UNIVERSITY OF TOKYOAn exclusive study of theSupersymmetric model using a novelsoft tau identification method with the
ATLAS detector

Mark Musashi Hashimoto

A thesis submitted in partial fulfillment for the
degree of Master of Sciencein theGraduate School of Science

February 2010

Abstract
Mark Musashi Hashimoto

This thesis presents an exclusive analysis of the mSUGRA coannihilation region ditau “golden” decay chain using Monte Carlo simulations of the ATLAS detector. The
aim of the analysis is to reconstruct the invariant mass distribution of the two taus
which arise from this chain, Mτ,τ , and to estimate the distribution’s endpoint. The
determination of this endpoint is very important for ascertaining whether the mSUGRA
coannihilation region is the correct description of the universe, and then for determining
the model’s parameters. The first tau of this decay chain is relatively hard and it isefficiently reconstructed by the standard ATLAS tau reconstruction algorithm. On theother hand the second tau is very soft, and as such it is inefficiently reconstructed due tothe algorithms’ relatively high seed thresholds and stringent identification requirements.
We develop a new analysis specific method for reconstructing this soft tau which employs
a number of novel techniques, and which is optimised for the low energy region. We
find that by using the two algorithms to reconstruct the respective taus, we are able toreconstruct the Mτ,τ endpoint better than by simply using the ATLAS algorithm forboth of them. We obtain a final result of M τ,τ endpoint = 58 ± 16 (stat) ± 5 (sys) GeV

at the ATLAS coannihilation reference point with E CM = 10TeV and an integrated
luminosity of 63 fb−1 .

Acknowledgements
First and foremost I would like to offer sincere thanks to my project supervisor Tomio
Kobayashi for giving me the opportunity to perform this research at ICEPP. It has beena very edifying experience and I will take with me a great number of lessons and new
skills. My deep thanks also to Shoji Asai for his many hours of discussions and directions
which helped to shape the path of this research. I would like to express my gratitude
to Naoko Kanaya for putting up with many-a-tiring email from me, and who was also
very helpful to me on my visits to CERN. Thanks also to Junichi Tanaka for his manysuggestions and helpful discussions and to Toshio Namba for early instruction in thedetails of experimental physics. I would also like to thank Tetsuro Mashimo who wasvery helpful to me with with the details of the ICEPP computing system. Finally forthe people at ICEPP I would like to thank my fellow students for help with technicaldetails of ATLAS analysis, and for generally helpful discussions about physics, and also
the ICEPP secretaries for making the day-to-day run so smoothly.
This research was performed in collaboration with a number of colleagues at Freiburg
University. I would like to express my gratitude to Karl Jakob, Michel Janus, Xavier
Portell and Jochen Dingfelder for many useful discussions and suggestions. I would
like to give particular thanks to Stan Lai for his enthusiastic help and support over theperiod of this research.
During my time in Japan I was supported financially by a scholarship from the Japanese
Ministry of Education, Culture, Sport, Science and Technology (MEXT). I would liketo offer my thanks for this opportunity to study in Japan.
Last but certainly not least my deep gratitude to my family. Their unwavering support
for me is the reason that I am at this point. Also, thank you to my Phoebe. It would
have been a much steeper road without you.

iv

Contents
Abstractiii

Acknowledgementsiv

List of Figuresix

List of Tables

xiii

Abbreviations

xv

1 Theory and Motivation
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Matter and Forces . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Mass and the Higgs mechanism . . . . . . . . . . . . . . . . . . . .
1.1.4 The tau lepton . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.5 Problems with the Standard Model . . . . . . . . . . . . . . . . . .
1.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 The Minimal Supersymmetric Standard Model . . . . . . . . . . .
1.2.3 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 SUSY breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.5 Minimal supergravity . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.6 The coannihilation region . . . . . . . . . . . . . . . . . . . . . . .
1.2.6.1 Experimental constraints on mSUGRA phase space . . .
1.2.6.2 The coannihilation region reference point used for thisanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
2
2
3
4
6
6
8
8
9
10
10
11
11
11
13

2 The LHC and the ATLAS detector
15
2.1 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Physics goals and detector overview . . . . . . . . . . . . . . . . . 18
2.2.2 The magnet systems . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 The ATLAS inner detector . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3.1 The pixel and SCT detectors . . . . . . . . . . . . . . . . 21
2.2.3.2 The transition radiation tracker . . . . . . . . . . . . . . 24
2.2.4 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24v

vi

Contents

2.2.5
2.2.6

2.2.4.1 The EM calorimeters . . . . . . . . . . . . . . . . . . . .
2.2.4.2 The hadronic calorimeters . . . . . . . . . . . . . . . . .
The muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . .
The trigger and DAQ system . . . . . . . . . . . . . . . . . . . . .

25
26
27
28

3 Phenomenology of mSUGRA Scenarios and the Coannihilation Region 29
3.1 General phenomenology of mSUGRA events . . . . . . . . . . . . . . . . . 30
3.1.1 Production processes and decay cascades . . . . . . . . . . . . . . 30
3.1.2 Parameter definitions for SUSY analysis . . . . . . . . . . . . . . . 32
3.2 Phenomenology of coannihilation region golden decay events . . . . . . . . 33
3.2.1 The golden decay chain and the analysis of this study . . . . . . . 33
3.2.2 Golden decay kinematics . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Monte Carlo Simulation and the ATLAS Reconstruction Algorithms 37
4.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Physics Object Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.1 Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.2 Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.4 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.5 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.6 Missing Transverse Energy . . . . . . . . . . . . . . . . . . . . . . 44
4.2.7 Standard Tau Reconstruction with tauRec . . . . . . . . . . . . . 46
4.2.7.1 Tau Decay Topology . . . . . . . . . . . . . . . . . . . . . 46
4.2.7.2 The tauRec algorithm reconstruction . . . . . . . . . . . 47
4.2.7.3 The tauRec algorithm discrimination . . . . . . . . . . . 50
4.3 tauRec performance in the mSUGRA coannihilation region . . . . . . . . 55
4.3.1 Prong multiplicity and charge reconstruction . . . . . . . . . . . . 55
4.3.2 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.3 Direction reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.4 Discrimination performance . . . . . . . . . . . . . . . . . . . . . . 60
5 Soft Tau Reconstruction
65
5.1 The soft tau tagging and reconstruction algorithm . . . . . . . . . . . . . 65
5.1.1 The soft tau π ± reconstruction and selection . . . . . . . . . . . . 67
5.1.1.1 Truth level study . . . . . . . . . . . . . . . . . . . . . . . 67
5.1.1.2 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1.1.3 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.1.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.2 The soft tau π 0 reconstruction and selection . . . . . . . . . . . . . 73
5.1.2.1 Truth level study . . . . . . . . . . . . . . . . . . . . . . . 73
5.1.2.2 Excluding the π ± cluster . . . . . . . . . . . . . . . . . . 75
5.1.2.3 Selecting π 0 clusters with
EMFracClusterClassificationTool . . . . . . . . . . . 77
5.1.2.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 The soft tau likelihood method . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

vii

Contents
5.2.2

Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6 Mτ,τ Endpoint Analysis
93
6.1 Physics object definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 SUSY selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.3 Soft tau selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.4 Final cut flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.5 Mτ,τ contribution from the backgrounds . . . . . . . . . . . . . . . . . . . 102
6.5.1 The SM contributions . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.5.2 The SUSY combinatorial background contribution . . . . . . . . . 105
6.6 Final Mτ,τ analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7 Systematic Studies, Discussion and Outlook
109
7.1 Systematic studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.1.1 Systematic study of the linear fit . . . . . . . . . . . . . . . . . . . 109
7.1.2 Systematic study of tau fake rate . . . . . . . . . . . . . . . . . . . 110
7.1.3 Systematic study of tau and jet energy scales . . . . . . . . . . . . 112
7.2 Comparison of soft tau search method with other methods . . . . . . . . . 113
7.2.1 Comparison with tauRec . . . . . . . . . . . . . . . . . . . . . . . 113
7.2.2 Comparisons with simple geometric methods . . . . . . . . . . . . 115
7.3 Analysis of a different coannihilation point . . . . . . . . . . . . . . . . . . 116
7.4 Discussion of the form of the Mτ,τ spectrum fitting function . . . . . . . . 117
7.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.5.1 A new endpoint determination method . . . . . . . . . . . . . . . . 118
7.5.2 Including the signal soft tau π 0 information in the Mτ,τ distribution120
8 Conclusion

123

A Plots of tauRec discrimination variables

125

B Plots of PDFs used for the soft tau likelihood method

127

C Systematic study plots

137

Bibliography141

List of Figures
1.1

The constraints on the mSUGRA phase space provided by existing experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 A map of the LHC with its four main detectors located around its ring .
2.2 The dipole magnet system of the LHC . . . . . . . . . . . . . . . . . . . .
2.3 A cutaway overview of the ATLAS detector . . . . . . . . . . . . . . . . .
2.4 The ATLAS magnet system layout . . . . . . . . . . . . . . . . . . . . . .
2.5 Plan view of the ATLAS inner detector . . . . . . . . . . . . . . . . . . .
2.6 3D view of charged particles traversing the inner detector elements . . .
2.7 The ATLAS calorimetry system . . . . . . . . . . . . . . . . . . . . . . .
2.8 A sketch of a section of the barrel EM calorimeter . . . . . . . . . . . . .
2.9 The ATLAS muon system . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 The logical flow of the ATLAS trigger system . . . . . . . . . . . . . . . .

16
17
19
21
22
23
25
26
27
28

3.1
3.2
3.3
3.4

30
31
35

3.5
4.1
4.2
4.3
4.4
4.5
4.6
4.7
5.1
5.2
5.3
5.4

The main SUSY production processes at the LHC . . . . . . . . . . . . .
A typical topology for an mSUGRA event . . . . . . . . . . . . . . . . .
The truth level kinematic distributions for the signal hard and soft taus .
The truth level distribution of the distance between the coannihilation
region signal hard and soft taus . . . . . . . . . . . . . . . . . . . . . . .
The truth level Mτ,τ distribution of the coannihilation region signal hardand soft taus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The track multiplicity of tauRec objects . . . . . . . . . . . . . . . . . . .
The pT resolutions for the tauRec algorithm . . . . . . . . . . . . . . . .
pT linearity of the tauRec algorithm . . . . . . . . . . . . . . . . . . . . .
Direction resolutions of the tauRec algorithm . . . . . . . . . . . . . . . .
Comparison of tauRec likelihood function for true taus and QCD jets. .
Fake rate vs. efficiency performance plots for tauRec . . . . . . . . . . .
Signal efficiency plots for the tauRec algorithm for the “medium” likelihood cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic of the soft tau search method . . . . . . . . . . . . . . . . . .
The truth level kinematic distributions for the π ± of the hadronic single
prong signal soft tau of the coannihilation region . . . . . . . . . . . . . .
The distance between the truth level π ± from the hadronic single prong
signal soft tau, and the closest reconstructed track . . . . . . . . . . . . .
pT , η, and φ resolutions for the π ± from the hadronic single prong modesof the signal soft tau of the coannihilation region . . . . . . . . . . . . . .

ix

35
36
56
58
59
60
61
62
63
66
68
69
69

List of Figures
Track reconstruction efficiencies of the hadronic single prong signal softtau π ± as functions of pT and η . . . . . . . . . . . . . . . . . . . . . . .
5.6 The track quality quantities for the signal π ± and the background tracks
within the search area around the signal hard tau . . . . . . . . . . . . .
5.7 Comparison of the isolation and p T of the seed quality signal and background tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Truth level energy distributions for the π 0 coming from single prong signal
soft tau decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 The truth level correlation between the distance from the π ± to the π 0 ,and the pT of the π ± , for the signal soft tau 1 and 2-π 0 modes . . . . . .
5.10 The distance between the signal π ± in the middle layer of the calorimeter,
and the closest cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.11 Comparison of the ET in the calorimeter to the pT of the signal π ± track
5.12 The number of clusters collected in a cone of 0.2 around the signal π ±impact in the calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.13 Probability that a cluster comes from a π 0 as a function of hρi of thecluster and λcenter of the cluster . . . . . . . . . . . . . . . . . . . . . . .
5.14 The change in the EM-like classification efficiency of π 0 clusters and π ±clusters as EM f raction is varied . . . . . . . . . . . . . . . . . . . . . .
5.15 The change in the number of clusters around the signal π ± which areclassified as EM-like, as EM f raction is varied. . . . . . . . . . . . . . . .
5.16 Plots showing the quality of the π 0 reconstruction for the soft tau searchalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.17 Schematic illustrating the “half-cone” method used for calculating soft
tau selection likelihood variables when the soft tau candidate is close to
the hard tau candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.18 The likelihood functions of the soft tau likelihood method . . . . . . . . .
5.19 The improvement in the soft tau likelihood method when the half-cone
method is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 Comparison of the performance of the soft tau likelihood method withthe tauRec likelihood method in the fake rate - efficiency plane . . . . . .

x

5.5

70
71
72
74
74
76
76
76
78
79
80
82

87
88
88
90

ETmiss vs PTjet1 + PTjet2 for coannihilation region signal events, and for SM
background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 ∆φjet2,M ET vs. ∆φjet1,M ET for coannihilation region signal events and
QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3 Comparison of MT for the coannihilation region signal events, W → τ, νand tt . . . . . . . √. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.4 Optimisation of S/ N with respect to the cut on soft tau candidate
pT,track , and the likelihood cut . . . . . . . . . . . . . . . . . . . . . . . . 99
6.5 The number of soft tau candidates which remain in the soft tau searcharea before and after the soft tau likelihood cut . . . . . . . . . . . . . . 100
6.6 The cut flow of the SUSY and soft tau selections . . . . . . . . . . . . . . 102
6.7 tt contribution to the Mτ,τ spectrum . . . . . . . . . . . . . . . . . . . . 103
6.8 W → τ, ν contribution to the Mτ,τ spectrum . . . . . . . . . . . . . . . . 104
6.9 Z → ν, ν contribution to the Mτ,τ spectrum . . . . . . . . . . . . . . . . 105
6.10 Contributions to the Mτ,τ spectrum from background SUSY events . . . 106
6.1

List of Figuresxi

6.11 The contributions to the Mτ,τ spectrum from the coannihilation signal,and each of the background processes . . . . . . . . . . . . . . . . . . . . 107
6.12 The fit of the final Mτ,τ spectrum . . . . . . . . . . . . . . . . . . . . . . 108
7.1
7.2

7.3

7.4
7.5
7.6

The contributions to the Mτ,τ spectrum from the coannihilation signal
and the SUSY background when tauRec is used for both taus’ selections. 114
The contributions to the Mτ,τ spectrum from the coannihilation signal,and each of the background processes when simple geometric methods areused for the soft tau selection. . . . . . . . . . . . . . . . . . . . . . . . . 116
The contributions to the Mτ,τ spectrum from the lighter mass point coannihilation signal, and each of the background processes + the linear fit of
the final Mτ,τ distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 117
The fit of the final Mτ,τ distribution with a gaussian + linear function . . 118
The fit of the final Mτ,τ distribution with a log-normal function . . . . . 119
Comparison of the Mτ,τ distribution when complete visible information
is used for the signal soft tau, and when only the π ± information is used 121

A.1 Distributions for the tauRec calorimeter seeded algorithm for W → τ, ν
and J2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.2 Distributions for the tauRec track seeded algorithm for W → τ, ν and J2 126
B.1 The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track is in the range 2GeV < p track < 5GeV . . . . 128
B.2 The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track is in the range 5GeV < p track < 10GeV . . . . 129
B.3 The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track has ptrack > 20GeV . . . . . . . . . . . . . . . 130
B.4 The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track is in the range 2GeV < p track < 5GeV . . . . 131
B.5 The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track is in the range 5GeV < p track < 10GeV . . . . 132
B.6 The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track has ptrack > 20GeV . . . . . . . . . . . . . . . 133
B.7 The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track is in the range 2GeV < p track < 5GeV . . . . 134
B.8 The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track is in the range 5GeV < p track < 10GeV . . . . 135
B.9 The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track has ptrack > 20GeV . . . . . . . . . . . . . . . 136
C.1
C.2
C.3
C.4
C.5
C.6
C.7
C.8

Mτ,τ spectrum when “hard” tau fake rate is increased . . . . . . . . . . . 137
Mτ,τ spectrum when “soft” tau fake rate is increased . . . . . . . . . . . 137
Mτ,τ spectrum with decrease in tau energy scale . . . . . . . . . . . . . . 138
Mτ,τ spectrum with increase in tau energy scale . . . . . . . . . . . . . . 138
Mτ,τ spectrum with decrease in tau energy resolution . . . . . . . . . . . 138
Mτ,τ spectrum with decrease in jet energy scale . . . . . . . . . . . . . . 139
Mτ,τ spectrum with increase in jet energy scale . . . . . . . . . . . . . . . 139
Mτ,τ spectrum with decrease in jet energy resolution . . . . . . . . . . . 139

List of Tables
1.1
1.2
1.3
1.4
1.5

Standard Model particle listing . . . . . . . . . . . . . . . . . . . . . . . . 3
The main tau decay modes and branches . . . . . . . . . . . . . . . . . . 7
The particle spectrum which results from the MSSM . . . . . . . . . . . 9
The ATLAS coannihilation region reference point mass spectrum . . . . . 13
The relevant decay branches of the ATLAS coannihilation region reference
point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1

LHC parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1
4.2

The Monte Carlo samples used for this analysis . . . . . . . . . . . . . .
Track quality criteria for the track seeded and calorimeter seeded algorithms of tauRec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Migration of true one and three prong taus into other prong categories
with tauRec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charge misidentification for tauRec objects reconstructed with 1 or 3
tracks and matched to true taus from a coannihilation region sample . .

4.3
4.4
5.1
5.2
5.3
6.1
6.2
6.3
6.4
7.1
7.2
7.3

39
48
57
57

Track quality criteria for the soft tau tagging algorithm seed track andisolation track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Cut flow for coannihilation single prong signal soft tau π ± with the soft
tau search algorithm seed track selection cuts . . . . . . . . . . . . . . . . 73
Single prong tau decay mode classification efficiency of the soft tau searchalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
ATLAS standard reconstruction physics object definitions used for thisanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
The cut flow of the SUSY and soft tau selections . . . . . . . . . . . . . . 101
The proportions of the Mτ,τ analysis backgrounds which come from truetaus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
The breakdown of the SUSY background contribution . . . . . . . . . . . 106
The variation in the result of the linear M τ,τ fit when the fit range andthe binning are altered . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Sources of energy scale systematic uncertainties and their effects on theMτ,τ endpoint determination . . . . . . . . . . . . . . . . . . . . . . . . . 112
Comparison of the level of the signal above the statistical fluctuation,
when using the soft tau likelihood selection, and two simple geometricsoft tau selection methods. . . . . . . . . . . . . . . . . . . . . . . . . . . 116

xiii

Abbreviations
AOD

Analysis Object Data

ATLAS

A Toroidal LHC AapparatuS

ATLFAST

ATLas FAST simulation

BG

BackGround

CERN

Conseil Européen pour la Recherche Nucléaire(European Organisation for Nuclear Research)

CERN

A Toroidal LHC AapparatuS

CSC

Cathode Strip Chambers

CSC

Computer System Commisioning

DAQ

Data AcQuisition

EM

ElectroMagnetic

ESD

Event Summary Data

GUTGrand Unified Theory

LAr

Liquid Argon

LEP

Large Electron Positron collider

LHC

Large Hadron Collider

LLH

Log LikeliHood

LSP

Lightest Supersymmetric Particle

MDT

Monitored Drift Tubes

MSSM

Minimal Supersymmetric Standard ModelmSUGRA

minimal SuperGRAvity (model)

NLSP

Next to Lightest Supersymmetric Particle

OS

Opposite Sign

PDF

Probability Distribution Function

QCD

Quantum ChromoDynamics
xv

xvi

Abbreviations
QED

Quantum ElectroDynamics

RPC

Resistive Plate Chambers

SCT

SemiConductor Tracker

SS

Same Sign

SUSY

SUperSYmmetry

TGC

Thin Gap Chambers

TRT

Transition Radiation Tracker

VEV

Vacuum Expectation Value

WMAP

Wilkinson Microwave Anisotropy Probe

For my Poppa

xvii

Chapter 1

Theory and Motivation
For the few hundred years since the birth of Science scientists have striven for everdeeper intuition and understanding of the mechanisms which give rise to the observed
dynamics of the universe, backed up by a rigorous and uncompromising demand forexperimental verification. The story of science, and in particular of the fundamental
studies of physics, has been a ever deepening probe in to the structure of the material
universe and the dimensions within which it manifests.
It has also been a story which may begin with the study of individual and seemingly
disparate phenomena, but always leads to a deeper and more general understandingof the ways in which these seemingly unrelated phenomena , at their base, follow thesame patterns which arise from the same general laws. It is a story of descriptionsof very limited scope, being combined or generalised to a description of more generalapplicability.
The standard model of particle physics as developed and rigorously tested in the latter
half of the twentieth century is the culmination of these efforts, and describes to an
extreme accuracy a great deal of the structures and dynamics of the universe. At thesame time it is widely agreed that this theory can not be a “final” description of theuniverse. It’s most blaring emission is any mention of the force with which the wholeenterprise of physics began, gravity. Besides this though there are a number of otherunsatisfactory aspects to the theory which are signs that the path is wide open for
the next step in the development of particle physics. This new physics is expected
to manifest at the newest generation particle accelerator facility at CERN, the Large
Hadron Collider (LHC), thus it is widely predicted that the next tens of years will yielda new paradigm for particle physics development.

1Chapter 1. Theory and Motivation

2

This chapter will begin with a general description of the standard model which will
culminate with a discussion of its deficiencies which are the motivation for the quest for
a new theory. This will lead on to the discussion of one of the most promising theoreticalcandidates for beyond-the-standard-model physics, so-called “supersymmetry”. The
focus will be on the minimal gravity mediated version of the theory, and also only on aparticular region of its parameter space, the so-called coannihilation region. This will set
the context for the next chapter which is devoted to the discussion of the Large Hadron
Collider experiment, and one of it multi-purpose detectors, the ATLAS detector.

1.1

The Standard Model

1.1.1

Overview

The standard model (SM) of particle physics was developed in the 1970s and is a theory
which describes the structure and dynamics of the fundamental constituents of matterby combining two of the most important breakthroughs of the early twentieth century,
namely special relativity and quantum mechanics. The result is a description of bothmatter and the forces which govern them in terms of point like particles (matter) exchanging other point like particles (the forces). The theory predicts that these particles
possess an internal degree of freedom which exhibits many of the properties of angularmomentum, and thus is named “spin”. The amount of spin which the particle possesses
determines whether it is a matter particle, or “fermion” (half integer spin), or a force
particle, or “boson” (integer spin).
It is understood that in the present universe there are four distinct forces which mediate
all interactions of matter: The so-called strong and weak forces, which, due to theirextremely short range are unfamiliar to our everyday experience, and the electromagnetic
force and gravity. The SM is actually an internally consistent combination of two socalled “gauge field theories”, quantum chromodynamics (QCD) which describes thestrong force, and quantum electroweak theory, which is a unified description of theelectromagnetic and weak forces. As mentioned above the SM does not describe thegravitational force and its best description is still Einstein’s theory of general relativity,
which is laid out in a seemingly completely distinct formalism to its standard model
counterparts.
One subtlety of the SM is in its description of mass. Directly incorporating mass terms
in to the SM Lagrangian breaks its gauge invariance resulting in a theory with diverging
parameters which are not recoverable through renormalisation. It is obvious that particles indeed do have mass though and so a different mechanism is required to describe itChapter 1. Theory and Motivation
Generation
Leptons
Quarks

1
 
e
,
νe
 
u
,
d

2

µ
,
νµ
 
c
,
s



3
 
τ
ντ
 
t
b

3
Charge
−1
0
+2/3
−1/3

Mass
511keV, 105.7MeV, 1.78GeV< 2eV
1.5 − 3.3MeV, 1.27GeV, 171.3GeV
3.5 − 6.0MeV, 105MeV, 4.20GeV

Table 1.1: The Standard Model particles listed by lepton/quark category, and by
generation, and grouped in to their doublets. The electric charge and the masses of theparticles are included. [1]within the theory. The best candidate for this is the so-called Higgs mechanism whereby
particles gain mass through so-called “spontaneous symmetry breaking”.
The standard model has been extremely rigorously tested over the past few decades atever higher energy particle accelerators and other experiments, and the result of every
test has found to be consistent with it.

1.1.2

Matter and Forces

The fermions of the SM can be distinctly divided in to two categories: those which feelthe strong force (quarks) and those which don’t (leptons). These are further subdivided
in to three so-called generations with each successive generation having larger and larger
masses. The origin of this three generation structure is not understood and is one of anumber of unsatisfactory (though not invalidating) aspects of the SM. The second andthird generations are inherently unstable and decay very quickly to the first generation
meaning that virtually all of the matter in the universe is composed of the first generation fermions. The matter particles grouped by category and generation are shown in
Table 1.1
As alluded to above the standard model is a “gauge theory” of matter and forces. Forces
naturally arise out of the gauge formalism when the Lagrangian that describes the matterfield is required to be invariant under certain local transformations. The forms of thesetransformations are not necessarily self-evident but have been motivated by experiment.
Here a local transformation means that the transformation is space-time dependent.
The simplest example to consider is the local U (1) Q gauge transformation for the QEDelectron field, where the Q denotes that the conserved quantity in the interaction is theelectric charge. The form of this transformation is ψ → e iθ(x) ψ, where the x dependence
makes explicit the local nature of the transformation. This particular transformation
corresponds to a simple local rotation of the phase of the electron field. In order tomaintain the invariance of the Lagrangian under this rotation a term is added which

Chapter 1. Theory and Motivation

4

describes an interaction with a massless boson, a so-called “gauge boson”. This boson
turns out to be the photon which is the mediator of the electromagnetic interaction.
The interaction of matter and forces thus arises very naturally out of a symmetry of the
Lagrangian.
A similar procedure is followed for deriving the weak interaction, except that this time
the fermions are grouped in to so-called doublets (see Table 1.1). These doublets share asimilar behaviour under the weak interaction so that, for example, a charged lepton canemit or absorb a W boson and convert in to the corresponding neutrino. The analogueof electric charge for the weak interaction is the “weak isospin”, which is conserved in
the interaction. The gauge transformation for the weak interaction is SU(2), and theresult this time is three vector bosons. Of particular interest for the weak formalism isthe vector-axial form of the interaction, 12 (1 − γ5 ), which only selects the left handed
components of the particles (right handed components of anti-particles) , thus violating

the parity symmetry.
The unification of the electromagnetic and weak interaction is achieved by requiring
invariance of the Lagrangian under the gauge group SU (2) L × U (1)Y , where the sub-script L makes explicit that only the left handed components of the particles transform

under SU (2) and the subscript Y indicates that the U (1) transformation of this unified
electroweak group is not the same as the QED group discussed above, and the conserved
quantity is the so-called “weak hypercharge” (Y). This procedure results in 4 massless
vector bosons, Wµ1,2,3 coming from the SU (2)L symmetry group and Bµ coming fromthe U (1)Y group.
The strong force only affects the quark sector of the SM particles and it conserves
so-called “colour” charge. Each quark (anti-quark) listed in Table 1.1 comes in threevarieties of this colour. Their interaction arises from imposing invariance under theSU (3) symmetry group. From this arises the eight massless QCD gluons which mediate
the strong force between the quarks. Of particular interest is the non-observation offree quarks or gluons which leads to the idea of “colour confinement”, the mechanism
by which quarks are bound in to colourless hadrons.

1.1.3

Mass and the Higgs mechanism

Up to this point we have only discussed gauge particle theory in terms of massless
fermions and bosons. Of course many of the fermions and bosons do have mass andin particular, the masses of the vector bosons which mediate the weak force have beenshown through precise measurements at the Super Proton Synchrotron (SPS) collider
in the 1980s to be rather large. A naive approach for generating masses for the weakChapter 1. Theory and Motivation

5bosons would be to explicitly add mass term for them to the Lagrangian. Such massterms in the Lagrangian do not respect the SU (2) × U (1) gauge symmetry and lead toa non-renormalisable theory.

A different approach is to generate mass through the so called “Higgs Mechanism”. The
basic idea of this approach is to introduce mass terms in to the Lagrangian byway of
introducing a new field, which is an SU (2) doublet (and as such has four degrees of
freedom). This field has a potential of the form

V (Φ) = −µ2 Φ†i Φi + λ(Φ†i Φi )2(1.1)(µ2 , λ > 0) which has a local maxima at Φ = 0 and thus a non-zero vacuum expectation
value. Instead there are infinite degenerate minima of the potential at Φ † Φ = 21 µ2 /λ.
This is the famous “Mexican hat” potential. “Spontaneous symmetry breaking” occurs
when we choose a particular minimum around which to perform the expansion of Φ.
Reinserting this expansion in to the Lagrangian turns out to result in one of the degrees√
of freedom of the Higgs field becoming a massive boson of mass M H = 2µ 1 . The
remaining degrees of freedom mix with the massless electroweak vector bosons to resultin 3 massive weak vector bosons (W ± and Z) and the massless electromagnetic boson(the photon).
The masses of the W bosons are predicted to be
mW = g2 ν/2

(1.2)

√
where g2 is the coupling strength of the bosons W µi , and ν = µ/ λ. The mass of the Zboson is related to mW via
mZ = mW / cos θW(1.3)

where tan θW = g1 /g2 is the ratio of the coupling constants for the bosons B µ and Wµi .
θW , or the Weinberg angle, is a measure of the amount of mixing between B µ and Wµ3 .
This ratio is one of the predictions of the Higgs theory which it has been possible to test
(though the Higgs boson itself is still elusive).
The generation of mass for the massive fermions is achieved by adding so-called Yukawa
terms to the Lagrangian of the form

Lyukawa = −Ge eLi Φi eR + h.c.
1

µ is a free parameter of the theory and as such the Higgs mass is not determined.

(1.4)

Chapter 1. Theory and Motivation

6

where h.c. denotes the hermitian conjugate. This is an interaction between the left
handed electron doublet, the right handed electron and the scalar doublet Φ i . Ge is a
coupling constant which parameterises the strength of the interaction and is determinedby experiment. Substituting the expansion of the Higgs field in to the above equation√
yields mass terms like −Ge ν/ 2 × ee where we can see that the mass of the fermion is
proportional to the Yukawa coupling G e . Thus we see that the strength of the Higgs
coupling for fermions is proportional to the mass of the fermions (square of masses forvector bosons) which is a characteristic feature of the Higgs coupling.

1.1.4

The tau lepton

Of particular importance to this study is the SM tau lepton (symbol τ ) so some detailsof it follow. The tau is the 3rd generation equivalent of the electron and similarly has acorresponding neutrino ντ . The tau itself was discovered in 1975 by Martin Lewis Perlet al. at the SPEAR electron-positron collider ring at SLAC using the LBL magnetic
detector [2]. The current combined experimental value of its mass is 1776.84 ± 0.17 MeV

while its mean lifetime is (290.6 ± 1.0) × 10 −15 s (cτ = 87.11µm) [1]. This appreciable
lifetime means that the decay length significance is expected to be appreciable at the

ATLAS detector, and measurements of it are expected to help to discriminate taus frombackground objects (see Section 4.2.7.3).
The large mass of the tau means that it is the only lepton which can decay to hadrons,
and as such it has a rich spectrum of decay modes. The main decay modes are listed inTable 1.2 but they can be succinctly summarised as follows. All tau decays are via theweak interaction and in order to conserve lepton number a tau neutrino always results
which escapes detection. The tau goes to leptons about one third of the time (halfmuon, half electron) while the remaining two thirds go to hadrons. As will be describedin Section 4.2.7.1 it is these hadronic modes which are the measured signal for most tau
measurements at ATLAS. Of these about 70% are so called “single prong” where thetau decays to a single π ± plus some number of π 0 , while 21% are “three prong” where
the tau decay to 3 π ± plus some number of π 0 . There are a small fraction of analogous
K ± modes and some small fraction of higher odd number prong modes which are notincluded in the table.

1.1.5

Problems with the Standard Model

We conclude this review of the SM with a description of the problems which it has.
These problems form the motivation for the development of SUSY, which is the subjectof the next section.

Chapter 1. Theory and Motivation

7

DECAY MODEµ− ν µ ντe− ν e ντ
π − ντ
π − π 0 ντ
π − 2π 0 ντ
2π − π + ντ
2π − π + π 0 ντ

BRANCH(17.36 ± 0.05)%(17.85 ± 0.05)%(10.91 ± 0.07)%(25.51 ± 0.09)%(9.29 ± 0.11)%(9.32 ± 0.07)%(4.61 ± 0.06)%

Table 1.2: The main tau decay modes and branches [1]. Modes are listed for τ − , but
the exactly analogous modes exist for τ + .

As mentioned before, prior to any internal problems with the SM, there is the “elephantin the room” problem that it completely ignores the gravitational force. If one assumes
that all of the fundamental constituents of the universe are describable under one “theoryof everything”, then this problem alone is enough to lead one to believe that the SM isincomplete.
Other features of the universe which the SM fails to address are the dark matter (23%of the energy of the universe), and the dark energy (72% of the energy of the universe),
which are both experimentally observed phenomena.
Another “problem” with the SM, is not exactly a problem, but an issue of the displeasure that one feels at the seeming arbitrariness of such features as the number of freeparameters of the theory (19) and the 3 generation structure of the fermions. In analogy to the periodic table structure, one is drawn to believe that there is some deeper
underlying and more “simple” structure which is responsible for these features.
Finally the major internal feature of the theory which leads one to the “incomplete”
hypothesis is the so-called “hierarchy problem”. There are a number theoretical andexperimental arguments which place constraints on the Higgs mass. These suggest thatthe mass should be somewhere in the range 130-190 GeV. Unfortunately for the SM a
fermion of mass mf and Yukawa coupling λf contributes to the square of the Higgs mass
via

2
∆MH
=−

|λf |2 2(ΛU V + · · · )
8π 2

(1.5)

where ΛU V is the so-called “ultra-violet cut-off” and is the energy scale at which new
2 and,
physics enters. Summing these contributions leads to quadratic divergences in M H

if we set ΛU V to the Planck scale, a large Higgs mass results. The only way to avoid
this problem within the SM model requires a high level of fine-tuning which leads one
to seek other solutions to the problem.

Chapter 1. Theory and Motivation

1.2

Supersymmetry

1.2.1

Overview

8

As mentioned in the previous section, there are a number of issues with the SM which
form the motivation for theoretical extensions to it. The most popular and promisingof these extensions is supersymmetry. [3]We have seen in the formulation of the SM model the important role that symmetries
and their breaking mechanisms have played. Supersymmetry extends these ideas to encompass a new symmetry; It is posited that the universe respects a symmetry between
fermions and bosons. In terms of the theoretical formulation, this is equivalent to saying that the theory is invariant under a operator which transforms fermionic states tobosonic states i.e. an operator which changes half integer spin particles in to integer
spin particles, and vice versa. Thus in an unbroken supersymmetric model, every SM
fermion has a bosonic “superpartner” with the same mass and quantum numbers, andvice versa.
One of the main reasons that it is expected that some form of supersymmetry will becorrect is that it solves the above-mentioned hierarchy problem in a natural way. It turns
out that the new superpartner states of the SM fermions can add radiative corrections
terms to the Higgs mass which cancel the terms coming from the SM fermions, thus
rendering the Higgs mass safe from such corrections.
Another attractive property of supersymmetry is that it allows the gauge couplingstrengths of the SM to become unified at the GUT scale. This comes about since
the running of the gauge coupling strengths from the electroweak to the GUT scale isdependent on the particles which are manifest over that energy range. If SUSY exists
at the electroweak scale then these runnings are affected in such a way the three couplings converge at the GUT scale. It is expected that in the Grand Unified Theory these
coupling constants should unify at the GUT scale. This is a very compelling piece oftheoretical evidence for weak scale supersymmetry.
Finally supersymmetric theories which respect R-parity (see Section 1.2.3). provide an
excellent candidate for dark matter. This is because the lightest supersymmetric particle(LSP) is required to be stable, and, given that it has the correct properties, such as being
neutral, it can explain the observed excess in mass in the universe above that which isvisible. We will see in section Section 1.2.6 that requiring the LSP to be the dark matterparticle helps to constrain the phase space of supersymmetric models.

Chapter 1. Theory and Motivation
Particle
Quark
Lepton
W
B
Gluon
Higgs

SymbolqlWBg
H u , Hd

9
Spin
1
2
1
2

1
1
1
0

Superpartner
SquarkSleptonWino
Bino
GluinoHiggsino

Symbol
q̃
l̃
W̃
B̃
g̃
H̃u , H̃d

Spin
0
0
1
2
1
2
1
2
1
2

Table 1.3: The particle spectrum which results from the MSSM.

1.2.2

The Minimal Supersymmetric Standard Model

The minimal supersymmetric standard model (MSSM) is the supersymmetric extension
to the standard model which results in the minimum number of extra particles. These
particles are listed next to their SM counterparts in Table 1.3. The names of the superpartners of fermions are given by placing an “s” in front of the fermion name, while forthe bosons the name is suffixed with an “ino”. Superpartners are denoted symbolicallyby placing a tilde over the corresponding particle symbol.
While the doubling of most of the SM particles is relatively simple, the Higgs requires
special attention. It turns out that a single Higgs is not sufficient in the MSSM to
explain the coupling between the Higgs and up and down type quarks. Instead it isrequired that there are two complex SU (2) L doublets hu and hd where the subscripts
u and d denote that each Higgs couples to up and down type quarks respectively. This
then results in eight degrees of freedom for the Higgs sector, and, when electroweak
symmetry breaking occurs within the MSSM framework, three of these mix with the W
and B bosons to give W ± , Z while the remainder become Higgs scalar mass eigenstates
which are denoted h0 , H 0 , A0 and H ± .
Below is listed the ways in which all of the SUSY states listed in Table 1.3 mix to form
the physical eigenstates. Note that the subscripts L and R refer to the superpartnerof the respective chiral components of the SM fermions (the superpartners do not havechiral components since they are spin zero). Also note that the mixing in the squarkand sfermion sectors is typically proportional to the mass of the associated SM fermion,and thus it is large for the third generation.
Hu0 , Hd0 , Hu+ , Hd− → h0 , H 0 , A0 , H ± (Higgs)t̃L , t̃R , b̃L , b̃R → t̃1 , t̃2 , b̃1 , b̃2 (Stop/Sbottom)
τ̃L , τ̃R → τ̃1 , τ̃2 (Staus)
B̃ 0 , W̃ 0 , H̃u0 , H̃d0 → χ̃01 , χ̃02 , χ̃03 , χ̃04 (Neutralinos)

Chapter 1. Theory and Motivation

10±W̃ ± , H̃u+ , H̃d− → χ̃±
1 , χ̃2 (Charginos)

1.2.3

R-parity

R-parity is defined as

PR = (−1)3(B−L)+2s(1.6)

where B is baryon number, L is lepton number and s is spin. It is introduced in to the
MSSM as a conserved multiplicative quantum number assigned to each particle in orderthat such phenomena as the measured lower limit of the proton lifetime can be explained.
The SM particles acquire an R-parity of +1 while the SUSY particles acquire an R-parityof -1. Conservation of R-parity has a number of consequences for the phenomenology of
SUSY events, of which the most important are listed below:

1. In accelerator collisions sparticles must be created in pairs
2. The LSP must be stable
3. All sparticles must decay to states with an odd number of sparticles (usually one)

1.2.4

SUSY breaking

If the supersymmetry were a perfect symmetry of nature, then the masses of the superpartners would be exactly the same as those of their SM counterparts, and thus theywould have already been observed in collider experiments (no spin 1 particle has everbeen observed with the same mass as the electron). Thus, in order to remain viable, thesupersymmetry must be broken somehow, resulting in the masses of the superpartners
becoming large. This is analogous to the spontaneous symmetry breaking of electroweak
theory. In order to break the supersymmetry without spoiling the desired cancellations
to the radiative corrections of the Higgs mass, the mass differences between the SM andSUSY particles must not be too large. Thus the breaking terms must be “soft”. It isthus postulated that the breaking is mediated to the MSSM from a “hidden sector” ofparticles where these particles have little or no direct coupling to the supersymmetricparticles. The SUSY Lagrangian can thus be written

L = LSU SY + Lsof t(1.7)

Chapter 1. Theory and Motivation

11

where the LSU SY component is invariant under supersymmetry, while the L sof t com-ponent breaks it by introducing mass terms for the sparticles. This soft component
introduces an unwieldy 105 new parameters to the theory.
Though supersymmetry is required to be broken in order to result in the large sparticle
masses, the exact mechanism of this breaking is open to speculation.

1.2.5

Minimal supergravity

One popular candidate for mediating supersymmetry breaking is so-called “supergravity”. Here we focus on the minimal supergravity model (mSUGRA) which is the SUSY
model studied in this thesis. In this scheme the breaking is mediated from the hidden
sector by the graviton. A number of constraints are placed on the MSSM which resultsin the theory being parametrised in five variables. They are• m0 : The universal scalar mass at the GUT scale.
• m1/2 : The universal gaugino mass at the GUT scale.
• A0 : The universal trilinear coupling strength of sfermions and Higgs at the GUT
scale.

• tan β: β is the ratio of the VEVs of Hu and Hd .
• sign(µ) The sign of the Higgsino mass parameter.
One of the attractive features of the mSUGRA model, and the reason why it is thefocus of a large portion of SUSY phenomenological research, is its predictive power fromjust these five variables. Furthermore a number of constraints can be placed on thesevariables from existing experimental data. One of the important open areas of the phasespace is the so-called “coannihilation region”, which is the focus of this study, and whichis the subject of the next section.

1.2.6

The coannihilation region

1.2.6.1

Experimental constraints on mSUGRA phase space

As mentioned above the mSUGRA phase space can be constrained by existing experimental data. The strongest of these constraints, given that the LSP is the source ofdark matter, is provided by the WMAP satellite which has measured the dark matter

Chapter 1. Theory and Motivation

12

density to be ΩCDM h2 = 0.1126+0.0161−0.0181 .[4] Given some input parameters to mSUGRA,
the density of the LSP arising from the processes in the early universe can be calculated,
and this is required to be consistent with the measured value. Other constraints on thephase space include the lower limit placed on the mass of the lightest charged sparticle
provided by direct SUSY searches, the lower limit on the Higgs mass from direct Higgs
searches, and the measurement of b → sγ decay.
Figure 1.1 show the allowed regions of the mSUGRA phase space under these constraints
where for this plot, tan β has been set to 10, sign(µ) > 0 and A 0 = 0. The thin strip
allowed right on the border where the LSP becomes charged (becomes the stau) is known
as the “coannihilation region”. In this border region the lightest neutralino becomes nearmass degenerate with the stau. It is for this reason that the region is allowed, since,
when the masses of these two particles are near degenerate, their coannihilation in theearly universe is efficient enough to account for the observed amount of dark matter.

Figure 1.1: The constraints on the mSUGRA phase space provided by existing
experimental data. For this plot tan β = 10, µ > 0 and A0 = 0. The dark blue regions
are the allowed regions from the WMAP measurement of the dark matter density (thelighter blue is the region that was constrained by the data previous to WMAP). The
brown shaded areas are where the LSP is charged. Green regions are disallowed byb → sγ measurements. Pink regions are favoured by measurements of the anomalous
magnetic moment of the muon. Also included are the constraints provided by the lower
limits on the Higgs mass (114GeV) and the χ±
1 mass (104GeV). [5]Chapter 1. Theory and Motivation

g̃
ũL
d˜L
b̃1
t̃1
˜lL
τ̃1
ν̃L
χ̃01
χ̃03
χ̃±
1

Mass[GeV]
829
761
765
702
565
252
147
237
140
462
262

13
Mass[GeV]
ũR
d˜R
b̃2
t̃2
l̃R
τ̃2
ν̃τ
χ̃02
χ̃04
χ̃±
2

736
734
732
756
153
253
235
262
480
479

Table 1.4: The ATLAS coannihilation region reference point mass spectrum (Isajet
7.79), where ũ ∼ c̃, d˜ ∼ s̃, ẽ ∼ µ̃ = ˜l and ν̃e ∼ ν̃µ = ν̃L .

1.2.6.2

The coannihilation region reference point used for this analysis

For this study the following parameter point in the coannihilation region was used

• m0 = 70GeV• m1/2 = 350GeV• tan β = 10

(1.8)

• A=0
• µ>0

This is the standard ATLAS coannihilation region reference point (known in ATLAS
parlance as “SU1”). It has a cross section of 2.58 pb at E CM = 10TeV, which is the
LHC collision energy used for this study (see Section 4.1).
Table 1.4 lists the resulting mass spectrum for this point while Table 1.5 lists the coannihilation region decay branches which are most relevant for this analysis. In particular
we note the small mass difference between the τ̃ 1 and the χ̃01 which, as discussed above,
allows for the efficient coannihilation of these two particles in the early universe. On theother hand, from a collider experiment point of view, it means that a τ̃ 1 produced in acollision will decay to an extremely soft tau. It is the reconstruction of this very softtau, and the resulting reconstruction of the “golden decay” M τ,τ spectrum endpoint,
which is the focus of this thesis (see Section 3.2.1).

Chapter 1. Theory and Motivation

g̃

Decay
q̃L , qq̃R , qb̃1 , bb̃2 , bt̃1 , t

χ̃02

14

BR
19%
37%
16%
10%
18%

Decay
q̃L → χ̃02 , q
q̃R → χ̃02 , qb̃1 → χ̃02 , bb̃2 → χ̃02 , bt̃1 → χ̃02 , tt̃2 → χ̃02 , t

BR
31-32%
3%
23%
8%
15%
10%

Decay

BR

Decay

BR

l̃L , lτ̃1 , τν̃L , ν

7%
21%
38%

l̃R , lτ̃2 , τν̃τ , ντ

3%
3%
23%

Decay
τ̃1 → χ̃01 , τ

BR
100%

Table 1.5: The relevant decay branches of the ATLAS coannihilation region reference
point (Isajet 7.79).

Chapter 2

The LHC and the ATLAS
detector
Since its inception in post-war 1950’s Europe, the European Organisation for Nuclear
Research (CERN) has been one of the main focus points for high energy frontier fundamental physics, and international scientific collaboration. Its experiments have pushed
the boundaries of our fundamental knowledge of the universe for the last fifty years witha number of them resulting in Nobel Prizes. At the end of 2009 after a couple of technical hiccups the Large Hadron Collider (LHC), the latest of these great experiments
came online and was able to successfully circulate and collide beams at a world record
setting energy of 1.18 TeV per beam. The following chapter gives a brief outline of thismachine, followed by some technical details of one of its multipurpose detectors, the
ATLAS detector.

2.1

The LHC

The LHC is a high energy proton proton collider constructed in the old LEP experiment
tunnel which is 27km in circumference and approximately 100 metres below the FrancoSwiss border. It has a design proton-proton collision energy of 14TeV with a peakluminosity of 1034 cm−2 s−1 making it the worlds most powerful particle accelerator, bya factor of seven in energy and 100 in luminosity. These beams will be collided at
the locations of the four main detector around the collider ring. Prior to the protons
being injected in to the LHC they are accelerated to an injection energy of 450GeV
in 3 stages: an initial linac and booster, the Proton Synchrotron (PS) and the Super
Proton Synchrotron (SPS). For some short periods the LHC will also be used as a heavy

15

Chapter 2. The LHC and the ATLAS detector

16

ion collider, colliding lead ions in order to study the postulated quark-gluon plasma.
Figure 2.1 shows the overall layout of the machine and its main detectors.

Figure 2.1: A map of the LHC with its four main detectors located around its ring.
[6]

The accelerator itself consist of two interleaved synchrotron rings which share the samemechanical structure and cryostat. The circulating beams are bent with 1232 8.2T superconducting NbTi dipole magnets, while focussing is achieved with 858 quadrupole
magnets. In addition there are over 6000 other magnets for correcting the beam dynamics. All of these magnets must operate at a super-fluid helium temperature of 1.9K
making the engineering requirements of the machine particularly challenging. Acceleration is achieved with 8 RF cavities per beam with a maximum field strength of 5.5
MV/m. Figure 2.2 depicts an LHC dipole magnet with its various components visible.
Some of the other parameters of the machine are summarised in Table 2.1

Chapter 2. The LHC and the ATLAS detector

Figure 2.2: The photo on the top shows the first interconnection being made between
LHC cryomagnets. [7] The figure on the bottom shows the cross-section of the LHC
dipole magnet. [8]17Chapter 2. The LHC and the ATLAS detector
Parameter
Beam collision energy
Beam injection energy
Machine circumference
Design Luminosity
Protons per bunch
Bunch period
Bunches per beam
Dipole field at 7TeV
Maximum RF Cavity strength
Power consumption

18
Value
7 TeV
0.45 TeV
26658.833 m
1034 cm−2 s−1
1.15 × 1011
25ns
2835
8.33 T
5.5 MV/m
120 MW

Table 2.1: Some of the LHC parameters. Most parameters are for design luminosity.

2.2

The ATLAS detector

In the following a brief outline of the ATLAS detector will be given. Particular attention
will be paid to the subsystems which are most relevant to this thesis, which are the innerdetector tracker and the EM calorimetry system. For further details the reader is referredto [9].

2.2.1

Physics goals and detector overview

The ATLAS detector (A Toroidal Lhc ApparatuS) is the largest of the LHC detectors
and is one of its two multipurpose detectors. Its main physics goals are• The search for the Higgs boson, or some other mechanism for electroweak symmetry breaking• The search for physics beyond the SM (SUSY, extra dimensions etc.)• The search for the source of the large CP violation• Further precision measurements of known SM phenomena
The small cross sections for many of the interesting events (∼ 1 − 100 pb) against the

backdrop of a large proton proton inelastic cross section (∼ 10 mb) places very highdemands on the performance of the ATLAS detector. Not only will ATLAS have to

trigger on interesting events out of 10 9 inelastic events/s, it will have to do so in pile up
conditions where an average of 23 inelastic events will arise in each bunch crossing at
design luminosity. Precision measurements of the resulting particles of interesting eventsis also a high priority. The various subsystems of the detector have been designed inChapter 2. The LHC and the ATLAS detector

19order to achieve these exacting standards and each plays a different role in the accurate
measurement and identification of particles. The inner detector tracker and the solenoid
magnet provide precise momentum, direction and vertexing information for the charged
particles in an event, as well as electron identification. The EM and hadronic calorimeters provide energy and direction measurements of photons, electrons, taus and jets, andalso identification information for objects from their energy deposit shapes. Finally themuon and the outer toroidal magnet systems provide information on the event’s muons.
Figure 2.3 show the general layout of the ATLAS detector, with a cutaway showing
where each of the above components is located within it. Each of these components will
be further discussed in coming sections.

Figure 2.3: A cutaway overview of the ATLAS detector showing the locations of its
various components. [9]The coordinate system for the ATLAS detector is defined with respect to the interaction
point with the z-axis pointing in the direction of the beam, the x-axis toward the centreof the LHC and the y-axis upwards. In polar coordinates, θ is the angle made with the zaxis while the azimuthal angle φ is measured around the beam axis. Instead of the polar
angle the more useful pseudorapidity, η = − ln tan θ/2, is usually used. The distancep∆R in η, φ space is defined as ∆R = ∆η 2 + ∆φ2 . Generally speaking, the ATLAS
detector is constructed in three “sections”. The “barrel” section components cover theregions of small |η|, and are constructed in barrel shapes which are concentric with thebeam. The “endcap” section components cover larger |η| regions and are constructedin wheels which are coaxial with the beam and placed some distance in z from theinteraction point. The “forward” components (consisting of the forward calorimeters)

Chapter 2. The LHC and the ATLAS detector

20

are for measurements at very large |η|, and are constructed similarly to the “endcap”

components. η coverage for each component depends on its radial distance from the
beam.

2.2.2

The magnet systems

The ATLAS detector is fitted with two distinct magnet system. The first is the innerdetector NbTi superconducting solenoid which provides standard bending of charge particles in the inner detector for momentum measurements and charge discrimination. It
is 5 tonnes, 5.3m in length, 2.4 m in diameter and provides a 2 T field along the beamline, enough to provide an accurate measurement of particles up to a momentum of 100
GeV. All of this is achieved with a thickness of only 45 mm (0.66 radiation lengths).
A thin solenoid magnet is essential in order to minimise the amount of dead material
before the calorimeters.
The second magnet system is rather peculiar to the ATLAS detector and comprises theouter toroidal magnets which are designed to provide bending to muons for the muon
system. There are 3 such toroids, the barrel toroid and two endcap toroids, providing
fields of 1 T and 0.5 T respectively. The fields for each toroid are provided by 8 NbTi
superconducting “racetrack” shape coils assembled radially and symmetrically aroundthe beam axis. The barrel toroid is 25.3 m in length and 20.1 m in diameter, while theendcap toroids are a more modest 5 m in length and are inserted in to the ends of thebarrel toroid to provide overlap in the “transition” region. The bending provided by thetoroids is essentially in the R − η plane. The toroid system provides for measurementsof muons of up to a momentum of ∼ 6TeV.

The relative layout of the components of the magnet systems is illustrated in Figure 2.4

2.2.3

The ATLAS inner detector

The accurate measurement of charged particle momentum and charge is achieved in
ATLAS with its three component inner detector system in combination with the solenoid
magnetic field. This system provides measurements of charged particles up to |η| < 2.5
and down to a pT of ≈ 0.5 GeV.

The extreme density of particles close to the interaction point means that high granularity is required in the inner layers of the tracker in order to discriminate individual
particles. High granularity is also a prerequisite for achieving the precise momentum
and vertex measurements which will enable the aforementioned physics goals to be met.
The pixel and microstrip layers (SCT) of the inner detector enable ATLAS to achieveChapter 2. The LHC and the ATLAS detector

21

Figure 2.4: The ATLAS magnet system layout. The magnet systems are highlighted
in red. The central solenoid is located inside the calorimeter volumes. The large barrel
toroid is visible with the smaller endcap toroids inserted in to the spaces at its end.[9]these goals. The transition radiation detector exterior to these silicon based systems
supplements these measurements, and also offers the benefit of electron discrimination
capabilities. Figure 2.5 shows a plan view of one of the quadrants of the inner detector,
showing the dimensions and coverage of each of its components.
Figure 2.6 shows 3-D images depicting charged tracks traversing the barrel inner detector
and the endcap inner detector.

2.2.3.1

The pixel and SCT detectors

Precision tracking is performed by the two inner most silicon semiconductor based systems.
The highest granularity pixel layers are the closest to the interaction point and consistof three layers in the barrel region concentric around the beampipe, and three layers ineach of the endcap regions, placed in disks perpendicular to the beam pipe. Typicallythree layers are crossed by each particle. The layers are constructed from 1744 modules
each containing 46080 effective pixels of a minimum size in R − φ × z(R) in the barrel(endcap) of 50 × 400µm2 (90% of pixels). In each module pixel arrays are bump bonded

to 16 front end integrated read out circuits, each of which serve 18 × 160 pixel diodes.

The result is a total of 80.4 million read out channels. The intrinsic accuracies per
module are 10µm(R − φ) and 115µm(z) in the barrel and 10µm(R − φ) and 115µm(R)in the endcaps. The measurement of the inner most pixel layer mostly determines theChapter 2. The LHC and the ATLAS detector

22
ID end-plate

3512

CryostatSolenoid coil
PPF1

R1150

712

Radius(mm)

R1066

848

PPB1

2710
R1004

TRT(end-cap)

TRT(barrel)
1

R563
R514
R443
R371
R299

R122.5
R88.5
R50.5
0

2

3

4

5

6

7

8

9 10 11 12

1

2

3

Cryostat
4

5

6

7

8

R644
R560

SCT(barrel)

SCT (end-cap)

R408

R438.8Pixel
support tube

R337.6

Pixel PP1

R275

R229

Beam-pipe

Pixel

R34.3
1299.9934749
400.5 580
1399.7495 650 853.8 1091.5

01771.42115.22505

2720.2z(mm)Envelopes

Pixel

R122.5
R88.5

R149.6
R88.8

R50.5

Pixel

45.5<R<242mm|Z|<3092mm

SCT barrel

255<R<549mm|Z|<805mm

SCT end-cap

251<R<610mm
810<|Z|<2797mm

TRT barrel

554<R<1082mm|Z|<780mm

TRT end-cap

617<R<1106mm
827<|Z|<2744mm

00Figure 2.5:

400.5

495

580 650

Plan view of a quadrant of the ATLAS inner detector showing thedimensions and coverage of each of its components.[9]accuracy of secondary vertex measurements, which are important for tau discrimination
due to the taus finite decay length. This first layer is known as the “B” layer.
As the distance from the beam pipe increases the density of traversing particles decreases
meaning that the discrimination of individual particles is less sensitive to the granularityof the tracker. As such the SCT layers of the inner detector are composed of modules
containing silicon strips of 63.6 mm length and 80µm pitch. Wafers containing thesestrips are placed back to back giving an effective strip length of 123.2 mm. In thebarrel the SCT contains four layers, with each layer composed of two sets of wafers.
One set in each layer has the strips running parallel to the beam such that the R − φdirection is accurately measured. The other set is placed at a stereo angle of 40 mradwith respect to the other which allows a z-direction measurement of ∼ 2mm resolution.

The endcap set ups are similar but this time the wafers are placed in 9 disks with the
R − φ measurement performed by wafers placed with tapered strips running radially.

The intrinsic accuracies per module are 17µm(R − φ) and 580µm(z) in the barrel and17µm(R − φ) and 580µm(R) in the endcaps. The total number of readout channels in
the SCT is 6.3 million.

Chapter 2. The LHC and the ATLAS detector

Figure 2.6: 3D view of charged particles traversing the inner detector elements. The
top figure depicts a 10 GeV pT charged track propagating at η = 0.3. The bottom
figure depicts two 10 GeV pT charged tracks propagating at η = 1.4 and η = 2.2. Notethat the TRT only extends to η = 2.[9]23Chapter 2. The LHC and the ATLAS detector
2.2.3.2

24

The transition radiation tracker

The transition radiation tracker is a drift tube tracking system which allows tracks to
be followed out to about a radial distance of a metre in the barrel. It was devised
as a cheap alternative to silicon systems for the outer track measurements but still
provides a high number of relatively accurate measurements in the R − φ direction.

The basic components of the system are 4 mm diameter “straw” drift tubes which have

31µm diameter gold-plated tungsten wire running down their centre acting as the anode,
and aluminium plated inner walls which act as the cathode. Straws are layered in the
direction of the beam axis in the barrel region while in the endcaps they are directedin the radial direction. In the barrel the wires are electrically split in the middle near
η = 0. The straws are filled with a mixture of Xe CO 2 and O2 . Amplification of ionised
particles is ∼ 2.5 × 104 and this charge is read out at each end of the straw, thus only

information in R − φ is obtained. The accuracy is expected to be 170µm per straw.

A particularly interesting feature of the TRT is its electron discrimination capability
which is achieved by stimulating “transition radiation” between the straws. Transition
radiation is a phenomenon whereby relativistic charged particles crossing the boundary
between materials of different dielectric constants emit photons. This phenomenon canbe thought of as the charged particle “shaking off” the difference in its electric field as
it crosses such a boundary. The energy loss on a transition is dependant on the Lorentz
factor of the particle, E/mc2 , and as such, for a given energy, lighter charged particles
such as electrons will emit much more transition radiation than, for example, hadrons.
In order to stimulate significant transition radiation, the space between the straws isfilled with a polypropylene/polyethylene fibre. The photons thus emitted by electrons
are in the x-ray region, and the Xe within the straws present a high interaction crosssection to these. Thus a number of “high” threshold hits in the TRT is characteristic ofan electron traversing it. Electron identification with this method alone is expected to be
90% for a pion rejection of ≈ 100. Such measurements will be used in tau identification

methods of this study in order to avoid considering the electrons arising from π 0 γ-ray
conversion when determining the isolation of tau single prong modes (Section 5.1.1).

2.2.4

Calorimeters

The ATLAS calorimeters are situated outside of the solenoid and the inner detector.
They can be generally divided in to two components: The EM calorimeters and thehadronic calorimeters. The EM calorimeters’ primary purpose is to measure electron
and photon energy while the hadronic calorimeters are designed to measure the energyof the hadronic components of jets. All combined they provide coverage up to |η| < 4.9.

Chapter 2. The LHC and the ATLAS detector

25

All of the ATLAS calorimeters are so-called “sampling” calorimeters, meaning thatinactive layers of the calorimeters stimulate showering while active layers measure afraction of this shower energy. It should also be noted that all ATLAS calorimeters are
non-compensating, so that correction of hadronic energy deposits must be done at thesoftware level. Figure 2.7 shows the layout of the entire calorimetry system.

Figure 2.7: A cutaway view of the ATLAS calorimetry system.[9]2.2.4.1

The EM calorimeters

The ATLAS EM calorimeter covers a range up to |η| < 3.2 and is divided in to abarrel component (|η| < 1.475) and two endcap components (1.375 < |η| < 3.2). The
barrel component of the calorimeter is indeed a “barrel” shape concentric with thebeam pipe, while the two endcaps are each composed of two coaxial wheels. The region
where these two components meet is known as the “crack” region, and has a degraded
performance due to the presence of considerable dead material (≈ 7 radiation lengths)
from services. This has a significant effect on physics analyses in this region, as will beshown throughout this study.
The EM calorimeters are lead-liquid argon (LAr) sampling calorimeters with a characteristic accordion shape which enables complete φ coverage with no gaps. In the precision
physics region of |η| < 2.5 the calorimeter is segmented longitudinally into successively

coarser grained (laterally) layers: the “strip” layer, “middle” layer and “third” layer.

Chapter 2. The LHC and the ATLAS detector

26This geometry is shown in Figure 2.8. Combined, the EM calorimeter presents ≈ 22−24
radiation lengths to particles entering it.

Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Towe∆η = 0 r
.1

2X0

47
0m

m

η=0

16X0
TriggeTow r∆ϕ = 0er
.0982

m

m

4.3X0

15

00

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

ϕSquare cells in
Layer 2∆ϕ = 0.0245∆η = 0.025
m/8 =4∆η = 0 .69 mm.0031
Strip cells in Layer 1

37.5m

η

Figure 2.8: A sketch of a section of the barrel EM calorimeter. We can see the finegranularity in the first or “strip” layer. The granularity becomes increasingly coarser
in the middle and third layers.[9]The fine granularity of the EM calorimeter allows for good separation of clusters arisingfrom close by particles (see for example the description of the topological clustering
algorithm of Section 4.2.2), and also good discrimination of, for example, photons andhadrons, based on shower shape. Such shower shape information will be utilised in thetau identification algorithm of Section 5.1.2 in order to identify π 0 clusters arising fromtau decay.

2.2.4.2

The hadronic calorimeters

The hadronic calorimeters can be divided in to three subsystems, the tile calorimeters,
the hadronic endcap calorimeters and the forward calorimeters.
The tile calorimeter is located directly exterior to the barrel EM calorimeter. Its barrel
covers the range |η| < 1.0 while the “extended” barrels cover the range 0.8 < |η| < 1.7.

It too is divided longitudinally and laterally to provide for jet shape measurements.
Steel absorbers are used while scintillating tiles providing the active medium.

Chapter 2. The LHC and the ATLAS detector

27

The hadronic endcap calorimeters cover the region 1.5 < |η| < 3.2 and are locatedbehind the EM endcaps. Like the EM calorimeters they are LAr calorimeters but of asimpler plate design using copper as as the absorption medium.
The forward calorimeters cover 3.1 < |η| < 4.9 and ensure a high coverage of the ηrange. For accurate measurement of the missing transverse energy, an important signal

for SUSY events, this high coverage is very important. The calorimeter is a high density
copper and tungsten + LAr construction ensuring a high level of forward jet containment.

2.2.5

The muon spectrometer

There are two essential function of the ATLAS muon system. The first is the precision
measurement of charged particles which exit the calorimetry system. This is performedby the Monitored drift tubes (MDTs) and the Cathode strip chambers (CSCs). The
second role is to provide a fast trigger for the ATLAS experiment in the event of suchparticles, and this is achieved with Resistive plate chambers (RPCs) and Thin gap
chambers (TGCs). The layout of the entire muon system is depicted in Figure 2.9. We
can see that as with the rest of the detector, the low |η| barrel systems are arranged
concentrically around the beam pipe, in three layers. The high |η| endcap systems arearranged in to four coaxial wheels.

Figure 2.9: A cutaway view of the ATLAS muon system.[9]Chapter 2. The LHC and the ATLAS detector

2.2.6

28

The trigger and DAQ system

The design luminosity bunch crossing rate for the LHC is 40 MHz. Present storage anddata handling capabilities require this rate to be reduced to around 200 Hz. This isachieved in ATLAS with a 3 stage trigger. The first is hardware based and combines
reduced granularity signals from a number of the detector components. It looks forsuch things as the presence of high p T jets, electrons, photons, taus, muons and large
ETmiss , which are all signs of interesting physics events. The trigger decision must be
made within 2.5µs during which time the data is stored in “pipe line” memory close to
the detector. Good events and their “regions of interest” are then passed to the leveltwo trigger which analyses these regions exploiting the full granularity of the detector.
Finally the level three trigger performs a full reconstruction of the event and fromthis decides which events are to be committed to memory for later physics analysis.
Figure 2.10 depicts the basic logical flow of this process.
Interaction rate
~1 GHzBunch crossing
rate 40 MHz

CALO

MUON TRACKING
Pipelinememories

LEVEL 1
TRIGGER< 75 (100) kHz

Derandomizers
Readout drivers(RODs)

Regions of Interest
LEVEL 2
TRIGGER

Readout buffers(ROBs)~ 1 kHzEvent builder
Full-event buffers
andprocessor sub-farms

EVENT FILTER~ 100 Hz

Data recording

Figure 2.10: The logical flow of the ATLAS trigger system. [10]Chapter 3

Phenomenology of mSUGRA
Scenarios and the Coannihilation
RegionIn Chapter 1 the theoretical basis for mSUGRA and in particular the coannihilation
region were presented. In this chapter the general phenomenology of mSUGRA eventsand the experimental methods for discriminating such events from the SM backgroundwill be described. Also a focussed discussion of the phenomenology of coannihilation
region mSUGRA will be given, and the particular details of the kinematics of the socalled “golden decay” chain presented. It is the reconstruction of two of the taus arisingfrom this decay chain which is the basis of this thesis.
Here we should make a note of the distinction between a general “inclusive” analysis
of mSUGRA, and an “exclusive” one. Near the beginning of the LHC running the
focus for mSUGRA analysis will be on establishing whether or not it actually exists.
The strategy for this will be to search for excesses of certain quantities over the entire
event sample which are consistent with mSUGRA expectations. These quantities aredescribed in the next section and, if weak scale supersymmetry exists, excesses above
SM expectations should be visible at the LHC with only a few fb −1 of data. This will
constitute “discovery” of supersymmetry. Such an analysis is “inclusive”.
On the other hand in order to understand the details of the correct mSUGRA model,
for example the sparticle masses and decay widths, more focussed analyses of particulardecay chains will be necessary. These are the so-called “exclusive” analyses. Because
the scope of the event sample is necessarily narrowed with such analyses, they require
much higher statistics than inclusive ones. As such they will be the focus of analyses
29Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region30

at the LHC after mSUGRA discovery, and only once ∼ 10 0 s of fb−1 of data have beencollected. The golden decay chain analysis of this study is an exclusive one, and thedetails will be give in Section 3.2.1.

3.1

General phenomenology of mSUGRA events

3.1.1

Production processes and decay cascades

Being a hadron collider means, given that mSUGRA is the correct model for describing
beyond-the-standard-model physics, that the SUSY production particles at the LHC
will be coloured, i.e. the LHC will be a “squark and gluino factory”. Figure 3.1 shows
the main production processes for these sparticles in the proton-proton collisions at the
LHC.
g

g̃

q

g

g̃

q

q̃

g

q̃

g

g̃

g̃

g̃

q̃
g

q̃

g̃
q̃

q

q̃

Figure 3.1: The main SUSY production processes at the LHC.

At the LHC energy scale these coloured particles are in general relatively heavy comparedto the other sparticles which leads to their cascade decay to the LSP via the various othersquarks, gauginos and the sleptons. The requirement of the conservation of R-parity
means that sparticles must be created in pairs in LHC collisions. It also means that the
decay of a sparticle must result in a state with an odd number of sparticles (where inpractice this is usually one). The decay of these sparticles is analogous to the decay of
their SM counterparts: Gluinos can decay via the analogous process to gluon splitting(for the case mg̃ > mq̃ ), to a squark-quark pair, or squarks may decay via the analogous
process to gluon emission to a gluino and a quark (for the case m q̃ > mg̃ ). For this latter
case, if the gluino is lighter than all of the squarks, it will go to a 3-body decay via an
off-shell squark to a two quark + gaugino final state. Any resulting squarks can thendecay via the analogous charged or neutral current processes to quarks and gauginos.
Finally any resulting gauginos (except the LSP) will decay in analogous processes to the
SM gauge bosons resulting in SM leptons, SM gauge bosons or a Higgs particle, plus theChapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region

31

LSP. The kinematic constraints of the particular point in the mSUGRA parameter space
will determine the allowed cascades which the SUSY production particles will take.
Combining all of this, a typical mSUGRA production and decay process is illustrated
in Figure 3.2. The generally large mass difference between the squarks/gluino and theelectroweak gauginos means that squark/gluino decay will result in a number of very
energetic quarks which will be observed in the detector as a number of characteristicvery hard jets. Then, if the decay goes via leptons there is the possibility of a numberof hard leptons 1 . Finally the conservation of R-parity means that the two final LSPs
will be stable thus will traverse the detector. In order for the LSP to be a candidate fordark matter it is required to be neutral and weakly interacting. Since the LSP will also
be massive the result is a so-called Weakly Interacting Massive Particle (WIMP). In thecase of the mSUGRA model this will be a neutralino. These two massive neutralinos
will thus escape the detector undetected resulting in the final characteristic SUSY signalof an imbalance in the sum of the transverse momentum measured in the detector.

e

νe

±

q

χ̃01
χ̃±
1
q
q̃
g̃

p

p
q̃
τ±
q

χ̃02
τ∓
χ̃10

Figure 3.2: A typical topology for an mSUGRA event.
1
In the case of the coannihilation region, one of the leptons can be very soft, but this is a rather
unique signature.

Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region

3.1.2

32

Parameter definitions for SUSY analysis

Below are listed some of the parameters used to distinguish SUSY events. As mentioned
above, it is the excesses in a number of these quantities which will constitute SUSY
discovery. For this exclusive study cuts on these quantities will be used to isolate a puresample of coannihilation region events. These cuts will be described in Chapter 7.
1. Hard jets
A typical SUSY selection will require some number of hard jets in the event. The
justification of this was described above. For this analysis the requirement will be
for two hard jets, as will be described in Section 6.2.
2. Missing transverse energy
Missing transverse energy, ETmiss , is the imbalance in the vectorial sum of themeasured ET . This arises from particles such as neutralinos and neutrinos escaping
the detector. For the case of mSUGRA events, large E Tmiss will arise from theescape of the two LSPs.
3. Effective mass
For this analysis, the effective mass, M ef f , is defined as
Mef f = PTjet1 + PTjet2 + ETmiss(3.1)

which is a measure of the total activity in the detector. For mSUGRA this quantity
is highly correlated with the SUSY mass scale.
4. Distance between missing transverse energy and jets
For the copious QCD di-jet background in LHC collisions, E Tmiss will typically bein the direction of the jets, since E Tmiss from these events will largely arise fromeither neutrinos arising from weak processes within the jet, or from jet energy mismeasurement. For SUSY events there is no such correlation between the directionof the jets and the escaping LSP. Thus a cut on the minimum distance between
jets and ETmiss , ∆φjet i,M ET , is effective at reducing QCD background.
5. Transverse mass
The transverse mass, MT , is defined as
MT2 = m2τ + m2χ + 2(ETτ ETmiss − pτT · pmiss
)
T

(3.2)

where
ETτ =

q

(pτT )2 + m2τ , ETmiss =q(pmiss)2 + m2χ ,
T

(3.3)

Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region

33mτ , and pτT are the mass and transverse momentum of the hardest reconstructed
tau in the detector, and pmiss
is the missing transverse momentum vector. m χ isT
the mass of the escaping particle which is the source of the E Tmiss , and is usuallyassumed to be zero. The distribution of M T for W → τ, ν decays exhibits a

Jacobian peak at the W mass, thus a cut on this quantity is effective at reducing
this background.

3.2

Phenomenology of coannihilation region golden decay
eventsOnce a pure SUSY sample is isolated using cuts on the above parameters one can perform
a more focussed exclusive analysis. Below we define the exclusive analysis which is the
subject of this study.

3.2.1

The golden decay chain and the analysis of this study

The escape of the two LSPs from the detector means that the direct measurement ofsparticle masses via the formation of invariant mass quantities is impossible. Instead
SUSY exclusive analyses focus on the measurement of invariant mass endpoints. [11] [12][13] In particular the cascade decay q̃ → q χ̃ 02 → qll̃ → qllχ̃01 is kinematically constrained,
and the relationships between the endpoints of the invariant mass distributions of thevisible products can be solved to give the masses of the sparticles in the cascade.
For this thesis we consider the following decay chainq̃ → q χ̃02 → qτ τ̃1 → qτ τ χ̃01

(3.4)

This is the so-called “golden decay”. Though the analysis of this particular chain iscomplicated by the further loss of energy from the tau neutrino, it is important since it
contains the information of the mass of the τ̃ 1 . Also, in some parts of the coannihilation
region, the branching of χ̃02 via taus can be as high as 90% meaning that this may be
the only viable option for obtaining information about the χ̃ 02 .

Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region

34

In order to calculate the sparticle masses, the endpoints of M τ1 ,τ2 , Mτ1 ,q , Mτ2 ,q andMτ1 ,τ2 ,q can be measured. These endpoints can be shown to have the following relationships [14]q(Mχ̃20 − Mτ̃2 )(Mτ̃2 − Mχ̃20 )/Mτ̃221q
2 − M 2 )(M 2 − M 2 )/M 2
(M
Mτmax
=
q̃
τ̃
1 ,q
χ̃02
χ̃20
χ̃20
q
max
2
2
2
2
Mτ2 ,q = (Mq̃ − Mχ̃0 )(Mτ̃ − Mχ̃1 )/(2Mτ̃2 − Mχ̃21 )
2
0
0
q
max
2
2
2
2
2
Mτ1 ,τ2 ,q = (Mq̃ − Mχ̃0 )(Mχ̃2 − Mχ̃1 )/Mχ̃2
Mτmax
=
1 ,τ2

2

0

0

(3.5)

0

As will be shown in the next section the most challenging measurement in the coannihilation region is that of the second tau of the decay chain. It will be shown that thistau is extremely soft.
The focus of this study is exclusively on the reconstruction of this very soft tau, withthe goal being the efficient reconstruction of the M τ,τ distribution. This will allow foran accurate-as-possible determination of the M τ,τ endpoint which can then be used,along with analyses of the tau-jet endpoints, to determine the masses of the decay chain
sparticles via the relations 3.5.

3.2.2

Golden decay kinematics

Before embarking in to the details of the method used for the soft tau reconstruction,
we first give the details of the kinematics of the golden decay. The distributions for thissection are made from the generator level information of the Monte Carlo samples which
will be outlined in the next chapter. We note here that the fraction of the coannihilation
region event sample containing the two-tau χ̃ 02 → τ τ̃1 → τ τ χ̃01 chain is 7%.
Figure 3.3 shows the pT,vis , ηvis and φvis distributions of the two taus coming from theabove decay chain, where henceforth vis denotes the visible component of the taus. Also,from here the first tau of the decay chain is referred to as the “signal hard tau”, while
the second tau is referred to as the “signal soft tau”. Indeed, we can see that the “hard”
tau is relatively very hard due to the large mass difference between the χ̃ 02 and the τ̃ ofthe decay chain, while the “soft” tau is relatively very soft due to the near degeneracyof the τ̃ and the χ̃01 . The means of their pT,vis are 79GeV and 9.3GeV respectively.
We note that the softness of this signal soft tau makes its identification in the ATLAS
detector difficult, and thus the reconstruction of the final M τ,τ distribution particularly
challenging.

Events/fb /bin−1

"Hard" tau−1

Events/fb /GeV

Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region"Soft" tau

1

10−1

35

"Hard" tau

1.2"Soft" tau

1
0.8
0.6

10−2

0.4
0.2

10−3
50

100

150

200

250

300

0
−4

350
400
MC
PT,vis [GeV]

−3

−2

−1

0

1

2

3

4
ηMC
vis

0.6

−1

Events/fb /bin

0

0.5
0.4
"Hard" tau0.3"Soft" tau

0.2
0.1
0

−3

−2

−1

0

1

2

3

φMC
vis

C
MC
Figure 3.3: The truth level distributions of pM
T,vis (top left), ηvis (top right) andMC
φvis (bottom) for the coannihilation region signal hard and soft taus.

Figure 3.4 shows the distribution of the distance between the two taus, where again only
the visible information is taken into account. We can see that there is a tendency forthe soft tau to be rather close to the hard tau. This is due to their mutual boost which
is provided by their parent χ̃02 . In Section 5.1 we will use this containment to help to−1

Events/fb /bin

reduce the background to our final reconstruction.

1.2
1
0.8
0.6
0.4
0.2
0
0

1

2

3

4

5
MC
∆ Rτ,τ,vis

Figure 3.4: The truth level distribution of the distance between the coannihilation
region signal hard and soft taus. Only the visible components are considered.

Chapter 3. Phenomenology of mSUGRA Scenarios and the Coannihilation Region

36

Finally Figure 3.5 shows the truth level Mτ,τ distributions. The blue line show the
distribution taking all of the tau energies in to account. We see that there is a nicesharp edge to the distribution, which is similar to those which can arise in the electron
and muon channels. The red line shows the distribution taking only the visible tau
energy into account. We see that the loss of the neutrino energies smears the distribution
backwards, resulting in a very gradual tail towards the endpoint. As we will discuss in
Section 7.4 the gradual nature of this endpoint makes the correct determination of it all−1

Events/fb /GeV

the more challenging.
Full

1.4

Visible

1.2
1
0.8
0.6
0.4
0.2
0
0

10

20

30

40

50

60

70

80

90

100
MMC
τ ,τ

Figure 3.5: The truth level Mτ,τ distribution of the coannihilation region signal hardand soft taus. The blue line shows the distribution using the full tau energies, while
the red line shows the distribution using only the visible components of the energies.

Chapter 4Monte Carlo Simulation and the
ATLAS Reconstruction
Algorithms
We begin this Chapter with a brief summary of the Monte Carlo simulation programs andsamples used for this analysis. We then move quickly on to a description of the physics
object reconstruction algorithms used in ATLAS. As emphasised in the previous chapter
the most important reconstruction particle for this analysis is the tau lepton. Thus while
the descriptions of most of the reconstruction algorithms will be brief, considerable space
will be devoted to the description of the ATLAS tau reconstruction algorithm and its
performance. The details of this algorithm will set the context for the next chapter
which is devoted to the description of the novel soft tau tagging algorithm which has
been developed.

4.1

Monte Carlo Simulation

Monte Carlo simulations of LHC physics processes and the subsequent traversal of particles through the ATLAS detector allow for studies of the detector before actual datataking begins. Such things as the optimisation of trigger menus, the optimisation ofparticle reconstruction algorithms and studies of the discovery potential of the detector
can be performed, to a certain extent, before the LHC comes online.
At ATLAS the Monte Carlo simulations and their analyses are performed within the
Athena framework [15]. The simulation consists of several steps which are briefly outlined below:
37Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

38

Event Generation
At this step the actual physics processes of the proton-proton collisions of the LHC are
simulated. For this study the simulation is done at E CM = 10TeV since it was expectedthat the collision energy would be at this level for some time due to problems with the
LHC magnets. A number of Monte Carlo generators are used in Athena providing event
simulation of a wide variety of processes. Collision simulation is based on the partonmodel of the proton where the partons share the proton momentum according to given
PDFs. For this study we use Athena version 14.2.20.1 for event generation.
The signal SUSY events for this thesis were generated with a combination of programs.
Isajet was used to calculate the weak scale phenomenology of mSUGRA which result
from given mSUGRA parameters. These are then used as input to Jimmy and Herwig
which together generate the entire underlying event including parton showering andhadronisation.
tt events are generated using the MC@NLO package which calculates the matrix elements
to next to leading order. These are used as input to Jimmy+Herwig which generate theunderlying event.
For W and Z boson processes the Alpgen package was used which creates the partonlevel interaction. This is then used as input to Jimmy + Herwig which again create theentire underlying event.
Finally QCD processes were simulated using Pythia which is capable of describing theentire hard QCD event.
The Tauola package is used within Athena to describe the decay of tau leptons.
The samples used for this thesis are outlined in Table 4.1. In order to gain enoughstatistics for this analysis, some private tt and Z → ν, ν samples were created with an

event filter of ETmiss > 140GeV, PTjet1 > 110GeV and PTjet2 > 60GeV. These filters
were sufficiently below the analysis cuts such that the various distributions of non-filter
samples matched the filtered samples’ distributions well after the analysis cuts were
made. Besides the event filter the events were created in exactly the same way as theofficial ATLAS samples. Further justification of the SM background samples used will
be given in Section 6.4.
It should also be noted that, samples which were found to be negligible when cuts wereapplied to AOD samples were not downloaded/generated at ESD level. These include,for example Z → ν, ν with 0, 1 or 2 partons and W → τ, ν with 0 or 1 parton 1 .
1These become negligible due to the requirement of 2 jets and a tau for this analysis.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms
Process
SUSY Signal
tt, not fully hadronic
W → τ, ν + jets
Z → τ, τ + jets
Z → ν, ν + jets
QCD J4QCD J5QCD J6QCD J7QCD J8Generator
HerwigMC@NLO
AlpgenAlpgenAlpgenPythiaPythiaPythiaPythiaPythiaσ [pb]
2.58
374
948
308
165
152000
5129
112
1.08
0.0011

39

Corresponding Lum [fb −1 ]
62.8
21.8
1.1
3
7
0.0033
0.078
2.90
370
349k

Table 4.1: The Monte Carlo samples used for this analysis.

Detector Simulation and Digitisation
The traversal of the final state particles from the event generation stage through thedetector is simulated using the GEANT4 package. A very detailed geometry of theentire detector is used in the simulation, along with empirical magnetic field maps andthe results of various subdetector beam tests. The energy deposits of this detector
simulation are then converted into digital signals via a digitisation simulation. The
output of this is the Raw Data Object (RDO). This is the point at which the simulation
data and real data will converge. For this study we use Athena version 14.2.10.1 for thedetector simulation and Athena version 14.2.25.8 for the digitisation.
Reconstruction
At this point the RDO needs to be converted in to a form that is meaningful to theend user. This is the job of the reconstruction software. The digital signals of the RDO
are reconstructed in to physics objects which can be used for physics analysis. The
output of this stage is the Event Summary Data (ESD) or the Analysis Object Data
(AOD). The latter is a rarefied and smaller version of the former, and should be the form
that most end users analyse. For this study the more detailed ESD was required, sincedetailed cell-level information of the calorimeter was used. More detailed information of
the various reconstruction algorithms is given in the following chapters. For this study
we use Athena version 14.2.25.8 for the reconstruction.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

4.2

Physics Object Reconstruction

4.2.1

Tracks40

As the copious charged particles produced in a collision pass through the inner detector
they produce hits in its various components as outlined in Section 2.2.3. These basic data
form the basis for track reconstruction which in turn forms the basis for a number of theother reconstruction algorithms, most notably for this analysis the tau reconstruction
algorithm. The default track finding algorithm uses the pixel and first SCT layers’ hits
to identify track candidates which originate from near the interaction point. After a first
fitting stage in which fake tracks are rejected the candidate track is propagated throughthe remaining layers of the inner detectors to find other associated hits. If the track
candidate is within the range of the TRT (|η| < 2) the fit using only the silicon layers iscompared to the fit using the both silicon layers and the TRT, and the better of the two
is used for the final track reconstruction. All tracks reconstructed as originating fromthe interaction point are then used in interpolating the primary vertex.
The reconstruction of tau vertices/impact parameters is of particular interest to thisstudy since such information is used to help to identify taus. Also of interest to this study
is not only the intrinsic tracking efficiency of pions, but also the charge identification
efficiency. These details will be discussed further in Chapters 5 and 6.

4.2.2

Clusters

Clusters are the energy conglomerations which arise when particles enter the electromagnetic and hadronic calorimeters. As with reconstructed tracks, clusters form an
important basis for many of the other reconstruction algorithms.
There are two main types of clustering algorithms used in ATLAS. The first type is theso-called “sliding window” algorithm, [16][17] while the second is the so-called “topological clustering” algorithm.[16][18]While the sliding window algorithm is used by the default electron/photon reconstruction, the newer-to-ATLAS topological clustering algorithm has many exciting possibilities for physics objects with more than one final state particle. Topological clusters areused for the standard ATLAS tau reconstruction algorithms, for the jet reconstruction
algorithm used for this analysis and for for the E Tmiss calculation. They will also be
used for soft tau identification in the soft tau tagging algorithm which will be describedin Chapter 5. Thus for this cluster reconstruction review the main focus will be on the
topological clustering algorithm.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

41

Sliding Window Clustering
The basic idea of the sliding window clustering algorithm is to create clusters by collecting cells within a given sized cone, and forming a cluster if they collectively pass acertain threshold. This is done in practice by “sliding” a cone of a certain size over theentire calorimeter. If the sum of the energy in the cells passes a certain threshold thenthe cluster is added to a container. If two clusters are found to overlap within a certain
distance then the smaller of the two is discarded.
In ATLAS there are two sliding window algorithms. The first creates EM clusters where
only cells from the EM calorimeter are used as input. The second creates hadronicclusters where cells from all of the calorimeters are used. Various particle/jet reconstruction algorithms can use the different sliding window clusters as input, e.g. thedefault electron/photon reconstruction algorithm uses the EM clusters as input.
Topological Clustering
The philosophy employed for the topological clustering algorithm is very different fromthat of the sliding window algorithm. Its aim is to define the borders of “blobs” of energy
in the calorimeter by successively adding neighbouring cells of a given pre-cluster to thepre-cluster if the neighbour has energy over a certain threshold. Three thresholds aredefined for the algorithm. In the following E denotes the energy of a cell and σ denotes
its noise level.
• Seed Threshold Pre-clusters are seeded by cells which have |E|/σ above the“seed threshold” (4 for the standard algorithm).

• Neighbour Threshold Cells in the pre-cluster which have |E|/σ above the“neighbour threshold” are asked for their neighbour cells (2 for the standard algo-rithm).
• Cell Threshold Only cells with |E|/σ above the “cell threshold” are added tothe pre-cluster (0 for the standard algorithm).

Cells with negative values but for which the absolute value is greater than the thresholds
are included in order to avoid a bias from noise.
It can be the case that clusters arising from 2 different particles get merged in to one
pre-cluster by this algorithm. Thus a cluster splitting algorithm is employed to split
pre-clusters around their maxima. By default maxima are defined as cells with:• E>500MeV

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

42• Neighbour cells that all have energy less than it• At least 4 neighbours
A similar procedure is followed to the original topological clustering procedure but now
the above defined maxima are used as seeds. Cells at the border of split clusters areshared by each bordering cluster with a weight which is dependant on the distance fromeach cluster and the energy of each cluster. Only cells that are members of the original
topocluster are used.
The power of the topological clustering method is its ability to, for example, separate twoclusters which arise from two different particles in the calorimeter when these particles
are close together. This is a particular advantage for calorimeters as fine grained as the
ATLAS calorimeters. Furthermore noise can be suppressed with judicious choices in thevarious threshold parameters of the algorithm.[19]Calibration of clusters
Once calorimeter clusters have been identified the difficult next step is to calibrate
them. Calibration though depends on what kind of physics object caused the cluster.
The various particle and jet reconstruction algorithms which make use of the clusters
have their own calibration schemes and so each do their own calibrations.
The interesting point about the topological clustering though is that, in a region of thecalorimeter through which many particles have traversed, individual clusters for eachparticle can be isolated. Thus for physics objects with more than one final state particle(jets, taus) it is possible to a certain extent to analyse its individual components. Individual components can be identified as EM or hadronic, calibrated accordingly, thenhave their 4-vectors summed to give the final product. Although this calibration procedure (so-called “Local Hadronic Calibration”) is not yet used as the default procedure
for any of the particle reconstruction algorithms, its use is being investigated for jet
algorithms with topological clusters as inputs and also for E Tmiss reconstruction. It isalso used by the soft tau tagging algorithm of Chapter 5 as a tool for identifying EM
clusters in a tau jet. The calibration proceeds as follows: [19][20]

1. Classify the cluster as EM or hadronic by analysing the shape of the cluster - thevarious so-called “cluster moments” (see Section 5.1.2.3 for more details)
2. If the cluster is hadronic apply a position and energy dependant e/π weight. If thecluster is EM apply a position and energy dependant detector response correction.
3. Make corrections for upstream and lateral energy losses

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

43

The correction factors are derived from single electron and pion MC simulations.

4.2.3

Jets

Being a hadron collider means that the LHC will produce copious QCD jets. Also, as
described in Chapter 3, a large jet multiplicity is a characteristic of SUSY events whichmeans that accurate reconstruction of them is important. Furthermore the precise reconstruction of ETmiss is of vital importance to SUSY event discrimination, and accurate
jet reconstruction is one of the most critical components of E Tmiss reconstruction.
There are a number of jet algorithms employed by the collaboration and each can be supplied with different parameterisations, different inputs and different split/merge mechanisms [21]. For reconstruction of jets in this thesis only the so-called “seeded conealgorithm” was used with a cone size of 0.4 and topological clusters as input (Athenacontainer name:Cone4H1TopoJets, henceforth TopoJets). This algorithm takes high E T
topological clusters as seeds and adds the 4 momentum of the clusters in a cone of 0.4
around its η, φ direction. It then calculates a new η, φ direction from this 4 momentum
sum and iterates this procedure until the difference between the initial and final directions falls below a certain threshold i.e. a stable jet is found. After all of the seeds havebeen used it may be the case that some jets overlap. If this is the case then the following
split/merge procedure is followed: If the two overlapping jets share more than 50% of
the ET of the lower ET jet, then the 2 jets are merged. If it is less than 50% then eachoverlapping cell is associated to the jet to which it is the closest in direction. Only jetswith pT > 7.5GeV are finally stored.
For this algorithm the so called “H1” global calibration scheme is employed which isthe default for ATLAS jet calibration. The basic idea of this method is that energy
depositions from EM particles should have a relatively high density compared to thosefrom hadrons. Thus each cell in a jet is weighted by a factor which is a function of
its energy density, and to correct for position dependence, its position. These functions
have been determined by minimising the resolution of jets in Monte Carlo simulations
with respect to the Monte Carlo truth particles. Residual non-linearities in p T and η
are further corrected with an additional calibration function of these variables.

4.2.4

Electrons

Although, along with muons, electrons are of secondary importance to this analysis,
they still must be reconstructed efficiently since a lepton veto will be applied[21].

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

44Standard electron reconstruction is seeded by EM sliding window clusters. Various
corrections for position dependant responses and upstream losses are applied. A match
to a reconstructed track with E/p < 10 is attempted and if one is found that has notbeen flagged as a conversion track then the cluster track pair are electron candidates.
Stringent rejection of up to 105 against jets faking electrons is required by many analyses
and so various cut regimes are in place to achieve rejection up to this level. They comprisecuts on various parameters derived from both the inner detector and the calorimeters.
Typical efficiencies for electrons with E T > 17GeV with “medium” cuts are 77% for arejection factor of about 2000.

4.2.5

Muons

Muons are one of the easier SM particles to identify in the ATLAS detector due to thefact that they are the only SM charged particle which will reach past the calorimeterswith any great efficiency. Many interesting physics events contain high p T isolatedmuons which originate from the interaction point while non-interesting events do not somuch. The ability to select such muonic events purely thus makes them a good flag forsome interesting events. On the other hand, for this analysis they will be used to veto
SUSY-like background events which contain muons.
The standard muon reconstruction algorithm in ATLAS begins by reconstructing track
segments within each of the three stations of the muon system. These are then linked
together to form muon tracks. These are then extrapolated through to the interaction
point, taking in to account both energy losses and multiple scattering in the calorimeter.
A matching track from the inner detector track reconstruction is then found and a combined fit is performed. The quality of this entire fit determines whether the pair is kept
as a “good” muon candidate. Standard background to “good” muons are both actual
muons which come from π and K decays (which do not originate from the interaction
point), and also low energy photons and neutrons coming from cavern background. Cavern background depends strongly on beam luminosity. Typical efficiencies for “good”
muons in a J/ψ sample are at the level of 76% with a fake rate of ≈ 1 per 1000 events

when a pT > 10GeV cut is made. Most of the inefficiency arises from areas in η withbad coverage from the muon system.

4.2.6

Missing Transverse Energy

As mentioned previously a precise E Tmiss measurement is of vital important for not
only SUSY searches but for most new physics searches. True E Tmiss is the imbalance inthe vectorial sum of ET which arises from particles such as neutralinos and neutrinos

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

45

escaping the detector. ETmiss is measured by the default algorithm by summing theET of H1-calibrated calorimeter topoclusters and reconstructed muons. Muon energy
deposited in the calorimeter is then corrected for. Furthermore calibration of cells associated to high pT physics objects (electrons, taus etc.) are refined using the calibration
schemes of the respective reconstruction algorithms. Finally energy loss arising in thecryostat between the EM and hadronic calorimeters is corrected for.
Fake ETmiss can arise in the detector from a number of sources which all degrade theETmiss resolution. These include:• High energy particles escaping down the very forward regions of the detector.
• Poor reconstruction of particles passing through other bad-coverage areas of thedetector (e.g. crack region).

• Poor resolution of deposited energy in regions with large amounts of dead material
before the calorimeter.

• Dead regions of the detector.
• Inefficiencies in muon detection and fake muons.
• Noise arising from intrinsic calorimeter noise.
• Noise arising from pile-up conditions.
The ATLAS detector is designed to avoid as much as possible energy loss in the forward
regions as described in Chapter 2. Nevertheless some very forward particles will be able
to escape down the beam pipe and such losses are unavoidable.
As much as possible corrections for energy losses in poorly instrumented areas of thedetector and regions with large amounts of dead material are corrected using factors
derived from Monte Carlo simulation.
Instrumental noise is difficult to study with Monte Carlo simulation but it is expectedthat refined analyses taking in to account such effects will be developed as the understanding of the detector is improved with run-time.
Most fake ETmiss arising from muons comes from missed real muons rather than fromfake muons. These muons are missed, as mentioned above, predominantly in the regionsof bad coverage by the muon system. These contribute significantly to non-gaussian tails
in the ETmiss resolution. Work is underway to recover such lost muons with algorithms
using inner detector tracks and calorimeter deposits as seeds.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

46

Intrinsic calorimeter noise from the ≈200k calorimeter channels alone contributes aconstant factor of around 13GeV to the E Tmiss resolution. Compared to a simple E/σ

cut on calorimeter cells, using cells from the standard topocluster algorithm suppresses
both intrinsic calorimeter noise and soft pile-up noise significantly.

4.2.7

Standard Tau Reconstruction with tauRec

The final and most pertinent reconstruction for this analysis is for tau leptons. Taus play
an important role in many analyses at the LHC. For the case that the mass of the Higgs
is only slightly above the present exclusion region the decay to taus becomes important.
Also, for many regions of the mSUGRA phase space including the co-annihilation region,the τ Yukawa coupling becomes large and τ˜1 becomes lighter than its first and second
generation counterparts meaning that χ̃ 02 decaying to τ̃ becomes predominant.[11]4.2.7.1

Tau Decay Topology

As outlined in Section 1.1.4 tau decays can be generally divided in to two types; hadronicmodes and leptonic modes. The leptonic mode visible products (electron 17.8% andmuon 17.4%) are too difficult to distinguish from primary leptons of the event andso tau reconstruction at ATLAS focusses on the hadronic modes only. These can befurther divided in to single prong (1 π ± , 70% of hadronic) and three prong (3 π ± ,21% of hadronic) modes, each of which can also have some number of π 0 s associatedto it (refer to Table 1.2). There are a small number of modes containing 5 π ± but
it is believed that attempting to identify these would lead to an unacceptable level of
QCD background. Also a small fraction of analogous K ± modes exist but these will beidentified along with their π ± counterpart decay modes and so not special attention tothem is necessary.
There are a number of challenges when it comes to tau reconstruction. The first andmost obvious is the fact that taus have a tau neutrino as a final state particle meaningthat a substantial fraction of the tau energy is lost from the detector. Tau reconstruction
then focuses only on the visible information of the tau.
A second challenge for hadronic tau reconstruction, especially at a hadron collider, isthe rejection of copious QCD jets. Compared to a QCD jet a tau-jet is rather wellcollimated since the opening angle of its decay products will be limited to m τ /Eτ .
In the inner detector the tau system will appear as an isolated low track multiplicity
collimated system with none of the tracks having any characteristics of an electron (e.g.
high threshold TRT hits) or a muon (little energy deposition in the calorimeters). ThereChapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

47should be 1 or 3 “good ” tracks 2 , the invariant mass of the tracks should be less than
the tau mass and the absolute value of the sum of their charges should be equal tounity. Furthermore the tau has a finite decay length which can result in a significancein the size of the impact parameter which can be used to identify them as a tau. In thecalorimeter the energy should be well collimated and isolated with possibly a large EM
component for the case of decays to π 0 s. On average about 55% of the energy of taus iscarried by π 0 decay products.

4.2.7.2

The tauRec algorithm reconstruction

There are two distinct approaches to tau reconstruction used in ATLAS and each approach is seeded by one of the two different manifestations in the detector of the tau
decay described above.[22][23]• The calorimeter seeded approach is seeded by the TopoJets.
• The track seeded algorithm is seeded by a small number of “good” tracks.
The two approaches have their own individual merits but their combined performance isbetter than either one individually. We will outline the two algorithms below and how
they have recently been combined in to a single algorithm( tauRec) 3 in order to optimise
overall tau reconstruction performance. Further ahead in Section 4.3 I will discuss their
combined performance in the mSUGRA co-annihilation point of this analysis.
The track seeded approach begins with “good” tracks as defined in the second columnof Table 4.2. The main thrust of these cuts is to make sure that fake tracks as well
as secondary tracks arising from hadronic interaction in the inner detector are rejected.
Tracks of somewhat less stringent quality are then associated to the seed track if they
are within a cone of ∆R < 0.2. The quality cuts for these tracks are defined in thethird column of Table 4.2. A lower pT cut for these tracks is offset by a requirementof a B layer hit in the tracker. Also the B-layer hit and the cut on the ratio of high to
low threshold hits in the TRT aims to reduce contamination from conversion electrons
coming from π 0 decay photons. In the case that the candidate has a total of two tracks,LTa third track is searched for by dropping the χ 2 and NTHT
RT /NT RT requirements. ThisP
track is only added to the seed if it makes | Q| = 1.
2

“Good” track will be defined below but it suffices to say for now that it means a track that comesfrom very close to the interaction point, and not from photon conversion.
3
Historically the calorimeter seeded algorithm was known as tauRec while the track seeded algorithm
was known as tau1p3p. Since Athena version 14 these two algorithms have been combined in to a single
tau reconstruction algorithm named tauRec.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms
Track criteriapT [GeV]|η| <Impact parameter d0 [mm] <Silicon Hits Nsi ≥TRT hits NT RT ≥ (when |η| < 1.9)
Normalised χ2 <Pixel Hits Npixel ≥B-layer hits Nblay ≥LT
High/Low threshold hit ratio NTHT
RT /NT RT <

Seed
track
6
2.5
1
8
10
1.7
no cutno cutno cutAssociated
track
1
2.5
1
8
no cut
1.7
1
1
0.2

48

Loose
track
1
2.5
1.5
6
no cut3.5
1
no cutno cutTable 4.2: Track quality criteria for the track seeded algorithm (Seed track andAssociated track) and for the calorimeter seeded algorithm (Loose track) of tauRec.

The calorimeter seeded approach begins with H1 calibrated TopoJets. Only TopoJets
with ET > 10GeV and |η| < 2.5 are used. Tracks which pass certain quality cuts areassociated to the seed if they are within a cone of radius ∆R < 0.3 of the TopoJet.
These track quality cuts are shown in the fourth column of Table 4.2.
Now for the case that a track seeded tau is matched to within ∆R < 0.2 of a calorimeter

seeded tau, only one candidate is built. Thus candidates can be calorimeter seeded,
track seeded or they can have both seeds. For the case that they have both seeds (mostcandidates have both seeds) the best parts of the original two algorithms have been used
to optimise the reconstruction. The following will describe the methods used for energy
and direction calculations, and the method for tau discrimination, for each of the threecases.
Energy calculation
Firstly if the candidate has a calorimeter seed its energy is calculated entirely fromcalorimeter information. This is the approach of the original calorimeter based algorithm
and in general has superior performance compared to the track based method. The H1
calibration scheme used for QCD jets (Section 4.2.3) is initially used to correct the
TopoJet to the hadronic scale. This calibration scheme though has been optimised for
QCD jets which have a significantly different EM component from taus, thus an extra
correction for the tau energy level has been derived as a function of E T , η and the numberof tracks associated to the tau candidate, by comparing Monte Carlo information withthe reconstructed taus.
For the case that the candidate is only track seeded a so-called energy flow approachis used. This was originally contrived as a means of improving the energy resolution ofChapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

49

low pT taus by using the track information as well as the calorimeter information. Firstthe different components of the tau energy in the calorimeters are separated as follows:• The pure EM energy, ETemcl , which is seeded by an isolated EM cluster• The charged EM and hadronic energies, E TchrgEM and ETchrgHAD seeded by the
impact point of the track(s) is each layer of the calorimeter• The neutral EM energy, ETneut , seeded by the vertex direction of the tau seed track.
Only cells not used for the collection of the above two contributions are used.

Note that only cells within ∆R < 0.2 of the leading track are used in the following:
The general idea is to first remove the contribution of the π ± from the calorimeter andthen add up the rest of the energy assuming that it comes from π 0 s. In practice thisis done by removing the energy in a cone of ∆R < 0.0375 around the track(s) in the
EM calorimeter (ETchrgEM ), and in a cone of ∆R < 0.2 in the hadronic calorimeter, andthen replacing this with the pT of the track(s). The cone used for the EM calorimeter issmall in order to avoid removing π 0 energy as much as possible. This of course is not aconsideration for the energy in the hadronic calorimeter. Following this step isolated EM
clusters are searched for (ETemcl ). These are required to have little hadronic leakage andmust be outside the ∆R < 0.0375 cone described above. These correspond to π 0 which
are well separated from their charged counterparts in the calorimeter. It is not always
the case that π ± and π 0 are well separated in the calorimeter though, so any cells thathave not been used in the previous two steps, and which are in a cone of ∆R < 0.2 ofthe position of the track at the vertex, are added up at the EM scale in order to accountfor non-isolated π 0 contributions. Also some factors accounting for π 0 energy leakage
in to the π ± cone, and for π ± energy leaking outside of the cone are corrected for withPP
factors
resETchrgEM andresETneutEM . These are calculated by comparing p trackTwith ETchrgEM to check for leakage of hadronic energy outside the small collection cone,

and also comparing ptrackwith ETneutEM to check for whether neutral energy is large
Tenough to assume that a substantial amount has leaked in to the collection cone.[24]Thus the energy is summed as:

ETef low = ETemcl + ETneut +X

ptrack+T

X

resETchrgEM +X

resETneutEM(4.1)

Direction calculation and charge/number-of-tracks reconstruction
For the direction calculation the track seeded approach is given precedence. For candidates with a track-seed the direction of the tau candidates is calculated from the direction

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

50of the track at its vertex for single track candidates, and the p T -weighted barycentre
for the case of multi-track candidates. For candidates with only a calorimeter seed,
the direction is calculated as the E T -weighted barycentre of the calorimeter cells of the
TopoJets. The charge of the candidate is calculated as the simple sum of its associatedtracks, where again the tracks from the track seed are given precedence.

4.2.7.3

The tauRec algorithm discrimination

Identification of taus in tauRec is performed by calculating a number of variables. Thesevariables are designed to exploit the tau characteristics and they focus on such factors
as the narrowness of the tau-jet, the isolation of the tau track system and the finite path
length of the tau before decay. The variables are listed below:

DISCRIMINATION VARIABLES FOR CALORIMETER SEEDEDCANDIDATES• The electromagnetic radius Rem :The electromagnetic radius Rem is defined as

Rem =

Pn

i=1 ET, iq(ηi − ηaxis )2 + (φi − φaxis )2Pn,
i=1 ET, i(4.2)

where i runs over all cells associated to the tau within a cone of ∆R < 0.4 of thetau axis. It can be thought of as an energy weighted width of the tau in the EM
calorimeter.
• The Hadronic radius Rhad :The hadronic radius Rhad is defined as

Rhad =Pn

i=1 ET, iq(ηi − ηaxis )2 + (φi − φaxis )2Pn,
i=1 ET, i(4.3)

where i runs over all cells associated to the tau within a cone of ∆R < 0.4 of
the tau axis. It can be thought of as an energy weighted width of the tau in the
hadronic calorimeter.
• ET over pT of the leading track: ET /pTtrk1 :The ratio of the ET of the tau to the pT of the leading track. The leading trackof a tau decay carries a relatively large fraction of the tau energy.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

51• Number of hits in the η strip layer:
The number of hits in the finely segmented first layer of the EM calorimeter with
E>200MeV and within ∆R < 0.4 of the tau axis are counted. Only tau decays
with π 0 are expected to deposit significantly in this layer and even these shouldhave a small number of hits compared to a QCD jet.
• Lifetime signed pseudo impact parameter significance:
The transverse impact parameter is defined as the distance of closest approach of
the leading track to the beam axis, in the plane perpendicular to the beam axis.
This distance is divided by the impact parameter resolution which is calculated
from all primary tracks. This gives a significance of the parameter. Also, if thevector defined as being perpendicular from the beam axis, and pointing in the
direction of the point of closest approach of the track, “faces away” from the track
direction, then the sign of this quantity is made negative, otherwise positive. A
tau’s leading track is expected to “face” the same way as the direction in which
the pre-decay tau moved (and thus the lifetime signed pseudo impact parametershould be positive for a tau).
• Isolation fraction in the calorimeter, I:
The isolation fraction is defined asI=0.1<∆R<0.2
i ET,iP ∆R<0.4 ,j ET,jP(4.4)

where the i and j run over all EM calorimeter cells in a cone around the tau axis
with 0.1 < ∆R < 0.2 and ∆R < 0.4, respectively, and E T, i and ET, j denote thecell ET . Taus are expected to have a small isolation fraction.
• Transverse energy width in the η strip layer, ∆η:The transverse energy width ∆η is defined as
v
u Pn
strip
2
u
i=1 ET i (ηi − ηaxis )
t
∆η =
.
Pn
strip
i=1 ET i(4.5)

where the sum runs over all strip cells in a cone with ∆R < 0.4 around the tau axis
and ETstrip
is the corresponding strip transverse energy. This is another quantityimeasuring energy narrowness, but using only the finely-segmented-in-η strip layerof the EM calorimeter, and only in the η direction.
• Transverse flight path significance, L xy /σLxy :Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

52

For candidates with more than one track associated to them, the tracks’ vertex isreconstructed. The transverse flight path significance is defined as the transverse
distance of this vertex from the primary vertex L xy , divided by its uncertainty
σLxy .
• Centrality fraction in the calorimeter, C f rac :The centrality fraction is defined as
PET, i
Cf rac = P i,
j ET, j(4.6)

where the i and j run over all EM calorimeter cells in a cone around the tau axis
with ∆R < 0.1 and ∆R < 0.4, respectively, and E T, i and ET, j denote the cell ET .
This is another isolation parameter.
Figures showing examples of the distributions of these variables for the process W → τ, ν,and for background J2 samples can be found in Appendix A.

DISCRIMINATION VARIABLES FOR TRACK SEEDED CANDIDATES• Ratio of the hadronic energy to the sum of the tracks’ transverse moP
menta, ETchrgHAD / ptrk
T :Ratio of the energy in the hadronic calorimeter (EM scale) in ∆R < 0.2 of the tau
direction to the sum of the tracks’ p T• The electromagnetic radius, EM radius:
Similar to Rem for the calorimeter seed except calculated with respect to the trackderived directionPn
i=1 ∆Ri ET, i
EM radius = P,
ni=1 ET, i(4.7)

where i runs over all cells associated to the tau within a cone of ∆R < 0.4 of the
track derived tau axis.
• Isolation fraction in the isolation region, EtIsolF rac:
The isolation fraction in the isolation region is defined as
P
ET, i
,
EtIsolF rac = P i
j ET, j(4.8)

where the i and j run over all EM calorimeter cells in a cone around the tau axis
with 0.2 < ∆R < 0.4 and ∆R < 0.4, respectively, and E T, i and ET, j denote thecell ET . This is similar to Cf rac , but the inverse quantity, with slightly different
cone size.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

53• The invariant visible mass , Minvariant :Minvariant is defined as the invariant mass calculated with the tracks, and the
4-momentum of ETemcl (which should correspond to π 0 ).
• Fraction of transverse energy in the isolation region, IsolationF raction
IsolationF raction is defined as
P
ET, i
,
IsolatinF raction = P i
j ET, j(4.9)

where the i and j run over all both EM and hadronic calorimeter cells in a conearound the tau axis with 0.1 < ∆R < 0.2 and ∆R < 0.2, respectively, and E T, i
and ET, j denote the cell ET . This quantity is similar to the calorimeter seed
quantity I, except that cells from both EM and hadronic calorimeter are used andthe cone sizes differ.
core :• Number of tracks, Ntrk

The number of tracks associated to the tau within a cone of ∆R < 0.2 of the tau.
isol :• Associated tracks in isolation region, N trk

The number of tracks associated to the tau within the region 0.2 < ∆R < 0.4 of
the tau.
hits:• Number of calorimeter strips, Nη−strip

The same quantity as “Number of hits in the η strip layer” defined for the calorimeter seed above, except calculated with respect to the track derived direction.
• Width of the energy in strips, (∆η) 2 :Similar to the “transverse energy width in η strip layer” defined for the calorimeter
seeded tau above, except that the width is now defined as the variance in the ηcoordinate, weighted by the transverse energy in a given strip.

2(∆η) =

P
strip
2
2( ni=1 ETstrip
i=1 ET i (ηi − ηaxis )i (ηi − ηaxis ))
−
Pn
P
strip
2
( ni=1 ETstrip
i=1 ET ii )Pn(4.10)

where the sum runs over all strip cells in a cone with ∆R < 0.4 around the tau
axis and ETstrip
is the corresponding strip transverse energy.
i• The invariant mass of the tracks, M trk :Mtrk is defined as the invariant mass of the tracks associated to the tau (forcandidates with more than one track).

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

54• Transverse flight path significance, L xy /σLxy :Exactly the same as for the calorimeter seed, except that tracks come from thetrack seeded algorithm.
• Width of tracks, T rackW idth:
T rackW idth is defined as the variance in the η coordinate over the tracks, weighted
by the pT of the tracks (for candidates with more than one track)

T rackW idth =

Pn

2
trk
(
i=1 pT i (ηi − ηaxis )Pn trk−i=1 pT iPntrk2
i=1 pT i (ηi − ηaxis ))Pn trk 2( i=1 pT i )(4.11)

where the sum runs over all tracks associated to the tau.

Figures comparing these variables for the ATLAS Tau Working Group benchmark process W → τ, ν, and for background QCD jets, can be found in Appendix A.
There are a number of ways to use these variables for discrimination. A so-called “safe”
cut based method will be used during early running stages of the experiment but as
understanding of the detector is improved a better performing multi-variate method will
be used. Probability density functions (PDFs) for tau signal and QCD background havebeen created by the ATLAS Tau Working Group with high statistics from Z → τ, τMonte Carlo simulations, and from QCD simulations respectively. These PDFs werebinned in pT,vis in order to take account of the change in their shape in the different
energy regions. Then when a tau candidate is reconstructed by tauRec, these PDFs areused to create a likelihood variable for the candidate as described below.
In tauRec the following variable is constructed for each tau candidate:

d=

k=nV
Xars
k=1

log

pSk (xk )pB
k (xk )

(4.12)

where the sum is over the discrimination variables described above, x k is the value ofthe variable k for the candidate, and p Sk (xk ) and pB
k (xk ) are the probability density at
the value xk for the signal PDF and for the background PDF respectively. It is easy to
see that, when the probability density returned from the signal PDF is higher than thatfrom the background PDF for some variable, the contribution to the summation will bepositive. Otherwise it will be negative. Thus the variable d gets pushed in the positive
direction when the value for a variable is more tau-like, and in the negative direction
when the value for a variable is background-like.
Because this likelihood method has been trained for rejecting QCD jets, on its own, it
does not perform well for electron rejection. For this purpose there has been a separate

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

55

electron veto developed. The electron veto is a similar likelihood algorithm which isapplied only when the tau candidate is a single track candidate. The algorithm performs better than a simple electron-tau overlap removal procedure, yielding an electron
efficiency of 5% for a tau efficiency of 95% for taus arising from Z → τ τ decay. For

muon rejection a simple requirement of E > 5GeV in the calorimeter around the leading
track is required.

4.3

tauRec performance in the mSUGRA coannihilation
regionThe following section outlines studies undertaken on the performance of the tauRec
algorithm in the mSUGRA coannihilation region. It will begin with giving the qualityof the kinematic reconstruction of the taus, and finish with the algorithm’s rejection
power. We will see that while tauRec performs well for reconstructing and identifying
taus with PT,vis > 20GeV, its performance in the low energy region is poor. As wasoutlined in Chapter 3, for this analysis, reconstruction and identification of low energytaus is vital. A number of lessons were learnt from the performance of tauRec in the
low energy region which formed the basis for the development of a soft tau tagging
algorithm. This algorithm is the subject of the next chapter.
In the following tauRec reconstruction of true taus in the coannihilation region, andfake taus in QCD di-jet samples are compared. The following matching conditions areused.

• True taus are considered as reconstructed by tauRec if the truth level visible
component is matched to a tauRec object within ∆R < 0.2.

• Fake taus are considered as reconstructed by tauRec if the truth level jets arematched to tauRec objects within ∆R < 0.4

Furthermore, comparison is made between soft object reconstruction and hard object
reconstruction. For this purpose a soft object is defined as an object with p T,vis <20GeV, while a hard object is defined as an object with p T,vis > 20GeV.

4.3.1

Prong multiplicity and charge reconstruction

Correct reconstruction of the charge of tau candidates is important for this analysis.
Subtracting same sign pairs of tau candidates from opposite sign pairs of tau candidates

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

56

helps to reduce the background from the M τ,τ distribution, as will described in Chapter
6.
Figure 4.1 shows the distribution of the number of tracks associated to tauRec objects
for true taus and fake taus, separately for soft objects (p T < 20GeV), and hard objects(pT > 20GeV). The ratio of 3-prong candidates to 1-prong candidates for true taus is
expected to be 30%. The reconstructed ratio is 15.0 ± 0.2% for soft candidates matched

to true taus, and 31.9 ± 0.2% for hard candidates matched to true taus. Thus we cansee that while the track multiplicity ratio is reconstructed quite well for harder taus, it

is about half of what it should be for soft taus, due to inefficiencies in reconstructing
the soft tracks of 3 prong taus. The QCD spectrum is smooth with peaks at 1 for soft

0.6

Signal0.5

Background

A.U.

A.U.

jets and at 3 for hard jets.
0.6

Signal0.5

Background

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

2

4

6

8
10
Number of tracks

0

0

2

4

6

8
10
Number of tracks

Figure 4.1: The track multiplicity of tauRec objects. The left hand plot shows themultiplicity of objects with reconstructed pT < 20GeV, while the right hand plot shows
the multiplicity for objects with pT > 20GeV. The multiplicities for fake taus (from a
J2 QCD sample) and real taus (from a coannihilation sample) are shown superimposed.

As mentioned above, tauRec reconstructs the charge of the tau candidate simply as thesum of the charges of the associated tracks. Table 4.3 shows the migration of 1 and
3 prong true taus in to other track multiplicity categories. Results for soft taus andhard taus are shown separately. For hard taus, 1 prong taus are reconstructed with 1
track 83.6% of the time, while 3 prong taus are reconstructed with 3 tracks 71.4% of
the time. For soft taus, 1 prong taus are reconstructed with 1 track 74.7% of the time,
while 3 prong taus are reconstructed with 3 tracks 41.0% of the time. Again we see
the inefficiency of track reconstruction for soft taus significantly reducing the number ofcorrectly reconstructed 3-prong candidates.
Complimentary to Table 4.3 is Table 4.4 which shows the charge misidentification fortrue taus which have been reconstructed with 1 or 3 tracks. We focus only on taus
reconstructed with 1 or 3 tracks since this is a standard identification cut for taus for reducing background and charge misidentification. Results for soft taus and hard taus areshown separately. We can see that for hard taus, the rate of charge misidentification isChapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

one-prong
three-prong
one-prong
three-prong

Reconstructed Reconstructed Reconstructed
as 1-trackas 2-track
as 3-track
M
C
TAUS WITH pT,vis < 20GeV
74.7%
8.6%
2.9%
13.2%
36.1%
41.0%
C > 20GeV
TAUS WITH pM
T,vis
83.6%
6.8%
3.8%
10.8%
11.4%
71.4%

57

Reconstructed
as 3-track>
3.8%
9.0%
2.1%
6.3%

Table 4.3: Migration of true one and three prong taus from a coannihilation region
sample into other prong categories with tauRec. Statistics are shown for taus withCMC
pM
T,vis < 20GeV and pT,vis > 20GeV separately.

Reconstructed Reconstructed
as 1-track
as 3-trackC < 20GeV
TAUS WITH pM
T,vis
Correct Q
95.7%
85.5%
Incorrect Q 4.3%
14.5%
C
TAUS WITH pM
T,vis > 20GeV
Correct Q
96.5%
92.9%
Incorrect Q 3.5%
7.1%
Table 4.4: Charge misidentification for tauRec objects reconstructed with 1 or 3
tracks and matched to true taus from a coannihilation region sample. Statistics are
MCCshown for taus with pM
T,vis < 20GeV and pT,vis > 20GeV separately.

3.5% for taus reconstructed with 1 track and 7.1% for taus reconstructed with 3 tracks.
For soft taus this increases to 4.3% for taus reconstructed with 1 track, and 14.5% fortaus reconstructed with 3 tracks. Charge misidentification arises from a combination ofeffects. Single prong tau charge misidentification may arises from π 0 decay gamma ray
conversion electrons being associated to the tau, or from track contamination from theunderlying event. On the other hand 3 prong tau charge misidentification may arise frominefficient reconstruction of softer tracks combined with conversion electrons being associated to the tau and also from event contamination. Inherent charge misidentificationof individual tracks also plays a role.
From Figure 4.1 it is obvious that requiring that hard tauRec objects have exactly one
or three associated tracks will significantly reduce the QCD background. Requiring an
odd number of tracks is also necessary for obtaining a meaningful charge for the tau.
The requirement of 1 or 3 tracks will be used as one of the identification cuts for thecoannihilation region signal hard tau further ahead. For softer taus we can see thatallowing only 1 prong candidates to pass can reduce the QCD background significantly.
Allowing 3 prong candidates is likely to introduce much more background from jets.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

4.3.2

58

Energy reconstruction

Figure 4.2 shows plots of the pT resolution for the two different algorithms of tauRec,with the resolutions of true soft taus and true hard taus superimposed. Since the energy
reconstruction of the calorimeter seeded algorithm takes precedence over that of the
track seeded algorithm, the track seeded resolution is for candidates which only have a
track seed.
We can see that the calorimeter seeded algorithm resolution peak is shifted by a few
percent to the positive for both hard and soft taus. This is due to the quite large energy
collection area (0.4 cone) used. For the busy environment of a SUSY event this tends tobe contaminated with other energy. Further evidence of this is the high end tail which
is present. On the other hand we see that the track seeded algorithm, which is more
selective about the energy it uses, has a well placed peak for hard taus but a slightly
positive shifted peak for soft taus. The positive shifted peak for soft taus is likely toarise from energy double counting in its energy flow method. High end tails still exist
for the track seed method. For the calorimeter seeds, a gaussian fit of the peaks yields
σs of 18% and 7% for soft and hard taus respectively, while for the track seeds these are

0.1

A.U.

A.U.

15% and 8%.
0.09

τ with PT >20GeV

0.08

τ with PT >20GeV

0.08

τ with PT <20GeV

τ with PT <20GeV

0.07
0.06

0.06

0.05

0.04

0.04

0.02

0.02

0.03
0.01

0
-1

-0.8 -0.6 -0.4 -0.2

00.2

0.4 reco
0.6 0.8 MC 1
(P -PMCT,vis)/P
T

T,vis

0
-1

-0.8 -0.6 -0.4 -0.2

00.2

0.4 reco
0.6 0.8 MC 1
(P -PMCT,vis)/P
T

T,vis

Figure 4.2: The pT resolutions for the true taus reconstructed by the tauRec algorithm in a SUSY coannihilation region sample. The left hand plot shows the resolution
for the calorimeter seeded algorithm while the right hand plot shows the resolution for
the track seeded algorithm. The red lines are taus with pT,vis < 20GeV while the bluelines are taus with pT,vis > 20GeV.
C
Figure 4.3 shows the pT linearity of the tauRec reconstruction as functions of p M
T,vis ,
M C and φM C for all true taus (no separation of hard and soft taus). The linearity is
ηvis
vis

shown separately for the calorimeter seeded algorithm and the track seeded algorithm.
We can see, as shown also by the resolution plot of Figure 4.2, that the calorimeter
seeded algorithm suffers from a positive shift in the reconstructed p T . It becomes worse
at lower pT when contamination from the rest of the event may become relatively moresignificant. The track seeded algorithm also significantly overestimates p T in the lower

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

59

pT region, most probably from problems with double counting and contamination, whileat higher pT it underestimates the energy, likely due to π 0 energy being subtracted
along with π ± energy in the π ± energy subtraction step. The linearity as a function of
M C shows distortions in the crack regions of the calorimeter, while in φ M C it is fairly
ηvis
vis

1.3

MC

Preco
T /PT,vis

MC

Preco
T /PT,vis

uniform.
Calorimeter seed

1.2

Track seed

1.1

1.4

Calorimeter seed

1.3

Track seed

1.2

1

1.1

0.9

1

0.8

0.9
20

40

60

80

0.8
-3

100 120 140 160 180 200
MCPT,visMC

Preco
T /PT,vis

0.7
0

1.5

-2

-1

0

1

2

3
ηMC
vis

1.5
1.4

Calorimeter seed

1.3

Track seed

1.2
1.1
1
0.9
0.8

-3

-2

-1

0

1

2

3

MC
vis

φ

C
MC
MC
MC
Figure 4.3: preco/pM
TT,vis as a function of pT,vis (top-left), ηvis (top-right) and φvis ,(bottom) for true taus reconstructed by tauRec in a SUSY coannihilation region sample.
The blue line shows the linearity for the calorimeter seeded algorithm, while the redline shows the linearity for the track seeded algorithm.

4.3.3

Direction reconstruction

Figure 4.4 shows the η and φ resolutions of both the calorimeter and track seeded algorithms. Since the direction reconstruction of the track seed algorithm takes precedence
over that for the calorimeter seed, the calorimeter seeded resolution is for candidates
which only have a calorimeter seed. Resolutions for soft and hard taus are shown superimposed. We can see that, overall, the direction reconstruction of the track seededalgorithm is better than that of the calorimeter seed, as expected. Furthermore thedirection reconstruction of harder taus is better for the track seeded algorithm, likely
due to a smaller chance of interaction in the tracking material for more energetic tracks.
The direction reconstruction of the calorimeter seeded algorithm is also better for hardChapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

60

taus due to the narrower deposition area of hard taus in the calorimeter. This narrower area arises from narrower showers from more boosted taus and from opposite sign
particles diverging less in the detector magnetic field. The effect of opposite sign particle divergence is particularly apparent in the calorimeter seeded φ resolution for soft
taus, where we can see that the 3-prong taus’ track divergence significantly degrades φ

A.U.

0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.2

A.U.

reconstruction performance.
τ with PT >20GeV

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vis

0
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0

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0.2
reco MCφ -φvis

Figure 4.4: The direction resolutions of the tauRec algorithm, for true taus in a
SUSY coannihilation region sample. The plots on the left show resolutions for thecalorimeter seeded algorithm while those on the right show resolutions for the track
seeded algorithm. The plots on the top show the direction resolution in η while thoseC
on the bottom show the resolution in φ. Resolutions for taus with pM
T,vis > 20GeV (red)MC
and with pT,vis < 20GeV (blue) are shown superimposed.

4.3.4

Discrimination performance

After the reconstruction step it is then necessary to apply identification cuts to thetauRec objects in order to reject background. This is done with a cut on the likelihood
variable discussed above. Figure 4.5 compares this likelihood curve for true taus froma coannihilation sample, and for jets from a J2 sample. It shows the curves for hard
objects and soft objects superimposed. It is obvious that discrimination is much easierfor harder objects than softer objects. As taus become softer their signals become more
and more similar to those of soft jets.

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

A.U.

0.08

61

τ with PT,vis>20GeV

0.07

τ with PT,vis<20GeV

0.06

jet with P <20GeV

jet with P T>20GeV
T

0.05
0.04
0.03
0.02
0.01
0
−50 −40 −30 −20 −10

0

10

20

30

40
50
Likelihood

Figure 4.5: Comparison of the tauRec likelihood for true taus and QCD jets. Plotsfor soft objects (pT < 20GeV) and hard objects (pT > 20GeV) are shown superimposed.

In addition to a cut on the likelihood, we also apply some other cuts for “identification”
in order to reduce background further. These are the electron and muon vetoes, therequirement that the object has exactly one or three associated tracks, and the requirement that |Q| = 1 for the object. Furthermore, we only consider objects in the region|η < 2.5| which is the kinematic region within which tauRec attempts reconstruction.
We thus we define tau efficiency in the coannihilation region

signal =number matched tauRec with 1,3 tracks, µ, e veto, |Q| == 1, LLH > LLH cut
number of MC taus within |η| < 2.5(4.13)

Similarly the fake rate is defined asjet =

number matched tauRec with 1,3 tracks, µ, e veto, |Q| == 1, LLH > LLH cut
number of MC jets within |η| < 2.5(4.14)The denominator used for jet is simply the number of MC jets in the kinematic region(with no requirement on number of associated tracks). Figure 4.6 shows the performanceof the likelihood variable as curves in the  jet , signal plane. As the likelihood variable cut
is loosened the signal efficiency increases but at the same time so does the jet efficiency.
Curves are shown for different regions of the p T spectrum and for one and three prong
candidates separately.

1
−1

10

10−2

Fake Rate

Fake Rate

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

10GeV<pT<30GeV
30GeV<pT<60GeV
60GeV<pT<100GeV

1
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Efficiency

62

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60GeV<pT<100GeV

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1
Efficiency

Figure 4.6: Fake rate vs. efficiency for tauRec. The left hand plot shows theperformance for single prong taus while the right hand plots shows the performance forthree prong taus. Definitions of fake rate and efficiency are given in the text.

In tauRec there are pre-defined cuts in the likelihood variable named “loose” “medium”
and “tight” They are designed to roughly correspond to signal efficiencies of 70%, 50%
CMCMC
and 30% respectively. Figure 4.7 show the dependency of signal on pM
T,vis , ηvis and φvis

for the medium cut. Curves for one and three prong candidates are shown separately.
M C and φM C have an extra requirement on
Note that the efficiency plots as functions of η vis
visCthem that pM
T,vis > 20GeV. Also shown for reference are curves for the “reconstruction”

efficiency. This is simply the efficiency that tauRec reconstructs the object (before theidentification cuts of Equation 4.13).
We can see clearly that that the “reconstruction” efficiency is very low for the low p T,vis
region for both one and three prong cases. This is a result of the E T > 10GeV requirement for the calorimeter seeded algorithm, and the p T > 6GeV requirement for the
track seeded algorithm. Also, the likelihood cut is rather harsh on the “identification”
Cefficiency all the way up to pM
T,vis 40GeV. This is in order to contain the large QCD

statistics in the lower pT regions.
We now summarise the implications of the performance of tauRec in the low energy
region for the reconstruction of soft taus.
• In order to reduce jet background it is best to focus only on reconstructing single
prong taus.

• Energy reconstruction of low energy taus is very difficult, and it tends to be overestimated• Using the tracks of the taus results in a better direction reconstruction.
• It is necessary to reduce the seed threshold in order to efficiently reconstruct very
soft taus.

1

Efficiency

Efficiency

Chapter 4. Monte Carlo Simulation and the ATLAS Reconstruction Algorithms

0.9
0.8
0.7

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00Efficiency

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vis

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2

3

0
φMC
vis

ID efficiency

−3

−2

−1

0

1

2

3

φMC
vis

Figure 4.7:
Reconstruction and identification efficiencies for the tauRec algorithm as functions of
MC
C
MC
pM
T,vis (top), ηvis (middle), and φvis (bottom). The left hand plots show the efficiencies
for single prong taus while the right hand plots show the efficiencies for three prong taus.
The curves for reconstruction efficiency and identification efficiency are superimposed.
The cut used for identification is the “medium” likelihood cut. Note that the plots ofMCCMCefficiency as functions of ηvis
and φMvis have a requirement that pT,vis > 20GeV.

Chapter 5

Soft Tau Reconstruction
In chapter 3 the importance of efficiently reconstructing taus with p T,vis < 10GeV forthe reconstruction of the Mτ,τ edge was shown. In the previous chapter, the performance of tauRec in the low pT region was shown to be poor, and thus its capability
for reconstructing the Mτ,τ edge can be inferred to be also poor. This chapter describes
the development of an entirely new method for tagging the coannihilation region golden
decay soft tau in the ATLAS detector. It should be emphasised that there are techniques
employed in this method which are analysis specific, so that rather than being a generalsoft tau reconstruction algorithm, it is an algorithm for tagging a soft tau when it isin the vicinity of some other easier-to-reconstruct object. This was deemed a necessary
requirement in light of the fact that there is such an overwhelming background arisingfrom low pT QCD jets.
The section begins with studies of reconstruction of the signal soft tau π ± tracks and π 0clusters. The development of a likelihood method for discrimination is then describedfollowed by studies of its performance compared to tauRec.

5.1

The soft tau tagging and reconstruction algorithm

A number of methods were used in order to contain the large jet background to the low
pT tau search. They can be summarised as follows:• Confine the search to single prong taus
• Contain the search to events with well reconstructed hard tauRec and also confine
the search to the geometrical vicinity of this object.

• Use a likelihood method to discriminate the soft tau
65

Chapter 5. Soft Tau Reconstruction

66

As was described in Section 4.3.1 the background to the Mτ,τ spectrum can be significantly reduced in the low pT region if we focus only on tagging the single prong modesof the soft tau i.e. if we search for isolated tracks. Although this requirement effectively
cuts out 21% of the hadronic mode tau signal, it is deemed judicious in order to reduce
the overwhelming QCD background in the low p T region.
As was described in Section 3.2.2 (refer Figure 3.4) the signal soft tau is often fairly
close to the signal hard tau due to the underlying boost provided by their mutual
parent χ̃02 . Thus we can reduce the background by confining the search for the signal
soft tau to the vicinity of a well reconstructed tauRec object. Furthermore a final
discrimination against jets can be made with a likelihood method along the lines of thetauRec likelihood method, but optimised for the low p T region. Thus the algorithm canbe succinctly summarised as “a search for a low p T , isolated, tau-like track inthe vicinity of a hard tauRec object”. Figure 5.1 illustrates this approach.
Hard TaudR<2Soft Tau
track

Tracks fromQCD BG

Figure 5.1: The single prong soft tau π ± track is searched for within a cone of ∆R < 2around the candidate hard tau.

In concrete terms the algorithm proceeds as follows:• Select signal hard tau candidates with p T,vis > 15GeV using tauRec (cuts for thisselection will be outlined in Section 6.1).

• Select soft tau candidates by collecting tracks within a cone of ∆R < 2 of the hardtau candidate and apply to these certain quality and isolation requirements.

• Search for π 0 candidate clusters around the soft tau candidate track.
• Use the π 0 candidate clusters and other information to create a likelihood vari-able for determining the tau-likeness of the soft tau candidates. Dispose of thecandidates which are not sufficiently tau-like.

Chapter 5. Soft Tau Reconstruction

67• Of the soft tau candidates which remain select the most tau-like of the candidates.
This approach differs from the traditional approaches of reconstructing the M τ,τ endpoint which tend to focus on selecting events with two well reconstructed taus.[21] [11][25] [26] Instead the focus here is on “searching out” the softer tau around the hardtau. The problem with the requirement of two well reconstructed taus is that the signal
soft taus are so soft and thus so difficult to identify that traditional tau reconstruction
algorithms will often miss them, either through stringent cuts on seed energy, or throughstringent cuts on identification cuts. Here, rather, the approach is to select hard taus in
SUSY like events, and then select tracks around it which are “sufficiently” tau-like. If
there is more than one soft tau candidate then the most tau-like one is chosen.
The following two subsections describe studies of the reconstruction and identificationof the signal soft tau single prong mode π ± tracks and π 0 clusters.

5.1.1

The soft tau π ± reconstruction and selection

The quality of the information coming from the tracking measurements in the innerdetector is of superior quality relative to that coming from the calorimeters for isolated
charged objects in the low pT region. Thus the decision was made to use tracks aroundthe reconstructed hard taus as seeds for the soft tau tagging algorithm. This motivation
is similar to that for the development of the track seeded algorithm in tauRec, which
is designed for tau reconstruction in the lower p T region, albeit with a limit of pT,vis &10GeV .
We saw in the study of tauRec that reconstruction of the tau energy is rather difficultand so for this study only the single prong track energy is used for the final M τ,τ
distribution. π 0 information is used only for tau discrimination. This point is further
discussed in Section 7.5.2. We also saw that reconstructing the tau direction from track
information results in a better quality direction reconstruction. Using the seed track forthe soft tau direction reconstruction will guarantee a good direction reconstruction.

5.1.1.1

Truth level study

Figure 5.2 shows the truth level distributions of the π ± for the three single prong modesof the signal soft tau. pT , η and φ are shown, with distribution for the 0-π 0 , 1-π 0 and 2π 0 modes superimposed. We can see that, as expected, the lower π 0 multiplicity modes’
π ± have higher pT than the higher multiplicity modes since they get a larger share of
the tau energy. The mean values of the p T for the 0,1 and 2-π 0 mode π ± tracks are 9.2
GeV, 4.6 GeV and 3.9 GeV respectively.

1

68
0.07

0−π0 mode normalised to unity

0−π0 mode normalised to unity

Chapter 5. Soft Tau Reconstruction
0−π0 mode
1−π mode02−π0 mode−1100−π0 mode1−π0 mode0.06

2−π0 mode

0.05
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20

30

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0

40

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50
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PT [GeV]

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3

4
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0−π0 mode

0.035

1−π0 mode2−π0 mode

0.03

0.025
0.02

0.015
0.01

0.005
0

−3

−2

−1

0

1

2

3

φMC

Figure 5.2: The truth level kinematic distributions for the π ± of the hadronic single
prong signal soft tau of the coannihilation region. The top left plots show pT , the top
right η, and the bottom φ. Separate plots for the 3 single prong modes are shownsuperimposed. The 0 − π 0 distributions are normalized to unity.

5.1.1.2

Reconstruction

Figure 5.3 shows the distance between the truth level π ± and the closest reconstructed
track, where all single prong modes have been combined. p T > 2GeV and |η| < 2.5 (theextent of the inner tracker) cuts are imposed at the truth level. Unless otherwise speci-

fied, from here, all plots involving the π ± tracks will have these cuts imposed. In lightof the ∆RM C,reco distribution we set the track matching condition to ∆R M C,reco < 0.01
and use this condition for the definition of “π ± is reconstructed”. With this definition
the misidentification of the reconstructed π ± tracks is only 0.04%.
Figure 5.4 shows the pT , η, and φ resolutions for the reconstructed track of the matched
π ± s. The gaussian fit of the pT resolution yields a width of σ = 1.69%.
Figure 5.5 shows the reconstruction efficiency of the signal soft tau single prong π ±tracks, as a function of pT and η, where the ∆RM C,reco < 0.01 condition is used. The
efficiencies for the 3 single prong modes are combined in these plots. The p T > 2GeV cut
is not imposed on the efficiency vs. pT plot, so as to illustrate the efficiency dependence inthe low pT region. We can see that the reconstruction efficiency levels off to around 90%
for pT & 2GeV and falls dramatically for pT . 700MeV which is around the expected

A.U.

Chapter 5. Soft Tau Reconstruction

69

10−1

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10−3

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0

0.01

0.02

0.03

0.04
0.05
∆ RMC π± , track

A.U.

A.U.

Figure 5.3: The distance between the truth level π ± from the hadronic single prong
signal soft tau, and the closest reconstructed track. A pT > 2GeV and |η| < 2.5 cut is
imposed at the truth level. From now we use ∆RM C π± ,track < 0.01 as the matchingcondition for the signal π ± .

0.09

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0.02 0.04 0.06 0.08 MC0.1(P− PMC
T,π± )/P0−0.01−0.008−0.006−0.004−0.002 0

0.0020.0040.006 0.008 0.01
η
−ηMC
track

T,π±

π±

A.U.

T,track

0.08
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−0.01−0.008−0.006−0.004−0.002 0

0.0020.0040.006 0.008 0.01
φ
−φMC
track

π±

Figure 5.4: pT , η, and φ resolutions for the π ± from the hadronic single prong modesof the signal soft tau of the coannihilation region.

Chapter 5. Soft Tau Reconstruction

70

lower limit for the performance of the tracking detectors [21]. Inefficiencies of trackingof π ± at low pT arise because of the large material effects in this region. We can also
see that the efficiency falls of with increasing |η| which is again a result of increased

probability for interactions as the amount of material traversed by the π ± increases. A
small dip at η ≈ 0 can be seen where there is an increase in the traversed material in1

Tracking efficiency

Tracking efficiency

the SCT and TRT detectors.
0.9

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π±

Figure 5.5: Track reconstruction efficiencies of the hadronic single prong signal softtau π ± as functions of pT and η. The pT > 2GeV cut is not imposed on the truth level
for the efficiency vs. pT plot.

5.1.1.3

Selection

Now in order to seed the soft tau tagging algorithm the quality cuts of the tracks needed
to be decided. The quantities used for the track seeded algorithm of tauRec were checked
and ultimately it was decided that the same quality requirements would be used for thisalgorithm. The only exception was the reduction of the p T cut from 6 GeV to 2 GeV. As
discussed in Section 4.3.4, it is necessary to reduce the seed threshold in order to increase
the soft tau reconstruction efficiency. The 2 GeV cut is a preliminary cut for choosing
the soft tau candidates and studies for optimising it for the M τ,τ analysis will be outlined
in Section 6.3. Figure 5.6 shows the distributions of the track quality quantities for the
single prong signal soft tau π ± tracks, and for the background to these tracks which
are the other reconstructed tracks in the region ∆R < 2 of the reconstructed hard tau.
These comprise both real tracks (mainly from jets) and fake tracks. The p T > 2GeV
cut, and a standard χ2 /d.o.f < 1.7 cut is applied to both signal and background tracks
for these plots. The track quality cuts for the soft tau tagging algorithm seed are shownin the second column of Table 5.1.
Since it was decided that only single prong modes would be considered fairly stringent
isolation requirements can be made on the algorithm seed track. Seed tracks are considered as isolated if no tracks of a given quality are reconstructed within ∆R < 0.2 of71

Signal normalised to unity

10

Signal π±

1

Background

10−1
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10Background

1
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0

Signal normalised to unity

Signal normalised to unity

Chapter 5. Soft Tau Reconstruction

0.5

1

1.5
2
d0 [mm]

0

102

5

10

15

20
Silicon Hits

Signal π±

10Background

1
−1

10

10−2
10−3
10−4
0

10

20

30

40

50
TRT Hits

Figure 5.6: The track quality quantities for the signal π ± , and the backgroundtracks within the search area around the signal hard tau. The signal distributions arenormalised to unity. The soft tau search algorithm seed track cuts are |d0 | < 1mm,
number of silicon hits ≥ 8, and TRT hits ≥ 10 (when |ηtrack | < 1.9).

Track criteriapT [GeV]|η| <Impact parameter d0 [mm] <Silicon Hits Nsi ≥TRT hits NT RT ≥ (when |η| < 1.9)
χ2 /d.o.f <Pixel Hits Npixel ≥B-layer hits Nblay ≥LT
High/Low threshold hit ratio NTHT
RT /NT RT <Seed track
2
2.5
1
8
10
1.7
no cutno cutno cutIsolation track
1
2.5
1
8
no cut1.7
1
1
0.2

Table 5.1: Track quality criteria for the soft tau tagging algorithm seed track andisolation track.

Chapter 5. Soft Tau Reconstruction

72

it. The quality requirements for the “isolation tracks” are shown in the third columnof Table 5.1. The same requirements as those for the “associated tracks” of the tauRec
track seeded algorithm were used. These have been optimised to be stringent enough to
exclude tracks arising from conversion electrons coming from π 0 → γ, γ decay, and so

are ideal for checking the isolation of the π ± coming from taus with π 0 decay products.
The left hand plot of Figure 5.7 shows the distribution for the distance from the seed
track to the closest “isolation track”. The distribution for the signal π ± tracks and forthe background to these tracks are shown superimposed, where again the backgroundare the seed tracks in the region ∆R < 2 of the reconstructed hard tau which do notcome from the signal soft tau. We can see that a track isolation cut of ∆R < 0.2 removes
a lot of the background which mainly comes from jet activity. The right hand plot of
Figure 5.7 shows the pT distributions of the signal and background. For this plot the
track cut has been reduced to pT > 1GeV in order to illustrate the rise in the backgroundbelow the 2GeV cut. As mentioned before, a tentative cut of p T > 2GeV was made on

Signal π±

1

Background

10−1
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0

Signal normalised to unity

Signal normalised to unity

the seed track but this will be optimised in the full background analysis of Section 6.3.
1

Signal π±
Background

10−1

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1

1.5

2

2.5

3
3.5
4
∆ Rcandidate, closest track

0

1

2

3

4

5

6

7

8

9
10
PT [GeV]Figure 5.7: The left hand plot shows the distance between the seed quality track,and the closest “isolation quality” track, for both signal and background seed tracks.
The right hand plot compares the pT of the signal and background seed quality tracks.

5.1.1.4

Performance

Table 5.2 shows the cut flow for the 3 single prong modes when the seed track quality
cuts are made. It also shows how the mean number of background tracks within the soft
tau search area changes with the cuts. We can see that around quarter of the signal islost by confining the search area to ∆R < 2 around the signal hard tau. We can also
see that the pT > 2GeV cut biases the remaining soft tau signal towards the lower π 0multiplicity modes, since the higher π 0 multiplicity modes have softer π ± tracks. Afterall of the seed track requirements an average of 1.3 tracks besides the signal π ± trackChapter 5. Soft Tau Reconstruction

No cut|η| < 2.5
ReconstructedWithin ∆R < 2 of hard tau|d0 | < 1mm
Si hits≥ 8
TRT hits≥ 10
χ2 < 1.7
pT > 2GeV
Isolated0-π 0 mode[/fb−1 ]
8.2
7.9
7.1
5.1
5.1
5.0
4.6
4.4
4.1
3.8

73
1-π 0 mode[/fb−1 ]
18.9
18.3
14.1
10.4
10.3
10.3
9.4
8.9
6.3
5.9

2-π 0 mode[/fb−1 ]
6.7
6.5
5.0
3.7
3.7
3.6
3.3
3.1
2.1
2.0

mean no. BG
in search area

30.1
16.5
15.1
13.5
12.0
7.9
1.3

Table 5.2: Cut flow for coannihilation single prong signal soft tau π ± with the soft tau
search algorithm seed track selection cuts. Cut flows for each of the 3 considered decay
modes are shown separately. The fifth column shows the mean number of backgroundtracks which remain in the soft tau search area as the cuts are made on the seed tracks.

remain in the search area around the signal hard tau. Thus, on average, the likelihood
method will need to select the signal soft tau π ± track from out of 2.3 tracks.

5.1.2

The soft tau π 0 reconstruction and selection

The fact the signal soft taus are not very boosted means that any π 0 coming fromtheir decay can be relatively separated from the π ± in the calorimeter. It is possible
to exploit this fact to help to discriminate these taus from background. The following
section outlines the algorithm developed for selecting any π 0 clusters coming from thesoft tau decay.

5.1.2.1

Truth level study

Figure 5.8 shows the truth level energy distributions of the π 0 coming from the 1-π 0 and
2-π 0 modes for the signal soft tau. We can can see that, as expected, the 2-π 0 mode π 0
are less energetic than the 1-π 0 mode π 0 due to the tau energy being shared amongst
more decay products. The mean energy of the π 0 from the 1-π 0 mode decay is 7.33GeV
while the mean energies of the π 0 s coming from the 2-π 0 mode decay are 6.94GeV and
3.01GeV. Particularly for the 2-π 0 mode, the reconstruction of such low energy clusters
in the calorimeter is extremely challenging due to material in front of the calorimeter.
Figure 5.9 shows the truth level correlation of the distance between the π ± and theπ 0 (s) at the interaction point, ∆Rπ±,π0 , and the pT of the π ± , pT,π± , for both 1 and
2-π 0 modes. If the tau is less boosted then the p T of the π ± will be lower. As can be74

1−π0 mode normalised to unity

Chapter 5. Soft Tau Reconstruction

1−π0 mode2−π0 mode 1st π0
2−π0 mode 2nd π0

10−2

10−3

10−4
0

Figure 5.8:

5

10

15

20

25
30
EMC [GeV]

Truth level energy distributions for the π 0 coming from the 1-π 0 and
2-π 0 signal soft tau single prong mode decays.

seen, as the pT of the π ± becomes smaller, the distance between the π ± and the π 0
grows larger due to this smaller boost. Thus we can see that we can size the searcharea for π 0 clusters around the vertex direction of the π ± track according to pT,π± .
The pT,π± dependant search area that is used for the π 0 selection algorithm is shownsuperimposed on the figure. It is a cone of 0.4 for 2GeV < p T,π± < 5GeV, 0.2 for
5GeV < pT,π± < 10GeV, and 0.1 for 20GeV > pT,π± . This is an improvement on thetauRec track seeded algorithm method of searching for π 0 clusters which employs only

10.9

1−π0 mode

0.8∆Rπ± , π0∆Rπ± , π0

a fixed cone size (∆R < 0.2).
1
0.9

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0
0

5

10

15

20

25
30
MC
PT,π± [GeV]

2−π0 mode

0.8

0
0

5

10

15

20

25
30
MC
PT,π± [GeV]

Figure 5.9: The truth level correlation between ∆Rπ±,π0 and pT,π± for the signal
soft tau 1 and 2-π 0 modes. The correlation for the 1-π 0 is shown on the left, while thecorrelation for the 2-π 0 mode is shown on the right. For the 2-π 0 mode the histogramsfor each π 0 are added together.

Chapter 5. Soft Tau Reconstruction
5.1.2.2

75

Excluding the π ± cluster

The basic procedure for the π 0 cluster search algorithm is as follows.
• The seed track is propagated to the middle layer of the calorimeter and the primarycluster of the track is searched for. This cluster is excluded from the search forthe π 0 clusters.
• Clusters are then searched for in a search cone around the vertex direction of theseed track. The size of this search cone is p T,π± dependant as described above.

• Only clusters which pass certain EM-like criteria are accepted as π 0 candidate
clusters.

For the purpose of excluding the π ± cluster from the search, and for attempting toresolve up to two π 0 clusters (from the single prong 2-π 0 mode), the topological clustering
algorithm of Section 4.2.2 was used. This clustering algorithm performs better than afixed cone algorithm for resolving clusters which are close together in the calorimeter.
In order to exclude the π ± cluster from the π 0 search we find the closest cluster to theπ ± position in the middle layer of the calorimeter. The matched cluster is required tohave E > 1GeV when it is calibrated to the hadronic scale 1 . Figure 5.10 shows the
distribution of the distance between the track position in the middle calorimeter and thematched cluster, ∆Rtrack,cluster , for the signal π ± . For this section of the study, only the0-π 0 mode is used to avoid contamination from any π 0 . Also, only soft taus which are∆R > 0.8 from the signal hard tau are used to avoid contamination from the signal hardtau. It is obvious that at such low energy the match between the π ± track and cluster
is not always good (∆Rtrack,cluster can be rather large). This is because of significant
multiple scattering before the calorimeter.
At low energy the shower arising from the π ± is also wider and may result in a number of secondary clusters in the calorimeter. We can observe this affect by looking at
ET,cluster /pT,track for the matched cluster. This is shown in the left hand plot of Figure 5.11. Note that these clusters are corrected for energy loss before the calorimeter.
Obviously not all of the π ± energy is contained in this cluster. The right hand plot of
the same figure shows ET /pT again, but now with the sum of the ET of all of the clusters
in a cone of 0.2 around the π ± . We can see that the energy is mostly fully recovered.
Figure 5.12 shows the number of clusters which are collected in this cone. We can seethat for most of these low energy π ± the energy in the calorimeter is dispersed amongst
greater than one clusters.

Chapter 5. Soft Tau Reconstruction

76

A.U.

0.06
0.05
0.04
0.03
0.02
0.01
0
0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2∆ Rπ± , cluster

Figure 5.10: The distance between the signal π ± in the middle layer of the calorimeter, and the closest cluster. For this plot only the π ± from the 0-π 0 mode is shown inorder to avoid contamination from π 0 .

A.U.

A.U.

0.03

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0
−2

−1.5

−1

−0.5

0

0.5
(E

T,cluster1
1.5− PT,track)/P

0
−2

2

−1.5

−1

−0.5

T,track

0

0.5
(E

1
1.5
− PT,track)/P

T,cone2

A.U.

Figure 5.11: The left hand plot shows ET,cluster /pT,track where the track is the signal
π ± track, and the cluster is the closest matched cluster in the calorimeter. The righthand plot shows ET /pT again, but this time with the ET of all of the clusters within
0.2 of the π ± track summed.

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

2

4

6

2

T,track

8
10
Number of clusters

Figure 5.12: The number of clusters collected in a cone of 0.2 around the signal π ±impact in the calorimeter. For this plot only the 0-π 0 mode is shown in order to avoid
contamination from any π 0 .

Chapter 5. Soft Tau Reconstruction

77

Now the best that we can do to remove the primary π ± cluster from π 0 candidacy is toremove it only if is close to the impact of the π ± in the calorimeter. Otherwise there isa risk of removing π 0 clusters as well. Thus we only remove the π ± matched cluster if
it is within ∆R < 0.04 of the π ± track at the middle layer of the calorimeter. For thecase that the match is not good, π 0 clusters will be discriminated using only cuts onenergy and shower shape, as will be described below. Note that this π 0 discrimination
will potentially be against a number of low energy secondary π ± clusters, and thus will
be quite challenging.

Selecting π 0 clusters with

5.1.2.3

EMFracClusterClassificationTool
The next step is to select EM-like π 0 candidates from the remaining clusters. This
“EM-likeness” is determined with a package within Athena named
EMFracClusterClassificationTool. The algorithm in this package is the default algorithm used for classifying topological clusters in Athena as EM or hadronic. Its algorithm
works by classifying a cluster as EM or hadronic by comparing it with the phase space
population predicted by single π ± and single π 0 Monte Carlo simulations in Athena.[19]A 4-dimensional phase space in |η|, E cluster , log 10 λcentre and log10 hρi is used, where

λcenter is the distance of the shower centre from the front face of the calorimeter along
the shower axis, and hρi is the first moment in energy density
hρi =

1
Enorm

×

X

Ei ρi , Enorm =i|Ei >0

X

Ei

(5.1)

i|Ei >0

For the above formula, Ei and ρi are the energy and energy density of the ith cellrespectively. The sum is over the cells in the cluster. This phase space is populatedwith equal numbers of π ± and π 0 , with an energy range of 200MeV - 2TeV. Assuming aprobability ratio of π ± to π 0 production of 2:1, a weight is then calculated for each bin
i in the phase space0nπ
EM f raction = π0 i π±
ni + 2ni0where nπi is the fraction of π 0 in the bin and nπi

±

(5.2)

is the fraction of π ± . By default if

a candidate cluster falls in to a bin which has EM f raction > 0.5, then the cluster isclassified as EM, though this setting can be altered if desired.
1
Calibration for clusters matched to seed tracks for this algorithm is done using Local Hadronic
Calibration, as described in Section 4.2.2.

Chapter 5. Soft Tau Reconstruction

78

Figure 5.13 shows the probability that a cluster comes from a π 0 as a function of hρi ofthe cluster, and λcenter of the cluster, when the above mentioned Monte Carlo procedure

is followed. η and Ecluster are fixed for these plots. The hot areas of the plots are thebins which are highly populated with π 0 , while the cold areas are the bins which arehighly populated with π ± . Green areas are those regions of the phase space where there
is a lot of overlap between π ± and π 0 . The left hand plot is for 1GeV< Ecluster <2GeV
clusters, while the right hand plot is for 8GeV< E cluster <16GeV clusters. We can seethat π 0 clusters tend to populate areas of lower λ center , and higher hρi as we would
expect for EM clusters. We can also see that there are a lot more areas of green forthe low energy plot. This means that the phase spaces of π ± and π 0 overlap. This isbecause the showers of π ± and π 0 look more and more similar as their energies becomes
smaller. This makes it more difficult to distinguish the two at low energy.

Figure 5.13: Probability that a cluster comes from a π 0 as a function of hρi of thecluster and λcenter of the cluster. Both plots are for the region 0.2 < |η| < 0.4, but theleft hand plot is for clusters with 1GeV< Ecluster <2GeV, while the right hand plot isfor clusters with 8GeV< Ecluster <16GeV. [19]While the classification efficiency with the default boundary of EMfraction=0.5 for π 0
clusters with E > 50GeV is rather good at 80 - 85%, this efficiency falls off to 50% at
5GeV and 23% at 1GeV. This is due to the substantial overlap in the phase space of
π ± and π 0 at low energy, i.e. low energy π ± clusters look very similar to low energy π 0clusters.
In order to optimise the classification efficiency of our signal π 0 clusters, and thus to
optimise the decay mode classification efficiency of our signal tau, this EM f raction
setting was changed.
The EMfraction setting was optimised using the following procedure. Monte Carlo
π 0 s from the 1-π 0 mode signal tau were matched to topoclusters. Only events with

Chapter 5. Soft Tau Reconstruction

79

Eπ0 > 1GeV and where the π 0 were within the π 0 search cone around the π ± wereconsidered. The cluster was considered matched if it was not the same as the π ± cluster(i.e. the π 0 did not overlap with the π ± in the calorimeter), and the distance between thetruth level π 0 and the cluster was less than 0.1. These π 0 were considered as “findable”.
Then the EM f raction setting was varied to try to find the setting at which this π 0cluster was the only EM-like cluster within the π 0 search cone.
Figure 5.14 shows the efficiency of EM-like classification as the EM f raction setting isvaried, both for the π 0 cluster, and for reference, the π ± cluster, of the 1-π 0 mode. We

Efficiency

Efficiency

see that as the EM f raction setting is increased the efficiencies drop off, as expected.
0.92
0.9

0.35

0.88
0.86

0.3

0.84

0.25

0.82
0.8

0.2

0.78
0.76

0.15

0.74
0.72

0.4

0.1

0.2

0.3

0.4

0.5
EM fraction

0.1

0.1

0.2

0.3

0.4

0.5
EM fraction

Figure 5.14: The change in the EM-like classification efficiency of the signal 1-π 0
mode π 0 cluster (left), and π ± cluster (right), as EM f raction is varied.

The left hand plot of Figure 5.15 shows, for the 1-π 0 mode, the number of clusters inthe π 0 search cone which are classified as EM-like, after the primary π ± cluster was
removed, as discussed above. The plots from varying the EM f raction setting from 0.1- 0.5 are shown superimposed. Mostly only the π 0 cluster is classified as EM-like, thus
the peak at 1. We can see though that, as the EM f raction setting is decreased, thenumber of clusters classified as EM-like increases. This is because many of the secondary
π ± clusters are also classified as EM-like. Events with greater than one EM-like cluster
can also arise from the two π 0 gamma rays actually forming two separate clusters.
Finally the right hand plot of Figure 5.15 shows the fraction of the selected events forwhich the π 0 cluster is the only EM-like cluster found, as EM f raction is varied. The
maximum is for a setting of 0.2. That is to say that, with the above π 0 search algorithm,
the maximum number of 1-π 0 events will be correctly classified when EM f raction is
set to 0.2. We thus use this setting for selecting π 0 clusters from around the π ± track.

A.U.

1800

80

EM fraction > 0.1

1600

EM fraction > 0.2

1400

EM fraction > 0.3

Efficiency

Chapter 5. Soft Tau Reconstruction

0.73
0.72

EM fraction > 0.4

1200
1000

0.71
0.7

EM fraction > 0.5

0.69

800

0.68

600

0.67

400

0.66

200

0.65

0
0

1

2

3

4

5
6
7
Number EM−like clusters

0.64

0.1

0.2

0.3

0.4

0.5
EM fraction

Figure 5.15: The left hand plot shows the number of clusters around the signal π ±which are classified as EM-like, as EM f raction is varied. The right hand plot show thefraction of events for which the signal π 0 cluster is the only cluster which is classified
as EM-like, as EM f raction is varied. Only the 1-π 0 mode is used, and the primary
π ± cluster is removed as described in the text.

This algorithm(tauRec)0-π 0 mode
1-π 0 mode
2-π 0 mode
J2 jets

0 EM clusters

1 EM clusters

2 EM clusters> 2 EM clusters

54%(74%)32%(33%)
19%(14%)41%(13%)30%(19%)36%(15%)33%(10%)30%(3%)

10%(2%)
19%(3%)
25%(2%)
18%(0)

7%(0)
13%(1%)
23%(1%)
11%(0)

Table 5.3: Single prong tau decay mode classification efficiency of the soft tau searchalgorithm. For comparison the classification efficiency of tauRec is shown in brackets.
For a fairer comparison, only taus with 5GeV < pT,vis < 10GeV are considered here.
tauRec classifications do not add up to 100% because only the track seed algorithm
has a π 0 search algorithm. For reference the classification for QCD jets in a J2 sample
is also shown.

5.1.2.4

Performance

Table 5.3 show the classification performance of this algorithm for the single prong
mode signal taus which have been reconstructed. For comparison the classification performance for tauRec is also shown, for those signal tau which tauRec has reconstructed.
The pT range for the taus is limited to 5GeV < p T,vis < 10GeV. It should be notedthat the classifications of tauRec do not add up to 100% because only the track seeded
objects have a π 0 search algorithm. It is obvious that the classification performance of
this algorithm is better than that for tauRec, but mainly due to the fact that most of the
1 and 2-π 0 signal tau which are reconstructed by tauRec are done so by the calorimeter
seeded algorithm. This is because the low p T tracks of these modes do not pass the
track seed pT threshold, while the clusters (which include the π 0 energy) do pass thecalorimeter seed threshold.

Chapter 5. Soft Tau Reconstruction

81

There are a number of sources of classification inefficiency for the soft tau search algorithm. One of the main sources for decay modes with π 0 s is from the Ecluster > 1GeV
requirement for the π 0 search algorithm. Also, as mentioned above, the misclassificationof secondary π ± clusters as EM-like, and π 0 clusters as non-EM-like is significant in
the low energy region. There are also some classification inefficiencies from losses of π 0clusters outside the π 0 search cone.
Finally Figure 5.16 shows plots of the quality of the π 0 reconstruction for this algorithm.
Energy resolution plots are shown in the top row. The bottom row shows the quality of
the reconstruction of the π ± , π 0 system invariant mass. Only signal from 1-π 0 and 2-π 0modes which have been correctly classified are shown. We can see that
The gaussian fit of the energy resolution of the 1-π 0 mode π 0 yields σ = 9.5%. It is
14.2% for the first π 0 of the 2-π 0 mode. The reconstruction for the second π 0 of the2-π 0 mode is poor and so the resolution has not been fit. Recall that this π 0 has a meanenergy of only 3GeV. It is also in the vicinity of another, more energetic π 0 , and alsoa π ± , making reconstruction very difficult. Nevertheless it seems that a cluster whichcorresponds to the second π 0 has been found, since the resolution plot is centered aroundzero.
The invariant mass of the 1-π 0 tau is reconstructed quite well, as can be seen from thecomparison with the truth level distribution. The 2-π 0 reconstruction is not as good,
due to the difficulty of reconstructing the 2nd π 0 . Both of these distributions, among
others, will be used in the discrimination of the signal soft taus from the background.
This is the subject of the next section.

5.2

The soft tau likelihood method

Now that the information about soft tau candidate π ± tracks, and soft tau candidate π 0 clusters is obtained, it is now necessary to further discriminate these isolated
track+cluster systems from QCD jets. For this purpose a likelihood method was developed. The inspiration for the method was taken from the tauRec likelihood method, butwith some modifications which are specific to the low energy region, and some modifications which are specific to this analysis. The likelihood method will be described below
with an emphasis on its differences from the tauRec method. Then the performance ofthe method will be shown, with a comparison against tauRec.

Chapter 5. Soft Tau Reconstruction

82

0.1
0.08
0.06
0.04
0.02
0
−2

−1.5

−1

−0.5

0

0.5

1
1.5
2
reco
MC
MC
(E
− ET )/E

A.U.

T

0.16

1st π02nd π0

−1

−0.5

0

0.5

1
1.5
2
reco
MC
MC
(E
− ET )/E

T

0.2

0.18

0.24
0.22
2−π0 MODE
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−2
−1.5

A.U.

1−π0 MODE

T

T

0.25

Reconstructed

1−π0 MODE

A.U.

A.U.

0.12

Reconstructed

0.2

MC

2−π0 MODE
MC

0.14
0.12

0.15

0.1
0.08

0.1

0.06
0.04

0.05

0.02
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8
2
Mπ± , π0

0
0

0.5

1

1.5

2

2.5
3
Mπ± , π0 , π012Figure 5.16: Plots showing the quality of the π 0 reconstruction in the soft tau searchalgorithm. The top row shows the energy resolution of the π 0 s while the bottom row
shows the invariant mass of the π ± , π 0 system. In the left column are the plots forthe 1-π 0 mode, while the in the right column are the plots for the 2-π 0 mode. The
invariant mass distributions are compared with the truth level distributions. Only
correctly classified signal is shown.

5.2.1

Description

The majority of the discrimination variables employed by tauRec focus on discriminating taus by the relative narrowness of their overall structure. For very soft taus thediscrimination power of these “narrowness” variables becomes worse. The advantage wehave with soft taus though is that, while the opening angle of the decay products becomes larger and hence the tau jet becomes wider, at the same time the decay products
become more distinguishable in the calorimeters. Thus rather than looking at the overallnarrowness of the tau jet, it was decided to attempt to look at the narrowness of only
the π ± energy depositions, and to consider the π 0 components completely separately.
This approach means that, effectively, we are only measuring the narrowness of a single
π ± in the calorimeter. We thus take advantage of the quite different topology of softtaus in the calorimeters.
Thus the basic thrust of the likelihood method is to• Identify the EM-like depositions in the calorimeter that are likely to come from π 0(as outlined in Section 5.1.2)

Chapter 5. Soft Tau Reconstruction

83• Remove these depositions from the calorimeter and then calculate the “narrowness” likelihood variables.

• Use both π ± and π 0 components to form other likelihood variables (such as invariant masses).

Below are listed separately the variables which are calculated with the EM-like clusters
removed, and the variables which are calculated using the EM-like cluster information,
along with variables which only use track information. Some of the variables are very
similar to those used in tauRec (with some differences, for example, in the calorimeter
cells which contribute), but are listed along with the other variables for completeness(refer to Appendix B for PDFs of these variables).
DISCRIMINATION VARIABLES USING CALORIMETER AND
TRACK INFORMATION, EXCLUDING EM-LIKE CLUSTERS• The electromagnetic radius, Rem :The electromagnetic radius Rem is defined as

Rem =

Pn

i=1 ET, iq(ηi − ηaxis )2 + (φi − φaxis )2Pn,
i=1 ET, i(5.3)

where i runs over non-EM-like cells within a cone of ∆R < 0.4 of the π ± position
2 . This is similar to the variable used in tauRec.

• Transverse energy width in the η strip layer, ∆η:The transverse energy width ∆η is defined as
v
u Pn
strip
2
u
i=1 ET i (ηi − ηaxis )
t
∆η =
.
Pn
strip
i=1 ET i(5.4)

where the sum runs over all non-EM-like strip cells in a cone with ∆R < 0.4 of theπ ± position and ETstrip
is the corresponding strip transverse energy. This is similarito the variable used in tauRec• Isolation fraction in the calorimeter, I:
The isolation fraction is defined as

2

P
ET, i
I = Pi,j ET, j

(5.5)

From here “non-EM-like cells” means cells belonging to topoclusters which have not been classified
as EM-like, and “π ± position” means the position of the π ± at the relevant layer of the calorimeter.

Chapter 5. Soft Tau Reconstruction

84

where the i and j run over all non-EM-like cells belonging to cones around the π ±position with ∆R < 0.2 and ∆R < 0.4, respectively, and E T, i and ET, j denote thecell ET . This is similar to the tauRec isolation variable, except that the numerator
is the sum of cell with ∆R < 0.2 instead of 0.1 < ∆R < 0.2.
• Ratio of hadronic and EM energy, HADoverEM :The ratio of hadronic to EM energy is defined asPnET,iHADoverEM = Pni=1
j=1 ET,j(5.6)

where the i and j run over all non-EM-like cells in cones of ∆R < 0.4 of the π ±position, in the hadronic calorimeter, and the EM calorimeter respectively.
• ETEM over pT of the seed track, ETEM /pT :The ratio of sum of the ET of non-EM-like cells within ∆R < 0.4 of the π ± position
to the pT of the seed track. Only cells from the EM calorimeter are used. This issimilar to the variable used in tauRec.
• ETHAD over pT of the seed track, ETHAD /pT :The ratio of sum of the ET of non-EM-like cells within ∆R < 0.4 of the π ± position
to the pT of the seed track. Only cells from the hadronic calorimeter are used.
• Number of hits in the η strip layer:
The number of hits in the finely segmented first layer of the EM calorimeter with
E>100MeV and within ∆R < 0.4 of the π ± position are counted. Only non-EMlike cells are considered. This is the same as for tauRec, except that the thresholdis reduced to 100MeV (which is still well above the 12 - 15MeV noise level in the
strip layer).

DISCRIMINATION VARIABLES USING CALORIMETER AND
TRACK INFORMATION, USING EM-LIKE CLUSTERS

Note that these variables are only calculated for the case that exactly one or two EM-likeclusters are identified.

• The invariant visible mass, Minvariant :Minvariant is defined as the invariant mass of the seed track and the EM-like clusters.

Chapter 5. Soft Tau Reconstruction

85• The distances between the π ± and the EM-like clusters, ∆Rπ± ,π1,20 :∆Rπ± ,π1,20
is defined as the distance between the π ± at the interaction point, andthe 1 or 2 EM-like clusters.
• The distance between the two EM-like clusters, ∆R π10 ,π20 :∆Rπ10 ,π20 is defined as the distance between the two EM-like clusters.
DISCRIMINATION VARIABLES USING ONLY TRACKINFORMATION• The distance to the closest track, ∆R π± ,closesttrack :∆Rπ± ,closesttrack is defined as the distance between the seed track and the closest
track of “isolation track” quality, as defined in Table 5.1. This is another measureof the isolation of the system, but using information from the inner detector.
• The number of tracks in the isolation zone, N T RACK 02 04:
N T RACK 02 04 is defined as the number of tracks of “isolation track” quality,
as defined in Table 5.1, in the region 0.2 < ∆R < 0.4. Recall that the seed track
is required to be isolated within ∆R < 0.2.
• Lifetime signed pseudo impact parameter significance:
This parameter is exactly the same as that used for tauRec. It is a measure of
the significance of the impact parameter. Refer to Section 4.2.7.3 for a complete
description.

The likelihood variable using these variables is calculated in the same way as for thetauRec algorithm (refer Section 4.2.7.3). PDFs for the signal and background werecreated from Monte Carlo simulations. Signal PDFs were created using the signal soft
tau from the coannihilation region sample. Background PDFs were created with a J2
sample. Separate PDFs have been created for 0, 1 and 2 π 0 modes.
The same likelihood variable as tauRec is calculated from these PDFs:

d=

k=nV
Xars
k=1

log

pSk (xk )pB
k (xk )

(5.7)

where the sum is over the discrimination variables, x k is the value of the variable k forthe candidate, and pSk (xk ) and pB
k (xk ) are the probability density at the value x k forChapter 5. Soft Tau Reconstruction

86

the signal PDF and for the background PDF respectively. No electron veto has been
implemented for this method.
The classification by the π 0 cluster finding algorithm determines which PDF set is used
(0,1 or 2 π 0 ). For candidates with greater than 2 EM-like clusters, the discrimination
variables using the EM-like cluster information are not calculated, and the 0-π 0 PDF
set is used. PDFs were binned by the momentum of the seed track as follows: 2GeV <ptrack < 5GeV, 5GeV < ptrack < 10GeV and ptrack > 10GeV.
Figures showing the final PDFs used for the likelihood method are located in Appendix B. They are divided by decay mode classification (single prong 0-π 0 , 1-π 0
and 2-π 0 ), and then further by seed track momentum range (2GeV < p track < 5GeV,
5GeV < ptrack < 10GeV and ptrack > 10GeV). The signal and the background PDFs areshown superimposed in these plots. We can see that the discrimination power of somevariables is much better than others. In particular it is obvious that the discrimination
power of the track based variables is relatively powerful. This is likely due to the factthat the depositions from low energy object in the calorimeter tends to be dispersed.
We can also see that the variables involving the π 0 clusters adds extra discrimination
power to the likelihood. This is an improvement on the tauRec method which only used
one variable involving π 0 candidates (Minvariant ), and then only for the track seededalgorithm.
In addition to the different approach for creating the likelihood variables mentioned
above, we have implemented another somewhat analysis specific modification to thelikelihood method. The discrimination power of the “narrowness” and “isolation” variables used in this method are contingent on the activity in the vicinity of the soft tau
candidate. That is to say that if there are tracks close to the soft tau candidate whichcome from other objects, or if there are depositions in the calorimeter close to the candidate which come from other objects, the power of the variables is diminished. It was
shown in Figure 3.4 that the signal soft tau is often very close to the very energetic
signal hard tau. Thus, firstly, tracks which are associated to the reconstructed hard tau
candidate are excluded from the calculation of variables which involve track information(e.g. the number of tracks in the area 0.2 < ∆R < 0.4 around the soft tau candidate).
Secondly, when calculating likelihood variables involving calorimeter information, if thesoft tau candidate is within ∆R < 0.8 of the hard tau candidate, only calorimeter cells
in the half cone furtherest away from the hard tau candidate were used. Figure 5.17
shows a schematic illustrating the half cone method. This method was not used for theπ 0 cluster search. The improvement in discrimination power using this method will be
discussed below.

Chapter 5. Soft Tau Reconstruction

Hard Tau

87

Soft Tau
track

Figure 5.17: When the soft tau candidate is within ∆R < 0.8 of the hard tau candidate, only the half cone furtherest from the hard tau candidate is used for calculating
a number of the likelihood variables.

5.2.2

Performance

Figure 5.18 shows final discrimination power of the likelihood functions for the signal
and the background. Likelihood functions for 0, 1 and 2-π 0 modes are shown andthe functions are plotted separately for the momentum ranges in which the likelihood
variables are binned. Only the correctly classified signal is shown. We can see that,indeed, the extra variables using the π 0 information do add to the discrimination powerof the likelihood method. But as will be described below, this power is diminished whencandidates are incorrectly classified.
Figure 5.19 show the improvements in the discrimination power of the likelihood functions when the above-mentioned half-cone method is used. Only soft tau candidates
within the cut-off distance of ∆R < 0.8 are shown. We can see that this method provides a small improvement in discrimination power for the signal soft taus which areclose to the signal hard tau.
Figure 5.20 compares the performance of this method’s likelihood function with thatof tauRec. As in Section 4.3.4 this is shown as a line in the jet , signal plane, where
similarly signal is defined as
number matched soft candidates with LLH > LLH cut
number of MC taus

(5.8)

number matched soft candidates with LLH > LLH cut
number of MC jets

(5.9)

signal =and jet is defined asjet =

Chapter 5. Soft Tau Reconstruction

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Figure 5.18: The likelihood functions of the soft tau likelihood method for the 0-π 0mode (top), 1-π 0 mode (middle) and 2-π 0 mode (bottom). The functions are shown
separately for candidates with seed tracks in the range 2 < GeVptrack < 5GeV (left),
5 < GeVptrack < 10GeV (middle) and 10 < GeVptrack (right). The signal here are thecorrectly classified coannihilation region soft taus, while the background are jets in a
J2 QCD sample.

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Figure 5.19: The improvement in the soft tau likelihood method when the half-cone
method is used. The left hand plot shows the likelihood function for taus/jets which
are within ∆R < 0.8 of the hard tau candidate, when the half-cone method is not used.
The right hand plot shows the same but for when the half-cone method is used.

Chapter 5. Soft Tau Reconstruction

89

where “matched” means for the signal that the soft tau candidate track has been matchedto within ∆R < 0.01 of the truth level π ± , and for background means that the soft tau
candidate has been matched to within ∆R < 0.2 of a truth level jet. For  signal thesignal soft tau from the coannihilation region is used while a J2 sample is used for  jet .
No hard tau candidate requirement is made for this comparison. Only taus and jets with
|η| < 2.5 are considered and only taus from a particular decay mode are considered at atime. The denominator for jet is all MC jets in the kinematic region. Figures are shown
separately for the 0, 1 and 2-π 0 modes and for different regions of the p T spectrum. Fora fair comparison a seed track cut of p T,track > 5GeV is used for the soft tau method,which is 1GeV lower than the track cut used for tauRec in order to compensate for theincrease in the maximum attainable efficiency that the calorimeter seeded algorithm oftauRec provides 3 .
We can see that in the region 5GeV < pT < 10GeV the new soft tau discrimination
method performs significantly better than tauRec for the 0 and 1-π 0 modes. The 2-π 0modes performs slightly worse. The better performance of the lower π 0 multiplicity
modes can be understood in two ways. Firstly the classification efficiency for the lower
multiplicity modes is significantly better, which means that the calculated discrimination
variables are being compared to the “correct” PDF set. Thus although the extra π 0variables do provide extra discrimination power for the higher π 0 multiplicity modes,
misidentification of π 0 clusters will result in a degradation in performance.
Secondly the tauRec algorithm has an advantage over the soft tau method since it
has a calorimeter seeded algorithm. The calorimeter seeded algorithm has a particularadvantage for higher π 0 multiplicity modes in the low energy region since, for thesemodes the π ± track will be particularly soft, and so will often fall below the thresholdof a track seeded algorithm. On the other hand the combined energy of the π ± andπ 0 s is more likely to pass the calorimeter seed threshold. In addition the π 0 decay
conversion electrons will contribute significantly to inefficiencies in the π ± passing seed
track isolation requirements.
We can also see that in the higher energy region of 10GeV < p T < 20GeV, the performance of tauRec is better for all modes. This can be understood again from the advantage that tauRec gains from having a calorimeter seeded algorithm. The contribution
to the reconstruction efficiency coming from the calorimeter seeded algorithm becomesvery significant when the tau energy is greater than the calorimeter seed threshold.
Nevertheless the overall performance for the soft tau tagging algorithm is better in theregion 5GeV < pT < 10GeV as can be seen in the combined performance plot at the3

The cut on the seed track ultimately used for the optimisation of the signal to background ratio for
the Mτ,τ reconstruction is actually lower than this, as will be described in Section 6.3

1Soft tau method

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Figure 5.20: Fake rate vs. efficiency plots comparing the performance of the soft
tau likelihood method with tauRec. Comparisons are made for 0-π 0 taus (top), 1-π 0taus (2nd row), 2-π 0 taus (3rd row) and the combined performance for all single prong
modes (bottom). The left hand plots are for the taus/jets with 5GeV < pT < 10GeV
and the right hand plots are for taus/jets with 10GeV < pT < 20GeV. A seed track
cut of ptrack > 5GeV is used for a fair comparison with tauRec.

Chapter 5. Soft Tau Reconstruction

91

bottom left of Figure 5.20. Furthermore the soft tau tagging algorithm has also been
optimised for even lower energies than this, where the tauRec algorithm efficiency isvirtually zero due to its high seed thresholds. The majority of the signal soft tau which
we are attempting to tag have pT < 10GeV, so the performance of the algorithm in theregion pT > 10GeV is of secondary importance. It will be shown in the next sectionthat indeed the better performance of the soft tau tagging algorithm in the lower energy
region results in a better reconstruction of the M τ,τ endpoint as compared to tauRec.

Chapter 6Mτ,τ Endpoint Analysis
In Chapter 4 the algorithm to be used for reconstructing the coannihilation region signal
hard tau (tauRec) was described. In Chapter 5 the development of a new algorithm
for reconstructing the coannihilation region signal soft tau was outlined. The following
chapter presents the final analysis of the coannihilation region M τ,τ distribution endpoint
reconstruction.
The chapter will begin with the study of the selection of SUSY events from the copious standard model background which will arise in LHC collisions. This includes therequirement of a signal hard tau candidate using tauRec. The optimisation of the selection of the signal soft tau will then be outlined. Finally the analysis of the resultingMτ,τ distribution will be given.
Prior to all of this though it is necessary to briefly give some technical details of thedefinitions of physics objects used. This is the subject of the next section.

6.1

Physics object definitions

Table 6.1 outlines the definitions of all of the ATLAS standard reconstruction objects
used for this analysis (excludes the soft tau definition). The recommendations for physics
object identification cuts given in reference[21] were used.
As well as the definition of physics objects it is also necessary for a procedure for socalled “overlap removal” to be implemented. “Overlap” arises, for example, when a setof calorimeter clusters is reconstructed (and identified) as different physics objects. Thisoccurs because reconstruction algorithms are executed independently. Overlap removal
needs to be implemented in order to avoid double counting of objects. The procedure
for removing such overlaps is as follows:93

Chapter 6. Mτ,τ Endpoint Analysis
Physics
objectJets

Algorithm

94
Athena container
nameCone4H1TopoJets

Electrons

0.4 radius cone,
topological cluster input,
H1 calibration
egamma

Muons

STACO

StacoMuonCollection

Taus

tauRec

TauRecContainer

ETmiss“Refined Calibrated”

MET RefFinal

ElectronCollection

Identification cutsη < 2.5, p T > 20GeV

η < 2.5, p T > 10GeV,
medium” ID cut,etcone20 isolation
η < 2.5, p T > 10GeV
isCombinedMuon,χ2 /d.o.f. < 100,
etcone20 isolation
η < 2.5, p T > 15GeV,“medium” LLH cut,
1,3 tracks,|Q| == 1, e, µ veto
N/A

Table 6.1: ATLAS standard reconstruction physics object definitions used for thisanalysis. Object overlap removal procedure is described in the text.

Reconstructed taus which are selected using the criteria of Table 6.1 already have aneffective electron veto applied so that electrons faking taus are reduced. This electron
veto has a better performance than a simple overlap removal procedure between electrons
and taus as described in Section 4.2.7.3. Thus rather than removing taus which overlap
electrons, in this analysis we remove electrons which overlap taus. This is in order tomaintain tau efficiency as much as possible. Furthermore we remove jets which overlap
taus. The overlap criteria used is ∆R < 0.4 between the reconstructed objects.
The jet reconstruction algorithm can reconstruct an electron as a jet. On the other handelectrons selected with the criteria of Table 6.1 have very few jets faking electrons. Thus
a jet overlapping an electron within ∆R < 0.2 is removed.
Electrons and muons can arise from the decay of particles within a jet. These electrons
and muons are not of interest in themselves in this analysis, and so electrons that are
between 0.2 < ∆R < 0.4 of a jet, or muons which are within ∆R < 0.4 of a jet areremoved.

6.2

SUSY selection

The overall phenomenology of SUSY events was outlined in Section 3.1. The main
characteristics which distinguish SUSY events from SM background are a number ofenergetic jets arising from the cascade decay of gluinos and squarks, possible leptons,Chapter 6. Mτ,τ Endpoint Analysis

95

and large ETmiss arising from the escape of two χ̃01 from the detector. In this section we
describe the SUSY selection cuts used to isolate a pure SUSY sample. Note that all of
the following plots have a requirement of a tau with p T > 15GeV.
For this analysis the requirement on the number of energetic jets is set to two. Figure 6.1
shows plots of ETmiss vs. PTjet1 +PTjet2 for the signal events from the coannihilation region
sample and for the various SM processes. Recall that the definition of effective massused for this analysis only involves the two hardest jets and E Tmiss : Mef f = ETmiss +PTjet1 + PTjet2 . Thus a cut on effective mass of x can be viewed in the E Tmiss , PTjet1 + PTjet2
plane as a line running from ETmiss = x to PTjet1 + PTjet2 = x. In order to supplement
the rejection of copious soft tau background , rather hard cuts on E Tmiss , PTjet1 , PTjet2
and Mef f are used for this analysis to reduce SM background as much as possible. The
following cuts on PTjet1 , PTjet2 and ETmiss , are used
1. PTjet1 > 180GeV
2. PTjet2 > 90GeV
3. ETmiss > 200GeV
4. Mef f > 700GeV
These cuts are illustrated in the plots of Figure 6.1 1 . The background process that willpass these cuts with the greatest efficiency is tt which also has energetic jets and large
ETmiss which comes from W decay. Of course significant numbers of other SM processes
such as QCD di-jet will pass these initial cuts due to their sheer numbers of statistics
but the efficiency is rather smaller.
After this first set of cuts the largest background still remaining is QCD di-jet processes
which have large jet transverse energy (>J4). In order to reduce these further a requirement of a minimum distance in φ between E Tmiss and the first and second jets ismade.

5. ∆φjet1,M ET > 0.2
6. ∆φjet2,M ET > 0.2
Correlation plots between ∆φjet1,M ET and ∆φjet2,M ET are shown in Figure 6.2 withthese cuts superimposed. These cuts effectively reduce the QCD contribution by around
Note that with separate cuts on the PT s of the first and second jets, the vertical cut on PTjet1 + PTjet2
is not strictly accurate, but is drawn for illustrative purposes.
1Chapter 6. Mτ,τ Endpoint Analysis
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Figure 6.1: ETmiss vs PTjet1 + PTjet2 for the coannihilation region signal events (topleft), tt (top right), W → τ, ν (middle left), Z (middle right) and QCD (bottom).
The cuts imposed on these quantities are superimposed. Normalisation for each plot isarbitrary.

70% while reducing the signal by only 3%. This is because the E Tmiss from QCD di-jet
processes arises either from neutrinos coming from weak processes within the jet (realETmiss ), or from mismeasurements of jet energy in the calorimeter (fake E Tmiss ). ETmiss incoannihilation events mostly comes from the two χ̃ 01 whose directions are not correlated
to the directions of the cascade jets.
In order to reduce the contributions of W and Z boson decay to electrons and muons wealso apply a lepton veto to the analysis. The reconstruction efficiency of electrons andmuons in the ATLAS detector is relatively very good and so this cut allows us to ignore
the contributions from W → e, ν, W → µ, ν, Z → e, e and Z → µ, µ, since they will beinsignificant relative to W → τ, ν and Z → τ, τ .

jet2,MET

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Figure 6.2: ∆φjet2,M ET vs. ∆φjet1,M ET for coannihilation region signal events (left)
and for QCD (right). Cuts made on these quantities are shown superimposed.

7. Lepton vetoThis cut is also quite effective at reducing further tt contributions, since the branchingratio of “not fully hadronic” decay of tt is 54%.
Next we make a requirement of a tauRec object with p T > 15GeV .
8. PT,τ > 15GeV
While this is effective at reducing the standard model background, its most importantrole is in reducing the combinatorial background from SUSY events. Recall that only
7% of SUSY events will contain the “golden” decay chain so in order to cleanly reconstruct the Mτ,τ endpoint it is necessary to reduce this SUSY background as much as
possible. The SUSY combinatorial background efficiency for this cut is 5% while thesignal efficiency is 40%.
The final cut that we make before the soft tau selection is on M T . For this analysis
the transverse mass is calculated using the hard tau candidate and the E Tmiss . Recall
that the MT distribution from W → τ, ν will exhibit a Jacobian peak at the W mass
so that a cut around the W mass is effective at reducing this contribution. In fact, a

cut on MT is also quite effective for reducing contributions from tt. This is because asemi-leptonically decaying tt event will produce an on shell W boson which can go via
W → τ, ν. Figure 6.3 shows the MT distributions for signal, W → τ, ν, and tt events,

where indeed we can see the peak around the W mass (80GeV) for W → τ, ν and tt.

This peak is is somewhat smeared compared to, for example, W → e, ν, due to theexistence of the second neutrino coming from the τ decay, and from jets faking taus.
For this analysis we make a cut on MT of 90GeV

Chapter 6. Mτ,τ Endpoint Analysis

98−1

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Figure 6.3: Comparison of MT for the coannihilation region signal events, W → τ, νand tt.

6.3

Soft tau selection

Now that the selections have been applied to heavily reduce the SM contributions, andto some extent the SUSY BG contribution, the final selection that must be made is forthe signal soft tau. The details of this algorithm were outlined in Chapter 5 but here we
optimise the cut on the soft tau candidate track, p T,track , and also the likelihood of the√candidate LLH. Figure 6.4 show a plot in two dimension of S/ N as a function of thecut on pT,track and the LLH, where S is the number of signal events for which the signal
hard and soft taus have been correctly selected by their respective algorithms, and N
is the total number of events which remain with both a hard and soft tau candidate.
This quantity was chosen as the optimising parameter since the uncertainty in the final
fit of the Mτ,τ spectrum will depend on the total statistics remaining N . Only thecontributions from background SUSY events are used for this plot, as the SM backgroundcontributions are small in comparison. We can see that the optimal cuts on the soft tau
candidates are at around pT,track > 3GeV and LLH > 3. Unfortunately it was necessary
to enlarge the acceptance of this cut by changing it to p T,track > 2.5GeV and LLH > 0√
in order to maintain statistics in the SM samples. This means a drop in S/ N from
6.40 to 6.16
As a preliminary to the presentation of the final cut flow we study the efficiency of thelikelihood method for selecting the signal soft tau from out of a number of soft tau

LLH cut

Chapter 6. Mτ,τ Endpoint Analysis
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2.52357 2.58199 2.49615

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5 3.67452 4.60419 5.2445 5.47777 5.52607 5.3033 4.9807 4.59279 4.26401 4.06128 3.51123 3.34894 2.96648 2.85714 2.56205
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3.61385 4.81241 5.71187 6.20453 6.24152 6.09711 5.84314 5.56038 5.22002 4.97067 4.26001 4.11597 3.8025 3.65655 3.33623
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0 3.35197 4.48757 5.41484 6.15942 6.34389 6.24926 5.94434 5.81263 5.56809 5.40842 4.83094 4.70231 4.47278 4.08327 3.71463
3.32774 4.35979 5.31029 6.05931 6.25741 6.15451 5.89437

5.7358 5.54256 5.41637 4.87177 4.64838 4.46076 4.10126 3.73705

3.26696 4.14215 5.02347 5.82067 6.15481 6.09596 5.9123 5.78003 5.59419 5.46664 4.99467 4.76199 4.4809 4.12837 3.71568
3.19836 4.03396 4.86816 5.61353 5.97732 5.93244 5.75086 5.58746 5.36752
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3.92887 4.74671 5.45116 5.86887 5.85845 5.74004 5.64053 5.43043 5.40062 4.95434 4.77422 4.58947 4.33463 3.79249−53.15182 3.87447 4.60419 5.27282 5.65393 5.65422 5.57773 5.47789 5.2933 5.28435 4.89667 4.74039 4.58993 4.28597 3.70485
3.14559 3.84791 4.58811 5.23337 5.61022 5.60868 5.54208 5.43877 5.31369
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4.26673.63154.2792 3.66576

3.11945 3.77217 4.43523 4.99587 5.32272 5.31705 5.26344 5.22784 5.16886 5.19575 4.85172 4.71038 4.50877 4.26283 3.65734−10 3.11885 3.77051 4.42345 4.96903 5.28308 5.26804 5.22012 5.20021 5.13616 5.1631 4.82811 4.69071 4.49415 4.24666 3.64898
1
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Figure 6.4: S/ N as a function of the cut on soft tau candidate pT,track , and thelikelihood cut, where S is the number of signal events for which the hard and soft taus
have been correctly selected, and N is the total number of events which remain with acandidate hard and soft tau.

candidates around the signal hard tau. That is we would like to know how often thelikelihood method actually correctly selects the signal soft tau when there is greater than
one candidate remaining.
The blue line in Figure 6.5 shows the number of soft tau candidates which remain aroundthe signal hard tau after all of the selection cuts, but before the soft tau likelihood
cut. Only events for which the hard tau is correctly reconstructed, and the soft tau
is reconstructed within the search cone, are shown. We can see that, before the soft
tau likelihood cut 52% of the events are background free (there are no other soft tau
candidates except for the signal soft tau). 96 of the events have more than one soft tau
candidate in the search cone (there are other tracks besides the signal soft tau track
within the search cone). Of these 96 events, 63 of the signal soft tau tracks pass thelikelihood cut, then of these 63, 56 are correctly selected as the most tau-like candidate.
Thus we can see that the selection efficiency for the soft tau likelihood method, for thecase that there is more than one candidate to choose from, is at least 58%. For reference,
the number of soft tau candidates which remain around the signal hard tau after the
likelihood cut is shown as the red line if Figure 6.5. Only events for which the signal softtau passes the likelihood cut are shown.

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Events/63fb−1

Chapter 6. Mτ,τ Endpoint Analysis

Pre LLH cut

100

Post LLH cut

80
60
40
20
0

0

2

4

6
8
10
Number of soft tau candidates

Figure 6.5: The number of soft tau candidates which remain in the soft tau searcharea before (blue) and after (red) the soft tau likelihood cut. Only events for which thesignal soft tau survives the selection cuts are shown for each plot.

6.4

Final cut flow

Table 6.2 show the final cut flow, before the OS-SS subtraction. It includes both the
SUSY selection and the soft tau selection, for the signal and the various backgrounds. It
shows the cut flow normalised to the signal sample integrated luminosity of 63fb −1 . The
samples used were outlined in Section 4.1. For this study we assume that the trigger
rate for the events which pass the SUSY cuts will be close to 100%, since we require
such a large ETmiss , and high energy jets.
Note that signal events for which the signal hard tau is not selected as the hardest tau
by tauRec are migrated to “SUSY BG” at that cut. Similarly for the soft tau selection.
1 of the final 150 signal events actually had the signal soft tau (coming from the τ̃ 1 )identified by tauRec, and the signal hard tau identified by the soft tau search algorithm.
The signal soft tau was a factor 2.8 harder than the signal hard tau for this particular
event. 1 event for which the hard and soft taus are correctly reconstructed has the hard
tau with a misidentified charge. This event is added to the SUSY background category.
Complimentary to this table is Figure 6.6 which shows the cut flow in graphical form.
We can see that the major background which remains is the SUSY combinatorial BG,
which is a factor 3 larger than the combined SM background. We can see that the major
contributions from SM processes arises from both tt and W → τ, ν, which both havesignificant ETmiss .

There are a couple of points to note about the Monte Carlo samples used for this final
analysis. Recall that with the lepton veto, the W and Z to µ and e become negligible

Chapter 6. Mτ,τ Endpoint Analysis
Cut
No cutPTjet1 > 180GeV
PTjet2 > 90GeV
ETmiss > 200GeV
Mef f > 700GeV∆φjet1,M ET > 0.2∆φjet2,M ET > 0.2
Lepton Veto
pT,τ > 15GeV
MT > 90GeVSoft tau selection

Signal
11.9k
8.88k
7.80k
6.11k
5.94k
5.93k
5.75k
3.40k
1.33k
905
150 ± 12SUSY BG
151k
120k
105k
85.0k
82.8k
82.7k
80.7k
56.9k
3.08k
1.86k
451 ± 21

101
tt
6.78M
784k
603k
77.1k
59.6k
59.2k
51.4k
26.0k
3.92k
494k
75 ± 17

W
59.7M
1.51M
879k
81.9k
66.7k
66.7k
59.5k
47.3k
10.9k
465
54 ± 54

Z
21.0M
594k
277k
103k
82.3k
82.2k
76.4k
76.3k
413
341
18.7 ± 8.4

QCD
9.91G
3.50G
3.16G
267k
263k
189k
75.2k
75.2k

Table 6.2: The cut flow of the SUSY and soft tau selections, normalized to an
integrated luminosity of 63fb−1 . Only the significant samples, as described in the text,
are used.

compared to their τ decay counterparts, and so ESD samples were not created for theseand they are not included in the final analysis. Also, ESD samples were not created for
Z and W samples which would become insignificant after the jet cuts (e.g. Z → ν, νwith 0 or 1 parton).

Also, only the QCD samples >J4 (leading jet E T > 140GeV) were found to have significant statistics after the cuts on ∆φ jet,M ET , and so only these are included in the table
2 . Even with this restriction it was impossible to create large enough QCD samples suchthat statistics remain at the final soft tau cuts. Statistics remain for each of the QCD
samples only up to the lepton veto. An estimate was made on the combined efficiencyof the hard tau pT cut, the MT cut, and the soft tau cuts by imposing these cuts, with arange of looser SUSY cuts preceding them. A conservative estimate of the efficiency ofthese cuts of 10−4 was made. It is expected that the contribution to the M τ,τ spectrum
from QCD should be similar to that of Z → ν, ν. We will show that the contribution

from Z → ν, ν is negligible compared to that from the SUSY combinatorial background.
Of interest here is whether or not the two tau candidates which are selected by theabove procedure are true taus or not. Table 6.3 summarises this information. We cansee that for 47% of the SUSY background at least one of the hard or soft candidates
is a true tau. For 9% of the SUSY background both candidates are true. 78% of theTrue/Fake SUSY background arises from correct identification of the signal hard tau
with incorrect identification of the signal soft tau. 24% of the True/True backgroundarises from correct identification of the signal hard tau with identification of a separate

tau from the signal soft tau in the event.
2
Statistics for other QCD samples run out at earlier cuts, but they quickly become insignificant
compared to those >J4 due to the low energy of their jets

Chapter 6. Mτ,τ Endpoint Analysis

102

Events/63fb−1

1011

10

SU1 signal events
All BGSU1 combinatorial BG
tT
W
Z
QCD

10

10

9

10

8

107
10

6

10

5

104
10

3

102
10
1

NO

CUT

JET

DPH
DPH
JET
MET
MEF
LEP
T
MT>
SOF
2PT
I_M
I_M
TON AU PT
90G
T TA
>20
F>7
ET_
ET_
>15
>18
>90
0Ge
00G
eV
U
VE
GeV
JET
JET
0Ge
GeV
V
eV
1>0
2>0 TO
V
.2
.2

1PT

Figure 6.6: The cut flow of the SUSY and soft tau selections. Only the significant
samples, as described in the text, are used.

Process
SUSY BGtt
W → τ, ν
Z → ν, νTrue/True41
100

True/Fake
124
4
0
0

Fake/True46
200

Fake/Fake
240
19
1
5

Total
451
26
1
5

Table 6.3: The proportions of the backgrounds which come from true taus. The raw
Monte Carlo statistics for each sample are listed here.

In the SM background there are relatively few true taus arising from the selection procedure, though the statistics are very limited for the W → τ, ν case. In comparison,

the large true tau contribution in the SUSY background is to be expected due to theenhanced SUSY cross section for decay to taus and the large boost usually imparted tothese taus, plus the fact that many of the signal hard taus are relegated to backgroundfrom the misidentification of the signal soft tau.

6.5

Mτ,τ contribution from the backgrounds

The final step for this analysis is to subtract the M τ,τ distribution of the SS tau candidate
pairs from that of the OS sign pairs. This will reduce the uncorrelated pair backgroundsince uncorrelated SS pairs will arise at the same rate and with the same kinematics as
uncorrelated OS pairs. If there are no other correlated pairs present, in principal only
the Mτ,τ spectrum from our signal decay chain should remain.

Chapter 6. Mτ,τ Endpoint Analysis

6.5.1

103

The SM contributions

Due to the serious lack of statistics in the remaining SM background the shape of theMτ,τ contributions from each SM process were obtained by slightly loosening the SUSY
selection, and then this shape was normalised by the final statistics of the cut flow.
Contribution from tt
Figure 6.7 shows the Mτ,τ shape of the tt contribution after the OS-SS procedure. The
shape with the complete SUSY selection, and that with the loosened SUSY selection are
shown superimposed. For tt the SUSY selection was loosened as follows:• ETmiss > 200GeV → ETmiss > 100GeV

Events/63fb−1/4GeV• Mef f > 700GeV → Mef f > 600GeV
10
5
0
−5

All cuts
Loose SUSY cuts

−10
0

20

40

60

80

100
Mτ,τ

Figure 6.7: tt contribution to the Mτ,τ spectrum. The red line shows the shape withall of the selection cuts imposed while the black line shows the shape with the loosened
selection.

We can see that the contribution from tt after the loosened SUSY selection is not perfectly flat, due to the contribution from correlated leptons, arising from fully leptonic
decay tt events. Most of the correlated pair are true/fake or fake/true combinations,where one of the pairs is an electron. There is a possibility that this excess is slightly
underestimated with these looser cuts on E Tmiss , since fully leptonic tt decay is expected
to be enhanced with hard ETmiss cuts. The effect of any such increase on the final M τ,τspectrum is expected to be negligible though, since the absolute contribution from tt issmall compared to the SUSY combinatorial background.

Chapter 6. Mτ,τ Endpoint Analysis

104

Contribution from W → τ, νFigure 6.8 shows the Mτ,τ shape of the W → τ, ν contribution after the OS-SS procedure.

The shape with the complete SUSY selection, and that with the loosened SUSY selection
are shown superimposed. For W → τ, ν the SUSY selection was loosened as follows:• ETmiss > 200GeV → ETmiss > 100GeV• Mef f > 700GeV → Mef f > 200GeV• PTjet1 > 180GeV → PTjet1 > 100GeV• PTjet2 > 90GeV → PTjet2 > 50GeV

Events/63fb−1/4GeV• MT > 90GeV → MT > 50GeV
6
4
2
0
−2
All cuts−4

Loose SUSY cuts

−6
0

20

40

60

80

100
Mτ,τ

Figure 6.8: W → τ, ν contribution to the Mτ,τ spectrum. The red line shows theshape with all of the selection cuts imposed while the black line shows the shape withthe loosened selection.

The shape of the W → τ, ν Mτ,τ contribution is flat as expected, since there should not

be any correlated pairs, true tau or fake tau, in such events.
Contribution from Z → ν, νIt was found that Z → τ, τ became negligible compared to Z → ν, ν due to the large cutson ETmiss , thus only Z → ν, ν is considered for the M τ,τ shape contribution. Figure 6.9
shows the Mτ,τ shape of the Z → ν, ν contribution after the OS-SS procedure. The

shape with the complete SUSY selection, and that with the loosened SUSY selection are
shown superimposed. For Z → ν, ν the SUSY selection was loosened as follows:• ETmiss > 200GeV → ETmiss > 100GeV

Chapter 6. Mτ,τ Endpoint Analysis

105• Mef f > 700GeV → Mef f > 200GeV• PTjet1 > 180GeV → PTjet1 > 100GeV• PTjet2 > 90GeV → PTjet2 > 50GeV• MT > 90GeV → MT > 50GeV

Events/63fb−1/4GeV

which is the same as for W → τ, ν.
6
4
2
0
−2
All cuts−4

Loose SUSY cuts

−6
0

20

40

60

80

100
Mτ,τ

Figure 6.9: Z → ν, ν contribution to the Mτ,τ spectrum. The red line shows theshape with all of the selection cuts imposed while the black line shows the shape withthe loosened selection.

The shape of the Z → ν, ν Mτ,τ contribution is flat as expected, since again there should

not be any correlated pairs, true tau or fake tau, in such events.

6.5.2

The SUSY combinatorial background contribution

Table 6.4 shows the proportion of the main SUSY background processes which survive
the selection procedure. Unfortunately correlation between true and fake tau combinations is much more prevalent in the SUSY background compared to the SM background,
due to the other decay modes of the χ̃ 02 which produce opposite sign leptons, the possibility of correlated stop-top pairs from gluino decay which can go to opposite sign
leptons, and from χ̃±
1 pair production.
Figure 6.10 shows the various contributions from the SUSY background to the M τ,τspectrum. In order to maintain statistics only a lepton veto was applied for this plot
3 .

We can see that the contribution from the misidentified golden decay chain is flat,
3

The Mτ,τ contribution from the SUSY background used in the final Mτ,τ spectrum will be theone which results after all of the selection cuts. The loose selection used here is only to illustrate thecontributions to the OS-SS excess coming from each individual SUSY background process.

Chapter 6. Mτ,τ Endpoint Analysis

106

Side 1

Side 2All squarksχ˜02 → τ˜1 → χ˜01
χ˜02 → τ˜2 → χ˜01
χ˜02 → ẽ → χ˜01
Contains χ˜±All squarks
Anything
Anything
Anything
Contains χ˜±

1

1

Contains χ˜±All squarks
1
Other
TOTAL

Opposite
sign
34
67
21
9

Same
sign
24
62
8
3

36

27

70
18
255

52
20
196

Table 6.4: The breakdown of the SUSY background contribution.

albeit with a large statistical fluctuation in each bin. This fluctuation is due to the large
statistical error arising from the OS-SS subtraction. We can see that there is a significant
contribution from the process χ˜0 → τ̃ , τ → χ˜0 , τ, τ , which has a cross section a factor
22

1

8 smaller than the similar golden decay chain. The M τ,τ endpoint for this process is at

56GeV. The most significant contribution to the excess though comes from the processes
with jets for which the above-mentioned contribution from correlated stop-top pairs is

A.U.

expected to dominate.
250∼χ →∼τ 1 one side2
∼0 →∼τ one side
χ

20

2

2

0
∼
χ →~
e,∼
µ one side
2
±
∼
2xχ

15

jets

10

1

Sum of the above contribubutions
Total contribution, including others

5
0
−5
−10
0

Figure 6.10:

6.6

20

40

60

80

100

120

140

160
Mτ,τ

Contributions to the Mτ,τ spectrum from the various processes inbackground SUSY events.

Final Mτ,τ analysis

Finally each of the BG contributions are added to the signal to form the complete M τ,τspectrum. Figure 6.11 shows the individual contributions from each process. We can see

Chapter 6. Mτ,τ Endpoint Analysis

107

that by far the most significant background contribution comes from the SUSY combinatorial BG. This is due to both the large statistic which remain after the selection, andalso the OS-SS excess which exists from the remaining SUSY processes. We can see thatthe signal dominates the background in the lower M τ,τ region, though it has comparable
statistics to the background near the endpoint. For this analysis, the endpoint of thespectrum is found by a linear fit of the entire falling edge, so that the significance of the−1

Events/63fb /8GeV

signal near the endpoint is not absolutely critical, though it will play a significant role.
80

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30
20
10
0
−10
0

20

40

60

80

100

120
Mτ,τ

Figure 6.11: The contributions to the Mτ,τ spectrum from the coannihilation signal,and each of the background processes.

Figure 6.12 show the combined Mτ,τ spectrum which is fit by minimising the χ 2 of thefitting function with respect to the spectrum. The spectrum is fitted with the following
function using the MINUIT package

f (x) = (x < −p1
p1)(p0 x + p1 ) + (x > − ) × 0
p0
p0

(6.1)

where the inequality terms are logical booleans (equal to 0 or 1). The first summand
defines a first degree polynomial which crosses the x-axis at −p 1 /p0 , and only exists forx < −p1 /p0 , i.e. only below the x crossing. The second summand defines the function

f (x) = 0, and only exists for x > −p1 /p0 , i.e. only above the x crossing. By fittingwith this function we also take account of the M τ,τ spectrum above the x crossing of thelinear function, and the point where the two pieces of the function join is the positionof the Mτ,τ endpoint x = −p1 /p0 .
The fit to this function in the region 8GeV < M τ,τ < 80GeV yields an Mτ,τ endpoint of

−1

Events/63fb /8GeV

Chapter 6. Mτ,τ Endpoint Analysis

108
χ2 / ndf
Prob
p0
p1

80
70
60

6.179 / 7
0.519
−1.209± 0.271
69.8 ± 11.7

50
40
30

Reconstructed

20

MC

10
0
−10
0

20

40

60

80

100

120
Mτ,τ

Figure 6.12: The fit of the final Mτ,τ spectrum, with the function of Equation 6.1.

Mτ,τ endpoint = 58 ± 16 (stat) GeV(6.2)

with a minimised χ2 /d.o.f. of 6.2/7. This is consistent with the theoretical endpoint of
69 GeV.
The systematic studies of this fit, and studies of fitting with other functions will be
discussed in the next chapter.

Chapter 7

Systematic Studies, Discussion
and Outlook
In this chapter the systematic uncertainties of this M τ,τ endpoint analysis will be discussed, and an estimate of the systematic error in the final result will be made. Comparisons of the derived Mτ,τ spectrum with the spectrum derived from an analysis using
only tauRec will then be made. There will then be a discussion of attempts to fit theMτ,τ spectrum with a more sophisticated functional form. This will be followed by theapplication of the soft tau analysis to a different coannihilation SUSY point. Finally an
outline of the possible future direction of this study will be given.
Here we note that a number of the plots for for this chapter have been relegated toAppendix C with only the results from the plots (fitting of the histograms etc.) shownwithin the actual chapter text.

7.1

Systematic studies

7.1.1

Systematic study of the linear fit

As a continuation of the fitting result of the previous chapter, this section will estimate
the systematic uncertainty arising from the fit of the M τ,τ spectrum.
Table 7.1 shows the result of fitting the spectrum with the function of Equation 6.1,
while varying the fit range, and the binning of the spectrum. The largest systematiceffects on the reconstructed endpoint are ≈ +3.1GeV−0.6GeV .

109

Chapter 7. Systematic Studies, Discussion and Outlook
Range [GeV]
8 - 8016 - 80
24 - 80
8 - 728 - 648 - 8016 - 80
24 - 80
8 - 728 - 6416 - 80
16 - 64

Endpoint [GeV]
8 GeV bins
57.7
57.6
57.1
57.7
57.7
4 GeV bins
58.8
58.6
58.8
58.8
58.8
16 GeV bins
60.8
60.8

110
χ2 /d.o.f.
6.3/7
6.4/6
6.3/5
5.4/6
2.4/5
10.3/16
9.6/149.2/12
9.0/14
6.0/123.7/2
0.15/1

Table 7.1: The variation in the result of the linear Mτ,τ fit when the fit range andthe binning are altered.

7.1.2

Systematic study of tau fake rate

Two of the significant systematic uncertainties arising from the Monte Carlo simulation
are the fake rate from the hard tau selection and the fake rate from the soft tau selection.
In order to estimate the effect of an increase in these fake rates on the M τ,τ endpoint
derivation, both of these fake rates were increased in the simulation by hand.
Hard tau fake rate
The estimation of the fake rate arising from the likelihood cut in tauRec is dependanton the knowledge of the shower shapes of taus and jets in the calorimeter. There are
inherent limitations to the accuracy of the simulation of such complex processes, andalso inherent limitations to the basic knowledge of QCD jet production processes. For
example Monte Carlo simulation pion showers are slightly narrower and shorter than theshowers measured in calorimeter beam tests. A detailed study of the systematic error
arising from such uncertainties may involve altering such things as the Monte Carlosimulation fragmentation parameters, but here we simply increase the tau fake rate byhand.
In order to study the effect that such an increase in the hard tau selection fake rate
may have on the Mτ,τ spectrum, the likelihood cut at which fake tau were allowed to“pass” was reduced. For the Mτ,τ analysis the “medium” likelihood cut is used fordiscrimination. For this systematic study, fake taus were allowed to pass if they passed
only the “loose” likelihood cut, while true taus were still required to pass the “medium”

Chapter 7. Systematic Studies, Discussion and Outlook

111

cut. This loosening increases the fake tau rate by a factor of ≈ 2 − 3 in a QCD sample.

This is a rather conservative estimate of the increase and the real fake rate is not expected
to change to this extent from the simulation, once the detector is well understood.

The result of this procedure is a 30% increase in the background statistics from SUSY
combinatorial processes, a 50% increase for tt, no change for W → τ, ν (though thestatistics are very limited) and a 50% increase for Z → ν, ν.

Plots showing the contributions to the M τ,τ distribution from the signal and the various
backgrounds, along with the final fit of the spectrum can be found in Appendix C,
Figure C.1. The fit results in an endpoint ofMτ,τ endpoint = 57 ± 16 GeV(stat)(7.1)

Soft tau fake rate
Again the estimation of the fake rate arising from the soft tau search algorithm likelihood
cut is dependant on the knowledge of the shower shapes of taus and jets in the calorimeter. In order to study the effect that an increase in the soft tau selection fake rate may
have on the Mτ,τ spectrum, the pT,track and likelihood cuts of section Section 6.3 were
de-optimised:• pT,track > 2.5GeV → pT,track > 2.0GeV• LLH > 0 → LLH > −2
The result of this procedure is a factor 1.3 increase in the background statistics fromSUSY combinatorial processes, a factor 1.4 increase for tt, a doubling of W → τ, ν(though the statistics are again very limited) and a factor 5.7 increase for Z → ν, ν.

Plot showing the contributions to the M τ,τ distribution from the signal and the various
backgrounds, along with the final fit of the spectrum can be found in Appendix C,
Figure C.2. The fit results in an endpoint ofMτ,τ endpoint = 54 ± 17 GeV(stat)(7.2)

Chapter 7. Systematic Studies, Discussion and Outlook
SourceRecommended effectTau energy scale
overestimation
Tau energy scale
underestimation
Tau energy resolution
overestimation
Jet energy scale
overestimation
Jet energy scale
underestimation
Jet energy resolution
overestimation

E → 0.95E

112
Mτ,τ
endpoint
[GeV]
56.1

E → 1.05E

56.8√
E → smear with σ = 0.45 E

56.9

E → 0.93E (|η| < 3.2)
E → 0.85E (|η| > 3.2)
E → 1.07E (|η| < 3.2)
E → 1.15E (|η| > 3.2)√
E → smear with σ = 0.45 √E (|η| < 3.2)
E → smear with σ = 0.63 E (|η| > 3.2)

61.9
55.9
55.6

Table 7.2: Sources of energy scale systematic uncertainties and their effects on theMτ,τ endpoint determination.

We can see that, with these increases in the tau fake rate for both hard tau and thesoft tau algorithms, the Mτ,τ endpoint estimation changes by ≈−4 at the most. Thisdecrease is due to an increase in the statistics of the bins below the M τ,τ endpoint, whichtends to increase the slope of the linear fit.

7.1.3

Systematic study of tau and jet energy scales

There are a number of systematic uncertainties in the tau and jet energy reconstructionin the Monte Carlo simulation that may affect the final result of the M τ,τ spectrum fit.
One of the major uncertainties is the ability to correctly scale the hadronic contributions
in taus and jets to the correct level. Furthermore, there are uncertainties arising fromthe accuracy of the estimations of dead material effects, transverse energy losses fromthe energy collection area, lateral energy loss from punch through, and losses from low
energy tracks bending away from the calorimeter in the solenoid magnetic field. For thissystematic study the recommendations from the 2008 ATLAS CSC study were followed.
These systematic effects, and their results on the final M τ,τ endpoint determination aresummarised in Table 7.2. The plots of the resulting contributions to the M τ,τ spectrum,and the final fits of the spectrum can be found in Appendix C. We note that the ETmiss
for each event has also been corrected for each systematic uncertainty.
We can see that the Mτ,τ analysis is fairly robust against the systematic uncertainties inthe tau and jet energy scales, with a maximum deviation in the endpoint determinationof ≈+4−2 .

Chapter 7. Systematic Studies, Discussion and Outlook

113

For the total systematic uncertainty, the contributions from the above considerations
were assumed to be independent, and each contribution is added in quadrature. The
final estimation of the systematic uncertainty in the M τ,τ endpoint analysis isσsystematic,total =+5−5 GeV(7.3)

and the final result of the Mτ,τ spectrum endpoint becomesMτ,τ endpoint = 58 ± 16 (stat) ± 5 (sys)GeV(7.4)

We note that these systematics errors will be reduced when the Monte Carlo shower
shapes and energy calibrations are validated using real data.

7.2

Comparison of soft tau search method with other methods

7.2.1

Comparison with tauRec

In Section 5.2 a comparison between the performance of the soft tau likelihood method,
and the tauRec likelihood method was presented. It was shown that the overall performance of the soft tau likelihood method for reconstructing the signal soft tau, wassuperior to that of the tauRec likelihood method, when an appropriate cut was madeon the seed track pT . For the final Mτ,τ analysis though, the pT cut of the soft tau
search method was reduced to pT,track > 2.5GeV in order to optimise the signal soft tau
signal to background ratio. We would then like to check how the soft tau search methodMτ,τ spectrum with this lower pT cut compares with the Mτ,τ spectrum obtained using
tauRec to reconstruct the signal soft tau.
Since the seed thresholds for the tauRec algorithm are much higher than that of thesoft tau search algorithm (pT,track > 6GeV and ET,topojet > 10GeV), the numbers ofboth signal and background surviving the above SUSY selection, and a tauRec soft tau
selection, are very small. Because the absolute level of the background decreases with

Chapter 7. Systematic Studies, Discussion and Outlook

114

the tauRec thresholds, looser SUSY cuts are possible for the tauRec method. Thus only
the following cuts were made for the tauRec SUSY selection 1 :1. PTjet1 > 100GeV
2. PTjet2 > 50GeV
3. ETmiss > 100GeV
4. Mef f > 400GeV
5. Exactly 2 tauRec objects with the same identification cuts as Table 6.1, except no
pT cut is imposed on either. ∆Rτ,τ is required to be less than 2.
Unfortunately these cuts fall below the generator filter cuts used to create a number of
the SM backgrounds, so inclusion of the SM backgrounds would not be meaningful. Thus
only the SUSY combinatorial background is included. Figure 7.1 shows the contributions−1

Events/63fb /8GeV

to the Mτ,τ spectrum using this method.
30

SU1 signal

25

SU1 BG

20
15
10
5
0
−5
0

20

40

60

80

100

120
Mτ,τ

Figure 7.1: The contributions to the Mτ,τ spectrum from the coannihilation signal
and the SUSY background when tauRec is used for both taus’ selections.

There are a couple of differences between this spectrum and the spectrum of the soft tau
analysis to note. The first is that the signal M τ,τ distribution exhibits higher values thanfor the soft tau method. This is a result of a couple of effects. The first is that tauRec
reconstruction includes π 0 energy in the calculation, which results in a better quality
signal soft tau reconstruction and higher M τ,τ values. The second is the relatively hightauRec seed thresholds imposing a bias on the signal soft tau. For similar reasons the1

These are very similar cuts to those used in the Mτ,τ study of the 2008 ATLAS CSC note [21]. This
was a study performed at a collision energy of 14TeV

Chapter 7. Systematic Studies, Discussion and Outlook

115

SUSY background spectrum is located at higher values of M τ,τ also. This results inmore background being located near to the theoretical M τ,τ endpoint. We can see thatindeed the background dominates around the theoretical endpoint. It is obvious fromthis level of background near the endpoint, that the endpoint determination of the soft
tau selection method is superior to that using only tauRec, when, for the latter, theevents are selected in the way described above.

7.2.2

Comparisons with simple geometric methods

Now in order to observe the effect of the soft tau search likelihood selection on the M τ,τspectrum, we compare our result with two simple geometric methods for selecting thesoft tau. For these methods, exactly the same procedure is followed as for the soft tau
search method, except that rather than applying the likelihood cut and selecting themost tau-like candidate, we simply

1. Choose the closest soft tau candidate to the hard tau candidate in the soft tau
search cone OR
2. Choose the hardest soft tau candidate in the soft tau search cone.

Figure 7.2 shows the individual contributions to the M τ,τ spectrum arising from thesemethods. Comparing with Figure 6.11 we can see that although the relative level of OSSS excess in the background is similar to the soft tau likelihood method, the statisticalfluctuation arising in each bin from the OS-SS method is greater. This is because, forthese simple geometric methods, every hard tau candidate is paired with a soft tau
candidate. Table 7.3 compares the signal and background statistics which remain foreach of the methods for an integrated luminosity of 63 fb −1 . The final column shows the√value of S/ N , where S is the number of signal events for which the signal hard andsoft taus have been correctly selected by their respective algorithms, and N is the total
number of events which remain with both a hard and soft tau candidate. As describedin Section 6.3, this parameter gives an estimate of the level of the signal above thestatistical fluctuation when the OS-SS is used. We can see that the soft tau likelihood√
method gives a higher value of S/ N due to the fact that it rejects a large proportionof the fake soft tau candidates.

80

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

40

−1

60

Events/63fb /8GeV−1

Events/63fb /8GeV

Chapter 7. Systematic Studies, Discussion and Outlook

20

116

80

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

60
40
20

0

0

−20

−20

0

20

40

60

80

100

120
Mτ,τ

0

20

40

60

80

100

120
Mτ,τ

Figure 7.2: Left: The contributions to the Mτ,τ spectrum from the coannihilation
signal, and each of the background processes when the “closest candidate” method isused for the soft tau selection. Right: The contributions to the Mτ,τ spectrum whenthe “hardest candidate” method is used for the soft tau selection.

MethodSignalLikelihood
ClosestHardest150 ± 12175 ± 13186 ± 14SUSY
451 ± 211327 ± 36
1316 ± 36

BACKGROUNDtt
W
75 ± 1754 ± 54248 ± 27 161 ± 93
248 ± 27 161 ± 93

Z
19 ± 8122 ± 22122 ± 22√
S/ N
5.48 ± 0.57
3.88 ± 0.09
4.13 ± 0.10

Table 7.3: Comparison of the statistics remaining after all cuts for the signal andeach BG, and the level of the signal above the statistical fluctuation after all cuts andthe OS-SS subtraction, when using the soft tau likelihood selection method, the “closest
candidate” method and the “hardest candidate” method. Statistics are normalised to
63 fb−1 .

7.3

Analysis of a different coannihilation point

As another check of the robustness of this method it was applied to a coannihilation
region sample with slightly different parameters.

• m0 = 50GeV• m1/2 = 225GeV• tan β = 10

(7.5)

• A=0
• µ>0

Only m0 and m1/2 are reduced making it a lighter mass SUSY sample. It should be
noted that while this sample is in the coannihilation region, it is actually excluded by
the limit on the Higgs mass. The sample used corresponds to an integrated luminosityof 5.7fb−1 . The theoretical endpoint for this SUSY point is 58GeV.

Chapter 7. Systematic Studies, Discussion and Outlook

117

The left hand plot of Figure 7.3 shows the individual contributions to the M τ,τ spectrum
from the signal and various backgrounds. The right hand plot shows the fit using
Equation 6.1. The result isMτ,τ endpoint = 42 ± 11 GeV(stat)

(7.6)

70

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

50

−1

60

Events/5.4 /8GeV−1

Events/5.4 /8GeV

which is agreement with the theoretical value of 58GeV. The χ 2 /d.o.f. is 16.5/7.

40
30

60

40
30
20

10

10

0

0

−10
0

−10
0

40

60

80

100

120
Mτ,τ

16.53 / 7
0.02068−1.81± 0.37
75.17 ± 11.59

50

20

20

χ2 / ndf
Prob
p0
p1

70

Reconstructed
MC

20

40

60

80

100

120
Mτ,τ

Figure 7.3: Left: The contributions to the Mτ,τ spectrum from the lighter masspoint coannihilation signal, and each of the background processes. Right: The fit ofthis Mτ,τ spectrum, with the function of Equation 6.1.

7.4

Discussion of the form of the Mτ,τ spectrum fitting
function

As can be seen from the truth level Mτ,τ distribution in Figure 3.5 the functional formof the falling edge of the Mτ,τ spectrum is not exactly linear. A linear function is only
a first approximation of the shape. In fact the high end of the truth spectrum tails offvery slowly which makes the accurate determination of the endpoint very difficult, andan accurate estimation of the endpoint with a linear function virtually impossible. The
underestimation of the endpoint using the linear function is evidence that this high end
tail is not being accounted for in the linear fit.
In order to attempt to take account of the gradual high end tail of the spectrum it was
attempted to fit it with the following function

f (x) = C exp(x − x0 )22σ 2

+ (p0 x + p1 )(7.7)

Chapter 7. Systematic Studies, Discussion and Outlook

118

which is simply the sum of a gaussian and a linear function, with the linear function
forcing the gaussian to cross the x axis. Again the crossing of the x axis of this function
is to be identified with the Mτ,τ endpoint.
Figure 7.4 shows the result of this fit with the slope of the linear part of the function
constrained to be less than -0.3. It is interesting to see how the gaussian part of thefunction takes account of the Mτ,τ tail. Unfortunately the fit does not behave as desired
unless the slope of the linear part of the function is constrained to be less than zero(unless this slope is less than zero the function will not cross the x axis in the way thatis desired). The slope of the linear part of the fit always settles at the maximum allowed
slope. Thus this fitting procedure was not deemed to be robust, and the simple linear−1

Events/63fb /8GeV

function of Equation 6.1 was settled for.
χ2 / ndf
Prob
C
x0
σ
p
1
p0

80
70
60
50

3.778 / 2
0.151233.77 ± 11.73
23.79 ± 3.25
13.1 ± 5.2−0.3± 0.3
18.15 ± 11.35

40
30

Reconstructed

20

MC

10
0
−10
0

20

40

60

80

100

120
Mτ,τ

Figure 7.4: The fit of the final Mτ,τ distribution with a gaussian + linear function.

7.5

Outlook

Here we discuss two possible extensions to this study. The first is the use of a different
endpoint determination method. The second is the possible improvement from including
soft tau π 0 energy in the Mτ,τ distribution.

7.5.1

A new endpoint determination method

As discussed in the previous section the linear function that has been used to fit theedge of the Mτ,τ spectrum is only a first approximation and does not take account ofChapter 7. Systematic Studies, Discussion and Outlook

119

the gradual tail of the actual spectrum. In [21] the Mτ,τ spectrum is fit with a so-called“log-normal” function which is of the form


p0
1
2
f (x) =
exp − 2 (ln(x) − p1 )
x
2p2

(7.8)

The fit of the log-normal function to M τ,τ spectrum is shown in Figure 7.5. We cansee that the tail structure of the spectrum is much better described with this function
compared to the simple linear fit. This function does not explicitly contain the M τ,τ
endpoint but approaches the x axis asymptotically. Thus the endpoint must be found by
a calibration procedure where the correlation between the inflection point of the function

1
mIP = exp − p22
2

3−

s

4
1+ 2
p2

!

+ p1

!

(7.9)

and the theoretical endpoint is used.
This method then requires that samples for a number of different points in the coannihilation region are created, in order for the correlation to be determined. For the study
mentioned above, ATLFAST was used to create these samples. Unfortunately for thisstudy, more detailed calorimeter information is required (ESD level) and so the CPU
time necessary is rather large. It is planned that full simulation of some number ofpoints will be made, and a similar calibration procedure used to determine the endpoint−1

Events/63fb /8GeV

more accurately.
χ2 / ndf
Prob
p0
p1
p2

80
70
60

8.965 / 10
0.5354956 ± 149.8
2.971 ± 0.082
0.6991 ± 0.0563

50
40
30

Reconstructed

20

MC

10
0
−10
0

20

40

60

80

100

120
Mτ,τ

Figure 7.5: The fit of the final Mτ,τ distribution with a log-normal function.

Chapter 7. Systematic Studies, Discussion and Outlook

7.5.2

120

Including the signal soft tau π 0 information in the Mτ,τ distribution

For this study, the final Mτ,τ distribution was created using only the π ± componentof the signal soft tau. Thus any π 0 information is not included which will degrade theendpoint of the Mτ,τ distribution. There are a number of reasons why inclusion of π 0
information was found to be difficult. The first and most immediately obvious reason
is that the discrimination of π 0 clusters around the π ± track is very difficult, as canbe seen by the rather poor performance of the decay mode classification algorithm (seeTable 5.3). As mentioned previously, at these small energies the π ± energy tends to be
split amongst a number of small clusters in the calorimeter and a number of these look
like, and can be misidentified as, EM-like clusters. Also π 0 clusters often overlap π ±clusters, making their discrimination difficult. Thus a simple addition of π 0 clusters tothe π ± track will not be sufficient to correctly recover the π 0 energy.
Another approach is to use a method similar to the ones used in tauRec. The first
one that we consider is the tauRec track seed algorithm energy-flow method, which was
described in Section 4.2.7.2. This method attempts to subtract the π ± energy fromthe calorimeter, and then add the neutral calorimeter components to the track energy.
We saw in Figure 4.3 that, at low tau energies, there is the danger of double counting
and event contamination, which leads to an overestimation of the tau energy. This may
result in a systematic overestimation of the M τ,τ endpoint so care would have to betaken.
The second tauRec energy reconstruction method to consider is the calorimeter seedalgorithm method (again, refer Section 4.2.7.2). This simply adds the calorimeter energy
in a cone around some seed, and corrects it to the hadronic scale. Again we can see
from Figure 4.3 that at low energies the tau energy is overestimated, likely due to event
contamination. Thus we would again need to be careful not to end up with a systematic
overestimation of the Mτ,τ endpoint, especially since the soft tau is often very close to
the hard tau.
For reference Figure 7.6 shows the difference in the Mτ,τ distribution when the π 0 energy
is included in the calculation at the truth level. For this plot only the single prong modesof the signal soft tau are included, and a p T,track > 2.5GeV cut is applied to the π ±track. This cut means that the same bias towards lower multiplicity π 0 modes exists as
for this study (see Table 5.2). We can see that the quality of the endpoint is certainly
significantly improved if the π 0 information is included. Whether or not this information
can be correctly included at the reconstruction level is a matter for further study.

−1

Events/fb /GeV

Chapter 7. Systematic Studies, Discussion and Outlook

0.7

121

Visible0.6

Using only soft tau track

0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70

80

90

100
MMC
τ ,τ

Figure 7.6: The truth level Mτ,τ distribution for the case that only the signal soft
tau single prong modes are considered. The blue line shows the visible distribution.
The black line shows the distribution when only the π ± component of the signal soft
tau is used. A pT,track > 2.5GeV cut is imposed on the signal soft tau π ± .

Chapter 8

Conclusion
The LHC detector has recently come online and high energy collisions have been successfully achieved. It is expected that the coming years of LHC data will reveal extensions to
the SM of particle physics which are assumed necessary to explain a number its anomalies. One of the most promising theoretical extensions to the SM is supersymmetry, andin particular the mSUGRA model. The allowed phase space of this model is severely
constrained by a number of experimental measurements. One of the open regions of
the phase space is the so-called coannihilation region, which can explain the observed
density of dark matter in the universe. The masses of the LSP (χ̃ 01 ) and the NLSP (τ̃1 )are near degenerate in this region, which allows for their efficient coannihilation in theearly universe. Such coannihilation results in a density of the LSP which is consistent
with current dark matter density measurements.
In order to confirm the validity of the mSUGRA model and to check whether the coannihilation region is the region of the phase space which correctly describes the universe,
exclusive measurements of particular decay chains must be performed. The ATLAS detector at the LHC is expected to be able to perform such measurements, and in this thesis
we study its capability to measure the signal above the vast background using Monte
Carlo simulations. The signal which is studied arises from the so-called coannihilation
region “golden” decay chain:q̃ → q χ̃02 → qτ τ̃1 → qτ τ χ̃01

(8.1)

where in this study we focus on measuring the endpoint of the M τ,τ distribution. The
measurement of this endpoint, along with other invariant mass distribution endpoints
arising from this decay chain, allow for the calculation of the masses of the sparticles in
the chain.
123

Chapter 8. Conclusion

124Standard methods of reconstructing the M τ,τ endpoint require that each event has two
well reconstructed taus. Unfortunately for the coannihilation region the second tau ofthe decay chain is particularly soft due to the near degenerate mass of the χ̃ 01 and the τ̃1 .
As a result the standard ATLAS reconstruction algorithm does not reconstruct the softtau very efficiently due to its relatively high seed thresholds and stringent identification
requirements.
In light of this we have developed a new method for tagging this soft tau. We have
implemented a number of optimisations for reconstructing taus in the low energy region,and some novel analysis specific techniques. For example we exploit the separation of
the low-boost tau decay products in the calorimeter for identification, and take accountof the contamination from the other harder tau when calculating the soft tau likelihood
variables.
We have shown that this method has a better performance than the standard ATLAS
tau reconstruction algorithm for reconstructing the soft tau. We have also shown thatusing this method in conjunction with the ATLAS algorithm has a superior performancefor reconstructing the Mτ,τ endpoint of the decay chain, compared to using the ATLAS
algorithm for reconstructing both taus. We obtain a final result ofMτ,τ endpoint = 58 ± 16 (stat) ± 5 (sys) GeV(8.2)

at the ATLAS coannihilation reference point with E CM = 10TeV and an integrated
luminosity of 63 fb−1 .

Appendix A

Plots of tauRec discrimination
variables

!

$% $

"

#

&

'

,
()

*"

"

(

$

.

/

* &

+ "

&

*"

"

Figure A.1: The distributions of tauRec discrimination variables for the calorimeter
seeded algorithm for the process W → τ, ν, and for J2 background, as referred to in
section 4.2.7.3. Distributions for 1-prong and 3prong taus are shown separately. [22]125Appendix A. Plots of tauRec discrimination variables

! "

126

! "

! "

#

! "

$%"

&" '

! "

)
&"
$

#$ ( $

! "

*
'

+

$

*
! "

! "

)

$"

+$"

+ " $

! "

! "

#

! "

"( " - $

"$

,

! "

$-$

.$

Figure A.2: The distributions of tauRec discrimination variables for the track seededalgorithm for the process W → τ, ν, and for J2 background, as referred to in section
4.2.7.3. Distributions for 1-prong and 3prong taus are shown separately. [22]Appendix B

Plots of PDFs used for the soft
tau likelihood method
The plots in this appendix show the PDFs used for the soft tau likelihood method ofSection 5.2. They are divided by decay mode classification (single prong 0-π 0 , 1-π 0 , and
2-π 0 ), and then further divided by the seed track momentum range (2GeV < p track <5GeV, 5GeV < ptrack < 10GeV and ptrack > 10GeV).

127

Appendix B. Plots of PDFs used for the soft tau likelihood method
0.07
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128

−15

−10

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0

5

10
15
20
Impact parameter sig.

Figure B.1: The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track is in the range 2GeV < ptrack < 5GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method

0.08

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129

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Impact parameter sig.

Figure B.2: The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track is in the range 5GeV < ptrack < 10GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method

0.08

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Impact parameter sig.

Figure B.3: The PDFs used to form the soft tau algorithm likelihood, for the 0-π 0mode, when the seed track is in the range ptrack > 20GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method
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0.15
0.1

0.05

0.05
0

5

10

15

0
0

20
25
30
Number strip layer hits

0.09
0.08

1.5

2

2.5

3

3.5

4
Mπ±, π0SignalBackground

0.2

0.06

0.15

0.05
0.04

0.1

0.03
0.02

0.05

0.01
0.1

0.2

0.3

0.4

1

0.5

0.6

SignalBackground

0.8
0.6
0.4
0.2
0

5

10

0
0

0.7
∆Rπ±, π01520
N_TRACK_02_04

0.5

1

1.5

2

2.5

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−20

3

3.5
4
∆Rπ±, closest track

SignalBackground

A.U.

0
0

A.U.

1

0.25

0.07

0

0.5

A.U.

SignalBackground

A.U.

0

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.4: The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track is in the range 2GeV < ptrack < 5GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method
0.08

A.U.

0.07

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02
0.01

0.01
0.05

0.1

0.15

0.2

0.25

0.3

0.35

REM

SignalBackground

0.1

0
0

0.4

0.05

0.1

0.15

0.2

0.25

0.3

0.35

;
A.U.

A.U.

0
0

0.4
∆η

SignalBackground

0.5
0.4

0.08

0.3

0.06
0.04

0.2

0.02

0.1

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.16

0.7

0.8

0.9

A.U.

A.U.

0
0

1
I

SignalBackground

0.14
0.12

1

2

3

4
5
HADoverEM
SignalBackground

0.5
0.4

0.1

0.3

0.08
0.06

0.2

0.04

0.1

0.02
0
0

2

4

6

8

10

12

14

16

2

4

6

8

0.18

SignalBackground

0.5

0
0

18
20
ET,EM/PT

10
ET,HAD/PT

SignalBackground

A.U.

A.U.

SignalBackgroundA.U.

SignalBackground

0.08

132

0.16
0.14

0.4

0.12
0.3

0.1
0.08

0.2

0.06
0.04

0.1

0.02
0

5

10

15

0
0

20
25
30
Number strip layer hits
SignalBackground

0.08

1.5

2

2.5

3

3.5

4
Mπ±, π0SignalBackground

0.2

0.06

0.15

0.05
0.04

0.1

0.03
0.02

0.05

0.01
0.1

0.2

0.3

0.4

0.5

0.6

SignalBackground

1
0.8
0.6
0.4
0.2
0

5

10

0
0

0.7
∆Rπ±, π01520
N_TRACK_02_04

0.5

1

1.5

2

2.5

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−20

3

3.5
4
∆Rπ±, closest track

SignalBackground

A.U.

0
0

A.U.

1

0.25

0.07

0

0.5

A.U.

A.U.

0

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.5: The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track is in the range 5GeV < ptrack < 10GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method
0.08

0.08
0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0
0

0.05

0.1

0.15

0.2

0.25

0.12

0.3

0.35

REM

0.08

0.6

0.25

0.3

0.35

0.4
∆η

SignalBackground

0.4
0.3
0.2

0.02

0.1

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SignalBackground

0.2

0.18

0
0

1
I
A.U.

A.U.

0.2

0.5

0.04

1

2

3

4
5
HADoverEM
SignalBackground

0.9
0.8

0.16

0.7

0.14

0.6

0.12

0.5

0.1

0.4

0.08

0.3

0.06

0.2

0.04

0.1

0.02
0
0

2

4

6

8

10

12

14

16

2

4

6

8

0.18
0.16

0.5

10
ET,HAD/PT

SignalBackgroundA.U.

SignalBackground

0.6

0
0

18
20
ET,EM/PT

0.14
0.12

0.4

0.1

0.3

0.08
0.06

0.2

0.04

0.1

0.02
0

5

10

15

0
0

20
25
30
Number strip layer hits
A.U.

A.U.

SignalBackground

0.12

0.5

1

1.5

2

2.5

0.2

3

3.5

4
Mπ±, π0SignalBackground

0.18
0.16

0.1

0.14
0.12

0.08

0.1

0.06

0.08
0.06

0.04

0.04

0.02

0.02

0
0

0.1

0.2

0.3

0.4

0.5

0.6

∆Rπ±, π0SignalBackground

1
0.8
0.6
0.4
0.2
0

5

10

0
0

0.7

15
20
N_TRACK_02_04

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−20

0.5

1

1.5

2

2.5

3

3.5
4
∆Rπ±, closest track

SignalBackground

A.U.

A.U.

0.15

0.7

0.06

A.U.

0.1

0.9
0.8

0

0.05

;
A.U.

SignalBackground

A.U.

0
0

0.4

0.1

0

SignalBackground

A.U.

A.U.

SignalBackground

0.07

133

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.6: The PDFs used to form the soft tau algorithm likelihood, for the 1-π 0mode, when the seed track is in the range ptrack > 20GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method

0.12
0.1
0.08

0.18

0.1

0.16

0.08

0.14

0.04

0.04

0.02

0.02
0.1

0.15

0.2

0.25

0.3

0.35

0.4
REM

SignalBackground

0.4

0
0

0.1
0.08
0.06
0.05

0.1

0.15

0.2

0.25

0.3

0.35

;
0.3

0.4
∆η

SignalBackground

0

0.3
0.2
0.1

1

2

3

0.1

0.15

0
0

4
5
HADoverEM

2

4

6

8

10

12

14

16

SignalBackground

0.1
0.08
0.06
0.04
0.02
0
0

0.02
5

10

15

0
0

20
25
30
Number strip layer hits

0.14

1

1.5

2

2.5

3

3.5
4
Mπ± , π01, π02

SignalBackground

A.U.

A.U.

SignalBackground

0.16

0.5

0.16

A.U.

0

0.14

0.12

0.08

0.3

0.06

0.06

0.04

0.2

0.04

0.02

0.02

0
0

0
0

0.5

0.6

0.7
∆Rπ± , π02

1

0.1

0.2

SignalBackground

0.8
0.6
0.4
0.2
0

0

5

10

SignalBackground

0.1

0.2

0.3

0.4

0.5

0.6

0.7
∆Rπ± , π01

SignalBackground

0.1

15
20
N_TRACK_02_04

0.3

0.4

0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−20

0.5

0.6

0
0

0.7
∆Rπ01, π02

0.5

1

1.5

2

2.5

3
3.5
4
∆Rπ± , closest track

SignalBackground

A.U.

A.U.

0.4

10
ET,HAD/PT

0.4

0.1

0.08

0.3

8

0.5

0.12

0.2

6

0.6

0.1

0.1

1
I

0.16
0.14
0.12

0.04

0.05

4

0.2
0.18

0.06

0.1

2

0.22

0.1

0.15

0.9

SignalBackground

0
0

18 20
ET,EM/PT

0.08

0.2

0.8

0.1

0.12

0.3

0.7

0.05

0.14

0.25

0.6

0.2

A.U.

SignalBackground

0.4

0.35

0.5

A.U.

0
0

0.4

0.3
0.25

0.05

0.05

0.3

0.35

0.15

0.15

0.2

0.4

0.2

0.25

0.1

0.45

0.25

0.35

A.U.

0.12

A.U.

0.05

A.U.

A.U.

0
0

SignalBackground

0.2

0.12

0.06

0.06

0

A.U.

0.14

0.14

0.22

SignalBackground

A.U.

A.U.

SignalBackground

0.16

134

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.7: The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track is in the range 2GeV < ptrack < 5GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method

0.14
0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02
0.05

0.1

0.15

0.2

0.25

0.5

0.3

0.35

0
0

0.4

REM

A.U.

SignalBackground

0.05

0.1

0.15

0.2

0.25

0.3

0.35

;

0.4

0.4
∆η

SignalBackground

0.3

0

A.U.

0
0

A.U.

0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02

SignalBackground

A.U.

A.U.

SignalBackground

0.12

0.4

0.2

0.3

0.15

0.2

2

3

0.45

6

8

10

12

14

16

0.08

0.2

0.06

0.15

10

15

20
25
30
Number strip layer hits

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0
0

0
0

0.2

0.3

0.4

A.U.

0.1

0.5

0.6

0.7
∆Rπ± , π02

1

1

1.5

2

2.5

3

0
0

3.5
4
Mπ± , π01, π02

SignalBackground

10
ET,HAD/PT

SignalBackground

0.1

0.2

0.3

0.4

0.5

0.5

0.6

0.7
∆Rπ± , π01

SignalBackground

0.4
0.3
0.2
0.1
0.1

0.2

0.4
0.2
10

8

0.02
0.5

0.6

5

6

0.04

SignalBackground

0

4

0.06

0.8

0

1
I

0.1

0.16

0.14

0.9

0.08

A.U.

A.U.

SignalBackground

0.16

0.8

0.12

A.U.

5

2

0.2

15
20
N_TRACK_02_04

0.3

0.4

0.5

0.6

0
0

0.7
∆Rπ01, π02

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
−20

0.5

1

1.5

2

2.5

3
3.5
4
∆Rπ± , closest track

SignalBackground

A.U.

0

0.7

0.14

0.02
0
0

0.6

0.16

0.04

0.1
0.05

0.5

0.18

0.1

0.3
0.25

0.4

SignalBackground

0
0

18 20
ET,EM/PT

SignalBackground

0.12

0.35

0

4

0.14

SignalBackground

0.4

2

A.U.

A.U.

0
0

4
5
HADoverEM

A.U.

1

0.3

0.1

0.05

0
0

0.2

0.2

0.1
0.1

0.1

0.5

0.25

0.3

SignalBackground

A.U.

0.14

135

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.8: The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track is in the range 5GeV < ptrack < 10GeV.

Appendix B. Plots of PDFs used for the soft tau likelihood method

0.16

0.16

0.12

0.12

0.1

0.1

0.2
0.15

0.06

0.06

0.1

0.04

0.04

0.05

0.02

0.02
0.05

0.1

0.15

0.2

0.25

0.3

0.35

REM

0.05

0.1

0.15

0.2

0.25

0.3

0.35

;
0.45

0
0

0.4
∆η

SignalBackgroundA.U.

SignalBackground

0.9

0
0

0.4

A.U.

0
0

0.4

0.7

0.35

0.6

0.3

0.5

0.25

0.4

0.2

0.4

0.3

0.15

0.3

0.2

0.1

0.2

0.1

0.05
1

2

3

0
0

4
5
HADoverEM
SignalBackground

0.6

4

6

8

10

12

14

16

SignalBackground

10

15

0
0

20
25
30
Number strip layer hits
A.U.

SignalBackground

0.25

1

1.5

2

2.5

0.2

3

0
0

3.5
4
Mπ± , π01, π02

SignalBackground

0.3

0.12

0.25

0.4

0.5

0.6

0
0

0.7
∆Rπ± , π02

0.4

0.5

0.6

0.7
∆Rπ± , π01

SignalBackground

0.1

0.1

0.2

0.8
0.7
0.6

0.3

0.4

0.5

0.6

0
0

0.7
∆Rπ01, π02

0.5

1

1.5

2

2.5

3
3.5
4
∆Rπ± , closest track

SignalBackground

0.22
0.2
0.18
0.16
0.14
0.12

0.5
0.4
0.3
0.2
0.1
0

0.3

0.05

SignalBackground

0.9

0.2

0.2

A.U.

0.3

0.1

0.15

0.02
0.2

10
ET,HAD/PT

SignalBackground

0.4

0.14

0.04

0.1

8

0.35

0.1

A.U.

0
0

0.5

0.06

0.05

6

0.1

0.08

0.1

4

0.05

0.16

0.2

0

5

10

1
I

0.2

0.18

0.15

0.9

0.15

A.U.

5

2

0.25

0.02
0

0.8

SignalBackground

0
0

18 20
ET,EM/PT

0.04

A.U.

0

0.7

0.1
2

0.06

0.1

0.6

0.5

0.1

0.2

0.5

0.6

0.08

0.3

0.4

0.7

0.12

0.4

0.3

0.8

0.14

0.5

0.2

A.U.

0
0

0.1

0.9

0.8

A.U.

A.U.

0.25

0.08

0.08

SignalBackground

A.U.

0.14

0.14

A.U.

SignalBackground

A.U.

A.U.

SignalBackground

0.18

136

15
20
N_TRACK_02_04

0.1
0.08
0.06
0.04
0.02
0
−20

−15

−10

−5

0

5

10
15
20
Impact parameter sig.

Figure B.9: The PDFs used to form the soft tau algorithm likelihood, for the 2-π 0mode, when the seed track is in the range ptrack > 20GeV.

Appendix C

Systematic study plots

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

Events/63fb /8GeV−1

Events/63fb /8GeV

The plots of this appendix relate to the systematic studies of Chapter 7.
χ2 / ndf
Prob
p0
p1

80
70
60

9.756 / 7
0.2028−1.342± 0.297
76.73 ± 12.72

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

−1

80
60

χ2 / ndf
Prob
p0
p1

100

−1

SU1 signal
All backgrounds
SU1 BGtT
W
Z

100

Events/63fb /8GeV

Events/63fb /8GeV

Figure C.1: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the fake rate for the signal hard tau selection isincreased as described in Section 7.1.2. Right: The linear fit of the Mτ,τ distribution.
3.951 / 7
0.7854−1.717± 0.352
92.76 ± 15.66

80
60

40

40

20

20

Reconstructed
MC

0
0

0
20

40

60

80

100

120
Mτ,τ

0

20

40

60

80

100

120
Mτ,τ

Figure C.2: Left: The contributions to the Mτ,τ spectrum from the signal and each of
the background processes when the fake rate for the signal soft tau selection is increased
as described in Section 7.1.2. Right: The linear fit of the Mτ,τ distribution.

137

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

138

Events/63fb /8GeV−1

Events/63fb /8GeV

Appendix C. Systematic study plots

χ2 / ndf
Prob
p0
p1

80
70
60

4.131 / 7
0.7645−1.273± 0.261
71.46 ± 11.53

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

Events/63fb /8GeV−1

Events/63fb /8GeV

Figure C.3: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the tau energy scale is decreased as described in
Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

χ2 / ndf
Prob
p0
p1

80
70
60

7.988 / 7
0.3336−1.236± 0.272
71.44 ± 11.71

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

Events/63fb /8GeV−1

Events/63fb /8GeV

Figure C.4: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the tau energy scale is increased as described in
Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

χ2 / ndf
Prob
p0
p1

80
70
60

6.597 / 7
0.472
−1.266± 0.267
72.04 ± 11.66

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

Figure C.5: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the tau energy resolution is decreased as describedin Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

139

Events/63fb /8GeV−1

Events/63fb /8GeV

Appendix C. Systematic study plots

χ2 / ndf
5.176 / 7
Prob0.6385p0−0.9726 ± 0.1720
p1
60.04 ± 9.14

80
70
60
50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

Events/63fb /8GeV−1

Events/63fb /8GeV

Figure C.6: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the jet energy scale is decreased as described in
Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

χ2 / ndf
Prob
p0
p1

80
70
60

2.801 / 7
0.9028−1.276± 0.282
73.38 ± 12.22

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

SU1 signal
All backgrounds
SU1 BG
tT
W
Z

70
60
50
40
30

−1

80

Events/63fb /8GeV−1

Events/63fb /8GeV

Figure C.7: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the jet energy scale is increased as described in
Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

χ2 / ndf
Prob
p0
p1

80
70
60

6.734 / 7
0.4571−1.269± 0.273
71.91 ± 11.75

50
40
30

Reconstructed

20

20

MC

10

10

0

0

−10
0

−10
0

20

40

60

80

100

120
Mτ,τ

20

40

60

80

100

120
Mτ,τ

Figure C.8: Left: The contributions to the Mτ,τ spectrum from the signal and eachof the background processes when the jet energy resolution is decreased as described in
Section 7.1.3. Right: The linear fit of the Mτ,τ distribution.

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