.
It is important to remember that this is not actually the cross section of the e + e − →
t¯t → b¯bq¯qq¯q process, but of the b¯bq¯qq¯q final state. However the absolute uncertainty of this
measurement is equivalent in the approximation where there is no error on the efficiency
calculation and the efficiencies remain equal. This can be seen by noting that no term would
change in the the uncertainty, expressed as: √ N ALL /(ε ∫ Ldt). Incidentally if the efficiency
increases, which is what one would expect, given that some event selections are targeted to
the reconstruction of the top quark and W boson masses, the absolute error will decrease as
a result.
6.6 Summary
This chapter showed that the precision achievable when measuring the top mass in the
hadronic t¯t is between 45 MeV and 49 MeV, depending on the used assumptions. It also
established that the cross section of the b¯bq¯qq¯q process can be measured with a precision of
1.3 fb. All the precisions are quoted without systematic uncertainties.
The chapter also described the event selection process used in the hadronic t¯t study.
The importance of the b tagging and kinematic fitting algorithms for the event selection and

6.6 Summary 123
reconstruction has been outlined. As this is a feasibility study, not all the used analysis tools
were yet optimized. It is therefore foreseen that the achievable resolutions will improve.

Chapter 7
Quark Charge and Forward Backward
Asymmetries
From the list of observables that have been described in the introductory theory chapter only
the forward backward asymmetries of the top quark and of its decay product, the bottom
quark, still need to be addressed. As has been already described in the relevant section these
will provide an insight into the top Electro-Weak couplings. More specifically the top quark
forward backward asymmetry tests the Z tt coupling, while the bottom quark observable
measures the W tb coupling.
Performing the desired measurements in a leptonic or semi-leptonic t¯t channel should be
a relatively easy task. The charges of the leptons (µ and e) are in fact well known as they are
rather simple to reconstruct. From these it is then possible to unambiguously reconstruct
the charges of the top quark from which the lepton originated and of the matching bottom
quark. Differently in the hadronic b¯bq¯qq¯q, which has the largest statistics, no such solution is
possible and a method must be devised in order to calculate the charge of the bottom quark
by using the jet originating from it. As the charge of the b quark is -1/3 and the charge of
the ¯b quark is +1/3 this is equivalent to distinguishing the b quark from the ¯b quark. Several
techniques used to reconstruct the quark charge are described below.
124

7.1 Vertex Charge 125
7.1 Vertex Charge
The first method that has been developed is the vertex charge. This method has been
implemented by the author into the LCFI Vertex software and as such it aims not only to
reconstruct the charge of the bottom quarks but also of the charm quarks. Slightly different
assumptions are made for different flavours and it is therefore important to first determine
the quark flavour. To calculate the vertex charge of a bottom jet all tracks that are thought
to belong to the decay chain are identified and the vertex charge is given by the sign of the
sum of their charges. The rare cases in which the vertex charge has an absolute value above
2, or below -2, indicating significant mistakes in the assignment of tracks to the decay chain,
are discarded in the determination of the quark charge sign. To assign tracks to the b quark
decay chain the same approach is used as the one described in the flavour tagging chapter
of this thesis for the momentum corrected vertex mass. The parameters used for a charm
jet can instead be found in Appendix B.
Fig. 7.1 demonstrates the ability to distinguish the parton charge of heavy flavour jets.
As this is part of the LCFI vertex software it is presented for the LDC detector using the same
91.2 GeV sample as the one described in Chapter 5. No information about the parton charge
is obtained for the case of a reconstructed vertex charge of zero, the dominant contribution
to which is from decays of neutral B-mesons with vertices with even number of tracks. Good
charge separation can instead be achieved by selecting jets with non-zero reconstructed
vertex charge, mostly coming from charged B-mesons. Table 7.1 quantifies the performance
of parton charge identification with standard LCFI Vertex parameters. The ratio of correct
over wrong charge identification is better for c jets than for b jets, and the reconstruction
quality is found to degrade slightly with increasing collision energy, as expected.
This method however suffers from a series of inefficiencies: only a fixed point on the
purity efficiency trade-off is available to the final user, the method is not applicable in case
no vertex has been found in the jet and it is not designed to distinguish between b and ¯b
quarks in the case of neutral mesons. Incidentally b (¯b) quarks fragment into neutral mesons
in more than 50% of the events. While performing this final analysis it has been decided

htemp
Entries 1660
Mean 0.3177
RMS 0.957
htemp
Entries 791
Mean 0.2946
RMS 0.7427
htemp
Entries 733
Mean 0.7913
RMS 0.8185
htemp
Entries 733
Mean 0.7913
RMS 0.8185
htemp
Entries 733
Mean 0.7913
RMS 0.8185
htemp
Entries 440
Mean 0.5455
RMS 0.7964
htemp
Entries 733
Mean 0.7913
RMS 0.8185
htemp
Entries 733
Mean 0.7913
RMS 0.8185
7.2 Momentum Weighted Vertex and Jet Charge 126
Vertex Charge b Quark
Vertex Charge b Quark − Charged Hadrons Only
Jets
700
600
Q_MC>0
Jets
400
350
Q_MC>0
500
Q_MC

VertexCONTChargeBquark
Entries
371207
Mean 0.1121
RMS 0.2511
7.2 Momentum Weighted Vertex and Jet Charge 127
Vertex Charge
MC Type
Reconstructed Vertex Charge
Correct Ambiguous Wrong No Vertex/Tracks
91.2 GeV b jets 32.8% 33.1% 12.2% 21.9%
c jets 14.6% 27.4% 3.2% 54.8%
500 GeV b jets 27.0% 23.9% 13.5% 35.6%
c jets 13.0% 24.5% 4.2% 58.4%
Table 7.1: Performance of parton charge identification using LCFI Vertex default settings.
Any non-zero vertex charge measurement with the same (opposite) sign as the parton charge
is labelled correct (wrong). Jets with a reconstructed vertex charge of zero are called ambiguous.
Jets where no vertices are present, or where no tracks pass the strict track quality
criteria for the vertex charge measurement (applicable only for c quark jets), are listed in
the rightmost column.
where Q T is the charge of the track, p T is the momentum of the track and k is a user defined
parameter; as expected the sums are performed only on the tracks associated with the vertex.
The performance of such method for discriminating the parton charge can be seen in fig.
7.2(a). Differently from the previous section the evens used in the plot are from the 174.0
GeV b¯bq¯qq¯q template sample. Only b quark jets at MC level with a neural net b tag higher
than 0.4 are being included.
Events
8000
7000
6000
5000
Momentum Weighted Vertex Charge
bbar quark
b quark
purity
Momentum Weighted Vertex Charge − Performance
0.85
0.8
0.75
4000
0.7
3000
2000
1000
0.65
0.6
k = 0.3
k = 0.1
k = 1.0
0
−1 −0.5 0 0.5 1
Momentum Weighted Vertex Charge
0.55
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
efficiency
(a)
(b)
Figure 7.2: Momentum weighted vertex charge a) distributions for b and ¯b quark jets, k
parameter used = 0.3 b) purity vs efficiency curves for different weighting parameters k.
Analysis performed on a b¯bq¯qq¯q sample with 500 GeV centre of mass energy.
Fig 7.2(b) instead shows the purity/efficiency performance for different values of the
k parameter. As a comparison it can be noted that the standard vertex charge, applied
to the same sample, obtains a purity of 76.6% with an efficiency of 44.5%. For the same

VertexCONTChargeBquark
Entries
371207
Mean 0.06994
RMS 0.1782
7.2 Momentum Weighted Vertex and Jet Charge 128
efficiency value the results with the new method are 76.8% if the k parameter is set to 0.3
and 77.2% if the k parameter is set to 0.1. The k value used in the rest of the analysis is
0.3. In fact, although the algorithm with this setting performs marginally worse than with
a k value of 0.1 or 0.05 at high efficiencies, it performs substantially better when a high
purity is required. The uncertainty on the presented purity measurements, calculated with
the formula σ p = √ p(1 − p)/n, is 0.1%, where p is the purity.
However all the jets without a secondary vertex have been completely excluded from
this calculation. These represent 3.2% of the total number of jets originating from a b
quark, assuming the event selection of a neural net b-tag higher than 0.4. Since ideally
one would like to be able to determine also the charge of these jets an additional method,
the momentum weighted jet charge [64], has been implemented. As the name suggest the
algorithm is identical to the one already described in equation 7.1. The track selection
process is however slightly different; the sum is now performed over all the tracks present in
the jet rather than in the vertex.
Events
12000
10000
Momentum Weighted Jet Charge
bbar quark
b quark
purity
Momentum Weighted Jet Charge − Performance
0.85
0.8
8000
0.75
6000
0.7
4000
2000
0.65
0.6
k = 0.3
k = 0.1
k = 1.0
0
−1 −0.5 0 0.5 1
Momentum Weighted Jet Charge
0.55
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
efficiency
(a)
(b)
Figure 7.3: Momentum weighted jet charge a) distributions for b quark and ¯b quark jets,
k parameter used = 0.3 b) purity vs efficiency curves for different weighting parameters k.
Analysis performed on a b¯bq¯qq¯q sample with 500 GeV centre of mass.
The performance of the algorithm can be seen in fig. 7.3(a). Fig. 7.3(b) instead shows
the dependence of the performance on the value used for the k parameter. Also in this
case the value of 0.3 has been chosen as optimal. At first inspection the performance of the
two algorithms appears very similar; the vertex charge performing just slightly better. It is

7.2 Momentum Weighted Vertex and Jet Charge 129
therefore worth analysing whether the two methods are conveying the same information, in
which case using just one algorithm could suffice, or whether by combining the two algorithms
one can extract additional information and hence improve the final result.
purity
1
0.95
0.9
0.85
Momentum Weighted Vertex Charge
purity
1
0.95
0.9
0.85
Momentum Weighted Jet Charge
b/bbar
B−/B+
B0bar/B0
0.8
0.8
0.75
0.75
0.7
0.65
0.6
b/bbar
B−/B+
B0bar/B0
0.7
0.65
0.6
0.55
0.55
0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
efficiency
0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
efficiency
(a)
(b)
Figure 7.4: Performance of a) momentum weighted vertex charge and b) momentum weighted
jet charge in distinguishing B + from B − and ¯B 0 from B 0 .
The performance of the algorithms has therefore been tested under the presence of only
charged mesons B + and B − and only neutral mesons B 0 and ¯B 0 . Fig. 7.4(a) show that
the momentum weighted vertex charge is able to distinguish very well between B + and B − ,
while having almost no discriminatory power when it comes to B 0 and ¯B 0 . Differently the
performance of the momentum weighted jet charge, fig. 7.4(b), is more similar between the
two cases and the algorithm can separate reasonably well also B 0 and ¯B 0 . It also should
be noted that neutral mesons (both B 0 and B S ) can oscillate. While in this process the
charge of the meson does not change, the charge of the b quark does. This introduces a
further smearing to the distributions. In this analysis, while the B 0 / ¯B 0 (and the B S / ¯ B S )
oscillations have been included at MC level they have not been studied in detail. Indeed
the oscillation of the neutral mesons is expected to have a rather small effect on the B 0
mesons, which have a frequency of oscillation of ≈ 0.5 × 10 12 s − 1, which implies a period
of oscillation larger than their mean lifetime (≈ 1.5 × 10 −12 s). Hence a small effect is
expected. Differently in the case of B S mesons the effect should be large as the frequency (≈
18 × 10 12 s − 1) implies a period of oscillation that is much smaller than their mean lifetime
(≈ 1.5 × 10 −12 s). Hence the smearing in the case of B s mesons is much more significant

7.2 Momentum Weighted Vertex and Jet Charge 130
and the techniques presented for parton charge discrimination are hence less effective. For
the purpose of evaluating the performance of the algorithms the original parton produced
at the Feynman diagram level has been used. Once again it must be remembered that all
the results regarding the momentum weighted vertex charge do not include jets where no
secondary vertex has been found ( about 3.2% of the b jets, after the event selection described
in the previous chapter has been performed).
The difference between the two algorithms derives from the different physical principle
that they are based on. The jet charge algorithm is based on exploiting the fact that the
most energetic hadrons have a higher probability of containing the charge of the quark that
initiated the jet. In order to explain the reasoning one needs to start by making the fair
assumption that the original quark is also the one with the the highest energy in the jet.
In order for the original quark to undergo hadronization a new quark pair must then be
produced. The hadronization process of the original quark absorbs only one of the two
quarks. If after the fragmentation the resulting meson is charged the reasoning becomes
trivial, given that all the other quarks have a lower momentum. If instead the resulting
meson is neutral, then the second most energetic meson has to be considered. Because of
momentum conservation considerations this meson most probably contains the second quark
produced in the mentioned pair production. Its charge must then be the same as the charge
of the original quark. The charge of the second meson can hence be either zero or of the same
absolute value as the original quark. If the charge is zero the same reasoning can be repeated
for the next most energetic meson. A much more detailed explanation of this principle can
be found in [65].
The principle behind the vertex charged algorithms is instead based on precisely determining
all the tracks that derive from the vertex. In this case the aim is to directly determine
the charge of the meson. The momentum weighting conveys some information on the reliability
of the track. Additionally, because of the same reasons as the one discussed in the
case of the jet charge, it also contains some indication on the probability that the track
derives from the original B meson. Given the rather poor performance of the vertex charge

RatioVertexCONTChargeBquark
Entries 100
Mean 0.6233
RMS 0.4541
R Distribution − Momentum Weighted Jet Charge
Entries 100
Mean 0.7089
RMS 0.391
7.3 Combined Charge 131
in distinguishing between B 0 and ¯B 0 such information is only minimal.
7.3 Combined Charge
As the two different methods contain rather different information it has been decided to
combine them into a single discriminatory variable. Ideally one would like to include also
other discriminatory parameters (examples are the lepton charge and the dipole charge
algorithms), however, do to a lack of manpower, these have not yet been implemented.
The method chosen for the combination of the parameters is the one presented in [66].
If fi b (x i ) is the probability density functions for the b quark for variable x i and f¯b
i (x i ) is the
equivalent distribution for the ¯b quark then for each discriminating variable x i a parameter
r i is defined:
r i = f¯b i (x i )
f b i (x i)
(7.2)
which effectively is the ratio of the probability distributions; the index i denotes the discriminating
variable. While ideally one would perform such calculation in functional form in
this analysis this has been approximated to the ratio of entries in each bin of the histograms
presented in fig. 7.2(a) and fig. 7.3(a).
R Distribution − Momentum Weighted Vertex Charge
R Distribution − Momentum Weighted Jet Charge
r
2
10
r
2
10
10
10
1
1
−1
10
−1
10
−2
10
−1 −0.5 0 0.5 1
Momentum Weighted Vertex Charge
−2
10
−1 −0.5 0 0.5 1
Momentum Weighted Jet Charge
(a)
(b)
Figure 7.5: f¯b
i (x i )/f b i (x i ) for a) momentum weighted vertex charge and b) momentum
weighted jet charge.
Fig. 7.5(a) and fig. 7.5(b) present the r i values obtained for each bin of the momentum

DtotBquark
Entries
47966
Mean 0.2709
RMS 0.5316Combined
7.3 Combined Charge 132
weighted vertex charge and the momentum weighted jet charge. As this is a MC calculation
it is, of course, performed on the 174.0 GeV template sample. For each data event a combined
tagging variable can then be defined:
r = ∏ i
r i (7.3)
please note that the value of r i , previously calculated on the MC sample, is the one corresponding
to the value of x i calculated in the data event. Clearly this method, as most
multi-variable combination methods, works best in the case that the discriminating variables
are uncorrelated.
Given the definition of r, if r < 1 then the reconstructed jet is naturally more likely to be
a b quark and if r > 1 the jet is more likely to originate from ¯b quark. The range of possible
Events
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
Charge
b quark
bbar quark
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Combined Charge
(a)
purity
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
Combined Charge − Performance
Combined Charge
Momentum Weighted Jet Charge
Momentum Weighted Vertex Charge
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
efficiency
(b)
Figure 7.6: Combined charge a) distributions for b quark and ¯b quark jets b) purity vs
efficiency curves for combined charge, momentum weighted vertex charge and momentum
weighted jet charge. Please note that the calculation is performed after all the event selections,
as explained in the previous chapter, have been performed.
values for r is therefore between 0 and ∞. For the purpose of graphical representation and
convenience of the end user a variable whose limits are -1 and +1 has been devised. The
combined charge variable is therefore defined as:
C = 1 − r
1 + r . (7.4)

7.4 Bottom Quark Forward Backward Asymmetry 133
A jet with C > 0 is more likely to derive from a b quark and a jet with C < 0 is more likely
to derive from a ¯b quark. Fig. 7.6(a) shows the result of the charge recombination technique
when performed on the 174.0 GeV template sample after all the events selections described
in the previous chapter have been performed. Fig. 7.6(b) instead shows the improved performance
of the combined charge when compared with the independent momentum weighted
vertex charge and momentum weighted jet charge.
7.4 Bottom Quark Forward Backward Asymmetry
The combined charge can now be applied to calculate the forward backward asymmetries
of the b and t quarks. Before this task has been attempted some final event selections have
been performed. Firstly all the events reconstructed with a top mass lower than 155 GeV or
higher than 195 GeV have been rejected. The mass value used is the one after the kinematic
fit, as described in the previous chapter dealing with the top mass measurement.
It has also been decided to investigate the possibility of performing an event selection
based on the reconstructed charge of the quarks. For this purpose one would like to use the
information derived from both jets. Assuming that the event is actually a b¯bq¯qq¯q, rather
than an event from the SM background, and that the quark identification has been correctly
performed, the charge calculations performed on the two jets are really two uncorrelated
measurements of the same quantity. The two b jets must in fact have opposite absolute
values for their charge. The combined charges of the two jets with the highest neural net b
tags are therefore multiplied and used as an event selection parameter. Fig. 7.7(a) shows
such distribution for the signal and the background events. The main aim of this process
is not to reject the SM background, not plotted, but to reject the background deriving
from the events in which the b quark has been mistagged or the charge of such quark
has been misreconstructed. An event charge is labelled as misreconstructed only when the
reconstructed combined charge of the ¯b jet is higher than the combined charge of the b jet.
Similarly to the case of the b tagging event selection, presented in the previous chapter,

ChargeMultiplyTOPHARDEYPTBcut
Entries 150303
Mean −0.06762
RMS 0.3435
7.4 Bottom Quark Forward Backward Asymmetry 134
Events
6000
5000
4000
3000
2000
Combined charge jet1 * combined charge jet2
All bbqqqq events
Wrong charge + mistagged
Mistagged
Signal/sqrt(Signal + Background)
140
120
100
80
60
40
Combined Charge Event Selection Optimization
1000
20
0
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Combined Charge b−jet1 * Combined Charge b−jet2
(a)
0
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Combined Charge b−jet1 * Combined Charge b−jet2
(b)
Figure 7.7: Combined charge b jet-1 × combined charge b jet-2 a) distribution for reconstructed
events, mistagged evens and events with misidentified charge b) event selection
optimization using a S/ √ S + B maximization technique.
also in this case an optimization has been attempted and the value of S/ √ S + B has been
maximized. Fig. 7.7(b) shows the results of such optimization. Note that for the purpose
of this optimization also the SM background has been included. Interestingly enough the
S/ √ S + B result suggests that all events should be included. Under these conditions the
total efficiency of the analysis is 22.7%, while the purity is 58.1%. The impurities derive
45.9% from the SM background, 45.0% from the charge misreconstruction and 9.1% from
the quark misidentification.
The calculation of the forward backward asymmetry as defined in equation 1.13 can
now be performed. Fig. 7.8 shows the distribution with respect to cos(θ) of the signal
and background events used in this calculation. For the purpose of this calculation, the
two jets with the highest neural net b tags have been used. Of these the jet with a higher
combined charge has been declared as originating from a b quark, while the other b jet has
been declared as originating from a ¯b quark. The angle θ of the reconstructed b jet has been
used as an approximation of the angle of the original b quark.
Table. 7.2 instead shows the results of the A fb calculation, as defined in equation 1.13, for
different event selections, to check the stability of the result. The number of correctly reconstructed
b¯bq¯qq¯q events is calculated for the forward and backward hemispheres independently.
For this purpose the SM background is subtracted from the total number of reconstructed

quarkscosthetaALLEYPTBcut
Entries
29122
Mean 0.1191
RMS 0.6081
7.4 Bottom Quark Forward Backward Asymmetry 135
b quarks
6000
5000
Events Used for b quark A_fb
Events used for b quark A_fb
Mistagging + SM Background
4000
SM Background
3000
2000
1000
0
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
cos(theta)
Figure 7.8: Events used for the calculation of the b quark A fb . No event selection is performed
using the combined charge. However, in order to qualify as a b rather than ¯b quark, the
combined charge of the jet must be higher than the one of the other b jet present in the
event. Notice that, as explained in the previous chapter, only two b jets are assumed to be
present in each event. These are the jets with the highest neural net b tags.
events. The number of events left is then multiplied by the purity of the reconstruction,
accounting for all the events where the charge has been misidentified or where the b jet has
been mistagged. When calculating the purity, only the quark and charge misidentification
are used as a background and the SM background is not included, since it is substracted separately.
Note that separate purities have been calculated for the forward and the backward
hemispheres. The equation applied to each hemisphere therefore is: N b = (N tot − N SM ) ∗ p,
where N b is the number of b jets correctly identified and therefore used in the calculation,
N tot is the total number of events reconstructed, N SM is the standard model background
and p is the purity of the reconstruction.
For each event selection the uncertainty has been calculated with three different assumptions.
The lowest uncertainty, σ 1 , assumes that the efficiency of tagging and the standard
model background have been perfectly simulated at MC level and therefore do not contribute
to the achievable precision of the forward backward asymmetry. The only uncertainty term
therefore is √ N tot,θ)90 ◦ where N tot,θ)90 ◦ is the number of events whose b quarks have
been reconstructed in the forward (backward) region of the detector. Clearly this includes
both signal and background events. For the second evaluation, σ 2 , the uncertainty derived

7.4 Bottom Quark Forward Backward Asymmetry 136
from the purity of the tagging defined as σ p = √ p(1 − p)/n, where n is the total number
of events passing the event selection process has been also considered. Finally the third
evaluation, σ 3 , considers also an additional Poissonian uncertainty equal to the square root
of the reconstructed Standard Model background events. It has to be noted that, if the
uncertainty on the SM background is treated as a binomial error and therefore included into
the purity calculation, the quoted results do not vary. In each of the three cases the uncertainty
has been calculated separately for the forward and backward regions and subsequently
the standard error propagation method has been used to evaluate the uncertainty on each
asymmetry calculation. Possible systematic uncertainties have been neglected.
b quark A fb
Event Selection A fb σ 1 σ 2 σ 3
Charge b jet-1 × Charge b jet-2 < 1.0 0.293 0.006 0.007 0.008
Charge b jet-1 × Charge b jet-2 < 0.5 0.293 0.006 0.007 0.008
Charge b jet-1 × Charge b jet-2 < 0.0 0.289 0.007 0.008 0.009
Table 7.2: Reconstructed A fb for the b quark and the respective uncertainties. The different
uncertainties (σ 1 ,σ 2 ,σ 3 ) have been calculated with different assumptions as explained in the
text of this section.
From these results (table 7.2) it is clear that an uncertainty of less than 0.01 is achievable
when the b quark A fb is calculated. It is also clear that the devised method performs in a
stable manner. Incidentally the calculated uncertainty on the A fb can be improved if the
results of the calculation of the b quark are combined with the ones from the ¯b quark. The
Lagrangian used in equation 1.11 is in fact CP conserving. However since on an event basis
the directions of the b and ¯b are highly correlated because of the large boosts to the t and ¯t
quarks the combination of the results in the centre of mass frame is not at all a trivial task
and it will probably lead only to a small improvement.
It is now possible to compare the results with the theoretical predictions. This will also
allow us to convert the calculated asymmetry resolutions into sensitivity to anomalous form
factors, as defined in equation 1.11. Table 7.3 presents a series of predictions of the b quark
asymmetry for different values of the W tb anomalous couplings [16].
Given that the reconstructed results have been calculated with both anomalous couplings

7.4 Bottom Quark Forward Backward Asymmetry 137
b quark A fb - theoretical prediciton
B WR B WL A fb
0.0 0.0 0.279
0.0 -0.2 0.243
0.0 -0.4 0.218
0.0 -0.6 0.197
0.0 -1.0 0.169
-0.6 0.0 0.301
-1.0 0.0 0.315
Table 7.3: A fb asymmetries for the standard model and anomalous W tb vertices. Calculated
at a centre of mass value of 500 GeV and in the centre of mass rest frame.
equal to zero, the discrepancy between the results and the theoretical prediction is approximately
1.5 σ 3 . Although this can easily be a simple statistical fluctuation other possible
reasons behind this slightly large discrepancy should also be investigated. The difference can
derive from the use of a different MC generator (CompHEP [67, 68]) when calculating the
theoretical predictions or from the fact that the generated signal sample is an all inclusive
b¯bq¯qq¯q rather than e + e −
→ t¯t → b¯bq¯qq¯q. In fact if the A fb asymmetry is calculated at
MC level for the used sample the value of 0.291 is obtained. A result in perfect agreement
with the reconstructed values and that suggests no major systematic uncertainty has been
introduced by the performed analysis.
It can be also inferred from table 7.3 that the performed analysis is sensitive to the presence
of an B WL anomalous form factor whose absolute value is greater that approximately
0.05 or to the presence of a B WR form factor whose absolute value is greater than 0.3.
Finally, in order to check for any significant detector smearing leading to systematic
effects in A fb the angular resolution of the b jet θ angle with respect to the original b quark
has been plotted. Fig. 7.9(a) shows the angular resolution for the angle θ. It can be clearly
seen that the uncertainty is small, the root mean square of the distribution is 0.08 radians,
and that it will therefore not have a major systematic effect on the reconstructed asymmetry.
Incidentally if it did have an effect it would tend to smear the distribution plotted in fig. 7.8
and therefore lower the calculated asymmetry near the values of cos(θ) = 0. This is clearly
not observed. It has also been checked that the resolution does not decrease substantially

BquarkscosthetadiffangleTOPHARDEYPTBcut
Entries 103381
Mean −0.001433
RMS 0.08108
bquarkscosthetadiff2DTOPEYPTBcut
Entries 113341
Mean x 1.804
Mean y 4.158e−05
RMS x 0.659
RMS y 0.1178
7.5 Top Quark Forward Backward Asymmetry 138
in the very forward regions. As it can be seen in fig. 7.9(b) this is also not the case.
b quarks
14000
12000
Theta angle resolution − b quark
Theta angle resolution − b quark
10000
8000
6000
4000
2000
0
−0.4 −0.2 0 0.2 0.4
theta reconstructed − theta MC (radiants)
b quarks
3
10
2
10
10
1
1.5
1
0.5
theta reconstructed − theta MC (radiants)
0
−0.5
−1
−1.5
3
2.5
2
1.5
1
0.5
0
theta reconstructed
(a)
(b)
Figure 7.9: Resolution of the reconstructed b quark angle θ a) with respect to the θ of the
original MC level b quark b) also plotted vs. the reconstructed angle θ. The figures are
plotted after all the event selections used for the calculation of the b quark A fb and only the
quarks whose flavour and charge have been correctly identified are included.
7.5 Top Quark Forward Backward Asymmetry
The analysis of the top quark asymmetry is in principle identical to the one already presented
for the b quark. The only added complication is that, differently from the b quark, where the
angle θ of the b jet can be used as a very good approximation to the angle θ of the original
b quark, the direction of the top quark must be reconstructed from its decay products.
This results in a combinatorial problem that is identical to the one faced when trying to
reconstruct the top quark mass, discussed in the previous chapter. The same tool, the
kinematic fitter, has therefore been used. More specifically the direction of the top quark is
calculated from the combination of jets that minimizes the χ 2 Tot
value of equation 6.1. The
jets’ energies and momenta used are the ones calculated from the kinematic fitter. A further
complication is that the charge of the top quark cannot be directly established. Therefore,
the charge of the b quark is used. If a reconstructed b quark jet is part of the three jets
used to reconstruct the top quark then the top quark is declared as a t. If instead a ¯b jet
is present the quark is declared as a ¯t. Given the constrains set to the kinematic fitter only
one such quark will be present in each jet. Only the two jets with the highest neural net b

quarkscosthetaALLEYPTBcut
Entries
29122
Mean 0.1341
RMS 0.6075
7.5 Top Quark Forward Backward Asymmetry 139
tags are in fact considered as originating from b quarks.
t quarks
6000
5000
Events Used for t quark A_fb
Events used for t quark A_fb
Mistagging + SM Background
4000
SM Background
3000
2000
1000
0
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
cos(theta)
Figure 7.10: Events used for the calculation of the t quark A fb . No event selection is
performed using the combined charge. However, in order to qualify as a t rather than ¯t
quark, the combined charge of the b jet used to reconstruct the top quark must be higher
than the one of the other b jet present in the event. Notice that, as explained in the previous
chapter, only two b jets are assumed to be present in each event. These are the jets with
the highest neural net b tags.
Once the momentum of the top quark has been established the distribution of top quark
events with respect to their cos(θ) can be plotted. Fig. 7.10 shows such distribution and
also includes the Standard Model and the mistagging backgrounds.
Subsequently the same A fb calculations have been performed as the ones described in the
previous section for the b quark case. The results of these calculation can be seen in table
7.4. It is once again clear that the analysis is stable. Not surprisingly the uncertainties are
roughly equivalent to the ones obtained for the b quark. The calculated asymmetries can be
compared to the one calculated at MC level: 0.351. Given that the MC result with no event
selection applied and the reconstructed results are less than 0.5 σ away there seems to be
no major presence of systematic biases from the analysis.
Finally, in the same fashion as for the b quark, the θ angle resolution has been calculated.
Fig. 7.11(a) shows such distribution. In agreement with expectations the resolution is worse
than the one presented for the b quark. The RMS is 0.19 radians. This however should not
pose a significant systematic bias to the calculation. In fact only the very central events of the

TquarkscosthetadiffangleTOPHARDEYPTBcut
Entries 103381
Mean 0.000761
RMS 0.1974
Tquarkscosthetadiff2DTOPEYPTBcut
Entries 113341
Mean x
1.274
Mean y 0.01863
RMS x 0.6527
RMS y 0.4129
7.6 Summary 140
t quark A fb
Event Selection A fb σ 1 σ 2 σ 3
Charge b jet-1 × Charge b jet-2 < 1.0 0.356 0.006 0.007 0.008
Charge b jet-1 × Charge b jet-2 < 0.5 0.348 0.006 0.007 0.008
Charge b jet-1 × Charge b jet-2 < 0.0 0.353 0.007 0.008 0.009
Table 7.4: Reconstructed A fb for the t quark and the respective uncertainties. The different
uncertainties (σ 1 ,σ 2 ,σ 3 ) have been calculated with different assumptions as explained in the
text of the previous section.
7.10 distribution will ever be smeared enough to change hemisphere when reconstructed. The
asymmetry in this region is however small and therefore has only a marginal contribution to
the total calculated A fb . Fig. 7.11(b) instead shows that there is no substantial degradation
of the resolution in the forward regions.
t quarks
10000
Theta angle resolution − t quark
Theta angle resolution − t quark
8000
6000
t quarks
3
10
2
10
4000
2000
0
−1 −0.5 0 0.5 1
theta reconstructed − theta MC (radiants)
10
1
3
2
1
theta reconstructed − theta MC (radiants)
0
−1
−2
−3
3
2.5
2
1.5
1
0.5
0
theta reconstructed
(a)
(b)
Figure 7.11: Resolution of the reconstructed t quark angle θ a) with respect to the θ of the
original MC level t quark b) also plotted vs. the reconstructed angle θ. The figures are
plotted after all the event selections used for the calculation of the t quark A fb and only the
quarks whose flavour and charge have been correctly identified are included.
7.6 Summary
This chapter dealt with the determination of the forward backward asymmetries (A fb ) of the
t quark and its decay product, the b quark, in the hadronic t¯t channel. It has been determined
that both of these can be measured with a precision of 0.008, without the inclusion of any
systematic biases. The achievable resolution of the b quark A fb has been compared to the

7.6 Summary 141
theoretical predictions in the case of W tb anomalous couplings.
Three different methods (the vertex charge, the momentum weighted vertex charge and
the momentum weighted jet charge), used for determining the charge of the b quark from
which a heavy jet has originated, have also been described. An algorithm for recombining
the last two of the mentioned methods has been implemented. The performance of the
implemented methods has been tested; a charge identification purity of up to 80% was
achieved with efficiency of 60% assuming that the jet flavour has been correctly tagged. The
collection of these methods forms the backbone of the A fb analysis.

Chapter 8
Conclusion
The main aim of this thesis, the study of the proprieties of the top quark at the International
Linear Collider by employing the SiD detector concept, has been achieved. The analysis has
been performed in the fully hadronic channel e + e − → t¯t → b¯bq¯qq¯q with a 500 GeV centre of
mass energy and it resulted in the calculation of the achievable precisions for the following
observables:
• the top mass: 49 MeV.
• the cross section of the e + e − → t¯t → b¯bq¯qq¯q process: 1.3 fb.
• forward backward asymmetry of the top quark: 0.008.
• forward backward asymmetry of the b quark from the top decay: 0.008
All the quoted values are to be interpreted as in absence of any systematic biases.
Throughout the work particular care has been devoted to the development and testing
of algorithms and techniques that have a wider scope and applicability. The implemented
heavy jet identification is therefore described in great detail and its performance has been
extensively tested within the ILD/LDC framework on a 91.2 GeV dijet and a 500 GeV dijet
sample. Using the 91.2 GeV centre of mass energy sample it has been found that b jets can
be selected with a 90% purity for an efficiency of 70%. At 500 GeV centre of mass energy,
142

Chapter 8. Conclusion 143
assuming the same efficiency, the purity decreases to 80%. The algorithm has also been
tested within the SiD framework and more specifically with b¯bq¯qq¯q events, which are the
signal of the performed top analysis.
Three quark charge reconstruction algorithms have been implemented. These are the vertex
charge, the momentum weighted vertex charge and the momentum weighted jet charge.
Their performance has been tested by tagging the b quarks of the b¯bq¯qq¯q sample. The vertex
charge has also been tested for b and c quarks with the ILD/LDC 91.2 GeV dijet sample.
The momentum weighted vertex charge and the momentum weighted jet charge have been
also combined in a single discriminating variable which has been shown to improve the reconstruction
performance. By using this variable a purity of up to 80% is achievable with
an efficiency lower than 60% when the charges of well identified b quarks are being reconstructed.
This study has been performed on the b¯bq¯qq¯q sample.
A separate study of the CPC2 sensor capacitance has also been performed, the final aim
being the minimization of the clock current needed to operate the sensor; currently 10 A for
a 10 cm 2 sensor. The pixel capacitance has been found to be 3.11 ± 0.05 nF/cm 2 . The
main contribution has been found to come from the intergate capacitance which accounts
for 87% of the total pixel capacitance. Subsequently a series of different gate designs have
been investigated with the help of finite element modelling and of test structures.
Finally the experimental set-up developed for the testing of the CPC2 sensor has been
described together with the software data acquisition. A study of the CPC2 noise has been
performed which allowed to achieve a low noise operation: 70e − RMS noise.

Appendix A
CPC2 Bias Voltages
Figure A.1: Schematic of the CPC2 Bias Voltages.
In the noise analysis performed in Chapter 4 the substrate voltage is set to 0 V. The
voltage across the buried channel, which is not shown in the picture, and which has been
referred to also as V Ref has been set to 16 V. The voltage of the output gate (OG) is set to
2 V. The RD voltage is set to 15 V, OD is instead set to 16 V, while CS is grounded. All
these voltages are to be interpreted as DC. Additionally an AC voltage of 2 V is used for
the clock.
144

Appendix B
LCFI Vertex Flavour Tagging
Software Parameters
ZVRES flavour tag vertex charge
parameter value parameter value parameter value
w IP 1 N L 5 T qb,max (mm) 1
k 0.125 p trk,NL,min (GeV) 1 (L/D) qb,max
2.5
R 0 0.6 p trk,NL−1,min (GeV) 2 (L/D) qb,min
0.18
χ 2 TRIM 10 N trks,min 1 V I,qb 1
χ 2 0 10 χ 2 norm,max 20 T qc,max (mm) 1
T max (mm) 1 (L/D) qc,max
2.5
(L/D) max
2.5 (L/D) qc,min
0.5
(L/D) min
0.18 V I,qc 0
V I 2
N σ,max 2
w PT,max 3
w corr,max 2
(b/σ b ) cut 200
Table B.1: LCFI Vertex Default Parameters
Values of code parameters used for the results presented in the LCFI Vertex flavour
tagging software chapter.
145

Bibliography
[1] L. H. Ryder. “Quantum field theory”. Cambridge Univ Press (1996).
[2] M. E. Peskin; D. V. Schroeder. “An introduction to quantum field theory”. Basic Books
(1993).
[3] S. L. Glashow. Nucl. Phys., 22 (1961) 579–588.
[4] A. Salam. In N. Svartholm, editor, “Elementary Particle Theory”, page 367. Almquist
and Wiksells, Stockholm (1969).
[5] S. Weinberg et al. Physical Review Letters, 19 (1967) 1264–1266.
[6] C.S; E. Ambler; R. W. Hayward; D. D. Hoppes; R. P. Hudson C. S. Wu. Physical
Review, 105 (1957) 1413–1415.
[7] P. W. Higgs. Physical Review, 145 (1966) 1156–1163.
[8] C. Amsler et al. Phys. Lett., B667. http://pdg.lbl.gov.
[9] J. Christenson; J. Cronin; V. Fitch; R. Turlay. Phys. Rev. Lett., 13, 138.
[10] S. T. Hill; E. H. Simmons. Phys. Rept., 381 (2003) 235–402.
[11] D. Chakraborty; J. Konigsberg. arXiv preprint hep-ph/0303092.
[12] A. Djouadi; J. Lykken; K. Mönig; Y. Okada; M. Oreglia; S. Yamashita. arXiv preprint
0709.1893.
[13] R. Barate et al. Phys. Lett., B565 (2003) 61–75.
[14] K. Hagiwara; K. Hikasa; K. Nakamura; M. Tanabashi; M. Aguilar-Benitez; C. Amsler
et al. Phys. Rev, D66 (2002) 1–213.
[15] J.A. Aguilar-Saavedra. Nuclear Physics, B812 (2009) 181 – 204.
[16] E. Boos; M. Dubinin; M. Sachwitz; H. J. Schreiber. The European Physical Journal,
C16 (2000) 269–278.
[17] M. Martinez; R. Miquel. The European Physical Journal, C27 (2003) 49–55.
146

Bibliography 147
[18] J. Brau; Y. Okada; N. Walker et al. arXiv preprint 0712.1950.
[19] N. Phinney; N. Toge; N. Walker et al. arXiv preprint 0712.2361.
[20] J. Resta-Lopez, P. N. Burrows, A. Latina & D. Schulte. arXiv preprint accph/0902.2915.
[21] L. Lilje; H. Hayano; N. Ohuchi; S. Fukuda; C. Adolphsen. TILC 2009.
http://tilc09.kek.jp.
[22] B. Barish. TILC 2009. http://tilc09.kek.jp.
[23] SiD Collaboration. “SiD Letter of Intent”.http://silicondetector.org/display/SiD/LOI
(2009).
[24] R. Lipton. International Workshop on Vertex Detectors-2007.
hhttp://vertex2007.syr.edu.
[25] SiD Collaboration. “SiD02”.http://confluence.slac.stanford.edu/display/ilc/sid02.
[26] M. J. Charles. arXiv preprint 0901.4670.
[27] S. Agostinelli; J. Allison; K. Amako; J. Apostolakis; H. Araujo; P. Arce; M. Asai; D.
Axen; S. Banerjee; G. Barrand et al. Nuclear Inst. and Meth., A506 (2003) 250–303.
[28] ILD Collaboration. “ILD Letter of Intent”. http://www.ilcild.org (2009).
[29] D. Schulte et al. Particle Accelerator Conference - 2007. http://pac07.org.
[30] W. Kilian; T. Ohl; J. Reuter. arXiv preprint 0708.4233.
[31] M. Moretti; T. Ohl;J. Reuter. arXiv preprint hep-ph/0102195.
[32] T. Sjostrand; S. Mrenna; P. Skands. arXiv preprint hep-ph/0603175v2.
[33] N. Graf; J. McCormick. Calorimetry in High Energy Physics, 867 (2006) 503–512.
[34] P. Mora de Freitas. Linear Collider Workshop-LCWS 2004.
http://polywww.in2p3.fr/actualites/congres/lcws2004.
[35] G. Musat. Linear Collider Workshop-LCWS 2004.
http://polywww.in2p3.fr/actualites/congres/lcws2004.
[36] T. Johnson. Snowmass Workshop-2005. http://www.slac.stanford.edu/econf/C0508141.
[37] BR S. Catani; Y. L. Dokshitzer; M. Olsson; G. Turnock; B. R.Webber. Physics Letters,
B269, 3-4 (1991) 432–438.
[38] F. Gaede. Nuclear Instruments and Meth., A559 (2006) 177 – 180.
[39] O. Wendt; F. Gaede; T. Krämer. arXiv preprint physics/0702171.
[40] F. Gaede; T. Behnke; N. Graf; T. Johnson. arXiv preprint 0306114.

Bibliography 148
[41] J.R. Janesick. “Scientific charge-coupled devices”. SPIE press (2001).
[42] K. Stefanov. Nuclear Inst. and Meth., A569 (2006) 48–52.
[43] K. Stefanov. International Workshop on Vertex Detectors-2007.
hhttp://vertex2007.syr.edu.
[44] B. Hawes; D. Cussans; C. Damerell; E. Devetak; J. Fopma; R. Gao; J. Goldstein; T.
Greenshaw; N. Kundu; A.Nomerotski; C. Perry; K. Stefanov; S. Thomas; S. Worm.
accepted by Nucl. Instr. and Meth..
[45] P. Allport; D. Bailey; C. Buttar; D. Cussans; C. Damerell; N. De Groot; J. Fopma;
B. Foster; S. Galagedera; A. R. Gillman et al. “Linear Collider Flavour Identification:
Case for Support”. http://hepwww.rl.ac.uk/lcfi/lcfi 3 proposal.pdf (2005).
[46] D. Meeker. Users Manual, software homepage: http://femm. berlios. de/index. html.
[47] S. Worm et al. Nucl. Instrum. Meth., A582 (2007) 839–842.
[48] G. Moldovan; B. Jeffery; A. Nomerotski; A. Kirkland. Nucl. Instrum. Meth., A604
(2009) 108 – 110.
[49] D. Bailey et al. arXiv preprint 0908.3019.
[50] D. J. Jackson. Nucl. Instrum. Meth., A388 (1997) 247–253.
[51] J. Thom. Technical Report, DE2002-798982; SLAC, 585.
[52] S. Gorbunov; I. Kisel. CBM-SOFT-note-2007-003.
http://www.gsi.de/documents/DOC-2007-May-14-1.pdf.
[53] T. Abe. Nuclear Inst. and Meth., A447 (2000) 90–99.
[54] R. Hawkings. LC-PHSM-2000-021. http://www-flc.desy.de/lcnotes/notes.
[55] D. Buskulic et al. Phys. Lett., B313 (1993) 535–548.
[56] P. Abreu;. Eur. Phys. J., C10 (1999) 415.
[57] K. Abe et al. Phys. Rev. Lett., 79 (1997) 590–596.
[58] J. Abdallah et al. Eur. Phys. J., C32 (2004) 185–208.
[59] A. Hocker; P. Speckmayer; J. Stelzer; F. Tegenfeldt; H. Voss; K. Voss; A. Christov;
S. Henrot-Versille; M. Jachowski; A. Krasznahorkay Jr. et al. arXiv preprint
physics/0703039.
[60] T. Behnke; N. Graf; A. Miyamoto. ILC-MEMO-2008-001.
http://ilcdoc.linearcollider.org/collection/Memos?ln=en.
[61] L. Lyons. “Statistics for nuclear and particle physicists”. Cambridge University Press
(1986).

Bibliography 149
[62] B. List; J. List. LC-TOOL-2009-001. www-flc.desy.de/lcnotes/notes/.
[63] R. Cassell. Arxiv preprint arXiv:0902.2694.
[64] R. Akers et al. Z. Phys., C66 (1995) 19–30.
[65] R. D. Field; R. P. Feynman. Nuclear Physics, B136 (1978) 1 – 76.
[66] D0 Collaboration. Physical Review, D74.
[67] E. Boos et al. Nucl. Instrum. Meth., A534 (2004) 250–259.
[68] A. Pukhov et al. arXiv preprint hep-ph/9908288.