studies of r-parity violating supersymmetry with the atlas...

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Studies of R-parity violatingsupersymmetry with the ATLAS

detector

Alan Wyn Phillips

ofEmmanuel College

A dissertation submitted to the University of Cambridge

for the degree of Doctor of Philosophy

September 2008

i

Studies of R-parity violating supersymmetry with the

ATLAS detector

Alan Wyn Phillips

Abstract

This thesis investigates signatures of R-parity violating (RPV) supersymmetry (SUSY)

in the context of the ATLAS detector at the LHC. SUSY models in which R-parity

is violated through the lepton-number violating λ′221 coupling are studied, focusing on

two cases; in the first case the lightest supersymmetric particle (LSP) is a χ01, and in

the second case the LSP is a τ1. Monte Carlo studies using the full ATLAS detector

simulation are shown. It is predicted that RPV SUSY models with a τ1 LSP will often

be characterised by a high τ -lepton multiplicity in SUSY events. This thesis presents

an investigation into the expected τ -reconstruction performance in such models using

simulated ATLAS data. The impact of the event topology associated with a non-zero

λ′221 coupling on the τ -reconstruction performance is discussed. The measurement of

the χ01 mass is demonstrated for models with a χ0

1 LSP and non-zero λ′221 coupling. An

exclusive method focusing on the reconstruction of χ01 → µqq decays is demonstrated,

using a data-driven method for estimating the combinatoric background. The extension

of these methods to the case of a τ1 LSP with τ1 → µqqτ decays is also discussed.

In addition, this thesis presents work involving aspects of both the experimental hard-

ware and simulation software that are essential to physics analysis in ATLAS. Firstly,

results from the analysis of some of the initial DAQ test data taken during the macro-

assembly phase of the Semiconductor Tracker are shown. Secondly, the development of

software tools for the fast simulation of τ -reconstruction algorithms is described. Here,

performance studies of the track-based τ -reconstruction algorithm (tau1p3p) are pre-

sented with the results incorporated into the ATLFAST fast simulation package.

ii

Declaration

This dissertation is the result of my own work, except where explicit reference is made

to the work of others, and has not been submitted for another qualification to this or

any other university. This dissertation does not exceed the word limit for the respective

Degree Committee.

Alan Wyn Phillips

iii

Acknowledgements

In providing the financial support that has enabled me to undertake this degree, I would

like to thank both the University of Cambridge and PPARC/STFC for the award of

a Millennium Scholarship (2004–2006), and a PPARC/STFC Studentship (2006–2008).

I am also very grateful to Emmanuel College for providing the additional travel funds

that enabled me to attend an overseas summer school.

I take this opportunity to thank my supervisors who have guided me through my time as

a PhD student: Andy Parker, for both his expert advice on all aspects of physics analysis,

and for his calming influence and confidence-building discussions; and Janet Carter, for

her help and advice relating to my work involving the ATLAS Semiconductor Tracker.

I would also like to thank the members of both the Cambridge Supersymmetry Working

Group and the Cambridge ATLAS Group, especially Bryan Webber, Ben Allanach,

Frederic Brochu and Christopher Lester.

For much of the analysis presented here I have made use of software tools and simulated

data samples that are the result of collaboration-wide effort within ATLAS. In addition,

I would like to thank Peter Richardson for providing the Monte Carlo tools for the RPV

study. I would also like to offer my thanks to the members of the ATLAS Tau Working-

Group and the ATLFAST task-force for their guidance on aspects of τ -reconstruction and

fast simulation. In particular, I would like to mention Elzbieta Richter-Was for her help

with the subtleties of τ -reconstruction algorithms and suggestions about approaches to

fast simulation; and Simon Dean for his help in implementing my code into ATLFAST. I

would like to thank everyone involved in the SCT barrel macro-assembly for introducing

me to the inner workings of the SCT and for their good company during long shifts.

The Cavendish HEP Group has provided a fun and friendly environment to work in,

and I wish to thank all my colleagues for making it so, with particular mention going to

Jeremy Dickens, Martin White and John Chapman. A special word of thanks goes to

Stephen Duffield, Alan Elder and Hannah Turner-Stokes for their good friendship and

for ensuring that my PhD years were also an experience outside the lab. Last but not

least, I’d like to thank my parents: Ken and Irene, and my sisters: Anna, Helen and

Ruth, for all their support.

iv

Preface

This thesis is the culmination of work carried out at the Cavendish Laboratory, Cam-

bridge, between October 2004 and September 2008. It serves as documentation of the

various studies I have performed during this time, centred around the ATLAS detector

and the Large Hadron Collider (LHC) at CERN in Geneva. As I write this preface,

the superconducting magnets of the LHC have been cooled to 1.9 K and final prepara-

tions for the circulation of the first proton beams around the collider are being made.

Meanwhile, the ATLAS detector has been commissioned and is prepared to make mea-

surements of the first collisions delivered by the LHC, marking the start of a data-taking

period that will explore new frontiers of particle physics over the next decade.

The work presented in this thesis was carried out in preparation for the LHC start-

up and the operation of ATLAS. The content can be roughly divided into three main

sections involving separate (i) hardware, (ii) software and (iii) physics-analysis tasks.

After a brief theoretical motivation and an introduction to the details of the ATLAS

detector, chapter 3 details work relating to the macro-assembly phase of the ATLAS

Semiconductor Tracker (SCT). This phase involved the precision mounting of modules

onto the SCT barrel support-structures. In contributing to this effort, I participated in

the running of data acquisition (DAQ) shifts during the mounting process, and also in

the offline analysis of some of the initial DAQ test-data taken with the completed barrels

(the analysis of which is presented in this thesis).

Chapters 4, 5 and 6 proceed to discuss the reconstruction of hadronic τ -decays in ATLAS,

in particular focusing on work I performed in developing specialised fast simulation

tools to describe the performance of the tau1p3p τ -reconstruction algorithm. After an

introduction to both the principles behind τ -reconstruction in ATLAS and the details of

ATLAS’s fast simulation tools, two approaches towards implementing parametrizations

of the tau1p3p performance into the ATLFAST fast simulation package are discussed.

The final section of this thesis (chapter 7) details the development of analysis methods

designed to identify the characteristic features of R-parity-violating (RPV) Supersym-

metry (SUSY) models using simulated ATLAS data. If, as is widely predicted, nature

has provided a source of new physics, beyond that described by the Standard Model, at

v

energy scales accessible with the LHC, it is important that analysis methods are pre-

pared in order to exploit the data as it is recorded by ATLAS. One such extension to

the Standard Model is SUSY, a theory predicting the existence of a collection of new

particles that differ from their Standard Model counterparts in the value of their spin.

R-parity is a proposed symmetry relating the particles of the Standard Model to those of

SUSY. This thesis investigates SUSY models in which R-parity is violated and discusses

the different experimental signatures possible in cases where the lightest SUSY particle

(LSP) is either a χ01 or a τ1 (a less commonly studied scenario).

The identification of τ -leptons (or more specifically, the hadronic decays of τ -leptons)

in ATLAS is particularly relevant to SUSY models with a τ1 LSP. In many of these

models, SUSY events can be expected to contain a large τ -multiplicity. This raises the

possibility of an inclusive signature, based on the observation of a high τ -multiplicity,

being used to indicate the presence of a τ1 LSP. However, in order to exploit such a

signature in ATLAS, a good τ -reconstruction performance is essential. Using simula-

tions of the ATLAS detector, the τ -reconstruction performance in RPV SUSY events

is investigated. Considering the possibility of more exclusive signatures, this thesis also

discusses methods for reconstructing the mass of a χ01 LSP through χ0

1 → µqq decays.

Methods for reducing and modelling the combinatoric backgrounds are shown along with

an event selection procedure for rejecting Standard Model backgrounds. The extension

of these methods to models with a τ1 LSP are discussed, focusing on τ1 → µqqτ decays.

Contents

1 Physics Motivation 1

1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Mass in the SM and the Higgs Mechanism . . . . . . . . . . . . . 4

1.2 The τ -lepton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Limitations of the Standard Model . . . . . . . . . . . . . . . . . . . . . 6

1.4 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4.1 The Minimal Supersymmetric Standard Model (MSSM) . . . . . . 11

1.4.2 SUSY-breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.3 R-Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 The ATLAS experiment 19

2.1 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.1 Solenoid Magnet System . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.2 Pixel Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.3 Semiconductor Tracker (SCT) . . . . . . . . . . . . . . . . . . . . 26

2.3.4 Transition Radiation Tracker . . . . . . . . . . . . . . . . . . . . 27

vi

Contents vii

2.3.5 Anticipated Tracking Performance . . . . . . . . . . . . . . . . . . 28

2.4 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Electromagnetic Calorimeter (ECAL) . . . . . . . . . . . . . . . . 31

2.4.2 Hadronic Calorimeter (HCAL) . . . . . . . . . . . . . . . . . . . . 31

2.4.3 Anticipated Calorimeter Performance . . . . . . . . . . . . . . . . 34

2.5 Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5.1 Anticipated Muon Performance . . . . . . . . . . . . . . . . . . . 37

2.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 SCT Assembly Testing 39

3.1 Semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 SCT barrel module design . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Macro-Assembly and DAQ Testing . . . . . . . . . . . . . . . . . . . . . 48

3.5 Initial SynchTriggerNoise Analysis . . . . . . . . . . . . . . . . . . . . . . 50

3.5.1 Barrel 3 SynchTriggerNoise Analysis . . . . . . . . . . . . . . . . 51

3.5.2 Barrel 6 SynchTriggerNoise Analysis . . . . . . . . . . . . . . . . 58

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Tau reconstruction and fast simulation in ATLAS 65

4.1 ATLAS Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.1.1 Monte Carlo Generators and Event Simulation . . . . . . . . . . . 65

4.1.2 Reconstruction Algorithms . . . . . . . . . . . . . . . . . . . . . . 67

4.2 Tau Reconstruction Algorithms . . . . . . . . . . . . . . . . . . . . . . . 67

4.2.1 A calorimeter-seeded algorithm (taurec) . . . . . . . . . . . . . . 68

4.2.2 A track-seeded algorithm (tau1p3p) . . . . . . . . . . . . . . . . . 70

Contents viii

4.2.3 Further developments of the τ -reconstruction algorithms . . . . . 73

4.3 Fast Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5 A tau1p3p τ -tagging parametrization for ATLFAST 77

5.1 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2 The labelling and tagging of hadronic τ -decays in ATLFAST . . . . . . . 78

5.3 Parametrization Development . . . . . . . . . . . . . . . . . . . . . . . . 80

5.3.1 The tau1p3p energy scale for true and fake τ -jets . . . . . . . . . 80

5.3.2 Z → ττ analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.3 QCD dijet analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.3.4 Parametrization of performance . . . . . . . . . . . . . . . . . . . 91

5.4 Consistency checks with the Full Simulation . . . . . . . . . . . . . . . . 92

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6 A track-based approach to tau1p3p fast simulation 101

6.1 The Advantages of a Track-Based Approach to Fast Simulation . . . . . 101

6.2 Track Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.3 Reconstruction of candidate τ -jets . . . . . . . . . . . . . . . . . . . . . . 105

6.4 Energy and momentum resolution studies . . . . . . . . . . . . . . . . . . 109

6.5 Reconstruction Performance . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.6 Identification Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7 Studies of RPV SUSY models 133

7.1 RPV SUSY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 RPV signatures at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . 135

Contents ix

7.2.1 Example points in RPV mSUGRA parameter space . . . . . . . 140

7.3 Simulation, Ntuple Production and Particle ID . . . . . . . . . . . . . . . 147

7.4 Tau reconstruction in RPV SUSY events . . . . . . . . . . . . . . . . . . 150

7.5 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

7.5.1 Cut I — ΣET Selection . . . . . . . . . . . . . . . . . . . . . . . . 164

7.5.2 Cut II — Muon Selection . . . . . . . . . . . . . . . . . . . . . . 166

7.5.3 Cut III — Z-Veto . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

7.5.4 Cut IV — W-Veto . . . . . . . . . . . . . . . . . . . . . . . . . . 170

7.5.5 Cut V — Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . 172

7.5.6 Event selection performance and background rejection . . . . . . . 173

7.6 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

7.7 Measuring the χ01 LSP mass in point AP2 . . . . . . . . . . . . . . . . . 182

7.7.1 Mass combinations . . . . . . . . . . . . . . . . . . . . . . . . . . 182

7.7.2 Combinatoric background estimation . . . . . . . . . . . . . . . . 183

7.7.3 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.8 Discovery Reach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.9 Measuring the τ1 LSP mass in point AP1 . . . . . . . . . . . . . . . . . 191

7.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

8 Summary 197

A Mass spectra for RPV points AP1 and AP2 199

B Statistical Analysis 203

B.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

B.2 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Contents x

B.2.1 Case I (n1 = 0, L1 = 1.0) . . . . . . . . . . . . . . . . . . . . . . . 207

B.2.2 Case II (n1 = 0, L1 = 1.0 and n2 = 0, L2 = 1.0) . . . . . . . . . . 207

B.2.3 Case III (n1 = 10, L1 = 10.0 and n2 = 10, L2 = 10.0) . . . . . . . 207

B.3 Combined Standard Model Background . . . . . . . . . . . . . . . . . . . 209

Colophon 211

Bibliography 213

List of Figures 221

List of Tables 227

Chapter 1

Physics Motivation

1.1 The Standard Model

1.1.1 Overview

Of the electromagnetic, weak, strong and gravitational fundamental forces, the Standard

Model (SM) has proved a highly successful theory in describing the first three (although

it does not yet incorporate gravity). In describing these three fundamental forces, the

electromagnetic and weak forces are described in a unified “electro-weak theory”, with

the strong force described by the theory of quantum chromodynamics (QCD). The union

of these theories make up the SM. Each of the incorporated forces is described by a gauge

theory, a theory that demands invariance under some set of local transformations1.

The SM attempts to explain the observed particle physics phenomena in terms of the

interactions and properties for a small group of elementary particles. The elementary

particle content of the SM can be divided into two types; the matter particles, and

the force-carrying particles that mediate the action of the fundamental forces. The

matter particles are spin-12

fermions, and are naturally separated into quarks and leptons

according to their interaction with the strong force. Quarks carry colour charge (the

conserved charge of QCD), where leptons carry no colour charge. Of the leptons, three

carry electromagnetic charge, and three are electrically neutral (the neutrinos). Unlike

the matter particles, the force particles of the SM are elementary spin-1 (vector) bosons.

1[1] gives a general introduction to gauge field theories and the SM.

1

Physics Motivation 2

As an example of how the interactions between matter and force particles can be

described using gauge field theories, one can consider the case of the electromagnetic

force between two charged particles (e.g. electrons). In such an interaction, one electron

emits a photon (the spin-1 force-carrying particle of the electromagnetic force) and re-

coils. The second electron then absorbs the photon, changing its motion. In the gauge

theory description the electromagnetic interaction arises through the requirement that

the Lagrangian is invariant under the action of a local gauge transformation on the

fermion field, ψ(x). Here the term “local” means that the parameter of the transfor-

mation, ω(x), is dependent on the space-time point x, with the transformation taking

the form ψ(x) → eiω(x)ψ(x). Such a transformation is termed a U(1) symmetry and is

the basis for quantum electrodynamics (QED). The local gauge invariance of the theory

requires the introduction of a new field describing a massless, spin-1 boson which, in the

case of QED, describes the photon.

In the SM, the electromagnetic and weak forces are described by a unified electro-

weak theory. In this theory invariance under the combined SU(2)L and U(1)Y groups of

transformations is required. The U(1)Y group described here is not the U(1) group of

QED as described above, instead it is known as the hypercharge gauge group (its relation

to electromagnetism will be described later). Invariance under this U(1)Y symmetry

results in the introduction of a massless vector boson field, denoted here by Bµ. The

charge associated with this symmetry is the weak hypercharge, Y .

A fermion field, ψ can be expressed as the sum of a left-handed component, ψL,

and a right-handed component, ψR, such that ψ = ψL + ψR. These are defined as the

chirality states of a fermion. For massless fermions these chiral states become equivalent

to helicity states (a physical observable that is the projection of the fermion’s spin onto

its direction of motion). The weak interactions are known to violate parity (that is they

give different interactions to the left-handed and right-handed components of the fermion

fields). The observed characteristics of the weak force indicate that it can be described

by requiring invariance of the Lagrangian under the group of SU(2) transformations (it

displays an SU(2) symmetry). Here the analogue of the QED electric charge is “weak

isospin”, whose conserved charge is I3, the third component of the weak isospin. This is

non-zero only for the left-handed fermions in the SM. Left-handed fermions form electro-

weak doublets, where right-handed fermions form electro-weak singlets, meaning that

only left handed fermions undergo weak interactions. In order to maintain invariance

under SU(2) transformations, the introduction of three massless gauge bosons is needed,

denoted here by W iµ (where i = 1, 2, 3). Two of these boson fields mix to form two


charged bosons

W ±µ =

(W 1

µ ∓ iW 2µ

)/√

2. (1.1)

The remaining W 3µ boson field mixes with the Bµ field (originating from the U(1)Y

invariance) to form the Zµ boson field and the photon (Aµ) boson field:

Zµ = cos θwW3µ − sin θwBµ, (1.2)

Aµ = sin θwW3µ + cos θwBµ (1.3)

where θw is the weak mixing angle describing the mixing between the Aµ and Zµ fields.

The emergence of these four boson fields is reassuring as they resemble the four electro-

weak vector bosons of the Standard Model. However, with the mechanism described

so far, these bosons are restricted to being massless and are therefore inconsistent with

the measured masses of the W± and Z bosons. The overall electro-weak symmetry can

be described by the combined SU(2)L×U(1)Y symmetry group (where the L subscript

indicates that that the weak isospin couples only to left handed particles). After spon-

taneous symmetry breaking (described below), the remaining U(1) symmetry is that of

QED, with a conserved electric charge, Q, given by

Q = Y + I3. (1.4)

The non-Abelian2 nature of the SU(2) group gives rise to the possibility of interactions

between the associated vector bosons (not possible in the case of the Abelian QED U(1)

symmetry).

The requirement of invariance under a third symmetry forms the basis of QCD. Here

the Lagrangian is required to be invariant under the transformations that form the SU(3)

group. This results in the introduction of eight gauge bosons, known as “gluons” (g)

and three conserved “colour” charges (termed “red”, “green” and “blue”). As previously

mentioned, quarks are the only fermions to carry colour charge. Unlike the photon of

QED, the gluons carry colour charge and can undergo self-interactions. Considering both

the electro-weak and QCD theories, the overall symmetry group of the SM is constructed

to be SU(3)× SU(2)L×U(1)Y .

The fermionic content of the SM is summarised in table 1.1. The electromagnetic,

2A group of transformations in which the transformations do not commute with each other is de-scribed as “non-Abelian”.


weak and strong charges for each particle are shown. The lightest generation (e, νe,

u and d) make up the “normal” matter that is observed in the universe. In addition

to this, the SM includes a further two, heavier generations which are similar but exist

at higher mass scales. The SM, as described above, does not incorporate right-handed

neutrinos. This is consistent for the case where the neutrinos are massless, but neutrinos

are now known to have very small masses. These could be described in the above model

by adding a right-handed gauge singlet (with no strong, weak or electric charge).

Families Colour Isospin I3 Y Q = I3 + Y

Leptons

(νe

e

)L

(νµ

µ

)L

(ντ

τ

)L

1 12

+12 −1

2

0

−12

−1

eR µR τR 1 0 0 −1 −1

Quarks

(u

d

)L

(c

s

)L

(t

b

)L

3 12

+12 +1

6

+23

−12

−13

uR cR tR 3 0 0 +23

+23

dR sR bR 3 0 0 −13

−13

Table 1.1: The fermionic particle content of the Standard Model. Also shown are thegauge quantum numbers for the different particles, where I3 is the third component ofthe weak isospin, Y is the hypercharge, and Q is the electric charge.

1.1.2 Mass in the SM and the Higgs Mechanism

One aspect of the SM that this discussion has yet to address is the origin of the masses of

the constituent particles. In particular, the mechanism by which the W± and Z bosons

become massive has yet to be explained. The answer lies in a process of spontaneous

symmetry breaking known as the Higgs mechanism [2]. This involves the introduction

of a complex scalar field, φ, and its conjugate, that form the SU(2) doublets

φ =

φ+

φ0

and φ =

φ0

φ−

, (1.5)

with four degrees of freedom. This is the Higgs field.


For an associated potential of the form

V (φ, φ) = µ2φφ+ λ(φφ)2 (

µ2 < 0), (1.6)

a degenerate minimum exists, allowing infinitely many choices of the vacuum state.

Spontaneous symmetry breaking (the spontaneous choice of a true vacuum state from

this degenerate minimum) leaves a true minimum with a non-zero vacuum expectation

value, breaking the SU(2)L×U(1)Y symmetry. As a result, one of the original degrees of

freedom is lost, generating a mass term for the Higgs field. The three remaining degrees

of freedom (known as Goldstone bosons) become the extra longitudinal polarisations

of the W± and Z bosons that are needed for them to acquire mass. The Higgs field

enables mass terms for the fermions to be included in the Lagrangian of the SM through

Yukawa couplings between the scalar Higgs and fermion fields. These Yukawa couplings

are proportional to the masses of the fermions and are parameters of the SM (their exact

values, and hence the fermion masses, are not yet understood).

This mechanism for electro-weak symmetry breaking successfully predicts the masses

and couplings of the W± and Z bosons, with theoretical predictions in very good agree-

ment with experimental measurements. The existence of a massive scalar boson (the

Higgs boson) is also predicted, but not the exact value of its mass. As it stands, the

Higgs boson has yet to be discovered and remains one of the most significant challenges

in experimental high energy physics, one which may well be realised at the LHC. The

combined experimental measurements from LEP have placed a lower bound on the mass

of the SM Higgs boson of 114.4 GeV at a 95 % confidence limit [3, 4].

1.2 The τ -lepton

Of particular relevance to the subject of this thesis is the physics of the τ -lepton. The

τ -lepton (discovered in 1975 [5]) is the heaviest of the three charged lepton species in

the SM, with a mass of 1.78 GeV.

At the LHC, the dominant production of τ -leptons can be expected from events

producing W± or Z gauge bosons3, Drell-Yan processes, and also from the production

of tt quark pairs (with τ -leptons produced through the leptonic decay channels of one

3The W± boson decays to τ -leptons with a branching ratio of BR (W → τν) = 11.3 %. The branch-ing ratio for Z bosons to pairs of τ -leptons is BR (Z → ττ ) = 3.4 %.


or both of the t-quarks). The momentum range of τ -leptons produced at the LHC

will typically span from below 10 GeV up to momenta of ∼ 500 GeV, with τ -lepton

signatures expected to be used both for SM measurements and as probes for new physics

[6]. Signatures from W± and Z boson decays, SM Higgs searches, and SUSY cascade

decays motivate the study of τ -leptons at lower momenta, whilst heavy Higgs searches

and the decays of possible heavy versions of the W and Z gauge bosons are possible

sources of τ -leptons at higher momenta.

The τ -lepton is unstable with a lifetime of 2.9× 10−13 s. It decays through weak

interactions, and is the only lepton that can decay into hadrons as well as leptons. Since

all decays produce at least one neutrino, τ -decays result in missing energy, leaving only

a visible component that is realistically detectable in a collider experiment. With both

hadronic and leptonic decay modes and the associated missing energy, the τ -lepton is

the most challenging lepton species to identify in collider experiments such as ATLAS.

Selected τ -decay modes are shown in table 1.2. Leptonic decay modes make up just

over a third of all decays, the remainder being hadronic modes. The hadronic decay

modes are dominated by final states containing both charged and neutral pions, and

can be separated into “1-prong” and “3-prong” modes, named according to the number

of charged particles produced. A small fraction (∼ 0.1 %) of the total decays are to

“5-prong” modes, but due to the low branching ratio and backgrounds from QCD jets,

these are hard to detect in the LHC environment.

1.3 Limitations of the Standard Model

The Standard Model, despite its significant successes, is not a complete theory. As it

stands, the SM involves at least 19 arbitrary parameters (3 gauge couplings, 6 quark

masses, 3 charged lepton masses, 3 weak mixing angles, a W boson mass, a Higgs boson

mass, a CP-violating CKM phase and a CP-violating vacuum angle)4. More significantly,

it does not incorporate gravity and one of its key constituents, the Higgs boson, remains

undiscovered. So clearly there are some remaining questions to be answered. Rather

than a complete theory, it is appropriate to consider the SM as an effective theory, one

that explains physics at the energy scales explored so far, but that will break down at

some higher energy scale, at which point additional new physics beyond the current SM

4If one were to incorporate massive neutrinos into the SM then one would also need further param-eters to describe the neutrino masses, mixing angles and CP-violating phases


Decay Mode Branching Ratio

τ → eνeντ 17.8 %

τ → µνµντ 17.4 %

τ → h±neut.ντ (1-prong) 49.5 %

τ → π±ντ 11.1 %

τ → π0π±ντ 25.4 %

τ → π0π0π±ντ 9.2 %

τ → π0π0π0π±ντ 1.1 %

τ → K±neut.ντ 1.6 %

τ → h±h∓h±neut.ντ (3-prong) 14.6 %

τ → π±π∓π±ντ 9.0 %

τ → π0π±π∓π±ντ 4.3 %

τ → π0π0π±π∓π±ντ 0.5 %

τ → π0π0π0π±π∓π±ντ 0.1 %

τ → (π0)π±π∓π±π∓π±ντ (5-prong) 0.1 %

Table 1.2: Selected τ -decay branching ratios. The branching ratios are those cur-rently implemented in the TAUOLA package used for Monte Carlo production in ATLAS.Adapted from [7]


is needed to correct for the shortcomings of the effective theory.

One missing piece of the SM is the elusive Higgs boson. The Higgs boson, the only

particle predicted by the SM that has yet to be detected, has been searched for at

several experiments, most notably at LEP and at the Tevatron [8], and this search will

be continued imminently at the LHC. Given the role that the Higgs mechanism plays

in the origin of mass in the SM, it is fair to say that the confirmation of its existence

will be a very important test of the SM. Despite the lack of a discovery so far, there are

several reasons to believe that the Higgs boson (or some other physics beyond the SM)

should be accessible in the energy ranges that will shortly be explored by the LHC.

One such hint originates from the amplitude for W–W scattering. This process

proves to be sensitive to the presence of new physics as, in the SM, this amplitude

breaks unitarity without the stabilising contribution from the Higgs boson. Demanding

that unitarity be satisfied allows an upper limit of mH ≤(8π√

2/3GF

)1/2 ' 1 TeV to be

placed on the Higgs mass [9]. In the case where the Higgs boson does not exist, then

some other new physics must be present at the TeV scale since unitarity can not be

broken. These energies will be accessible at the LHC, giving reason to expect to see

signs of new physics, be it the Higgs boson of the SM, or other physics beyond the SM.

Even with the potential discovery of the Higgs boson at the LHC, questions will still

remain over the details of the Higgs mass. More precisely, questions relating to the

magnitude of the quantum corrections to the Higgs mass that are predicted by the SM

due to the virtual effects of every particle that couples to the Higgs field. As illustrated

in figure 1.1(a), the coupling of the Higgs to a fermion f , with a mass mf and a coupling

strength λf , can result in corrections to the bare5 Higgs mass-squared,(m2

H

)0, such

that the observed Higgs mass, mH, is given by

m2H =

(m2

H

)0+ ∆m2

H. (1.7)

The corrections ∆m2H are of the following form

∆m2H =

|λf |2

16π2

[−2ΛUV

2 + 6m2f ln (ΛUV/mf ) + ...

]. (1.8)

5In renormalisable theories, the quantities appearing in the theory (such as particle masses) do notexactly correspond to the physically measured quantities. The bare quantities of the theory do not takeinto account the quantum corrections that occur due to virtual particle loops. In this context, the bareHiggs mass is the fundamental parameter of the theory, and should not be confused with the physicalHiggs mass that would be observed experimentally.


ΛUV represents an ultraviolet cut-off scale, for example the Planck massMP ∼ 1019 GeV.

It can be seen that the m2H corrections are of order ΛUV

2, forcing the bare Higgs mass

to this high scale. So, having already argued that a physical Higgs mass-squared of

(∼ 100 GeV)2 is needed, and presented with a bare Higgs mass at the MP scale, one

must rely on this bare Higgs mass being fixed extremely precisely (to one part in ap-

proximately 1016 if ΛUV ∼ MP) in order to reach agreement between the two scales.

This is known as the technical hierarchy problem and, whilst it is not exactly a failure of

the SM, it does represent an undesirable sensitivity in the theory. The ΛUV scale need

not be the Planck mass, although some new physics must intervene to create a suitable

cut-off resulting in mass corrections at the cut-off scale.

Having considered the quantum corrections resulting from fermion loops, one can also

consider the corrections resulting from a scalar particle, s, as illustrated in figure 1.1(b).

Diagrams of this sort result in the following additional corrections to m2H

∆m2H =

λS

16π2

[ΛUV

2 − 2m2S ln (ΛUV/mS) + ...

]. (1.9)

Whilst the corrections are still quadratically divergent in terms of ΛUV, the relative

minus sign between the fermion and scalar loops allows the possibility of a natural

cancellation of the divergent terms through the introduction of a series of scalar particles

to complement the fermions in the SM. For the introduction of two scalar particles for

each fermion, with couplings such that λS = |λf |2, a systematic cancellation of the

dangerously divergent terms can be achieved. Such a symmetry between fermions and

scalar particles is called supersymmetry (SUSY), and is the subject of section 1.4.

1.4 Supersymmetry

Supersymmetry (SUSY) is a proposed symmetry relating fermions and bosons, those

particles with half-integer and integer spins. The following section summarises possible

extensions to the SM incorporating supersymmetry. More detailed descriptions of super-

symmetry can be found in [10] and [11]. A supersymmetric transformation is governed

by operators, Q, which change the spin of a single-particle state by a value of ± 12,

transforming bosonic states into fermionic states and vice versa:

Q|Boson〉 = |Fermion〉; Q|Fermion〉 = |Boson〉. (1.10)


f

h h

(a)

S

h h

(b)

Figure 1.1: Quantum corrections to the Higgs mass arising from (a) fermion loops and(b) scalar loops.

The consequence of a SUSY extension to the Standard Model is that, for each boson

and fermion state in the SM, an additional state with spin differing by 12

will also exist.

These superpartners will display the same gauge couplings as their SM counterparts,

with only their spin differing.

As already mentioned, the introduction of these superpartners to the particle content

of the SM can address the technical hierarchy problem by offering a natural cancellation

of the quadratically divergent terms. Further motivation for supersymmetry can be

found by investigating the unification of the three gauge couplings of the SM forces in

a Grand Unified Theory (GUT). The aim of a GUT is to embed the SM into a more

fundamental theory. This involves finding a simple gauge group which, at some high

scale, is spontaneously broken to produce the SU(3)× SU(2)L×U(1)Y symmetry group

that is known to describe particle interactions very well at the electro-weak scale. Above

the scale at which unification occurs, ΛGUT, the couplings of the three fundamental

forces would be equal. By considering the renormalisation group equations (RGEs), one

can extrapolate how the coupling strengths vary with increasing energy scales. This

running is dependent on the accessible particles at any given scale, so will be affected

by the introduction of any new physics. The relevance of SUSY to unification theories

can be seen in figure 1.2. Here, the introduction of SUSY particles at the TeV scale

can result in gauge unification at a scale of ∼ 1016 GeV. A further, often discussed,

motivation for SUSY is inspired by the unexplained dark matter that is thought to exist

in the universe. SUSY models with an additional conserved global symmetry separating

SM particles from their SUSY counterparts (R-parity), can result in a massive stable


particle that is considered a good candidate for dark matter [12]. However this is not

strictly a property of SUSY, more the associated global symmetry, and SUSY models

without conservation of R-parity are possible and are the subject of further discussion

in chapter 7 of this thesis.

2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)

0

10

20

30

40

50

60

α−1

α1−1

α2−1

α3−1

Figure 1.2: The running of the inverse gauge couplings αi with the energy scale Q in theSM (dashed lines) and in the MSSM (solid lines). In the MSSM case the value α3(mZ)is varied between 0.113 and 0.123, and the thresholds for the sparticle masses are variedbetween 250 GeV and 1 TeV giving the error bands shown. Figure taken from [10].

1.4.1 The Minimal Supersymmetric Standard Model (MSSM)

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the SM that

incorporates supersymmetry by adding the corresponding superpartners to the existing

SM particles whilst maintaining a minimal particle content. In addition to the observed

fermions of the SM (the quarks and leptons), the particle content is expanded to include

a series of scalar particles, with two scalar particles for each fermion (one scalar for each

chiral degree of freedom of the fermion). This is conveniently understood by considering

each fermion as consisting of two components, each a Weyl spinor, with opposite chiral-

ity, with each chiral component being associated to a new scalar particle. Each scalar

particle and the corresponding Weyl spinor component of the fermion field are termed

superpartners and form chiral supermultiplets. These multiplets contain both fermion

and boson states such that the numbers of fermion and boson degrees of freedom are


equal. Whilst their relative spin is different, the members of a supermultiplet must have

the same electric charge, weak isospin and colour degrees of freedom.

In addition to these chiral supermultiplets, the gauge bosons of the SM form gauge

supermultiplets with spin-12

superpartners. This symmetry is imposed on the unbroken

massless gauge fields (W+, W−, W0 and B0). Like the chiral supermultiplets, the gauge

supermultiplets contain an equal number of boson and fermion degrees of freedom, with

the two helicity states of a massless gauge boson and the two degrees of freedom of

the fermion superpartners. When it comes to the Higgs sector, a further extension is

needed with respect to the SM. In the MSSM two Higgs doublets are required (rather

than the single Higgs doublet of the SM). The two doublets (labelled Hu and Hd) have

opposite hypercharge values and are required to provide masses for both u-type and d-

type quarks. When electro-weak symmetry breaking occurs in the MSSM, the two Higgs

doublets (and their conjugates) have 8 internal degrees of freedom. Three of these are

used to give masses to the Z and W± gauge bosons, with the other five producing five

massive Higgs bosons consisting of two neutral, CP-even scalars (h0 and H0), a neutral

CP-odd scalar (A0) and two charged scalars (H+ and H−). Of these scalars, the h0 closely

resembles the Higgs boson of the SM.

By convention, the names of new scalar particles in the chiral supermultiplets are

formed from the fermion name with a preceding “s” (e.g squarks and sleptons). Each

scalar is given a label (L or R) to associate the scalar particle to the appropriate fermion

degree of freedom (either the left- or right-handed fermion state). For the case of the

new fermions in the gauge supermultiplets, these are allocated names from the associated

gauge boson appended with “ino” (e.g the partners of the unbroken W and B electro-

weak gauge bosons are termed wino and binos respectively). Summaries of the chiral

supermultiplets and the gauge supermultiplets can be found in tables 1.3 and 1.4.

The sparticle states described so far correspond to the gauge eigenstates, however

the physical states of definite mass will correspond to linear combinations of the gauge

eigenstates. The gauginos and higgsinos mix to form charginos (χ±i ) and neutralinos

(χ0i ). Mixing will also occur in the squark and slepton states, although this is small for

the u,d and c,s families but more significant in the case of the third family6. The mixing

6The third-generation squarks and sleptons can have larger mass differences and substantial mixingcompared to their first- and second-generation counterparts. This is due to the smaller Yukawa andsoft couplings for the first- and second-generation.


of sparticles can be summarised by the following physical eigenstates:

B0, W0, H0u, H

0d → χ0

1, χ02, χ

03, χ

04 neutralinos

W ± , H+u , H

−d → χ±

1 , χ±2 charginos

τL, τR → τ1, τ2 stau

(tL, tR), (bL, bR) → (t1, t2), (b1, b2) stop and sbottom

Particles spin 0 spin 12

SU(3), SU(2), U(1)

squarks, quarks Q(

uL dL

) (uL dL

) (3, 2, 1

6

)(× 3 families) U u∗R u†R

(3, 1, −2

3

)D d∗R d†R

(3, 1, 1

3

)sleptons, leptons L

(ν eL

) (ν eL

) (1, 2, −1

2

)(× 3 families) E e∗R e†R

(1, 1, 1

)Higgs, higgsinos Hu

(H†

u H0u

) (H+

u H0u

) (1, 2, +1

2

)Hd

(H0

d H−d

) (H0

d H−d

) (1, 2, −1

2

)Table 1.3: A summary of the chiral supermultiplets in the MSSM.

Particles spin 12

spin 1 SU(3), SU(2), U(1)

gluino, gluon g g(

8, 1, 0)

gaugino / W+, W−, W0, W+, W−, W0(

1, 3, 0)

gauge boson B0 B0(

1, 1, 0)

Table 1.4: A summary of the gauge supermultiplets in the MSSM.

1.4.2 SUSY-breaking

It is clear that, should SUSY exist, it must be a broken symmetry at the electro-weak

scale. If this was not the case then scalar partners of the SM fermions would exist with


the same masses as the SM fermions. For example in addition to the well measured

electron, one would expect to have observed it’s two superpartners (the e±L and e±R )

both with a mass of 511 keV. Such particles have not been observed and would not have

escaped detection. Consequently, for SUSY to be a valid theory, it must be broken at

some scale such that the effects of SUSY are hidden at low energies (in an analogous

manner to that with which the electro-weak symmetry is broken in the SM).

In considering a mechanism for breaking SUSY it is important that the quadratic

divergences that were naturally cancelled by the initial introduction of SUSY are not

then reintroduced by attempts to break the symmetry at low scales. The cancellation of

divergent terms requires that the couplings to the Higgs field for the scalar and fermion

particles be related. This is the case for unbroken SUSY and must be maintained in

any SUSY-breaking model. In the MSSM this can be achieved through “soft” SUSY-

breaking, where the effective MSSM Lagrangian is of the form

L = LSUSY + Lsoft. (1.11)

The LSUSY component preserves SUSY whilst the Lsoft component contains all the possi-

ble terms which break the symmetry, but do not introduce dangerous divergences. This

general approach avoids the need to make assumptions about the physical form of the

breaking mechanism, however an uncomfortable consequence of this generality is the

introduction of 105 apparently arbitrary parameters (including the masses of the scalars

and fermions, couplings, and phases). On its own, such a large number of arbitrary

parameters is not ideal, however experimental limits on CP-violation and flavour mixing

constrain many of these parameters, indicating that some underlying organising principle

can simplify many of these terms. SUSY-breaking cannot be achieved using the MSSM

fields alone, so instead it can be assumed to come about through a “hidden sector” of

physics at some higher energy scale, whose shared interactions with the MSSM commu-

nicate the symmetry breaking to the “visible sector” of the MSSM. Here they provide the

soft breaking terms in Lsoft. There are several different proposals for scenarios that can

account for SUSY-breaking in a reasonable way. Minimal supergravity (mSUGRA) mod-

els provide one possible mechanism for SUSY-breaking (described in more detail below).

Another common SUSY-breaking model is gauge mediated SUSY-breaking (GMSB) in

which “messenger particles” couple both to SUSY-breaking processes in the hidden sec-

tor and indirectly to the particles of the MSSM through SU(3)× SU(2)L×U(1)Y gauge

interactions, resulting in symmetry breaking. A more detailed discussion of soft SUSY

breaking and the common breaking scenarios can be found in [10].


Gravity mediated SUSY-breaking

Gravity-mediated SUSY-breaking, or supergravity (SUGRA), models provide a popular

and commonly studied mechanism for breaking SUSY. In such models, communication

between the hidden sector and the MSSM is dominated by flavour-blind gravitational

interactions. In the simplest forms of these models, termed minimal supergravity or

mSUGRA models, Lsoft can be significantly simplified in terms of the following 5 pa-

rameters:

• m0 — a common mass for all scalar sparticles at the GUT scale,

• m 12

— a common gaugino mass at the GUT scale,

• A0 — a constant of proportionality between the SUSY breaking trilinear Hff

coupling terms and the SUSY conserving Yukawa couplings,

• tanβ — the ratio of the vacuum expectation values of the two MSSM Higgs dou-

blets,

• sgn(µ) — where µ is the SUSY higgsino mass parameter.

The values of these parameters allow the MSSM particle spectrum and interactions to

be determined (within the simplified context of mSUGRA). Whilst mSUGRA presents

an elegant mechanism for SUSY-breaking, even within the reduced parameter set of

the constrained mSUGRA framework, different parameter space points and regions can

result in very different phenomenology. In addition, this minimal approach may well be

too simplistic to describe all the details of SUSY in nature (should it exist). However

mSUGRA models do offer a good starting point and have been used extensively by

physicists (including the ATLAS collaboration) to provide benchmark points as examples

of possible SUSY phenomenology.

1.4.3 R-Parity

In the discussions presented so far, the MSSM is minimal in so much that it is contains

the minimum number of particles and couplings needed to produce a phenomenologically

viable model. The superpotential of the MSSM can be written as

WMSSM = UyuQHu − DydQHd − EyeLHd + µHuHd. (1.12)


The objects Hu, Hd, Q, L, U , D and E are the chiral superfields corresponding to the

supermultiplets shown in table 1.3. yu, yd and ye are the 3× 3 matrices containing

the Yukawa couplings. There are however additional terms to the superpotential that

have so far been neglected. These terms explicitly break either baryon-number (B) or

lepton-number (L) conservation. The non-observation of proton decay and the resulting

limits on its lifetime provide tight constraints on such terms, restricting the simultaneous

presence of baryon-number violating and lepton-number violating terms. The proposal

of a discrete symmetry, known as R-parity [13], has the effect of eliminating these B- or

L-violating terms.

The R-parity, Rp, of a given particle is defined as

Rp ≡ (−1)3(B−L)+2s (1.13)

where s is the spin of the particle. This implies that all SM particles have Rp = +1,

whereas their superpartners have Rp = −1. With R-parity conserving (RPC) models,

R-parity has a significant impact on the phenomenology. Conservation of R-parity

restricts SUSY particles to be produced in pairs, and forbids any decay modes of SUSY

particles where all the products are SM particles. Consequently, a collider signature

for a SUSY event will involve the production of two SUSY particles, each undergoing

a cascade decay through ever lighter SUSY states until the lightest supersymmetric

particle (LSP) is reached, which, by R-parity conservation, is required to be stable. In

order to be consistent with cosmological constraints, the LSP must be electrically and

colour neutral as such an object, if stable, would have already been detected [12]. A

neutral LSP (typically the χ01) cannot be ruled out by these arguments, and in fact

proves to be a popular candidate particle to explain the origins of dark matter in the

universe.

Despite the proton-decay constraints and the appealing possibility of explaining dark

matter, R-parity violating (RPV) models present an alternative solution. A more general

superpotential would include the additional terms that violate either baryon-number or

lepton-number:

W∆L=1 =1

2λijkLiLjEk + λ′ijkLiQjDk + κiLiHu, (1.14)

W∆B=1 =1

2λ′′ijkUiDjDk. (1.15)


where the family indices i = 1, 2, 3 are included. The λ, λ′ and κ terms shown in

equation 1.14 violate L by one unit, where the λ′′ terms in equation 1.15 violate B by

one unit. The existence of such terms could have dramatic effects, resulting in B- and

L-violating processes that have been ruled out experimentally. The most notable of

these effects would be rapid proton-decay. Figure 1.3 demonstrates how a combination

of λ′ and λ′′ couplings can lead to processes that would result in rapid proton decay

through decay modes such as p → π0e+. The experimental limits on the partial lifetime

of this decay mode are greater than 1033 years [11, 14]. However, in order to prevent fast

proton-decay it is sufficient to satisfy either L- or B-conservation (measurements on the

proton lifetime provide a strong limit on the product of L- and B-violating couplings).

¯

u

u

λ′′

λ′

¯s

u

u

d

Figure 1.3: A Feynman diagram demonstrating how a combination of non-zero λ′ andλ′′ couplings can result in rapid proton decay.

The introduction of non-zero RPV couplings to the MSSM can result in dramatic

changes to the phenomenology of SUSY models. The LSP is no longer stable, and

consequently the restrictions on its electrical neutrality are lifted, allowing alternative

particle species to act as the LSP. RPV signatures are the subject of chapter 7 and are

discussed in more detail there.

Chapter 2

The ATLAS experiment

2.1 The LHC

The Large Hadron Collider (LHC) [15] at CERN is a new hadron collider, designed to

collide protons together at an energy of 14 TeV around a 27 km ring. Bunches contain-

ing 1011 protons will collide at a rate of 40 MHz with a design luminosity of 1034 cm-2s-1.

These energies and luminosities are higher than any previous collider experiment, push-

ing back the frontier of experimental high-energy physics. This high luminosity is es-

sential for the benchmark physics processes to be investigated at the LHC, as many are

expected to have low cross sections. The high interaction rate means that every physics

event in the detector will be accompanied by ∼ 20 underlying inelastic collisions occur-

ring simultaneously in the detector providing a challenge in reconstructing and recording

interesting events above a background of low-energy events.

The LHC will be injected with protons at energies of 450 GeV from the Super Proton

Synchrotron (SPS) before being accelerated to energies of 7 TeV in the LHC (a process

which is expected to take ∼ 20 minutes, with an average energy gain of ∼ 0.5 MeV on

each turn). The beam is steered around the LHC ring by a series of superconducting

magnets (dipole, quadrupole and correcting magnets). To produce a 7 TeV proton beam

requires very high magnetic dipole fields of 8.3 T (achieved by lowering the temperature

of the dipole magnets to 1.9 K in a bath of superfluid helium).

The two counter-rotating proton beams are brought together at four points around

the LHC ring. At these positions, the beams collide with a centre of mass energy of

14 TeV, resulting in interactions that will be measured by the four main LHC experi-

18

The ATLAS experiment 19

Figure 2.1: The layout of the LHC underground areas. The four LHC experiments areshown, along with the SPS.

ments: ATLAS [16], CMS [17], LHCb [18] and ALICE [19]. The ATLAS detector is one

of the two “general purpose” experiments at the LHC (along with CMS) that hope to

identify, measure and understand the complex signs of new physics in amongst the huge

backgrounds of well understood processes.

2.2 ATLAS

ATLAS [16, 20] (‘A Toroidal LHC ApparatuS’) is the largest particle physics detector

ever built, with a length of 46 m and height of 25 m (see figure 2.2). The shape of

the ATLAS detector allows it to be conveniently described by a cylindrical (R, φ z)

coordinate system, with the z-axis of the cylinder aligned along the beam line. R is

the transverse radius from the beamline, φ is the azimuthal angle, with the origin of z

located at the nominal interaction point. An angle θ is also defined as the polar angle

from the z-axis. A positive x-axis is defined pointing from the interaction point to the

centre of the LHC ring, with a y-axis defined pointing vertically upwards.

Since protons are composite objects, the constituent partons that participate in the

proton-proton interactions carry an unknown fraction of the total momentum. As a re-

sult, in proton collisions at the LHC the initial z-momentum of the interacting system is

unknown. This leads to rapidity, y = 12ln [(E + pz) / (E − pz)], being a useful quantity


Figure 2.2: A labelled diagram of the ATLAS detector.

in describing particles in the detector. Rapidity has the advantage that differences in

this variable are invariant under longitudinal Lorentz boosts (convenient if the initial

z-momentum is unknown). A difficulty in calculating rapidity is that the mass of the

particle under consideration must be known, so pseudorapidity, η = − ln tan (θ/2), is

often considered. Pseudorapidity is a good approximation to the true rapidity (in the

relativistic limit) and is easier to compute. As a result, particles are often described in

terms of the parameters (pT, η, φ) where pT is the transverse component of the momen-

tum and φ is the azimuthal angle (as described above). Separations between particles

in the η–φ plane are commonly described in terms of ∆R =√

∆η2 + ∆φ2.

Collisions at the LHC are expected to provide new physics phenomena at the TeV

energy scale. As one of the LHC’s generic detectors, ATLAS has been designed to have

the ability to explore a broad physics programme with many different physics goals in

mind. A brief summary of the ATLAS physics programme is as follows:

Higgs Boson Searches:

The search for the SM Higgs boson is one of ATLAS’s principal aims. The Higgs bo-

son is a missing component of the SM and is widely expected to be observed at the LHC.

The production and decay mechanisms of the Higgs boson are expected to be depen-

dent on its mass, with a wide range of possibilities in the energies to be explored. As a

consequence of this, Higgs searches have been used as an important benchmark in estab-

lishing the performance of the ATLAS sub systems. At low Higgs masses (mH < 2mZ)


decays into hadrons are expected to dominate, but these are hard to observe because of

very large backgrounds from QCD. Instead it is expected that the H → γγ channel will

be the most useful for detection, along with channels resulting from associated Higgs

production such as ttH, WH and ZH, where a lepton from the decay of the associated

quark/vector boson can provide both a triggering mechanism and background rejection.

At higher masses (above ∼ 130 GeV) signatures in which a Higgs boson decaying into a

pair of Z bosons become increasingly useful (due to the increase in the H → ZZ branch-

ing ratio). Here searches will focus on channels where the Z bosons go on to decay to

pairs of oppositely charged leptons as this 4-lepton signature is experimentally clean.

Physics beyond the Standard Model can predict other significant experimental channels

for Higgs searches. For example, searches for Higgs bosons in supersymmetric models

are expected to have sensitivity in channels involving τ -leptons and b-tagging.

Electroweak and Strong Interactions:

The high LHC luminosity and increased cross-sections will enable further high preci-

sion tests of QCD, electro-weak and flavour physics. ATLAS will investigate many QCD

parameters, among them new measurements of parton distribution functions (PDFs).

QCD processes are expected to be a significant background to many physics signatures

so it is important that they are well understood. Precision electroweak measurements,

such as the W- and Z-boson masses, will be important in calibrating the detector. The

rate of top quark production at the LHC is expected to be a few Hz, allowing for higher

precision measurements than have been possible in previous experiments.

New Physics Searches:

ATLAS has been designed to be sensitive to many different new physics signatures.

Heavy gauge bosons with masses up to ∼ 6 TeV should be accessible at ATLAS, with

leptonic decay signatures requiring good lepton measurement and charge identification

for transverse momenta of up to the TeV scale. Supersymmetric models are predicted to

provide cascade decays resulting in a number of leptons and jets in the final state that,

if R-parity is conserved, will also result in significant EmissT . Other possible sources of

new physics include models proposing extra dimensions and TeV scale quantum gravity,

with possible experimental signatures from so called Kaluza-Klein excitations or from

mini-blackhole production.

The desire to study these physics goals places a series of requirements on the design

of the ATLAS detector. In summary, the basic design criteria include:


• efficient tracking at high luminosity for lepton momentum measurements and for

τ -lepton and heavy flavour identification.

• very good electromagnetic calorimetry for electron and photon identification, along

with full coverage hadronic calorimetry for accurate measurements of jet and miss-

ing transverse energy.

• high precision muon measurements up to high luminosity and over a wide range

of muon momenta, using a standalone muon spectrometer.

• a triggering system for particles at low transverse momentum thresholds that can

provide high efficiencies for most physics processes of interest.

• fast, radiation-hardened electronics and high detector granularity in order to cope

with the harsh LHC experimental conditions and the high particle fluxes.

These requirements have resulted in a design incorporating tracking, calorimetry and

muon spectrometry, along with a magnet system comprised of a central superconduct-

ing solenoid (providing a magnetic field for the Inner Detector volume), and a large

system of air-core superconducting toroids generating the magnetic field for the muon

spectrometer.

2.3 The Inner Detector

The Inner Detector (ID) (shown in figure 2.3) provides a capability for reconstructing

tracks and vertices from charged particles, measuring their momentum and charge sign.

The ID needs to make many precise measurements of the positions of the particles along

their flight-path in order to accurately reconstruct their tracks. Good track reconstruc-

tion is important for good momentum and vertex resolution, and to achieve this it is

important for the tracking elements to have a high efficiency for detecting charged parti-

cles, but at the same time have a low probability for registering erroneous hits. At high

luminosity there will be many charged particles passing through the ID and hence it is

important that the detector has high granularity and low occupancy in order to make

high precision space-point measurements.

To achieve this, the ID employs a combination of different tracking technologies over

its volume, making three sub-detectors. Maintaining a low material budget inside the


Figure 2.3: The ATLAS Inner Detector.

volume of the ID was an important design concern, but the desire for a high granularity

and high precision detector requires significant material in both the sensor support

structures and in providing the sensor services. To balance these concerns, the number

of high precision layers was limited by their high cost and the material they introduce

into the detector.

High precision and granularity are most important at inner radii near the beam

pipe, whereas, at outer radii the increase in volume and cost become more significant.

At inner radii, high-granularity tracking is achieved using silicon pixel and microstrip

technologies. Typically, a track will pass through three pixel layers and 8 microstrip

layers (giving four space points). At larger radii, a large number of tracking points

are provided by a straw tube Transition Radiation Tracker (TRT). The TRT provides

continuous track following with typically 36 points registered per track.

Collisions at the LHC result in unprecedented background radiation levels. The

high radiation environment presents a serious challenge to the ID, in particular the

silicon pixel and microstrip detectors where levels will be highest. A major factor is

the damage that radiation can cause to silicon detectors and their readout electronics.

Non-ionizing interactions with high-energy hadrons can result in recoiling silicon nuclei

being displaced from their lattice sites, degrading the sensor performance. The design of

the ID incorporates radiation hard components to limit the impact of radiation damage.

A summary of radiation levels for different regions of the ID is shown in table 2.1.


Region Fneq ( × 1012 cm−2/y) Ionization Dose (Gy/y)

Pixel layer 0 270 158000

Pixel layer 2 46 25400

SCT barrel layer 1 16 7590

SCT barrel layer 4 9 2960

SCT end-cap disk 9 14 4510

TRT outer radius 5 680

Table 2.1: Radiation levels at various locations in the ID. Fneq is the 1 MeV neutronequivalent fluence. The ionization dose is shown in units of Gy/y where one year corre-sponds to 8× 1015 inelastic proton-proton collisions (assuming an inelastic cross-sectionof 80 mb-1, a luminosity of 1034 cm-2 s-1 and a data-taking period of 107 s). Adaptedfrom [16].

In order to measure the momentum and charge sign of charged particles passing

through the ID, the ID volume is surrounded by a solenoid. The solenoid magnetic field

is along the direction of the beam axis, causing the tracks of charged particle to be bent

according to the transverse momentum of the particle. This orientation means that

tracks will be bent in the R-φ plane, and consequently, the design of the ID is optimised

to give the best resolution in this plane (to achieve the best momentum resolution).

2.3.1 Solenoid Magnet System

The ID solenoid provides an axial magnetic field of 2 T to the ID volume. The solenoid

is 5.8 m long with an inner diameter of 2.46 m and an outer diameter of 2.56 m, and is

designed so as to minimise the amount of material in front of the calorimeter (at normal

incidence the solenoid contributes only ∼ 0.66 radiation lengths). The coil is made from

an Al-stabilised NbTi conductor which is cooled to 4.5 K. This choice gives a high field

whilst optimising the thickness. The solenoid field will allow accurate measurements of

charged particles in the ID with momenta of up to 100 GeV.

2.3.2 Pixel Detector

The pixel detector is the innermost of the three sub-detectors. Here, nearest the inter-

action point, the requirement for high granularity and high precision measurements is


Figure 2.4: A diagram showing a section of the Inner Detector barrel with the differentsub-detectors. The radial distances of the sub-detectors from the beam axis are shown.

greatest. The pixel detector uses silicon pixels as a sensor medium in order to provide the

required precision and granularity. It is made of 1744 modules, each containing 46080

pixels with a minimum pixel size of 50× 400 µm2. All of the modules are identical, and

comprise a silicon sensor tile that is bump bonded to 16 front-end electronic chips (each

with 2880 readout channels to serve an array of 18× 160 pixels), providing a binary out-

put. The pixels are aligned such that the greatest precision is in the R-φ direction. The

modules are arranged in three barrel layers (at radii of 50.5 mm, 88.5 mm and 122.5 mm

as shown in figure 2.4) and two end-caps, each comprising three disc layers. In total,

the pixel detector reads out 80.4× 106 pixels.

To maintain noise performance over the period of operation of the detector and to

control the radiation damage that will occur, the pixels must be kept at temperatures of

∼ − 7 ◦C. Even then, the innermost pixel layer must be replaced after approximately

three years of running at design luminosity.

2.3.3 Semiconductor Tracker (SCT)

Like the pixel detector, the SCT uses silicon sensors to detect charged particles. Where

the pixel detector employs modules made up of silicon pixels, the increased distance of

the SCT from the interaction point and the larger area to be covered (the total area of


silicon used in the SCT is 63 m2) led to the decision to use silicon microstrips. The SCT

is made up of 4 coaxial cylindrical barrels, and two end-caps (each made of nine disk

layers). The barrels and end-cap disks are covered in silicon microstrip modules. The

innermost barrel is at a radius of 299 mm with the outer barrel at a radius of 514 mm.

The microstrips are formed on silicon wafers, with a strip pitch of 80 µm for the

barrel sensors. These wafers are arranged onto modules along with the module readout

electronics. The barrel modules use four 63.6 mm× 64 mm wafers combined into two

layers (each layer being formed from two wafers connected end-to-end to give a combined

sensor of length 128 mm). The strips are aligned on the module to give the greatest

accuracy in the R-φ direction. The two layers are offset by a small stereo angle of

40 mrad to give a measurement along the length of the strip (the z-direction in the

barrel modules). Each layer has 768 active strips which are read out by twelve 128-

channel ASIC chips. The SCT modules employ a binary readout, with a hit being

defined above a certain charge threshold.

The end-cap has four different types of module, used at three different radii on the

end-cap disks. As with the barrel modules, the end-cap modules are formed from two

layers of silicon offset by a relative rotation of 40 mrad. The silicon layers are trapezoidal

and have an average strip pitch of ∼ 80 µm.

In total, the SCT consists of 4088 modules (2112 barrel modules and 1976 end-cap

modules), giving a total of 6.3× 106 channels. The nominal SCT position resolution is

17 µm in the R-φ direction and 580 µm in the z-direction (barrel) and R-direction (end-

caps). Like the pixel detector, the SCT silicon detectors are required to be operated at

temperatures of ∼ − 7 ◦C in order to limit the effect of radiation damage on the noise

performance. Cooling is provided by a C3F8 evaporative cooling system (common to

both the SCT and pixel sub-detectors). A more detailed discussion of the SCT barrel

modules can be found in chapter 3.

2.3.4 Transition Radiation Tracker

At larger radii, the ID employs a Transition Radiation Tracker which is a straw tube sys-

tem for measuring hits from charged particles. Each of these straw tubes is a polyamide

tube with a diameter of 4 mm. These tubes are filled with a Xe-based gas mixture,

with the inside surface coated in a layer of aluminium which acts as a cathode. At the

centre of the tube is a 31 µm diameter tungsten wire, coated with a 0.5 µm to 0.7 µm


layer of gold. This acts as the anode. On passing through the straws, charged particles

ionize the gas, with the resulting ionization cluster drifting through the electric field

of the straw. The cathode operates at −1530 V resulting in a gain of 2.5× 104. The

drift-time gives a measure of the R-φ position within the straw. The anode wires inside

each barrel straw are electrically split at the midpoint and are read out through each

end. The gaps between the straws contain radiators made up of polypropylene fibres

(foils in the end-caps) that facilitate the production of transition radiation.

Transition radiation [21] occurs when a charged particle traverses a boundary between

materials of different dielectric constant. By using a periodic sandwich of many foils as a

radiator, interference effects can produce a threshold effect as a function of the Lorentz

factor, γ, allowing for discrimination between particles of different masses. In the TRT

this threshold is at γ∼ 1000, with electrons exceeding this threshold for momenta of

∼ 0.5 GeV and pions exceeding it for momenta of ∼ 140 GeV.

The straw tubes employ two independent thresholds when determining a hit. The

lower hit-threshold is designed to detect the charge from a minimally ionizing particle,

with the higher hit-threshold designed to detect the transition radiation photons (low

energy transition radiation photons are absorbed by the Xe gas mixture, resulting in

much larger signal amplitudes). The higher hit-threshold aids particle identification,

with electrons producing more transition radiation than pions. This discrimination is

optimal for tracks with pT∼ 5 GeV, with the separation power reducing for higher track

momenta.

2.3.5 Anticipated Tracking Performance

Track reconstruction software takes cluster information from the hits in the pixel and

SCT sub-detectors, along with drift circles from the TRT (calibrated from the TRT raw

timing information), and searches for tracks originating from the interaction region by

using the high precision information from the pixel and SCT layers and extrapolating

out into the TRT. Algorithms are also used to reconstruct the primary vertex, tracks

from photon conversions and secondary vertices.

The resolution of a given track parameter can be expressed as a function of pT as:

σX = σX (∞) (1⊕ pX/pT ) (2.1)


Track Parameter σX (∞) pX (GeV)

Inverse transverse momentum (1/pT) 0.34 TeV-1 44

Azimuthal angle (φ) 70 µrad 39

Polar angle cotθ 0.7× 10−3 5.0

Transverse Impact Parameter (d0) 10 µm 14

Longitudinal Impact Parameter (z0× sinθ) 91 µm 2.3

Table 2.2: The expected RMS track-parameter resolutions for ID tracks in the barrelregion (0.25 < |η| < 0.5). σX (∞) is the resolution corresponding to infinite trans-verse momentum, and pX is a constant describing the transverse momentum where thecontribution to the resolution from multiple-scattering is equal to that of the detectorresolution (see equation 2.1).

where X is the track parameter in question, σX (∞) is the resolution expected for a

particle at infinite momentum and pX is a constant. This expression works well at

both high-pT and at low-pT where the resolution is dominated by the intrinsic detector

resolution and by multiple scattering respectively. The expected resolution for different

track parameters is shown in this form in table 2.2. Along with multiple scattering, pions

interact hadronically with the material in the ID while electrons undergo bremsstrahlung.

Consequently, the track reconstruction efficiencies for pions and electrons, as a function

of η, reflect the amount of material in the detector (with poorer efficiencies beyond

|η| ∼ 1 due to the increased material in this region).

2.4 Calorimeter

The ATLAS calorimeters (see figure 2.5) are designed to give accurate measurements of

the energy of electrons, photons and jets. By measuring transverse energy, the calorime-

ter system is crucial to the measurement of EmissT . ATLAS, like many general purpose

detectors, has two main calorimeter systems, an electromagnetic calorimeter (ECAL)

and a hadronic calorimeter (HCAL). Electrons and photons interact differently with

matter compared to hadrons. Typically hadronic showers (characterised by the nuclear

interaction length λI) penetrate much more deeply than electromagnetic showers (char-

acterised by the radiation length X0). Consequently, as the names suggest, the ECAL is


Figure 2.5: The layout of the ATLAS calorimeters. Both the electromagnetic andhadronic calorimeters are shown.

optimised to measure the energy of electromagnetic showers, with the HCAL designed

to measure hadronic showers.

High-energy electrons typically lose energy by bremsstrahlung when traversing mat-

ter, producing photons, whilst photons undergo pair production of electrons and positrons.

The number of particles in an electromagnetic shower increases rapidly by these two

processes until the average energy drops below the critical value for bremsstrahlung to

occur, at which point further energy loss is through ionization. The radiation length is

a measure of the characteristic amount of matter traversed by these interactions, and is

the length scale used to describe electromagnetic cascades. Hadronic showers are built

up from hadrons undergoing multiple scattering interactions whilst passing through a

medium. However, unlike bremsstrahlung, multiple final states are possible in hadronic

interactions. The resulting showers are characterised by the nuclear interaction length

which is typically an order of magnitude greater than the radiation length.

It is important that the calorimeters provide good containment of electromagnetic

and hadronic showers in order to achieve good energy resolution as well as limiting

punch through into the muon system. The ECAL is more than 22X0 thick in the central

barrel, extending to more than 24X0 in the end-caps, keeping leakage from high energy

electromagnetic showers into the HCAL at acceptable levels. The calorimeter provides

a total thickness of 9.7 λI (11 λI including the outer supports) at η =0, sufficient to


control punch-through of hadronic showers into the muon chambers.

2.4.1 Electromagnetic Calorimeter (ECAL)

The ECAL is a lead-LAr detector where lead plates are used to absorb energy, with liquid

argon (LAr) being used as the sampling material. The ECAL exploits a complicated

accordion geometry in order to give complete φ coverage without any azimuthal cracks.

The accordion geometry is shown in more detail in figure 2.6.

The ECAL is divided into a barrel section (covering |η| < 1.475) and two end-caps

(covering 1.375 < |η| < 3.2). The transition region between the barrel and the end-caps

results in a crack in the coverage. The end-cap section of the ECAL is comprised of

two wheels, one covering 1.375 < |η| < 2.5 and the other covering 2.5 < |η| < 3.2. The

central η range (|η| < 2.5) is devoted to precision measurements as this is the η range

where the ECAL is matched to the ID. Here the ECAL is comprised of three longitudinal

layers and has has fine granularity suited to precision measurements of electrons and

photons. For 2.5 < η < 3.2 the ECAL consists of two longitudinal sections with a coarser

granularity. The granularity of the ECAL for different η ranges is summarised in table

2.3. A presampler layer covers the range 0 < |η| < 1.8 giving a measurement of the

energy lost from showers in front of the ECAL in this range.

The ECAL is a non-compensating calorimeter, and as such it responds differently to

electromagnetic and hadronic showers. Calibrations to correct this difference are applied

as part of the offline reconstruction software.

2.4.2 Hadronic Calorimeter (HCAL)

The HCAL is divided into three separate calorimeters:

1. Tile Calorimeter

2. LAr hadronic end-cap calorimeter

3. LAr forward calorimeter (FCAL)

These calorimeters provide coverage out to |η| = 4.9. The reach out to such high

η is important in giving a good missing transverse energy (EmissT ) resolution, whilst


∆ϕ = 0.0245

∆η = 0.02537.5mm/8 = 4.69 mm ∆η = 0.0031

∆ϕ=0.0245x4 36.8mmx4 =147.3mm

Trigger Tower

TriggerTower∆ϕ = 0.0982

∆η = 0.1

16X0

4.3X0

2X0

1500 m

m

470 mm

η

ϕ

η = 0

Strip towers in Sampling 1

Square towers in Sampling 2

1.7X0

Towers in Sampling 3 ∆ϕ×�∆η = 0.0245×�0.05

Figure 2.6: A detailed diagram showing the layout of the electromagnetic calorimeter.


EM Calorimeter

Granularity ∆η×∆φ versus |η|Barrel End-cap

Presampler 0.025× 0.1 |η| < 1.52 0.025× 0.1 1.5 < |η| < 1.8

1st Layer 0.025/8× 0.1 |η| < 1.4 0.050× 0.1 1.375 < |η| < 1.425

0.025× 0.025 1.4 < |η| < 1.475 0.025× 0.1 1.425 < |η| < 1.5

0.025/8× 0.1 1.5 < |η| < 1.8

0.025/6× 0.1 1.8 < |η| < 2.0

0.025/4× 0.1 2.0 < |η| < 2.4

0.025× 0.1 2.4 < |η| < 2.5

0.1× 0.1 2.5 < |η| < 3.2

2nd Layer 0.025× 0.025 |η| < 1.4 0.050× 0.025 1.375 < |η| < 1.425

0.075× 0.025 1.4 < |η| < 1.475 0.025× 0.025 1.425 < |η| < 2.5

0.1× 0.1 2.5 < |η| < 3.2

3rd Layer 0.050× 0.025 |η| < 1.35 0.050× 0.025 1.5 < |η| < 2.5

Table 2.3: A summary table showing details of the granularity of the ECAL in differentpseudorapidity ranges for each layer (including the presampler).

also allowing for the reconstruction of forward tag-jets. As previously mentioned, the

thickness of the HCAL provides good shower containment in order to minimise punch

through into the muon system.

The Tile Calorimeter is a sampling calorimeter comprising layers of iron and scin-

tillating tiles. Ionizing particles crossing the 3 mm scintillator tiles produce ultraviolet

light. This scintillating light is collected and read into photomultiplier tubes along wave-

length shifting fibres. These fibres convert the light from the ultraviolet to the visible

spectrum. The structure of the Tile Calorimeter is separated into barrel (|η| < 1.0) and

extended barrel (0.8 < |η| < 1.7) regions.

The Hadronic end-cap calorimeters are located behind the ECAL end-cap. They

extend from |η| = 1.5 to |η| = 3.2, thereby overlapping with both the Tile Calorimeter

and the FCAL. This is designed to reduce the drop in density in the gaps between the

different sections. Each end-cap consists of two independent wheels, each one built of 32

modules and two longitudinal sections, giving a total of four samplings. The hadronic

end-cap calorimeters use LAr as the active medium between copper plates.


The forward η regions are covered by the FCAL. Due to the longitudinal space

available to the FCAL, it has a high density design, comprising of three modules (one

made of copper, the other two tungsten). Like the ECAL and the hadronic end-cap

calorimeters, LAr is used as the sensitive medium in the FCAL.

2.4.3 Anticipated Calorimeter Performance

ECAL Performance

In order to achieve precise energy measurements in the ECAL, corrections must be

applied to optimise the energy resolution and linearity of response. These corrections

take the form of η-dependent longitudinal weights as follows:

E = s (η) [c (η) + w0 (η) ·EPS + Estrips + Emiddle + w3 (η) ·Eback] (2.2)

where EPS, Estrips, Emiddle and Eback correspond to the measured energies in the pre-

sampler, strip, middle and back layers respectively. s (η) acts as an overall scale factor,

c (η) corrects for any offset, w0 (η) corrects for upstream energy losses and w3 (η) corrects

for longitudinal leakage. The energy resolution (σE/E) can be expressed as a function

containing a stochastic term (a), a noise term (b) and a constant term (c):

σE/E =

√a2

E+b2

E2+ c2 (2.3)

The expected energy resolution has been studied through extensive simulations, val-

idated by results using test-beams. The expected stochastic terms, from simulation,

for the electron and photon energy resolutions are shown for three values of η in ta-

ble 2.4. Test-beam studies as part of the ATLAS Combined Test-Beam (corresponding

to η = 0.4 in ATLAS) give a stochastic term of (9.93± 0.15) % ·√

GeV and a constant

term of 0.2% (after subtraction of the noise term). The ECAL resolution is worse at

larger η compared to the central η region. A significant degradation in energy resolution

occurs in the 1.37 < |η| < 1.52 range where transition between the barrel and end-caps

occurs.


Stochastic Term

Electron Photon

η = 0.3 10.0% 10.2%

η = 1.1 15.1% 12.4%

η = 2.0 14.5% 12.1%

Table 2.4: Expected stochastic terms for the energy resolution of electrons and photonsat η = 0.3, η = 1.1 and η = 2.0.

HCAL Performance

As in the ECAL, the energy resolution of jets reconstructed in the combined calorimeter

system (both the ECAL and HCAL) can be expressed in a three parameter fit involving

stochastic, noise and constant terms. For central jets (0.2 < |η| < 0.4) the stochastic

term is ≈ 60%√

GeV, while the constant term is ≈ 3%. The noise term gives an

important contribution to the overall η-dependence of the jet resolution, increasing from

0.5 GeV to 1.5 GeV between the central barrel region and the end-cap region. This

increase in noise is due to the change from the low-noise tile calorimeter to the LAr

end-cap calorimeters which suffer from higher noise levels.

2.5 Muon System

Muons primarily lose energy through ionization. This, together with the muon lifetime,

means that muons will not be stopped in the ATLAS calorimeters (typically muons with

momenta above ∼ 3 GeV will pass through the calorimeters). In order to reconstruct

muons and measure their momenta, the ATLAS design incorporates a dedicated muon

spectrometer (see figure 2.7), located outside the hadronic calorimeters. This uses the

deflection power of a system of large superconducting air-core toroid magnets, and a

series of tracking chambers to detect and measure the momentum of charged particles

that have passed through the barrel or end-cap calorimeters. These tracking chambers

provide both trigger and precision hit information. In order to achieve a good momen-

tum resolution up to high muon momenta, a large magnetic field over a large distance is

desirable (the ID can provide good measurements for lower momenta tracks, but for mo-

menta & 100 GeV its momentum resolution becomes limited by the relatively small size


of the ID volume). It is anticipated that muons will be identified with momenta above

3 GeV, with precise momentum determination up to transverse momenta of ∼ 3 TeV.

The magnetic field for the muon spectrometer is provided by three air-core toroids

(one barrel toroid and two smaller end-cap toroids). Both the barrel and end-cap toroids

consist of eight “race-track” coils. The coils are made of an Al-stabilised Nb/Ti/Cu

conductor, which is cooled to 4.6 K during operation. The toroids generate an average

magnetic field of ∼ 0.5 T in the barrel (ranging from 0.15 T to 2.5 T), increasing to

∼ 1 T in the end-caps (ranging from 0.2 T to 3.5 T). Good magnetic field coverage is

provided up to |η| ∼ 2.6, however there are regions with low bending power, notably in

the transition region between barrel and end-cap toroids.

The field generated by the toroid magnet system is mainly in the φ-direction, there-

fore providing bending power in the R–z plane. The precision tracking chambers are

optimised to measure the coordinates of the track in the bending R–z plane. In the bar-

rel section the chambers are located parallel to the beam axis in three octagonal shells

at approximate radii of 5 m, 7.5 m and 10 m. In the end-caps, the chambers are located

perpendicular to the beam axis and form large wheels. Typically a muon propagating

out from the interaction point will pass through three muon stations, allowing three

precision measurements to be taken.

A combination of Monitored Drift Tubes (MDTs) and Cathode Strip Chambers

(CSCs) are used for the precision tracking. MDTs are used over most of the pseudo-

rapidity range except for higher pseudorapidities (2.0 < |η| < 2.7) where CSCs are used

for the inner layer. The particle fluxes and radiation levels are highest in this higher

pseudorapidity region, impacting on the muon reconstruction efficiency. Consequently,

the higher granularity CSCs are used in this region.

A requirement of the muon system is the capability to trigger on muon tracks. To

complement the precision tracking chambers, the muon system is instrumented with

a system of fast trigger chambers (the slower response time of the precision chambers

make them unsuitable for triggering). These are designed to return a trigger signal

within a few tens of nanoseconds of a charged particle passing. The trigger chambers

also measure both coordinates of the track, both in the bending and non-bending planes.

The trigger system has full φ coverage and covers the pseudorapidity range of |η| < 2.4,

using Resistive Plate Chambers (RPCs) in the barrel and Thin Gap Chambers (TGCs)

in the end-caps. These allow a trigger signal with a spread of 15 ns to 25 ns to be

delivered, within the trigger requirements for identifying a given bunch crossing.


Figure 2.7: The ATLAS muon system. The different muon chambers are labelled, alongwith the barrel and end-cap toroids of the muon magnet system.

2.5.1 Anticipated Muon Performance

The stand-alone tracks reconstructed by the muon spectrometer are reconstructed over

the range |η| < 2.7. For the region matching the geometrical acceptance of the ID

(|η| < 2.5), these stand-alone tracks are combined with ID tracks to give a combined

muon reconstruction. Combining tracks significantly improves the momentum resolu-

tion for low pT muons where the ID can provide the best measurement. At higher

pT, the muon spectrometer provides the best momentum measurement, allowing recon-

struction of muons with transverse momenta of up to 3 TeV. For low momenta tracks

(below 6 GeV) where muon tracks do not always reach the outer muon chambers, and

in regions where the geometrical acceptance of the muon spectrometer is reduced, the

stand-alone performance is improved by matching ID tracks to track segments in the

muon spectrometer. The fractional momentum resolution is expected to be ≈ 3% for

100 GeV muons and ≈ 10 % for 1 TeV muons. For |η| < 0.1 and 1.1 < |η| < 1.3 (the

transition region between barrel and end-cap where the middle muon stations will be

missing during initial data-taking) the performance is limited by gaps in the coverage of

the muon spectrometer. Some degradation of the performance can also be expected in

regions where support structures and the feet supporting the experiment are found.


2.6 Trigger

At design luminosity of 1034 cm-2s-1 ATLAS will experience a proton-proton interaction

rate of ∼ 1 GHz. The available technology and resources limit the rate of recording

event data to ∼ 200 Hz. Consequently, the trigger system is presented with the chal-

lenge of providing a rejection factor of ∼ 5× 106 against minimum-bias processes while

efficiently recording events corresponding to the new physics processes sought by AT-

LAS. To achieve this goal, the ATLAS trigger system has been designed using a Level-1

(L1) trigger and subsequent high-level trigger (including a Level-2 (L2) trigger and an

event filter (EF)) to reduce the data-taking rate to an acceptable level. Each trigger

level refines the trigger decision made at the previous level.

The L1 trigger uses a subset of the detector information to make a decision in less

than 2.5 µs, reducing the total event rate to 70 kHz (upgradeable to 100 kHz). The L1

trigger forms Regions of Interest (RoIs) from regions within the detector where it has

selected interesting features. The η and φ positions of these RoIs are passed on to the

high-level trigger. Whilst the L1 trigger decision is being formed, the event information

for all the channels is stored in memory pipelines contained in on-detector electronics.

The L2 and EF use an increased amount of detector information in order to make their

refined decisions. The full granularity and precision on all available detector information

in the RoI is used to reduce the event rate to ∼ 3.5 kHz after L2, processing each event

in ∼ 10 ms. The final event rate is reduced to ∼ 200 Hz by the EF. Events passing the

EF are then written to permanent storage with a final event size of ∼ 1.5 MByte.

Chapter 3

SCT Assembly Testing

The ATLAS semiconductor Tracker (SCT) was introduced in chapter 2. This chapter

describes the SCT in more detail, focusing on the SCT barrels and barrel modules and

also discusses the data acquisition (DAQ) system and its use in performance tests during

the macro-assembly of the SCT barrels.

The SCT is geometrically divided into three regions, a barrel region and two end-

caps. The barrel region is made up of four concentric cylindrical layers termed barrels

3 (the innermost layer), 4, 5 and 6 (the outermost layer). Each barrel layer is tiled

with a number of modules (the details of which are described in section 3.2). Rows of

12 modules are mounted parallel to the axis of the barrel cylinder on each barrel, the

number of rows determined by the barrel radius. The modules in a given row are labelled

Z−6 to Z+6 (as shown in figure 3.1), with the two halves of the barrel named Z− and

Z+. The modules are mounted such that they overlap in coverage in both the z- and

rφ-directions, with a tilt angle of ∼ 11◦ allowing overlap between adjacent rows. The

geometry of the barrels and the numbers of modules on each layer are summarised in

table 3.1. The barrel support-structures are made of lightweight carbon-fibre reinforced

plastic, and support both the modules and the services (low-mass tapes (LMTs) to

distribute power, cooling loops and optical data links). The modules were mounted

onto the barrel carbon-fibre support-structures during a macro-assembly phase, with

the completed barrels later shipped to CERN for integration with the rest of the Inner

Detector.

38

SCT Assembly Testing 39

Barrel Number Radius / mm Length / mm Rows Modules

Barrel 3 299 1492 32 384

Barrel 4 371 1492 40 480

Barrel 5 443 1492 48 576

Barrel 6 514 1492 56 672

Table 3.1: The barrel radius and number of modules for each of the four SCT barrellayers.

−3 −1 +1 +2−6 −5 −4 −2 +3 +4 +5 +6

Z− Z+

Figure 3.1: A diagram showing the module position numbering convention for a row ofmodules mounted on an SCT barrel. A single row of 12 modules is shown. Rows aredefined parallel to the z-axis. The barrel is separated into two halves, labelled Z− andZ+.

3.1 Semiconductor detectors

Semiconductors have a small energy gap between the occupied ‘valence band’ energy

levels and the next available energy levels (in the ‘conduction band’). In silicon the

energy required to promote an electron from the valence band to the conduction band

is 3.6 eV1. The properties of semiconductors can be controlled through the process of

doping, whereby group V or group III atoms are introduced to the semiconductor (silicon

in this case), displacing silicon atoms from some of the atomic sites in the lattice. The

addition of group V atoms (termed ‘donors’) contribute extra electrons at energy levels

just below the conduction band, producing an ‘n-type’ semiconductor. Dopants from

group III atoms (termed ‘acceptors’) introduce an empty energy level just above the

valence band which can readily be filled by a valence electron to introduce a hole. Such

semiconductors are known as ‘p-type’.

Bringing these two types of doped semiconductor together results in a p-n junction. A

1This is larger than the actual band gap in silicon which, as an indirect band gap semiconductor,also requires an associated phonon excitation to conserve momentum when making a transition.


gradient in the charge-carrier density across the interface causes the diffusion of electrons

and holes into the p- and n-type regions respectively. The diffusion of electrons leaves

behind fixed positively-charged donor ions, whereas the diffusion of holes leaves behind

fixed negatively-charged acceptor ions, resulting in regions of net charge either side of

the junction with no mobile charge carriers (a region known as the depletion region).

At equilibrium the potential difference across this region is called the ‘contact potential’

and its direction is such that it acts to prevent further diffusion of electrons into the p-

type region and holes into the n-type region. Any electron-hole pairs created inside this

depletion region will be swept out of the depletion region by the electric field associated

to the contact potential, giving the basis of an electric signal.

When electrons or holes are liberated in a semiconductor they will migrate (either

spontaneously or under the influence of an applied electric field) until they either re-

combine or are collected at an electrode. In the interests of efficient particle detection,

it is important to prevent recombination or other mechanisms of carrier loss2 as they

will reduce the measured pulse height. Consequently, it is important to have a short

enough collection time for carriers such that it is sufficiently less than the recombination

lifetime.

So far, a junction with no applied external voltage has been considered. Such a junc-

tion will function as a particle detector [22], however the performance of such a device

can be significantly improved by applying a reverse bias. An unbiased junction has a

low contact potential and therefore any introduced charge (such as the ionization from

a passing charged particle) will not move very quickly under the effect of the contact

potential alone. Consequently charge carriers will be readily lost to recombination and

trapping. By applying an external voltage, so as to reverse bias the junction, the po-

tential difference across the junction is increased and the width of the depletion region

increases either side of the junction. The reverse biased p-n provides a more effective

detector as charge carriers created within the larger depletion region can be quickly and

efficiently collected. A schematic diagram of a silicon microstrip detector is shown in

figure 3.2.

The properties of silicon after irradiation are very important in a silicon detector,

particularly at the LHC where, for 10 years of running, the SCT needs to withstand an

2The presence of ‘deep impurities’ (unlike the deliberate dopant impurities) can act as recombinationcentres that can capture both electrons and holes allowing them to recombine. Other defects in crystalscan cause charge carriers to become trapped, immobilising the carrier for a period of time long enoughto prevent the carrier contributing to the measured pulse.


� � ��

Al

charged particle

holes

electons

��

��

��P P P

n−type

Al Electrode 80 um

22 um

Si O2

N+

E−field

285 um

Figure 3.2: A schematic diagram showing a cross-section through a silicon microstripdetector. Strips of p-type semiconductor are formed on a bulk n-type semiconductor.The dimensions shown correspond to those used in the ATLAS SCT barrel sensors.Diagram taken from [23].

expected fluence3 of ∼ 2× 1014 (1 MeV neq) cm−2. The irradiation of a lightly doped,

n-type silicon can change the properties such that, with time, it type-inverts, becoming

increasingly p-type. This reduces the contact potential across the junction, requiring an

increased bias voltage to maintain detector performance. The sensors used in the SCT

barrel modules are of type (p+, n, n+)4 (as shown in figure 3.2), and after irradiation

can be expected to undergo type inversion such that they appear (p+, p, n+). Radi-

ation damage can increase leakage currents in the silicon, resulting in increased noise

levels. The leakage currents dissipate heat into the detector, which in turn can induce

further leakage currents5, leading to the threat of thermal run-away. Irradiated silicon

is also susceptible to a detrimental process known as “reverse annealing”. The effects of

radiation damage are strongly temperature-dependent, and can be controlled by main-

taining the sensors at a low temperature. In ATLAS, the SCT sensors will be kept at a

temperature of ∼ − 7 ◦C throughout their operation.

3The dose quoted here is normalized to that of 1 MeV neutrons.4p+ and n+ denote heavily doped p-type and n-type semiconductors respectively.5Leakage currents can be induced through thermally produced electron-hole pairs


Figure 3.3: A labelled diagram of an SCT barrel module. The length of the module is128 mm. Figure taken from [24]

3.2 SCT barrel module design

An SCT barrel module [24] (shown in figures 3.3 and 3.4) incorporates silicon wafers,

comprising p-n junctions under reverse bias, as the sensor element. The electron-hole

pairs liberated by passing charged-particles are swept towards the electrodes at the

opposite sides of the junction. These p-n junctions are produced in strips on the surface

of the silicon wafers (285 µm thick) using a p-strip on n-bulk design, with a strip pitch

of 80 µm. The wafers for all barrel modules are identical, with a rectangular geometry

(64 mm by 63.6 mm) and comprising 768 strips [25]. Each module is made of four wafers

in two layers (each layer being formed from two wafers connected end-to-end). The two

layers are offset by a small stereo angle of 40 mrad in order to give a measurement in the

z-direction (given that one layer is aligned along the z-direction in order to give precise

measurements in the R-φ direction). The pair of sensors on each barrel module allow a

nominal position resolution of 17 µm in the R-φ direction and 580 µm in the z-direction.

The strips are read out by application specific integrated circuits (ASICs) known as

ABCD3TAs [26]. These ‘front-end’ ASICs each read out 128 channels, so 12 chips are

used to read out all of the channels on a SCT module. The 12 ASICs are mounted on

a wrap-around electronic hybrid, each side of the hybrid holding six ASICs (the six on

the top side termed ‘link-0’ and the six on the bottom side termed ‘link-1’, in reference


Figure 3.4: A photograph showing several SCT barrel modules as mounted on a barrelsupport-structure.

to their corresponding optical read-out link). Each side has one master chip that is

responsible for transmitting all the data from that side off the module. In the event of

a chip failure, it can be bypassed so that the remaining data can be read out. Should a

master chip fail then the remaining chips on that link can be read out through the other

link, giving a level of redundancy.

A significant feature of the ABCD3TA chip design is the use of a binary readout.

This means that the only pulse-height information transmitted by the ASICs is a single

bit per channel denoting that the pulse was above a set threshold. The discriminator

threshold is a configurable parameter on the ABCD3TA. Ensuring that the calibration

of this threshold is correct is very important as no further pulse-height information is

transmitted off the module, and cannot be recovered later. The discriminator should be

set at a level that ensures a good efficiency at registering genuine hits whilst maintaining

a low noise occupancy level. The module design specifications require that the noise

occupancy per strip is < 5× 10−4 with an efficiency > 99 %.

A charged particle passing through the silicon detector deposits a small amount of

charge according to a Landau distribution [27]. Imperfections in the charge collection and

other sources of noise will adjust the shape of this distribution. At the stage where the

measured collected charge is seen by the threshold discrimination circuit, the distribution

can instead be described by the improved distribution given by a Landau convolved with


Charge (fC)0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

Figure 3.5: A diagram showing the deposited charge distribution of a MIP (solid line).Also shown is the noise charge distribution (dashed line) and the average occupancy asa function of threshold (thick line). Taken from [28].

a Gaussian. The same Gaussian noise can result in a fake hit being registered without the

passing of a charged particle, contributing to the noise occupancy. Figure 3.5 shows the

expected Gaussian-broadened charge deposition for a minimally ionized particle (MIP),

with a peak value of ∼ 3 fC. Also shown is the noise distribution (a Gaussian of width

∼ 0.15 fC). It can be seen that a 1.0 fC threshold is appropriate in removing noise hits

whilst maintaining a high signal efficiency.

Selecting a threshold to satisfy these requirements is fairly straight forward before the

modules are irradiated, but becomes more difficult with increased radiation exposure.

Each front-end ASIC has an 8-bit digital-to-analogue converter (DAC) which is used to

control the threshold globally across the chip. To compensate for any channel-to-channel

threshold variations, each channel has a further 4-bit DAC (known as a ‘TrimDAC’)

which has four different settings, allowing it to operate in different ranges (known as

‘trim ranges’). These different ranges allow the ASIC to compensate for the increased

channel-to-channel variations that will occur due to radiation damage over the module’s

lifetime. The binary hit data are required to be kept on the front-end chips long enough

for an ATLAS L1 trigger to be received. To accomplish this, the hit pattern is held in

a pipeline memory, 132 cells deep.

Optical links [29] are used to both read out the modules, and to receive trigger, timing

and control (TTC) information. The barrel on-detector optoelectronic components are

located in an opto-package on the carbon fibre brackets used to attach the modules to


the barrel structure. In total, each module has three optical links, two of which act as

readout links, and one of which is used to receive TTC signals. As already mentioned,

the two readout links provide a redundancy mode in case of a failure along one of the

links. Redundancy is also built into the TTC link whereby an electrical control line can

be set to receive a copy of the TTC signal from a neighbouring module in case of a TTC

signal failure.

Data leaving a module are passed, via a VDC6, to a VCSEL (Vertical Cavity Surface

Emitting Laser) within the opto-package. This VCSEL produces the optical signal that

is transmitted off-detector. Optical signals arriving at the opto-package are received by

a p-i-n diode. Here the signal is converted from optical to electrical form, and passed to

the DORIC4A ASIC which decodes the TTC data for further transmission to the front-

end ASICs. The connections between the opto-packages and the off-detector electronics

are through optical fibres. The fibres transmitting TTC commands to the modules are

called TX fibres, and those receiving data from the modules are known as RX fibres. To

ensure that data are successfully transmitted across the optical links, RX and TX DAC

thresholds are set at optimal values to ensure a sufficiently small (< 10−9) bit error rate.

3.3 Data Acquisition

The SCT Data Acquisition (DAQ) system [30] is used to configure the module ASICs,

communicate trigger information and transfer data from the front-end chips on each

module. The DAQ system is also used in calibrating the detector through a series

of functional tests that can test the operation of the modules and optimise the module

configurations. The SCT DAQ readout hardware consists of several different components

(see figure 3.6), including:

Read Out Drivers (RODs) — RODs provide the main module configuration, control

and data handling.

Back Of Crate (BOC) boards — These control the input and output to and from

the front-end modules (via TX and RX optical fibres) for the RODs and also

provide a link to the central ATLAS DAQ. Each ROD has a complementary BOC

board, and services 48 modules.

6The VCSEL Driver Chip (VDC) is a custom ASIC used to provide the required signal to drive theVCSEL


ROD CrateBusy

RODCrate

Controller

(RCC)

TTCInterfaceModule

(TIM)

Read OutDriver

(ROD)

Back OfCrate

(BOC)

VME

o

TTC(optical)

x16/crate x16/crate

Backplane Connections

o

Clock andControl (optical)48/BOC

o96/BOC

Data (optical)FrontEnd

Modules

o

Formatted data(optical)

Slink(1/BOC)

ROS(ATLASCentralDAQ)

ROD Busy

40 MHz Clock

ATLASTrigger System

FastCommands

And Serialised IDs

Figure 3.6: A block diagram showing the components of the SCT data acquisitionhardware. The main connections between the components are also shown. Figure takenfrom [30].

TTC Interface Module (TIM) — The TIM is used to accept trigger, timing and

control (TTC) signals that are received from ATLAS, and distribute them on to

the RODs/BOCs. The TIM can also be used to generate TTC information itself.

ROD Crate Controller (RCC) — The RCC is a rack mounted Linux PC that con-

figures and controls the functions of the other readout components within a crate.

Each crate contains one RCC, one TIM and up to 16 ROD/BOC pairs (reading

out up to 768 modules).

The SCT has two main modes of operation (i) physics data-taking mode, and (ii)

calibration mode. In physics data-taking mode, the TIM receives triggers from the

central ATLAS trigger system. They are then passed on to each of the RODs. Each

ROD communicates these signals through its BOC and on to the front-end modules. The

BOC receives the corresponding hit information from the modules and data formatting

takes place on the ROD. The data are passed from the ROD (through the BOC again)

and into the main ATLAS DAQ system.


In calibration mode, the SCT DAQ can operate without communication to the central

DAQ and without receiving triggers from the ATLAS trigger system. Instead, the TIM

is used to generate the TTC signal, and triggers can either be sent from the RODs or

from the TIM (if synchronization between the triggers is required). The ROD is used to

sample and histogram the data, with the resultant histograms passed through the RCC

and on to PC servers for analysis.

3.4 Macro-Assembly and DAQ Testing

Macro-assembly of the SCT barrels took place at Oxford (the macro-assembly site)

between June 2004 and August 2005. During this period, SCT barrel modules were

systematically mounted onto the barrel support-structures. This process was carried

out using custom robots [31] as the space between modules was very restricted (approx-

imately 1.6 mm in the region where adjacent modules overlap) and required that the

modules followed a very precise path as they were mounted, in order to prevent damage

to neighbouring modules.

An important part of the macro-assembly process involved running a series of DAQ

tests to check that the modules were successfully mounted, to measure their noise occu-

pancy, to confirm any known problem channels and to check for any new defects that

may have been introduced during the assembly process. A more detailed discussion of

the testing procedure and descriptions of the individual tests can be found in [30, 32–34].

Typically these tests were run at suitable gaps in the module mounting schedule where

∼ 24 newly mounted modules would be tested. The regular testing was carried out

under “warm” conditions, where a C4F10 cooling system was used and the temperature

on the modules (measured on the hybrids when powered) would be ∼ 28 ◦C. When the

module-mounting was completed for a barrel, the entire barrel was again tested7. At

this a point the assembly schedule allowed for a limited period of colder testing where a

C3F8 cooling system (similar to the final cooling system used in ATLAS) was used and

the modules were tested at temperatures of ∼ 12 ◦C (when powered). During this cold-

testing period, the main purpose of the testing was to identify any gross errors affecting

modules such that they may be corrected before the completed barrel was shipped to

CERN (the macro-assembly site being better equipped for the removal and remounting

of modules).

7Schedule constraints meant that barrel 5 was shipped to CERN before a complete test was madeat the macro-assembly site. A full series of tests were performed on reception at CERN.


The DAQ testing procedure (using the final DAQ electronics and power supplies)

involved several different tests designed to check different aspects of the DAQ module

readout. First, a series of basic tests was run on the modules to check the lines of

communication with the ASICs. These tests checked that the modules could see the

clock signal, receive configuration signals and be put into data-taking mode. The ability

to respond to a “Hard Reset” signal was also tested. An RX threshold test was run

to establish a safe threshold whereby the optical signal could be reliably converted

into electrical form by the data receiver on the BOC. Having established successful

communication with the modules, a series of digital tests were then run in order to

check for stuck pipelines (resulting in channels being “stuck on” or “stuck off” causing

excess noise occupancy or inefficiency respectively), for chip-counter faults and to test

that ASICs could be bypassed (a redundancy feature of the module design allows that in

the event of a chip failure, the data from the remaining chips can be read out, bypassing

the faulty chip).

The testing procedure then incorporated a series of tests aimed at calibrating the

front-end electronics. These calibration tests would typically make occupancy mea-

surements whilst varying a chip parameter (such as the threshold). Each channel has a

capacitor that can be used to inject test charges. Threshold scans performed for different

known injected charges were used to calibrate the discriminator threshold (allowing the

threshold to be calculated in units of input charge). Further scans were used to optimise

the TrimDAC settings to minimise channel-to-channel variations in the threshold.

Two of the DAQ tests that were carried out during barrel assembly were the NoiseOc-

cupancy and the related SynchTriggerNoise tests. In addition to participating in the

running of DAQ test shifts, both during the module-mounting process and during tests

on the full barrels, the author was responsible for the initial analysis of the SynchTrig-

gerNoise data taken during the cold testing at the macro-assembly site. The cold testing

of the barrels at the macro-assembly site provided the first data from running the com-

pleted barrels under cold conditions, an important first check of the performance of the

mounted modules. This is illustrated by the analysis of the first SynchTriggerNoise data

for barrels 3 and 6, presented in section 3.5.

The NoiseOccupancy test is a threshold scan without any injected charge. For each

threshold the noise occupancy is determined. The occupancy due to noise at 1 fC is

recorded as a reference point. The SynchTriggerNoise is designed to test the noise

occupancy when triggers are simultaneously sent to all configured modules. Like the

NoiseOccupancy test, the noise occupancy is measured with no injected charge, however


triggers are now sent synchronously, by the TIM to the modules, at a high trigger

rate (up to 100 kHz). The purpose of the SynchTriggerNoise test is to look for signs

of elevated noise occupancy when sending triggers to multiple modules synchronously,

checking for any correlated noise effects that would not show up when testing modules

individually or in smaller groups.

3.5 Initial SynchTriggerNoise Analysis

The analysis of the data from SynchTriggerNoise tests carried out during the macro-

assembly cold testing of barrels 3 and 6 served two main purposes:

i. to search for signs of any correlated noise effects that are present when running a

large number of modules with high-rate synchronous triggers

ii. to identify any gross problems with modules or any defects and to provide a cross-

check with the other DAQ tests

For a given module, the outputted raw data from the SynchTriggerNoise test contains

histograms (produced on the ROD) giving the number of hits for each of the module’s

1536 channels as a function of time (in bins of 1 s). The number of triggers per time bin,

the number of time bins and the nominal threshold can be adjusted. By knowing the

rate of triggers sent to the modules and the histogramming factor (the histogramming

code allowed for only 1 in every 15 triggers to be histogrammed), the channel occupancy

is given by:

Channel Occupancy =No. Hits on Channel

No. Triggers per Time Bin×No. Time Bins/15(3.1)

During the macro-assembly testing, an error in the SynchTriggerNoise test caused

fewer triggers to be sent to the modules than were requested. Tests requesting 1× 106

triggers per second actually sent only 16960 per second, where tests requesting 2× 105

triggers per second actually sent 3392 per second8. The following results have been cor-

rected accordingly. This lower trigger rate was not ideal for the purpose of testing for

8The TIM was configured to send a 16-bit number rather than the 32-bit number that the SynchTrig-gerNoise test requested. Consequently the 32-bit number was truncated resulting in fewer triggers beingsent than were requested. This was later corrected.


any differences associated with sending synchronous triggers compared to sending asyn-

chronous triggers as such differences are expected to be more significant when running

at high trigger rates.

3.5.1 Barrel 3 SynchTriggerNoise Analysis

Two SynchTriggerNoise tests were performed on the first barrel to be completed, barrel

3, during cold testing (runs 2177.5 and 2177.6). The two tests were performed for

different numbers of triggers and thresholds. Run 2177.5 sent 3392 triggers per time bin

with a threshold set at 0.9 fC. Run 2177.6 had a threshold of 1.0 fC with 16960 triggers

per time bin. One ROD failed during these tests, resulting in the loss of data from 48

modules (out of a total of 384 modules on barrel 3). A further module was removed

from the configuration due to a fault and was later replaced.

Considering data from run 2177.6 at a nominal threshold of 1.0 fC, figure 3.7 shows

the mean channel occupancy per module, and also the mean channel occupancy over

link-0 and link-1 of each module. It can be seen that the mean channel occupancies for

all modules are within the design specification (< 5× 10−4 at a threshold of 1.0 fC) with

the majority of modules exhibiting mean channel occupancies of less than 5× 10−5. The

highest mean channel occupancy is 1.16× 10−4. One can see that the mean occupancy

is typically higher on link-1 than on link-0 of the modules (this is an intrinsic property

of the modules). During the analysis of these data, individual chips with either high

noise levels or zero-noise were identified as these could be indications of problems with a

given module. Figure 3.8 shows the mean channel occupancy per module mapped over

the module position on the barrel. The positions of the 49 modules for which no data

were taken can clearly be seen.

To investigate whether the sending of synchronous triggers caused any global in-

crease in noise levels, the SynchTriggerNoise occupancies were compared to those from a

NoiseOccupancy test (with asynchronous triggers). Figure 3.9 shows the mean channel

occupancy, calculated from the NoiseOccupancy test data (for a threshold of 1.0 fC),

as a function of position on the barrel. Comparing this with figure 3.8, it can be seen

that the pattern of noisy modules is very similar, showing no signs of correlations in

the SynchTriggerNoise data that weren’t present in the NoiseOccupancy test. To get a

qualitative measure of the change in noise occupancy when sending synchronous triggers,

the ratio F is defined as


Mean channel occupancy0 0.02 0.04 0.06 0.08 0.1 0.12

-310×

Entri

es

1

10

Entries 335Mean 1.405e-05RMS 1.409e-05

Run 2177.6 at 1.0 fCModule Mean

(a) Mean channel occupancy over entire module

Mean channel occupancy0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-310×

Entri

es

1

10


Run 2177.6 at 1.0 fCLink-0 Mean

(b) Mean channel occupancy over link-0

Mean channel occupancy0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-310×

Entri

es

1

10


Run 2177.6 at 1.0 fCLink-1 Mean

(c) Mean channel occupancy over link-1

Figure 3.7: Mean channel occupancy per module over (a) the entire module, (b) link-0and (c) link-1. The data correspond to a SynchTriggerNoise test run on barrel 3 with anominal threshold of 1.0 fC (run 2177.6).


Z-position

Z-6

Z-5

Z-4

Z-3

Z-2

Z-1

Z+1

Z+2

Z+3

Z+4

Z+5

Z+6

Row

num

ber

0

5

10

15

20

25

30

Entries 335

Nois

e O

ccup

ancy

0

0.02

0.04

0.06

0.08

0.1

-310×Entries 335Barrel 3 : SynchTriggerNoise Test Results at 1.0fC

Figure 3.8: Mean channel occupancy per module as a function of barrel position for aSynchTriggerNoise test at 1.0 fC for barrel 3 (run 2177.6). The azimuthal rows of thecylindrical barrel (denoted by the row number) are shown unfolded and labelled by therelevant row number.


F =SynchTriggerNoise Occupancy at 1.0 fC

NoiseOccupancy Occupancy at 1.0 fC(3.2)

This ratio allows one to identify any significant changes in occupancy between the

two runs. It should be noted that changes in the run conditions between the two sets

of tests, such as the module temperatures and the time the modules had been powered,

can be expected to have an impact on the relative noise occupancy values.

Figure 3.10 shows the distribution of F for all modules on barrel 3. This shows a

narrow distribution with a mean of 1.03 but with a small number of isolated modules

displaying occupancies up to 4.5 times greater in the SynchTriggerNoise test than in

the unsynchronised NoiseOccupancy test. Figure 3.11 shows how F varies with module

position on the barrel, with only four modules seen to have significant differences of

F > 2. On inspection of these modules, one module (row 29, Z−6) was identified as

having a “noise slope” defect (a rare condition in which the module shows an increasing

noise occupancy over the last chips on link-1)[33]. This condition was found to be cured

when the neighbouring module was set to receive the redundant TX signal, resulting in

good noise performance. Each of the other three modules had a single bad channel with

high noise occupancy (two modules had a stuck pipeline defect) and weren’t seen as

significant problems. No large scale correlation between module position and increased

noise can be seen.

A second SynchTriggerNoise test was carried out on barrel 3. Run 2177.5 sent 3392

triggers per time bin with a nominal threshold of 0.9 fC. Since run 2177.5 was carried

out at a lower threshold than run 2177.6, one can expect a greater noise occupancy.

This is seen in the plot of mean channel occupancy per module for run 2177.5, shown

in figure 3.12(a). At this threshold, almost all modules have an occupancy less than

2.5× 10−4, with a small number of modules having higher occupancies (up to 4.2× 10−4).

Despite the lower threshold, this is still within the design specifications (at 1.0 fC).

Figure 3.12(b) shows a map of the mean channel occupancy per module with position

on the barrel. Comparing this with the equivalent plot for 2177.6 (figure 3.8), one can

see that the pattern of relatively noisy modules is very similar to the pattern for run

2177.6 at the higher threshold. Again, no significant correlation is seen.


Z-position

Z-6

Z-5

Z-4

Z-3

Z-2

Z-1

Z+1

Z+2

Z+3

Z+4

Z+5

Z+6

Row

num

ber

0

5

10

15

20

25

30

Entries 383

Nois

e O

ccup

ancy

0

0.02

0.04

0.06

0.08

0.1

-310×Entries 383Barrel 3 : NoiseOccupancy Test Results at 1.0fC

Figure 3.9: Mean channel occupancy per module as a function of position on the barrelfor the NoiseOccupancy test. This test sends non-synchronised triggers and recordsthe occupancy at a nominal threshold of 1.0 fC. The azimuthal rows of the cylindricalbarrel (denoted by the row number) are shown unfolded and labelled by the relevantrow number. All RODs were operational during this run.

Entries 335Mean 1.028RMS 0.2456

Fractional Noise change, F0.5 1 1.5 2 2.5 3 3.5 4 4.5

Entri

es

1

10

210 Entries 335Mean 1.028RMS 0.2456

Barrel 3

Figure 3.10: Occupancy ratio, F, comparing the SynchTriggerNoise test (synchronisedtriggers) with the NoiseOccupancy test (non-synchronised triggers). The mean value ofthe occupancy ratio 〈F 〉 = 1.028.


Z-position

Z-6

Z-5

Z-4

Z-3

Z-2

Z-1

Z+1

Z+2

Z+3

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Figure 3.11: The variation of the noise occupancy ratio, F , with position on barrel 3. Asmall number of modules show a significant increase in noise occupancy.


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Figure 3.12: Mean channel occupancies for modules on barrel 3 for a SynchTriggerNoisetest (run 2177.5 with a threshold of 0.9 fC).


3.5.2 Barrel 6 SynchTriggerNoise Analysis

As with the barrel 3 cold tests, two runs of the SynchTriggerNoise test were performed

on barrel 6, the second barrel to be completed, one test at 1.0 fC with 16960 triggers per

time bin (run 5913.0), and one at 0.9 fC with 3392 triggers per time bin (run 5913.1).

Unfortunately there were readout errors in the data from modules on the Z− half of the

barrel (see figure 3.13). The impact on run 5913.0 involved all modules on Z− failing to

read out any data for 41 bins (out of 51). For run 5913.1 only the first data bin (out of

21) was lost. The very tight schedule pressure prevented repeat tests being run during

the cold-testing period at the macro-assembly site. Despite the data errors for the Z−half of the barrel, the data for runs 5913.0 and 5913.1 were analysed to check for any

chip or channel errors.

During the cold tests of barrel 6, one module lost bias on link-1 (with serial number

20220330200858 at row 7, Z+5) resulting in very high occupancy on this link. This

was clearly observed in the SynchTriggerNoise data (see figure 3.14). This module

was replaced after cold testing and consequently has been removed from the following

analysis. A further seven modules were left out of the test due to problems configuring

them during the limited time available for cold testing.

The mean channel occupancy per module for run 5913.0 is shown in figure 3.15(a).

The mean occupancy over all modules is 2.51× 10−5, within the design specifications at

1.0 fC. However nine modules are seen to have mean occupancies greater than 5× 10−4.

Of these modules, seven had mean occupancies of ∼ 6–6.7× 10−4 due in each case to

a single channel with very high noise levels, and one module with mean occupancy of

∼ 1.2× 10−3 as a result of two channels with very high noise levels. The occupancy

for these modules would be significantly reduced by masking off these noisy channels.

A further module had a noise occupancy of ∼ 7× 10−4 and was found to have a noise

slope resulting in excessive noise on the last two chips on link-1. Figure 3.15(b) shows

the corresponding map of mean channel occupancy per module as a function of module

position. No correlations between noise occupancy levels and position are seen

The corresponding occupancy values for run 5913.1 at the lower threshold of 0.9 fC

are shown in figure 3.16. The higher overall mean occupancy of 7.3× 10−5 is expected

due to the lower threshold. Again, no large scale correlation of occupancy with position

on the barrel is observed.


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Figure 3.13: Examples of errors in the raw data for runs 5913.0 and 5913.1 for moduleson Z−. The histograms show the number of hits registered on a given channel as afunction of time, with the divisions between ASICs shown by dashed lines. For run5913.0 at 1.0 fC, all modules on Z− lost data from the 10th bin onward. For run 5913.1at 0.9 fC only the first bin for modules on Z− was lost.


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Figure 3.14: Module 20220330200358 lost bias on one half of the module during the coldtests and was later replaced. The high noise occupancy can clearly be seen on link-1 ofthis module.

3.6 Summary

The initial SynchTriggerNoise test data taken during cold testing of barrels 3 and 6 of

the SCT, before their shipment to CERN, have been analysed. The analysis of barrel 3

data showed no large scale increase in noise occupancy levels when sending synchronous

triggers, compared to non-synchronous triggers. Overall, the noise occupancy levels on

barrel 3 were within the design specifications, and no signs of correlated noise effects

were seen.

The SynchTriggerNoise raw data for barrel 6 was affected by readout errors, meaning

that there was not a complete set of data for the whole barrel. The analysed data show

no obvious correlations of noise occupancy with position on the barrel. A small number

of modules had higher noise occupancies than the specifications, due to individual noisy

channels and in one case excessive noise on a single chip. Masking off the defective

channels would improve the mean module occupancy in these cases. Overall, noise

occupancy levels are seen to be within design specifications and no large scale correlations

of noise occupancy due to synchronous triggers were seen.

The analysis of these initial data demonstrated the use of DAQ tests in detecting

problem channels and module defects, along with module calibration. With the success-

ful completion of the macro-assembly phase, the results of the DAQ tests were able to


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confirm that more than 99.7 % of the 3.2 million channels of the SCT barrel were fully

functional [30].

Following the completion of the macro-assembly and single-barrel testing of the four

SCT barrels, the barrels were assembled together and implanted in a thermal enclosure9

before being successfully inserted into the TRT barrel. The combined SCT and TRT

underwent testing including noise and cosmic-ray tests (testing the SCT when running in

physics mode as well as in calibration mode). The SCT barrel noise performance when

running in conjunction with the TRT was within the design specification [35]. The

combined SCT and TRT barrel was later lowered into the ATLAS cavern and installed

inside the detector.

9The thermal enclosure provides thermal insulation between the SCT (operating at ∼ − 7 ◦C) andTRT (operating at ∼ + 25 ◦C), contains a dry-nitrogen atmosphere to avoid condensation and acts asan electrical shield for the SCT.

Chapter 4

Tau reconstruction and fast simulation

in ATLAS

4.1 ATLAS Software

The ATLAS offline software has been designed to process the raw data from events

delivered by the ATLAS trigger and data acquisition systems, supplying processed results

to physicists and providing tools to perform analysis. Along with this, the offline software

also incorporates simulation tools allowing the software to be tested against controlled

physics processes produced by Monte Carlo event generators. The Athena [36] software

framework (based on the Gaudi [37] framework) provides a modular structure to contain

the many separate algorithms that make up the ATLAS offline software, along with

providing common services and communication between different components. Athena

algorithms are controlled and configured using Python scripts known as jobOptions.

4.1.1 Monte Carlo Generators and Event Simulation

Monte Carlo event generators are essential tools used to model the complex physics

processes involved in proton-proton interactions at the LHC. These Monte Carlo events

can then be passed through simulations of the ATLAS detector in order to replicate real

data as closely as possible. Simulations of Monte Carlo generated events can be used to

develop analysis strategies, to optimise and validate the performance of reconstruction

algorithms, and to relate experimentally measured variables to an underlying theory

63

Tau reconstruction and fast simulation in ATLAS 64

being investigated.

The main ATLAS simulation is based on the GEANT4 [38] simulation package.

This simulation (commonly described as “full simulation”) incorporates a very detailed

description of the ATLAS detector geometry and material distribution. The propagation

of particles through the detector is modelled, and hits in the sensitive detector elements

are registered, giving a record of where particles traversed the detector and the amount

of energy deposited. These ‘hits’ are then passed through a digitization step, producing

Raw Data Objects (RDOs). These RDOs are in the equivalent format to the real detector

output, and can then be passed onto the reconstruction software.

One of the limits of the full simulation is the time needed to simulate an event.

This typically takes several minutes per event, which when considering the statistics

required for many backgrounds at the LHC, presents an impossible task for the full

simulation alone. In the case of signals involving hadronically decaying τ -leptons, the

overwhelming cross-section from QCD dijet events is very restrictive in the levels of

background simulations that can be run.

The solution is to complement the full detector simulation with fast simulation tools

that aim to to use quicker, more approximate approaches to simulate events on a much

faster timescale. Such fast simulation tools allow for quick and approximate studies of

different physics models whilst also offering a practical way to perform studies requiring

very large samples. The longstanding ATLFAST package [39] is one such fast simula-

tion tool, and has been used in many studies in ATLAS. ATLFAST and its workings

are discussed in more detail in section 4.3. Recently, an extension to ATLFAST has

been developed (commonly known as ATLFAST-II [40]) which makes use of a shower

parametrization to provide a fast simulation of the ATLAS calorimeter that is detailed

enough to be used in conjunction with the full ATLAS reconstruction software. This of-

fers an intermediate level simulation that is slower than ATLFAST yet is still significantly

quicker than the full simulation. These different levels of simulation provide ATLAS with

the tools needed to perform Monte Carlo based analyses, with combinations of full and

fast simulations being used to allow both very detailed and high-statistics studies. Fast

simulation is of particular relevance to this thesis with chapters 5 and 6 discussing work

done in the development of parametrizations of τ -identification performance for use in

ATLFAST.


4.1.2 Reconstruction Algorithms

The role of reconstruction is to take the raw event data and, from this, derive the

information needed for physics analysis. Inner Detector tracks, calorimeter clusters

and standalone muon-tracks are reconstructed in the different detector systems. This

information is then combined to identify the physics objects to be used in analyses and

to measure their properties as accurately as possible (e.g. momentum, energy, charge

etc). Such objects include muons, electrons, photons, jets, τ -jets, b-jets and EmissT . The

task of reconstructing these objects is performed by a series of dedicated algorithms

within the Athena framework. Having run reconstruction on the raw data, the output

data includes AOD (Analysis Object Data) files which are the starting point for many

physics analyses. Of particular relevance to this thesis is the reconstruction of τ -leptons.

The algorithms used in the reconstruction and identification of this species are discussed

in section 4.2.

4.2 Tau Reconstruction Algorithms

Due to the nature of the decays of τ -leptons (with either leptonic or hadronic decay

products and missing energy from neutrinos) they are the most difficult lepton species

to reconstruct and identify. Since it is not possible to discriminate between leptons from

τ -decays and other prompt leptons, the hadronic decay modes are used as τ -signatures.

ATLAS has developed specific algorithms to reconstruct the hadronic decays of τ -leptons

from a combination of calorimetric clusters and Inner Detector tracks. To separate true

τ -decays from fake ones reconstructed from QCD jets, the algorithms make use of the

characteristics of hadronic τ -decays such as the presence of a narrow isolated cluster, a

low track multiplicity and a relatively large electromagnetic component.

ATLAS takes two complementary approaches to τ -reconstruction with the develop-

ment of two off-line algorithms:

i. A calorimeter-seeded algorithm

ii. A track-seeded algorithm.

Details of each of these algorithms are presented in sections 4.2.1 and 4.2.2. Over the

period of time in which this thesis has been prepared, the τ -reconstruction algorithms


have gone through several stages of development. The following discussion covers the

main principles behind the two algorithms. Where specific details are mentioned, they

are relevant to the Athena version used in the ATLAS CSC production samples (release

12 of Athena). This is the version of the software run in the simulations used in the

physics study presented in chapter 7.

4.2.1 A calorimeter-seeded algorithm (taurec)

The calorimeter-seeded algorithm [41, 42] takes clusters from the calorimeter as seed

candidates for τ -reconstruction. The clusters are formed, using a sliding-window ap-

proach, from CaloTowers which are the sum of all calorimeter layers on a grid of

∆η×∆φ = 0.1× 2π/64. The resulting clusters are groups of 5× 5 CaloTowers. The

barycentre of the cluster determines its (η,φ) position, with the energy calculated from

the calorimeter cells within ∆R < 0.4 of the barycentre. The taurec algorithm is in-

clusive in that it does not provide significant background rejection in the reconstruction

phase (the only seed requirement being the presence of a calorimeter cluster). Only

clusters with ET > 15 GeV are considered for τ -identification. The algorithm takes

the cells forming the candidate cluster and calculates a series of quantities used for

τ -identification using the full granularity of the calorimeters.

The quantities used to identify τ -jets from fake candidates are as follows:

• Electromagnetic radius. Defining ETi as the transverse energy for the ith of n

electromagnetic calorimeter cells in the cluster, the electromagnetic radius is given

by:

Rem =

∑ni=1ETi

√(ηi − ηcluster)

2 + (φi − φcluster)2∑n

i=1ETi

(4.1)

The discrimination power of this variable comes from the typical small transverse

shower profile of the τ -lepton.

• Calorimeter isolation. Hadronic τ -decays are well collimated and hence a tight

isolation criterion can be used. The effectiveness of this variable will depend on

the event type and will be less effective in more active environments.

• Number of associated tracks. Hadronic τ -decays are typically associated with

one or three charged tracks. The number of charged tracks, found inside a cone


of ∆R < 0.3 from the cluster centre, are counted. Despite the expected track

distribution of one or three tracks, candidates with zero, two or four tracks can be

expected due to track reconstruction efficiencies, track quality requirements and

pT threshold1. Candidate τ -jets are required to have between 1 and 3 tracks to be

identified.

• The reconstructed charge.

• Number of hits in the η strip layer. Jets tend to have more hits than hadronic

τ -decays.

• Transverse energy width in the η-strip layer. The width of the cluster in the η-strip

layer of the electromagnetic calorimeter proves to be a powerful discriminator. It

is less effective at high pT where QCD-jets become more collimated due to the

higher boost. The transverse energy width is defined as follows:

∆η =

√∑ni=1ETi(ηi − ηcluster)2∑n

i=1ETi

(4.2)

• ET/pT of the leading track. It is expected that the leading track in a hadronic

τ -decay will in general have a high fraction of the overall energy. QCD jets on the

other hand are expected to have a uniform distribution of energy and to also have

more neutral particles. This variable, formed from the total cluster ET divided by

the pT of the leading track, exploits the discrimination power of these features.

• Lifetime signed pseudo impact parameter significance. The pseudo (2-dimensional)

impact parameter, d0, is the smallest distance of a track from the beam axis. The

lifetime signed impact parameter is calculated from d0 and the cluster axis as:

σIP = d0/σd0 ∗ sign(sin(ϕcl − ϕtr)) (4.3)

where σd0 is the error on d0 from the track fitting, and ϕcl and ϕtr are the track

coordinates at the cluster and at the point of closest approach. This quantity is

constructed to have a positive value if the decay happens in the flight direction

of the track. Tracks from decays with a true lifetime are hence biased towards

positive values.

1A threshold of pT > 2 GeV was used for the simulated data samples analysed in chapter 7.


The algorithm employs a likelihood method for τ -identification and jet rejection.

The discriminating power of the above quantities are combined using a one-dimensional

Likelihood method [41]. This leads to improved rejection power compared with using

simple rectangular cuts alone.

4.2.2 A track-seeded algorithm (tau1p3p)

A second approach to τ -reconstruction is a track-based algorithm [42–44], seeding re-

construction from a leading track. A core cone of radius ∆Rcore = 0.2 is defined around

the track seed, with this cone being used for both the tracking and calorimetric sections

of the algorithm.

The leading seed track is required to pass a series of track quality selection cuts

(discussed in more detail in section 6.2), and must satisfy a transverse momentum cut

(pT > 9 GeV as default). The τ -jet has one or more constituent tracks, the seed track

and other associated tracks found in the core cone around the seed. The tracks are

required to be good-quality tracks with the number of good-quality tracks in the core

cone defining the number of prongs of the candidate τ -jet. Candidate τ -jets can be

reconstructed with between 1 and 3 tracks2.

The tau1p3p algorithm takes a more exclusive approach to τ -reconstruction, with

distinct reconstruction and identification steps. The reconstruction step, with its re-

quirement of a leading track with pT > 9 GeV, already provides strong rejection power

against the background from QCD before the identification step. Further rejection is

then achieved in the identification step. The effect of reducing the pT threshold of the

seed track has been considered as this would increase the τ -reconstruction efficiency

(especially at low pT where the 9 GeV threshold restricts the reconstruction efficiency)

but a lower threshold also requires a much stricter selection in the identification step in

order to remove backgrounds.

An energy flow approach [45] is used to define the energy of the candidate τ -jet in

the tau1p3p algorithm. This approach uses the measured track momentum to improve

the overall calorimetric measurement of the candidate τ -jet. In the case of hadronic τ -

decays, the energy flow algorithm considers energy deposition in the core cone, ∆Rcore.

2Later increased to include higher track multiplicities


With this method, the transverse energy of a candidate τ -jet, EeflowT , is defined as:

EeflowT = Eemcl

T +∑

ptrackT + EneuEM

T + resEchrgEMT + neuEneuEM

T (4.4)

Here the energy deposition in the electromagnetic calorimeter is identified as belonging

to one of several categories, with the calorimeter energy identified as being associated

with a track being replaced in the energy sum by the track momentum. The terms of

the energy flow equation are defined as:

• EemclT , the pure electromagnetic energy. The presence of an electromagnetic clus-

ter with no substantial hadronic leakage, and separated from any good-quality

tracks is used to seed the EemclT energy collection. Cells in the presampler, strips

and middle layers of the electromagnetic calorimeter are used in a window of

2 · 0.0375× 3 · 0.0375 (after any EchrgEMT contribution has been collected, as defined

below).

• EchrgEMT , the charged electromagnetic energy. Where the seed track (or any asso-

ciated track) impacts with the presampler, strip, middle and back layers of the

electromagnetic calorimeter, the distance of the impact point to the nearest cell is

found. Energy is collected in a narrow window (0.0375× 0.0375) and labelled as

EchrgEMT .

• EneuEMT , the neutral electromagnetic energy. This is the sum of the transverse

energies of any remaining electromagnetic calorimeter cells within the core cone

(with ∆Rcore = 0.2, as defined above). Only the presampler, strips and middle

layers contribute to EneuEMT .

•∑ptrack

T , the sum of the transverse momenta of the constituent tracks of the τ -jet

in question.

• resEchrgEMT and neuEneuEM

T are correction factors, one to account for the leakage

of photon showers into the cells which were flagged as being associated to tracks

(EchrgEMT ), and one to account for the double-counting leakage of energy deposits

from charged hadrons that fall into cells beyond those selected by the EchrgEMT

window.

The major advantage of the energy flow approach is that, whilst it gives good perfor-

mance for true τ -jets, it significantly underestimates the nominal energy of fake τ -jets


reconstructed from QCD jets. This is because ∆Rcore is too narrow to efficiently collect

the energy of a QCD jet. Also, a significant part of the neutral hadronic energy of a

QCD jet is omitted from the definition as the hadronic calorimeter doesn’t contribute

to the energy flow. This means that QCD jets will typically migrate to lower pT values,

improving the signal to fake ratio above a fixed pT cut.

As in the case for taurec, several variables with discrimination power against fake

τ -jets from QCD jets are used to make an identification decision for each candidate

τ -jet. Along with the core cone (∆Rcore = 0.2), an isolation cone is also defined where

∆Riso = 0.2− 0.4. The following combination of calorimeter and tracking variables are

used:

• The number of tracks in the isolation cone ∆Riso.

• The invariant mass of the track system M track (used for multi-prong candidates).

• The track width, calculated as the variance, is defined as:

W τtracks =

∑(∆ητ,track)2 · ptrack

T∑ptrack

T

− (∑

∆ητ,track · ptrackT )2

(∑ptrack

T )2(4.5)

• The electromagnetic radius, Rτem. Using only cells in the first three samplings

of the electromagnetic calorimeter (presampler, strips and middle layers), Rτem

is calculated from the cells around the seed, weighted by the transverse energy

deposition of the cell. Defining ∆Rτ,cell as the separation of the cell from the

direction of the tau1p3p candidate, the electromagnetic radius is given by:

Rτem =

∑∆Rτ,cell ·Ecell

T∑Ecell

T

(4.6)

• The number of strips, N τstrips with energy above a certain threshold.

• The η-strip width of the energy deposition, calculated as the variance in the η-

coordinate:

W τstrips =

∑(∆ητ,strip)2 ·Estrip

T∑Estrip

T

− (∑

∆ητ,strip ·EstripT )2

(∑Estrip

T )2(4.7)

• The fraction of energy deposited in the 0.1 < ∆R < 0.2 with respect to the total

energy in the ∆Rcore.


• The energy (at the EM scale) deposited in the electromagnetic and hadronic

calorimeters.

• The energy deposited in the hadronic calorimeter (at the EM scale) in ∆Rcore with

respect to the sum of the transverse momenta of the tracks.

• M eflow, the invariant mass of the candidate calculated from the combined four

momenta of the track system with that of the energy that is classed as EemclT or

EneuEMT .

As expected, there is some similarity between the identification variables used by the

tau1p3p algorithm with those used by the taurec algorithm (as described in section

4.2.1).

The identification is done by calculating discriminants from these variables. tau1p3p

offers several different discriminants, including a simple cut-based discriminant and dis-

criminants calculated using multivariate methods [46]. Two of the commonly used multi-

variate methods (and the two used in later sections of this thesis) are the Neural Network

and PDE-RS (Probability Density Estimator with Range Searches) [47] discriminants.

The multivariate methods show significantly improved performance when compared to

the simple cuts-based discriminant, giving better rejection against QCD jets for the same

efficiency. The different multi-variate approaches typically give similar discrimination

performance. However, a cut-based approach is a more robust method, and will be used

initially.

4.2.3 Further developments of the τ -reconstruction algorithms

The development of τ -reconstruction and identification algorithms in ATLAS has been

ongoing in preparation for the first data, with several changes in the algorithms since

the major part of this work was completed. A significant recent development in the

calorimeter-seeded approach is the use of topological clustering rather than the slid-

ing window clustering described earlier, giving a significant improvement in the τ -

reconstruction efficiency at low pT (below 25 GeV)[48]. Further developments have

been made to the track selection criteria, with the track-seeded algorithm expanding

to consider higher track-multiplicities (see chapter 6). The complementary track- and

calorimeter-seeded approaches have recently been merged into a single algorithm in order

to incorporate the advantages of the two approaches. In the merged approach [49], the


candidate τ -jets are reconstructed using both the track-seeded and calorimeter-seeded

approaches, with a combined approach to the subsequent τ -identification.

4.3 Fast Simulation

The ATLFAST fast simulation package [39] has been developed in order to simulate

large samples of signal and background events for physics studies, especially those that

require very high statistics. Fast simulation is essential to produce samples of simulated

events on scales that are impossible to achieve using full simulation alone due to the

CPU requirements of full simulation.

ATLFAST is a particle-level simulation that acts as an intermediate step between

simple parton-level analysis and the sophisticated full detector simulation. In order to

keep the CPU time required to process an event at a low enough level, no attempt is made

to perform a detailed simulation of particle interactions inside the material of the ATLAS

detector. Instead, the detector response is modelled by a series of parametrizations. The

fast simulation process is summarised below:

• Events generated by Monte Carlo generators are read in.

• The stable particles in the event are tracked through the detector’s magnetic field

(assuming a perfect homogeneous magnetic field in the central tracking volume).

The corresponding impact point on the calorimeter surface is calculated.

• The energies of hadrons, electrons and photons are distributed across a calorime-

ter cell map. For central rapidity values (|η| < 3.2) the cells have dimensions

∆η×∆φ = 0.1× 0.1, with larger cells of ∆η×∆φ = 0.2× 0.2 used for higher

rapidity values (3.2 < |η| < 5.0). The energy of the particle is deposited en-

tirely within the hit cell. There is no separation between the electromagnetic and

hadronic calorimeters.

• A clustering algorithm is run on the calorimeter cells. A simple cone clustering

algorithm is used, with a default cone size of ∆R = 0.4, seeded by cells with

energies greater than 1.5 GeV. Cells can only be associated with a single cluster.

With the exception of the seeded cone clustering algorithm, ATLFAST does not

have a separate reconstruction layer (although chapter 6 introduces developments in


applying a reconstruction layer for the fast simulation of τ -jets from ATLFAST tracks).

The reconstruction of physics objects is largely based on using the Monte Carlo truth

information.

Clusters are inspected to identify those which match electrons and photons in (η, φ)

space. These clusters are reassigned and removed from the list. The remaining clusters

are recorded as jets (as long as they have a transverse momentum greater than the jet

reconstruction threshold, which is 10 GeV by default). The true energy of these clusters

is smeared by resolution functions to obtain a “reconstructed” energy. There are separate

resolution functions to handle electron, photon and jet objects. More information on

these functions can be found in [50]. Muons from the Monte Carlo truth (those not

associated with a jet) are smeared using a pT-, η- and φ-dependent resolution function.

ATLFAST identifies τ -jets by tagging jets according to parametrized efficiencies de-

termined from the taurec performance. Jets are first labelled depending on whether

they originated from true τ -decays or not. The jets are then tagged on a statistical basis

with separate identification efficiencies for true τ -jets and rejection factors for fakes. This

is further discussed in section 5.2. For b- and c-jets a similar procedure is used whereby

jets are firstly labelled using the event generator information, and then parametrizations

of tagging efficiencies are applied on a statistical basis afterwards. Sections 5 and 6 in-

troduce updates to the fast simulation of τ -jets in order to incorporate the performance

of the tau1p3p algorithm into ATLFAST.

The missing transverse momentum of an event is calculated from the physics objects

(electrons, muons, photons and jets) along with any remaining cells not associated with

a jet.

Charged particles with pT > 500 MeV and |η| < 2.5 are considered as reconstructed

ATLFAST tracks. The parameters of these tracks are smeared according to parametrized

functions designed to account for measurement precision, energy loss and interactions in

the Inner Detector. The ATLFAST tracks are separated into three different categories

(i) hadrons, (ii) electrons and (iii) muons. Reconstruction efficiencies are not applied

by ATLFAST and are left to the user. A more detailed discussion on the design and

performance of ATLFAST can be found in [50].

Chapter 5

A tau1p3p τ -tagging parametrization

for ATLFAST

As a first step in the development of a fast simulation of the tau1p3p algorithm, the per-

formance of the tau1p3p algorithm was studied with the aim of developing a parametriza-

tion of signal identification and background rejection factors that could be applied to

ATLFAST to complement the existing τ -tagging algorithm (based on the performance

of the taurec algorithm).

5.1 Monte Carlo samples

The datasets used in this analysis are samples generated and simulated as part of the

official ATLAS production. The tau1p3p algorithm was run on these fully simulated

events producing a CBNT (n-tuple). For comparison with the fast simulation results,

the same events were also passed through ATLFAST (using release 11.0.41 of the Athena

software framework), adding the ATLFAST output to the same ntuple. This allows for

tau1p3p and ATLFAST to be compared easily on an event by event basis. The list of

samples used is shown in table 5.1. It should be noted that the early version of the

tau1p3p algorithm used in this study predates that described in section 4.2.2 as the

tau1p3p algorithm has been subject to considerable development over the course of this

thesis. The main difference being that, in the version of tau1p3p used for this study, the

reconstruction of candidate τ -jets is limited to those with either 1-prong and 3-prong

candidates. For the duration of this chapter, the notation “Tau1P” and “Tau3P” is used

74

A tau1p3p τ -tagging parametrization for ATLFAST 75

to describe 1-prong and 3-prong tau candidates respectively.

Later developments of the algorithm saw first the addition of 2-prong candidates,

and then the expansion to include higher track multiplicities (e.g. 4-, 5- and 6-prong

candidates). Other details regarding this version of the tau1p3p algorithm are that

the minimum pT requirement for associated tracks is 2 GeV (lowered to 1 GeV in later

versions of the algorithm), and that the definition of 3-prong candidates requires exactly

three good-quality tracks (later loosened to allow for candidates with two good quality

tracks and exactly one other track).

Description Code Generator # Events

QCD Background

Dijet J1 17-35 GeV 005010 Pythia 85150




Signal Z → ττ 005149 Pythia 15650

Table 5.1: The signal and background data samples used in this study to prepare aparametrization of the tau1p3p performance.

5.2 The labelling and tagging of hadronic τ -decays in

ATLFAST

ATLFAST reconstructs jets from clusters of cells (from its calorimeter model), with

the energy of the clusters smeared according to resolution functions (see section 4.3).

Using Monte Carlo truth information, jets are first “labelled” as either QCD jets (either

light-quark, charm or bottom) or as τ -labelled jets. Having been labelled, jets are then

“tagged” using the AtlfastB algorithm. In the case of τ -jets, The AtlfastB algorithm

takes the ATLFAST jet collection and randomly tags τ -labelled jets according to a

pT- and η-dependent efficiency. QCD-labelled jets are also mis-tagged according to a

parametrization of rejection factors.

The criteria for a jet to become τ -labelled are listed below (where patlfastT is the

transverse momentum of the ATLFAST jet, and pvisT is the true transverse momentum


of the visible component of the τ -decay):

• The visible transverse-momentum of the τ -decay must satisfy pvisT > 10 GeV

• The visible τ -decay component must be inside the Inner Detector acceptance (with

pseudorapidity |η| < 2.5)

• The visible τ -decay products are spatially matched to a jet with the cone defined

by ∆Rjet,τ−had < 0.3

• The energy of the jet in question is dominated by the τ -decay (pvisT /patlfast

T > 0.9).

These were the default τ -labelling criteria as defined in the ATLFAST version in

Athena release 11.0.41. These cuts do not give a perfect efficiency for τ -labelling jets

in the case of true τ -jets. It was found that the τ -labelling efficiency was lower than

desired, and in later versions of ATLFAST, the labelling criteria were altered to increase

the τ -labelling efficiency, but were not available at the time of this investigation. The

cut on pvisT /patlfast

T was changed such that pvisT /patlfast

T > (1− 2σ), where σ is the expected

jet energy resolution, resulting in a significantly higher τ -labelling efficiency [41].

The significance of this is that only ATLFAST jets that are τ -labelled are then

considered as signal jets when ATLFAST proceeds to tag τ -jets. A low labelling efficiency

will cause a systematic reduction in the number of signal jets that are considered for

tagging, so clearly a high efficiency is desired. The impact of a low labelling efficiency

when comparing full and fast simulation, is that the full simulation will show extra τ -jets

identified by the tau1p3p algorithm when compared to the fast simulation (assuming all

other effects being equal). The impact of the labelling is discussed further in section 5.4.

An existing parametrization of τ -tagging efficiencies and QCD rejection factors, based

on the performance of the taurec algorithm, was already implemented into ATLFAST.

The aim of this study was to provide corresponding τ -tagging factors for the tau1p3p

performance, in a parametrization that could easily be applied to the fast simulation

jets and implemented in ATLFAST (following the existing jet-tagging approach). Due

to differences in the signal efficiency and fake rates for Tau1P and Tau3P candidates,

it was intended for the τ -tagging procedure to provide separate parametrizations for

Tau1P and Tau3P candidates.

This approach was chosen so as to be easy to apply to ATLFAST without having to

make changes to the core code. Unfortunately this approach does create some limita-

tions, mainly from the limited information that is available in the ATLFAST jet output


(in particular, details regarding the number of, and charge of tracks associated to a

jet are not simply available in the jet output). Similarly, whilst jets are labelled as to

whether they originate from a true hadronic τ -decay, there is no flag to identify whether

the true τ -decay was a true 1-prong or 3-prong decay. As this information was not

available at runtime without making significant changes to the ATLFAST code, it was

decided to tag the τ -jets as either Tau1P or Tau3P on a purely statistical basis. An-

other significant complication comes the difference in the energy scale of full simulation

candidates and fast simulation jets. This is described in more detail in section 5.3.1.

5.3 Parametrization Development

5.3.1 The tau1p3p energy scale for true and fake τ -jets

As mentioned in section 4.2.2, the transverse energy of tau1p3p candidates (EeflowT ) is

determined by an energy flow method, based on the energy deposition in a narrow core

cone, of ∆Rcore = 0.2, around the seeding track. This gives a good representation of

the energy scale of true hadronic τ -decays, and underestimates the energy scale for fake

QCD candidates (a useful feature in achieving better rejection factors). This is because

a cone of ∆Rcore = 0.2 is too narrow to efficiently collect the energy of a QCD jet, and

since energy deposition in the hadronic calorimeter does not contribute to the energy

flow calculation, the neutral component of QCD jets is largely omitted.

The energy of an ATLFAST jet, reconstructed with a cone of ∆R = 0.4, is calcu-

lated from the energy deposits in the ATLFAST calorimeter model in this region. The

differences in the two definitions lead to differences in the energy scales as demonstrated

in figures 5.1 and 5.2. Here, both the energy flow and ATLFAST jet energy response

for true hadronic τ -decays (with visible transverse energy EvisT ) and QCD fakes (match-

ing partons with transverse energy EpartonT ) are shown. The transverse momentum of

ATLFAST jets is given by patlfastT . In these plots, τ -decays and partons from the Monte

Carlo truth are matched to both tau1p3p candidates and ATLFAST jets (requiring

∆R < 0.25), with the transverse energy response of the corresponding tau1p3p object

and ATLFAST jet shown. It can clearly be seen that, in the QCD dijet sample, there

is a significant difference in the distributions of the energy response for fake tau1p3p

candidates and the corresponding ATLFAST jet. For true hadronic τ -decays, which are

typically very well collimated, the two energy scales are in much better agreement, both


visT / Eobject

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Norm

alize

d Un

its /

0.01

5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

τ τ →Tau1P Signal ZvisT / Eatlfast

TpMean 1.05RMS 0.113

visT / Eeflow

TEMean 0.991RMS 0.133

(a) Tau1P

visT / Eobject

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Norm

alize

d Un

its /

0.01

5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16τ τ →Tau3P Signal Z

visT / Eatlfast


visT / Eeflow


(b) Tau3P

Figure 5.1: Transverse energy response for true, full simulation tau1p3p τ -jets (Eeflow

T /EvisT – dashed line), and the corresponding uncalibrated ATLFAST jet

(patlfastT /Evis

T – solid line). EvisT is the true visible transverse energy of the associated

hadronic τ -decay. The comparison for fully simulated Tau1P (left) and Tau3P (right)candidates with their matching ATLFAST jets are shown. The tails in the ATLFASTresponse result from the large default cone size of ∆R = 0.4 used to reconstruct theenergy of the τ -jet.

for the means and variances.

As a consequence of this, it is assumed that, for true τ -decays, the patlfastT and Eeflow

T

energy scales are equivalent. However, this is not the case for fake tau1p3p candidates.

Care must therefore be taken to distinguish between the two energy scales (one cannot

assume that patlfastT ≈ Eeflow

T for fake tau1p3p candidates). In terms of the parametriza-

tion, this has the impact that, in order to get agreement between the transverse energy

distributions for fake tau1p3p candidates in the fast and full simulation, the fake τ -jets

in the fast simulation must have their energy rescaled. This is achieved by applying a

scaling factor to the energy and momentum of the fast simulation jet. This scaling fac-

tor is drawn randomly from the distribution of EeflowT /patlfast

T for ATLFAST jets and the

matching fake Tau1P (or Tau3P) candidates from the full simulation. The distribution

of EeflowT /patlfast

T is shown in figure 5.3 for Tau1P candidates in different patlfastT ranges. As

these histograms are filled only if a candidate is reconstructed in both the full simulation

and the fast simulation, there is a kinematic constraint that the transverse momentum

of the ATLFAST jet, patlfastT , is greater than 10 GeV (the transverse momentum of a


partonT / Eobject

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Norm

alize

d Un

its /

0.07

5

0

0.05

0.1

0.15

0.2

0.25 Tau1P QCD J1, J2, J3 partonT / Eatlfast


partonT / Eeflow


(a) Tau1P

partonT / Eobject

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Norm

alize

d Un

its /

0.07

5

0

0.05

0.1

0.15

0.2

0.25 Tau3P QCD J1, J2, J3 partonT / Eatlfast


partonT / Eeflow


(b) Tau3P

Figure 5.2: Transverse energy response for fake, full simulation tau1p3p τ -jets(Eeflow

T /EpartonT – dashed-line), and the corresponding uncalibrated ATLFAST jet

(patlfastT /Eparton

T – solid line). EpartonT is the true transverse energy of the associated

parton. The plots show the comparison for fully simulated Tau1P (left) and Tau3P(right) candidates with their matching ATLFAST jets.


cluster reconstructed in ATLFAST is required to be above this default threshold for the

cluster to be accepted as a jet). In order to respect this threshold, the scaling factor is

redrawn randomly from the distribution if the rescaled transverse momentum falls below

this 10 GeV kinematic constraint. The difference between the two energy scales adds

complexity to the problem, as demonstrated by the extra set of parametrized functions

required to perform the rescaling.

5.3.2 Z → ττ analysis

To investigate the performance of tau1p3p, signal and QCD background events, sim-

ulated using the full ATLAS detector simulation, were passed through the tau1p3p

algorithm. The same events were also passed through ATLFAST. Z → ττ events were

used to provide a signal sample, as shown in table 5.1. For a given event, the τ -labelled

fast simulation jets are matched to the true Tau1P and Tau3P candidates from the

full simulation of the same event. Using this information, a parametrization for the

probability with which τ -labelled jets should be tagged as τ -jets was calculated.

Figure 5.4 shows the patlfastT distribution of τ -labelled fast simulation jets in the

Z → ττ sample; also shown are the subset of these jets that match a full simulation

tau1p3p candidate (shown separately for the 1-prong (Tau1P) and 3-prong (Tau3P)

tau1p3p candidates). For the signal sample, a signal reconstruction factor, ρreco1P/3P, is

defined as the fraction of τ -labelled jets that are also reconstructed by tau1p3p in the

full simulation:

ρreco1P/3P =

Number of τ -labelled jets reconstructed as a Tau1P/3P candidate

Total Number of τ -labelled jets(5.1)

where an ATLFAST jet is “reconstructed as a Tau1P/3P candidate” if it is separated

from a full simulation Tau1P/3P candidate in (η, φ) space with ∆R < 0.2. It should be

noted that the reconstruction factors are normalized to all hadronic τ -decays, and not

separately into 1-prong and 3-prong. More explicitly, they incorporate the branching

ratios BR(τhad → 1P)∼ 75% and BR(τhad → 3P)∼ 25%.

Figure 5.5 shows the corresponding signal reconstruction factors, ρreco1P and ρreco

3P , as

a function of patlfastT . Also shown are the approximate branching ratios for hadronic tau

decays into either one prong or three prongs. It can be seen that ∼ 50 % of all the τ -

labelled jets are reconstructed by Tau1P over the patlfastT range shown. Similarly, 10–25 %

of the total number of τ -labelled jets are reconstructed as Tau3P. Whilst ρreco1P is roughly


atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

020406080

100120140160180200 Tau1P

< 20 GeVatlfastT

10 GeV < p

Mean = 0.86 RMS = 0.16

(a) 10 GeV < patlfastT < 20 GeV

atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

0

50

100

150

200

250

300 Tau1P < 30 GeVatlfast

T20 GeV < p

Mean = 0.72 RMS = 0.17

(b) 20 GeV < patlfastT < 30 GeV

atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

0

50

100

150

200

250Tau1P

< 40 GeVatlfastT

30 GeV < p

Mean = 0.67 RMS = 0.17

(c) 30 GeV < patlfastT < 40 GeV

atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

0

20

40

60

80

100

120


T40 GeV < p

Mean = 0.65 RMS = 0.17

(d) 40 GeV < patlfastT < 50 GeV

atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

0

10

20

30

40

50

60


T50 GeV < p

Mean = 0.62 RMS = 0.18

(e) 50 GeV < patlfastT < 60 GeV

atlfastT / peflow

TE0 0.2 0.4 0.6 0.8 1 1.2 1.4

Arbi

trary

Uni

ts /

0.07

5

0

5

10

15

20

25

30

35Tau1P

< 70 GeVatlfastT

60 GeV < p

Mean = 0.62 RMS = 0.2

(f) 60 GeV < patlfastT < 70 GeV

Figure 5.3: The distribution of EeflowT /patlfast

T for fake tau1p3p candidates in differentranges of patlfast

T . These histograms show a comparison between Tau1P candidates andtheir matching ATLFAST jets; similar plots are available for Tau3P candidates. Thesehistograms are used to rescale the energy and momentum of ATLFAST QCD jets thatare mis-tagged as tau1p3p.


(GeV)atlfastTp

0 10 20 30 40 50 60 70 80 90 100

Num

ber /

10

GeV

0500

10001500200025003000350040004500

Not Reconstructed Reconstructed as Tau1PReconstructed as Tau3P

Figure 5.4: A stacked plot showing the patlfastT distribution for ATLFAST τ -labelled jets.

Also shown are the subset of these jets that are also reconstructed as Tau1P (blue), orTau3P (green), in the full simulation.

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90

reco

1PρSi

gnal

Rec

on. F

acto

r

00.10.20.30.40.50.60.70.80.9

1

1P) ~ 0.75→ hadτBR(

(a) Tau1P

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90

reco

3PρSi

gnal

Rec

on. F

acto

r

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

3P) ~ 0.25→ hadτBR(

(b) Tau3P

Figure 5.5: Signal reconstruction factors, ρreco1P/3P, for ATLFAST τ -labelled jets as a func-

tion of patlfastT , for (a) Tau1P and (b) Tau3P. Also shown are the approximate branching

ratios for hadronic τ -decays into 1-prong and 3-prongs. There is a strong dependence onthe Tau3P reconstruction factor as function of patlfast

T . This is due to a low efficiency fortracks with low pT being accepted as good quality. Note that the signal reconstructionfactors, ρreco

1P and ρreco3P , include the branching ratios in their values.

flat with patlfastT , ρreco

3P drops off for low values of patlfastT . The strong pT dependence for

reconstructing Tau3P candidates is caused by a low efficiency for low-pT tracks passing

the good-quality selection in forming Tau3P candidates.


Whether a reconstructed tau1p3p candidate goes on to pass the identification step

is dependent on the PDE-RS discriminant cut used to separate signal taus from fakes.

Figure 5.6 shows the normalized distributions of the PDE-RS discriminating function for

both signal and background candidates. A signal identification factor, ρident1P/3P, is defined

as the fraction of τ -labelled jets that match a tau1p3p full simulation candidate that is

identified by PDE-RS:

ρident1P/3P =

Number of τ -labelled jets identified as Tau1P/3P

Total Number of τ -labelled jets(5.2)

where an ATLFAST jet is “identified as Tau1P/3P” if it is separated from a Tau1P/3P

candidate with ∆R < 0.2 and also passes a PDE-RS discriminant cut.

Figure 5.7 shows the signal identification factors, ρident1P/3P, for a discriminant cut of

PDE-RS > 0.85. Also shown is the signal reconstruction factor ρreco1P/3P. The choice

of PDE-RS cut is important in determining the overall efficiency with which τ -jets

are identified, and with it the fake rate. Decreasing the PDE-RS discriminant cut

increases the number of tau1p3p candidates being identified, and hence increases ρident1P/3P

(with an upper limit set by ρreco1P/3P). Figure 5.8 shows how the signal identification

factor varies with PDE-RS cut, for each 10 GeV patlfastT bin, for Tau1P candidates. A

good approximation to the value of PDE-RS cut that is needed to give a desired signal

identification factor can be calculated from the curves fitted through these points.

For Tau1P candidates the PDE-RS cut was optimised in each 10 GeV bin to give

a flat signal identification factor. For Tau3P candidates, given the falling shape of the

signal reconstruction factor (shown by ρreco3P in figure 5.5), it was impossible to achieve

a flat signal identification factor over the entire transverse momentum range of the

parametrization. As a consequence, it was decided to vary the signal identification factor

as a function of patlfastT . For bins where patlfast

T < 40 GeV, the PDE-RS cut is optimised

to give a Tau3P signal identification factor that matches the shape of the Tau3P signal

reconstruction factor. For patlfastT > 40 GeV, the PDE-RS cut is optimised to give a flat

signal identification factor. To demonstrate this, the optimised PDE-RS cuts to give

signal identification factors of ρident1P = 35% and ρident

3P = 8% (for patlfastT > 40 GeV) are

shown in figure 5.9.

It is assumed here that the ATLFAST energy scale and the tau1p3p energy flow

scale are equivalent (i.e. it is assumed that the shape of the ρident1P/3P histograms would

be the same regardless of whether they were plotted as a function of the patlfastT or as a

function of EeflowT ), as discussed in section 5.3.1. This approximation is a good one for


PDE-RS0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Norm

alize

d Un

its/0

.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14Tau1P

True CandidatesFake Candidates

(a) Tau1P

PDE-RS0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Norm

alize

d Un

its/0

.02

00.010.020.030.040.050.060.070.080.09 0.347

Tau3PTrue CandidateFake Candidate

(b) Tau3P

Figure 5.6: Normalized distributions of the PDE-RS discriminating function for signal(solid line) and background (dashed line). The distributions are shown separately for(a) Tau1P and (b) Tau3P candidate τ -jets.

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90

Iden

tifica

tion

Fact

or

00.10.20.30.40.50.60.70.80.9

1Tau1P PDE-RS Cut = 0.85

reco1P

ρ ident1P

ρ

(a) Tau1P

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90

Iden

tifica

tion

Fact

or

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Tau3P PDE-RS Cut = 0.85

reco3P

ρ ident3P

ρ

(b) Tau3P

Figure 5.7: Signal identification factors, ρident1P/3P, for ATLFAST τ -labelled jets as a func-

tion of patlfastT for (a) Tau1P and (b) Tau3P. A constant discriminant cut of PDE-

RS > 0.85 is used for both Tau1P and Tau3P candidates to determine the identificationfactor. Also shown is the signal reconstruction factor, ρreco

1P/3P.

true hadronic τ -jets (as in this case) but is not appropriate for fake QCD candidates

(due to large differences in the two energy scales for fakes).


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

10 - 20 GeVatlfastT

p


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

20 - 30 GeVatlfastT

p


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

30 - 40 GeVatlfastT

p


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

40 - 50 GeVatlfastT

p


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

50 - 60 GeVatlfastT

p


Efficiency0 0.1 0.2 0.3 0.4 0.5 0.6

PDE-

RS C

ut

0.7

0.75

0.8

0.85

0.9

0.95

1Tau1P

60 - 70 GeVatlfastT

p


Figure 5.8: The variation of the signal identification efficiency, ρident1P , with PDE-RS cut

for Tau1P candidates. Each graph corresponds to a different range of patlfastT . The curves

shown here give a good approximation to the PDE-RS cuts needed to give a desiredsignal identification factor.


(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t1Pρ

Iden

tifica

tion

Fact

or

0

0.1

0.2

0.3

0.4

0.5

0.6Tau1PIdentification Factor = 35%

(a) Tau1P

(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t3Pρ

Iden

tifica

tion

Fact

or

0

0.02

0.04

0.06

0.08

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0.12

0.14 Tau3PIdentification Factor = 8%

(b) Tau3P

(GeV)eflowTE

0 10 20 30 40 50 60 70

PDE-

RS C

ut

0.6

0.7

0.8

0.9

1


(c) Tau1P

(GeV)eflowTE

0 10 20 30 40 50 60 70

PDE-

RS C

ut

0.6

0.7

0.8

0.9

1


(d) Tau3P

Figure 5.9: An example of user selected signal identification factors for (a) Tau1Pand (b) Tau3P; and the corresponding PDE-RS discriminant cuts that are required toachieve the selected identification efficiency: (c) and (d). Note that the “identificationfactor” label corresponds to the identification factor for patlfast

T > 40 GeV in the Tau3Pcase. For Tau3P candidates with patlfast

T < 40 GeV, the actual identification factor isreduced to follow the shape of reconstruction factor, ρreco

3P .


5.3.3 QCD dijet analysis

Having studied the identification of signal hadronic τ -decays, the next step was to inves-

tigate the rejection of fake tau1p3p candidates in order to calculate the rejection factors

for mis-tagging ATLFAST QCD jets as τ -jets. Samples of fully simulated QCD dijet

events were used to provide fake tau1p3p candidates (see table 5.1). As with the signal

sample, these events were also passed through ATLFAST. The full simulation tau1p3p

candidates were matched to ATLFAST QCD jets in a cone of ∆R < 0.2, only consid-

ering jets with |η| < 2.5 (to match the acceptance range of the tau1p3p algorithm). A

rejection factor Rreco1P/3P is defined as:

Rreco1P/3P =

Total Number of QCD-labelled jets with |η| < 2.5

Number of QCD-labelled jets reconstructed as Tau1P/3P candidate(5.3)

where a jet is “reconstructed as a Tau1P/3P candidate” if it is separated from a

Tau1P/3P candidate with ∆R < 0.2. The rejection factor Rreco1P/3P gives a measure of the

chance that an ATLFAST QCD-labelled jet will also be reconstructed as a Tau1P/3P

candidate in the full simulation.

To take into account the PDE-RS identification step of the tau1p3p algorithm, a

further rejection factor, Rident1P/3P, is defined as:

Rident1P/3P =

Total Number of QCD-labelled jets with |η| < 2.5

Number of QCD-labelled jets identified as Tau1P/3P(5.4)

where a jet is “identified as Tau1P/3P” if it is separated from a Tau1P/3P candidate

with ∆R < 0.2 that also passes the chosen PDE-RS discriminant cut.

The definition of the two types of rejection factor, Rreco1P/3P and Rident

1P/3P, is analogous

to the previous definition of ρreco1P/3P and ρident

1P/3P, in that they demonstrate the algorithm’s

performance (the jet rejection in this case) after each of the reconstruction and identi-

fication steps. More explicitly, Rreco1P/3P gives a measure of the jet rejection after just the

reconstruction step, and Rident1P/3P gives a measure of the rejection performance after both

the reconstruction and identification steps.

Figure 5.10 shows the values of Rreco1P/3P and Rident

1P/3P as a function of patlfastT . The values

of Rreco1P/3P give a good demonstration of the rejection power of the tau1p3p algorithm

at the reconstruction stage (unlike the taurec algorithm, which has a more inclusive

approach to the reconstruction step, the tau1p3p algorithm gives a significant rejection


of background at the reconstruction step).

For the calculation of Rident1P/3P, the PDE-RS cuts applied to the Tau1P and Tau3P

candidates are those optimised to give the signal identification factors ρident1P = 35%, and

ρident3P = 8% respectively (as shown in figure 5.9). It should be noted that the PDE-RS

cuts are applied according to the EeflowT value (the transverse energy associated with

the full simulation tau1p3p candidate), whereas the rejection values are histogrammed

according to the patlfastT of the matching fast simulation jet. These two scales are not the

equivalent for fake tau1p3p candidates, as already shown in section 5.3.1.

It can be seen that rejection factor values of Rident1P/3P∼ 100–200 are achievable for

the chosen signal identification factors. The rejection factors increase sharply as patlfastT

approaches the 10 GeV cut-off for jet reconstruction in ATLFAST.

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90 100

QCD

Rej

ectio

n Fa

ctor

210

310 = 35%ident

1PρTau1P: Signal Ident. Factor

reco1PR ident

1PR

(a) Tau1P

(GeV)atlfastT

p0 10 20 30 40 50 60 70 80 90 100

QCD

Rej

ectio

n Fa

ctor

1

10

210

310

410

510

610 = 8%ident

3PρTau3P: Signal Ident. Factor

reco3PR ident

3PR

(b) Tau3P

Figure 5.10: Histograms showing the rejection factors for (a) Tau1P and (b) Tau3P.Rident

1P and Rident3P correspond to the PDE-RS cuts optimised to give signal identification

factors of ρident1P = 35% for Tau1P, and ρident

3P = 8% for Tau3P.

5.3.4 Parametrization of performance

Figures 5.11 and 5.12 show how Rident1P/3P varies with the choice of ρident

1P/3P for 1-prong

and 3-prong decays respectively. Each point represents the Rident1P/3P value for a given

value of ρident1P/3P. Each plot represents a different 10 GeV wide patlfast

T range. The graphs

are fitted with exponential functions in order to parametrize the relationship between

signal identification and background rejection for each bin. From these functions one


can calculate the appropriate rejection factor for a chosen identification factor. Figure

5.13 shows the patlfastT dependence on the QCD jet rejection for a selection of signal

identification factors. The results are shown for both Tau1P and Tau3P candidates. This

parametrization can be applied to the ATLFAST jet collection in order to recreate the

full simulation performance of the tau1p3p algorithm in the fast simulation. τ -labelled

jets are tagged as τ -jets with efficiencies given by the ρident1P/3P values, and QCD-labelled

jets are mis-tagged as τ -jets according to the corresponding Rident1P/3P rejection factors

(with their energy and momenta rescaled to account for the energy scale difference).

The parametrization is limited to the range 10 GeV < patlfastT < 70 GeV for Tau1P

candidates; and 20 GeV < patlfastT < 70 GeV for Tau3P candidates. For those jets with

patlfastT > 60 GeV, the signal identification and QCD jet rejection are assumed to be flat.

Near the upper patlfastT limit of this study there are systematic uncertainties due to the

lack of ATLFAST jets with patlfastT above 70 GeV, given the need to rescale their energies

to account for the energy flow algorithm.

It was decided to limit the Tau3P identification efficiency to be zero for τ -labelled

jets with patlfastT < 20 GeV, due to the low value of ρident

3P for Tau3P candidates below this

point. In order to be consistent with this, a further rejection is applied to those QCD

jets initially tagged as Tau3P, whose rescaled pT is less than 20 GeV (otherwise there

would be only fake Tau3P candidates with rescaled pT < 20 GeV).

5.4 Consistency checks with the Full Simulation

To test whether the parametrization gives an accurate representation of the full simula-

tion results, an algorithm was written to apply the tau1p3p tagging efficiencies to the

ATLFAST jet collection. The algorithm loops over the ATLFAST jets in each event,

and then tags τ -labelled jets as either Tau1P or Tau3P candidates according to a user

defined efficiency. QCD-labelled jets are then mis-tagged as either Tau1P or Tau3P with

a probability determined by the jet transverse momentum.

This parametrization was applied to the ATLFAST events in the Z → ττ sample

(005149) and the QCD dijet samples (005010, 005011, 005012) (prepared using re-

lease 11.0.41 as described in section 5.1). To investigate whether the fast simulation

parametrization performance accurately reproduces the tau1p3p performance of the full

simulation, the number of identified τ -jets, and their transverse energy distributions,


Identification Factor0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Reje

ctio

n

210

310Tau1P

10 - 20 GeVatlfastT

p



Reje

ctio

n

210

310Tau1P

20 - 30 GeVatlfastT

p



Reje

ctio

n

210

310Tau1P

30 - 40 GeVatlfastT

p



Reje

ctio

n

210

310Tau1P

40 - 50 GeVatlfastT

p



Reje

ctio

n

210

310Tau1P

50 - 60 GeVatlfastT

p



Reje

ctio

n

210

310Tau1P

60 - 70 GeVatlfastT

p


Figure 5.11: Signal identification versus background rejection curves for the parametriza-tion of Tau1P candidate τ -jets. Each plot corresponds to a different 10 GeV bin inpatlfast

T . The points are fitted with an exponential to determine the relationship betweenthe identification and rejection factors.


Identification Factor0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Reje

ctio

n

210

310Tau3P

20 - 30 GeVatlfastT

p



Reje

ctio

n

210

310Tau3P

30 - 40 GeVatlfastT

p



Reje

ctio

n

210

310Tau3P

40 - 50 GeVatlfastT

p



Reje

ctio

n

210

310Tau3P

50 - 60 GeVatlfastT

p



Reje

ctio

n

210

310Tau3P

60 - 70 GeVatlfastT

p


Figure 5.12: Signal identification versus background rejection curves for the parametriza-tion of Tau3P candidate τ -jets. Each plot corresponds to a different 10 GeV bin inpatlfast

T . Below 40 GeV the efficiency is reduced to match the shape of ρreco3P (see figure

5.9). The points are fitted with an exponential to determine the relationship betweenthe identification and rejection factors.


(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t1Pρ

Iden

tifica

tion

Fact

or

0

0.1

0.2

0.3

0.4

0.5

0.6Identification Factor = 25%Identification Factor = 30%Identification Factor = 35%Identification Factor = 40%

Tau1P

(a) Tau1P signal identification factors

(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t3Pρ

Iden

tifica

tion

Fact

or

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 Identification Factor = 6%Identification Factor = 7%Identification Factor = 8%Identification Factor = 9%

Tau3P

(b) Tau3P signal identification factors

(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t1P

QCD

Jet

Rej

ectio

n R

210

310

Identification Factor = 25%Identification Factor = 30%Identification Factor = 35%Identification Factor = 40%

Tau1P

(c) Tau1P rejection factors

(GeV)atlfastT

p0 10 20 30 40 50 60 70

iden

t3P

QCD

Jet

Rej

ectio

n R

210

310

Identification Factor = 6%Identification Factor = 7%Identification Factor = 8%Identification Factor = 9%

Tau3P

(d) Tau3P rejection factors

Figure 5.13: Several choices of signal identification factor, ρident1P/3P for (a) Tau1P and

(b) Tau3P; and the corresponding jet rejection factors Rident1P/3P: (c) and (d). These his-

tograms make up the parametrization of the tau1p3p performance. τ -labelled jets aretagged as Tau1P/3P with an efficiency equal to ρident

1P/3P; while QCD jets are tagged accord-ing to the rejection factors shown. It should be noted that the Tau3P parametrizationis limited to jets above 20 GeV due to the low ρreco

1P/3P of Tau3P candidates below this

value. After tagging, the energy and momentum of fake τ -jets is rescaled (as discussedin the text), which can lead to a further rejection for Tau3P τ -jets, above that shownhere, if the rescaled energy falls out of the kinematic acceptance (i.e. if the rescaled pT

is less than 20 GeV for Tau3P τ -jets).


have been compared for both the full and fast simulation. To investigate the effect

of changes to the τ -labelling procedure in ATLFAST, two fast simulation samples of

Z → ττ events were prepared using release 12.0.4 of the Atlas software, one with the

old τ -labelling scheme (as present in release 11.0.41) and one with the new τ -labelling

scheme (now the default in ATLFAST). The fast simulation samples used in this com-

parison were configured with efficiencies of ρident1P = 35% for Tau1P, and ρident

3P = 8% for

Tau3P. The full simulation PDE-RS discriminant cuts were set accordingly.

Figure 5.14 shows the comparison of full and fast simulation for true hadronic τ -

decays in the Z → ττ sample. Two fast simulation distributions are shown, one for the

old τ -labelling scheme, and one for the new scheme. It can be seen that there are more τ -

jets identified by the full simulation (both Tau1P τ -jets and Tau3P τ -jets). This is due to

the τ -labelling efficiency in ATLFAST (as only jets that are τ -labelled are considered for

tagging as signal candidates). Whilst the τ -labelling efficiency is less than 100 % there

will be extra taus identified by the full simulation that aren’t considered for identification

by the fast simulation. Later developments in ATLFAST have increased the labelling

efficiency (as can be seen in the better agreement between the full simulation and the fast

simulation with the new τ -labelling scheme in figure 5.14), but there is still a systematic

difference between the full and fast simulation results.

The labelling efficiency can be accounted for by only considering full simulation

tau1p3p candidates that match τ -labelled jets in ATLFAST. Figure 5.15 shows a com-

parison between fast simulation (using the old τ -labelling scheme) and full simulation

(adjusted to account for the τ -labelling efficiency). When this is considered, it is seen

that the numbers of tau1p3p candidates from the fast and full simulation are in agree-

ment, as expected. The transverse energy distributions are also consistent.

Figure 5.16 shows a similar comparison for the fake tau1p3p candidates originating

from QCD dijet events. The numbers of Tau1P and Tau3P τ -jets are in fairly good

agreement. The transverse energy distribution for fake τ -jets from full simulation is

compared to the distribution for fast simulation τ -jets (the distribution both before and

after rescaling is shown). The transverse energy distribution of the fast simulation after

rescaling gives greater consistency with full simulation τ -jets than before rescaling. The

transverse energy distribution before rescaling shows some structure corresponding to

the coarse 10 GeV binning of the rejection factors. This is due to the rejection changing

more rapidly than the 10 GeV binning. This is most noticeable at low ET, where the

rejection factor is most rapidly changing. This effect is smoothed out by the energy

rescaling procedure, giving a smooth distribution.


These figures serve as a consistency check to show that, within the limitations of the

method, the fast simulation faithfully reproduces the performance of the full simulation

for the data samples examined. For a more complete view, it would be useful to inves-

tigate other sources of signal and background (e.g. SUSY and tt events) to see how the

performance is related to the event environment.

5.5 Summary

By investigating the reconstruction and identification performance of the tau1p3p al-

gorithm, signal identification factors and background rejection factors were determined.

These factors were calculated from the fraction of ATLFAST jets which matched the

τ -jets reconstructed and identified by tau1p3p in the full simulation. A pT-dependent

fast simulation parametrization of the tau1p3p performance, for use in ATLFAST to tag

jets, is presented. A fast simulation parametrization of the tau1p3p algorithm, based

on the work presented in this chapter, was added to ATLFAST 1 and included in release

12.0.4 of the official ATLAS software.

It is noted that there are limitations in this jet-based approach to parametrization the

τ -identification performance of the track-based tau1p3p algorithm. Whilst ATLFAST

jets provide a good match for the clusters used to seed the taurec algorithm, they are

very different objects to the narrower track-seeded objects that make up the candidate

τ -jets that are reconstructed by the tau1p3p algorithm. The extra parametrization

required to account for the difference in energy scale between the fast simulation jets and

the reconstructed candidate tau1p3p τ -jets in the full simulation, adds an undesirable

extra layer of complexity. Also, the lack of track information in the ATLFAST output,

with the consequence that τ -labelled jets are tagged as 1-prong or 3-prong decays on a

purely statistical basis, is not ideal. The efficiency with which true hadronic τ -decays

are labelled in ATLFAST limits how accurately the fast simulation can reproduce the

full simulation performance. The updated ATLFAST τ -labelling scheme improves the

performance but is still not ideal. A more advanced and desirable approach is to seed

the identification of τ -jets from tracks in the fast simulation. The development of this

alternative approach is presented in chapter 6 of this thesis.

1The parametrization implemented in ATLFAST in release 12.0.4 has some marginal differences tothat presented here. These differences are small compared to the errors associated with the parametriza-tion.


(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

100

200

300

400

500

600

700

800τ τ →Tau1P Z

FullSim-labellingτFastSim New

-labellingτFastSim Old

(a)

(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

20

40

60

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120τ τ →Tau3P Z

FullSim-labellingτFastSim New

-labellingτFastSim Old

(b)

Num. Prongs0 1 2 3 4 5

Num

ber

0

1

2

3

4

5

6

310×

τ τ →Tau1P3P Z FullSim

-labellingτFastSim New -labellingτFastSim Old

(c)

Figure 5.14: A comparison of the true τ -jets identified by the full simulation andthose identified with the fast simulation parametrization of the tau1p3p performance.(a) Transverse energy distributions of identified Tau1P τ -jets from both the full simu-lation and the fast simulation parametrization. The fast simulation is shown for boththe new and old τ -labelling schemes. (b) Equivalent plots for Tau3P. (c) Comparison ofthe total number of Tau1P and Tau3P τ -jets identified in the full and fast simulation.The results are for a user defined efficiency of ρident

1P = 35% for Tau1P, and ρident3P = 8%

for Tau3P in ATLFAST.


(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

100

200

300

400

500

600τ τ →Tau1P Z

-Labelling EffectτAdjusting for

FullSim (Adjusted)FastSim

(a)

(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

20

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100τ τ →Tau3P Z

-Labelling EffectτAdjusting for


(b)


Num

ber

0

1

2

3

4

5

310×

τ τ →Tau1P3P Z -Labelling EffectτAdjusting for


(c)

Figure 5.15: As figure 5.14 except here the full simulation results have been adjustedto account for the τ -labelling efficiency. (a) Transverse energy distributions of identifiedTau1P τ -jets from both the full simulation and the fast simulation parametrization.The fast simulation shown here uses the old τ -labelling scheme. (b) Equivalent plots forTau3P. (c) Comparison of the total number of Tau1P and Tau3P τ -jets identified in thefull and fast simulation. The results are for a user defined efficiency of ρident

1P = 35% forTau1P, and ρident

3P = 8% for Tau3P in ATLFAST.


(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

100

200

300

400

500

600Tau1P J1, J2, J3

FullSimFastSim (before rescaling)FastSim (after rescaling)

(a)

(GeV)TE0 10 20 30 40 50 60 70 80 90 100

Num

ber /

3.3

GeV

0

20

40

60

80

100 Tau3P J1, J2, J3FullSimFastSim (before rescaling)FastSim (after rescaling)

(b)


Num

ber

00.20.40.60.8

11.21.41.61.8

2

310×

Tau1P3P J1, J2, J3FullSimFastSim

(c)

Figure 5.16: A comparison of the fake τ -jets identified by the full simulation andthose identified with the fast simulation parametrization of the tau1p3p performance(using samples of QCD dijet events). (a) Transverse energy distributions of identifiedTau1P τ -jets from both the full simulation, and the fast simulation (before and afterrescaling). (b) Equivalent plots for Tau3P. (c) Comparison of the total number of Tau1Pand Tau3P τ -jets identified in the full and fast simulation. The results are for a userdefined efficiency of ρident

1P = 35% for Tau1P, and ρident3P = 8% for Tau3P in ATLFAST.

Chapter 6

A track-based approach to tau1p3p

fast simulation

6.1 The Advantages of a Track-Based Approach to Fast

Simulation

As discussed in chapter 5, the jet-tagging approach to fast simulation of tau1p3p proved

to be limited in a few key areas. In order to address these limitations and to take

account of developments in the tau1p3p algorithm, a track-seeded approach to the fast

simulation of the tau1p3p algorithm was developed.

The motivation for a track-seeded approach to fast simulation was to overcome some

of these limitations by adding a τ -reconstruction layer to ATLFAST that would mimic

the reconstruction of the track-based τ -jets from the full tau1p3p algorithm. ATLFAST

tracks would be used to seed the reconstruction, with identification efficiencies applied

to the reconstructed τ -jets. This approach has the following main benefits:

• it allows the accurate simulation of the number of tracks both for signal and fake

candidates. Similarly, the track based approach naturally gives the charge of the

candidate.

• the separation of the reconstruction and identification steps removes the need to

parametrize rejection factors of ≈ 1000 and instead involves only rejection factors

of ≈ 10.

98

A track-based approach to tau1p3p fast simulation 99

• no separate parametrization for rescaling the energy of reconstructed τ -jets is

needed.

6.2 Track Parametrization

The tau1p3p algorithm uses good-quality tracks to seed the reconstruction of τ -jets.

“Good-quality” tracks are those tracks that pass a series of selection cuts. ATLFAST

does not apply track reconstruction efficiencies when forming tracks, and neither does it

account for the fraction of tracks that would pass the quality cuts used by the tau1p3p

algorithm. Consequently, the efficiency with which tracks are reconstructed, and the

fraction of tracks which then pass the good quality selection cuts, was investigated using

fully simulated events. This was done separately for electron, muon and pion tracks

(identified from the Monte Carlo truth).

A combination of QCD dijet events and Z → ττ events were used as a source of

pion tracks, with samples of Z → µµ and Z → ee events providing muon and electron

tracks. These events were official ATLAS samples, fully simulated and reconstructed

using the full Monte Carlo production chain. Firstly the track reconstruction efficiency

for electrons, muons and charged pions was investigated as a function of the particle’s

true transverse momentum (pMCT ). The corresponding track reconstruction efficiencies

are shown in figure 6.1.

The corresponding reconstructed tracks were then tested against the following selec-

tion cuts:

• the track fit quality satisfies χ2/Ndf ≤ 1.7

• number of Pixel and SCT hits ≥ 8

• number of TRT hits ≥ 10 (for |η| < 1.9)

• transverse impact parameter d0 < 1.0 mm

These cuts correspond to those used for selecting a good-quality track seed by the

tau1p3p algorithm in the release 13 of Athena. During the course of this study, the

tau1p3p algorithm was still undergoing a period of development, and as such these cuts

were susceptible to change. In particular it should be noted that prior to release 13,


a further requirement on the number of high threshold TRT hits being ≤ 5 was used

(as this provided some rejection against electron tracks). This condition was relaxed

for release 13 as a dedicated electron veto was developed and incorporated into the

identification step [51]. A further development in the release 13 branch involved the

introduction of a separate set of track quality cuts for the second and third tracks. For

these tracks the requirement on the number of TRT hits is replaced by a requirement

that the ratio of high-to-low threshold TRT hits is less than 0.2, and that there is a hit in

the B-layer. These changes were designed to minimise the acceptance of tracks coming

from photon-conversions. At the time of writing, no extension of the fast simulation

algorithm to allow for separate track quality parametrizations for the leading seed track

and associated tracks has been implemented. As such, the same parametrization (cor-

responding to the seed track quality cuts as defined in the above list) is applied to all

ATLFAST tracks. The efficiency with which tracks corresponding to pions, muons and

electrons pass these cuts is shown in figure 6.2. This efficiency is shown as a function of

the reconstructed transverse momentum of the track (ptrackT ).

In order to account for both the track-reconstruction efficiency and the track-quality

efficiency when considering ATLFAST tracks, these two results were combined into an

overall track quality parametrization (see figure 6.3). For a track with a given transverse

momentum, the overall efficiency was calculated by taking the product of the track re-

construction efficiency with the the track quality efficiency. In making this combination,

it was assumed that pMCT ≈ ptrack

T as the error associated with this assumption would

not be significant in terms of the overall parametrization. The variation with pseudo-

rapidity was not considered in the parametrization, and may lead to some differences

when comparing the pseudorapidity distributions of candidate τ -jets in the full and fast

simulation.

The track quality parametrization is applied to ATLFAST tracks as the first step of

the algorithm. For each fast simulation track in a given event, a decision is made as to

whether the track is deemed to have good quality. The three separate parametrizations

from pions, electrons and muons are used for hadronic, muon and electron ATLFAST-

tracks respectively. Depending on the pT of the track in question, the overall track-

quality efficiency is calculated by linearly interpolating between the points (shown in

figure 6.3). The track is tagged randomly according to this efficiency.


(GeV)MCTMC Truth Particle p

10 20 30 40 50 60

Trk

Reco

nstru

ctio

n Ef

f.

0

0.2

0.4

0.6

0.8

1

1.2

PionsMuonsElectrons

Figure 6.1: Track reconstruction efficiencies for pions, muons and electrons as a functionof the particle’s transverse momentum (pMC

T ). Particles are only considered with pMCT >

500 MeV.

(GeV)trackT

Track p10 20 30 40 50 60

Trk

Qua

lity F

ract

ion

0

0.2

0.4

0.6

0.8

1

1.2

PionsMuonsElectrons

Figure 6.2: Efficiency with which tracks pass the track-quality selection cuts as a functionof the transverse momentum of the reconstructed track, ptrack

T . The efficiency for pion,muon and electron tracks are shown separately


(GeV)trackT

Track p10 20 30 40 50 60

Ove

rall T

rk Q

uality

Effi

cienc

y

0

0.2

0.4

0.6

0.8

1

1.2

PionsMuonsElectrons

Figure 6.3: Overall parametrization of the efficiency with which pions, muons and elec-trons are both reconstructed as tracks and pass the track- quality cuts. This parametriza-tion is applied to ATLFAST tracks prior to the track-seeded reconstruction of τ -jets.

6.3 Reconstruction of candidate τ -jets

The mechanism used to reconstruct candidate τ -jets in ATLFAST was designed to mimic

that of the full tau1p3p algorithm. For each event, the algorithm loops over the ATL-

FAST tracks searching for a seed track, from which, a candidate τ -jet can be built. The

seed track is required to have the following properties:

• ptrackT ≥ 9.0 GeV.

• flagged as being of good quality by the track quality parametrization.

• separated from other candidate τ -jets with ∆R ≥ 0.4. This is to prevent overlap

of candidate τ -jets and double counting.

Once a seed track has been found, the next step is to search for nearby tracks in a

reconstruction cone around the seed. To be consistent with the full tau1p3p algorithm,

the size of the cone was set to be ∆Rreco = 0.2. The associated tracks have a looser

transverse momentum cut than the seed track, requiring ptrackT ≥ 1.0 GeV.


The number of prongs associated with the candidate τ -jet is defined as the number

of good quality tracks within the core reconstruction cone of ∆Rreco = 0.2 (including

the seed track), with the exception of 3-prong τ -jets where the combination of two good

quality tracks and one other track is also labelled as a 3-prong τ -jet candidate. An

extra condition requiring that the sum of the charges of the three tracks be | ± 1| is also

applied. These definitions are summarised in table 6.1. Again, they are chosen to agree

with those used in the full tau1p3p algorithm. The η and φ position of the candidate

τ -jet is then defined by the position of the seed track for 1-prong candidate τ -jets,

or the position of the momentum-weighted centre of the track system for multi-prong

candidates.

Ntrack

Number of “good Requirements on

quality” tracks “other” tracks

1-prong 1 —

2-prong 2 No other tracks

3-prong3 —

2 Exactly 1 other track

n-prong (n > 3) n —

Table 6.1: Definition of the number of tracks for a candidate τ -jet.

The energy and mass of the candidate τ -jet are calculated using a method designed

to approximate the energy flow method used in the full reconstruction algorithm (see

equation 4.4).

Firstly, the transverse momentum of any good-quality (ptrack,GQT ) tracks in the cone

∆Rreco (including the seed track) are summed to give the charged contribution to the

transverse energy of the candidate τ -jet (EchgT ).

EchgT =

Ntrack∑i=1

ptrack,GQTi

(6.1)

In addition to the charged component, energy deposits in the ECAL from the neutral

particles inside ∆Rreco need to be considered. The algorithm loops over the Monte Carlo

truth information to find neutral particles within the reconstruction cone. The neutral


component of a candidate τ -jet’s energy is dominated by neutral pions so the transverse

energy of neutral pions found inside the reconstruction cone is summed to give a measure

of the neutral transverse energy, EMCT . For completeness, a contribution to this sum is

also made for any neutrons that are found. A fraction of the neutron’s true energy

can be expected to be deposited in the ECAL. This fraction is estimated to be 30%

by default. However there is a large uncertainty on this figure and it is expected to be

broadly distributed in reality. This is not a significant factor as the effect of neutrons

on the overall performance is small.

In addition to this, the energy from charged particles inside ∆Rreco whose tracks

failed the track-quality parametrization, is also considered. These charged particles do

not contribute to EchgT by virtue of their track not being flagged as being good-quality

but it can be expected that these particles will deposit a fraction of their energy in

the ECAL and as such should contribute towards EneuT . From studies shown in [45],

it was decided that it would be reasonable to estimate that on average these tracks

would deposit approximately 50% of their energy in the electromagnetic calorimeter

(although in reality this fraction can be expected to be broadly distributed depending

on the position of the shower in the calorimeters). Consequently a weighted contribution

from the transverse momentum of any other tracks that are not flagged as being of good

quality (ptrack,OtherT ) is added to the neutral component of the τ -jet’s energy.

Both the invariant mass of the combined track system, M track (only non-zero for

candidates with greater than one track) and the invariant mass of the neutral component

of the energy with the charged component M eflow are calculated. The mass of the

candidate τ -jet is defined as the maximum of these two values. For 1-prong τ -jets, the

fast simulation method (as described so far) will not accurately reproduce the mass

distribution of the reconstructed τ -jet candidates. For these τ -jet candidates where

M track = 0, the mass is given by M eflow. For true hadronic τ -decays with no neutral

pions, the fast simulation will typically return a mass of exactly zero. This is because

in this case EneuT = 0 (i.e. all the energy is contained in the charged component) leading

to a value of M eflow = 0.

In reality it is expected that EneuT will often be non-zero in these cases, as calorimeter

noise and the leakage of energy from the charged component of the decay into calorimeter

cells that aren’t flagged as matching a track, will provide contributions to EneuT . To

account for this, a small amount of “noise” energy (EnoiseT ) is added to the neutral

energy sum, encouraging a non-zero mass (where otherwise the mass would be exactly

zero). This “noise” energy is given by EnoiseT = |ε|

∑ptrack

T where ε is a number drawn


randomly from a Gaussian distribution of width σnoise (with a cut off at |ε| < 3σnoise).

In order to generate a mass, the position of the “noise” energy deposition must be offset

from that of the track system, whilst still located inside ∆Rreco. The separation from

the position of the seed track was assumed to be Gaussian (with σposition = 0.1). Further

discussion of this effect and investigations to determine a suitable value of σnoise are

shown in section 6.4.

Considering all theses effects, the neutral component of the candidate τ -jet’s trans-

verse energy is given by:

EneuT =

∑EMC

T + 0.5×∑

ptrack,OtherT + Enoise

T (6.2)

Furthermore, The overall energy of the candidate τ -jet is then given by:

E =(εchgE

chgT + εneuE

neuT

)cosh (η) (6.3)

where εchg and εneu are smearing factors determined randomly for each candidate from

Gaussian distributions with widths of σchg and σneu respectively (discussed in section 6.4).

Since release 13 of the ATLAS software, the tau1p3p algorithm has incorporated

electron and muon vetoes to reject candidates created from lepton tracks. The fast

simulation algorithm identifies candidate τ -jets that are formed from electron or muon

tracks using the Monte Carlo truth. In order to replicate the performance of the tau1p3p

algorithm in rejecting candidate τ -jets reconstructed from electron and muon tracks, veto

efficiencies are applied to such candidates in the fast simulation. According to studies

of the lepton veto performance using full simulation [52], veto efficiencies of 98 % for

candidate τ -jets mis-reconstructed from electron tracks, and 96 % for candidates mis-

reconstructed from muon tracks, are applied by the fast simulation (resulting in a flag

being set in the output).

During the reconstruction process, the candidate τ -jets are checked as to whether

they originate from a true hadronic τ -decay. The fast simulation candidate τ -jets are

matched to true hadronic τ -decays using the Monte Carlo truth. Those fast simulation τ -

jets that are found to have a spatial separation ∆R < 0.2 from the visible component of a

true hadronic τ -decay are flagged as originating from a true τ -lepton. This information is

used in the identification step to differentiate between true and fake τ -jets when applying

the identification parametrization.


All reconstructed τ -jet candidates are written to the output AtlfastTauJet1p3p

container in the AOD. No check on overlap between the candidate τ -jets and any other

ATLFAST objects (e.g. jets, electrons etc) is carried out. This should be done by the

user during analysis to ensure that there is no double counting.

6.4 Energy and momentum resolution studies

In order for the fast simulation energy and momentum resolution to be in good agreement

with that of the full algorithm, the four-momentum of the candidate τ -jet is smeared.

In order to apply appropriate smearing functions to the fast simulation candidate τ -jets,

the resolution performance for the full simulation is first studied. Figures 6.4 and 6.5

show the offset in the reconstructed transverse momentum from the true value for true

1- and 3-prong τ -jet candidates from full simulation. Figures 6.6 and 6.7 show how this

offset varies as a function of the true visible transverse momentum of the τ -decay, pvisT .

The transverse momentum of the reconstructed candidate τ -jet is denoted by precoT . It

can be seen that the (precoT − pvis

T )/pvisT distributions for 1-prong and 3-prong τ -jets are

quite different, with the distribution for 3-prong τ -jets narrower by a factor of ∼ 3. The

distributions also show some non-Gaussian tails, particularly in the 3-prong case.

Having fitted the (precoT −pvis

T )/pvisT distribution with a Gaussian (a good approximation

of the peak, but not the tails of the distribution) in different transverse momentum slices,

figure 6.8 shows how the the width of the distribution varies as a function of transverse

momentum. This is shown for both 1-prong and 3-prong candidate τ -jets. As previously

mentioned, the resolution for 3-prong τ -jets (≈ 3 %–4 %) is narrower than for 1-prongs

(≈ 8 %–10 %). The 3-prong τ -decays are typically dominated by the charged component,

and consequently the resolution is dominated by the measurement of the momenta of

the constituent tracks. 1-prong τ -decays typically have a larger neutral component. The

difference in the resolution of the 1-prong and 3-prong τ -jets can be understood to arise

from the resolution on the neutral component of the decay. This is demonstrated in

figure 6.8 where the width of the offset distribution for 1-prong τ -jets after various cuts

on the fraction of the τ -jet’s transverse energy originating from the tracks, is shown. It

can be seen that increasing the dominance of the track component of the 1-prong energy

narrows the distribution, tending towards that of the 3-prong τ -jets. This indicates that

the resolution on the charged component of the energy is ≈ 3 %–4 %. This figure also

implies that the resolution on the neutral component contributes significantly to the


visT) / pvis

T - precoT(p

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Entri

es /

0.02

0

1000

2000

3000

4000

5000

6000Mean = -0.00514

= 0.089σ

Figure 6.4: (precoT − pvis

T )/pvisT for true 1-prong tau1p3p τ -jets from full simulation (for

Z → ττ events). A Gaussian fit to the peak is also shown (red line).

overall energy resolution for 1-prong τ -jets. In the energy flow method, the calculation

of the neutral component of the energy can be complicated when clusters from neutral

pions overlap with clusters from charged pions, or if there is significant leakage of energy

from the charged pion outside of the calorimeter cells assigned to the corresponding

track.

As a consequence, it was decided to smear the charged and neutral components

separately in the fast simulation algorithm. The results shown in figure 6.8 were used

to estimate appropriate smearing functions to use. Gaussian distributions of width

σchg = 0.035 and σneu = 0.40 were used to smear the charged and neutral components

of the energy respectively (as described in the previous section). There will be a sig-

nificant error associated with this choice of σneu, although the overall effect of this on

the resolution is not expected to be great. The fast simulation is not expected to per-

fectly reproduce the shape of the resolution distributions, although with these smearing

functions it is possible to produce a good approximation.

As previously mentioned, a noise contribution to the neutral energy is required in

order to reasonably reproduce the mass distribution of τ -jet candidates. The justification

for this can be seen in figure 6.9 which shows the mass distribution for 1-prong candidate

τ -jets in a sample of Z → ττ events for the full simulation and also for the fast simulation


visT) / pvis

T - precoT(p

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Entri

es /

0.02

0

500

1000

1500

2000

2500

3000

3500 Mean = 0.00598 = 0.0317σ


T )/pvisT for true 3-prong tau1p3p τ -jets from full simulation (for

Z → ττ events). A Gaussian fit to the peak is also shown (red line).

Entri

es /

0.02

/ 1

GeV

020406080100120140160180200220240

visT) / pvis

T - precoT(p

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

(GeV

)vis Tp

0102030405060708090

100


T )/pvisT as a function of pvis

T for true 1-prong tau1p3p τ -jets (forZ → ττ events).


Entri

es /

0.02

/ 1

GeV

0

20

40

60

80

100

120

140

160

180

visT) / pvis

T - precoT(p

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

(GeV

)vis Tp

0102030405060708090

100


T )/pvisT as a function of pvis

T for true 3-prong tau1p3p τ -jets fromfull simulation (for Z → ττ events).

(GeV)visTp

0 10 20 30 40 50 60 70 80 90 100

σ

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16 True 1-prong > 0.85)T/Etrack

T pΣTrue 1-prong (

> 0.90)T/EtrackT

pΣTrue 1-prong ( > 0.95)T/Etrack

T pΣTrue 1-prong (

True 3-prong

Figure 6.8: The variation in the fitted width of the (precoT −pvis

T )/pvisT distribution with pvis

T

for 1-prong and 3-prong tau1p3p τ -jets. The distribution is narrower for 3-prong thanfor 1-prong τ -decays. Also shown are values for 1-prong τ -decays for several differentcuts on the fractional contribution from tracks to the total transverse energy.


Mass [GeV]0 0.5 1 1.5 2 2.5

Nor

mal

ized

Units

/ 0.

1 G

eV

0

0.1

0.2

0.3

0.4

0.5 = 0.00001noiseσFast Sim. = 0.015noiseσFast Sim. = 0.03noiseσFast Sim.

Full Simulation

Figure 6.9: The mass distribution of 1-prong fast simulation candidate τ -jets (fromZ → ττ events) for different values of σnoise. The corresponding distribution for 1-prongcandidate τ -jets from full simulation is also shown. A large peak at zero mass develops asσnoise tends to zero. The addition of noise significantly improves the agreement betweenthe fast and the full simulation.

with three values of σnoise. For a negligible value (σnoise = 0.00001) it can be seen that

the mass distribution is sharply peaked at zero. By broadening the noise distribution,

values for the mass are smeared away from this peak into a more natural distribution

that is in good agreement with the full simulation results.

Figures 6.10 and 6.11 show the variation of the pT-offset distributions of 1- and 3-

prong τ -jets for different values of σnoise. It can be seen that the value of σnoise has

an impact on the distribution, with increasing σnoise values increasing the offset of the

distribution. Consequently, a value of σnoise = 0.015 was chosen so as to give the de-

sired correction to the mass distribution of 1-prong candidates, without introducing too

significant a shift in the pT reconstruction. The resulting bias of the peak from the full

simulation distribution is within the limits expected for a fast simulation. The non-

Gaussian tails of the (precoT −pvis

T )/pvisT distributions present in the full simulation are not

accurately replicated in the fast simulation, although it is deemed that the fast simula-

tion resolution function presented here is a good approximation. The addition of noise

does not have any effect on the definition of the (η,φ) position of the candidate τ -jet as

this is determined solely from the track(s).


visT)/pvis

T-precoT(p

-0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4

Nor

mal

ized

Units

/ 0.

02

0

0.02

0.04

0.06

0.08

0.1 = 0.00001noiseσFast Sim. = 0.015noiseσFast Sim. = 0.03noiseσFast Sim.

Full Simulation

1-prong


T )/pvisT for true 1-prong fast simulation candidate τ -jets (from

Z → ττ events) for different values of σnoise. Also shown is the corresponding distributionfor 1-prong candidate τ -jets from full simulation.

visT)/pvis

T-precoT(p

-0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4

Nor

mal

ized

Units

/ 0.

02

00.020.040.060.08

0.10.120.140.160.18 = 0.00001noiseσFast Sim.

= 0.015noiseσFast Sim. = 0.03noiseσFast Sim.

Full Simulation

3-prong


T )/pvisT for true 3-prong fast simulation candidate τ -jets (from

Z → ττ events) for different values of σnoise. Also shown is the corresponding distributionfor 3-prong candidate τ -jets from full simulation.


6.5 Reconstruction Performance

Figures 6.12, 6.13, 6.14, 6.15 and 6.16 show comparisons of the reconstruction perfor-

mance of the fast simulation with that of the full tau1p3p algorithm for several different

samples. Comparisons of the number of reconstructed τ -jets the Ntrack distribution, the

pT-, η- and φ-distributions and the reconstructed charge are shown. The results show

that the number of fast simulation candidate τ -jets reconstructed per event is a good

match for the lower pT samples, but for the higher pT QCD samples it can be seen that

the fast simulation is reconstructing fewer candidate τ -jets.

The Ntrack distribution is typically well reproduced, although there is a systematic

reduction in the number of fast simulated 2-prong τ -jets when compared to the full

simulation, compensated by an excess of 3-prong τ -jets, suggesting that the labelling

of candidates with two “good quality” tracks and one “other” track does not translate

perfectly from the full simulation to the fast simulation. Furthermore, for higher track

multiplicities the track parametrization can be expected to deteriorate as it does not

specifically consider any reduction in the track quality that would occur for multiple

tracks in close proximity.

The precoT distribution of candidate τ -jets is well reproduced for the Z → ττ sample

and the lower pT QCD dijet samples. For higher pT dijet events, the fast simulation

distribution begins to deviate from the full simulation. The distributions of the η and φ

positions of the fast simulation candidate τ -jets are in good agreement with those from

full simulation.

Figure 6.17 shows a comparison between full and fast simulation for the reconstruc-

tion resolution of true τ -jets. The pT-, η- and φ-resolutions of reconstructed τ -jet can-

didates corresponding to true hadronic τ -decays are shown for both the full and fast

simulation. The reconstructed candidate τ -jets are matched to the visible component of

true hadronic τ -decays with a ∆R < 0.2. The resolutions are shown separately for re-

constructed 1-prong and 3-prong candidate τ -jets. It can be seen that there is excellent

agreement for the η and φ resolutions. The fast simulation does not exactly reproduce

the pT resolution of the full tau1p3p algorithm, but it can be seen that it presents a

reasonable approximation. As discussed in section 6.4, the resolution function for the

full simulation is a complicated function, and it isn’t expected that a particle level fast

simulation will perfectly reproduce the full simulation shape.


Num. Taus per event0 2 4 6 8

Entri

es /

Even

t

0

0.1

0.2

0.3

0.4

0.5ττ→Dataset: Z

Fast SimFull Sim

(a) Number of reconstructed candidate τ -jets per event.

N-track0 2 4 6 8

Entri

es /

Even

t

0

0.2

0.4

0.6

0.8

1

1.2

1.4 ττ→Dataset: ZFast SimFull Sim

(b) Track multiplicity of reconstructed can-didate τ -jets.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 ττ→Dataset: ZFast SimFull Sim

(c) Transverse momentum distribution of re-constructed candidate τ -jets.

recoη-2 0 2

Entri

es /

Even

t

0

10

20

30

40

50

-310×ττ→Dataset: Z

Fast SimFull Sim

(d) Pseudorapidity distribution of recon-structed candidate τ -jets.

recoφ-2 0 2

Entri

es /

Even

t

0

5

10

15

20

25

30

35


Fast SimFull Sim

(e) Phi distribution of reconstructed candi-date τ -jets

Charge-5 0 5

Entri

es /

Even

t

00.10.20.30.40.50.60.70.80.9 ττ→Dataset: Z

Fast SimFull Sim

(f) Charge of reconstructed candidate τ -jets

Figure 6.12: A comparison of the track-based τ -reconstruction performance using thefast simulation to that of the full simulation (release 13.0.30) for the Z → ττ sample.All histograms are normalized by the total number of events in the sample.



Entri

es /

Even

t

0

0.2

0.4

0.6

0.8

1

1.2 Dataset: QCD J1Fast SimFull Sim


N-track0 2 4 6 8

Entri

es /

Even

t

05

101520

2530

3540

45-310×

Dataset: QCD J1Fast SimFull Sim


(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

2

4

6

8

10

12

14

16

-310×Dataset: QCD J1

Fast SimFull Sim


recoη-2 0 2

Entri

es /

Even

t

0

0.5

1

1.5

2

2.5

3


Fast SimFull Sim


recoφ-2 0 2

Entri

es /

Even

t

0

0.5

1

1.5

2

2.5

3-310×



Charge-5 0 5

Entri

es /

Even

t

0

5

10

15

20

25

30

35

40


Fast SimFull Sim


Figure 6.13: A comparison of the track-based τ -reconstruction performance using thefast simulation to that of the full simulation (release 13.0.30) for the J1 QCD dijetsample. All histograms are normalized by the total number of events in the sample.



Entri

es /

Even

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0

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0.4

0.5

0.6

0.7



N-track0 2 4 6 8

Entri

es /

Even

t

00.020.040.060.08

0.10.120.140.160.180.2

0.22Dataset: QCD J2

Fast SimFull Sim


(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

10

20

30

40

50


Fast SimFull Sim


recoη-2 0 2

Entri

es /

Even

t

0

2

4

6

8

10

12

14

16-310×



recoφ-2 0 2

Entri

es /

Even

t

0

2

4

6

8

10

12


Fast SimFull Sim


Charge-5 0 5

Entri

es /

Even

t

00.020.040.060.08

0.10.120.140.160.18 Dataset: QCD J2

Fast SimFull Sim


Figure 6.14: A comparison of the track-based τ -reconstruction performance using thefast simulation to that of the full simulation (release 13.0.30) for the J2 QCD dijetsample. All histograms are normalized by the total number of events in the sample.



Entri

es /

Even

t

0

0.1

0.2

0.3

0.4

0.5



N-track0 2 4 6 8

Entri

es /

Even

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0.05

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0.15

0.2

0.25

0.3

0.35



(GeV)recoT

p0 50 100 150 200

Entri

es /

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t

0

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20

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40

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60


Fast SimFull Sim


recoη-2 0 2

Entri

es /

Even

t

0

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20

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35

40-310×



recoφ-2 0 2

Entri

es /

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t

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25


Fast SimFull Sim


Charge-5 0 5

Entri

es /

Even

t

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45Dataset: QCD J3

Fast SimFull Sim


Figure 6.15: A comparison of the track-based τ -reconstruction performance using thefast simulation to that of the full simulation (release 13.0.30) for a J3 QCD dijet sample.All histograms are normalized by the total number of events in the sample.



Entri

es /

Even

t

0

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0.4



N-track0 2 4 6 8

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(GeV)recoT

p0 50 100 150 200

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30

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40

45-310×



recoη-2 0 2

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es /

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50


Fast SimFull Sim


recoφ-2 0 2

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es /

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t

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Fast SimFull Sim


Charge-5 0 5

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es /

Even

t

0

0.1

0.2

0.3

0.4

0.5



Figure 6.16: A comparison of the track-based τ -reconstruction performance using thefast simulation to that of the full simulation (release 13.0.30) for a J4 QCD dijet sample.All histograms are normalized by the total number of events in the sample.


visT )/pvis

T - precoT(p

-1 -0.5 0 0.5 10

0.02

0.04

0.06

0.08

0.1

0.12Fast Simulation1-Prong Fast SimulationFull Simulation

1-Prong

(a) pT-resolution for 1-prong τ -jets.

visT )/pvis

T - precoT(p

-1 -0.5 0 0.5 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18Fast Simulation3-Prong Fast SimulationFull Simulation

3-Prong

(b) pT-resolution for 3-prong τ -jets.

visη - recoη-0.1 -0.05 0 0.05 0.1

-410

-310

-210

-110Fast Simulation1-Prong Fast SimulationFull Simulation

1-Prong

(c) η-resolution for 1-prong τ -jets.

visη - recoη-0.1 -0.05 0 0.05 0.1-410

-310

-210

-110

Fast Simulation3-Prong Fast SimulationFull Simulation

3-Prong

(d) η-resolution for 3-prong τ -jets.

visφ - recoφ-0.1 -0.05 0 0.05 0.1

-410

-310

-210

-110Fast Simulation1-Prong Fast SimulationFull Simulation

1-Prong

(e) φ-resolution for 1-prong τ -jets.

visφ - recoφ-0.1 -0.05 0 0.05 0.1-410

-310

-210

-110

Fast Simulation3-Prong Fast SimulationFull Simulation

3-Prong

(f) φ-resolution for 3-prong τ -jets.

Figure 6.17: A comparison of the pT-, η- and φ-resolutions for true candidate τ -jets inthe full simulation (dashed line) and the fast simulation (solid line). The resolutions areshown separately for both reconstructed 1-prong (left) and 3-prong (right) candidateτ -jets (using Z → ττ events). All histograms are normalized to unit area.


6.6 Identification Step

The final step of the fast simulation process is to make an identification decision for

each reconstructed candidate τ -jet. This is done by applying a parametrization of the

efficiency with which fully simulated candidate τ -jets pass the identification cuts.

Since the τ -identification requirements for different analyses are expected to vary,

it was decided to provide a simple parametrization corresponding to the baseline cuts-

based discriminant as a default. For custom based analyses, the user can either provide

alternative parametrization files during runtime (this was designed to be configurable

using job options) or apply a custom parametrization during the offline analysis (as

all the reconstructed τ -jets are saved to the AOD). For the following discussion, a full

simulation τ -jet is described as “identified” if it passes the cuts-based discriminant and

the electron and muon vetoes. This identification criteria is then used to prepare a

corresponding parametrization for use in ATLFAST.

The identification performance of the tau1p3p algorithm was investigated using cen-

trally produced samples of Monte Carlo events simulated as part of the ATLAS CSC

exercise. Samples of Z → ττ events were used to provide signal τ -leptons, and QCD

dijet events (taken from different pT ranges) were used as a source of fake τ -jets to de-

termine the rejection power of the algorithm. The samples are summarised in table 6.2.

Sample Dataset Code Number of Events

Z → ττ 005188 196,800

QCD dijets

J1 (17–35 GeV) 005010 392,850

J2 (35–70 GeV) 005011 227,550

J3 (70–140 GeV) 005012 404,800

J4 (140–280 GeV) 005013 379,650

Table 6.2: The fully simulated Monte Carlo event samples used to generate the identi-fication parametrization.

For each fully simulated sample, the fraction of tau1p3p reconstructed τ -jets that

are also identified is calculated. A reconstructed candidate τ -jet is determined to be

“true” if it is matched to the visible component of true hadronic τ -decays in a cone of

∆R < 0.2. Candidates that don’t satisfy this criteria are labelled as “fake”.


Table 6.3 shows the fraction of true candidate τ -jets that pass the identification

cuts for a sample of Z → ττ events. These candidates were used as a source of true

τ -leptons in preparing the fast simulation parametrization. Table 6.4 shows the fraction

of identified candidate τ -jets for each of the J1, J2, J3 and J4 QCD dijet samples. It can

be seen that there is a significant variation in the fraction of candidate τ -jets passing the

identification step for different QCD dijet samples. With QCD events providing the most

significant backgrounds in τ -reconstruction, a combination of these four dijet samples

was used to provide the fake candidate τ -jets used to parametrize the identification

performance for fake τ -jets.

1-Prong 2-Prong 3-Prong

Z → ττTrue Taus Reconstructed 118,893 15,604 36,184

True Taus Identified 79,626 (67%) 10,504 (67%) 27,864 (77%)

Table 6.3: A summary of the numbers of true reconstructed τ -jets (matched to truehadronic τ -decays from the Monte Carlo truth) passing the tau1p3p cut based discrim-inant for Z → ττ events.

1-Prong 2-Prong 3-Prong

J1Taus Reconstructed 12,834 11,227 8,654

Taus Identified 3,933 (31%) 3,883 (35%) 3,122 (36%)


Taus Identified 3,832 (23%) 6,336 (28%) 9,586 (29%)


Taus Identified 5,815 (15%) 10,498 (20%) 18,505 (15%)


Taus Identified 4,332 (10%) 6,926 (14%) 11,122 (8%)

Table 6.4: The percentage of fake reconstructed τ -jets passing the tau1p3p cut baseddiscriminant for fully simulated QCD dijet events in different pT ranges. Only thenumbers corresponding to 1-, 2- and 3-prong candidate τ -jets are shown.

Candidate τ -jets are categorised based on whether they are a true or fake candidate

and on their number of prongs. The candidates are separated according to whether


they are 1-prong, 2-prong, 3-prong or have a higher track multiplicity (four or more

prongs). When considering both true and fake candidate τ -jets, this leads to a total

of eight categories, each one with a separate identification parametrization. Since true

candidate τ -jets with greater than three prongs are very rare, it was decided that a

separate parametrization for these cases was not necessary, and the same parametrization

as for the 3-prong candidates was used. The reconstructed candidate τ -jets are randomly

tagged as to whether they are identified according to probabilities drawn from these

parametrizations. The algorithm reads in these parametrizations from external files

(so allowing the user to apply their own parametrization should they so wish). These

parametrizations are pT dependent and are split into two η regions (a central region

with |η| < 1.25 and a high-η region (1.25 < |η| < 2.5). Within the bounds of the

parametrization the probability of being tagged is calculated by a linear interpolation

of the points of the parametrization. Outside the bounded points, the probability is

assumed to be constant. The default parametrizations are shown in figures 6.18 and

6.19.

The tau1p3p algorithm’s identification discriminants are designed to reject fakes

reconstructed from QCD jets. They are not optimised to reject fake τ -jets reconstructed

from electron or muon tracks. These fake candidate τ -jets have a significantly higher

probability of passing the identification discriminant than fakes from QCD. In the full

tau1p3p algorithm, separate muon and electron vetoes have been included to reject

leptonic fakes. Since QCD is the dominant source of background, it was decided not

to add extra parametrizations to the fast simulation specifically for the identification of

fake τ -jets from electron and muon tracks. In reality fake candidate τ -jets from leptons

will have a significantly higher probability of passing the discriminant cut than QCD

fakes. However, since the electron and muon veto efficiencies are high (see section 6.3),

this does not have a significant effect.

As a test of the overall identification performance of the fast simulation, figures 6.20

and 6.21 show comparisons between the identification performance of the full and fast

simulation for both a sample of Z → ττ events and a sample of SUSY 1 events respec-

tively.

The Z → ττ sample was used as the model on which the signal parametrizations

were developed, and as such comparisons for this sample provide a useful consistency

check. The fast simulation shows a good agreement with the full simulation results in

1The SUSY point studied is the ATLAS SU3 “Bulk region” benchmark point; an mSUGRA pointwith m0 = 100 GeV, m 1

2= 300 GeV, A0 = -300 GeV, tanβ = 10 and sgn(µ) = +.


(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.10.20.30.40.50.60.70.80.9

1True 1-prong

|<1.25η||<2.5η1.25<|

(a) 1-prong

(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.10.20.30.40.50.60.70.80.9

1True 2-prong

|<1.25η||<2.5η1.25<|

(b) 2-prong

(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.10.20.30.40.50.60.70.80.9

1True 3-prong

|<1.25η||<2.5η1.25<|

(c) 3-prong

Figure 6.18: The identification efficiency with which true (a) 1-prong, (b) 2-prong and(c) 3-prong τ -jet candidates are identified by the tau1p3p algorithm. The efficiencyis shown as a function of pT and for two η-regions (i) |η| < 1.25 (black points) and(ii) 1.25 < |η| < 2.5 (red points). The parametrization is calculated from a sample ofZ → ττ events (details of which are shown in table 6.2).


(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.05

0.10.150.2

0.250.3

0.350.4

0.450.5

Fake 1-prong|<1.25η|

|<2.5η1.25<|

(a) 1-prong

(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.05

0.10.150.2

0.250.3

0.350.4

0.450.5


|<2.5η1.25<|

(b) 2-prong

(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.05

0.10.150.2

0.250.3

0.350.4

0.450.5


|<2.5η1.25<|

(c) 3-prong

(GeV)T

p10 20 30 40 50 60 70 80 90 100

Iden

t. Fr

actio

n

00.05

0.10.150.2

0.250.3

0.350.4

0.450.5

Fake 4/5/6-prong|<1.25η|

|<2.5η1.25<|

(d) 4/5/6-prong

Figure 6.19: The identification efficiency with which fake (a) 1-prong, (b) 2-prong, (c) 3-prong and (d) 4/5/6-prong candidate τ -jets are identified by the tau1p3p algorithm. Theefficiency is shown as a function of pT and for two η-regions (i) |η| < 1.25 (black points)and (ii) 1.25 < |η| < 2.5 (red points). The parametrization is calculated from a mixedsample of J1, J2, J3 and J4 dijet events (details of which are shown in table 6.2).


both the transverse momentum and pseudorapidity distributions. Figures 6.20(d) and

6.20(e) show the transverse momentum distributions for 1- and 3-prong candidate τ -jets

that are matched to true hadronic τ -decays. It can be seen that the fast simulation

reproduces the full simulation performance in these cases, confirming that the separate

parametrizations for true 1- and 3-prong τ -jets perform well.

As a further test of the performance, a comparison between the fast and full simula-

tion for SUSY events is also shown. Typically, SUSY events involve two cascade decays

producing multiple jets and leptons in the final state, often with more activity in the

detector than for simpler Z → ττ events. As SUSY events have a different topology to

the Z → ττ sample used in generating the parametrization, this comparison allows some

measure of how sensitive the performance of the fast simulation is to different event

topologies. It can be seen that the fast simulation is in good agreement with the full

simulation.

Figure 6.22 shows the Ntrack spectra for identified candidate τ -jets in both the fast

and full simulation for different QCD dijet samples. The fast simulation provides a

reasonable reproduction of the Ntrack spectra for the requirements of fast simulation,

and represents an improvement on previous methods of fast simulation. The main

discrepancy between the full and fast simulation comes from the numbers of 2-prong

candidate τ -jets. Figure 6.20(a) shows the Ntrack spectrum for the identified τ -jets, and

whilst the numbers of 1- and 3-prong τ -jets are in reasonable agreement, there is a large

deficit in the number of 2-prong τ -jets. This deficit originates from the reconstruction

step, and is common to all samples investigated. For many analyses only 1- and 3-prong

candidate τ -jets will be used as signal, however for analyses that require the observation

of a dip in the Ntrack spectrum for 2-prong τ -jets as a signal for the presence of hadronic

τ -decays (e.g. W → τν analyses in early data) this effect will cause a systematic bias.

For such analyses, a further tuning could be applied in order to correct for this effect.


N-track0 2 4 6 8

Entri

es /

Even

t

0

0.1

0.2

0.3

0.4

0.5

0.6ττ→Dataset: Z

Fast SimFull Sim

(a) The track multiplicity of identified can-didate τ -jets.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

10

20

30

40

50

60

70-310×

ττ→Dataset: ZFast SimFull Sim

(b) The transverse momentum distributionof all identified τ -jets candidates.

recoη-2 0 2

Entri

es /

Even

t

02468

1012141618202224


Fast SimFull Sim

(c) The pseudorapidity distribution of allidentified τ -jets candidates.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

5

10

15

20

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35

40


Fast SimFull Sim

(d) The transverse momentum distributionof true identified 1-prong candidates.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

02468

101214161820


Fast SimFull Sim

(e) The transverse momentum distributionof identified true 3-prong candidates.

Figure 6.20: A comparison of the performance of the full and fast simulations for identi-fied candidate τ -jets for the Z → ττ sample. All histograms are normalized by the totalnumber of events in the sample.


N-track0 2 4 6 8

Entri

es /

Even

t

00.020.040.060.08

0.10.120.140.160.180.2

0.22 Dataset: SUSYFast SimFull Sim

(a) The track multiplicity of identified can-didate τ -jets.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

5

10

15

20

25-310×

Dataset: SUSYFast SimFull Sim

(b) The transverse momentum distributionof all identified candidate τ -jets.

recoη-2 0 2

Entri

es /

Even

t

02468

1012141618

-310×Dataset: SUSY

Fast SimFull Sim

(c) The pseudorapidity distribution of allidentified candidate τ -jets.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

2

4

6

8

10-310×


(d) The transverse momentum distributionof true identified 1-prong candidates.

(GeV)recoT

p0 50 100 150 200

Entri

es /

Even

t

0

0.5

1

1.5

2

2.5

3

3.5

4-310×


(e) The transverse momentum distributionof true identified 3-prong candidates.

Figure 6.21: A comparison of the performance of the full and fast simulations for iden-tified candidate τ -jets for the SUSY sample. All histograms are normalized by the totalnumber of events in the sample.


N-track0 2 4 6 8

Entri

es /

Even

t

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4

6

8

10

12

14-310×


(a) J1 QCD dijet sample

N-track0 2 4 6 8

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es /

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50


Fast SimFull Sim

(b) J2 QCD dijet sample

N-track0 2 4 6 8

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Fast SimFull Sim

(c) J3 QCD dijet sample

N-track0 2 4 6 8

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es /

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30

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50


Fast SimFull Sim

(d) J4 QCD dijet sample

Figure 6.22: A comparison of theNtrack spectra for identified track-based τ -jets in the fastsimulation and full simulation (release 13.0.30) for QCD dijet samples. All histogramsare normalized by the total number of events in the sample.


6.7 Summary

Having investigated expanding the existing τ -tagging functionality in ATLFAST to in-

corporate the tau1p3p performance, the advantages of an explicit track-seeded approach

to fast simulation became apparent. Such an approach being a better reflection of the

tau1p3p algorithm being modelled. The development of an algorithm for the reconstruc-

tion and identification of track-seeded τ -jets within the ATLFAST program has been

presented. The approach uses ATLFAST tracks to seed a dedicated τ -reconstruction

layer, demonstrating the use of a pT-dependent track-quality parametrization in the re-

construction of candidate τ -jets. The resulting reconstruction performance is a good

reproduction of the full simulation performance, with good position and momentum

resolution and reproduction of the Ntrack spectrum (not previously simulated in ATL-

FAST).

A parametrization of the τ -identification performance has been developed. The sim-

ple parametrization aims to reproduce the performance of the tau1p3p cut-based dis-

criminant. Further development of the algorithm could include a more advanced identifi-

cation parametrization, incorporating the performance of the multi-variate discriminants

(e.g the Neural Network discriminant) for a range of signal efficiencies. In light of the

developments in a merged τ -reconstruction algorithm, there is scope for reflecting this

in future fast simulation developments.

The algorithm, as presented here, has been incorporated into ATLFAST in version

14 of Athena and is run by default in ATLAS Monte Carlo production. This chapter

concludes the development work on the fast simulation of τ -reconstruction presented in

this thesis. The scope of the thesis now shifts towards studies of RPV SUSY models in

ATLAS.

Chapter 7

Studies of RPV SUSY models

The phenomenology of R-parity conserving (RPC) SUSY models has been studied in

great depth in ATLAS in preparation for data taking at the LHC [42, 53]. R-parity

violating (RPV) [54, 55] models can result in very different phenomenology to that

expected for R-parity conserving models (high-multiplicity final states, no guarantee

of large missing energy signatures) and consequently different analysis techniques are

needed. Various studies of RPV models have been carried out in the context of ATLAS

(mainly based on fast simulation results) [56–60].

This chapter presents studies into R-parity violating models and their detection at

ATLAS using the full ATLAS detector simulation. This analysis has been run in parallel

with the ATLAS CSC 1 exercise, with official CSC Monte Carlo simulations providing

samples of Standard Model backgrounds2. The analysis focuses on two SUSY points,

defined in an mSUGRA framework, extended to include RPV couplings. The two points

are defined such that one explores the possibility of a τ1 LSP, and the second deals

with the more commonly considered case of a χ01 LSP. The full simulation allows a

more detailed study to be performed in preparation for the analysis of data during LHC

running.

1The ATLAS Computing System Commissioning (CSC) exercise involved a large Monte Carlo pro-duction. These simulated data were used to test the ATLAS computing systems and to develop physicsanalyses.

2No RPV SUSY signal samples were produced by the ATLAS central CSC production. The need fora custom MC generator required signal samples to be produced privately

129

Studies of RPV SUSY models 130

7.1 RPV SUSY

As introduced in chapter 1, supersymmetry (SUSY) provides a theoretically interest-

ing extension to the Standard Model (SM), that can address several of the limitations

that it currently faces. The minimal supersymmetric Standard Model (MSSM) offers

an extension to the SM incorporating SUSY. In the MSSM, a discrete global sym-

metry is introduced which, if conserved, has the effect of eliminating the possibility

of baryon-number (B) and lepton-number (L) violating terms from the superpotential.

This symmetry is known as “R-parity”, with a conserved quantum number, Rp, defined

for a particle with spin s, as

Rp = (−1)3(B−L)+2s =

+1 for SM particles

−1 for their superpartners(7.1)

The conservation of Rp has the effect of excluding the following terms

WRPV =1

2λijkLiLjEk + λ′ijkLiQjDk +

1

2λ′′ijkUiDjDk + κiLiHu (7.2)

from the superpotential (as discussed in section 1.4.3). However, RPC models are not

the only option when considering SUSY extensions to the SM. Despite the constraints

posed by the non-observation of proton decay, RPV models cannot be ruled out and it

is therefore important to study them in the context of the LHC. Proton decay limits

imply that it is sufficient that only one of B and L be conserved. In other words, it

is possible to have a non-zero contribution from either the trilinear λ, λ′ or bilinear κ

terms, or a non-zero contribution from the trilinear λ′′ terms in equation 7.2 without

giving unphysical proton decay rates. Focusing only on the trilinear couplings, figure 7.1

illustrates the possible couplings that may exist should any of λ, λ′ or λ′′ be non-zero.

The MSSM with Rp conservation has over 100 free parameters, with significantly

more parameters when it is extended to include Rp violation [61]. Such a parameter set

is not practical for phenomenological study, so simpler models are typically investigated.

In this analysis the mSUGRA model is used, with its five associated parameters (m0,

m 12, A0, tanβ and sgn(µ)). To incorporate Rp-violation into mSUGRA [62, 63], the

model is extended to include a single non-zero RPV coupling

Λ ∈{λijk, λ

′ijk, λ

′′ijk

}. (7.3)


˜−

ν

`−

λ

(a) λ-type coupling

q

¯

q

λ′

(b) λ′-type coupling

q

q

q

λ′′

(c) λ′′-type coupling

Figure 7.1: Examples of trilinear RPV couplings. The arrows on the (s)quark and(s)lepton lines denote the flow of B and L respectively.

in addition to the five mSUGRA parameters. The single non-zero RPV coupling is

defined at the GUT scale. However it should be noted that the existence of a single RPV

coupling at the GUT scale can result in the dynamical generation of other couplings at

the electro-weak scale.

7.2 RPV signatures at the LHC

In RPC models, sparticles are constrained to be produced in pairs, each of which are

restricted to decay to an odd number of sparticles (typically one). This results in the

lightest supersymmetric particle being stable. Arguments based on the non-observation

of massive, stable, charged particles lead to the requirement that the LSP carry no

electric or colour charge [12]. Such a particle must be weakly interacting and would

have been produced in abundance in the early universe. These properties make the

LSP in RPC SUSY models a popular explanation for the dark matter present in the

universe. The consequences for collider experiments are that the sparticles are pair

produced leading to two cascade decays through lighter sparticle states. These cascades

proceed until the LSP is reached, at which point no further decays are possible, and the

invisible LSP leaves the detector. Such events will be characterised by a large missing

transverse momentum (pmissT ). This characteristic is commonly used in the analysis of

RPC models in order to separate SUSY events from SM backgrounds.

The introduction of Rp-violating (RPV) couplings can have a dramatic influence on


the expected experimental signatures at the LHC. The difference between RPV and RPC

SUSY signatures is controlled by both the flavour and strength of the RPV coupling Λ.

For Λ & 10−2, Rp-violation can result in significant changes to the SUSY mass spectrum,

sparticle production, branching ratios and decay chains. For intermediate values of the

coupling, 10−4 . Λ . 10−2, the dominant effect is that the LSP becomes unstable (with

no significant alteration to the rest of the decay chain). As a consequence, pmissT does not

necessarily represent a strong signature in RPV SUSY, and other features need to be

exploited. For this range of coupling, one can expect a prompt decay of the LSP, with

the flavour of the coupling and the species of LSP determining the overall event topology.

For smaller Λ values, the lifetime of the LSP can be expected to become significant on

the scale of the detector. LSP decays can be expected to result in detached vertices that

could provide a further signature to help reduce backgrounds.

The following combination of tools were used in order to investigate physics signatures

in RPV SUSY models. The SOFTSUSY [64] package3 was used to calculate the mass

spectra and RPV couplings at given points in mSUGRA parameter space and for a

chosen value of the RPV coupling at the GUT-scale. The output was then passed

through ISAWIG 1.200 and ISAJET 7.64 [65] in order to calculate the sparticle decay

rates. In addition, the possible 2- and 4-body decay rates for the RPV decay modes of

the τ1 were calculated using a modified version of Herwig 6.5 [66–69].

Figure 7.2 shows the mass difference between the χ01 and the τ1 for a slice through

RPV mSUGRA parameter space. Here one can clearly see two regions, one where the

LSP is a χ01, and another region where the τ1 is the LSP. The τ1 LSP region is particularly

interesting as it is excluded in RPC models. However with R-parity violation, this region

becomes accessible. The signatures in these different regions are summarised below.

χ01 LSP

Where the χ01 is the LSP, it will typically decay via a 3-body decay, an example of which

being shown in figure 7.3(a). The resulting decay products will be dependent on the

type of coupling. For λ-type couplings one will expect leptons in the final state, λ′-type

couplings will give leptons and quarks and λ′′-couplings will give multiple quarks in the

final state. Unless Λ couples directly to τ -leptons, the production of τ -leptons in SUSY

events will be limited to the decay products of higher mass sparticles rather than the

decay of the LSP.

3A pre-release version of SOFTSUSY 3.0 was used.


(GeV)1/2m300 320 340 360 380 400 420 440 460 480 500

(GeV

)0

m

020406080

100120140160180200

(GeV

)st

au -

mnt

lino

m

-80

-60

-40

-20

0

20Neutralino LSP

AP2

AP1

Stau LSP

Figure 7.2: A parameter space scan overm0 andm 12

showing the mass difference between

the χ01 and the τ1 (Meχ0

1−eτ1) with A0 = 0 GeV, tanβ = 20 and sgn(µ) = +. A non-zero

RPV coupling of λ′221 =0.01 is set. The dotted line shows the line where Meχ01

=Meτ1.

τ1 LSP

Where the τ1 is the LSP there are two distinct decay modes - 2-body and 4-body decays.

The 2-body decay will occur where the τ1 directly couples via Λ (e.g when Λ = λ′311).

Where the τ1 does not couple directly, it is forced to decay through a 4-body decay

(an example of which is shown in figure 7.3(b)). An interesting feature of the 4-body

decay mode is the presence of a τ -lepton. This is common to many different choices of

coupling and originates from the decay to the intermediate virtual χ01, rather than the

dominant coupling itself. For regions of parameter space where the τ1 is the LSP, SUSY

cascade decays will be forced to decay into a τ1, often through an on-shell χ01, resulting

in the sequential decay shown in figure 7.4. Clearly, for regions of parameter space where

the τ1 is the LSP, and 4-body τ1 decay modes dominate, a large τ -multiplicity can be

expected. This is further illustrated by figure 7.5 which shows the mean τ -multiplicity

per event for a scan through mSUGRA parameter space. The τ1 LSP region is seen to be

characterised by a high τ -multiplicity. The τ -multiplicity distributions for two example

points (one with a τ1 LSP and one with a χ01 LSP) are shown in figure 7.6.


χ0

1µ−

µ∗

L

λ′221

c

d

(a) The 3-body decay of a χ01 LSP

τ−1

d

c

µ−

χ0∗

1

µ∗

L

τ−

λ′221

(b) The 4-body decay of a τ1 LSP

Figure 7.3: Feynman diagrams showing examples of (a) the 3-body decay of a χ01 LSP

and (b) the 4-body decay of a τ1 LSP. The particle content of the final state is determinedby the “flavour” of the RPV coupling (corresponding to a dominant λ′221 in this case).

τ+

τ−

τ−1

χ01

µ−

c

d

(

χ01

)

∗

Figure 7.4: A typical segment of a SUSY decay chain in models with a τ1 LSP. Twoτ -leptons are produced for each chain of this type, with ∼ 4 τ -leptons per event. Thiswill be common to many choices of coupling (λ′221 6= 0 in this case) as long as the 4-bodyτ1-decay dominates.


(GeV)1/2m300 320 340 360 380 400 420 440 460 480 500

(GeV

)0

m

020406080

100120140160180200

-lept

ons

per e

vent

τNu

mbe

r

1

1.5

2

2.5

3

3.5Neutralino LSP

AP2

AP1

Stau LSP

Figure 7.5: A parameter space scan over m0 and m 12

showing the mean number of τ -

leptons produced per SUSY event. A non-zero RPV coupling of λ′221 =0.01 is set alongwith A0 = 0 GeV, tanβ = 20 and sgn(µ) = +. The τ1-LSP region clearly shows anelevated number of τ -leptons.

Num. Taus per Event0 1 2 3 4 5 6 7 8 9

Norm

alize

d Un

its

0

0.1

0.2

0.3

0.4

0.5 Mean = 3.63 RMS = 0.854

(a) AP1

Num. Taus per Event0 1 2 3 4 5 6 7 8 9

Norm

alize

d Un

its

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35Mean = 1.23 RMS = 1.15

(b) AP2

Figure 7.6: The number of τ -leptons per SUSY event for points (a) AP1 and (b) AP2.


7.2.1 Example points in RPV mSUGRA parameter space

In order to explore the phenomenology of RPV SUSY models in more detail, two points

with a non-zero λ′221 coupling have been defined for further study. It should be noted

that the preference of this coupling over other possible choices is not motivated by spe-

cific experimental or theoretical arguments, however it does offer particularly interesting

experimental signatures with leptons and quarks in the final state allowing the recon-

struction of all the decay products. It was decided to investigate cases with prompt LSP

decays and as such a value of λ′221 = 0.01 was chosen (with all other couplings zero at

this scale)4. The limits on this coupling are ∼O(0.1) [61].

As shown in figure 7.2, the two points, labelled AP1 and AP2, are defined such that

they have a τ1 LSP and χ01 LSP respectively (see table 7.1). The overall mass scale and

SUSY production cross-sections are similar for the two points. More detailed discussions

for each of these points are presented below, with tables of sparticle masses, decay modes

and branching ratios found in appendix A.

m0 m12

A0 tanβ sgn(µ) λ′221

AP1 80 GeV 400 GeV 0 GeV 20 + 0.01

AP2 110 GeV 390 GeV 0 GeV 20 + 0.01

Table 7.1: A summary table showing the mSUGRA parameters and RPV-couplings forpoints AP1 and AP2.

Point AP1: A τ1-LSP with λ′221 6= 0

Point AP1 has been selected as an example RPV SUSY point with a τ1 LSP. The

λ′221 6= 0 coupling results in the RPV τ1-decay modes as shown in table 7.2. At this

point, the τ1 decays via 4-body decay modes, dominated by decay modes through a

virtual neutralino (with a small contribution from decay modes proceeding via a virtual

chargino). The chosen coupling determines that, for the dominant decays through a

virtual neutralino intermediate, a τ -lepton is produced, along with two quarks and either

a muon or a neutrino. From an experimental perspective, the decay modes of the

form τ1 → µqqτ are particularly interesting as each of the decay products are detectable

4Along with the mSUGRA parameters shown, the following parameters were set in SOFTSUSY:mtop = 175 GeV, MGUT = 2× 1016 GeV and weak-scale quark mixing set to be solely in the up sector


(although some energy will be lost from the neutrino associated with the hadronic τ -

decay). The presence of a muon in the final state will also provide a target to trigger

on. From a sample of Monte Carlo generated SUSY events, 63.6 % contained at least

one τ1 → µqqτ decay, with 15.6 % containing two τ1 → µqqτ decays. The lifetime of the

LSP can be a significant feature of RPV SUSY models. In the case chosen here, the τ1

has a lifetime of 6.8× 10−14 s, resulting in prompt decays in the detector (cτ ∼ 20 µm),

so detached vertices are not expected to be a significant signature at this point.

LSP Mass (GeV) Channel (BR) Channel (BR)

τ−1 151.0 νµ s d τ− (35.1%) µ+ c d τ− (25.5%)

νµ s d τ− (20.0%) µ− c d τ− (14.5%)

µ− s d ντ (4.5%) νµ c d ντ (0.5%)

Table 7.2: The decay modes and branching ratios for the τ1 LSP in point AP1.

The pT distribution for the resulting τ1s is shown in figure 7.7(a), with a mean

of 281 GeV and a tail extending out above 1 TeV. Consequently, the resultant decay

products are liable to experience a significant Lorentz boost. The impact of this can be

seen in figures 7.7(b) and 7.7(c). Here, the separation of the τ1 parent from its daughter

particles is shown. As expected, the daughter particles tend to be emitted along the

direction of the τ1 parent, becoming increasingly collimated as the pT, and the associated

Lorentz boost, increase.

The daughter particles produced during τ1 → µqqτ decays have pT-distributions as

shown in figure 7.8. In such decays, the mean pT of the hardest quark is 130 GeV, whilst

that of the softer quark is 47.3 GeV. The mean pT of the muon is 76.3 GeV, and τ -lepton

is 53.6 GeV, both with tails extending out to above 200 GeV. The soft pT distribution

for the τ -leptons is quite significant, as when only the visible component of the τ -decay

is considered, the low pT can hinder τ -reconstruction. It should be noted that these

distributions will be fairly model specific, and can be expected to vary with the mass of

the τ1 LSP. However the pT distribution of the τ -leptons will be dependent on the mass

difference between the τ1 LSP and the χ01 NLSP 5. This is often small and hence one

can expect that soft τ -leptons will be significant over a large proportion of the τ1 LSP

parameter space.

5The NLSP is the “next lightest supersymmetric particle”.


(GeV)T

p1τ∼0 500 1000 1500

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500 Mean = 281 GeVRMS = 192 GeV

(a)

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30

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45-310×

(b)

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ean

Pare

nt-D

au. S

ep. <

0.2

0.4

0.6

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1

1.2

1.4

1.6

(c)

Figure 7.7: Characteristics of the τ1 LSP, and its decay, in point AP1. (a) The τ1 pT

distribution. (b) The ∆R-separation of the daughter particle from the τ1 parent. (c) Aprofile histogram showing the variation in the parent-daughter separation as a functionof the pT of the parent τ1. Only decays of the form τ1 → µqqτ are included.


(GeV)T

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(a) Muons

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00.20.40.60.8

11.21.41.61.8

310×

Mean = 130 GeVRMS = 86.9 GeV

Hard Quark


Soft Quark

(b) Quarks (The higher-pT quark is shownby the solid line and the lower-pT quark bythe dashed line)

(GeV)T

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0.4

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1

1.2

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Tau Lepton

(c) Taus

Figure 7.8: The pT-distribution of the daughter particles from τ1 → µqqτ decays (pointAP1).


Point AP2: A χ01-LSP with λ′

221 6= 0

To provide an example of a point with a χ01 LSP, a second SUSY point was defined. The

point is similar to AP1 in all aspects except that the values of m0 and m 12

have been

adjusted so that the mass ordering of the χ01 and τ1 are reversed. As a consequence, for

this point the χ01 now decays through RPV decays and the τ1 (now the NLSP) decays

to an on-shell χ01. As in the case of AP1, the RPV coupling is set to λ′221 = 0.01 at

the GUT scale. The 3-body χ01 decay modes, summarised in table 7.3, produce two

quarks in association with either a muon or neutrino. The decay modes of the form

χ01 → µqq are particularly interesting as they allow for the complete reconstruction of

the χ01 mass from its decay products, giving a promising experimental signature, aided

by the presence of a muon which should help to both reduce backgrounds from QCD

and also provide a target to trigger on. For SUSY Monte Carlo events generated at

this point, 66.0 % contained at least one χ01 → µqq decay, with 16.9 % of the events

containing two χ01 → µqq decays.

LSP Mass (GeV) Channel (BR) Channel (BR)

χ01 157.9 νµ s d (29.0%) νµ s d (29.0%)

µ− c d (21.0%) µ+ c d (21.0%)

Table 7.3: The decay modes and branching ratios for the χ01 LSP in point AP2.

Like point AP1, the decay products of RPV decays are typically collimated along the

direction of the parent, as illustrated in figure 7.9. The pT distributions of the muons

and quarks produced in χ01 → µqq decays are shown in figure 7.10. When compared to

the equivalent distributions for the LSP decays in AP1, the typical pT of the daughter

particles is slightly higher than for AP1 (here the LSP mass is slightly heavier and the χ01

decays are 3-body, rather than the 4-body τ1 decays in AP1). Again, these distributions

can be expected to depend on the LSP mass and hence the point in parameter space.


(GeV)T p01χ∼

0 500 1000 1500

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eV

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500 Mean = 290 GeVRMS = 199 GeV

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nt-D

au. S

ep. <

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

(c)

Figure 7.9: The characteristics of the χ01 LSP and its decay in point AP2. (a) The χ0

1 pT

distribution. (b) The ∆R-separation of the daughter particle from the χ01 parent. (c) A

profile histogram showing the variation in the parent-daughter separation as a functionof the pT of the parent χ0

1. Only decays of the form χ01 → µqq are included.


(GeV)T

p0 100 200 300 400 500

Entri

es /

5 G

eV

0100200300400500600700800900


Muon

(a) Muons

(GeV)T

p0 100 200 300 400 500

Entri

es /

5 G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4

310×

Mean = 160 GeVRMS = 98 GeV

Hard Quark


Soft Quark

(b) Quarks (The higher-pT quark is shownby the solid line and the lower-pT quark bythe dashed line)

Figure 7.10: The pT-distribution of the daughter particles from χ01 → µqq decays (point

AP2).


7.3 Simulation, Ntuple Production and Particle ID

To prepare a sample of fully simulated RPV SUSY events, the following steps were

taken:

• Event Generation — The modified version of Herwig used for the generation of

RPV SUSY events was interfaced to Athena. Jimmy [70] was used to generate

the underlying event and TAUOLA [71] to decay the τ -leptons (consistent with the

ATLAS CSC production).

• Simulation and Digitization — These steps were carried out using Athena version

12.0.6.5. Jobs were configured and run over the Grid6 using GANGA [72].

• Reconstruction — Once simulated, the RDO files were reconstructed, again using

Athena version 12.0.6.5 over the Grid.

In total, 24,125 events were simulated for point AP1, and a further 24,000 events were

simulated for point AP2. These samples were generated privately using official ATLAS

software for the simulation and reconstruction steps. The two samples correspond to

a luminosity of 6.35 fb-1 and 5.71 fb-1 respectively. In addition to the signal samples,

a series of fully simulated SM background samples were available, with the dominant

backgrounds expected to come from QCD, tt, and the production of W/Z bosons in

association with jets. The list of samples considered is shown in table 7.4. The Monte

Carlo generators used for the SM backgrounds were Pythia [73] (QCD dijets), MC@NLO

[74, 75] (tt) and Alpgen [76] (W/Z samples). The cross-sections for these samples are also

shown. The SUSY and QCD cross-sections are the result of leading order calculations

(with a ∼ 20 % error). The tt cross-section is the result of a next-to-leading order (NLO)

calculation with an assigned error of 12 % [77]. The Alpgen cross-sections for the W

and Z samples have been normalized to NNLO calculations using the recommended K-

factors of 1.15(1.24) for W (Z) respectively, with an assigned error of 3 % [77]. The SM

samples considered were those that were expected to be backgrounds for the inclusive

analyses presented in sections 7.5 to 7.9.

As will be described in section 7.5, an event selection procedure has been proposed

to select RPV SUSY events from SM backgrounds. The applied cuts include a require-

ment of ≥ 6 jets (with pT > 25 GeV), a W-veto and a Z-veto. In addition to the

6Motivated by the anticipated high LHC data rates, the Grid is a distributed computing system thatprovides a data storage and analysis infrastructure for the entire high energy physics community thatwill be used by the LHC and other experiments.


above SM backgrounds, one might also consider the possible contribution from pairs

of vector bosons. The cross-sections for the production of WW, ZZ and WZ pairs are

expected to be ∼ 70 pb, ∼ 11 pb, ∼ 27 pb respectively. Of these processes, the channels

that would be significant to the studies presented here are WW → µνqq, ZZ → µµqq and

WZ → µνqq/µµqq, although in each case further jets would be required to pass the 6-jet

requirement. No Monte Carlo simulations were available for the WW/ZZ/WZ + jets

processes that would be needed to investigate this background, however after the con-

sideration of the branching ratios into these channels, the reduction in rate due to the

requirement of additional jets and the expected rejection power of the W- and Z-vetoes,

it is expected that these backgrounds will be small.

The EventView [78] package was used to process the AOD files for the physics samples

mentioned above, producing n-tuple files that could be easily analysed using ROOT [79].

Since the physics objects contained within the AOD may overlap with each other (for

example calorimeter clusters being reconstructed as both an electron and a jet), a con-

sistent set of object identification and overlap removal cuts were applied to the AOD

objects in order to prepare n-tuple files suitable for analysis. A summary of the par-

ticle identification criteria can be found in table 7.5. The different physics objects are

inserted into a “view” of each event with priorities as listed below. To accommodate

and investigate the two separate tau reconstruction algorithms, two views of each event

were created, one using taurec and one using tau1p3p.

Muons: Reconstructed muons4 with pT > 10 GeV and |η| < 2.5 are inserted. All

muons are required to be ‘combined’ (such that a track from the muon spectrometer

is matched to a track from the Inner Detector) and only the best match is used. The

candidate muons for use in later analysis are required to satisfy isolation requirements,

with a calorimeter isolation cut demanding that the total transverse energy in a cone of

∆R < 0.2 around the seed muon is less than 10 GeV. A further spatial isolation cut is

applied, requiring that the muon be separated from the nearest jet (where pjetT > 20 GeV)

with ∆R > 0.4.

Electrons and photons: Electrons and photons reconstructed with the egamma algo-

rithm are inserted, requiring a pT > 10 GeV and |η| < 2.5. Electrons are required to

pass the (isEM & 0x3FF) = 05 selection. Similarly photons are required to satisfy an

4Only muons reconstructed using the ATLAS StacoMuon algorithm are considered as recommendedby the ATLAS Muon combined performance working group.

5The (isEM & 0x3FF) = 0 cut is a medium electron selection requiring calorimeter shower shapecuts be passed but not cuts on the track-matching, E/|p| and TRT hits.


Sample # Events σ (pb) L (fb-1) Data set

SUSY

AP1 24125 3.8 6.35 private

AP2 24000 4.2 5.71 private

QCD

J3 (pT 70–140 GeV) 344050 6.16× 106 5.6× 10−5 005012

J4 (pT 140–280 GeV) 377400 317× 103 1.2× 10−3 005013

J5 (pT 280–560 GeV) 284450 12.5× 103 0.023 005014

J6 (pT 560–1120 GeV) 391800 344 1.14 005015

J7 (pT 1120–2240 GeV) 191575 5.71 33.6 005016

tt a

(→ `h/``) 436886 450 0.97 005200

(→ hh) 45660 383 0.12 005204

W → µν + n jets b

n = 2 49450 676 0.073 006109

n = 3 47000 200 0.24 006110

n = 4 31954 57.9 0.55 006111

n = 5 9750 20.8 0.47 006112

Z → µµ + n jets c

n = 2 47650 64.1 0.74 008144

n = 3 47000 20.3 2.32 008145

n = 4 42500 5.7 7.46 008146

n = 5 11200 2.1 5.33 008147

W → τν + n jets b

n = 2 6000 146 0.041 006115

n = 3 1500 46.5 0.032 006116

n = 4 2900 14.0 0.21 006117

n = 5 2000 5.5 0.36 006118

Z → ττ + n jets c

n = 2 42350 26.5 1.60 008156

n = 3 3500 8.6 0.41 008157

n = 4 31300 2.5 12.5 008158

n = 5 9250 0.96 9.64 008159

Table 7.4: A table showing a list of Monte Carlo samples used. The cross-section (σ)and corresponding integrated luminosity (L) are shown for each sample.

a` and h represent leptonic and hadronic t-quark decay modes respectively.bFiltered to include at least 1 electron/muon with pT > 10 GeV and |η| < 2.7cFiltered to include at least 2 electrons/muons for Z → ee/µµ, or at least 1 electron/muon for

Z → ττ , with pT > 10 GeV and |η| < 2.7


identification cut of (isEM & 0xFF) = 06. These cuts correspond to those recommended

by the ATLAS Electron/Gamma combined performance working group. Electrons are

considered isolated if the total transverse energy in a cone of ∆R < 0.2 around the given

electron is less than 10 GeV. Isolated electrons are further required to have a spatial

separation from the nearest jet (with pjetT > 20 GeV) of ∆R > 0.4 7. Electrons are

rejected if a jet is found with 0.2 < ∆R < 0.4. In the case where ∆R < 0.2, the jet is

rejected instead (through the overlap removal). Photons are only inserted if they have

an isolation transverse energy of less than 10 GeV (again in a cone of ∆R < 0.2).

Taus: Similar cuts are applied to the τ -jets from the taurec and tau1p3p algorithms

in forming the two views of the event. τ -jets are inserted with a higher priority than an

overlapping jet (it is typical that τ -jets are also reconstructed as jets). Consequently,

changes to the tau selection cuts can impact on the number of inserted jets in an event.

Candidate τ -jets are required to pass cuts of pT > 15 GeV and |η| < 2.5. Only candidate

τ -jets with 1 or 3 tracks and a charge of ± 1 are considered. Furthermore, the following

identification discriminant cuts are applied: (i) For taurec, a Likelihood cut of LL >

4; (ii) For tau1p3p, a Neural Network cut of NN > 0.5(0.9) for 1-prong (3-prong)

candidates.

Jets: Jets reconstructed using the Cone4Tower algorithm (using a cone jet algorithm of

radius ∆R = 0.4) are inserted. Only jets with pT > 20 GeV and |η| < 2.5 are considered

as candidate jets in the following analysis. It should be noted that any jets matching an

electron with ∆R < 0.2 are removed through the overlap removal process.

Missing Transverse Energy: The missing transverse energy (EmissT ) is provided by

the MET RefFinal variable. The corresponding sum of transverse energy deposited in

all calorimeter cells (ΣET) is also calculated.

7.4 Tau reconstruction in RPV SUSY events

As has already been indicated, the identification of τ -leptons in ATLAS (or more specif-

ically, the hadronic decays of τ -leptons) is particularly relevant to SUSY models with

a τ1 LSP. This is because for SUSY events in these models, a large τ -multiplicity is

6The (isEM & 0xFF) = 0 photon selection is determined by a series of cuts based on the showershape properties in different compartments of the calorimeter.

7Unlike the analyses presented in [42, 53], no rejection of electrons in the crack region(1.37 < |η| < 1.52) has been applied.


Muons Electrons Photons

Collection Key StacoMuonCollection ElectronCollection PhotonCollection

pT > 10 GeV > 10 GeV > 10 GeV

|η| < 2.5 < 2.5 < 2.5

Calorimeter ET < 10 GeV ET < 10 GeV ET < 10 GeV

Isolation (in ∆R < 0.2) (in ∆R < 0.2) (in ∆R < 0.2)

Other ∆R > 0.4 from Jet isEM flag = 0x3FF isEM flag = 0xFF

(where pjetT > 20 GeV) ∆R > 0.4 from Jet

(where pjetT > 20 GeV)

Tau Jets Jets

Collection Key TauJetCollection TauJet1p3pCollection Cone4TowerParticleJets

pT > 15 GeV > 15 GeV > 20 GeV

|η| < 2.5 < 2.5 < 2.5

CalorimeterN/A N/A N/A

Isolation

Other 1 or 3 tracks 1 or 3 tracks

Likelihood > 4 NN > 0.5 (1-prong)

NN > 0.9 (3-prong)

Table 7.5: A summary of reconstructed physics object definitions and selection cuts. Forthe purpose of investigating the τ -reconstruction performance, cuts for both the taurec

algorithm (with collection key TauJetCollection) and the tau1p3p algorithm (withcollection key TauJet1p3pCollection) are shown. The object types are listed in thepriority order with which they are inserted into the view of the event.


expected should the τ1 decay predominantly through 4-body decays. This raises the

possibility of an inclusive signature, based on the observation of an excess of events with

a high τ -multiplicity, being used to indicate the presence of a τ1 LSP. The detection of

these τ -leptons could provide an important handle towards understanding the under-

lying physics in such models. The advantage of such an inclusive signature would be

its model independence, as a high τ -multiplicity would be common to a large area of

mSUGRA parameter space and for many different types of RPV coupling (λ, λ′ and

λ′′).

RPV SUSY point AP1 provides an example of such a model. For the fully simulated

events produced for this point, the τ -reconstruction and identification performance has

been studied. Based on the knowledge that RPV SUSY events often have high par-

ticle multiplicities (in this case the RPV couplings giving large numbers of jets and

muons, along with τ -leptons), one might expect the τ -reconstruction to be affected by

the topology of such events.

The true visible transverse momentum (pvisT ) distribution of hadronic τ -decays in the

AP1 sample is shown in figure 7.11. As expected, it can be seen that most of the τ -

leptons in SUSY events originate from the χ01 and τ1 decays. The pvis

T distribution is

peaked at low pT, with a significant fraction being too soft to be reconstructed (32 %

with pvisT < 10 GeV). Figure 7.11(b) shows the separate distributions for hadronic τ -

decays originating from a τ1 parent, and from a χ01 parent. It can be seen that the

pvisT -distribution is greater for τ -leptons originating from τ1 parents (

⟨pvis

T

⟩= 32.7 GeV)

than those from χ01 parents (

⟨pvis

T

⟩= 16.9 GeV).

As mentioned in section 7.3, the fully simulated data used in this study were prepared

using release 12 of the ATLAS software. Detailed descriptions of the τ -reconstruction

algorithms in ATLAS can be found in chapter 4. Due to the fast pace of development of

the τ -reconstruction algorithms during the course of this thesis, in particular relating to

the tau1p3p algorithm, there are a few points to note regarding this version, mainly that

the reconstruction of tau1p3p candidates is limited to those with Ntrack ≤ 3, and there

is no explicit lepton veto (although the overlap removal prioritises muons and electrons

ahead of τ -jets, offering some rejection power, however this is not as effective as the

dedicated vetoes that have since been introduced in later software releases).

To investigate the performance of both the tau1p3p and taurec reconstruction al-

gorithms, the true hadronic τ -decays are matched to the nearest reconstructed τ -jet.

Figure 7.12 shows the ∆R-separation of the true hadronic τ -decay from the nearest τ -


(GeV)visT

True Tau p0 50 100 150 200

Entri

es /

5 G

eV

0123456789

310×

0 50 100 150 2000123456789

310×

All Hadronic TausStau-1 ParentNeutralino-1 ParentChargino-1 ParentNeutralino-2 Parent

(a) pvisT distribution for all hadronic τ -

decays in the AP1 sample. The parentparticle of the τ -lepton is shown by thecolour coding.

(GeV)visT

True Tau p0 50 100 150 200

Entri

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5 G

eV

00.5

11.5

22.5

33.5

44.5

310×

Stau-1 ParentMean = 32.7 GeVRMS = 34.7 GeV

Neutralino-1 ParentMean = 16.8 GeVRMS = 15.6 GeV

| < 2.5)visη(For |

(b) Separate pvisT distributions for true

hadronic τ -decays originating from τ1-decays (blue line) and χ0

1-decays (red line).

Figure 7.11: The distribution of true visible transverse momentum (pvisT ) for hadronic

τ -decays. The histograms correspond to 24125 events from sample AP1.

jet (figure 7.12(a) for tau1p3p candidates, and figure 7.12(b) for taurec candidates).

For the tau1p3p candidates, a sharp peak can be seen as ∆R→ 0, corresponding to

correctly reconstructed τ -jets. A similar peak can be seen in the taurec distribution,

but there is also a shoulder in the distribution extending to ∆R∼ 0.4 indicating a popu-

lation of true hadronic τ -decays with a small yet clear spatial offset from the associated

reconstructed τ -jet.

Investigating this feature further, figure 7.13 shows the separation of true τ -decays

from the nearest τ -jet (with transverse momentum precoT ) as a function of the offset in

transverse momentum ((precoT − pvis

T )/pvisT ). For the tau1p3p algorithm (figure 7.13(a)), a

clear peak can be seen at the origin corresponding to correctly reconstructed τ -decays

with both good momentum and spatial reconstruction. The corresponding plot for the

taurec algorithm shows a similar peak at the origin due to correctly reconstructed τ -

decays. The population of true τ -decays matching reconstructed τ -jets with ∆R . 0.4

can clearly be seen, and shows a correlation with an increasing pT offset (giving values

of precoT larger than pvis

T ). This is consistent with the calorimeter clusters used to seed the

taurec algorithm being pulled away from the true position by the contamination from


R (Truth - Reco)∆0 0.5 1 1.5 2

Entri

es /

0.02

210

310

410

(a) tau1p3p

R (Truth - Reco)∆0 0.5 1 1.5 2

Entri

es /

0.02

210

310

(b) taurec

Figure 7.12: The separation of true hadronic τ -decays from the nearest reconstructedτ -jet candidate. The histograms correspond to 24125 events from sample AP1.

Entri

es /

0.08

/ 0.

01

1

10

210

310

visT

) / pvisT

-precoT

(p-1 0 1 2 3 4 5 6 7

R (T

ruth

- Re

co)

∆

0

0.1

0.2

0.3

0.4

0.5

(a) tau1p3p

Entri

es /

0.08

/ 0.

01

1

10

210

visT

) / pvisT

-precoT

(p-1 0 1 2 3 4 5 6 7

R (T

ruth

- Re

co)

∆

0

0.1

0.2

0.3

0.4

0.5

(b) taurec

Figure 7.13: The separation of true hadronic τ -decays from the nearest reconstructedτ -jet versus the corresponding offset in pT (for sample AP1).

nearby energy deposits from other nearby sources (such as jets).

The narrower reconstruction cone used by the tau1p3p algorithm appears to be less


susceptible to contamination from outside sources. However, it should also be noted

that tau1p3p algorithm is more selective in its reconstruction of τ -jets (with tight re-

quirements on track multiplicity and quality in the reconstruction step). The taurec

algorithm is more inclusive in its reconstruction, being seeded from calorimeter clus-

ters. As such, the taurec algorithm is likely to still be seeded in cases with significant

contamination, where the tau1p3p algorithm’s seed criteria may prevent a seed being

formed.

To investigate the reconstruction efficiency of the two algorithms, a cut was applied to

select those true hadronic τ -decays found with ∆R < 0.2 from the nearest reconstructed

τ -jet. These true τ -decays are then deemed to be “reconstructed”. The reconstruction

efficiency as a function of pvisT for both algorithms is shown in figure 7.14. Also shown

is the efficiency after the further requirement that the matching reconstructed τ -jet has

either one or three tracks and has unit reconstructed charge. This additional requirement

is motivated by the characteristic Ntrack distribution for hadronic τ -decays. In order to

control the number of fakes, those τ -jets that do not satisfy these additional requirements

are rejected.

Figure 7.14(a) shows that the tau1p3p algorithm reconstructs 50–55 % of all true

hadronic τ -decays (with 40–45 % satisfying the additional reconstructed Ntrack and

charge requirements). Figure 7.14(b) shows the corresponding reconstruction efficiencies

for the taurec algorithm. It can be seen that the taurec algorithm has a much higher

overall reconstruction efficiency (over 80 % for pvisT & 80 GeV), however only ∼ 25 %

of hadronic τ -decays are reconstructed as τ -jets that satisfy the additional Ntrack and

charge requirements.

Since the reconstruction of hadronic τ -decays originating from the 4-body τ1-decay

is of particular interest here, figure 7.15 shows the analogous reconstruction efficiencies

for the subset of true hadronic τ -decays that originate from the decay of a τ1. The

marked difference from the plots shown in figure 7.14 is the drop off in efficiency at

higher pvisT . The τ -leptons with high pvis

T typically originate from τ1-decays where the

τ1 has a significant Lorentz boost, collimating the decay products, often resulting in

overlap between the τ -decay and the associated jets. This further demonstrates the

effect of contamination on the reconstruction performance. For tau1p3p candidates, the

overall reconstruction efficiency falls as pvisT increases. However the overall reconstruction

efficiency of the more inclusive taurec algorithm is less affected (a seed cluster will

still form in the presence of jet contamination, however the position and momentum

resolution of the such clusters will be worsened as illustrated in figure 7.13). When


(GeV)visT

True Tau p0 20 40 60 80 100 120 140 160 180 200

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Figure 7.14: τ -reconstruction efficiency for all true hadronic τ -decays as a function ofpvis

T (yellow markers). The efficiency after making the further requirement that thematching reconstructed τ -jet has Ntrack = 1 or Ntrack = 3 and unit charge, is alsoshown (blue markers). A true τ -decay is labelled as “reconstructed” if it is separatedby ∆R < 0.2 from the nearest τ -jet.

(GeV)visT

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(b) taurec

Figure 7.15: As figure 7.14, except only considering the subset of τ -leptons that originatefrom a τ1-decay.

the further requirement on the Ntrack and reconstructed charge are considered, both

algorithms show a reduction in efficiency at higher pvisT .

The pT-resolution of the two algorithms is shown in figure 7.16. Here, only re-

constructed τ -jets passing the additional Ntrack and reconstructed charge selection are


visT

) / pvisT

-precoT

(p-1 0 1 2 3 4 5 6 7

Entri

es /

0.04

1

10

210

310| > 0.4vis

T) / pvis

T-preco

T16.2 % with |(p

(a) tau1p3p

visT

) / pvisT

-precoT

(p-1 0 1 2 3 4 5 6 7

Entri

es /

0.04

1

10

210

310

| > 0.4visT

) / pvisT

-precoT

25.2 % with |(p

(b) taurec

Figure 7.16: The pT resolution for all correctly reconstructed τ -decays. The matchingreconstructed τ -jet is required to have Ntrack = 1 or Ntrack = 3 and unit charge.

considered. The tau1p3p algorithm has fewer events in the tails of the pT-resolution

distribution with 16 % of such candidates having |(precoT − pvis

T )/pvisT | > 0.4. For taurec

the corresponding value is 25 %.

So far only the reconstruction efficiency for the two algorithms has been considered.

The RPV SUSY events contain a significant number of true hadronic τ -decays, but

due to the high jet multiplicity in the events there will also be a significant number

of fakes. A further cut is required to make an identification decision, to separate true

τ -jets from fake ones. First of all, considering the tau1p3p algorithm, figure 7.17 shows

the Neural Network discriminant (NN) distributions for true and fake τ -jets (shown

separately for 1-prong and 3-prong tau candidates). Only τ -jets with Ntrack = 1 or 3

and unit charge are entered in the histograms. Fake τ -jets originating from electrons or

muons are removed using the MC truth. Cuts are placed at NN > 0.5 and NN > 0.9 for

1-prong and 3-prong candidates respectively. These cuts have not been highly optimised

and it can be seen that, even when considering only signal events, there is a large

contribution from fake τ -jets at high NN values, particularly for 3-prong τ -jets. Similarly,

the identification performance for the taurec algorithm was investigated. Figure 7.17(c)

shows the corresponding distribution of Likelihood (LL) values for taurec τ -jets. An

identification cut of LL > 4 was chosen.


As can be seen in figure 7.18, the identification performance in these RPV SUSY

events is significantly reduced when compared to SM events. Here the NN and LL dis-

tributions are shown for true τ -jets from Z → ττ events and fake τ -jets from QCD events

(the dominant sources of fake τ -jets in the SM). The more congested environment in

the RPV SUSY events reduces the discrimination power for both the taurec Likelihood

and the tau1p3p Neural Network discriminants.

Having applied the above identification cuts, the τ -identification efficiency (the ef-

ficiency after both reconstruction and identification) for both algorithms is shown in

figure 7.19. The corresponding identification efficiencies for the subset of τ -leptons that

originate from a τ1 parent are shown in figure 7.20. The efficiencies are comparable for

the two algorithms (noting that the fake rate is not demonstrated in these plots) with

identification efficiencies of ∼ 10 % achieved. For τ -leptons originating from τ1-decays,

the identification efficiency falls off with pvisT (after peaking at pvis

T ∼ 40 GeV).

Figure 7.21 shows the corresponding number of τ -jets passing the identification se-

lection for both tau1p3p and taurec (after the EventView overlap removal described in

section 7.3). The significant difference in the numbers of 3-prong candidates between the

two algorithms is due to a looser identification cut being placed on the 3-prong tau1p3p

candidates than for taurec. The number of fake τ -jets passing the identification is also

shown.

Clearly, the relative identification efficiency and fake rate will depend on the choice of

NN and LL cuts. It should be noted that the above cuts have not been overly optimised

and should be treated as an example of the expected identification performance. It can

be seen that the reconstruction and subsequent identification of τ -leptons is challenging

in RPV SUSY events.

The use of a signature based solely on the observation of a high τ -jet multiplicity as

a possible discovery channel for RPV SUSY models with a τ1 LSP will be very difficult.

Figure 7.22 shows the number of identified τ -jets per event for a simulated sample of

RPV SUSY events from point AP1 (normalized to an integrated luminosity of 5 fb-1).

Also shown is the corresponding distribution for a sample of tt events (expected to be

one of the dominant sources of SM backgrounds). No clear signal is present.

In order to isolate a significant signal, one could make additional cuts. However,

additional cuts may reduce the model independence of the analysis, and could limit the

coverage to a more restricted region of parameter space. One of the major difficulties

in extracting a τ -multiplicity signature bears its origins in the soft pvisT spectrum for


NN Discriminant0 0.2 0.4 0.6 0.8 1

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1 True TauFake Tau

(Ele/Mu Fakes removed using MC)

(c) taurec

Figure 7.17: The distribution of Neural Network and Likelihood discriminants for true(green line) and fake (red line) reconstructed τ -jets in sample AP1. Shown separatelyare: (a) the NN discriminant for tau1p3p candidates with Ntrack = 1, (b) the NNdiscriminant for tau1p3p candidates with Ntrack = 3, and (c) the LL discriminant fortaurec candidates. Only reconstructed τ -jets with unit charge and either Ntrack = 1 orNtrack = 3 are considered. τ -jets matching a true electron or muon are excluded. Allhistograms are normalized to unit area.



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(b) tau1p3p: 3-prong

Likelihood-30 -20 -10 0 10 20 30

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1 True TauFake Tau

(Ele/Mu Fakes removed using MC)

(c) taurec

Figure 7.18: As figure 7.17 except considering sources of true and fake τ -jets fromStandard Model processes. Z → ττ events are used as a source of true τ -jets, with QCDevents a source of fake τ -jets. All histograms are normalized to unit area. It can be seenthat the discrimination performance is significantly better in this case compared to thatof the RPV SUSY events (see figure 7.17).


(GeV)visT

True Tau p0 20 40 60 80 100 120 140 160 180 200

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Passes Ident. Cut

(b) taurec

Figure 7.19: As figure 7.14, with additional plots showing the overall reconstructionand identification efficiency (red points) for both tau1p3p and taurec. A true hadronicτ -decay is “identified” if the matching reconstructed τ -jet has Ntrack = 1 or 3, has unitcharge and passes an identification cut. For tau1p3p this identification cut is NN > 0.5and NN > 0.9 for 1-prong and 3-prong τ -jets respectively. For taurec, the identificationcut is LL > 4.

(GeV)visT

True Tau p0 20 40 60 80 100 120 140 160 180 200

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Passes Ident. Cut


(a) tau1p3p

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Passes Ident. Cut


(b) taurec

Figure 7.20: As figure 7.20, except only considering the subset of τ -leptons that originatefrom a τ1-decay.


trackN0 1 2 3 4

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ber

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trackN0 1 2 3 4

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(After overlap removal)

(a) tau1p3p

trackN0 1 2 3 4

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ber

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taurecTrue TausFake TausElectron FakesMuon Fakes

(After overlap removal)

(b) taurec

Figure 7.21: The number of τ -jets passing the identification selection for both tau1p3p

and taurec algorithms (after the removal of over-lapping objects using EventView) inAP1 events. The colour-coding shows the relative proportion of true τ -jets, fake τ -jetsand misidentified electrons or muons. The numbers correspond to a sample of 24,125AP1 events.


Num Tau0 1 2 3 4 5 6 7

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l + X→ttbar

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610RPV

l + X→ttbar

(b) taurec

Figure 7.22: The number of τ -jets per event for RPV SUSY events (AP1) and tt events.The histograms are normalized to an integrated luminosity of 5 fb-1. No clear excess canbe seen in the distribution for RPV SUSY events over tt events (expected to be one ofthe more dominant SM backgrounds).

τ -leptons in point AP1. This results in a significant fraction of τ -leptons produced in

RPV SUSY events being below the reconstruction limits for ATLAS. The low pT of τ -

leptons is a feature determined by the small mass difference between the τ1 and χ01 LSP,

and will be common to a large region of parameter space. Furthermore, the reconstruc-

tion and identification of higher pT τ -leptons will be impaired by the high-multiplicity

environment, with the performance for the high-pvisT tail of distribution suffering in-

creasingly from collimation with the other τ1-decay products. The RPV SUSY point

considered here has a dominant non-zero λ′ coupling. One might expect that with a

λ-type coupling, where a τ1 LSP would decay into leptons, the extraction of a τ multi-

plicity signature may be easier (fewer jets in the final state), however the proximity to

nearby electrons or muons will still present difficulties to τ -identification. For λ′′-type

couplings, where any 4-body τ1 decays will involve three quarks, one can expect a similar

if not worse τ -identification performance to that demonstrated here (due to the higher

jet multiplicity in the final state).

A more model dependent approach to the analysis of RPV SUSY models is presented

in the following sections where the characteristics of the chosen λ′221 coupling are used

to select RPV SUSY events from a SM background, and methods of reconstructing the


mass of the LSP are explored.

7.5 Event Selection

In order to select a sample of RPV SUSY events whilst also controlling the contribution

from Standard Model processes, a series of selection cuts are applied:

1) Cut I — ΣET selection

2) Cut II — Muon selection

3) Cut III — Z-Veto

4) Cut IV — W-Veto

5) Cut V — Jet selection

These selections take advantage of characteristics of points AP1 and AP2 to select

RPV SUSY events and reject the SM backgrounds. Each selection is defined and de-

scribed in detail in the following text. For the following analysis, the tau1p3p algorithm

was used. This choice has no impact on the motivations for any of the following selec-

tion cuts. The cuts are motivated by the dominant λ′221 coupling in points AP1 and

AP2, and aim to use the expected high jet multiplicity and also the presence of muons

to select events. Consequently they should be efficient for either the χ01 LSP or τ1 LSP

cases. Where possible the cuts have not been optimised to the specific SUSY point being

considered (other than the choice of RPV coupling). Instead the main motivation has

been the rejection of SM backgrounds.

7.5.1 Cut I — ΣET Selection

A cut on the sum of the transverse energy deposited in the calorimeter (ΣET) offers

significant rejection power against SM backgrounds which typically have lower ΣET

values. The ΣET does not include a contribution from reconstructed muons. In the

case of QCD dijet events, a ΣET cut is effective at removing lower pT events (with their

huge cross-section). Clearly such a cut becomes less effective for higher pT QCD dijets,

however the sharply falling QCD cross-section means that the rate of such events is


(GeV)TEΣ0 1000 2000 3000 4000

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02468

101214161820

−310×AP1 (Excludes 17.9%)

AP2 (Excludes 16.4%)

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TJ3 (p (Excludes 100%)

280−560 GeV)T

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1120−2240 GeV)T

J7 (p (Excludes 0.00157%)

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−310×+2jνµ→W

(Excludes 100%)

+5jνµ→W (Excludes 94.9%)

Figure 7.23: ΣET distributions for SUSY events and selected SM backgrounds. TopLeft: RPV SUSY events, top right: QCD dijet samples (for different pT slices), bottomleft: leptonic tt events, bottom right: W → µν + n jets events (shown for n = 2 andn = 5). Each plot is normalized to unit area.

much smaller than for the lower pT dijets, and effective rejection power can be achieved

through other cuts. A cut requiring ΣET > 1000 GeV was chosen, motivated by the

ΣET distributions of SM backgrounds (in particular tt as this proves to be one of the

more significant backgrounds). Figure 7.23 demonstrates the effectiveness of such a cut

for both signal and SM background samples.

The ΣET distributions for the two RPV SUSY samples show a double peaked struc-

ture, with one population below the selection cut threshold. Figure 7.24 shows the

ΣET distributions for different SUSY production processes. One can see that the higher

ΣET population is dominated by squark and gluino production processes, with the lower


population the result of the production of neutralinos and charginos. The selection cut

chosen here excludes this lower population, focusing on the dominant production of

squarks and gluinos.

(GeV)TEΣ0 1000 2000 3000 4000

Entri

es /

80 G

eV

00.20.40.60.8

11.21.41.61.8

310×

0 1000 2000 3000 400000.20.40.60.8

11.21.41.61.8

310×Production Mode

(22.2 %)g~R

q~

(20.4 %)g~L

q~

(11.7 %)R

q~R

q~

(12.8 %)R

q~L

q~

(12.4 %)L

q~L

q~

(5.77 %)g~g~

(4.09 %)±χ∼0χ∼

(2.13 %)±χ∼±χ∼

(1.13 %)l~ l~

All modes

Figure 7.24: ΣET distribution for 24000 AP2 events. The ΣET distribution for all SUSYevents is shown by the red, dashed line. The contributions from selected productionprocesses are shown separately according to the colour coding. Two populations canclearly be seen, the higher ΣET population dominated by squark and gluino production,with the lower population originating mainly from neutralino and chargino production.

7.5.2 Cut II — Muon Selection

The presence of muons in the RPV decay modes encourages a cut to select only events

with at least one candidate muon, whilst also providing strong rejection against the

QCD background. Typically, reconstructed muons in QCD events will either be mis-

reconstructed or originate from the decay of c- and b-quarks within jets. These muons

typically have low-pT and are often associated with jets, motivating the following muon

selection cuts:

• Transverse momentum, pT > 20 GeV


• Calorimeter Isolation (in a cone of ∆R < 0.2), EconeT < 10 GeV

• Separation from nearest jet (for pjetT > 20 GeV), ∆Rµ−j > 0.4

As previously mentioned, boosted LSPs can result in highly collimated decay prod-

ucts, with the muon closely separated from the associated quarks in the decay. The

corresponding activity in the calorimeter around these boosted muons results in a low-

ering of the efficiency with which the reconstructed signal muons pass the calorimeter

isolation and jet separation cuts.

Figure 7.25 shows the separation of the true signal muons from the nearest recon-

structed jet in the event. It can be seen that the high-pT muons (typically originating

from the decay of a boosted LSP) are spatially closer to the nearest jet. Consequently,

the jet separation cut does not efficiently select these boosted decays. The failure to

select these decays will not necessarily have a significant effect on the subsequent mass

reconstruction, as the jets from these same decays have a higher probability of merging

into a single jet.

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0.12 RPV Decay Muons:

< 400 GeVT200 GeV < True p < 100 GeVT10 GeV < True p

Figure 7.25: Left: The separation of Monte Carlo muons from the nearest reconstructedjet, ∆RMC

µ−j , as a function of the true muon pT. Only signal muons from the RPV decayof the LSP are included, with ∆RMC

µ−j calculated as the separation from the nearestreconstructed jet. Only jets satisfying pT > 20 GeV and |η| < 2.5 are considered. Theevents correspond to the AP2 sample. Right: The corresponding ∆RMC

µ−j plots for twodifferent pT slices: 10 < pT < 100 GeV (red, solid line) and 200 < pT < 400 GeV (blue,dashed line). The jet separation cut is shown. Both distributions are normalized to unitarea.


Figure 7.26 shows the reconstruction efficiency, as a function of the true muon pT,

for the true muons from χ01 → µqq decays. Also shown are the efficiencies when various

calorimeter isolation cuts are also applied to the reconstructed muon. It can be seen

that the calorimeter isolation cut causes a reduction in the efficiency for higher-pT muons

(particularly noticeable for the absolute isolation cut of EconeT < 10 GeV). It can be seen

that relaxing the isolation cut (by adding a component relative to the muon’s ET) can

reduce the loss in efficiency at high-pT. However, when this calorimeter isolation cut is

applied in conjunction with the jet separation cut it can be seen that the jet separation

cut dominates, and any significant benefit in signal efficiency due to the addition of a

relative component to the isolation cut is washed out (see figure 7.27). As a result,

an absolute calorimeter isolation cut of EconeT < 10 GeV was chosen (with no relative

component).

The performance in rejecting QCD events as a function of ΣET is demonstrated in

figure 7.28. No strong dependence on the ΣET can be seen, consistent with 0.013 % of

QCD events passing the selection.

(GeV)T

True Muon p0 100 200 300 400

Effic

ienc

y

00.10.20.30.40.50.60.70.80.9

1

Only Calo. Isolation Applied

Reconstructed

etcone20 < 10 GeV

T E×etcone20 < 10 GeV + 0.1


Figure 7.26: The muon reconstruction efficiency, as a function of pT, for signal muons(only those originating from the RPV decays of the LSP). The events correspond to theAP2 sample. The efficiency is shown for cases with (i) no calorimeter isolation (trian-gles); (ii) an absolute isolation cut Econe

T < 10 GeV (yellow circles); (iii) an additionalrelative contribution of 0.1×Eµ

T (red circles) and 0.3×EµT (blue circles). One can see

that the calorimeter isolation requirements reduce the efficiency for higher pT values.This effect is reduced with the addition of a relative contribution to the isolation cut.


(GeV)T

True Muon p0 50 100 150 200 250 300 350 400

Effic

ienc

y

00.10.20.30.40.50.60.70.80.9

1After Calo. Isolation & Jet Separation Cuts

etcone20 < 10 GeV


Figure 7.27: The muon reconstruction efficiency after applying both calorimeter isolationand jet separation cuts. Two different calorimeter isolation cuts are shown (as describedin figure 7.26). See the main text for a description of the jet separation cut.

(GeV)TEΣ0 1000 2000 3000

Effic

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Total Fraction Passing = 208 / 1589275 = 1.31e-04

Figure 7.28: The fraction of QCD dijet events passing the muon selection cuts as afunction of ΣET. The fraction of events passing the muon selection for the combinedQCD dijet samples is 1.31× 10−4. No significant correlation with the value of the ΣET

can be seen.


7.5.3 Cut III — Z-Veto

The muon selection cuts provide significant rejection power against SM backgrounds

without genuine sources of isolated muons. However, for other SM processes further

rejection power is required. One such background is expected to arise from Z-bosons

produced in association with jets. To reject such events, a Z-veto is applied where,

for events with two reconstructed muons (at least one of which having passed the

muon selection requirements listed above), the di-muon invariant mass, mµµ, is cal-

culated. Any events with mµµ falling inside a window around the known Z-boson mass,

86 GeV < mµµ < 96 GeV, are excluded (see figure 7.29).

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Figure 7.29: Distributions of mµµ for different physics samples. Left: Z → µµ + jets,right: RPV SUSY sample AP2. The histograms only contain events with exactly twomuons (at least one of which having passed the muon selection requirements).

7.5.4 Cut IV — W-Veto

In a similar vein, a veto is applied to reject events whereby the candidate muon (having

passed the muon selection) has originated from the decay of a W-boson. The transverse

mass, mT, is defined as:

mT =(2pµ

TpmissT (1− cos ∆φ)

) 12 (7.4)

where ∆φ is the azimuthal separation between the muon and the direction of missing

energy. mT is only calculated for events with exactly one muon passing the muon


selection requirements listed in section 7.5.2. Of such events, those with mT < 90 GeV

are rejected (see figure 7.30). Events with a greater number of candidate muons pass the

veto. This cut provides rejection against backgrounds both from W-bosons produced

in association with jets, and also tt events (where tt background remaining after the

previous muon selection cuts can be expected to be dominated by events where a t-

quark decays through the muon channel, t → bW → bµν). Unfortunately this is at the

expense of a significant fraction of the RPV SUSY events. In order to control the large

tt cross-section, a hard cut is needed.

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020406080

100120140160180200 AP2

Excludes 42.8%

Figure 7.30: Distributions of mT for different physics samples. Top left: W → µν + jets,top right: tt and bottom: RPV SUSY sample AP2. Only events with exactly one muonpassing the muon selection requirements, listed in section 7.5.2, are considered.


7.5.5 Cut V — Jet Selection

The jet selection cuts are motivated by the details of the RPV coupling being inves-

tigated. For the dominant λ′ coupling being studied here, one can expect each SUSY

cascade decay to end in a LSP-decay producing two jets (originating from the quarks in

the decay). With squark and gluino production being dominant, one can expect further

jet production at the head of each decay chain. It is therefore reasonable to expect at

least six jets in a given SUSY event. Figure 7.31 shows the distribution for the number

of jets per event for the SUSY AP2 sample. The merging of overlapping jets can lower

the number of jets actually seen (this is particularly significant in the case where the

LSP is highly boosted, resulting in collimated decay products). Such merged jets are

not useful for the purpose of reconstructing the mass of the LSP in this analysis. The

decay of squarks/gluinos at the start of each SUSY decay chain will typically produce

two hard jets per event, motivating a cut on the pT of the two hardest jets in the event.

In summary, the following jet selection cuts are applied:

• Transverse momentum of the hardest jet, p(0)T > 200 GeV

• Transverse momentum of the second hardest jet, p(1)T > 100 GeV

• The number of candidate jets (with pT > 20 GeV and |η| < 2.5), Njet ≥ 6

jetN0 5 10 15 20

-1Ev

ents

/ 5

fb

0

0.5

1

1.5

2

2.5

3

3.5

4

310×

Mean = 6.98 RMS = 2.11

Figure 7.31: The number of jets per event for AP2. Only jets satisfying pT > 20 GeVand |η| < 2.5 are considered.


7.5.6 Event selection performance and background rejection

Tables 7.6, 7.7 and 7.8 give a summary of the event selection performance for both

RPV SUSY and SM background Monte Carlo samples. The expected number of events

after the event selection is shown for each sample, normalized to an integrated luminosity

(L) of 5 fb-1. Due to the large cross-sections for some of the SM backgrounds, the avail-

able statistics were not sufficient in all samples. Consequently, where the cuts remove

all the events in a sample, the 90 % confidence limit is quoted. For the two RPV SUSY

samples considered, the expected number of events after event selection are ∼ 3000–3400

for L = 5 fb-1. Of the SM backgrounds, the dominant observed contribution comes from

tt events (∼ 480), with a further significant contribution from W → µν + jets (∼ 250).

For the QCD samples with adequate statistics (J6 and J7), there is no significant

contribution. However, for the lower-pT QCD samples (J3, J4 and J5), the available

statistics do not allow the precise contributions to be established. The Poisson confidence

limits show that the contribution from QCD cannot be discounted initially (however, it

can be seen that one runs out of statistics before fully exploring the rejection power of

the muon, W -veto and jet cuts).

For the W → µν + n jets samples, the dominant contribution comes from those

events with higher numbers of additional jets (n = 5). For the samples with a lower

numbers of jets (n = 2, 3), the results are statistically limited before the full rejection

power of the jet selection cuts is applied. The contributions from these samples are

neglected as the rejection power of the jet selection cut will increase with decreasing

values of n, giving small contributions compared to the n = 5 case.

Whilst the small sample statistics for W → τν + jets result in significant confidence

limits, the contribution from W → τν + jets is also expected to be negligible. In the case

of W → τν + jets, one can argue that the expected rate of events passing the selection

cuts would be lower than that for W → µν + jets as the branching ratio for τ → µνµντ

and the softer pT spectrum of the resulting muon would both reduce the efficiency of

W → τν + jets events passing selection with respect to W → µν + jets events.

For the other backgrounds considered, Z → µµ + jets contributes ∼ 50 events (an

order of magnitude lower than the more dominant backgrounds already discussed), and

the contributions from Z → ττ + jets are seen to be a further order of magnitude smaller.

For both the Z → µµ + jets and Z → ττ + jets sets of samples, the limits placed on the

contributions where n = 2, 3 are small and are neglected.


Sam

ple

Tot

alC

uts

L=

5fb

−1

Eve

nts

Cut

IC

ut

IIC

ut

III

Cut

IVC

ut

VSUSY

AP

124

125

1981

383

0081

1748

9438

0829

99(8

2.1%

)(3

4.4%

)(3

3.6%

)(2

0.3%

)(1

5.8%

)

AP

224

000

2005

580

4578

9450

1139

2634

35(8

3.6%

)(3

3.5%

)(3

2.9%

)(2

0.9%

)(1

6.4%

)

tt

tt→

``/h

`43

6886

6789

1167

1156

273

9347

9(1

.55%

)(0

.267

%)

(0.2

65%

)(0

.062

5%)

(0.0

213%

)

tt→

hh

4566

016

232

20

0<

96

(3.5

5%)

(0.0

0438

%)

(0.0

0438

%)

(0%

)(0

%)

(90%

CL)

QCD

J334

4050

890

00

0<

2.06

0×

105

(0.0

259%

)(0

%)

(0%

)(0

%)

(0%

)(9

0%C

L)

J437

7400

1434

00

00

<96

66

(0.3

8%)

(0%

)(0

%)

(0%

)(0

%)

(90%

CL)

J528

4450

5989

311

110

0<

505

(21.

1%)

(0.0

0387

%)

(0.0

0387

%)

(0%

)(0

%)

(90%

CL)

J639

1800

3910

3237

371

14.

4(9

9.8%

)(0

.009

44%

)(0

.009

44%

)(0

.000

255%

)(0

.000

255%

)

J719

1575

1915

7233

336

10.

1(1

00%

)(0

.017

2%)

(0.0

172%

)(0

.003

13%

)(0

.000

522%

)

Tab

le7.

6:E

vent

sele

ctio

ncu

tflow

:SU

SY

,tt

and

QC

D.


Sam

ple

Tot

alC

uts

L=

5fb

−1

Eve

nts

Cut

IC

ut

IIC

ut

III

Cut

IVC

ut

V

W→µν+njets

W→

µν

+2j

4945

020

1717

30

<15

7

(0.0

404%

)(0

.034

4%)

(0.0

344%

)(0

.006

07%

)(0

%)

(90%

CL)

W→

µν

+3j

4700

010

664

6319

0<

49

(0.2

26%

)(0

.136

%)

(0.1

34%

)(0

.040

4%)

(0%

)(9

0%C

L)

W→

µν

+4j

3195

437

024

123

945

19.

1(1

.16%

)(0

.754

%)

(0.7

48%

)(0

.141

%)

(0.0

0313

%)

W→

µν

+5j

9750

499

335

334

7123

245

(5.1

2%)

(3.4

4%)

(3.4

3%)

(0.7

28%

)(0

.236

%)

W→τν+njets

W→

τν

+2j

6000

20

00

0<

280

(0.0

333%

)(0

%)

(0%

)(0

%)

(0%

)(9

0%C

L)

W→

τν

+3j

1500

41

10

0<

356

(0.2

67%

)(0

.066

7%)

(0.0

667%

)(0

%)

(0%

)(9

0%C

L)

W→

τν

+4j

2900

6010

100

0<

56

(2.0

7%)

(0.3

45%

)(0

.345

%)

(0%

)(0

%)

(90%

CL)

W→

τν

+5j

2000

142

2424

00

<31

(7.1

%)

(1.2

%)

(1.2

%)

(0%

)(0

%)

(90%

CL)

Tab

le7.

7:E

vent

sele

ctio

ncu

tflow

:W→

µν

+n

jets

and

W→

τν

+n

jets

.


Sam

ple

Tot

alC

uts

L=

5fb

−1

Eve

nts

Cut

IC

ut

IIC

ut

III

Cut

IVC

ut

V

Z→µµ+njets

Z→

µµ

+2j

4765

015

114

20

<15

(0.0

315%

)(0

.023

1%)

(0.0

0839

%)

(0.0

042%

)(0

%)

(90%

CL)

Z→

µµ

+3j

4700

013

811

561

360

<5

(0.2

94%

)(0

.245

%)

(0.1

3%)

(0.0

766%

)(0

%)

(90%

CL)

Z→

µµ

+4j

4250

054

948

223

612

14

2.7

(1.2

9%)

(1.1

3%)

(0.5

55%

)(0

.285

%)

(0.0

0941

%)

Z→

µµ

+5j

1120

060

551

525

414

553

49.5

(5.4

%)

(4.6

%)

(2.2

7%)

(1.2

9%)

(0.4

73%

)

Z→ττ+njets

Z→

ττ

+2j

4235

028

1010

20

<7

(0.0

661%

)(0

.023

6%)

(0.0

236%

)(0

.004

72%

)(0

%)

(90%

CL)

Z→

ττ

+3j

3500

123

30

0<

28

(0.3

43%

)(0

.085

7%)

(0.0

857%

)(0

%)

(0%

)(9

0%C

L)

Z→

ττ

+4j

3130

062

515

915

97

0<

1

(2%

)(0

.508

%)

(0.5

08%

)(0

.022

4%)

(0%

)(9

0%C

L)

Z→

ττ

+5j

9250

711

180

180

114

2.1

(7.6

9%)

(1.9

5%)

(1.9

5%)

(0.1

19%

)(0

.043

2%)

Tab

le7.

8:E

vent

sele

ctio

ncu

tflow

:Z→

µµ

+n

jets

and

Z→

ττ

+n

jets

.


Revisiting the QCD background, table 7.9 shows the rejection of QCD events after

the application of only the muon selection cuts and the W/Z-vetoes (cuts II, III and IV).

Combining the events from the different QCD samples, one can see that out of a total

of 1,589,275 events, 208 pass the muon cut (0.013 %) and only 8 events (0.0005 %) pass

both the muon selection and W/Z-vetoes. The rejection power from these cuts alone

suggest that there is further significant rejection power that is not used by the limited

simulated data statistics. This implies that the selection cuts offer further rejection

against the low-pT QCD background than the confidence limits in table 7.6 suggest

(provided there aren’t strong correlations between the combined muon selection cut and

W-veto, and the ΣET selection cut).

Figure 7.28 shows no significant correlation between the efficiency with which QCD

events pass the muon cuts with the ΣET of the event. The very small statistics available

for events going on to also pass the W-veto do not allow a full test of the correlation of

this cut to be established with the ΣET cut. However it is reasonable to assume that

the higher pT QCD events would be more likely to pass the mT cut (a non-zero pmissT is

needed to generate a significant mT value, with larger pmissT values expected in the QCD

events at higher pT scales). Consequently, the assumption that the rejection power of

the combined muon selection and W-veto is uncorrelated with the ΣET of the event will

be conservative for the low-pT QCD events for which there are limited statistics (e.g.

samples J3 and J4). To factor this effect into the event selection performance for the

J3, J4 and J5 QCD samples, the confidence levels are adjusted in accordance with the

expected remaining rejection power of the muon selection and W-veto cuts (applying

a cut efficiency of 0.0005 % to the events remaining after the output of the ΣET cut

for samples J3 and J4, and a cut efficiency of 3.8 % to the events remaining after the

W-veto cut for sample J5). It should be noted that this does not take into account

the further effect of the jet selection (cut V), which should provide some extra rejection

power (although this is expected to show some significant correlation with the ΣET cut).

The resulting background contributions for the QCD samples are summarised in table

7.10. It can be seen that the background contribution from QCD is at a controlled level

even before the jet selection is considered for samples J3, J4 and J5.

The contributions from the different sources of background are combined to give

an overall measure of the expected SM background. The probability density functions

(PDFs) for each sample are combined to give an overall PDF for the number of SM events

passing the event selection. Table 7.11 shows the overall numbers of signal and back-

ground expected in 5 fb-1 of data (the full statistical analysis is described in appendix B).


The combined SM background is predicted to be 986 +119−121 (stat)± 102 (xsec). The event

selection process indicates that RPV SUSY events can be selected from SM events with

a signal to background ratio (S/B) of 3.04± 0.37 (stat) +0.27−0.33 (xsec) for point AP1, and

3.48± 0.43 (stat) +0.31−0.37 (xsec) for point AP2. The errors on the cross-sections, (xsec),

are assumed to be correlated.

SampleTotal Cuts

L = 5fb−1

Events Cut II Cut III Cut IV

QC

D

J3 34405055 55 0 < 2.060× 105

(0.016%) (0.016%) (0%) (90% CL)

J4 37740040 40 0 < 9666

(0.0106%) (0.0106%) (0%) (90% CL)

J5 28445043 43 1

220(0.0151%) (0.0151%) (0.000352%)

J6 39180037 37 1

4.4(0.00944%) (0.00944%) (0.000255%)

J7 19157533 33 6

0.9(0.0172%) (0.0172%) (0.00313%)

Table 7.9: Event selection cut flow for cuts II, III and IV only: QCD.

Sample Events in L = 5 fb-1

J3 < 91.7

J4 < 69.3

J5 < 213

J6 4.4± 4.4

J7 0.1± 0.1

Table 7.10: The background contribution from QCD after event selection for L = 5 fb-1.The confidence limits are adjusted to incorporate the expected redundant rejection powerfrom cuts II, III and IV.


Sample Events in L = 5 fb-1 S/B

SM 986 +119−121± 102 —

AP1 2999± 49± 600 3.04± 0.37 +0.27−0.33

AP2 3435± 55± 687 3.48± 0.43 +0.31−0.37

Table 7.11: A summary of numbers of SUSY and SM events after the event selec-tion process for both SUSY points AP1 and AP2. Also shown is the S/B ratio whereSUSY events are considered as signal S, and the SM events are considered as back-ground B. The statistical and cross-section errors are quoted separately in the formA±σstat.±σx−section. The errors in the SM and SUSY cross-sections are taken to becorrelated in calculating S/B.

7.6 Triggers

The ability to trigger on signal events is clearly essential to any prospects of observing

RPV SUSY in ATLAS. For the RPV coupling studied here, with high jet multiplicities

and muons in the final state, the topology of SUSY events implies that multi-jet and

muon triggers will be useful in extracting a signal from the detector.

From the standard ATLAS CSC trigger menu8, the following trigger items were in-

vestigated:

1) mu20i — a single muon trigger with a threshold of pT > 20 GeV

2) 3jet65 — a multi-jet trigger, requiring three jets above a 65 GeV threshold

3) 4jet50 — a multi-jet trigger, requiring four jets above a 50 GeV threshold

The mu20i trigger is expected to be unprescaled when running at a luminosity of

1033 cm-2s-1 (as planned for the early running period) and provides efficient selection

of signal events. By also considering a combination of a muon and multi-jet trigger

one can enhance the trigger efficiency. The available multi-jet options in the CSC trigger

menu are 3jet65 and 4jet50. However the final trigger menu for running at 1033 cm-2s-1

is not finalised and the trigger thresholds may be higher than those presented here ([80]

suggests thresholds of 110 GeV and 165 GeV for the 3- and 4-jet triggers). Table 7.12

shows the efficiency with which RPV SUSY events are triggered by the above triggers

8The trigger menu run by default during the Monte Carlo production for the ATLAS CSC exercise.


(and the “OR” combination of the mu20i trigger with each of the 3jet65 and 4jet50

triggers). Also shown are the efficiencies for the subset of events that pass the event

selection cuts. It can be seen that a combination of muon and multi-jet triggers selects

92–95 % of all RPV SUSY events and > 99 % of those that pass the event selection, thus

providing efficient performance for collecting signal events. Without considering multi-

jet triggers, the mu20i trigger selects 88 % of those events passing the event selection. As

an indication of how the trigger selection efficiency is sensitive to the transverse energy

threshold of the multijet trigger, figure 7.32 shows the efficiency with which events pass

either the mu20i trigger or have 3 (or 4) reconstructed jets above a varying threshold in

transverse energy. Whilst reconstructed jets do not exactly correspond to the jet trigger

objects that are used to form a trigger decision, they can provide a good approximation.

It can be seen that the 3- or 4-jet triggers should offer significant additional efficiency

(above the baseline mu20i trigger) for a significant range of trigger thresholds.

Trigger

Efficiency Efficiency

(All Events) (Events Passing ES)

AP1 AP2 AP1 AP2

mu20i 58.4% 52.0% 88.4% 87.5%

3jet65 87.9% 90.5% 97.8% 98.6%

4jet50 82.1% 85.4% 94.6% 95.9%

mu20i | 3jet65 94.6% 95.2% 99.7% 99.8%

mu20i | 4jet50 92.2% 92.9% 99.3% 99.4%

Table 7.12: A table showing the efficiency with which RPV SUSY events for points AP1and AP2 pass selected triggers. The percentage of events passing the triggers are shownboth for all events in the samples, and for the subset of events that also pass the eventselection (ES) cuts.


(GeV)TThreshold E0 100 200 300 400 500

Effic

ienc

y (%

)

0

20

40

60

80

100

(Pre ES)T3 Jets above E (Pre ES)T4 Jets above E (Post ES)T3 Jets above E (Post ES)T4 Jets above E

(a) AP1

(GeV)TThreshold E0 100 200 300 400 500

Effic

ienc

y (%

)

0

20

40

60

80

100

(Pre ES)T3 Jets above E (Pre ES)T4 Jets above E (Post ES)T3 Jets above E (Post ES)T4 Jets above E

(b) AP2

Figure 7.32: The percentage of RPV SUSY events for point (a) AP1 and (b) AP2 thateither pass the mu20i trigger or have at least 3 (or 4) reconstructed jets with transverseenergies above a given threshold (ET). The efficiency is shown separately for eventsbefore (blue lines) and after the event selection (red lines).


7.7 Measuring the χ01 LSP mass in point AP2

The focus of this analysis now moves on to point AP2, looking in particular at the

reconstruction of the mass of χ01 LSP. Having applied a series of event selection cuts to

reduce the SM background (as described in section 7.5.6), the surviving events undergo a

mass reconstruction process, aimed at determining the χ01 mass through the observation

of χ01 → µqq decays. The SUSY signal selected by the event selection process contains a

variety of different decay chains. However almost all events will include two χ01s, with the

muon selection cuts picking events where at least one χ01 decays through the χ0

1 → µqq

channel.

7.7.1 Mass combinations

In order to reconstruct the χ01 mass (Meχ0

1), a method based on calculating the invariant

mass for combinations of a muon and two jets is employed. The challenge of finding

the correct combinations in a high-multiplicity environment leads to a significant combi-

natorial background from SUSY events in addition to the remaining SM contributions.

To counter the combinatorial background the following procedure is used. An isolated

muon is used to seed the combination, forming an invariant mass with two associated

jets. Cuts are applied to the transverse momentum of the first associated jet, pj1T , and

second associated jet, pj2T , while the associated jets are restricted to lie in a reconstruction

cone centred on the seed muon (with cone-size ∆Rµjj). The cut values are summarised

below.

1) A seed muon with pµT > 20 GeV (satisfying the isolation and jet separation cuts

described in section 7.5.2)

2) An associated jet with 20 GeV < pj1T < 250 GeV, |η| < 2.5 and ∆Rµjj < 1.5

3) A second associated jet with 20 GeV < pj2T < 150 GeV, |η| < 2.5 and ∆Rµjj < 1.5

Figure 7.10(b) shows the pT distributions of the decay quarks, motivating the above

cuts on jet-pT. By only considering jets within a cone of ∆Rµjj < 1.5 from the seed

muon, one can exploit the collimation of the χ01 decay products. In its extreme, this

collimation will have a detrimental affect on the reconstruction of χ01 decays as it will

lead to the merging of the two decay jets and will also impact on the muon’s isolation


(as demonstrated in figures 7.25 and 7.27). However, for moderate boosts the decay

products will tend to be closely associated. The jets and muons that form incorrect

combinations will not be expected to show any significant correlation in their position

so the cut on ∆Rµjj acts to reduce the SUSY combinatorial background (and also the

SM background).

Since each seed muon can only be associated with one χ01 decay, for seed muons

forming multiple combinations, each of the resulting Mµjj values are weighted by the

reciprocal of the total number of combinations, 1/Ncom. A cut requiring that Ncom ≤ 3

is applied such that seed muons forming higher numbers of combinations are rejected

(in such cases, for any correct combinations that are found, there will be at least three

incorrect combinations contributing to the combinatorial background).

Figure 7.33 shows the Mµjj distribution. A mass-peak can be seen above a back-

ground distribution. The dominant background originates from the SUSY combinatorial

background, with a smaller SM contribution. Monte Carlo truth information is used to

separate the signal peak from the SUSY combinatorial background in a process where

the true quarks and muons from signal χ01 → µqq decays are matched to the recon-

structed muons and jets that make a combination. The magnitude of this combinatoric

background may itself be considered a signature of some new physics. This is because

the λ′221 RPV coupling results in decays to muons, so one can expect to see an excess of

muons with respect to electrons in SUSY events. One would expect that the combina-

toric background for Mµjj combinations to be larger than for a corresponding analysis

where electrons were considered instead of muons (once any differences in electron and

muon reconstruction efficiencies were considered). In the SM alone, the production of

muons and electrons would be expected to occur at approximately the same rate. This

aspect of the RPV phenomenology has not been exploited in the analysis presented here.

7.7.2 Combinatoric background estimation

As shown in figure 7.33, the Mµjj distribution shows a mass-peak above a broader back-

ground distribution. In establishing the presence of a signal mass-peak, it is important

to estimate the shape of the background distribution, a process made more difficult by

the peak in the background shape lying relatively close to the signal peak. The back-

ground shape is not known, and whilst one may attempt to fit an arbitrary functional

form to the background, it would be more desirable to establish this shape from data.

A data-driven approach to estimating the background shape is presented below.


(GeV)jjµM0 100 200 300 400 500 600

/ 10

GeV

-1Nu

mbe

r / 5

fb

0

50

100

150

200

250

300

0 100 200 300 400 500 6000

50

100

150

200

250

300SUSY SignalSUSY Combin. BGSM BG

01

χ∼

Figure 7.33: A stacked plot showing the Mµjj distributions for RPV SUSY point AP2,where (i) SUSY signal, (ii) SUSY combinatorial background and (iii) SM backgroundare shown separately. Only events passing the event selection are considered.

For each of the n events passing the event selection, “manufactured” events are

formed by merging the muons from one event with the jets from another event. In total,

n(n−1) manufactured events are formed (see figure 7.34). By construction, the position

of the muons in these events will not be correlated with the jets, unlike those found in

events with true χ01 decays. By forming the Mµjj distribution from the manufactured

events, an estimate of the background distribution is obtained. The background estimate

is shown in figure 7.35, weighted to correspond to the same total number of events.

7.7.3 Systematic Errors

The uncertainty in the precise shape of the background distribution will be a source of

systematic error on the reconstruction of the χ01 mass. In order to test the sensitivity of

the measurement to the background model used to subtract the background shape from

the Mµjj distribution, a second approach to modelling this background was tested. This

is demonstrated in figure 7.36, where a function of the form:

f (x) = kxa (1− x)b (7.5)

is used to fit the background shape. In this model x is defined to be a linear function of

Mµjj such that f (x) = 0 at appropriate values of Mµjj (a low cut-off determined by the


η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

η-3 -2 -1 0 1 2 3

φ

-3

-2

-1

0

1

2

3

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Jets

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Figure 7.34: A schematic diagram describing the merging of uncorrelated muons andjets from different events in order to create a set of “manufactured” events. Thesemanufactured events are studied in order to model the background distribution.


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Figure 7.35: Left: A stacked plot showing the Mµjj distribution for RPV SUSY pointAP2 (as figure 7.33). The estimated background distribution (red line) is also shown(normalized to the same number of events). Right: The Mµjj distribution after back-ground subtraction. The peak is fitted with a Gaussian.

kinematic constraints of the combination cuts, and a high cut-off where the Mµjj can

safely be assumed to be negligible). The motivation for this functional-fit method is to

use the rising and falling tails of the distribution (where no signal events are expected)

to infer the full distribution beneath the peak in an independent way to that presented

in section 7.7.2. This functional-fit model is therefore reliant on understanding where

the tails of the signal distribution lie (as it is important not to be biased by the presence

of signal when fitting the background). Where the peak can clearly be seen above the

background one can be confident of selecting signal free regions. However this may not

always be the case.

Figure 7.36 demonstrates that the functional-fit provides a good description of the

background, allowing a clear mass-peak to be seen. A comparison with the background

subtraction by the independent data-driven method demonstrated in figure 7.35 gives

a measure of the sensitivity of the χ01 mass measurement to the understanding of the

underlying background distribution. Table 7.13 shows the value of the reconstructed χ01

mass for these two methods and it can be seen that the Meχ01

measurement is robust to

the choice of background model. However the predicted number of background events is

susceptible to a larger systematic error which will have an implication on the significance

of the observed peak in data. With the data-driven method, the estimated number of

background events inside a mass window of 120 GeV < Mµjj < 200 GeV, is B = 675


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1.1 GeV±Mean = 158.7 1.2 GeV±Sigma = 9.245

Figure 7.36: Left: A stacked plot showing the Mµjj distributions for RPV SUSY pointAP2 (as figure 7.33). The rising and falling tails of the distribution are used to fit afunction of the form kxa(1 − x)b as a further estimate of the background distribution(blue line). Right: The Mµjj distribution after subtraction of this function. The peakis fitted with a Gaussian.

events. The functional-fit method gives B = 932. The difference in the two values

gives a measure of the systematic error associated with the definition of the background

model. Consequently a systematic error of 30 % is assigned to the value of B calculated

from the background model.

It should be noted that the SM distribution is given by the simulated events passing

the event selection. As discussed in section 7.5.6 and appendix B, the contribution from

QCD is limited by statistics, and is not accounted for in the SM distribution shown here.

The total number of SM events passing the event selection is predicted by the statistical

analysis (summarised in table B.3) to be 986 +119−121± 102. After event selection, no events

are available for the J3, J4 and J5 QCD samples, so no contributions could be made to

the Mµjj distribution shown in figure 7.33. The total (luminosity weighted) number of

SM events included in the Mµjj distribution shown is 792 events. This is ∼ 20 % lower

than the 986 +119−121± 102 calculated in appendix B. The impact of this discrepancy on the

measurement of Meχ01

will be a second order effect as an increase in the SM contribution

will also be reflected in the the estimation of the combinatoric background and subtracted

accordingly. The impact on the discovery reach will be larger as the relative number

of signal to background combinations below the Mµjj peak will be affected. However

since the systematic error on the background shape is large and the SUSY combinatoric

background dominates the SM contribution, this effect is not considered to be significant


Bgnd. Model χ01 Mass Peak Peak

∆Rµjj α β Ncom (GeV) ST /BT ST /√

BT

1.5 ✓ ✗ ≤ 3 158.5± 1.3 0.47 14.1

1.5 ✗ ✓ ≤ 3 158.7± 1.1 0.47 14.1

2.0 ✓ ✗ ≤ 3 158.6± 1.6 0.36 10.9

2.5 ✓ ✗ ≤ 3 157.3± 2.1 0.30 7.54

1.5 ✓ ✗ = 1 157.8± 1.3 0.64 14.5

1.5 ✓ ✗ Any 158.2± 1.3 0.42 13.6

2.5 ✓ ✗ = 1 162.0± 5.0 0.47 6.7

2.5 ✓ ✗ Any 159.6± 2.5 0.20 7.4

Table 7.13: A summary table showing the reconstructed χ01 mass for different recon-

struction parameters. Background model “α” corresponds to the data-driven approach,whilst model “β” corresponds to the functional-fit approach. Also shown are the ST/BT

and ST/√BT values calculated in a window of 120 GeV < Mµjj < 200 GeV using the

Monte Carlo truth.

when compared to the other sources of error.

The sensitivity of the background estimate to the value of ∆Rµjj is demonstrated in

figure 7.37 (for cone sizes of ∆Rµjj = 2.0 and ∆Rµjj = 2.5). The impact on the value

of the reconstructed mass for different cone sizes is shown in table 7.13. The method is

robust with respect to the choice of cone size, with the reconstructed χ01 mass not signif-

icantly affected by changes to ∆Rµjj. Defining a window of 120 GeV < Mµjj < 200 GeV

around the mass-peak, the values of ST/BT and ST/√BT are also shown in table 7.13 for

varying ∆Rµjj values. Here the total weight of signal combinations (ST ) and the weight

of background combinations (BT ) are calculated from the Monte Carlo truth informa-

tion. These true numbers are quoted in order to provide a measure of the performance

of the mass combination procedure and should not be confused with any measure of

discovery potential. It can be seen that the relative background contribution increases

with increased ∆Rµjj, with the smaller choice of ∆Rµjj = 1.5 giving the best ratio of

signal to background in the peak. Whilst the reconstructed mass is not found to be

sensitive to the cone size, the signal significance is increased by considering a smaller

cone.


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Figure 7.37: Mµjj distributions (as described in figure 7.35) for varying ∆Rµjj values.

Since the reconstruction of Meχ01

involves the combination of two jets, one can expect

that the error in establishing the jet-energy scale (JES) will be one of the more significant

systematic errors in making this measurement (and should dominate over the uncertainty

in the muon measurement). The sensitivity of the Meχ01

measurement to the JES was

investigated in a procedure involving the rescaling of the jet 4-momenta in steps of

2.5 % between −7.5 % and 7.5 %. Neither the event selection, nor the ΣET value were

changed during the rescaling process. The impact of a systematic offset in the JES on

the measured value of Meχ01is shown in figure 7.38. It can be seen that Meχ0

1varies linearly

with the JES, with a resulting systematic error of 1.3 GeV for every 1.0 % uncertainty

in the JES.

7.8 Discovery Reach

The analysis presented here has demonstrated a method for directly reconstructing the

mass of the unstable χ01 LSP as occurring in point AP2. As an indication of the discovery

potential of such a signature in ATLAS, the significance of the signal is now discussed. It

should be noted that when considering RPV SUSY models there is a very large parameter

space to explore, over which the SUSY mass scale and production cross-section can vary.

These variations will have an effect on the discovery potential as a function of the point


JES Offset (%)-10 -5 0 5 10

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)jjµ

Peak

M

150

155

160

165

170 JES sensitivity = 1.3 GeV / 1.0 %

= 157.9 GeV01

χM

Figure 7.38: The sensitivity of the χ01 mass measurement to the JES.

in SUSY parameter space.

Figure 7.39 shows the simulated Mµjj distribution (normalized to L = 5 fb-1) with

an estimate of the background as determined by the data-driven method. The dominant

error on the background is the systematic error associated with the background shape

(∼ 30 %). Counting combinations inside a window of 120 GeV < Mµjj < 200 GeV, the

total weighted number is T = 1297± 42 with the data-driven background model pre-

dicting a background contribution of B = 675± 202. The error on B is dominated by

the systematic error in the background model, whilst the statistical error is very small.

Defining S = T−B, the significance of the signal peak is given by S/√B = 24.0± 11.5.

Here the systematic error (48 %) dominates the statistical error (7 %). Extrapolating

this result to lower numbers of events suggests that a significance of S/√B = 5.0± 2.8

could be achieved with an integrated luminosity of L = 0.2 fb-1. The statistical error of

28 % is still very much less than the systematic error of 48 %. This suggests that the

observation of such a signal would be possible in early data. An integrated luminosity of

L = 6 fb-1 is predicted during running in 2009 [81] (at a peak luminosity of 1033 cm-2s-1).

The above method provides a simple measure of the signal significance. In an analysis

using real ATLAS data, it would be important to carefully consider the choice and width

of the window in which the peak is observed when considering a possible signal. The cuts

presented here have not been strongly optimised and it is important that cuts are not

over-optimised in order to enhance the signal peak. More detailed statistical methods

could take into account the shape of the signal peak and background distributions in


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Figure 7.39: The Mµjj distribution for point AP2 with the data-driven background es-timate and the associated systematic error band. ∆Rµjj = 1.5 and Ncom ≤ 3. The sys-tematic error band shows a 30 % uncertainty. A window of 120 GeV < Mµjj < 200 GeVis applied around the peak.

determining the signal significance. However, in the context of the analysis presented

here, and when considering a single point in a large parameter space, the benefits of using

more advanced methods are limited. Clearly uncertainties in the delivered luminosity,

the Monte Carlo cross-sections and trigger efficiencies will determine the exact timescale

of discovery should such a RPV SUSY model exist, not forgetting the possible variation

in SUSY mass-scale and production cross-section. However, should such a model exist

in nature, the reconstruction of the χ01 mass in RPV SUSY models with decays of the

form χ01 → µqq can be expected in the first years of running.

7.9 Measuring the τ1 LSP mass in point AP1

Having discussed the measurement of the χ01 LSP mass for point AP2, the application of

similar methods is considered for the more complicated case of a τ1 LSP in point AP1.

This is more difficult for several reasons:

• The 4-body τ1 → µqqτ decay requires the combination of four decay products,

increasing the complexity of the combinatorial background.

• The presence of a τ -lepton in the decay will reduce the efficiency with which signal


combinations are formed. This is both due to the branching ratio of τ -leptons into

leptonic decay modes and the challenges of τ -reconstruction in RPV SUSY (see

section 7.4).

• The decay chains in point AP1 are often more complicated than those in point

AP2, with additional τ -leptons produced higher up the decay chain (see figure 7.4).

Following the previous discussion on the reconstruction of χ01 → µqq decays, it is

possible to apply the same approach in reconstructing the mass of the virtual χ01 com-

ponent (M(eχ01)∗) of τ1 → µqqτ decays (i.e. (χ0

1)∗ → µqq). In this case, whilst there will

be no mass-peak in Mµjj, M(eχ01)∗ will be kinematically limited such that M(eχ0

1)∗ < Meτ1

.

Consequently one can explore the possibility of observing an “end-point” in the Mµjj

distribution at Mµjj = Meτ1. For point AP1, the true distribution of M(eχ0

1)∗ is shown

in figure 7.40(a). The observation of such an end-point would require both a very good

understanding of the combinatoric background, and a good detector resolution. The

advantage of such a method would be that it does not involve the direct identification

of the τ -lepton.

Applying the method for forming Mµjj combinations described in section 7.7.1, the

resultant Mµjj distribution is shown in figure 7.40(b). Again one can see a large combi-

natoric background (dominated by a contribution from SUSY events, with a smaller SM

contribution), above which lies a signal distribution. For the statistics available here,

the shape of the combinatoric background masks the presence of the signal distribution.

Without the presence of the strong mass-peak found in the case of the χ01 LSP, the signal

distribution is less distinct from the background. As in the case of the χ01 LSP, the same

data-driven method for estimating the background can be applied. This is also shown

in figure 7.40(b). However, as previously discussed, the systematic error for this method

is quite large (∼ 30 %), and a more detailed analysis may be needed in order to achieve

the accuracy necessary to identify such an end-point in the Mµjj distribution.

The analysis can be extended to also consider the τ -lepton produced in the τ1 → µqqτ

decay. One can form combinations of a muon, two jets and a τ -jet in an attempt to

reconstruct the τ1 mass peak. Any such peak will be slightly offset from the true τ1

mass due to the energy lost by the invisible neutrino in the τ -decay. Combinations

are formed following the same cuts as those used in forming the 3-body χ01 → µqq decay

combinations (described in section 7.7.1). An additional requirement is made demanding

that a τ -jet is also found inside ∆Rµjjτ < 1.5, and the invariant mass of the combination,

Mµjjτ , is calculated. A cut is placed on the number of combinations that any seed muon


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01τ∼

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Figure 7.40: (a) The mass distribution of the virtual neutralino (M(eχ01)∗) in τ1 → µqqτ

decays. (b) A stacked plot showing the Mµjj distributions for RPV SUSY point AP1,where the (i) SUSY signal, (ii) SUSY combinatorial background and (iii) SM backgroundare shown separately.


can form (Ncom ≤ 3).

Figure 7.41 shows the Mµjjτ distribution for point AP1. Combinations where each of

the four reconstructed objects are successfully matched to a true τ1 → µqqτ decay are

shown separately from the SUSY combinatorial background. From the limited statistics

available, no clear signal can be observed. Counting the number of signal combinations

inside a peak window of 120 GeV < Mµjjτ < 200 GeV for an integrated luminosity of

5 fb-1, the true number of signal combinations is ST = 12.3± 3.0 above a background

(calculated from the truth) of BT = 47.7± 5.4 giving ST/√BT = 1.8± 0.4. Extrapolat-

ing these numbers to higher integrated luminosities, one might expect to get a significant

signal of ST/√BT > 5, with an integrated luminosity of ∼ 40 fb-1. This does not repre-

sent a discovery reach, rather the point at which significant statistics to identify a mass

peak might be collected assuming a perfect understanding of the background shape.

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01τ∼

Figure 7.41: The Mµjjτ distribution for RPV SUSY events for point AP1. The SUSYsignal, SUSY combinatoric background and SM background are shown. Only eventspassing the event selection are considered. Mµjjτ combinations are formed using a coneof ∆Rµjjτ < 1.5. Only combinations where Ncom ≤ 3 are included in this histogram. Inthis case, no SM contribution passes the combination cuts.

7.10 Conclusions

By considering an extended form of mSUGRA, this chapter has discussed SUSY scenar-

ios in which R-parity is violated. The study presented here has focused on the case of a


non-zero λ′221 coupling, and has explored the phenomenology of two cases, one where the

LSP is a χ01 and another where it is a τ1. In these τ1 LSP models the τ1 is unstable, and

for RPV couplings such that the 4-body decay modes are dominant, the τ1-LSP region of

mSUGRA parameter-space is characterised by a large multiplicity of τ -leptons in SUSY

events. The full ATLAS detector simulation has been used to prepare simulations of

two points in this parameter space, one point with a τ1 LSP (AP1) and another with

a χ01 LSP (AP2). For both points the RPV coupling at the GUT scale was λ′221 = 0.01

(with all other couplings zero at this scale), resulting in the prompt decay of the τ1 or

χ01 LSP.

In considering the suitability of a high multiplicity of τ -leptons as a possible inclusive

signature for RPV SUSY models with a τ1 LSP, the performance of the ATLAS τ -

reconstruction algorithms was investigated. It was found that:

• The position of τ -leptons resulting directly from τ1 decays was seen to be closely

correlated to the positions of the associated decay-quarks (due to the Lorentz boost

of the parent τ1).

• The reconstruction and identification of hadronic τ -decays in RPV SUSY events

was found to be adversely affected by the nearby jet-activity and the typical low-pT

of the signal τ -leptons.

• The multiplicity of reconstructed τ -jets does not provide a strong signature for

RPV SUSY in the case considered here. More generally, for models where a τ1 LSP

decays through 4-body modes due to a dominant λ′- or λ′′-type coupling, it can be

expected that the identification efficiency for τ -leptons will be significantly reduced

by the associated jet-activity resulting from the quarks produced in the decay of

the τ1.

By considering the specific characteristics of RPV-decays through a λ′221 coupling,

namely the presence of muons and jets in the final state, an exclusive analysis has been

developed. This analysis employs a series of event selection cuts that have been shown to

reduce the SM backgrounds whilst efficiently selecting RPV SUSY events, demonstrating

that S/B ratios of ∼ 3 and ∼ 3.5 can be expected for points AP1 and AP2 respectively.

The decay χ01 → µqq (as occurring in point AP2) provides an interesting experimen-

tal signature. In the analysis presented in section 7.7.1, an experimental approach to

determining Meχ01

is described. Using a data-driven method to approximate the domi-

nant combinatoric background to this process, a significant signal can be expected in


the first year of data. The mass of the χ01 LSP can be accurately determined, with the

dominant error on its value expected to originate from any uncertainty in the jet energy

scale (the sensitivity of the measured mass to the offset in the JES has been predicted

to be 1.3 GeV/1.0 %).

The extension of similar methods to measure the mass of the τ1 LSP in point AP1

through τ1 → µqqτ decays is also discussed. However since this is a more complicated

channel than the χ01 → µqq case, requiring the identification of an additional hadronic

τ -decay, significant statistics will be required to extract a signal. The limited simulated

statistics available in this study indicate that, given a sufficient understanding of the

combinatoric background, an integrated luminosity of greater than 40 fb-1 will be needed

in order to achieve a 5σ signal for this channel.

Chapter 8

Summary

The LHC is on the verge of exploring physics at energies never before seen in particle

colliders. It is widely predicted that physics beyond the Standard Model will become

apparent at the TeV energy scale. The ATLAS detector has been assembled in order

to record the high-energy proton collisions at the LHC and look for evidence of new

physics.

An important component of the ATLAS detector is the Inner Detector which pro-

vides the ability to track charged particles as they travel out from the interaction point

and towards the calorimeters. The SCT (one of three sub-detectors that make up the

Inner Detector) has been successfully commissioned and incorporated into the ATLAS

detector. One of the major stages in this process was the macro-assembly of the SCT

barrels, during which the barrel modules were precisely mounted onto barrel support-

structures. Along with running DAQ testing shifts during the module mounting process,

I performed an initial analysis using the initial data from the SynchTriggerNoise DAQ

tests run on the completed SCT barrels at the macro-assembly site. The analysis of

this first SynchTriggerNoise data for SCT barrels 3 and 6 was presented in chapter 3 of

this thesis. The analysis of this data played an important role in confirming that the

modules were successfully mounted and operating correctly with no gross defects after

the macro-assembly process.

Chapters 4 to 6 of this thesis presented a study of the performance of the tau1p3p τ -

reconstruction algorithm in the context of developing a fast simulation parametrization

for use with ATLFAST. Fast simulation tools play an important role in simulating event

samples that require very large statistics, a situation that is particularly relevant to stud-

193

Summary 194

ies involving hadronic τ -decays where QCD processes can provide a huge background.

I have discussed a method based on extending the pre-existing “jet-tagging” approach

to tau fast simulation to incorporate the tau1p3p algorithm. In order to address the

discussed limitations of the “jet-tagging” method, a second, more advanced approach

was shown. This “track-based” method used ATLFAST tracks to seed the reconstruc-

tion of fast simulation τ -jets in order to better replicate the full tau1p3p algorithm.

The “track-based” approach to tau fast simulation was successfully implemented into

ATLFAST in release 14 of the ATLAS software.

The final section of this thesis investigated R-parity-violating Supersymmetry (RPV)

signatures in ATLAS. Using samples of fully simulated RPV SUSY events, two points

in RPV SUSY parameter space were studied in detail. Using a non-zero, lepton-number

violating coupling, λ′221 = 0.01, one point was chosen to have an unstable τ1 LSP, with

the second point chosen to have an unstable χ01 LSP.

Motivated by the high τ -multiplicity associated with SUSY events for models with

a τ1 LSP, chapter 7 demonstrated the expected τ -reconstruction performance in such

models. The observed τ -reconstruction efficiency was seen to be reduced by the high-

multiplicity environment in RPV SUSY events due to the collimation of τ -leptons with

nearby jets in the event. This indicates that inclusive signatures based solely on the

observation of a high τ -multiplicity will not be possible for all τ1 LSP scenarios.

For a model with a χ01 LSP, the reconstruction of the χ0

1 mass has been demonstrated

by considering χ01 → µqq decays. A set of event selection cuts have been shown to

effectively select signal events from a SM background. The determination of the χ01

mass using combinations of muons and jets has been shown, with a data-driven model

being used to estimate the large combinatoric background. In such models, a significant

signal can be expected in early data. The extension of similar methods to the more

complicated τ1 LSP case, through the reconstruction of τ1 → µqqτ decays, has also been

studied.

Appendix A

Mass spectra for RPV points AP1 and

AP2

Tables A.1 and A.2 show the masses of the sparticles at points AP1 and AP2. Also shown

are the dominant decay modes for each sparticle decay along with the corresponding

branching ratio.

195

Mass spectra for RPV points AP1 and AP2 196

MassMode BR Mode BR

(GeV)eτ−1 151.0 νµsdτ− 0.351 µ+cdτ− 0.255

νµsdτ− 0.200 µ−cdτ− 0.145

µ−sdντ 0.045eχ01 162.1 eτ +

1 τ− 0.500 eτ−1 τ+ 0.500

ee−R 180.1 eχ01e− 1.000

eµ−R 180.1 eχ01µ− 1.000

eνe 280.0 eχ01νe 1.000

eνµ 279.1 eχ01νµ 0.907 sd 0.093

eντ 276.3 W+eτ−1 0.535 eχ01ντ 0.465

ee−L 291.1 eχ01e− 1.000

eµ−L 290.3 eχ01µ− 0.900 cd 0.100

eτ−2 297.7 eχ01τ− 0.465 Z0eτ−1 0.285

h0eτ−1 0.250edR 827.6 eχ01d 0.922 νµs 0.036

µ−c 0.036euR 830.9 eχ01u 0.995

esR 827.7 eχ01s 0.995

ecR 830.7 eχ01c 0.995edL 861.5 eχ−1 u 0.619 eχ0

2d 0.315eχ−2 u 0.035euL 857.8 eχ+1 d 0.648 eχ0

2u 0.318

esL 861.3 eχ−1 c 0.618 eχ02s 0.314eχ−2 c 0.035ecL 857.6 eχ+

1 s 0.646 eχ02c 0.318eb1 778.8 eχ−1 t 0.386 eχ02b 0.243eχ−2 t 0.194 W−et1 0.091eχ0

1b 0.036 eχ03b 0.029eχ0

4b 0.020et1 648.3 eχ+1 b 0.439 eχ0

1t 0.243eχ+2 b 0.169 eχ0

2t 0.150eb2 818.0 eχ−2 t 0.439 W−et1 0.147eχ04b 0.108 eχ−1 t 0.092eχ03b 0.092 eχ0

1b 0.063eχ02b 0.058

MassMode BR Mode BR

(GeV)et2 837.0 eχ+1 b 0.232 eχ0

4t 0.229eχ+2 b 0.165 Z0et1 0.112eχ02t 0.097 eχ0

3t 0.089

h0et1 0.053 eχ01t 0.024eχ0

2 305.0 eτ +1 τ− 0.229 eτ−1 τ+ 0.229eνµντ 0.075 eντντ 0.075eνµνµ 0.062 eνµνµ 0.062eνeνe 0.058 eνeνe 0.058eχ01h

0 0.036 eµ−L µ− 0.023eµ−L µ+ 0.023 ee−L e− 0.021ee−L e+ 0.021eχ03 524.4 eχ−1 W+ 0.276 eχ+

1 W− 0.276eχ02Z

0 0.231 eχ01Z

0 0.094eτ +1 τ− 0.023 eτ−1 τ+ 0.023eχ0

4 538.8 eχ−1 W+ 0.258 eχ+1 W− 0.258eχ0

2h0 0.173 eχ0

1h0 0.069eτ +

2 τ− 0.026 eτ−2 τ+ 0.026eχ−1 305.0 eτ−1 ντ 0.432 eνµτ− 0.169eνµµ− 0.136 eνee− 0.128eχ0

1W− 0.044 eµ−L νµ 0.043ee−L νe 0.038eχ−2 539.3 eχ0

2W− 0.274 eχ−1 Z0 0.247eχ−1 h0 0.196 eχ0

1W− 0.082eτ−2 ντ 0.048 eνµτ− 0.042eµ−L νµ 0.034 ee−L νe 0.034eg 934.4 et1t 0.095 et1t 0.095eb1b 0.087 eb1b 0.087eb2b 0.054 eb2b 0.054edRd 0.045 edRd 0.045esRs 0.044 esRs 0.044ecRc 0.042 ecRc 0.042euRu 0.042 euRu 0.042ecLc 0.024 ecLc 0.024euLu 0.024 euLu 0.024esLs 0.022 esLs 0.022edLd 0.022 edLd 0.022

Table A.1: The masses, decay modes and branching ratios (BR) for sparticles in pointAP1. Only decay modes with a branching ratio of greater than 2 % are shown. RPVdecays are shown in bold.

Mass spectra for RPV points AP1 and AP2 197

MassMode BR Mode BR

(GeV)eχ01 157.9 νµsd 0.290 νµsd 0.290

µ−cd 0.210 µ+cd 0.210eτ−1 164.6 eχ01τ− 1.000

ee−R 192.2 eχ01e− 1.000

eµ−R 192.2 eχ01µ− 1.000

eνe 283.6 eχ01νe 1.000

eνµ 282.8 eχ01νµ 0.913 sd 0.087

eντ 279.8 eχ01ντ 0.572 W+eτ−1 0.428

ee−L 294.6 eχ01e− 1.000

eµ−L 293.8 eχ01µ− 0.905 cd 0.095

eτ−2 300.8 eχ01τ− 0.549 Z0eτ−1 0.240

h0eτ−1 0.206edR 812.6 eχ01d 0.922 νµs 0.036

µ−c 0.036euR 815.8 eχ01u 0.995

esR 812.8 eχ01s 0.995

ecR 815.6 eχ01c 0.995edL 845.6 eχ−1 u 0.618 eχ0

2d 0.314eχ−2 u 0.036euL 841.8 eχ+1 d 0.647 eχ0

2u 0.318

esL 845.4 eχ−1 c 0.617 eχ02s 0.314eχ−2 c 0.036ecL 841.6 eχ+

1 s 0.646 eχ02c 0.317eb1 763.6 eχ−1 t 0.386 eχ02b 0.245eχ−2 t 0.194 W−et1 0.089eχ0

1b 0.036 eχ03b 0.030eχ0

4b 0.020et1 634.6 eχ+1 b 0.445 eχ0

1t 0.239eχ+2 b 0.166 eχ0

2t 0.150eb2 803.1 eχ−2 t 0.441 W−et1 0.145eχ04b 0.111 eχ0

3b 0.094eχ−1 t 0.088 eχ01b 0.065eχ0

2b 0.056

MassMode BR Mode BR

(GeV)et2 822.1 eχ+1 b 0.231 eχ0

4t 0.230eχ+2 b 0.168 Z0et1 0.111eχ02t 0.096 eχ0

3t 0.088

h0et1 0.051 eχ01t 0.024eχ0

2 296.9 eτ +1 τ− 0.338 eτ−1 τ+ 0.338eχ01h

0 0.059 eνµντ 0.050eντντ 0.050 eνµνµ 0.034eνµνµ 0.034 eνeνe 0.031eνeνe 0.031eχ03 513.0 eχ−1 W+ 0.277 eχ+

1 W− 0.277eχ02Z

0 0.230 eχ01Z

0 0.095eτ +1 τ− 0.022 eτ−1 τ+ 0.022eχ0

4 527.6 eχ−1 W+ 0.261 eχ+1 W− 0.261eχ0

2h0 0.173 eχ0

1h0 0.069eτ +

2 τ− 0.025 eτ−2 τ+ 0.025eχ−1 296.9 eτ−1 ντ 0.654 eνµτ− 0.116eνµµ− 0.078 eχ01W

− 0.076eνee− 0.070eχ−2 528.1 eχ0

2W− 0.277 eχ−1 Z0 0.248eχ−1 h0 0.196 eχ0

1W− 0.083eτ−2 ντ 0.047 eνµτ− 0.040eµ−L νµ 0.033 ee−L νe 0.033eg 913.5 et1t 0.095 et1t 0.095eb1b 0.089 eb1b 0.089eb2b 0.054 eb2b 0.054edRd 0.044 edRd 0.044esRs 0.044 esRs 0.044ecRc 0.042 ecRc 0.042euRu 0.042 euRu 0.042ecLc 0.023 ecLc 0.023euLu 0.023 euLu 0.023esLs 0.021 esLs 0.021edLd 0.021 edLd 0.021

Table A.2: The masses, decay modes and branching ratios (BR) for sparticles in pointAP2. Only decay modes with a branching ratio of greater than 2 % are shown. RPVdecays are shown in bold.

Appendix B

Statistical Analysis

In chapter 7, the Standard Model (SM) background is modelled through a series of

datasets, each corresponding to a different physics sample (as summarised in table 7.4).

Each dataset comprises a different number of simulated events with an associated cross-

section and integrated luminosity. Since the cross-sections for different processes can

be very different, and the number of simulated events restricted by the computational

demands of the full simulation process, the corresponding integrated luminosities can

vary significantly and, in some datasets, are very restricted by the available statistics.

In this appendix, a statistical method is used to combine the different SM background

datasets in order to calculate the combined SM contribution after the application of the

event selection cuts (section 7.5).

B.1 Method

For each of N independent datasets, the observed number of events passing a series of

selection cuts is given by

{n} = {n1, n2, . . . , nN} . (B.1)

In each case there is a true expected number of events, λT , that will pass the event

selection cuts for the corresponding dataset:

{λT } = {λT 1, λT 2, . . . , λT N} . (B.2)

198

Statistical Analysis 199

Since each dataset corresponds to a different integrated luminosity, there is an associated

luminosity scaling factor for each dataset (relative to a common integrated luminosity)

{L} = {L1,L2, . . . ,LN} . (B.3)

The probability of observing a given number of events ni passing the cuts is deter-

mined according to the Poisson distribution:

P (n|λ) =λne−λ

n!(B.4)

That is, the probability of observing n events given a known, true expected value of λ.

However this is not the situation that we are considering. Here we are presented with

the observed number of events and want to infer the value of λT i from the value of ni.

To proceed we can apply a method based on Bayes Theorem [82]:

P (λT i|n = ni) =P (n = ni|λT i)P (λT i)

P (ni)(B.5)

This formalism rephrases the question and asks what is the probability of a given value of

λT i given the observed data? The posterior probability, P (λT i|n = ni), is a probability

density function (PDF) that is calculated from the likelihood, P (n = ni|λT i), and the

prior probability, P (λT i), with an appropriate normalisation. The likelihood function

is calculated from equation B.4, however it is important to note that the likelihood

function does not take the form of a Poisson distribution (a discrete distribution in n

given a fixed value of the mean, λ). Instead the equation is inverted to give a distribution

that is continuous in λ for a fixed value of n (for the purposes of this discussion this is

labelled here as an “Inverted Poisson” distribution). The relationship of the Inverted

Poisson distribution to the Poisson distribution is shown in figure B.1.

The form of the prior is a subjective choice and should represent any prior belief as

to the value of the parameter being inferred (in this case λT i). One possibility for the

choice of prior is that of a uniform distribution (the prior being a constant, reflecting no

prior beliefs as to the value of λT i). Upon making this choice, it can be shown that the

mean of the resultant posterior distribution (equal to the Inverted Poisson distribution

introduced earlier) has a bias to higher values than the data might suggest (i.e. for ni

observed events, the mean value of λT is given by 〈λT i〉 = ni + 1). In the context of the

problem faced here, that is inferring the expected number of background events, such a

bias will be conservative. An alternative, commonly considered, choice of prior is a scale


n0 2 4 6 8 10 12 14 16 18

λ

02468

1012141618

)λP(

n |

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(a) P (n|λ) = λne−λ/n!

n0 2 4 6 8 10 12 14 16 18 20

)λP(

n |

00.05

0.10.150.2

0.250.3

0.350.4

0.450.5

Poisson=1 )λP( n | =5 )λP( n | =10 )λP( n |

(b) Discrete Poisson distributions for(i) λ = 1, (ii) λ = 5, and (iii) λ = 10

λ0 2 4 6 8 10 12 14 16 18 20

)λP(

n |

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0.5Inverted Poisson

)λP( n=1 | )λP( n=5 | )λP( n=10 |

(c) Continuous Inverted Poisson distribu-tions for fixed values of n. (i) n = 1,(ii) n = 5, and (iii) n = 10

Figure B.1: (a) The Poisson probability calculated as a function of n and λ. (b) Thediscrete Poisson distribution for selected fixed values of λ. (c) The continuous InvertedPoisson distributions for fixed values of n. It is important to note that the Poisson andInverted Poisson distributions are different for a given fixed value (the function is notinvariant under the interchange n↔ λ).


invariant prior of the form P (λT i) ∝ 1/λT i. This choice of prior gives a more optimistic

statement that, for a dataset with n observed events, 〈λ〉 = n. However for the case

where ni = 0, the posterior probability diverges at λT i = 0, implying that there is zero

possibility that λT i is anything other than zero (clearly an overly optimistic statement).

With these arguments in mind, it was decided that the most appropriate choice of prior

would be a uniform prior. Consequently the posterior PDF for the expectation value of

a given dataset is:

P (λT i|n = ni) =λT

nii e

−λT i

ni!(B.6)

where ni is a constant of the dataset. Further discussion on the choice of prior can be

found in [83].

So far we have established the posterior PDF for each dataset, allowing us to calculate

credible intervals on the value of λT for each dataset. The final step is to take these

statements about the individual datasets and combine them to make an overall statement

about the total background. The true expected number of events from the combined

background, ΛT , is defined as the sum of the expected numbers of events for each dataset

(multiplied by the corresponding luminosity factor):

ΛT =N∑

i=1

λT iLi. (B.7)

The corresponding PDF for the value of ΛT is P (ΛT | {n}).

In order to calculate P (ΛT | {n}), a numerical method is employed. For each of the

N datasets, a proposed value λTSi is randomly sampled from P (λT i|n = ni). This is

achieved through the rejection sampling [84] of P (λT i|n = ni), using a uniform proposal

density (with cut-offs at ni± 5×√ni, outside of which P (λT i|n = ni) is negligible).

From these sampled values a proposed total background ΛTS is calculated:

ΛTS =

N∑i=1

λTSi Li. (B.8)

This process is repeated, histogramming the ΛTS values. The resultant histogram (suit-

ably normalized) gives a measure of P (ΛT | {n}).


B.2 Test Cases

In order to demonstrate the method, several simple test cases have been considered.

Descriptions of which are found below. Where mentioned, the 90 % credible limit (CL)

refers to the value of ΛT such that the interval∫ ΛT

(90%)

0P (ΛT | {n}) dΛT = 0.9.

B.2.1 Case I (n1 = 0, L1 = 1.0)

Here the simple case of a single input dataset is considered. In this case the com-

bined probability distribution function P (ΛT | {n}) is the same as the single input

P (λT i|n = ni). The 90 % CL predicts that ΛT < 2.3 (see figure B.2(a)).

B.2.2 Case II (n1 = 0, L1 = 1.0 and n2 = 0, L2 = 1.0)

In this case, two independent datasets are considered, in each case no events are seen

to pass the event selection. The expected combined background, ΛT , is described by

the probability density function P (λT i|n = ni) as shown in figure B.2(b). This predicts

that ΛT < 3.88 with a 90 % CL. Note that this is less than the 2× 2.3 = 4.6 which one

might naively expect given the CL on a single dataset as described in case I.

B.2.3 Case III (n1 = 10, L1 = 10.0 and n2 = 10, L2 = 10.0)

Here, two independent samples with non-zero results are considered. Also, each sample

is subject to a luminosity weighting (for simplicity the same weighting factor of 10

is considered in both cases). The P (ΛT | {n}) distribution predicts a mean value of

〈ΛT 〉 = 220 (see figure B.2(c)).


ΛCombined 0 1 2 3 4 5 6 7 8 9 10

) |

{n}

ΛP(

0

2

4

6

8

10

-310×

Norm

aliz

ed C

umul

ativ

e Su

m

0

0.2

0.4

0.6

0.8

1

90% C.L. 2.3

Mean = 1 RMS = 0.998

(a) Case I: A single dataset with n1 = 0, L1 = 1.0

ΛCombined 0 1 2 3 4 5 6 7 8 9 10

) |

{n}

ΛP(

0

0.5

1

1.5

2

2.5

3

3.5

-310×

Norm

aliz

ed C

umul

ativ

e Su

m

0

0.2

0.4

0.6

0.8

1

90% C.L. 3.88

Mean = 2 RMS = 1.4

(b) Case II: Two independent datasets with n1 = 0,L1 = 1.0 and n2 = 0, L2 = 1.0

ΛCombined 0 50 100 150 200 250 300 350 400 450 500

) |

{n}

ΛP(

0

1

23

4

56

7

89

-310×

Norm

aliz

ed C

umul

ativ

e Su

m

0

0.2

0.4

0.6

0.8

1

90% C.L. 281

Mean = 220 RMS = 46.9

(c) Case III: Two independent datasets with n1 = 10,L1 = 10.0 and n2 = 10, L2 = 10.0

Figure B.2: The P (λT i|n = ni) distributions for (a) Case I (b) Case II and (c) Case III.


B.3 Combined Standard Model Background

As first discussed in section 7.5, the significant SM backgrounds after the event selection

procedure are summarised in table B.3 and figure B.3. Combining these backgrounds

according to the Bayesian method described earlier, using a constant prior probability,

the total combined SM background contribution is Λ = 986 +119−121± 102 normalized to an

integrated luminosity of 5 fb-1, where the error quoted is of the form A±σstat.±σx−section.

Here, the error on the cross-section is assumed to be correlated between the different

background samples. The statistical error corresponds to the 68.2 % central credible

interval of P (ΛT | {n}).

Sample ni Li

J3 0 39.9

J4 0 30.1

J5 0 92.6

J6 1 4.39

J7 1 0.149

tt 93 5.155

W → µν + 4 jets 1 9.09

W → µν + 5 jets 23 10.64

Z → µµ + 4 jets 4 0.67

Z → µµ + 5 jets 53 0.938

Z → ττ + 5 jets 4 0.519

Total BG Λ = 986 +119−121 at 68.2 % CCI

Table B.1: A summary table of significant SM backgrounds. For each dataset theobserved number of events passing the event selection cuts (ni) is shown, along with aluminosity weighting factor (Li), normalized to a total integrated luminosity of 5 fb-1.Also shown is the mean combined background, quoted with the statistical errors definedfor a 68.2 % central credible interval (CCI).


ΛCombined 400 600 800 1000 1200 1400 1600 1800 2000

) |

{n}

ΛP(

0

0.5

1

1.5

2

2.5

3-310×

Norm

aliz

ed C

umul

ativ

e Su

m

0

0.2

0.4

0.6

0.8

1

90% C.L. 1.15e+03

Mean = 986 RMS = 128

Figure B.3: The P (λT i|n = ni) distribution for the combined Standard Model back-ground after event selection.

Colophon

This thesis was made in LATEX2ε using the “hepthesis” class [85].

206

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List of Figures

1.1 Quantum corrections to the Higgs mass . . . . . . . . . . . . . . . . . . . . . . 10

1.2 The running of SM and MSSM gauge couplings αi and Grand Unification . . . 11

1.3 Proton decay resulting from non-zero RPV couplings . . . . . . . . . . . . . . . 17

2.1 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 The ATLAS Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 The ATLAS Inner Detector barrel section . . . . . . . . . . . . . . . . . . . . . 26

2.5 The ATLAS Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 The ATLAS Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . 32

2.7 The ATLAS muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 SCT barrel layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 A schematic diagram showing a cross-section through a silicon microstrip detector 42

3.3 SCT barrel module schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4 SCT barrel module photograph . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 The deposited charge distribution for a MIP and corresponding noise distribution 45

3.6 SCT DAQ hardware block diagram . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.7 Mean channel occupancy per module for run 2177.6 of barrel 3 . . . . . . . . . 52

214

List of Figures 215

3.8 The mean channel occupancy per module as a function of position on barrel 3

for a SynchTriggerNoise test (run 2177.6). . . . . . . . . . . . . . . . . . . . . . 53

3.9 The mean channel occupancy per module as a function of position on barrel 3

for a NoiseOccupancy test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.10 The ratio of noise occupancy for a SynchTriggerNoise test and a NoiseOccupancy

test of barrel 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.11 Variation of noise occupancy ratio with module position on barrel 3 . . . . . . 56

3.12 Mean channel occupancy per module for run 2177.5 of barrel 3 . . . . . . . . . 57

3.13 Example of the data errors present in the SynchTriggerNoise taken data during

runs 5913.0 and 5913.1 on barrel 6 . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.14 Example of the raw SynchTriggerNoise data from a faulty module on barrel 6 . 60

3.15 Mean channel occupancy per module for run 5913.0 of barrel6 . . . . . . . . . . 61

3.16 Mean channel occupancy per module for run 5913.1 of barrel6 . . . . . . . . . . 62

5.1 The ET response for true τ -jets in full and fast simulation . . . . . . . . . . . . 81

5.2 The ET response for fake τ -jets in full and fast simulation . . . . . . . . . . . . 82

5.3 EeflowT /patlfast

T distributions for fake tau1p3p candidates . . . . . . . . . . . . . . 84

5.4 patlfastT distribution for ATLFAST τ -labelled jets . . . . . . . . . . . . . . . . . 85

5.5 Signal reconstruction factors, ρreco1P/3P, as a function of patlfast

T . . . . . . . . . . . 85

5.6 PDE-RS distributions for true and fake tau1p3p candidates . . . . . . . . . . . 87

5.7 Signal identification factors, ρident1P/3P, as a function of patlfast

T . . . . . . . . . . . 87

5.8 The variation of ρident1P with PDE-RS cut for Tau1P . . . . . . . . . . . . . . . . 88

5.9 Signal identification factors and the corresponding PDE-RS discriminant cuts . 89

5.10 QCD rejection factors for Tau1P and Tau3P candidates . . . . . . . . . . . . . 91

5.11 Tau1P signal identification versus background rejection curves . . . . . . . . . . 93

5.12 Tau3P signal identification versus background rejection curves . . . . . . . . . . 94

5.13 Signal identification and jet rejection factors . . . . . . . . . . . . . . . . . . . . 95

List of Figures 216

5.14 A comparison of the true τ -jets identified by the full simulation and the fast

simulation parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.15 As figure 5.14 with the full simulation results adjusted to account for the τ -

labelling efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.16 A comparison of the fake τ -jets identified by the full simulation and the fast

simulation parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.1 Track reconstruction efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.2 Track quality efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.3 Overall track efficiency parametrization . . . . . . . . . . . . . . . . . . . . . . 105

6.4 (precoT − pvis

T )/pvisT for true 1-prong τ -jets from full simulation . . . . . . . . . . . 110


T )/pvisT for true 3-prong τ -jets from full simulation . . . . . . . . . . . 111


T )/pvisT vs pvis

T for true 1-prong τ -jets from full simulation . . . . . . . 111


T )/pvisT vs pvis

T for true 3-prong τ -jets from full simulation . . . . . . . 112

6.8 Variation in (precoT − pvis

T )/pvisT width with pvis

T for 1-prong and 3-prong τ -jets . . 112

6.9 Mass distributions for 1-prong candidate τ -jets . . . . . . . . . . . . . . . . . . 113


T )/pvisT for true 1-prong ATLFAST τ -jets for varying σnoise . . . . . 114


T )/pvisT for true 3-prong ATLFAST τ -jets for varying σnoise . . . . . 114

6.12 τ -reconstruction performance in ATLFAST and the full simulation: Z → ττ . . 116

6.13 τ -reconstruction performance in ATLFAST and the full simulation: J1 QCD . 117




6.17 τ -jet pT-, η- and φ-resolutions τ -jets in ATLFAST and the full simulation . . . 121

6.18 The signal identification efficiency as a function of pT, for two η slices . . . . . 125

6.19 The fake identification efficiency as a function of pT, for two η slices . . . . . . 126

6.20 τ -identification performance in ATLFAST and the full simulation: Z → ττ . . . 128

List of Figures 217

6.21 τ -identification performance in ATLFAST and the full simulation: SUSY . . . 129

6.22 τ -identification performance in ATLFAST and the full simulation: QCD . . . . 130

7.1 Trilinear RPV couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.2 Meχ01−eτ1

as a function of m0 and m 12

. . . . . . . . . . . . . . . . . . . . . . . . 137

7.3 The 3-body χ01 decay and 4-body τ1 decay modes . . . . . . . . . . . . . . . . . 138

7.4 SUSY decay chain segment in models with a τ1 LSP . . . . . . . . . . . . . . . 138

7.5 τ -lepton multiplicity in SUSY events as a function of m0 and m 12

. . . . . . . . 139

7.6 τ -lepton multiplicity in SUSY events . . . . . . . . . . . . . . . . . . . . . . . . 139

7.7 Characteristics of the τ1 → µqqτ decay (point AP1) . . . . . . . . . . . . . . . 142

7.8 pT-distributions of the daughter particles from τ1 → µqqτ decays . . . . . . . . 143

7.9 Characteristics of the χ01 → µqq decay (point AP2) . . . . . . . . . . . . . . . . 145

7.10 pT-distributions of the daughter particles from χ01 → µqq decays . . . . . . . . 146

7.11 pvisT distributions for true hadronic τ -decays in RPV SUSY (point AP1) . . . . 153

7.12 ∆R of true hadronic τ -decays from the nearest reconstructed τ -jet (point AP1) 154

7.13 Position offset vs pT offset for true hadronic τ -decays (point AP1) . . . . . . . 154

7.14 τ -reconstruction efficiency (point AP1) . . . . . . . . . . . . . . . . . . . . . . . 156

7.15 τ -reconstruction efficiency. The subset of τ -leptons from τ1-decays . . . . . . . 156

7.16 The pT-resolution for all correctly reconstructed τ -decays . . . . . . . . . . . . 157

7.17 NN and LL distributions for true and fake τ -jets. RPV SUSY events . . . . . 159

7.18 NN and LL distributions for true and fake τ -jets. Standard Model events . . . 160

7.19 τ -reconstruction and identification efficiencies in RPV SUSY events (point AP1) 161

7.20 τ -reconstruction and identification efficiencies in RPV SUSY events (point AP1).

Showing the subset of τ -leptons originating from τ1 decays . . . . . . . . . . . . 161

7.21 The number of τ -jets passing the identification selection for both tau1p3p and

taurec algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

7.22 The number of τ -jets per event for RPV SUSY and tt events . . . . . . . . . . 163

List of Figures 218

7.23 ΣET distributions for SUSY events and selected SM backgrounds. . . . . . . . 165

7.24 ΣET distributions for separate SUSY production processes (point AP2) . . . . 166

7.25 Nearest-jet separation for muons produced in χ01 → µqq decays (point AP2). . . 167

7.26 Muon reconstruction efficiency as a function of pT for signal muons (point AP2) 168

7.27 Muon reconstruction efficiency as a function of pT for signal muons after apply-

ing a jet separation cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

7.28 The fraction of QCD events passing the muon selection as a function of ΣET . 169

7.29 mµµ distributions for SUSY and selected SM backgrounds . . . . . . . . . . . . 170

7.30 mT distributions for SUSY and selected SM backgrounds . . . . . . . . . . . . 171

7.31 The number of jets per event for AP2. . . . . . . . . . . . . . . . . . . . . . . . 172

7.32 Efficiency vs EjetT threshold for RPV SUSY events passing a combined mu20i

trigger and jet multiplicity cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

7.33 Mµjj distribution for point AP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.34 Diagram detailing event merging . . . . . . . . . . . . . . . . . . . . . . . . . . 185

7.35 Mµjj distributions with a modelled background distribution (point AP2) . . . . 186

7.36 Mµjj distributions with a functional-fit of the background (point AP2) . . . . . 187

7.37 Mµjj distributions for (a) ∆Rµjj = 2.0 and (b) ∆Rµjj = 2.5. . . . . . . . . . . 189

7.38 Meχ01

sensitivity to the JES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

7.39 Mµjj distribution with background systematic error band . . . . . . . . . . . . 191

7.40 M(eχ01)∗ (from MC) and Mµjj distributions for point AP1 . . . . . . . . . . . . . 193

7.41 Mµjjτ distribution for point AP1 . . . . . . . . . . . . . . . . . . . . . . . . . . 194

B.1 The Poisson probability calculated as a function of n and λ . . . . . . . . . . . 205

B.2 P (λT i|n = ni) for different example scenarios . . . . . . . . . . . . . . . . . . . 208

B.3 P (λT i|n = ni) for the combined SM background after event selection . . . . . . 210

List of Tables

1.1 The fermionic particle content of the Standard Model . . . . . . . . . . . . . . 4

1.2 Selected τ -decay branching ratios. . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 The MSSM chiral supermultiplets . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 The MSSM gauge supermultiplets . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 ID radiation levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 ID track-parameter resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 ECAL Granularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4 Electron and photon energy resolution . . . . . . . . . . . . . . . . . . . . . . . 35

3.1 SCT barrel radii and numbers of constituent modules . . . . . . . . . . . . . . 40

5.1 The signal and background data samples studied . . . . . . . . . . . . . . . . . 78

6.1 Definition of the number of tracks for a candidate τ -jet . . . . . . . . . . . . . 106

6.2 Monte Carlo event samples used to generate the identification parametrization 122

6.3 The number of true reconstructed/identified τ -jets in signal data . . . . . . . . 123

6.4 The number of fake reconstructed/identified τ -jets in background data . . . . . 123

7.1 mSUGRA parameters and RPV-couplings for points AP1 and AP2 . . . . . . . 140

7.2 The τ1 LSP decay modes and branching ratios (point AP1) . . . . . . . . . . . 141

7.3 The χ01 LSP decay modes and branching ratios (point AP2) . . . . . . . . . . 144

219

List of Tables 220

7.4 Monte Carlo sample list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.5 Physics object definitions and identification cuts . . . . . . . . . . . . . . . . . 151

7.6 Event selection cut flow: SUSY, tt and QCD . . . . . . . . . . . . . . . . . . . 174

7.7 Event selection cut flow: W → µν + n jets and W → τν + n jets . . . . . . . . 175

7.8 Event selection cut flow: Z → µµ + n jets and Z → ττ + n jets . . . . . . . . . 176

7.9 Event selection cut flow: QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

7.10 QCD contribution after event selection adjusted to incorporate redundant re-

jection power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

7.11 Summary of numbers of SUSY and SM events after the event selection process 179

7.12 Trigger efficiencies for RPV SUSY events . . . . . . . . . . . . . . . . . . . . . 180

7.13 Summary table showing the reconstructed Meχ01, ST /BT and ST /

√BT . . . . . 188

A.1 Sparticle masses and decay modes. Point AP1 . . . . . . . . . . . . . . . . . . . 200

A.2 Sparticle masses and decay modes. Point AP2 . . . . . . . . . . . . . . . . . . . 201

B.1 Summary table showing details of the significant SM backgrounds . . . . . . . 209

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