論文 / 著書情報
Article / Book Information
題目(和文)
Title(English)

Search for long-lived gluinos using high-track-multiplicity displaced
vertices with the ATLAS detector at √s = 13 TeV

著者(和文)

本橋和貴

Author(English)

Kazuki Motohashi

出典(和文)

学位:博士(理学),学位授与機関:東京工業大学,
報告番号:甲第10583号,
授与年月日:2017年6月30日,
学位の種別:課程博士,
審査員:陣内 修,柴田 利明,河合 誠之,中村 隆司,久世 正弘

Citation(English)

Degree:Doctor (Science),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第10583号,
Conferred date:2017/6/30,
Degree Type:Course doctor,
Examiner:Osamu Jinnouchi,Toshi-aki Shibata,Nobuyuki Kawai,Takashi
Nakamura,Masahiro Kuze

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)

Ph.D Thesis
Search for long-lived gluinos using
high-track-multiplicity displaced√ vertices
with the ATLAS detector at s = 13 TeV

Kazuki Motohashi
Tokyo Institute of Technology,
Department of Physics

c Copyright 2017 by Kazuki MotohashiAbstract

Many extensions of the Standard Model of particle physics predict the existence ofheavy and long-lived particles. A Split-SUSY model often predicts long-lived supersymmetry (SUSY) particles which decay inside the inner tracking volume of the ATLAS
detector and they can be reconstructed as displaced vertices (DVs). A Split-SUSY model
is one of phenomenologically motivated SUSY models that is consistent with the squark
masses of O(10 − 1000) TeV implied by the observed Higgs mass of 125 GeV. It would
also explain the relic density of dark matter when gaugino co-annihilation mechanism
is realised. The decay point of the long-lived particle is reconstructed by ﬁnding thecrossing point of the tracks of charged particles. The charged particles with a large impact parameter cannot be reconstructed eﬃciently with the ATLAS standard tracking
strategy, therefore a special “large radius tracking” criteria were adopted after the chainof standard tracking. The large radius tracking criteria use detector hits which were left
after the standard tracking and the requirements on impact parameters and the numberof hits of the tracks are relaxed.
A search for direct production of long-lived gluino pairs which transform into Rhadrons in ﬁnal states with massive DVs with high track-multiplicity and missing transverse momentum has been performed using proton-proton collision data from the 2016
data taking period corresponding to an integrated luminosity of 32.7 fb−1 recorded at√
s = 13 TeV by the ATLAS detector. In order to cover a wide range of parameter space
miss channel is investigated in this dissertation.
of a Split-SUSY model, a generic DV+ET
One of the powerful features of the search for new physics via massive and high-trackmultiplicity DVs is the extremely low level of background. No SM particles result in thesignature and only experimentally induced backgrounds become important. DVs arisingfrom hadronic interaction with detector materials are signiﬁcantly reduced using a threedimensional detector material map created with a data-driven method. The number of
DVs which were accidentally merged with a neighbour DV and fall into the signal region
was found to be negligible. The number of DVs randomly crossed by track is estimatedusing templates of DV mass distributions constructed by adding a track to a seed vertex
and re-calculating its invariant mass.
Not only explicit improvements such as the increase of the LHC beam energy andinstallation of a new layer of pixel detector into the ATLAS detector but also several
improvements and re-optimisations have been made over the analysis of the LHC Run-1.
miss signiﬁcantly improved the signal
A newly developed event ﬁlter purely based on ET
acceptances for scenarios with small mass diﬀerence between the gluino and neutralino.
The ﬁlter requirement to ﬁnd jets which are not associated with tracks from the primary
miss cut. In addition, a method tovertex was replaced with a simple calorimeter-based ET
estimate remaining DVs which were not vetoed by the material map has been developed
and criteria for validation of the background estimation methods have been improvedto accommodate the R-hadron speciﬁc signatures. Two diﬀerent validation regions wereconstructed by inverting the material veto requirement, or setting an upper limit on themiss and the smallest diﬀerence of azimuthal angle between selected jets and E miss .
ET
TNo displaced vertices are observed in the signal region, and exclusion limits at 95%
conﬁdence level are set for a range of production cross-sections and long-lived-particle
lifetimes in a Split-SUSY model, where gluino decays to a pair of quarks and the lightest
2neutralino. The excluded limits are set for an interval of proper decay length cτ = 1–
10000 mm. The exclusion limit on gluino mass was set up to 2400 GeV. There is asigniﬁcant gain compared to the limit in the previous results up to ∼ 1600 GeV. In
addition, a wide range of parameter space with small mass diﬀerence between gluino andneutralino has been excluded up to ∼ 1600 GeV. This small mass-splitting scenario had
not been investigated in the previous results.

3

Acknowledgement

At the end of my odyssey as a doctoral course student for three years, I would like tothank many people without whom this dissertation would not have been ﬁnished. Since
it is hard to mention all the people in a few paragraphs, I would like to thank some ofthem explicitly here.
First of all, I wish to thank my supervisor, Associate Professor Osamu Jinnouchi,
who has been unprecedentedly helpful and gone the extra mile to support me. He did
not force me to work following his strategy at all but he allowed me to pursue my own
interests. A door of his oﬃce is always opened for seamless discussion with students,and his advises and suggestions with prudence paved the vague way in front of me all
the time. His brilliance is beyond description and it should be one of the best decisions
in my entire life to choose this lab when I was an undergraduate. Connecting the dots
looking backwards, the goodness of ﬁt seems to be perfect.
I would like to thank all the members in the displaced vertex search group in the
ATLAS SUSY group. Especially, convener of the analysis group, Dr. Jordi DuarteCampderros, has displayed his exceptional leadership at all times. I also have to mention
the fact that he is excellent as not only a physicist but also a programmer. I have learned
a lot of things from his beautiful, concise and well-readable analysis codes. AssistantProfessor Hidetoshi Otono kindly invited me to this very interesting analysis topic. He
had been eager to discuss the analysis with me as a sort of a local supervisor at CERN.
Dr. Nora Emilia Pettersson, who was one of the main analysers of Run-1 analysis on
the displaced vertex search and was a member of Jinounchi lab before, provided memuch of advices and benevolently took her much time for discussion. Dr. Christian
Ohm had devoted to construct infrastructure of the analysis as well as guided us along
a right way to convergence of analysis. It might not be too much to say that I could
not even look at the data properly without his huge eﬀort. Professor Abner Soﬀer isa man of great insight. His suggestions always make sense and essential for our group.
Dr. Lawrence Lee Jr found several ﬂaws in our analysis. He then immediately suggested
solutions and ﬁxed them. The analysis results could not have been published without
his excellent works. I would like to thank the other members, Dr. Michael Flowerdew,
Dominik Krauss, Jennifer Kathryn Roloﬀ as well.
My sub-supervisor, Professor Masahiro Kuze, has constantly provided me profoundknowledge regarding a wide range of physics as well as techno pop. If I had got less
opportunities to chat with him, my devotion to a social networking service would havediverged to inﬁnity.
I would like to thank extraordinary staﬀs, Dr. Ryo Nagai, Dr. Minoru Hirose, Dr. Hideyuki Oide and Assistant Professer Hideki Okawa for their kind advices on the analysis.
Discussions with Daiki Yamaguchi and Kazuki Todome, who are PhD students at Jinnouchi lab were very helpful. I enjoyed chat and tea time with my oﬃce mates in thelab, Hiromi Sawai and Shinichi Sato. The other members in the lab, Hitomi Tokutake,
Keisuke Koda, Asawatavonvanich Thanawat, Eunchong Kim and Knut Zoch, made mydays in the lab well oﬀ.
I also would like to thank friends who had lived in a house with me, located in FerneyVoltaire near from CERN for two years, Dai Kobayashi, Shota Suzuki, Takuto Kunigo
and Atsushi Mizukami. I was helped very much by their great skills at cooking. I enjoyed4

spending holidays around CERN with my friends, Takuya Nobe, Yoichi Nonomiya, Shion
Chen, Shohei Shirabe, Takuya Honda, Shunsuke Honda, Daiki Hayakawa and other niceguys. I would like to give special thanks to Keralino Sandorovich, who has had enormous
inﬂuence on me.
Finally, the best thanks my dear parents, Tatsuaki and Yoko for their love and support
to me, my sister, Megumi, and brother, Yusuke.
This work was supported by JSPS KAKENHI Grant Number JP15J10809. I could
have hot meals and live in a warm house preventing bitter winds thanks to JSPS.

5

Contents
1 Introduction

8

2 Theoretical Background and Motivation for Displaced Vertex Search
2.1 Introduction to the Standard Model
2.1.1 Elementary particles and forces
2.1.2 Limitations of the Standard Model
2.2 Introduction to Supersymmetry (SUSY)
2.2.1 The Minimal Supersymmetric Standard Model (MSSM)
2.2.2 Supersymmetry breaking
2.2.3 SUSY after the Higgs Discovery
2.3 Dark Matter Relic Density
2.3.1 Gaugino Co-annihilation

11
11
12
12
14
15
16
17
18
20

3 The LHC and ATLAS Experiment
3.1 The Large Hadron Collider
3.2 The ATLAS Detector
3.2.1 Inner Detector
3.2.2 Calorimeters3.2.3 Muon Spectrometers
3.2.4 Trigger System
3.2.5 Luminosity Detectors

23
23
26
27
31
32
33
34

4 Object Reconstruction
4.1 Track and Vertex
4.1.1 Standard Tracking
4.1.2 Reconstruction of Tracks with Large Impact Parameters4.1.3 Primary Vertex Reconstruction
4.1.4 Displaced Vertex Reconstruction
4.2 Electron and Photon
4.3 Muon
4.3.1 Combined reconstruction
4.4 Jet
4.5 Missing Transverse Momentum

36
36
36
41
41
43
44
45
45
45
46

5 The Displaced Vertex Analysis
5.1 Introduction
5.2 Dataset Information
5.2.1 Data Samples
5.2.2 Simulated Samples
5.3 Background Sources

47
47
48
48
49
50
6

CONTENTS

5.4
5.5

5.6

5.7

5.8

Overview of Signal, Control and Validation Regions
Event Selection and Cleaning
5.5.1 Triggering and Filtering
5.5.2 Good Runs List
5.5.3 Event Cleaning
5.5.4 Primary Vertex
5.5.5 Non Collision Background Veto
5.5.6 Oﬄine Missing Transverse Energy Cut
Vertex Selection
5.6.1 Fiducial Volume
5.6.2 DV Displacement
5.6.3 Vertex Fit Quality
5.6.4 Material Veto
5.6.5 Disabled Module Veto
5.6.6 Number of Tracks and DV Mass
Background Estimation
5.7.1 Hadronic Interaction
5.7.2 Merged Vertices
5.7.3 Random Crossing Tracks
5.7.4 Validation of the Background Estimation
5.7.5 Systematic Uncertainties on Background Estimation Methods
Results
5.8.1 Total Background Estimate and Event-Selection Transfer Factor

51
53
53
56
56
56
56
59
62
62
63
63
63
64
65
65
67
68
69
75
81
86
86

6 Interpretation in Supersymmetry
6.1 Introduction
6.2 Lifetime Reweighting
6.3 Systematic Uncertainties on the Signal Eﬃciency
6.3.1 Tracking/Vertexing Performance
6.3.2 ISR and FSR Modelling
6.3.3 Pileup Re-weighting
6.3.4 Summary of Uncertainties on the Signal Eﬃciency
6.4 Exclusion Limits

92
92
93
93
94
95
97
97
99

7 Conclusion

103

A Hadronic interactions
A.1 Hadronic interactions in material-dominated detector regions
A.2 Geant4 studies

105
105
107

7

Chapter 1

Introduction
One of the answers to the fundamental questions of physics such as what kind of substances exist in the universe and what kind of principles describe interaction between
them is the Standard Model (SM) of particle physics [1–4]. The SM is a powerful theory that describes strong force, weak force, electromagnetic force based on the gauge
principle and can describe almost all of currently known quantum phenomena. The A
Toroidal LHC ApparatuS (ATLAS) experiment [5], conducted using the Large Hadron
Collider (LHC) [6] of the European Nuclear Research Organisation (CERN), achieved ahistorical success to discover the Higgs boson which were the last undiscovered particles
of SM [7, 8]. With that, it can be said that the SM has been completed. However, it
is also a fact that phenomena that SM can not explain, such as dark matter suggested by space observation by e.g. Planck satellites [9, 10] and neutrino oscillation [11],exist. Various theories such as supersymmetry have been proposed as Beyond the Standard Model (BSM), and its veriﬁcation has been challenged in the ATLAS experiment,
however, BSM signs have not been obtained yet.
One of the main ATLAS programs is search for the Supersymmetry (SUSY) [12–20].
The minimal realisation of supersymmetric extension of the Standard Model is called
Minimal Supersymetric Standard Model (MSSM). The MSSM could shed light on several
open questions which cannot be explained by the SM. Figure 1.1 shows the unexplained
issues (big questions) and the proposed theoretical models (big ideas). If the lightest
neutralino is the lightest SUSY particle (LSP), it is generally stable and its coupling isof weak interaction, and thus it is a promising candidate of dark matter. Introducing the
MSSM, the running coupling constants of the strong and electroweak interactions meet
accurately at the grand uniﬁcation energy scale, ΛGUT ≈ 1016 GeV [22]. Naturalnessof a theory requires an additional symmetry in order to naturally explain the observed
Higgs mass at the electroweak scale regardless of the huge quantum corrections up to the
Planck scale. The SUSY relates fermions and bosons so that the corrections are canceled
if the SUSY is realised around TeV scale. If the evidence of supersymmetry is conﬁrmed,
it is nothing short of revolutionary.
Nevertheless, the observation of the Higgs boson has signiﬁcantly changed the prospects for naturalness. The observed Higgs mass of about 125 GeV [23] implies thatthe mass scale of SUSY particles is much higher than the electroweak scale [24]. This isconsistent with the lack of evidence of the SUSY so far in some sense. Rather, a relatively high-scale SUSY has several advantages in phenomenological aspects. The ﬂavourchanging neutral current processes and the electric dipole moments of the SM particles
are suppressed [25, 26], the proton decay rate is reduced [27] and the gravitino problem

8CHAPTER 1. INTRODUCTION

Big Questionsry
t a teen osi
em p
El om
.C
vs
es
rc
Fo
w
Ne
of
n
igi orOr lavFofnigi erOr att
M

r
te
at

ion
at
i fi c
Un
ss
lne
ra
tu
Na
of
n
igi B
Or WS
E

M
rk
Da

Big
Ideas
SUSY

Compositeness,
Extra dimensions
Extended
Higgs Sector
Top
Partner
W’/Z’
MinimalDark Matter
HiddenSector???

Multiverse

Figure 1.1: Overlap between the questions and ideas discussed in the conference ofPlanning the Future of U.S. Particle Physics (Snowmass 2013) [21].
in cosmology is evaded [28] thanks to the heavy SUSY particles.
A Split-SUSY [24, 29] is one of successful high-scale SUSY models. In Split-SUSY,
scalar SUSY particles are heavy at the SUSY breaking scale, while fermions are lighter.
Typically the fermion masses are chosen around a TeV scale as expected by the “WIMP
miracle” [30] and to realise the gauge coupling uniﬁcation. Although the mass of scalar
SUSY particles had been free parameter before, the 125 GeV Higgs mass has strongly
constrained the scalar mass in the range from about 10 TeV to 105 TeV [24].
A Split-SUSY model often predicts long-lived gluino, a fermionic superpartner ofgluon, which forms R-hadron [31] and decays inside the inner tracking volume of the
ATLAS detector and it can be reconstructed as displaced vertices (DVs). A search fordirect production of long-lived gluino pairs in ﬁnal states with massive DVs with hightrack-multiplicity and missing transverse momentum has been performed using protonproton collision data from the 2016 data taking period corresponding to an integrated√
luminosity of 32.7 fb−1 recorded at s = 13 TeV by the ATLAS detector at the LHC.
√
Compared to the previous search using the 2012 data at s = 8 TeV [32], the beamenergy has been increased by about 60% and it leads to an increase the production
cross section of new physics. A newly installed layer of the ATLAS pixel detector has
improved the performance of charged particles tracking [33]. Not only the improvementof the apparatuses but also several reﬁnements of the analysis have been performed sothat it has gained much higher sensitivity to yet-unexplored signal scenarios.

Outline of the thesis
This thesis begins by considering the motivation for high-scale supersymmetry and toprobe it using displaced vertices in Chapter 2. Chapter 3 and 4 introduce the experimental framework: the overview of the ATLAS detector, the object reconstructions andthe performances. Chapter 5 is devoted to describe full information of the analysis on9CHAPTER 1. INTRODUCTION

the displaced vertex search with the ATLAS detector using the data taken in 2016. The
results are interpreted in supersymmetry and conclusions are given in Chapter 6 andChapter 7, respectively.

Contributions
Energy frontier experiments have grown in the past several decades and anyone canno longer contribute to every ﬁeld of the experiment. The LHC-ATLAS experiment isa highly collaborative project in which more than 3,000 researchers have participated.
A large number of missions are divided among them. This dissertation also cannot beﬁnished without the many individual works which contribute both directly and indirectly.
Major contributions of the author are summarised in the following.

Chapter 3: The ATLAS Experiment
The author contributed to the quality assurance of sensor modules of the new Pixel
detector layer (IBL). After installing the IBL into the ATLAS detector, the author wasin charge of monitoring data quality (DQ) of the Pixel detector and developing softwares
to be used there.

Chapter 4: Object Reconstruction
The author contributed to implementation and validation of secondary vertexing algorithm. Especially, a functionality to merge vertices within a distance of 1 mm andsome additional track quality requirements were implemented by the author.

Chapter 5: The Displaced Vertex Analysis
The author has been a main analyser and contributed to essentially every aspect ofthe displaced vertex analysis toward the Moriond 2017 conference from the beginningto the end of the analysis. The author’s analysis results have been approved by the
ATLAS collaboration and were shown in public at the international conference. At
ﬁrst, the author estimated the sensitivity of the signal scenarios of interest, produced
and validated simulation samples. The author also participated in validation of thelarge radius tracking and secondary vertexing algorithm using the samples. The author
has been responsible for the data-driven background estimation and estimation of theassociated uncertainties. The author regularly shared analysis status in the analysis
group and got feedback from them.

Chapter 6: Interpretation in Supersymmetry
The author has been responsible for estimation of the signal acceptances and uncertainties
except for the tracking-related one. In particular, the author was solely responsible for
implementation of a tool for the estimation. The estimated values were used as input
for limit setting by collaborators.

10Chapter 2Theoretical Background andMotivation for Displaced Vertex
SearchThe SUSY is one of the most attractive extensions of the SM. SUSY could shed lighton several problems which cannot be explained by the SM. It provides a dark mattercandidate, and might be able to play essential role for the uniﬁcation of the coupling of
the fundamental forces. An introduction to the MSSM shall be given in this chapter.
A particular attention is paid for consistency with the observed Higgs mass and dark
matter relic abundance.

2.1

Introduction to the Standard Model

The SM of particle physics [1–4] is a quantum ﬁeld theory which explains the interactions
between elementary particles with great accuracy. The SM was established in 1970s and iscomposed of a uniﬁed theory of electromagnetic and weak forces, which is called GlashowWeinberg-Salam theory, and Quantum Chromodynamics (QCD), which describes strong
force. These theories are described with renormalisable gauge ﬁelds and based on thefollowing symmetry
SU (3)C ⊗ SU (2)L ⊗ U (1)Y
(2.1)
where C, L and Y are the colour charge, the weak isospin and the hypercharge, respectively. The dynamics of the quantum state and the fundamental ﬁelds of the SM can be
described by the Lagrangian LSM :1/ + ψi yij ψj φ + h.c. + |Dμ φ|2 − V (φ),
LSM = − Fμν F μν + iψ̄ Dψ
4

(2.2)

where F and D are the strength tensors of the gauge ﬁelds (photon, W , Z, gluon), termswith a ψ include fermions (quarks and leptons), and terms with a φ include the Higgs
boson. yij denotes a matrix of Yukawa couplings, and V (φ) represents the Higgs potential. Each term deﬁnes the behaviour of the elementary particles and it can be calculated
following the Feynmann rules. The fundamental forces are propagated by exchange ofvirtual particles (gauge bosons) carrying energies and momenta. The properties of theparticles of the SM shall be explained in the next section.

11

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

2.1.1

Elementary particles and forces

Elementary particles in the framework of the SM include the fermions (quarks andleptons), which are spin-1/2 particles and generally called “matter particles”, as well as
the bosons (gauge bosons and the Higgs boson), which are often called “force particles”.
The spins of gauge bosons are 1, while the Higgs boson is a spin-0 scalar particle. The
fermions have two eigenstates of left and right chirarities. The left-handed fermionsform SU (2)L doublets under weak interaction and the right-handed fermions form singlets. The neutrinos are assumed to be massless, so that only left-handed neutrinos are
considered. The matter sector of the SM can be summarised as follows.
  
  
     
cL
tL
νeL
νμL
ντ L
uL
dL
sL
bL
eL
μL
τL
eR
μR
τR
u R , d R c R , s R tR , b R
The massless gauge bosons W i ; i = 1, 2, 3 and B are the mediators of the electroweak
interaction and the gluon g is the carrier of the strong force. Although the gauge symmetry forbids mass terms of any particles, the electroweak gauge bosons acquire masses
after spontaneous symmetry breaking of the SU (2) electroweak symmetry. The mass
eigenstates (W ± , Z, and γ) are written as:1
W ± = √ (W 1 ∓ W 2 )2
    3
Zcos θW − sin θWW,=
sin θWcos θW
B
γ

(2.3)

(2.4)

where the Weinberg angle θW is deﬁned by:sin θW =

e
,
g2

(2.5)

where e and g2 are the electric charge and the SU (2) gauge coupling constant. The
masses of quarks and leptons (mf ) are given by:vλfmf = √ ,2(2.6)

where v is the vacuum expectation value of the Higgs ﬁeld and λf is the Yukawa coupling,respectively.
On 4th of July 2012, a new boson with the mass of ∼ 126 GeV was observed by
ATLAS and CMS Collaborations simultaneously [7, 8]. The property of the boson wasmeasured further and found to be consistent with the Higgs boson in 2013. The observation of the Higgs boson veriﬁes the mechanism that spontaneously breaks the electroweak symmetry and gives masses to particles. The measured value of the Higgs massis 125.5 ± 0.2 (stat.) +0.5
−0.6 (syst.) GeV [23]. The particles of the SM and their properties
are summarised in Fig. 2.1.

2.1.2

Limitations of the Standard Model

The SM has extraordinarily accurate predictive power of phenomena of high energy
physics experiments as shown in Fig. 2.2. No signiﬁcant deviation from theoretical
calculation has been observed over a vastly wide range of energy scale. However, the SM
12

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

Figure 2.1: An overview of the properties of the particles in the Standard Model [34].
cannot answer a few open questions. For instance, the fourth fundamental force, gravity,
is not formulised at all and neutrinos are assumed as massless particles although theneutrino oscillation has been thoroughly conﬁrmed which is a clear evidence of non-zeroneutrino mass.
Within the SM, the bare mass parameter of the Higgs is corrected by large quantum
loop corrections which are proportional to the cut oﬀ scale (Planck scale),δm2H ∝

λ2f Ncf
8π 2

Λ2 ,

(2.7)

where λf and Ncf are the Yukawa coupling and the number of colours of fermion f .
These corrections are about 16 digits larger than the observed mass of the Higgs aroundthe electromagnetic scale. Without any additional mechanisms, it is necessary to cancelout the 16 digits of contributions from the bare mass and the corrections to obtain theobserved Higgs mass. This huge magnitude of cancelation is regarded as unnatural andoften called ﬁne-tuning. It is expected that there is an additional symmetry or mechanism
to avoid the ﬁne-tuning from the point of view of naturalness of a theory.
The SM contains no candidate particle for dark matter which comprises approximately 27% of the energy of the whole universe. The neutrino is a stable, neutral
and weakly interacting particle, however the amount of neutrinos in the universe is notenough to explain the observed relic density of dark matter. Also the nature of dark energy which accounts for approximately 68% of the total energy in observable universe is13

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

σ [pb]

Standard Model Production Cross Section Measurements
1011
106
5

10

total (x2)

ATLAS

inelastic

Run 1,2nj ≥ 1
0.1 < pT < 2 TeV

Status: August 2016

Preliminary√s = 7, 8, 13 TeVTheory√
LHC pp s = 7 TeV
Data 4.5 − 4.9 fb−1

nj ≥ 20.3 < mjj < 5 TeV√
LHC pp s = 8 TeV

pT > 25 GeV

104nj ≥ 0103

nj ≥ 1

Data 20.3 fb−1

nj ≥ 0

LHC ppnj ≥ 0

Data 0.08 − 14.8 fb−1

total

pT > 100 GeV nj ≥ 2 nj ≥ 1

102

nj ≥ 3 nj ≥ 2

101

n ≥3
nj ≥ 4 jnj ≥ 51

nj ≥ 6nj ≥ 4nj ≥ 5nj ≥ 610−1

t -channj ≥ 1Wt

nj ≥ 2nj ≥ 5nj ≥ 7WW WW

s -chan

total

WZ
WZ
ZZ

WZ

ggF

H→WW

ZZ

Wγ
Zγ

nj ≥ 4nj ≥ 6H→ττnj ≥ 5nj ≥ 7

VBF

Zγ

H→WW

nj ≥ 8n ≥6nj ≥ 7 j

10−2

WW

ZZ

nj ≥ 4nj ≥ 3√s = 13 TeV

H→γγnj ≥ 7

H→ZZ →4
W ±W ±

10−3

WZ

pp Jets

R=0.4

γ

W

Z

tt̄

t

VV

γγ

H

Vγ tt̄Wtt̄Z tt̄γ Zjj WW Zγγ Wγγ VVjj

ﬁd.

ﬁd.

ﬁd.

ﬁd.

tot.

tot.

ﬁd.

ﬁd.

ﬁd.

tot.

tot.

EWK

ﬁd.

ﬁd.

Excl.

tot.

ﬁd.

ﬁd.

EWK

ﬁd.

Figure 2.2: Summary of several Standard Model total and ﬁducial production crosssection measurements, corrected for leptonic branching fractions, compared to the corresponding theoretical expectations [35]. All theoretical expectations were calculated at
NLO or higher.
entirely unknown in the framework of the SM. As a result, the mass of ordinary baryonicmatter contributes only about 5% of the universe.

2.2

Introduction to Supersymmetry (SUSY)

A number of extensions of the SM have been proposed in order to solve these questions.
One of the well-motivated solutions is adding extra dimensions to the observed 3+1 spacetime dimensions. This makes the eﬀective Planck scale smaller, in a certain model, to anorder of scale of extra dimension. As a result, the hierarchy between the electromagnetic
scale and the Planck scale would be signiﬁcantly reduced.
Another attractive theory beyond the SM is SUSY [12–20]. The SUSY is based ona generalisation of space-time transformation which relates fermions and bosons. The
operator Q performs this type of transformations with1
Q |Fermion = |Boson ,Q |Boson = |Fermion .

(2.8)

Because the angular momentum must be invariant in both sides of each equation in
Eq. (2.8)2 , the Q is a fermionic operator that carries spin angular momentum 1/2. Haag1
2

This section follows the convention adopted in Ref. [36].
A fermion is a particle with the spin of an odd half integer, while a boson has the integral spin.

14

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

Table 2.1: Fields in the MSSM and the SU (3) ⊗ SU (2) ⊗ U (1) quantum numbers.
Names

SUSY ﬁeld

SM partner

Quantum numbers
SU (3)SU (2)U (1)squarks, quarks

Q(ũL , d˜L )(uL , dL )

8

1

1
6

(×3 families)

ū
d¯

ũ∗R
d˜∗

u†R

3

1

− 23

R

d†R

3

1

1
3

sleptons, leptons

L(ν̃, ẽL )(ν, eL )

1

2

− 12

(×3 families)

ē

ẽ∗R

e†R

1

1

1

Higgs, higgsinos

Hu(H̃u+ , H̃u0 )(Hu+ , Hu0 )

1

2

1
2

Hd

(H̃d0 , H̃d− )(Hd0 , Hd− )

1

2

− 12

gluino, gluon

g̃

g

8

1

0

winos, W bosons

0
± W
W

W± W0

1

3

0

bino, B boson

B̃ 0

B0

1

1

0

Lopuszanski-Sohnius theorem [37] highly constrains a form of the supersymmetry algebra
which is consistent with the 4-dimensional quantum ﬁeld theory. The operators Q and
its hermitian conjugate, Q† , satisfy the following schematic anti-commutation and commutation relations:(2.9){Q, Q† } = P μ ,{Q, Q} = {Q† , Q† } = 0,(2.10)[P μ , Q] = [P μ , Q† ] = 0,(2.11)

where P μ is the four-momentum generator of spacetime translations. It can be shownthat the Q operator also commutes with m2 = Pμ P μ using Eq. (2.11), i.e., the supersymmetric transformation does not change the mass of a particle. This can be interpreted
that the supersymmetric partner would have the same mass as its counterpart in theSM.
SUSY is an appealing theory that enables the uniﬁcation of the gauge coupling constants of strong, weak and electromagnetic interactions around a scale of the GrandUniﬁed Theory (GUT) around 1015−16 GeV. SUSY is also expected to combine the GUTwith the gravity since Einstein’s theory of general relativity is automatically derived by
imposing SUSY as a local symmetry in supersymmetric quantum ﬁeld theory.

2.2.1

The Minimal Supersymmetric Standard Model (MSSM)

Although there are varieties of supersymmetric extensions to the SM, the simplest one,
MSSM, is used as a representative model throughout this dissertation. A brief overview
of the MSSM is given in this section focusing on its phenomenology. More details canbe found, for instance, in Reference [36].
The MSSM introduces a super-partner for every particle of the SM with the same
quantum numbers and properties but with 1/2 spin diﬀerence as listed in Tab. 2.1.
In order to be consistent with the fact that the baryon number and lepton number

15

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

conservations have been tested precisely, a new symmetry called “R-parity” [38] is added
to the MSSM. R-parity, which is assumed to be conserved, is deﬁned as:
R = (−1)3(B−L)+2S ,(2.12)

where B and L are the baryon and lepton numbers, respectively and S is the spin. It iseasy to check that all SM particles have R-parity of +1, while SUSY particles (sparticles)
have R-parity of −1. In consequence of the R-parity conservation:
1. sparticles are produced in pairs,
2. decay products of sparticles include other sparticles,
3. the Lightest SUSY Particle (LSP) is stable.
This third outcome implies that the LSP is a possible candidate of the dark matter ofthe universe.
There is one complex Higgs doublet in the SM, however a single higgsino (the fermionic superpartner of the Higgs boson) would induce gauge anomaly, which is required tobe cancelled by renomalizability of the theory. The gauge anomaly occurs in general if
Y = 0,(2.13)
fermions

where Y is the hypercharge. Therefore, MSSM contains two chiral super-multipletswith two complex Higgs doubles Hu and Hd , which couple with up-type and down-type
super-multilets, respectively, and their fermionic super-partners, higgsinos.

2.2.2

Supersymmetry breaking

Since any sparticles have not been observed so far, even if SUSY is realised, it must bea broken symmetry. SUSY breaking terms of the Lagrangian should be soft in order toavoid ultraviolet divergences appearing in scalar masses. This means that the eﬀective
Lagrangian of the MSSM can be split into two components:
LMSSM = LSUSY + LSoft ,(2.14)

where LSUSY contains the interaction terms and preserves supersymmetric invariance,and LSoft is the SUSY breaking terms which are composed of only mass terms andcoupling parameters with positive mass dimension less than four.
The general form of soft SUSY breaking terms in the Lagrangian LSoft can be written
as:


1
1 ijk
1 ij
a a
i
Ma λ λ + A φi φj φk + B φi φj + C φi + h.c.
LSoft = −2
3!
2
(2.15)
2 i j∗− (m )j φ φi ,where φi is the scalar component of one of the MSSM superﬁelds, with m being interpreted as its mass, and λa the gaugino ﬁelds, with M their Majorana mass term. A,
B and C are the trilinear, bilinear and linear scalar interaction terms. The soft SUSY
breaking terms of the MSSM can be speciﬁed as:

1
W̃
W̃
+
M
B̃
B̃
+
h.c.
M
=
−
g̃g̃
+
M
LMSSM
3
2
1
Soft

2
˜
¯ d Q̃Hd − ē˜Ae L̃Hd + h.c.
˜Au Q̃Hu − dA
− ū
(2.16)
† 2
† 2
2 ˜†
2˜
†
2 ˜†
˜
¯
¯
˜
˜
− Q̃ mQ Q̃ − L̃ mL L̃ − ūmū ū − dm d − ēmē ēd̄− m2Hu Hu∗ Hu − m2Hd Hd∗ Hd − (μHu Hd + h.c.),16

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

where M3 , M2 , M1 are the gluino, wino and bino mass terms. Each of Au , Ad , Ae , isa complex 3 × 3 matrix in family space, with dimensions of [mass], in one-to-one correspondence with the Yukawa couplings. Each of m2Q , m2ū , m2d̄ , m2L , m2ē is a squark or
slepton mass term described as a 3 × 3 matrix in family space. mHu , mHu and μ are
mass terms which contributes to the Higgs potential. Without additional assumptions,
the MSSM contains 124 independent parameters which would be determined by experiments. The several parameters which are directly relevant to the following discussions
are summarised below:• Ma (a = 1, 2, 3): the soft SUSY breaking parameters of gaugino masses.
• tan β: the ratio of the vacuum expectation values of the two Higgs potentials:
tan β =

vu.
vd

(2.17)• m2Q , m2ū , m2d̄ , m2L , m2ē : the squark (and slepton mass) matrices. m2Q is for theleft handed squarks, (m2L is for the left handed sleptons) and m2ū and m2d̄ are forthe right handed ones (m2ē is for sleptons).
The neutral gauginos and higgsinos mix into four mass eigenstates called neutralinos
χ̃0i (i = 1, 2, 3, 4) because their quantum numbers are the same. The indices in i areordered in mass, i.e., χ̃01 is the LSP that is assumed to be stable in this dissertation. A
4 × 4 symmetric complex mass matrix describes the mixing at tree level as:⎛⎞
M1 0 MW tan θW cos β −MW tan β sin β⎜⎟
MW cos β
MW sin βM2⎟,(2.18)
Mχ̃0 = ⎜⎝⎠0−μ0where θW is the Weignberg angle.

2.2.3

SUSY after the Higgs Discovery

Although the energy scale of SUSY is sometimes expected to be located around TeVscale from the view point of naturalness, the lack of evidence for SUSY at the LHC andthe observed SM-Higgs boson with the mass of about 125 GeV implies that the masses ofsquarks might be much heavier than the electroweak scale (Fig. 2.3). Split SUSY [24,29],
motivated by the phenomenology rather than naturalness, is one of the theories whichmatch this situation. Split SUSY assumes the masses of SUSY partners of gauge bosons(gaugino) around O(1) TeV in order to make the LSP a candidate of the dark matter aslater shown in Section 2.3 and realise uniﬁcation of the gauge coupling constants, while
those of the other particles are expected to be at a much higher scale. At the expenseof naturalness, a high SUSY breaking scale could overcome several disadvantages of thephenomenology of the weak-scale SUSY models, such as diﬃculties to explain the absenceof the ﬂavour changing neutral current (FCNC), the electric dipole moments (EDMs) of
the SM particles and the small decay rate of the proton.
Within a typical parameter space of Split SUSY, a supersymmetric partner of gluon(gluino) becomes long-lived due to the heavy mass of squarks which is an intermediate
state of the decay chain of a gluino. If the mean lifetime of a gluino is longer than the
hadronization time scale (≈ (200 MeV)−1 ), a gluino transforms into a hadronic state,
17

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

Figure 2.3: The scalar mass scale in Split Supersymmetry as a function of tan β for a
Higgs mass ﬁxed at 125.5 GeV for no and maximal stop mixing [24]. The 1σ error bands
coming from the top mass measurement (which dominate over other uncertainties) arealso shown.
R-hadron [31], as analogous to the ordinary hadrons. If the lifetime of a gluino is anorder of ns, it often decays in the volume of the inner tracker of the ATLAS detector andit could be reconstructed as a displaced vertex (DV). Typically, a gluino decays to LSP
via a virtual squark with emitting a pair of quark and anti-quark (g̃ → q̄ q̃ → q̄q χ̃01 ). The
quarks would make hadronic showers resulting in higher charged-particle multiplicity
associated to the DV as the mass diﬀerence between gluino and the LSP becomes large.
The invariant mass of a DV calculated by the momenta of associated charged particles
would be large as well. Searching gluinos with this signature has a huge advantage interms of signal to background ratio since no SM particle creates such a DV with highcharged-particle multiplicity and the large invariant mass. In addition, it is diﬃcult tobe covered by the typical strategy of the SUSY search in the ATLAS experiment, which
requires the large missing transverse energy and multiple hard objects, such as jets or
leptons, pointing to a primary vertex.

2.3

Dark Matter Relic Density

The evidences of dark matter are conﬁrmed by a number of experimental observations,for instance, galactic rotation curves [39], the weak gravitational lensing [40] and theBullet Cluster [41], that consists of two colliding clusters of galaxies, oﬃcially named 1E
0657-558. The Lambda Cold Dark Matter (ΛCDM) model is often referred to as thestandard model of Big Bang cosmology, where Λ denotes a cosmological constant related
to dark energy and dark matter is assumed as cold, i.e., non-relativistic.
In the ΛCDM model, a sizeable amount of dark matter is generally expected to be
produced in the very early universe. When the temperature was much higher than mχ(the mass of dark matter), the cross sections of χχ̄ creation and annihilation (χχ̄  Y Ȳ ,where Y denotes a SM particle) were equally balanced. However, as the temperature of
the universe decreases below mχ , the χχ̄ creation process was exponentially suppressed,
while the annihilation rate was not changed signiﬁcantly in thermal equilibrium. A
mechanism to restrain the annihilation process is necessary, otherwise dark matter disappeared quickly, and then the dark matter relic density becomes inconsistent to the18CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

Figure 2.4: A schematic of the comoving number density of a stable species as it evolves
through the process of thermal freeze-out [42].
observed value. A possible mechanism is dilution of dark matters due to Hubble expansion. The Boltzmann equation Eq. (2.19) describes the competing eﬀects of Hubble
expansion and annihilation:dnχ
+ 3Hnχ = − σχχ̄ v (n2χ − n2χ, eq ),dt(2.19)

where nχ is the number density of dark matters, H is the Hubble parameter which represents the expansion rate of the universe, σχχ̄ v is the thermally averaged χχ̄ annihilation
cross section multiplied by their relative velocity, and n2χ, eq is the equilibrium value ofmχ ). Fig. 2.4 schematically shows how the numbernχ at very high temperatures (Tof density of dark matters goes as the temperature of the universe drops. In the limit ofT  mχ , the number of density of dark matters reaches a ﬁxed value. This condition isoften referred to as thermal freeze-out.
By solving Eq. (2.19) as shown in Reference [30], the resulting relic density of dark
matters is given approximately as:Ω χ h2 ≈mχ
1.04 × 109 GeV−1
1
·
,
√ ·
MPl
TFO g∗ a + 3bTFO /mχ

(2.20)

where Ωχ is the present-day density parameter of dark matter, h ≡ H/100 km s−1 Mpc−1
is the reduced Hubble constant, MPl is the Planck mass, TFO is the temperature at whichfreeze-out occurs, g∗ is the number of external degrees of freedom, a and b are terms in
the non-relativistic expansion, σχχ̄ v = a + b v 2 + O(v 4 ). Eq. (2.20) is simpliﬁed toEq. (2.21), which is accurate within an order of magnitude:Ωχ h2 ≈ 0.1 ×
19

3 × 10−26 cm3 s−1.
σv(2.21)

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

q

g̃
q̃

B̃

q

Figure 2.5: Feynman diagram of transition of bino (B̃) into gluino (g̃) via quark scattering.
The measured value of the relic density of cold dark matter by Planck Collaboration [9]using data taken in 2015 is ΩCDM h2 = 0.1198 ± 0.0015 [10]. Given the observed relicdensity and Eq. (2.21), the product of the annihilation cross section and the relative
velocity is required to be an order of 3 × 10−26 cm3 s−1 . This is similar to the value fora Weakly Interacting Massive Particle (WIMP) with the mass of O(100-1000) GeV [30].
Again, the MSSM predicts a particle with these properties (LSP) by an independentassumption. The coincidence is often referred to as “WIMP miracle”.

2.3.1

Gaugino Co-annihilation

If the bosonic SUSY partners are much heavier than the fermionic SUSY partners as
expected by Split SUSY model, candidates for dark matter in the Universe are the neutralbino, wino and Higgsino. In case that the supersymmetry is broken by the anomaly
mediation mechanism, the neutral wino naturally becomes the LSP. The thermal relicabundance of the wino with the mass of around 3 TeV can explain the observed dark
matter density. Higgsino with the mass of around 1 TeV can also explain the observed
dark matter density although the cross section of direct production of these particles isquite small so that they are actually far beyond the reach of the LHC.
The last candidate is bino dark matter. It is known that the bino dark matter usually suﬀers from over-production since the interaction between the bino and the SMparticles is suppressed in general. The gaugino co-annihilation mechanism can signiﬁcantly improves this situation [43, 44]. The co-annihilation between bino and gluino is
focused throughout this paper although bino-wino, and bino-wino-gluino co-annihilation
are possible as well.
Bino-gluino co-annihilation
In order to be consistent with the observed relic density ΩDM h2  0.12, the masses of binoand gluino (MB̃ and Mg̃ , respectively) should be degenerated, i.e., ΔM ≡ Mg̃ − MB̃ 
100 GeV [43]. If the bino-gluino co-annihilation is realised, it is also required thatthe chemical equilibrium between them, schematically B̃ B̃  g̃g̃, had been maintained
during freeze-out epoch in the very early universe, when the temperature was muchhigher than the dark matter mass. In other words, the transition rate of bino into
gluino via quark scattering, Γ(B̃q → g̃q) (see Fig. 2.5), should be enough faster thanthe Hubble expansion rate. This condition gives an upper bound on the mass scale ofsquarks (m̃) [44]:
3

MB̃ 4
TeV.
(2.22)m̃  250 ×
1 TeV

20

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

500450Ωh2 > 0.12

400

300

50

250

G

eV

0
10

G

eV

ΔM

5
=1

0G

eV

eV

m̃ [TeV]

350

13

0

G

200
150
100
50

500

1000

1500
2000
MB̃ [GeV]

2500

3000

Figure 2.6: Contour for the mass diﬀerence ΔM which makes the thermal relic abundance of bino DM equal to the observed DM density ΩDM h2 = 0.12 [44]. In the red
shaded region the bino DM is overproduced due to failure of bino-gluino co-annihilation,
numerically given in Eq. (2.22).
The rate of bino-gluino co-annihilation increases as the mass diﬀerence between binoand gluino becomes smaller or the mass of squark, which mediates the transition of bino
into gluino, becomes lighter. The mass diﬀerences ΔM with which the thermal relicabundance of bino explains the observed relic dark matter density ΩDM h2 = 0.12 areshown in Fig. 2.6. The parameter space forbidden by Eq. (2.22) is indicated as a red
shaded region.
In this scenario, the mass of gluino is assumed to be O(1) TeV, the LHC might
produce it. If it is the case, as discussed in Section 2.2.1, gluinos are produced in pair,and then a gluino decays into a quark, an anti-quark and a bino via exchange of virtual
squark. The decay length of gluino follows Eq. (2.23) [44]:cτg̃ = O(1) ×

ΔM
100 GeV−5 m̃100 TeV4cm.

(2.23)

Figure 2.7 shows the relation between the gluino decay length and the mass diﬀerence
between bino and gluino with the ﬁxed mass of squark (m̃) at 100 GeV. The black solidline represents the parameters that explain the observed dark matter density. It is shownthat a gluino typically has a decay length of cτg̃ > O(1) mm in this scenario. Such gluino
forms R-hadron and leaves a displaced vertex in a detector as discussed in Section 2.2.3.
A displaced vertex originated from a massive coloured particle is often associated with anumber of tracks and its invariant mass becomes larger than SM particles. This fact canbe used to probe this scenario in the ATLAS experiment. Further details on an analysis
on search for massive displaced vertex will be given in Chapter 5.

21

CHAPTER 2. THEORETICAL BACKGROUND AND MOTIVATIONFOR DISPLACED VERTEX SEARCH

250

150

(
0.12
2 =
Ωh

equ

il

um
ibri

1 mm

)

1 cm

1000

1500

50

1m

=

300

m̃

m̃ =
500

10 cm

0

TeV

10
=
m̃

50

Te
V

100

0T
eV

Mg̃ − MB̃ [GeV]

200

2000
2500
MB̃ [GeV]cτg̃100TeV =10 m
3000

3500

4000

Figure 2.7: Decay length of the gluino cτg̃100 TeV with the squark mass m̃ = 100 TeV
in coloured (almost horizontal) lines [44]. Mass diﬀerence ΔM with which the thermal
relic of the bino DM agrees to ΩDM h2 = 0.12 is also shown in the black solid line forthe case in which the bino-gluino chemical equilibrium is assumed to be kept until whenfreeze-out occurs, while the cases for m̃ = 100, 300 and 500 TeV are given in the dashedblack lines.

22

Chapter 3

The LHC and ATLAS Experiment
A brief overview of the LHC and ATLAS experiment is given in this chapter. Comparatively more spaces are devoted for subdetectors deeply related to this analysis. Full detailof the LHC and the ATLAS detector can be found in Ref. [6] and Ref. [5], respectively.

3.1

The Large Hadron Collider

The LHC is a circular particle accelerator located at the Centre for European Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire) on the border of
Switzerland and France. The LHC was constructed in the already existing undergroundtunnel of the Large Electron Positron (LEP) collider . Taking advantage of its exceptional circumference of about 27 km, the LHC complex has achieved to collide protons
and heavy ions with the world largest energy. The LHC has been operational with acentre of mass energy of 7 TeV from 2009 to 2011, 8 TeV in 2012 or 13 TeV since 2015as a proton-proton collider. Nominal design parameters of the LHC are summarised in
Tab. 3.1. In addition, the LHC carries out proton-lead and lead-lead collisions althoughthese interesting contents are not touched further in this dissertation.
Four main independent experiments have taken place at the four points of beamcollisions of the LHC. The experiments are known as, A Large Ion Collider Experiment(ALICE), ATLAS, Compact Muon Solenoid (CMS) and Large Hadron Collider beauty(LHCb), which are arranged along the circumference of the LHC as shown in Fig. 3.1. A
ﬂow of the beam acceleration begins with the production of protons from a simple bottleof hydrogen gas by applying an electric ﬁeld over the gas to remove their electrons.
The Linear accelerator 2 (Linac 2) with the length of 30 m accelerates the protons

Table 3.1: Nominal design parameters of the LHC as a proton-proton collider [6].
Parameter
Value
Ring circumference
26.7 km√
14 TeV
Centre of mass beam energy s
34
Instantaneous luminosity L
10 cm−2 s−1
Total cross section σtot
80 mb (= 8 × 10−26 cm2 )The number of protons per bunch
1.15 × 1011
The number of bunches in ring
2,808
Bunch spacing
25 ns
Average number of interactions per bunch crossing < μ >∼ 2323CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.1: The accelerator complex at CERN, showing the ﬂow of beam accelerationfrom the injectors to the LHC. A subset of the many experiments supported by theseaccelerators is also shown. [45]to the energy of 50 MeV. The beam is then injected to 157 m circumference Proton
Synchrotron Booster (PSB), which accelerates the protons to 1.4 GeV, and subsequently
is driven to 628 m circumference Proton Synchrotron (PS), which increases the beamenergy to 25 GeV. The Super Proton Synchrotron (SPS) with the circumference of 6.9
km receives the beam and accelerates it to 450 GeV before providing it for the LHC. The
beam is ﬁnally injected to the two beam pipes of the 26.7 km circumference LHC, which
accelerates the beam energy to 3.5 TeV (in 2010 and 2011), 4 TeV (in 2012), 6.5 TeV(in 2015 and 2016) and higher in the future.
A set of protons revolves clockwise in one of the two beam pipe, while a beam in
the other pipe circulates anticlockwise. The proton beams consist of bunches of protons.
The bunches are squeezed using quadruple magnets and collide with each other withthe crossing angle of 150-200 μrad at the interaction points where the above detectors
are located. The time interval between bunches is 25 ns, i.e., the collision frequency is
40 MHz. The occurrence rate of interesting physics events is related to the luminosity Lof the beams as well as the cross section of the event σ. The number of events in a unitof time is given as the product of the luminosity and the cross section:√
dNevents= Lσ( s),
dt
where

√

(3.1)

s is the collision energy in centre of mass system. The luminosity is described

24

18

ATLAS Online Luminosity

16

LHC Stable Beams

14

s = 13 TeV

Peak Lumi: 13.7 × 1033 cm-2 s-1

12
10
8
6
7/16 calibration

Peak Luminosity per Fill [1033 cm-2 s-1]

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

42

0
11/04 12/05 12/06 13/07 13/08 13/09 15/10 15/11
Day in 2016

Figure 3.2: The peak instantaneous luminosity delivered to ATLAS during stable beams
for pp collisions at 13 TeV centre-of-mass energy is shown for each LHC ﬁll as a functionof time in 2016 [47].

with the frequency of collision and variables related to the sizes of the beams:L

fcrossing Nbunch1 Nbunch2
,
4εβ ∗

(3.2)

where fcrossing is the collision frequency, Nbunch1 and Nbunch2 are the numbers of protons
in each bunch, ε is the beam emittance and β ∗ is the beta function at an interaction
2 /ε [46]. The
point which is related to the transverse size of the bunch σts as β = πσts
peak instantaneous luminosity of stable proton beams delivered to the ATLAS detector
in 2016 is shown in Fig. 3.2.
Increasing the luminosity links to a rise in the rate of interesting physics as well as
creation of pileup1 collisions within a bunch crossing. The ATLAS detector was designed
to record data eﬃciently in high pileup environment. Parameters on pileup generally usedin the ATLAS experiment are the number of reconstructed primary vertices NPV and theaverage number of interactions per bunch crossing μ. NPV is measured by the ATLAS
inner tracker, which can detect charged particles every 25 ns. As for μ, it is calculated
from the luminosity and averaged over certain interval of an event block. When μ is
ﬁxed, NPV is proportional to an amount of in-time pileup, which increases the energy
measured by calorimeters in an event. On the other hand, when NPV is ﬁxed, μ is aparameter for out-of-time pileup, which decreases observed energy due to negative energy
tail in pulse shape of the ATLAS liquid argon calorimeter2 [5]. The μ measured during
the 2016 data taking is shown in Fig. 3.3.
1

Due to the high luminosity, tens of collisions occur when a pair of proton bunches crosses on average.
In
thisdissertation, a vertex with the largest scalar sum of transverse momenta of associated tracks
|pT | is deﬁned as a primary vertex and the rest of collisions (vertices) is called pileup events.
2
The ATLAS liquid argon calorimeter is a sampling calorimeter which uses lead as absorber and liquidargon as active material. More detail of the calorimeter is given in Section 3.2.2.

25

200
180

ATLAS Online 2016, s=13 TeV ∫ Ldt=29.3 fb-1

160

<μ> = 24.2

140
120
100
80
60
7/16 calibration

Delivered Luminosity [pb-1/0.1]

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

40
20
0
0

5

10

15

20

25

30

35

40

45

50

Mean Number of Interactions per Crossing

Figure 3.3: The luminosity-weighted distribution of the mean number of interactions per
crossing for the 2016 pp collision data recorded [47]. All data delivered to ATLAS during
stable beams is shown, and the integrated luminosity and the mean mu value are givenin the ﬁgure.

3.2

The ATLAS Detector

The ATLAS detector is a large general purpose detector constructed for the measurementof proton-proton collisions and heavy ion-heavy ion collisions in the LHC. A cylindricalcoordinate system is commonly used in the ATLAS experiments because of its shape
shown in Fig. 3.4. The point of collision of proton bunches is deﬁned as the originof the coordinate system. A direction parallel to the beams is deﬁned as the z axis,
and the plane perpendicular to the beam direction is deﬁned as the x–y plane. The
positive direction of the x axis is pointing to the centre of the LHC ring, and the positive
direction of the y axis is the ground right above the detector. A positive side of thez axis is called ‘side-A’, and the negative side is called ‘side-C’. The azimuth angle φis the angle measured around the z axis and the polar angle θ is the angle against thez axis. A variable called pseudo-rapidityη = − ln[tan(θ/2)] is often used
 instead of
θ 3 . Transverse momentum pT ≡

p2x + p2y , transverse energy ET ≡Ex2 + Ey2 andmiss are momentum, energy, and missing energy projectedmissing transverse energy ET
on x–yplane, respectively. Distance between two objects in η–φ plane ΔR is deﬁned as
ΔR ≡ Δη 2 + Δφ2 .
The inner tracking detector (ID) consists of a silicon pixel detector (Pixel), a silicon
strip detector (SCT), and a transition radiation detector (TRT). The ID is surrounded by a superconducting solenoid magnet which applies a 2 T magnetic ﬁeld. A highdensity sampling electromagnetic (EM) calorimeter is located on the outside. The EM
calorimeter uses lead as an absorber and liquid argon (LAr) as active material. The
EM calorimeter consists of a barrel region on the centre side (|η| < 1.475), the outerwheel of the end cap region (1.375 < |η| < 2.5), the inner wheel of the end cap region(2.5 < |η| < 3.2). The region (|η| < 2.5) of the EM calorimeter where the ID exists insideis divided into three layers in the radial direction. The ﬁrst layer is ﬁnely segmented in
the direction of η, and possible to distinguish single photon shower from two photon
3

Rapidity y = 1/2 ln[(E + pz )/(E − pz )] is sometimes used for a heavy object, such as a jet, instead

of η

26

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.4: Sectional view of the ATLAS detector [48]. The height of the ATLAS detector
is 25 m, the length is 44 m, and the weight is approximately 7000 tons.
showers due to decay of π 0 . The ﬁrst layer is also used to improve the resolution of
the shower position and the shower direction measurement. In the region of |η| < 1.8
between the TRT and the EM calorimeter, there is a detector called pre-sampler, which
compensates for energy loss before the calorimeter. The Hadron calorimeter exploits two
diﬀerent technologies in barrel part with |η| < 1.7 and end cap part with 1.5 < |η| < 3.2.
The barrel portion is composed of a tile calorimeter that uses iron plates as absorber andaccumulates the energy with plastic scintillators, while the end cap portion is an LAr
calorimeter. In the forward direction (3.2 < |η| < 4.9), LAr calorimeters are used as bothelectromagnetic and hadron calorimeters. The muon spectrometer (MS) surrounds thecalorimeter and consists of three large superconducting toroidal magnets, high precision
tracking detectors, and detectors for high speed trigger. Each superconducting toroidal
magnets is made up of eight coils. By combining these detectors, highly accurate measurement of charged particles in the area of |η| < 2.5 can be realised. Also, photon, jet
and missing transverse energy are reconstructed by energy measurement at |η| < 4.9.
Further information on each subdetector are given in the coming sections.

3.2.1

Inner Detector

The ATLAS inner detector, which consists of three sub-detectors, Pixel detector (Pixel),
Semiconductor Tracker (SCT) and Transition Radiation Tracker (TRT), is surrounded
by a superconducting solenoid magnet which generates a 2 T magnetic ﬁeld. The tracker
is designed to provide precise track and vertex reconstruction with high momentum resolution within |η| < 2.5. The nominal lower track pT threshold is 400 MeV, although lower
threshold can be tuned for diﬀerent use cases. Electron identiﬁcation is also performed
with the TRT taking advantage of large amount of its transition radiation over a large
kinematic range of 500 MeV to 150 GeV within |η| < 2.0 corresponding to the coverageof the TRT in η direction. A schematic r–z cross section of the ATLAS inner detector
27

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.5: The r–z cross section of a schematic diagram of the ATLAS inner detector
for Run 2. The upper pad shows the whole Inner Detector, whereas the lower panel
shows a zoomed view of only the IBL (orange) and Pixel (purple) region. [49]is shown in Figure 3.5. The layout of the ATLAS inner detector is also illustrated in
Figure 3.6.
Pixel
The innermost subdetector of the ATLAS inner detector is the Pixel, which contains four
layers of high-granularity and highly radiation tolerant semiconductor modules.
The innermost layer of the Pixel detector is called Insertable B-Layer (IBL) [51, 52],
which was newly installed in May 2014 during the long shutdown 1 of the LHC in orderto preserve tracking performance from Run 2. The IBL modules are arranged in acylindrical layer which consists of 14 staves surrounding the beam pipe and the layer islocated at radius r of 33.25 mm from the interaction point. Each IBL stave contains 12
double-chip planar sensor modules located at the centre of the stave, and 4 single-chip 3D
sensor modules at each end of the stave, in the forward direction. The signal from eachsensor is processed by a new front-end (FE) readout chip FE-I4 [53] which is connectedwith the sensors by ﬂip-chip bump bonding at IZM4 . All planar sensors were produced
4

Fraunhofer IZM-Berlin, Gustav-Meyer-Allee 25, 13355 Berlin28CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.6: Computer generated cut-away view of the ATLAS inner detector. [50]at CiS5 and the 3D sensors were produced at CNM6 or FBK7 .
A conservative and well-established n+ -in-n technology is adopted for the IBL planar
pixel sensors, which is similar to the technology used for the original ATLAS pixel detector. The thickness of the IBL planar sensors is reduced to 200 μm and the inactiveedge is minimised to 200 μm, resulting in higher radiation tolerance and smaller insensitive region at the sensor edges.
The 3D sensor is a new technology with a complex fabrication process and it is oneof the most radiation-hard designs currently available. The 3D columns in the IBL 3D
sensor are obtained by processing each side of the silicon wafer. The n+ columns are
obtained by ﬁrst etching and then doping on the front side, and a similar process is thenapplied on the back side of the sensor to obtain the p+ columns [54]. This is the ﬁrst
time that the 3D sensor technology is used in a high energy physics experiment.
FE-I4 is the largest FE chip for pixel detectors for high energy physics. The FE-I4
is produced using the 130 nm CMOS technology and contains approximately 70 million
transistors. The pixel readout is arranged in 80 columns and 336 rows, and each pixel
has a size of 250 × 50 μm2 . Each chip has an area of 20.2 × 18.8 mm2 , of which 90%
corresponds to the active area on the sensor. Each pair of columns are further divided
into regions of 2 by 2 pixels that share a local memory, where hits can be stored locally
until a Level 1 trigger is received, avoiding the bottleneck problem of the existing FE
chip in which the buﬀers are located at the end of a double column [55].
The other three barrel layers and three endcaps contain 1744 planar sensor modules
and each is composed of 16 FE-I3 chips [55]. A 3D computer graphic of the Pixel detector
without the IBL is shown in Fig. 3.7. An FE-I3 chip contains 2880 pixels in a matrixof 18 columns and 160 rows, which are individually 250 μm thick and the pixel size is
400 × 50 μm2 . This segmentation achieves good position resolution, for instance, an
5

Forschungsinstitut fur Mikrosensorik und Photovoltaik GmbH, Konrad-Zuse-Strasse 14, 99099 Erfurt,
Germany
6
Centro Nacional de Microelectronica (CNM-IMB-CSIC), Campus Universidad Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
7
Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo di Trento, Italy

29

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.7: Cut-away view of the Pixel, part of the ATLAS inner detector [56]. The IBL
is not included here. The diameter and length of the pixel support frame is also shown.
individual layer resolution of 10 μm in the transverse (r − φ) plane and 115 μm in theaxial plane (z, barrel) or radial plane (r, endcaps). The three barrel layers of the Pixel
detector are located at r = 50.5, 88.5, and 122.5 mm from the interaction point and thethree endcap layers are located at z = 495, 580, and 650 mm from the interaction point.

SCT
The second subdetector of the ATLAS inner detector is called the SCT, which contains
several layers of microstrip silicon modules. 15,912 sensors in total forms four layers inthe barrel, and nine layers are located in the endcap. The length of a strip is 6 cm andit is arranged with a pitch of 80 μm. A SCT module is composed of a pair of two SCT
sensors tilted by 20 mrad against its counterpart to perform measurement of 3D positionof a charged particle. This segmentation achieves intrinsic accuracies of 17 μm in thetransverse (R-φ) plane and 580 μm in longitudinal (z for barrel or r for endcap) direction.
The total number of readout channels in the SCT is approximately 6.3 million.
The four barrel layers of the SCT are located at r = 299, 371, 443, and 514 mm fromthe interaction point and the nine endcap layers are located at z = 853.8, 934, 1091.5,
1299.9, 1399.7, 1771.4, 2115.2, 2505, and 2720.2 mm from the interaction point.
TRT
The third and outermost subsystem of the ATLAS inner detector is the TRT, which iscomposed of 370 thousand straw-shaped drift tubes with the diameter of 4 mm. Any
charged particles ionise the gas mixture of 70% Xe, 27% CO2 , and 3% O2 inside thestraws. The generated electrons are ampliﬁed when they drift in the electric ﬁeld towards
the central anode wire. The FE electronics samples the signal in 24 time bins with thewidth of 3.12 ns and compares it against a threshold corresponding to 300 eV. The
electrons take up to 48 ns to reach the wire on average. The arrival time of the ﬁrst
electron can be used to determine the position, where the particle passed through, fromthe centre of the straw.
30

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Table 3.2: Position and number information of the Pixel and IBL [51]. Positions ofsupport structures denoted as Envelop is also shown as well as those of the sensitive
materials.
Item
Beam pipe (with IBL)
IBL

Pixel
B-layer
Layer 1
Layer 2
Disk 1
Disk 2
Disk 3

Radial Extension[mm]
25 < R < 29

Length[mm]

Staves /Sectors

Modules

Pixels(×106 )

Envelope
Sensitive

31.0 < R < 40.0
< R >= 33.25|Z| < 332

14

224

12.0

Envelope
Sensitive
Sensitive
Sensitive
Sensitive
Sensitive
Sensitive

45.5 < R < 241.0< R >= 50.5
< R >= 88.5
< R >= 122.5
88.8 < R < 149.6
88.8 < R < 149.6
88.8 < R < 149.6|Z| < 3092
|Z| < 400.5|Z| < 400.5|Z| < 400.5< Z >= 495< Z >= 580< Z >= 650

22
38
52
8×2
8×2
8×2

286
494
676
48 × 248 × 248 × 2
Pixel Total

13.2
22.8
31.2
4.4
4.4
4.4
92.4

The regions between up to 73 (160) layers of polyimide straw tubes are ﬁlled withpolymer ﬁbres (barrel) or foils (endcaps). Transition radiation is emitted by highly
relativistic charged particles (with the Lorentz boost factor  1000) when they pass overthe boundary. In general, an amount of the transition radiation of an electron is larger
than that of a pion, which might mimic an electron, so that the TRT is used to identify
electrons as well. The position resolution of the TRT is signiﬁcantly poorer than the
Pixel or the SCT, with the entire detector providing a resolution of 130 μm. However
the TRT enhances momentum resolution with its long lever arm for continuous tracking.
The barrel of the TRT is positioned from 563 to 1066 mm in r with respect to theinteraction point, while the endcap covers 848 to 2710 mm in z. The coverage of thebarrel is within |η| < 1.0, and the endcap reaches up to |η| ≈ 2.0, rather than 2.5 likethe Pixel and SCT.

3.2.2

Calorimeters

The electromagnetic (EM) and hadronic calorimeters are combination of multiple subdetectors covering up to |η| < 4.9. The EM barrel calorimeter uses a liquid argon (LAr)as active medium and lead as absorbers. In the region with |η| < 1.7, the hadronic (Tile)
calorimeter is constructed from steel absorber and scintillator tiles with a ratio by volume
of approximately 4.7:1 and is separated into barrel (|η| < 1.0) and extended barrel (0.8 <|η| < 1.7) sections. The calorimeter end-cap (1.375 < |η| < 3.2) and forward (3.1 <|η| < 4.9) regions are instrumented with LAr calorimeters for both EM and hadronicenergy measurements. The LAr barrel has three longitudinal EM layers as shown in
Figure 3.8(a), the LAr end-cap has three EM layers (EMEC) and four hadronic layers(HEC), the forward LAr calorimeter (FCal) has three layers, and the Tile calorimeterhas three longitudinal layers. In addition, there is a pre-sampler (PS) layer in frontof the LAr electromagnetic calorimeter within |η| < 1.8 that provides a measurementof the energy lost in non-instrumented material in front of the EM calorimeter. The
31

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Photomultiplier

Wavelength-shifting fibre
Cells in Layer 3
Δϕ×Δη = 0.0245×0.05

Scintillator

Steel

TriggerTower
Δη = 0.
1

2X0

47

0m

m

η=0

16X0
TriggerTower
Δϕ = 0.
09

82

m

m

4.3X0

15

00

1.7X0
Δϕ=0.
0245x436.8m
mx4=147.3mm

Square cells in
Layer 2Δϕ = 0.

Source
tubes

0245

ϕ
Δη = 0.
025
m/8 =
4.
Δη = 0. 69 mm
0031
Strip cells in Layer 1

37.5m

η

(a)

(b)

Figure 3.8: (a) Sketch of a barrel module where the diﬀerent layers are clearly visible
with the ganging of electrodes in φ. The granularity in η and φ of the cells of each of
the three layers and of the trigger towers is also shown. (b) Schematic showing how
the mechanical assembly and the optical readout of the tile calorimeter are integrated
together. The various components of the optical readout, namely the tiles, the ﬁbres andthe photomultipliers, are shown. [5]analog signals of the LAr detector are sampled digitally once per bunch crossing over 4
bunch crossings and those measurements are converted to an energy measurement using
constants calculated using dedicated calibration runs [5,57]. During the 2012 data-taking
period, 5 samples instead of 4 were used in the LAr calorimeters energy measurement.
The LAr readout is sensitive to signals from the preceding 12 bunch crossings during
50 ns bunch spacing operation [5,57]. For the 25 ns bunch spacing scenario this increases
to 24 bunch crossings. The LAr detector has thus been exposed to more out-of-time
pile-up since 2015 run. In contrast, the fast readout of the Tile calorimeter makes it
relatively insensitive to out-of-time pile-up [58, 59].

3.2.3

Muon Spectrometers

The muon spectrometers (MS) are the outermost subdetectors of the ATLAS detector.
It is designed to reconstruct tracks of muons within the region up to |η| = 2.7. The
relative resolution of the momentum is better than 3% over a wide pT range and it is at
most 10% at pT ≈ 1 TeV. The MS employs a toroidal magnet ﬁeld provided by a systemof three superconducting air-core toroidal magnets with the bending integral of about
2.5 Tm in the barrel region and up to 6 Tm in the endcaps.
The MS is composed of one barrel (|η| < 1.05) and two endcap sections (1.05 <|η| < 2.7) as illustrated in Fig. 3.9. Four kinds of detectors, Resistive Plate Chamber(RPC), Thin Gap Chamber (TGC), Monitored Drift Tube (MDT) and Cathode Strip

32

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.9: The yz cross section of a schematic diagram of the ATLAS muon spectrometers [5]. The white rectangles represent the RPCs, the green boxes represent barrel
MDTs, the cyan boxes represent endcap the MDTs, the purple lines represent the TGCs
and the yellow box represents the CSC.
Chamber (CSC), are used for each purpose. RPC, which is formed by three doublet
layers for |η| < 1.05, and TGC consisting of one triplet layer followed by two doublets
for 1.0 < |η| < 2.4, provide precise position measurements of muons with typical spatial
resolution of 5 − 10 mm. These detectors are also used to trigger events in which a highmomentum muon exists, taking advantage of the great timing resolution. Three layers of
MDT provides a precise position and momentum measurement for muons passing througha region within |η| < 2.7. Typically a muon is detected at six to eight measurement points
on each MDT layer (chamber). Instead of MDTs, The inner layer for 2 < |η| < 2.7 isinstrumented with CSC which is composed of 32 four-layer chambers with high timing
resolution of few ns. The position resolution of the MDT and CSC for a single hit in
the bending plane (r–z plane) is about 80 μm and 60 μm, respectively. Despite the tens
metre size of the muon spectrometers, they are aligned with accuracy of 30-60 μm.

3.2.4

Trigger System

The vast majority of collision events is dominated by diﬀractive and inelastic QCD events
which is not targeted in the ATLAS experiment. The cross sections and corresponding
event rates of SM processes are shown in Fig. 3.10. The data acquisition (DAQ) systemof the ATLAS, however, cannot aﬀord to record all collision events. When the detectors
miss , a trigger is generated as adetect a particular event with high pT objects or large ET
go sign to record data.
The trigger in the ATLAS experiment is a two stage system including a hardwarebased Level-1 (L1), and the software-based High Level Trigger (HLT). The trigger system
reduces the event rate from the bunch-crossing rate of 40 MHz to 100 kHz at L1 andto an average recording rate of 1 kHz after passing the HLT. The L1 is based on fastcustom-made electronics; it collects coarse information from the calorimeter and the33

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

proton - (anti)proton cross sections
9

9

10

10

8

10

8

10

σtot

7

10

Tevatron

LHC

6

5

10

5

σb

4

10

4

10

3

3

10

jet

2

10

σjet(ET10> √s/20)
σW
σZ

1

10

0

10

2

10

jet

σjet(ET

1

10

0

10

> 100 GeV)

-1

-1

10

10

-2

-2

10

10

σWW

-3

10

{

-4

10

-5

10

MH=125 GeV

-6

-7

-4

10

σWH

-5

10

σVBF

10

10

-3

10

σt
σZZ
σggH

-2 -1

10

33

6

events / sec for L = 10 cm s

1010

σ (nb)

7

10

-6

10

WJS2012

-7

0.1

1

10

10

√s (TeV)Figure 3.10: Standard Model cross sections and corresponding event rates as a functionof collider energy, with 125 GeV Higgs [60].
muon spectrometer and processes it with a latency of less than 2.5 μs. The L1 trigger
is composed of four diﬀerent systems, i.e. the L1 calorimeter trigger system (L1Calo),
the L1 muon trigger system (L1Muon), the Central Trigger Processors (CTP) and the
L1 topological trigger modules (L1Topo). The HLT exploits fast oﬄine-like algorithms
to achieve higher resolution information than the L1. A processing time of the HLT isapproximately 0.2 s per event on average. Regions of interest (RoI) are deﬁned by the
L1, and precise objects reconstruction is performed typically only there in order to saveprocessing time. A schematic overview of the ATLAS Trigger and DAQ system is shownin Fig. 3.11.

3.2.5

Luminosity Detectors

The ATLAS uses several independent detectors for the luminosity measurement in order
to control its systematic uncertainties. An overview of representative ones are brieﬂy
introduced in this section.
The LUCID (Luminosity measurement Using a Cherenkov Integrating Detector) is
the only detector dedicated for luminosity measurement in the ATLAS. The LUCID
consists of twenty aluminium tubes with the length of 1.5 m and the diameter of 15 mm

34

CHAPTER 3. THE LHC AND ATLAS EXPERIMENT

Figure 3.11: The setup of the ATLAS trigger and data acquisition system for Run 2 [61].
The event and data rates are also given.
each. These tubes surround the beam pipe symmetrically at about ±17 m. When acharged particle comes into a tube with the momentum above the Cherenkov threshold,Cherenkov light is emitted and then detected by a photomultiplier tube (PMT). The
Beam Conditions Monitor (BCM) is a set of diamond sensors with the size of 1 × 1 cm2and 500 μm thickness each. Four sensor modules are located at the each side of the
ATLAS at z = ±184 cm and r = 55 mm. The Zero Degree Calorimeter (ZDC) is aneutral particle detector located at z = 140 m covering small acceptance of η > 8.3. The
ZDC consists of six modules which use tungsten plates as absorbers. Charged particles
generated in the plates go into quartz strips, and then Cherenkov light is emitted andread out by PMTs. The Diamond Beam Monitor (DBM) is composed of diamond andsilicon sensors covering the pseudo-rapidity range of 3.2 < |η| < 3.5. The DBM is locatedat z = ±90 cm and tilted by ∼ 70 mrad against the beam pipe. Four tracking telescopes(3 diamond + 1 silicon telescopes) are on each side. Each telescope consists of threelayers of diamond or silicon sensors integrated with FE-I4 as same as the IBL.
In addition, the Minimum Bias Trigger Scintillators (MBTS), located between the
inner detector and the EM calorimeter, is also used as one of the luminosity detectors
covering the interval of 2.1 < |η| < 3.8. Although the MBTS has large acceptance, it
saturates at high luminosity. The forward calorimeter (FCAL) can measure luminosity
by integrating energy deposition over long periods of time.

35

Chapter 4

Object Reconstruction
The conversion from detector readout signals to original physics objects is called object
reconstruction. The physics analysis in this dissertation predominantly uses tracks andvertices, and the sensitivity of the search largely depends on the performance of theirreconstruction. The standard reconstruction techniques of track and vertex as well as
the ones which are speciﬁc to this analysis are discussed in this chapter. Other physics
objects, such as electrons, muons, jets, and missing transverse momentum, are brieﬂyoutlined as they are partially used in the analysis as well.

4.1

Track and Vertex

One of the most fundamental and important parts of the physics analysis is track reconstruction. Charged particles are produced by the beam collisions, and they pass throughthe highly segmented detectors. They deposit the energies along their traverse throughthe detectors. By connecting the points where the detector hits are created, the paths ofcharged particles are reconstructed. Owing to the magnetic ﬁelds in the tracking volume,the path of a charged particle draws curve with a certain curvature. When a charged
particle with the transverse momentum pT passes through uniform magnetic ﬁeld B, therelation between pT , B and radius R of the circular motion is given as follows:pT [GeV/c] = 0.3 · B [T] · R [m].

(4.1)

A crossing point of at least two tracks is called vertex. The reconstruction of production or decay positions of particles (vertices) is performed by ﬁnding the crossing pointsof tracks. For any analysis, it is important to ﬁnd primary vertex to suppress eﬀects
from pileup collisions, and also b-jet tagging exploits a secondary vertex coming from thedecay of b hadrons.
The standard tracking and vertex reconstruction will be reviewed in Section 4.1.1
and 4.1.3. The special reconstruction of tracks with large impact parameters and vertices
largely displaced from the beam collision point will be given in Section 4.1.2 and 4.1.4,
respectively.

4.1.1Standard Tracking

The ATLAS inner trackers are composed of roughly two parts, ﬁnely segmented silicondetectors (Pixel and SCT) and thin long straw tube detector (TRT). Similarly, there

36

CHAPTER 4. OBJECT RECONSTRUCTION

Inside-Out
Data Preparation

Pre-processing
Silicon, TRT hits

Candidate Creation
Candidate Selection
Ambiguity Processing

Track Fitting
Si-Seeded + TRT hits

TRT Extension

Post-processing
Extended Tracks

Figure 4.1: Schematic diagram of the standard inside-out tracking ﬂow in the ATLAS
experiment.

are two approaches in the track reconstruction with the inner trackers: the main insideout track reconstruction and consecutive outside-in track reconstruction. The inside-out
track reconstruction creates track seeds from silicon hits and extend them to TRT track
segments, while the outside-in track reconstruction tries to extend TRT track segments
to silicon hits. More details of the standard track reconstruction will be discussed in thissection. Further technical and conceptual details of the standard track reconstruction of
the ATLAS are summarised in Ref. [62].
Inside-out Track Reconstruction
The primary track ﬁnding in the ATLAS inner detector is based on an inside-out strategy
for pattern recognition from measurement points. A schematic ﬂow of the standard
inside-out track ﬁnding is shown in Fig. 4.1. The inside-out track reconstruction can bedivided into roughly four parts as follows.
(1) Space Point Formation: The ﬁrst step of the inside-out track reconstruction isconverting detector measurements into points on three dimensional coordinate, called
space point objects. It is straightforward to form a space point from a measurementof Pixel which provides two dimensional position on its surface. A space point can becreated by using the position information of a measurement on the detector surface
and a position of the detector. As for a sensor of the SCT, a precise measurement isachieved only in transverse direction with respect to silicon strips. Since a SCT module
is composed of a pair of two sensors tilted by 40 mrad, a measurement on the counterpart
sensor is used to form a space point. When a pair of two SCT strips is found, the incident
angle of a charged particle can be roughly estimated. The rate to create fake space points
is reduced by restricting the incident angle to be compatible with the direction from thebeam spot to the space points.
(2) Space Point seeded Track Finding: The track candidate search is carried out
using the space point objects created in the previous step. To begin with, the track seed
search is performed by connecting three silicon hits. Conventionally, the constraint on
the z position of a primary vertex was used to suppress the number of seed combinations,however the standard seed search in this thesis is performed without the z constraint.
37

CHAPTER 4. OBJECT RECONSTRUCTIONy [mm]

r [mm]
500

400

400

200

300
0
200

-200

100

-400

0
-400

-200

0

200

400

-800

x [mm]

-600

-400

-200

0

200

400

600

800

z [mm]

Figure 4.2: Space point seeds in the ATLAS inner detector barrel for a tt̄ event [62]. The
space point seeds built of three measurements are spread over a large z-range that leads
to an increase of the track candidates for further processing.

The current one is more eﬃcient to reconstruct tracks in events such as H → γγ decays
without tight constraint on primary vertices. Fig. 4.2 shows the track seeds created
without z vertex constraint in a tt̄ event of Monte Carlo simulation (MC).
Once the track seeds are found, then the track road building is performed, that is
the further search of associated hits to a track candidate. The track parameters of thecandidates could have been biased because the procedure of the track candidate ﬁnding
was coarse. Therefore, the track is reﬁtted using a combination of a standard Kalmanﬁlter and smoother [63] based on a least squares approach to obtain more precise trackparameters. The Kalman ﬁlter, also known as linear quadratic estimation (LQE), is analgorithm that progressively estimates unknown variables using a set of measurements
by taking into account statistical noise and other uncertainties. This can be used toestimate the track information and the covariances in the environment where, e.g., ahuge number of hits exist and a trajectory does not always draw a simple curve due toscattering with detector materials.
(3) Ambiguity Solving: A large number of track candidates are created in the previous step of the track ﬁnding. Many of them are actually just fake tracks which are
accidentally reconstructed from unrelated hits. In order to reject such tracks, the track
candidates are ranked by order of the scores which are corresponding to the likelihoods.
Before assigning scores to the track candidates, they are reﬁtted using the reﬁned geometry information with a detailed material description, and the χ2 divided by the degrees
of freedom (reduced χ2 ) is obtained for each candidate. Not only reduced χ2 but also a
track scoring strategy [64] is used for the classiﬁcation of tracks. A qualitative overview
of the scoring strategy is given in Tab. 4.1. In general, the scoring rule is deﬁned to givea better score to a track with relatively larger number of associated hits. If a detector
layer does not have a hit on the intersection with a track, i.e. a track has a hole, a certain
amount of penalty is given to the track. In case that a track, passing through a region
where adjacent detector modules are overlapped as the track b in Fig. 4.3, has hits on
the both modules, a strong beneﬁt is added to the track score. When a hit is shared
between diﬀerent tracks, it is generally assigned to the track with better score and the38

CHAPTER 4. OBJECT RECONSTRUCTIONcbsensor hitamodule hit
holeambiguous hit

Figure 4.3: Simpliﬁed model of the ambiguity solving process, illustrated in the SCT
Barrel [62]. Tracks a, b and c have been found through the seeded track ﬁnding, butshare several hits. The χ2 /ndof may not be appropriate to distinguish a true from a faketrack, therefore dedicated track scoring that is optimised for each subdetector is used.
In the shown example, e.g. a module hit representing measurements on both sides of the
SCT silicon detector are scored relatively higher than two single hits without associatedbackside module. Hits in a overlap region as for track b are in particular high scored,
while holes on track, i.e. an expected hit that has not been found, lead to a penalty inthe track score.

other track is reﬁtted again without the shared hit. After iterations of this procedure,
the tracks whose scores are higher than a certain quality cut are stored.
(4) TRT Track Extension: The tracks which passed the ambiguity solving process
are further tried to extend to the TRT measurements. A line ﬁt is performed to estimate
whether the hits on a TRT track segment are compatible with the silicon track or not in
the r–φ coordinate for the barrel region and the r–z coordinate in the endcap regions,
respectively. Fig. 4.4 shows a result of the extensions of the silicon tracks into the TRT
for a MC generated tt̄ event. If the track score of the original silicon track is higher thanthat of the track after extension, the original one is stored and the TRT hits are treatedas outlier 1 measurements onto the track.
1

outlier is a term of statistics which represents a data point on a graph that is very much bigger orsmaller than the next nearest data point.

Table 4.1: Track characteristics that lead to beneﬁts or penalties in the ATLAS silicondetector track score [62].
Track characteristics Detector
Eﬀect on the track score
IBL/B-Layer holePixelstrong penalty
Layer holePixelpenaltyOverlap hit
Pixel, SCT strong beneﬁt
Sensor hole
SCT
weak penalty
Layer hole (module) SCT
strong penalty

39

CHAPTER 4. OBJECT RECONSTRUCTIONy [mm]
1000

Extension

500

0

-500

1000

Segment

-1000

-500

0
x [mm]

500

1000

Figure 4.4: The tt̄ event for the two possible TRT hit associations (only the barrel measurements): the brighter coloured hits show the extensions that originate from following
the space point seeded tracks into the TRT, the silicon space point objects are also shownin the same colour. The black circles mark the hits that have been associated to TRT
segments, which build the start point of the back tracking application. The particularpower of the back tracking approach is to ﬁnd the additional track segments, that havenot been found through the inside-out sequence, simply for the fact that no appropriate
silicon seed existed for the further extension process. This is mainly due to strong energy loss of the particle, or due to the fact that the track segments originate from photon
conversions or other decay vertices inside the Inner Detector volume.

Outside-in Track Reconstruction
The inside-out track reconstruction is optimised to ﬁnd relatively high pT tracks coming from the beam collision point. Tracks from secondary decay vertices of long-lived
particles, e.g. Ks , or from photon conversions into an electron-positron pair, are likely
missed. Electrons losing the energies as bremsstrahlung might fail to be reconstructed
as well. Such tracks are targets of the outside-in strategy of track reconstruction. The
outside-in track reconstruction is carried out in a similar ﬂow with the inside-out approach as schematically shown in Fig. 4.5. The TRT track segment ﬁnding exploits theHough transformation [65]. This transforms the TRT hit positions on a track into lines
which cross at the point in a parameter space. The crossing point speciﬁes the actual
parameters of the track line and the point can be determined by searching the positionof peaks in a histogram which contains the lines in a parameter space. This method
works when a track draws approximately straight line in the r–φ plane in the TRT barrel region and the r–z plane in the endcap part. The minimum pT threshold for tracks
is set at 2 GeV for the nominal outside-in tracking in 2016 data taking. Finally, thebackward tracking of the segments into the hits on the silicon detectors is performed andthe ambiguities are solved by the track scoring method.

40

CHAPTER 4. OBJECT RECONSTRUCTION

Inside-Out

Outside-In

Data Preparation

Candidate Creation
TRT Drift Circles

Candidate Selection
Ambiguity Processing

Track Fitting
TRT-Seeded + Si hits

Si-Inward Extension

Post-processing
TRT-Extended Tracks
TRT-Standalone Tracks

Figure 4.5: Schematic diagram of the standard outside-in tracking ﬂow in the ATLAS
experiment.

4.1.2

Reconstruction of Tracks with Large Impact Parameters

The ATLAS standard track reconstruction in the inner detector is composed of the two
approaches of inside-out (ﬁrst pass) and outside-in (second pass). A hypothetical heavy
long-lived particle is, however, not eﬃcient to be reconstructed with the standard tracking
because of its constraint on the impact parameters, denoted as z0 for the beam direction
and d0 for the transverse plane. Tracks from decay of the heavy long-lived particle arelikely to have the large impact parameters. In order to improve the tracking eﬃciency for
tracks with large impact parameters, a specialised third-pass tracking, re-tracking [66],is successively performed after the standard trackings. The re-tracking is based on thestandard inside-out sequence where the hits used to seed and construct the tracks are theleftovers of the previous steps. Some modiﬁcations in the algorithm cuts allow to increase
the eﬃciency for tracks with large impact parameters without including too many faketracks. The main diﬀerences with respect to the standard sequence are follows:
1. the allowed region to search hits for seeding is slightly extended to the larger radius.
2. the cuts in the transverse and longitudinal impact parameter are loosened.
3. some quality cuts (hit-related mainly) are re-tuned.
The cuts applied in the standard ATLAS tracking algorithms (inside-out and outside-in)
and re-tracking are listed in Tab. 4.2.

4.1.3

Primary Vertex Reconstruction

The procedure of primary vertex reconstruction can be divided into vertex ﬁnding andvertex ﬁtting [67]. An iterative approach is used to the primary vertex reconstructionin the ATLAS experiment. The detailed procedure and performance of the iterativealgorithm are described in Refs. [66, 68]. A brief overview of the primary vertex reconstruction is given in the following.
Tracks which passed the following requirements are considered to be used for constructions of the vertices [69]:• pT > 400 MeV

41

CHAPTER 4. OBJECT RECONSTRUCTION

Table 4.2: Cuts applied in the diﬀerent tracking algorithms.
cutinside-out outside-in large-d0 tracking
max d010 mm
100 mm
300 mm
250 mm
1500 mmmax z0400 MeV
2 GeV
500 MeVmin ptmin Pix hits
00
min Si hits
7
4
7
15
9∗
min TRT hits9∗min NOT Shared
64
5
max Shared1
1
2
max Si Holes2
2
2
max Pixel Holes1
2
1
max SCT Holes22
2
max Double Holes1
11∗ on track extension• |η| < 2.5• Number of silicon hits ≥ 9 if |η| ≤ 1.65 or 11 if |η| > 1.65
• Number of IBL hits + B-Layer hits ≥ 1• A maximum of 1 shared module (1 shared pixel hit or 2 shared SCT hits)• Number of Pixel holes = 0• Number of SCT holes ≤ 1
An outline of the procedure of the iterative algorithm using the selected tracks is asfollows:
1. The seed position of the vertex ﬁtting is determined as the mode (most probablevalue) of the impact parameters z0 with respect to the beam spot of all tracks. The
mode in z is calculated using the Half-Sample Mode algorithm [70].
2. Tracks which are compatible with the seed are grouped together for the successiveﬁtting.
3. With the seed position as the starting point and parameters of selected tracks as
input, the adaptive vertex ﬁtting algorithm with an annealing procedure [71] isused to estimate the position and covariance of the vertex. A weight reﬂecting thecompatibility with the estimated vertex and the annealing temperature parameteris assigned to each input track.
4. After the vertex candidate is created, tracks that are not already ﬁt to vertices arethen used to repeat the process for a new vertex ﬁnding from the seeding step.
The iterative algorithm is tuned in advance to avoid assigning a single track to multiple
reconstructed vertices.

42

CHAPTER 4. OBJECT RECONSTRUCTION

Pixel Layer-2

Track

Secondary Vertex

Track

Pixel Layer-2

Required Hits
Allowed Hits

Pixel Layer-1

Forbidden Hits

Pixel B-Layer

Secondary Vertex
Required Hits
Allowed Hits

Pixel Layer-1

Forbidden Hits

Pixel B-Layer

Track

Track

IBL

IBL

(a)

(b)

Figure 4.6: Schematic illustration of fake tracks rejection. (a) The vertex is between the
two layers of B-Layer and Layer-1 sensors. The tracks of the reconstructed secondary
vertex must not have hits on the layers inner than the vertex radius (i.e. IBL and BLayer), and must have hits on the closest layer outside the vertex (i.e. Layer-1). (b) The
vertex is close to the Pixel B-Layer sensors. In this example where the vertex is justinside the B-Layer, the tracks are not allowed to have hits on the IBL but may have hitson the B-Layer, and must have hits on the Layer-1. Analogous requirements are madeon vertices close to the other layers [49].

4.1.4

Displaced Vertex Reconstruction

Vertices which are displaced with respect to the beam collision point are reconstructed using the VKalVrt vertex reconstruction algorithm [72]. The input tracks to thisalgorithm are required to pass the following additional requirements:• Number of SCT hits ≥ 2• Transverse momentum pT > 1 GeV• Transverse impact parameter |d0 | > 2 mm
• Tracks are rejected if they have fewer than two Pixel hits and no TRT hits. Thisrequirement is eﬀective at removing fake tracks made up of hits in the SCT endcaps.
The algorithm, ﬁrst, creates a set of two-track “seed” vertices using the incompatibility
graph method [73]. The seed vertices are required to satisfy the ﬁtting quality cut ofχ2 /Ndof < 5. A functionality to reject a fake vertex is applied to these seed vertices. It
requires certain hit patterns in the Pixel and SCT for tracks associated with the seedvertices. The hit patterns depend on the position of the reconstructed vertex. Fig. 4.6(a)schematically shows how the fake-tracks rejection works when a vertex is reconstructedin the middle of two adjacent layers. If a vertex is formed by tracks which have hits in
the inner layers than the vertex position, the vertex is regarded as a fake and removed.
The tracks are also required to have hits in the neighbour layer at larger radii. If a vertex
is reconstructed around a detector layer, hits are required on the next outer layer andforbidden on the next inner layer as shown in Fig. 4.6(b).
The incompatibility graph is then applied again in order to use the surviving seedvertices to create all possible N -track vertices. At this point it is possible that the same43

CHAPTER 4. OBJECT RECONSTRUCTION

track is used in more than one vertex. An iterative “clean-up” algorithm is therefore
applied as follows:
1. For all tracks that are used in more than one vertex, the vertex+track combination
with the largest χ2 is found.
2. If this χ2 is greater than 6, or the two vertices are separated by more than 3σ(according to the uncertainties on their ﬁtted positions), the track is removed fromthat vertex.
3. Otherwise, the two vertices are merged and ﬁtted to obtain vertex parameters.
4. Return to step 1.
5. Once the process has converged such that there are no tracks shared between
vertices, a ﬁnal merging step is performed where pairs of vertices separated by lessthan 1 mm are merged, and the combined vertex is reﬁtted.

4.2Electron and Photon

The reconstruction of electrons and photons is performed on the measurements of electromagnetic showers in the electromagnetic calorimeter (ECAL). A brief overview of thereconstruction of electrons and photons is summarised in this section. Further details
can be found in, e.g. Refs. [74, 75].
The signal pulse from each calorimeter cell (of electromagnetic or hadronic calorimeter) is sampled by the readout electronics. The amplitude of the signal is estimatedby ﬁtting the sampled points with a template of signal shape. The amplitude is thenconverted into the energy deposited in the cell of the calorimeter using a hardware calibration.
The reconstruction of electrons and photons is performed using information of energy
deposits in the Electromagnetic Calorimeter (ECAL). The energy deposits in adjacentcells are summed up and a set of the cells are called a cluster. The standard clustering
algorithm for electrons and photons reconstruction in the ATLAS is the “sliding-window”
algorithm. This algorithm sums energy deposits in cells within a ﬁxed-size rectangular
window and the position of the window is scanned such that the energy in the window
is a local maximum. The cluster window size in the barrel region is deﬁned as 3 × 7 cells
in the middle layer of the ECAL. The size is equivalent to an area of size Δη × Δφ =0.075 × 0.175). On the other hand, a cluster size of 5 × 5 cells in the middle layer is usedin the endcap regions, corresponding to an area of Δη × Δφ = 0.125 × 0.125. The φ sizeof the cluster is increased because the electron trajectory is bended in the φ direction
due to the magnetic ﬁeld of the solenoid. In the endcaps, the eﬀect of the magnetic ﬁeld
is relatively small.
Electron and photon cannot be distinguished only from the energy deposits in the
ECAL. The classiﬁcation of them is based on the presence of tracks reconstructed in
the inner detector, which are associated with the ECAL clusters. If no track matches acluster, it is classiﬁed as an “unconverted photon”. If a pair of oppositely charged tracks
identiﬁed as electrons in the TRT is associated with a cluster and the tracks are nearlycollimated at the production vertex, the cluster is classiﬁed as a “converted photon”. In
order to take track reconstruction ineﬃciency at large radius, a cluster which matches
one track is also classiﬁed as a converted photon if the track have no hit on the innermost
44

CHAPTER 4. OBJECT RECONSTRUCTION

layer of the Pixel. The other clusters which are associated with track passing a certain
quality cut are classiﬁed as electrons.

4.3

Muon

The reconstruction of muon is performed using independent track reconstruction in the
inner detector (ID) and muon spectrometers (MS). The track reconstruction in the ID was
already given in Section Section 4.1. The track reconstruction in the MS is described in,e.g. Ref. [76]. This section is devoted to an overview of the combined muon reconstruction
using information of the ID and MS.

4.3.1

Combined reconstruction

Several algorithms are used in the combined muon reconstruction in order to minimise thegeometrical ineﬃciency. The combined muons are categorised into four types depending
on subdetectors used in reconstruction as follows:• Combined (CB) muon: is formed by globally reﬁtting the hits on the ID and MS.
The combined muons are generally reconstructed with an outside-in approach, i.e.
extrapolating a track in the MS inward to a matched ID track. An inside-out
reconstruction for combined muon is used as a complementary approach.
• Segment-tagged (ST) muon: is an ID track which, once extrapolated to the MS,
matches at least one local track segment in the MDT or CSC chambers (see Section 3.2.3. The ST muons are selected if muons go across only one layer of MSchambers to save those with low pT or passing regions where the MS do not cover.
• Calorimeter-tagged (CT) muon: is an ID track which is associated with an energy
deposit in the calorimeter compatible with a minimum ionising particle. The muonreconstruction eﬃciency for the region with |η| < 0.1 can be recovered by this type.
The MS does not fully cover the region with |η| < 0.1 due to cables and services of
the calorimeters and ID.
• Extrapolated (ME) muon: is the muon track in the region with |η| > 2.5 androughly originated from interaction point. The ME muons are used to extend themuon reconstruction acceptance to region with 2.5 < |η| < 2.7 which is out of theacceptance of the ID.
Overlaps between diﬀerent muon types are resolved by basically setting priority to CB ,ST, CT muons in order. The overlap with ME muons is resolved by selecting the trackwith better ﬁt quality and larger number of hits.

4.4

Jet

When a high pT gluon or quark is produced, it becomes a collimated bunch of hadrons,
called a jet. Jets are dominant objects in high energy proton-proton collision experiments
like the ones at LHC.
Jets in the ATLAS calorimeters are reconstructed mainly with the anti-kT algorithm [77],which is the standard jet ﬁnding algorithm in the ATLAS. The input for the algorithm
in this paper is topological calorimeter clusters (topo-clusters) [78, 79] with a positive45

CHAPTER 4. OBJECT RECONSTRUCTION

energy. The topo-clusters are built from topologically connected calorimeter cells that
contain a signiﬁcant energy deposit well above noise. The topo-clusters are reconstructedat the electromagnetic scale [80], i.e. calibrated to correctly measure the energy deposits
from electromagnetic showers in the calorimeter.
The anti-kT algorithm introduces distances di,j between entities (clusters, pseudojets) i and j and di,B between entity i and the beam axis deﬁned as the following:−2−2
di,j = min(kTi
, kTj
)

2
ΔRij
,
D2

(4.2)

−2
,
di,B = kTi(4.3)

2 = (η − η )2 + (φ − φ )2 and k , η and φ are respectively the transverse
where ΔRij
i
j
i
j
i
i
Ti
momentum, pseudorapidity and azimuthal angle of particle i. D is the jet-cone radiusparameter which is ﬁxed at 0.4 in the analysis of this dissertation. The clustering proceeds
by identifying the smallest of the distances between di,j and di,B . If it is a di,j , entities
i and j are combined. On the other hand, if di,B is the smallest, entity i is deﬁned asa jet and removed from the list of entities. The distances are then recalculated and theprocedure repeated until no entities are left.

4.5

Missing Transverse Momentum

miss is an important observable which represents the
The missing transverse momentum ETtransverse momentum carried by undetectable non-interacting particles such as neutrinos. The missing transverse momentum in ATLAS is reconstructed from the components
px(y) of the transverse momentum pT of the various contributions, given by
miss
Ex(y)
=−



px(y),i −i∈hard objects

px(y),j .

(4.4)

j∈soft signals

The second term of the right hand side of Eq. (4.4) is called soft term. The set of
miss :
observables is constructed from Ex(y)missET= (Exmiss , Eymiss ),
miss
miss
= |ET
|=
ET



(4.5)

(Exmiss )2 + (Eymiss )2 ,φmiss = arctan(Eymiss /Exmiss ).

(4.6)
(4.7)

miss is deﬁned as the vectorial sum of missing transverse moIn this dissertation, the ET
miss,imentum terms pTof hard objects, with i ∈ {e, γ, μ, jet}, and the corresponding soft
term pmiss,softconstructedfrom tracks which are not associated with the hard objects.
T
This yields γ μ  jet

miss
pT −
pT −
pT −
ptrack
.
(4.8)
=−
peT −
ET
T
electrons

muons

photons

jets

unused tracks

Object deﬁnition and procedure for overlap removal between objects found in the similar
position might diﬀer analysis-by-analysis. The particular selections for the analysis in
this dissertation are presented in Section 5.5.6.

46

Chapter 5

The Displaced Vertex Analysis
This chapter of the thesis describes a search for a long-lived supersymmetric partner of the√gluon in the data collected with the ATLAS detector in 2016 at s = 13 TeV. Final states
containing at least one massive displaced vertex with high track multiplicity and missing
transverse momentum are investigated. The search strategy and the backgrounds, which
dominantly originate from instrumental eﬀects, are introduced in this chapter.

5.1

Introduction

Search for massive long-lived particles is an important part of the ATLAS programs ofsearches for new physics [31]. Pioneering work was done in the ATLAS experiment with√pp collisions at s = 7 TeV in 2010 [81], which focused on a signature with Displaced
Vertices (DVs) associated with high-pT muons, predicted in a speciﬁc R-parity violating
model [82]. The same signature was investigated with the 2011 data of pp collisions at√√
s = 7 TeV [83] and 2012 data at s = 8 TeV [84]. Following these searches, othersignatures with displaced vertices were explored with the 2012 data, i.e., a DV associatedwith a high-pT lepton, or in an event with several high-pT jets or large missing transverse
miss ) [32, 85], which could explore more general R-parity violating models [82],energy (ETa Split SUSY model [24] and a Gauge-Mediated SUSY model [86].
√In this analysis, 32.7 fb−1 pp collision data at s = 13 TeV recorded in 2016 areused. The production cross section of heavy particles has signiﬁcantly increased as thebeam energy of the LHC has increased. In addition, a newly installed layer of the Pixel
detector (IBL) has improved the performance of track and vertex reconstruction [52].
The sensitivity to new physics phenomena which result in DVs has been expected toincrease thanks to these improvements.
As the ﬁrst such search in Run 2 of the LHC, a signature with a DV and signiﬁcantmiss
ET is focused. This channel is sensitive to large regions of phase space in the various
signal models and has the beneﬁt that complex uncertainties related to the reconstructionof muons and electrons from displaced decays are avoided. A Split SUSY model (seeSection 2.2.3) is considered here and the process of pair-production of long-lived gluinos
which hadronise into R-hadrons before decaying into two quarks and neutralino, shownas Fig. 5.1, is a target of this analysis.
The previous search in Run 1 [32, 85] targeted high-mass gluinos with a ﬁxed neutralino mass at 100 GeV, so that it was required that at least two energetic jets with
ET > 50 GeV and total pT of tracks associated with the jet is less than 5 GeV, called a
trackless jet requirement. The search presented in this dissertation also targets scenarios
47

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

q
p

p

q
g̃
g̃

q̃

χ̃01

∗

q̃ ∗

χ̃01
q
q

50

ATLAS Online Luminositys = 13 TeV

LHC Delivered

40
30

ATLAS Recorded
Total Delivered: 38.9 fb-1
Total Recorded: 36.0 fb-1

20
7/16 calibration

Total Integrated Luminosity [fb-1]

Figure 5.1: Feynman diagram representing production of long-lived gluinos in a Split
SUSY model, which form R-hadrons and give rise to displaced decays with hadronic
ﬁnal states.

100
18/04 16/05 13/06 11/07 08/08 05/09 03/10 31/10
Day in 2016

Figure 5.2: Cumulative luminosity as a function of time delivered to (green), recorded by
ATLAS (yellow) during stable beams for pp collisions at 13 TeV centre-of-mass energy
in 2016 [47].

in which a neutralino mass is close to a gluino mass. This mass relation would realise aso-called gaugino co-annihilation mechanism and thus it is favoured from the relic dark
matter abundance [44] as explained in Section 2.3.1.

5.2

Dataset Information

5.2.1

Data Samples√
The full dataset of ATLAS pp collision data at s = 13 TeV, recorded between April
and October in 2016, is used in the analysis. Figure 5.2 shows the integrated luminosity
as a function of time for the dataset. In total, 36.0 fb−1 of data was recorded, however,a part of the recorded data is not used due to the temporal detector failure or any otherdefects in data taking conditions. The events recorded during a certain interval of timein such bad condition are tagged as bad events in an ATLAS database. The events which
48

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Table 5.1: Data taking periods and the corresponding amount of the integrated luminosity for the 2016 dataset after the application of data quality requirements. Runs inperiod H were recorded with the beam condition of low μ for forward physics. Runs inperiod J were taken with β ∗ = 2.5 km for the measurement of elastic pp-scattering by
the “Absolute Luminosity For ATLAS” (ALFA) detector.
PeriodRun Numbers
Dates
Integrated Luminosity [pb−1 ]A
297730 - 300279 28 Apr. - 27 May.
552.7
B300345 - 300908 27 May. - 06 Jun.
1922.6
C
301912 - 302393 11 Jun. - 21 Jun.
2861.3D302737 - 303560 24 Jun. - 10 Jul.
4624.2
E303638 - 303892
10 Jul. - 16 Jul.
1481.0F
303943 - 304494
16 Jul. - 25 Jul.
3398.9G305380 - 306451 02 Aug. - 17 Aug.
3818.4
H
N/A
N/A
N/A
I
307126 - 308084 25 Aug. - 10 Sep.
5760.7
J
N/A
N/A
N/A
K
309375 - 309759 26 Sep. - 03 Oct.
2191.6
L
310015 - 311481 06 Oct. - 26 Oct.
6127.5A-L297730 - 311481 28 Apr. - 26 Oct.
32739.0
are not regarded as bad are added to a list. This list is called a Good Runs List (GRL).
According to the GRL, a total usable integrated luminosity corresponds to 32.7 fb−1 .
The total dataset is broken down into data-taking periods, with individual integrated
luminosities listed in Tab. 5.1.
As the standard ATLAS tracking algorithms are ineﬃcient for ﬁnding tracks with
impact parameters larger than 100 mm, track reconstruction has to be re-run with relaxed tracking parameters as shown in Tab. 4.2. This “re-tracking” procedure (see Section 4.1.2) requires low-level information such as hits on surfaces of the detectors. This isa time consuming process that is not allowed to be applied to the whole dataset in 2016.
It is necessary to prepare the data format with low-level information but containing muchless number of events. A speciﬁc event ﬁlter has been prepared to reduce events which
seem not to be interesting by applying certain kinematic cuts. Each group searching forlong-lived particles in ATLAS has designed a ﬁlter for its analysis. A ﬁlter used in thismiss as later shown in Section 5.5.1. After ﬁltering events,
analysis is based mainly on ET
the remaining number of events is required to be O(1)% of the original dataset. Thisdata format is designed speciﬁcally to give access to low-level detector and reconstruction
information for searches that need to do custom reconstruction or use unconventionalvariables based on low-level detector data.

5.2.2

Simulated Samples

The displaced vertex analysis makes use of a number of signal MC samples to determine
the expected signal eﬃciencies and to estimate uncertainties in the eﬃciency. For metastable R-hadrons, pair production of gluinos with masses (mg̃ ) between 400 GeV and2000 GeV with the neutralino mass varied between 100 and mg̃ − 30 GeV is simulatedin Pythia 6.4.28 [87]. The AUET2B [88] set of tuned parameters for the underlying
event and the CTEQ6L1 [89] parton distribution function (PDF) set are used. The
dedicated routines [90] for hadronization of heavy particles are used to simulate the49CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

production of R-hadrons. The cross sections are calculated at next-to-leading order(NLO) assuming a squark mass of 10 TeV. The most signiﬁcant contributions to the NLO
QCD corrections come from soft-gluon emission oﬀ the coloured particles in the initial andﬁnal state [91]. The resummation of soft-gluon emission is taken into account at next-toleading-logarithmic accuracy (NLO+NLL) [92–95]. The uncertainty on the cross-section
predictions are deﬁned as an envelope of cross-section predictions using diﬀerent PDF
sets (CTEQ6.6 [96] and MSTW2008 [97]) and factorisation and renormalisation scales,
as described in Ref. [91]. The nominal cross-section is obtained using the midpoint of
the envelope.
The ATLAS reconstruction simulation framework [98] using Geant4 [99–101] is used
for detector simulation. The dedicated routines based on the physics model described inRefs. [90, 102] are incorporated to emulate interactions of R-hadrons with matter. Thismodel assumes the cross section of 12 mb per nucleon for each light valence quark. Theinteraction of heavy parton is neglected. A gluino would form a R-hadron with one or
two quarks, or even with a single gluon [31]. In this analysis, the probability to form agluon-gluino bound state is assumed to be 10%.
The gluinos within R-hadrons decay via the process g̃ → qq χ̃01 using Pythia 6 as
illustrated in Fig. 5.1. The gluino lifetime (τ ) is varied from 0.01 to 50 ns. All simulated
samples include a modelling of pileup. The pileup modelling is done by adding the
expected number of minimum-bias pp interactions from the same (in-time pileup) andnearby (out-of-time pileup) bunch crossings. Simulated events are reconstructed using
the same software as the one used for the collision data. Pythia 6 can perform thesimulation of R-hadrons, however it suﬀers from inaccuracy for radiative eﬀects, known
as initial state radiation (ISR) or ﬁnal state radiation (FSR). To get a more accurate
description of them, additional samples of gluinos are generated using mg5 amcnlo [103],
interfaced to the Pythia 8.186 [104] parton shower model, with the A14 [105] set oftuning parameters together with the NNPDF2.3LO [106] PDF set. The distribution of
the transverse momentum of the gluino-gluino system simulated with Pythia 6 is thenreweighted to match the distribution obtained in samples of mg5 amcnlo.

5.3

Background Sources

One of the powerful features of the search for new physics via high-mass and high-trackmultiplicity DVs is the extremely low level of background. However, there are threesources of background, which may produce the massive non-signal DVs with high track
multiplicities as illustrated in Fig. 5.3.
• Hadronic interactions: Particles interacting with the detector material can produce secondary vertices, which are diﬃcult to be distinguished from DVs arisingfrom long-lived particle decays. These can potentially be massive and have a hightrack multiplicity to fall into the analysis signal region.
• Merged vertices: The last step in the vertexing algorithm are to merge vertices ifthey are within 1 mm from each other (see Section 4.1.4). Therefore, it is possiblethat two vertices from two diﬀerent decays are merged accidentally. The merged
vertex may have a high track multiplicity and large invariant mass.
• Random Crossings: A track, from an arbitrary source, which lies very close to
the real vertex might be reconstructed as a part of the vertex. If the angle at which
50

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

(a)

(b)

(c)

Figure 5.3: Illustrations of three sources of background which may result in massive nonsignal displaced vertices with high track multiplicities. (a) shows hadronic interaction
with a detector material, (b) shows a pair of vertices merged by the secondary vertexingalgorithm because the distance between them is less than 1 mm and (c) shows a vertex
at which an independent track randomly crosses with large opening angle.
a track crosses the vertex is large, the invariant mass of the vertex also becomeslarge. Thus, the number of tracks associated to the vertex as well as the invariant
mass of the vertex might become large enough to be included in the signal region.
The ﬁrst source of background, the hadronic interaction vertices, are signiﬁcantly
reduced by applying a material veto, where any vertices found in the dense material
regions of the detector are removed. Further details regarding the material veto arecovered in Section 5.6.4. The second source of background, merged vertices, is expected
to be small. In the previous search in Run-1 [32] it was found that the contribution ofthis source to the total background was 0.03%, which was a factor of ten smaller than
the statistical uncertainty applied to the estimation. The last source is the dominant
contribution of the backgrounds. The number of expected background vertices fromthese sources is estimated using a fully data-driven methods and shall be explained in
Section 5.7.

5.4

Overview of Signal, Control and Validation Regions

The displaced vertex search makes use of a signal region, several control regions andvalidation regions, all of which are deﬁned by multiple kinematic selections. Before
going into the details in Section 5.5, an overview of the regions is given to clarify theirroles and the requirements.
The signal region (SR) is deﬁned by a set of selections used to maximise the signalto-background ratio as well as to minimise the systematic uncertainties. A ﬁnal decision
whether signal events exist or not is done in this region. Several control regions (CRs) aredeﬁned by sets of basic selections and are used to estimate the numbers of backgroundvertices. The validation regions (VRs) are kinematically neighbouring regions to the SR
and are used to validate the methods of background estimation.
Table 5.2 contains a summary of the requirements that deﬁne the samples of events(and vertices considered within those events) used to derive the background estimatesand validate the estimation methods.

51

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Table 5.2: Deﬁnitions of the control, validation and signal regions in the analysis. The
validation and signal regions are deﬁned by the control region requirements and some
additional selections.
Control Region (CR):Event-level requirements:
DRAW_RPVLL ﬁlter:see description in Section 5.5.1

DAOD_SUSY15 ﬁlter:see description in Section 5.5.1

Event cleaning

Rejection of bad/corrupted events(LAr, Tile, TTC restart, . . . )Good Runs List

Removal of bad lumi blocks basedon data quality assessment

Primary vertex

At least 1 good PV, withtracks≥ 2 and |zPV | < 200 mm
NPV

Non-collision background veto

Reject events where the leading jet satisﬁes
fmax > 0.8 or fEM > 0.96

Vertex-level requirements:
Fiducial region

R < 300 mm and |z| < 300 mm

Vertex ﬁt quality

χ2 /Ndof < 5

Displacement from PV (in x–y plane)

PV−DV
dT
> 4 mmMaterial veto

Not in volume marked as dominated by material

Disabled-module veto

Not in volume aﬀected by disabled Pixel detector modules

miss
Low-ET
Validation Region (VRLM):(On top of CR requirements)

Additional event-level requirements:
misscutUpper ET

miss
Oﬄine calibrated ET< 150 GeV

miss
Upper Δφmin (ET, jets) cut

missΔφmin (ET, jets) < 0.75,
using all selected jets with pT > 30 GeV

Additional vertex-level requirements:
Track multiplicity

ntracks = 4

Invariant mass

mDV > 10 GeV(On top of CR requirements, except material veto)

Material Validation Region (VRM):
Additional vertex-level requirements:
Material region

The vertices considered are required to be in volume
marked as dominated by material

Track multiplicity

ntracks = 4

Invariant mass

mDV > 10 GeV(On top of CR requirements)

Signal Region (SR):
Additional event-level requirements:
misstriggerET

missRequiring the lowest unprescaled ET
trigger to pass

miss
ET
ﬁlter

Requiring a set of selections shown in Section 5.5.1

miss
cut
ET

miss
Oﬄine calibrated ET> 250 GeV

Additional vertex-level requirements:
Track multiplicity

ntracks ≥ 5

Invariant mass

mDV > 10 GeV

52

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS$""&$#)#'&$ 

&("'&

%)'    "! !"!
! !"!

''$%
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"'%##",&& ' '

'%!#%'+#Figure 5.4: Schematic ﬂow of data format conversion adopted in this analysis. The
dashed arrows represent the standard processes in ATLAS and the solids arrows represent
speciﬁc operations. DRAW RPVLL and DAOD SUSY15 in the parentheses are names of data
formats used in this analysis.

5.5

Event Selection and Cleaning

The selection of events of interest with signal characteristics is performed by applying asequential cuts described in the following sections

5.5.1

Triggering and Filtering

Due to limitation of the storage resources, data size of recorded collision events is required
to be reduced. This reduction is done in several steps as shown in Fig. 5.4. The detailsof each step are described in this section.
Triggering Events
Triggering events is an important ﬁrst step in the event selection. The trigger controls
what kinds of collision events are to be recorded. Every analysis must ﬁnd appropriate
triggers for its topologies at ﬁrst.
miss is used. The trigFor the search for meta-stable R-hadron, the trigger based on ET
gers used for this analysis is HLT xe100 mht L1 XE50 for period A-E and HLT xe110 mht L1 XE50
for period F-L, which were unprescaled for the entire periods, respectively. At the Highmiss as theLevel Trigger (HLT) level, the missing HT (MHT) algorithm calculates ET
negative vector sum of transverse energy of calibrated jets and its trigger thresholds aremiss (xe100 and xe110). At the L1 level, the cell algorithm
100 GeV and 110 GeV of ET
miss as theis used instead for the entire 2016 dataset. The algorithm calculates the ET
negative sum of transverse energy deposited in calorimeter clusters above a certain noise
threshold. The clusters are split as ﬁxed-size trigger towers. The size of a trigger tower is
0.1 × 0.1 in (η, φ) space in the barrel region but 0.2 × 0.2 in the forward regions becauseof reduced calorimeter granularity. The trigger threshold at the L1 level is 50 GeV ofmiss (XE50). The technical details of the implementation of E miss triggers at ATLASET
T
is discussed in Ref. [107].
miss calculation in the online HLT is generally not the same as that in oﬄine
The ET
miss might be calculated as smaller value than the oﬄine one
reconstruction. The online ET

53

Efficiency

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1.2

s = 13 TeV
HLT_xe110_mht_L1XE50

1
0.8
0.6
2016 data

0.4
0.2
0
0

~
∼0)=1070 GeV, τ=1 ns
MC: m( g ) =1200 GeV, m( χ
1

50

100

150

200

250

300

350

400

Offline missing E T [GeV]

Figure 5.5: Turn-on curve of HLT xe110 mht L1XE50 trigger for a certain MC signal (red)and 2016 data from Period F (black).

miss around the trigger threshold are sometimes
due to the resolution. Events with the ET
not recorded. Figure 5.5 shows the so-called turn-on curve of HLT xe110 mht L1 XE50.
The turn-on curve was derived using data samples recored with jets triggers. The curve
miss distribution of sampled events which passed thewas created by dividing the oﬄine ET
miss trigger by that of all sampled events. The triggering eﬃciency reaches 100% at theETmiss of approximately 200 GeV. The oﬄine E miss threshold is set at 250 GeV tooﬄine ETT
miss region
ignore the disagreement of the turn-on curve between data and MC in low-ET(see also Section 5.5.6).

DRAW Filtering
This analysis needs to do custom reconstruction and use unconventional variables basedon low-level detector data. The speciﬁc data format used is designed to give access to
low-level detector and reconstruction information.
In order to minimise the disk space used by this format, only a small subset of eventsare made available. To select them, tight trigger and oﬄine selections are applied to“skim” the data, while retaining the full RAW contents for the selected events. The
ﬁlters for the 2016 DRAW_RPVLL dataset related to this search require at least one of thefollowing triggers as a base selection:• HLT_xeXX_L1XEYY• HLT_xeXX_tc_lcw_L1XEYY• HLT_xeXX_topoclPS_L1XEYY• HLT_xeXX_topoclPUC_L1XEYY• HLT_xeXX_mht_L1XEYY
where XX = 90, 100, 110, 120, 130 and YY = 50, 55, 60. The following online algorithms
are used for the above triggers: a 2-sided 2-sigma noise suppression cell-based algorithm,

54

0.9
1
0.2
2
0.2
0

1000

1200

1400

1600

1800

10−1

10−2

0.2
1

800

0.2
0

0.8
8
0.2
1
0.2
0
0.2
0

0.2
1

0.8
6
0.2
2
0.2
1
0.2
3

0.8
2
0.2
1
0.2
0
0.2
0

0.7
8
0.2
3
0.2
0

600

2000

10−3

m ~g [GeV]m ~g[GeV](a) With trackless jets requirement

0.2
3

0.6
8
0.1
9
0.1
8
0.1
8

0.5
7
0.1
8
0.1
8
0.1
8

0.3
9
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4
0.1
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0.2
2

10−3

0.1
4

0.0
1

30

2000

0.2
2

1800

50

0.2
2

1600

80

0.1
9

1400

130

0.1
9

1200

1
m~g - 100

0.1
7

1000

Δm [GeV]

0.9
0
0.1
4

800

10−2

0.0
0

600

10−1

0.0
4

0.8
8
0.1
3
0.0
1

0.0
1

0.0
5

0.8
6
0.1
5
0.0
0

0.0
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0.0
5

0.8
2
0.1
3
0.0
1

0.0
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0.0
5

0.7
7
0.1
4
0.0
0

0.0
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0.0
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0.6
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0.1
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0.0
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0.0
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0.5
6
0.1
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30

0.0
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0.3
8

50

0.0
2

80

0.0
5

130

0.0
9

1
m~g - 1000.0
0Δm [GeV]

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS(b) Without trackless jets requiment

miss cut at 250 GeV for MC
Figure 5.6: Eﬃciencies of ﬁlter and oﬄine calibrated ET
samples of R-hadrons (a) with trackless jets requirement and (b) without trackless jets
miss threshold is raised to 180 GeV. The verticalrequirement but the topocluster-based ET
axis shows the mass diﬀerence between gluino and the lightest neutralino and the horizontal axis shows gluino mass. In case of Δm = Mg̃ − 100 GeV, the lightest neutralinomass is ﬁxed at 100 GeV. It is shown that the eﬃciencies for small Δm scenarios are
signiﬁcantly improved by removing trackless jets requirement.

a topocluster-based algorithm in local calibration weighted scale with no further corrections (tc lcw), an eta-ring pile-up subtraction (topoclPS), or a pile-up ﬁt procedure (topoclPUC), and an algorithm based on the sum of jet momenta (mht), respectively [108].
On top of the trigger selection, some oﬄine selections were applied depending on themiss is required to be large. The use ofdata taking period. The topocluster-based ET
miss is motivated because it is a simpler value that will not change
topocluster-based ET
throughout data-taking. The diﬃculty in the previous analysis [32] was that the skim
miss . The calibration is periodically imused a cut on one version of the calibrated ET
miss by theproved, therefore it was out of sync with the recommended analysis-level ET
time the analysis was completed. The existence of jets which are not associated with ID
tracks was also required in periods A-J in 2016. Such jets are typically called tracklessjets. The trackless jet was used in the analyses of the LHC Run 1 (-2012) as well, where
the targeted scenarios predicted signiﬁcant hadronic activity. This search also targets
scenarios with small mass diﬀerences between the long-lived particle and the LSP (seeSection 5.1). Such signatures do not provide displaced jets with enough energy to fulﬁlthe trackless jet requirements. For this reason, the ﬁlter for the displaced vertex searches
was changed during the year to use a simple but tighter requirement on topocluster-based
miss instead. This is justiﬁed by the increased signal eﬃciencies for the compressed sigET
nal scenarios shown in Fig. 5.6. In summary, the following oﬄine criteria were applied
depending on the data taking periods:
Periods A-J:

miss > 130 GeV AND any of the following requirements:
topocluster-based ET
at least one jet with pT > 70 GeV with SumPtTrk < 5 GeV,
at least two jets with 
pT > 25 GeV with SumPtTrk < 5 GeV,
where SumPtTrk =pT of tracks from the PV(with pT > 0.5 GeV) associated to the jet

Periods K-L:

miss > 180 GeV
topocluster-based ET

The SumPtTrk requirement was used to select trackless jets.
55

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Further Skimming and Corrections
The analysis data samples contain not only events passing the triggers and ﬁlter used inthis analysis but also those which passed other triggers, such as jet or lepton triggers, andother ﬁlters prepared for other analyses. For further data size reduction and corrections,a proper derivation [109], DAOD_SUSY15, is applied to the ﬁltered dataset. This skims thedata sample by selecting the events passing any of a set of triggers deﬁned within the
ATLAS long-lived searches groups. This list includes the lowest-threshold unprescaled
miss triggers used by this analysis. This is used only for data and no skimming is appliedET
to MC samples.

5.5.2

Good Runs List

As described in Section 5.2.1, data quality (DQ) information assessed by the DQ groupis summarised in Good Runs List (GRL). In the GRL, ﬂags of “good” or “bad” areassigned to each luminosity block in each run [110]. A luminosity block is the unit oftime for data-taking, and lasts about one minute. For instance, if more than 30% of
the modules in a Pixel layer is disabled for some reason in a certain luminosity block,an intolerable defect ﬂag is assigned to the block. The GRL is used to justify that thedataset used in the analysis are in good condition. Approximately the GRL discards 3%
out of the whole events passing the above selections.

5.5.3

Event Cleaning

The GRL provides the data quality information in the unit of luminosity blocks. Eventsin bad condition are sometimes not vetoed if the luminosity blocks pass the data quality
requirements. Events that contains the following problems are further vetoed:
1. LAr noise bursts and/or data corruption
2. corruption of the Tile data
3. non-operational cells in the Tile and Hadronic End Cap (HEC) calorimeters
4. the recovery procedure for single event upsets in the SCT

5.5.4

Primary Vertex

miss calculation from pile up collisions, the Primary
In order to suppress eﬀects on the ET
Vertex (PV) is required to be indentiﬁed. The events are required to contain at least one
good PV with at least two tracks, and z position |zPV | < 200 mm. When several such2vertices are available, the one with the largest Σ(ptrk
T ) is chosen as the selected PV.

5.5.5

Non Collision Background Veto

miss cut is applied, contribution from non-collision background (NCB)
When the large ET
processes becomes signiﬁcant. At the LHC, one of the main sources of NCB which comes
into the detector is so-called tertiary halo [111]. Tertiary halo is a bunch of protons thatescape the beam cleaning system and are scattered by the tertiary collimator (TCT)
positioned at |z| ≈ 150 m from the interaction point. Figure 5.7 shows a schematic
illustration of the LHC beam cleaning system and how tertiary halo is produced. Particles
which are produced by interaction between the tertiary halo and the TCT are generally

56

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Figure 5.7: Schematic illustration of the LHC cleaning system. Primary and secondary
collimators and absorbers in the cleaning insertions remove most of the halo. Sometertiary halo escapes and is intercepted close to the experiments by the TCT [111].

blocked by the shielding material, however high energy muons likely penetrate the shieldand leave large energy in the calorimeters via radiative energy losses. Such energy deposit
is reconstructed as a jet. Figure 5.8 shows the x–y position distribution of the CSC muontrack segments in an endcap region. The two clear peaks at φ = 0, ±π are corresponding
to a horizontal spread of the NCB, most likely due to bending in the dipole magnets.
miss angle distributions. The plot on the left hand side is
Figure 5.9 shows the azimuthal ET
for three diﬀerent selections on the dataset: all events passing the ﬁltering and skimming
miss > 250 GeV cut(black), all events passing the event-level selection including the ET(blue), and after also requiring a good DV passing all vertex selections except for thentracks and mDV cuts (red). On the right hand side, this red distribution is split up for
periods A-J and K-L showing that both periods are signiﬁcantly contaminated, i.e. bothof the two ﬁlters that were used for the processing of the data for the two periods selectnon-collision background events.
The event selection does not require any hard physics object associated to the PV,
and this means the search is more sensitive to contamination of non-collision background
events. The distribution of energy deposits by the jet, the shower shape and its direction
can be employed to discriminate collision jets from NCB-induced fake jets. Studying
many of the variables commonly used for jet cleaning, a few variables have been foundto have eﬃcient discriminating power between the events in the peaks around φ = 0 and
φ = ±π from non-collision background processes and the events not contaminated by
non-collision processes. In particular, when it is required that the leading jet has smallvalue of the maximum jet energy fraction in any single calorimeter layer (fmax ), thepeaks are dramatically reduced for one signiﬁcantly aﬀected run as shown in Fig. 5.10.
It is also found that non-collision background has a large electromagnetic energy
fraction (fEM ), deﬁned as the ratio of the energy deposited in the electromagnetic (EM)calorimeter to the total energy. This analysis vetoes events where the leading jet satisﬁes
either of these criteria:• fmax > 0.8
57CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

×10−3

y [m]

3
ATLAS Preliminary
2
1

0.12

May 13 - June 2 (7 runs)

0.1

No PV

0.08

0

Unpaired iso B1⎜ θpos -θdir ⎜> 5°

0.06

Side A−1

0.04

Entries: 14973

−2

0.02

−3
−3 −2 −1

0

1

2

0

3

x [m]

Figure 5.8: Distribution in the plane transverse to the beam pipe of the CSC muon
segments in EndCap A, in runs from May 13 to June 2nd in 2016, in events from unpaired
isolated bunches, without any primary vertex and passing a trigger requiring a jet withpT > 12 GeV [112]. A cut on the diﬀerence between the polar position and the polar
direction of the muon segment is applied. The distributions for each run are normalisedby the duration of the run in seconds, and the plot represents the average over all the
runs.

106
104

105

104
103

103

102

<3

<2

<1

0

1

2

3

METѮ>UDG@

<3

<2

<1

0

1

2 3
METѮ>UDG@

miss for the data. Left: all events passing the
Figure 5.9: Distributions of the φ of the ET
DRAW+SUSY15 selection (black), all events passing the event-level selection including
miss > 250 GeV cut (blue), and after also requiring a good DV passing all but thethe ET
ntracks and mDV cuts (red). Right: the events passing the last selection on the left but
separated for periods A-J (blue) and K-L (black).

58

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

100

80

60

40

20

0

<3

<2

<1

0

1

2

3
METѮ>UDG@

miss for one run signiﬁcantly contaminated by
Figure 5.10: The φ distribution of the ET
non-collision background before (green histogram) and after (blue markers) requiring
fmax < 0.7 for the leading jet.

• fEM > 0.96
Figure 5.11 shows the two-dimensional distributions for these variables for data (a)and an example signal MC sample (b). In summary, studies on a subset of the data anda representative set of signal MC samples indicate that the cuts above reject 90% of thedata in the φ peaks (i.e. almost all NCB) while rejecting < 1% of the signal events.
miss angle for events before and after the NCB vetoFigure 5.12 shows the azimuthal ET
described above. This is shown with and without an additional requirement the events
have a DV with at least 3 tracks, showing that the ﬁnal contribution of NCB on theanalysis is signiﬁcantly reduced after the explicit veto.

5.5.6

Oﬄine Missing Transverse Energy Cut

The displaced vertex analysis does not explicitly use electrons, photons and muons,miss calculation. The object deﬁnitions andhowever these objects are necessary for the ET
the strategy to solve overlap between them are described in this section.
Electron and Photon deﬁnition
An electron and a photon are reconstructed as clusters of energies in the electromagnetic
calorimeter and distinguished from each other by checking how many tracks match thecluster as described in Section 4.2. The electron is further required to pass the standard
loose quality requirements, named as LooseAndBLayerLLH [113]. On the other hand,the photon is required to pass the standard tight photon identiﬁcation criteria [114].
The tight requirements are chosen for photons because (unconverted) photons are reconstructed using only calorimeter information unlike electrons. The electron identiﬁcation
algorithm is the likelihood-based (LH) methods. It is a multivariate analysis (MVA) technique which deals with the signal and background probability density functions (PDFs)
of the several discriminating variables simultaneously. On the other hand, the photon
59

1

10−1

0.9
0.8
0.7

10−2

0.6
0.5

EM Frac

EM Frac

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1

10−2

0.9
0.8
0.7

10−3

0.6
0.5

0.4

0.4
−3

0.3

10

0.2 Data
Cuts remove 50.4%
0.1

10−4

0.3
100, 3ns
0.2 1200,
Cuts remove 0.6%
0.1

0
0 0.10.20.30.40.50.60.70.80.9 1

0
0 0.10.20.30.40.50.60.70.80.9 1

Frac Max Sampling

Frac Max Sampling

(a)

(b)

Figure 5.11: Two-dimensional distributions for the two variables proposed to use for theNCB veto, for (a) data and (b) an example signal MC sample.

w/o NCB Veto

w/o NCB Veto

w/ NCB Veto
w/ NCB Veto

104

10

103
−4 −3 −2 −1

0

1

2

3

4

1
−4 −3 −2 −100(7Ѯ>UDG@

(a)

1

2

3

4

0(7Ѯ>UDG@(b)miss φ distributions (a) for events passing the event-level selection
Figure 5.12: The ET
with and without the NCB veto described in the text and (b) the same selection but also
requiring the presence of a vertex with at least three tracks.

60

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

identiﬁcation method is based on independent cut-based selection on the several discriminating variables.
In addition, the electron is required to have the transverse momentum of pT > 10 GeV
and to be within the pseudo-rapidity range of |η| < 2.47. The photon pT is required to
be greater than 25 GeV and be within |η| < 2.37. The object is deﬁned as bad and to
be removed if its cluster is aﬀected by the presence of a dead readout board in the ﬁrst
or second layer of the EM calorimeter or by the presence of a dead high voltage power
supply (HV) region aﬀecting the three layers or by the presence of a masked cell in thecore of the cluster.
Muon deﬁnition
Muons are reconstructed in the inner detector and muon spectrometers independently
and then combined as shown in Section 4.3. In the analysis stage, the muon is required
to pass the medium muon identiﬁcation criteria [115]. Although there are four options of
the combined muon reconstruction, CB, ST, CT and ME (see Section 4.3), only CB andME tracks are used. The CB muons are required to have at least 3 hits in at least two
MDT layers, except for muons in the |η| < 0.1 where the detector coverage is not full. In
this region, tracks are required to have measurements on at least one MDT layer and at
most one MDT layer which does not have hits although a track is drawn on it. The ME
muons are required to have measurements on at least three MDT or CSC layers. Further
requirements are summarised in Ref. [115]. The kinematical selections are also appliedon the transverse momentum of pT > 10 GeV and the pseudo-rapidity of |η| < 2.7.
Jet deﬁnition
The jets in this analysis are built with the anti-kt algorithm using topological cluster
calibrated in the EM scale as inputs with a distance parameter of R = 0.4 as describedin Section 4.4. The full jet calibration scheme is applied to realise that the mean ofthe distribution for the ratio of the reconstructed jet energy to the truth jet energy isapproximately 1 in the wide η range. The jet calibration is generally called Jet Energy
Scale (JES). The Moriond2017 release1 of the JES calibration is used in this analysis.
The jet is also required to have the transverse momentum of pT > 20 GeV and be within
the pseudo-rapidity range of |η| < 2.8.
Overlap Removals
Since both electrons and jets are reconstructed as clusters in the calorimeters, a cluster issometimes identiﬁed as an electron and a jet at the same time. Also, a muon as a decay
product of a hadron in a jet is not supposed to be identiﬁed as a muon. Such “overlap”
must be resolved. The overlap removal strategy is described below.
Overlap removal between jets and leptons:
1. First apply the jet-electron overlap removal using baseline, non isolated, electrons:• If ΔR(jet, electron) < 0.2, the jet is removed and the electron is kept.
1
The Rencontres de Moriond is a series of one of the largest conferences in the high energy physics
community. A recommended set of calibrations and accompanying uncertainties was prepared for analyses
toward the Moriond2017 conference by the ATLAS combined performance groups.

61

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

2. Then apply the second jet-electron and jet-muon overlap removal using the remaining jets:• If ΔR(jet, electron) < 0.4, the electron is removed and the jet is kept.
• If ΔR(jet, muon) < 0.4, the muon is removed and the jet is kept unless thejet has less than 3 tracks with pT > 500 GeV, in which case the jet is removed
and the muon is kept instead.
Overlap removal between photons, jets electrons and muons:• If ΔR(photon, electron) < 0.4, the photon is removed and the electron is kept.
• If ΔR(photon, muon) < 0.4, the photon is removed and the muon is kept.
• If ΔR(photon, jet) < 0.4, the jet is removed and the photon is kept.
miss calculationET
miss is calculated as the momentum
Using the objects after resolving overlaps, the ETbalance of them with Eq. (4.8). In this analysis, the threshold of the oﬄine calibrated
miss is determined as the starting point of plateau of turn-on curve of combination of theETmiss trigger and the topocluster-based E miss cut which are required in the pre-selectionET
T(see Section 5.5.1). Figure 5.13(a) shows the turn-on curve of the topocluster-based
miss (MET LocHadTopo) with respect to the oﬄine calibrated E miss . The turn-on curveETT
was derived using data samples recored with jets triggers. The curve was created bymiss distribution of sampled events which passed the topoclusterdividing the oﬄine ET
miss cut by that of all sampled events. The topocluster-based E miss threshold inbased ETT
the ﬁlter is 130 GeV during period A-J and 180 GeV during period K-L, respectively.
miss > 180 GeV cut reaches plateau at
The turn-on curve of the topocluster-based ET
miss of 250 GeV. Figure 5.13(b) shows the turn-on
approximately the oﬄine calibrated ET
curve of eﬃciency for events passing the HLT xe110 mht L1XE50 trigger and topoclustermiss > 180 GeV cut for some MC signal and 2016 data of period F. In order tobased ET
reduce systematic uncertainty regarding the turn-on curve, the threshold of the oﬄine
miss is set at 250 GeV, corresponding to the starting point of the plateau region.
ET

5.6

Vertex Selection

This section is devoted to give descriptions on vertex selections for reducing backgroundlike vertices. The displaced vertex reconstruction itself is described in Section 4.1.4.

5.6.1

Fiducial Volume

The vertex position should be in the ﬁducial volume deﬁned as the region with rDV <300 mm and |zDV | < 300 mm. This volume is roughly corresponding to the region inside
the ﬁrst barrel layer of the SCT and within the coverage of the ﬁrst barrel layer of the
Pixel (IBL). The SCT ﬁrst layer is located around r = 299 mm and the z edge of the
IBL is at z = 331.5 mm as shown in Fig. 3.5.

62

Efficiency

Efficiency

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1
data16_13TeV PeriodF

0.8

1.2
1

DAOD_JETM1

s = 13 TeV
HLT_xe110_mht_L1XE50
MET_LocHadTopo > 180 GeV

0.8

0.6

MET_LocHadTopo > 100 [GeV]
MET_LocHadTopo > 110 [GeV]
MET_LocHadTopo > 120 [GeV]

0.6

MET_LocHadTopo > 130 [GeV]

0.4

MET_LocHadTopo > 140 [GeV]
MET_LocHadTopo > 150 [GeV]

0.4
2016 data

MET_LocHadTopo > 160 [GeV]

0.2

MET_LocHadTopo > 170 [GeV]
MET_LocHadTopo > 180 [GeV]

0.2

MC: 1200 GeV / 1070 GeV / 1 ns

MET_LocHadTopo > 190 [GeV]

0
0

50

100

150

200

250

300

350

400

0
0

50

100

150

200

Missing E [GeV]

(a)

250

300

350

400

Offline missing E T [GeV]T(b)miss (MET LocHadTopo)
Figure 5.13: (a) Turn-on curve of the topocluster-based ET
cut. (b) Turn-on curve of eﬃciency for events passing the xe110 2016 triggers and
MET LocHadTopo > 180 GeV cut in a MC signal and 2016 data of Period F.

5.6.2

DV Displacement

The vertex should be separated by at least 4 mm in the x–y plane from all reconstructedprimary vertices in the event. This cut is required to reduce DVs from decay of theStandard Model particles, such as B hadrons or τ leptons. For instance, the proper decay
length of B + meson in x–y plane is approximately 4 mm if its transverse momentum is
50 GeV.

5.6.3

Vertex Fit Quality

In order to reduce the vertices with bad ﬁtting quality, the upper limit on the reduced
χ2 of the ﬁtting is set at 5.

5.6.4

Material Veto

Nuclear interactions with the material in the inner detector are the largest source of background vertices with high track multiplicities. Distinguishing this type of backgroundvertices from displaced decays of long-lived particles is challenging. Any vertices foundin the volume of the detector occupied by dense material therefore needs to be vetoed.
A scheme to perform the veto is to construct a simpliﬁed map of these detector regions.
In the previous DV search in 2012 [32] a three dimensional map was constructed andused as a map to veto material interaction vertices. The map covers the whole ﬁducial
volume of r < 300 mm, |z| < 300 mm and in the full 2π in φ direction.
There are two methods used in the construction of the diﬀerent parts of the map.
The more complex structures of e.g. the pixel modules are extracted from vertices
reconstructed in minimum bias data, whilst geometrical approximations are made forthe more uniform shapes such as support rings. Figures 5.14(a) and 5.14(b) show twodimensional maps of the number of vertices which are located in the material region,
projected in the x–y plane and r–z plane, respectively.
The material veto must account for the slight movement of the detector due to its
weight when approximating the position of the beam pipe, for instance. The position ofthese approximations have then been validated in the 2016 dataset to ensure their posi-

63











−

−
−
− − −











300

ATLAS Preliminary s = 13 TeV, L = 32.7 fb-1

250

103

200
102

150
100

10
50
0
−300 −200 −1000x >PP@

100

200

300

Density of observed vertices [a.u.]

ATLAS 3UHOLPLQDU\ V 7H9/ IE

R [mm]

'HQVLW\RIREVHUYHGYHUWLFHV>DX@y >PP@CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1z [mm](a)(b)

Figure 5.14: Validation of the new material map. Two-dimensional maps of the numberof vertices which do not pass the material veto, projected in the (a) x–y plane and (b)r–z plane.

Table 5.3: Approximations of uniform shapes augmented by the oﬀsets created by thedecoupling of the beam pipe from the ATLAS cavern.
Material layer
Radius Thickness
x oﬀsety oﬀsetBeam pipe
24 mm
3 mm
0 mm −1.5 mm
Pixel support 1
29 mm
1.6 mm −0.3 mm −0.5 mm
Pixel support 2 42.5 mm
2.4 mm −0.2 mm−1 mm
Pixel support 3 68.5 mm
4.5 mm −0.1 mm −0.5 mm
tions are appropriate for the analysis described in this dissertation. The exact positionsof the geometry augmented by this eﬀect can be found in Tab. 5.3.
It should be noted that the material map is not perfect. Even if it were, there would bea chance that vertices arising from hadronic interactions with material in a vetoed region
could be reconstructed in the wrong location and survive the veto. However, as a cut,
it is eﬀective in drastically reducing high-track-multiplicity background vertices arisingfrom hadronic interaction. Contribution from vertices that were not vetoed correctly isquantiﬁed in the background estimation described in Section 5.7. Figures 5.15(a) and5.15(b) show two-dimensional maps of the number of vertices in the 2016 data before
material veto and after veto, respectively.
The volume vetoed by the material map is 42% of our ﬁducial volume (πr2 z 
3.14 · 302 · 60 cm3 ) in total.

5.6.5

Disabled Module Veto

The functionality of fake vertex veto described in Section 4.1.4 is eﬃcient to remove
vertices constructed from randomly crossing tracks. As shown in Fig. 4.6, tracks associated with a vertex are required to have hits on the next layer. However, if a moduleon the layer becomes disabled in the middle of data taking, the module does not havehits and thus the vertex gets vetoed by the scheme as shown in Fig. 5.16(a). Because ofthis, regions directly in front of pixel modules that have been disabled for any portion64

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

(a)

(b)

Figure 5.15:
Two-dimensional maps of the number of vertices in the 2016
DAOD SUSY15 data (a) before material veto and (b) after veto. The number of vertices
signiﬁcantly is reduced thanks to the veto in regions where detector materials are placed.

of the 2016 dataset are explicitly vetoed in order to properly account for this eﬀect inany simulation used. This conservative treatment should mitigate the problem at theprice of only a few percent reduced overall signal acceptance. The overall volume vetoedby this procedure is 3, 960 cm3 out of a total ﬁducial volume of 169, 645 cm3 , eﬀectively
vetoing 2.3% of the total ﬁducial volume. Figure 5.16(b) shows two-dimensional x–y
map of the number of vertices sliced in z direction after applying the disabled module
veto. Although some ineﬃcient regions are still not vetoed, this can be explained by
the presence of ineﬃcient modules. Some modules which contain dead readout chips are
ineﬃcient in detection of charged particles.

5.6.6

Number of Tracks and DV Mass

The Signal Region for vertex candidates is then deﬁned as Ntrk ≥ 5 and mDV > 10 GeV,
where mDV is the invariant mass of the vertex calculated using the charged pion mass
hypothesis for the tracks, i.e. instead of assuming massless tracks when calculating theinvariant mass of the combination, it is assumed that all tracks have the mass of a charged
pion. The vertex samples with Ntrk < 5 and/or mDV < 10 GeV are used for estimationof background DVs and validation of the estimation method.

5.7

Background Estimation

After the selections of events and vertices described in the previous section, the number of
DVs from the Standard Model particles in the signal region becomes negligible. However
there are still small contributions from experimental eﬀects to the background as shownin Section 5.3. The methods to estimate background and the results are given in thissection.

65

y [mm]y [mm]

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

100
102

50

100
102

50

0

0
10

10

−50

−50

−100

−100

1
−100

−50

0

50

1
−100

100

−50

0

50

x [mm]

100
x [mm](a)(b)

mDV [GeV]

Figure 5.16: (a) Two-dimensional map of the number of vertices within the region of|zDV | < 20 mm and rDV > 30 mm in x–y plane. (b) The same map as (a) but the disabledmodule veto is applied. The presence of ineﬃcient modules explains some ineﬃcientregions where are not vetoed.

102

10−2

10−3

10

10−4
1

10
Number of Tracks

Figure 5.17: The normalised two-dimensional distribution of mDV and track multiplicity
for DVs in events that pass all signal region event selection criteria for signal MC withthe gluino mass of 2000 GeV, the neutralino mass of 100 GeV and the gluino lifetime of
1ns. The red lines represent the boundary of the signal region requirements.

66

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

103
102
102
10
10

1

1
0

2

4

6

8

10

12

14

16

18

20

0

1

2

3

4

5

6

Invariant Mass [GeV]

7

8

9

10

Invariant Mass [GeV](a) 4-track DVs(b) 5-track DVs

102

10
10

1
1
0

1

2

3

4

5

6

7

8

9

10

Invariant Mass [GeV]

0

1

2

3

4

5

6

7

8

9

10

Invariant Mass [GeV](d) ≥7-track DVs(c) 6-track DVs

Figure 5.18: The invariant mass distributions of vertices with more than 3 tracks after
basic vertex selections. Red solid lines are ﬁtted exponential functions and Red dashedlines are extrapolation of them.

5.7.1

Hadronic Interaction

The huge number of vertices originated from hadronic interactions is signiﬁcantly reduced
thanks to the material veto applied using the data-driven material map. However, thematerial map does not perfectly describe detector materials and there is a non-negligible
possibility to hadronically interact with gaseous particles. A tiny fraction of them could
leak into the signal region accidentally. The number of such vertices is estimated bytaking advantage of the fact that the low mass peak in the invariant mass distribution isdominated by vertices from hadronic interaction; whereas the high mass tail is dominatedby vertices with random crossing track. Figure 5.18 shows the invariant mass distributions of vertices with more than 3 tracks after the CR selections (see Tab. 5.2). A simple
exponential function is used to ﬁt the tail of the low mass peak in the DV-mass distribution, and then is extrapolated to the high mass region, i.e. mDV > 10 GeV. Appendix A
conﬁrms and quantiﬁes the validity of the exponential assumption in this analysis byusing a material rich selection. The ﬁtted functions are exp(9.7 ± 0.3 − (1.1 ± 0.1) · m) for
4-track DVs, exp(7.9 ± 0.5 − 0.8 ± 0.1) · m) for 5-track DVs, exp(9.2 ± 1.3 − (1.1 ± 0.2) · m)
for 6-track DVs and exp(6.1 ± 1.4 − (0.7 ± 0.3) · m) for ≥ 7-track DVs, where the uncertainties are ﬁtting errors. The estimated number of hadronic interaction vertices with67

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

mDV > 10 GeV is 0.3 ± 0.10 for 4-track DVs, 0.93 ± 0.56 for 5-track DVs, 0.18 ± 0.2 for
6-track DVs and 1.0 ± 1.3 for ≥ 7-track DVs, where the uncertainties are ﬁtting errors.
Note that these estimations should be scaled by the event-base scale factor described in
Section 5.8.1, given that the sample is selected using the CR selection summarised in
Tab. 5.2.

5.7.2

Merged Vertices

Inside the beam pipe, the vacuum is good and no hadronic interactions are expected.
However due to the high-track density, there is a probability that two or more tracks crosseach other and get reconstructed as a displaced vertex. Additionally close-lying metastable-standard-model particles such as B-hadrons can give rise to vertices, typicallywith masses of a few GeV at maximum (though these are almost all removed by the
combination of the |d0 | > 2 mm cut and the requirement that the DV should be atleast 4 mm from the PV in the transverse plane). Due to the high density at smallrDV , it is conceivable that two vertices could get merged into a single vertex with asigniﬁcantly higher mass that could pass the signal region requirements. The estimationof this possibility is described in this section.
Vertex-pair distance method
The “vertex-pair distance method” [32] exploits the fact that the ﬁnal step of our vertexing algorithm merges pairs of vertices separated by less than 1 mm (see Section 4.1.4).
A random combination of 4 tracks can be viewed as two randomly merged 2-track combinations, and similarly for 5-track vertices and more. A pair of vertices within 1 mm ismerged by the secondary vertexing algorithm, and thus a model of vertex pair distanceis constructed to see how often the vertex pairs are separated by less than 1 mm. The
models used in this method are distributions of the separation distance between pairsof two-track vertices, or between two-track and three-track vertices in diﬀerent events.
In order to normalise this model, the separation distance between vertex pairs in thesame event is used. The idea is to use the bin (distance < 1 mm) of the model to estimate the background. (This bin will always be empty in the “same event” distance
distribution, because any vertex pairs here would have been merged into a single vertex.)
Figure 5.19(a) shows the modelled distribution for pairs of two-track vertices in diﬀerent
events, where the combination of vertices has mass > 10 GeV, and we can see that it looks
slightly diﬀerent from the distribution of vertex pairs in the same event. This motivates
the use of a weight, derived from the distributions in the z direction, to make the model
better match the “same-event” distribution. Figure 5.19(b) shows the distances between
pairs of two-track vertices in the z directions. The reason for the diﬀerence in the z
direction is the correlation between two-track vertices in the same event, which does notexist between the diﬀerent events. To correct this diﬀerence, a weight is obtained fromthe diﬀerence between the “diﬀerent-event” and “same-event” z-distance distributions,and applied to the 3D distance distribution. After the correction, the value of the model
at distances < 1 mm is taken as an estimate of the number of background vertices that
could have been formed from merging vertices.
Figure 5.20(d) shows the close-up distribution near 1 mm for ﬁve-track vertices madeof two-track and three-track vertices. Note that the same weight is applied. The estimated numbers of merged vertices are 3.69 ± 3.69 for 2 + 2 track vertex and 0.01 ± 0.01
for 2 + 3 track vertex. Note, as in the previous section, that the background estimation

68

Number of Vertices / mm

Number of Vertices / mm

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

0.016
0.014

data22'9

0.012

model22'9

0.01
0.008

model22'9

0.01
0.008

0.004

0.004

0.002

0.002

0

Ratio

0

Ratio

data22'9

0.012

0.006

0.006

1.5
1
0.5
0

0.014

1.5
1
0.5

50

100

150

200

250

Vertex Pair 3D Distance [mm]

0

50

100

150

200

250

Vertex Pair Z Distance [mm](b) z distance(a) 3D distance

Figure 5.19: (a) Three-dimensional distance and (b) z distance between vertex pairs
before weighting. The black points show the distance between the two-track vertices
in the same event. The red points show a model calculated from the distance between
two-track vertices in diﬀerent events. The invariant mass for the combination of the twovertices is required to be > 10 GeV.
is made using events before the event cuts, therefore the estimation have to be scaled by
the event-base scale factor described in Section 5.8.1.
In all these plots the black points indicate vertices found in the same event, while theblue line represents the model, constructed from pairs of vertices in diﬀerent events.

5.7.3

Random Crossing Tracks

Displaced vertices arising from the Standard Model processes, such as meta stableparticles, typically have low track multiplicity and mass. However, if a track from anarbitrary source gets mis-reconstructed as part of the vertex, it gets an additional track
multiplicity. In addition, there is a possibility that the random track crosses the vertex
with large opening angle by which the invariant mass becomes large enough to fall into
the signal region. A data-driven method has been developed to estimate contributionof this kind of random crossing tracks. A model of the invariant mass distribution ofvertices crossed by random crossing tracks is simulated by adding a track to a seed vertex
and recalculating the invariant mass of the vertex.
Three regions, categorised by the number of tracks associated with vertices, are usedin this method. The control region (CR) is made up of vertices with three tracks. The
3-track vertices are required to pass several quality cuts summarised in Tab. 5.2. The
validation region (VR) is made up of vertices with four tracks passing the quality cuts
but some requirements are changed. Finally, vertices with ﬁve or more tracks deﬁne thesignal region (SR).
The geometric ﬁducial volume deﬁned in Section 5.6.1 is divided into twelve individual regions as shown in Fig. 5.21. Invariant mass spectra of the vertices are createdindividually for these twelve regions. This division is made in order to consider the radial
dependence on the properties of reconstructed vertices and random tracks. The properties of the tracks associated to vertices varies signiﬁcantly with radial positions wherethe vertices were reconstructed because, for instance, the number of detector layers usedin the track reconstruction depends on a vertex position. Therefore, the shape of themass spectrum of the vertices with random crossing tracks depends on the radial regions
69




Number of vertex pairs / mm

1XPEHURIYHUWH[SDLUVPP

CHAPTER 5. THE DISPLACED VERTEX ANALYSISATLAS 3UHOLPLQDU\
V 7H9/ IE
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Different-event pairs

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104
s = 13 TeV, L = 32.7 fb-1
2+2 track vertices

Same-event pairs
Different-event pairs

3

10

102



10


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2

3

4

9HUWH[3DLU''LVWDQFH>PP@40
35

ATLAS 3UHOLPLQDU\s = 13 TeV, L = 32.7 fb-1
2+3 track vertices

6

7

8

9

10

(b) zoomed view of 2+2
1XPEHURIYHUWH[SDLUVPP

Number of Vertices / 5 mm(a) 2+2 merged vertices
45

5Vertex Pair 3D Distance [mm]Same-event pairs
Different-event pairs

30
25
20
15



ATLAS 3UHOLPLQDU\
V 7H9/ IE
WUDFNYHUWLFHVSame-event pairs
Different-event pairs





−

10
5
0

50

100

150

200

250

Vertex Pair 3D Distance [mm](c) 2+3 merged vertices

−






















9HUWH[3DLU''LVWDQFH>PP@(d) zoomed view of 2+3

Figure 5.20: (a) Three-dimensional distance between two-track vertex pairs, after weighting. The right histogram (b) is a close-up view of the left histogram. (c) Threedimensional distance between two-track and three-track vertices pairs, after weighting.
(d) A close-up view of the 3D distance between two-track and three-track vertices, after
weighting. The black points show the distance between the vertex pairs in the same
event. The blue lines show a model calculated from the distance between vertex pairs
in diﬀerent events. The value of the model at less than 1 mm gives the estimate for thenumber of high-mass four-track or ﬁve-track vertices from this method.

70

R [mm]CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

300
10

250

8

200

6

150

4

100

2

50
0
−300

0
−200

−100

0

100

200

300
Z [mm]

Figure 5.21: The properties of the displaced vertices changes as a function of rDV , depending on the track properties. Therefore, to produce a correct background estimation,
the ﬁducial volume is divided into twelve regions. The regions where detector materials
exist are vetoed in this ﬁgure.

as well.
This data-driven method relies on the hypothesis that the probability for a trackpassing nearby a vertex, and get associated to it in the vertex reconstruction, is irrespective of the number of tracks on the original vertex. Figure 5.22 schematicallydescribes the method for estimation of random crossing tracks. The method uses a vertex with (n − 1) associated tracks and adds a track to the vertex. Then, it becomes an-track vertex with larger mass than the original one. Eq. (5.1) deﬁnes the expression
for this model concisely and deﬁnes the components:
Pn (mDV ) = f · hn (mDV ),(5.1)

where hn (mDV ) is a template of the high-mass vertex distribution built from (n − 1)track vertices by adding a random track and recalculating the invariant mass. Pn (mDV )is the real mass distribution of n-track vertices of data which is output from the vertex
reconstruction algorithm, and f is the normalisation factor, also called a crossing factor.
A crossing factor represents the probability that a vertex is randomly crossed by anadditional track in the event. This is determined using data in the 3-track control
region.
Seed vertices and track templates
Seed vertices are deﬁned as (n − 1)-track vertices. Mass spectra of n-track vertices aremodelled by adding random tracks. All reconstructed vertices, passing the CR selection
criteria in Tab. 5.2 are considered as seed vertices. The seed vertices are divided into thetwelve radial regions.
The random tracks are sampled from track templates. The track templates are constructed by saving the track properties of (pT , η, Δφ) into three-dimensional histograms.
All tracks in reconstructed vertices, with the mass above 3 GeV and the number of associated tracks is at least 3, are used to create the track templates. Here, Δφ is deﬁned as
the relative azimuthal angle between the track and the direction of the PV-DV vector.
The relative angle is used instead of the absolute, in order to avoid creating vertices
71

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

.
+

 +

 +

+"#( )--

##1/ ")%/-+1/ ")1$+.* 1$
-/+ *(0$#1-+$ )--(,-/#$/1--!1 (,"/-00(,&% "1-/ )--'(&'+ 001 (*-%# 1

##1/ ")
,#..*51'$"/-00(,&%"1-/
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,#..*51'$"/-00(,&%"1-/

Figure 5.22: Schematic ﬂow of the method for estimation of random crossing tracks.
that would not be reconstructed by the vertex algorithm. For instance, if the absolute
angle is used, adding this track to a seed could easily create a vertex with a back-toback topology. Such vertices would not be found in data as they are removed by the
fake removal (see Section 4.1.4). A simple schematic in Fig. 5.23 shows how the relative angles of the track is deﬁned and how the track is added to a seed vertex. The
properties oftemplate tracks are shown in Fig. 5.24 for all radial regions. Only tracks
with ΔR ≡ (Δφ)2 + (Δη)2 > 1.0 are used to add to any seed vertices. Using tracks
with lower ΔR would be a waste of statistics as these vertices would not contribute tomodelling of high mass tail and fall outside the SR.
Constructing the invariant mass templates
The method is composed of the following three steps.
1. Construct templates for the DV mass distributions (hn (mDV )) of possible combinations of (n − 1)-track DV plus a random track (e.g. 2+1, 3+1, 4+1 and 5+1 or
higher).
2. Extract the normalisation factors f by scaling the mass templates from the randomtrack association method in the control region to the data, i.e. scaling the models of (2+1)-track vertices (h3 (mDV )) to those of the 3-track vertices in the data
(P3 (mDV )): +∞GeV P3 (mDV ) dmDV
f = 10(5.2)+∞
10 GeV h3 (mDV ) dmDV
3. Scale the estimated number of high-mass vertices with an event-based scale factor.
This scale factor accounting for the diﬀerence between the eﬃciency of the event
pre-selection and that of the ﬁnal event selection which also includes explicit trigger,
miss requirements.
ﬁlter and oﬄine ET

72

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Δφ


DV

PV


(i - 1) DVΔφRandom track

Figure 5.23: Schematic drawing showing the two steps of the random-track association
method. In the vertex labeled (1) the relative azimuthal angle Δφ (marked with thecurved red arrow) to the PV-DV direction (green dashed arrow) for each track in a DV
which are ﬁlled into the track templates, and templates of η and pT are built up in thesame way. The vertex labeled (2) shows how the random track generated from the track
templates are added to the (n − 1)-track seed vertex to construct an n-track DV. A mass
template is constructed by repeating the process many times. The concentric circles
represent a simpliﬁcation of a radial region of the ﬁducial volume.

73

Arbitrary Unit

Arbitrary Unit

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

0.12
0.1
0.08

Region 0+1

Region 2+3

Region 4+5

Region 6+7

Region 8+9

Region 10

0.06
0.05
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Region 11

0.03

0.04

0.02

0.02

0.01
−3

−2

−1

0

1

Region 2+3

Region 4+5

Region 6+7

Region 8+9

Region 10

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0.06

0Region 0+1

2

0

3

−3

−2

−1

0

1

2

Track η(b) Track φArbitrary Unit

Arbitrary Unit(a) Track η
0.35
0.3
0.25
0.2

3

Track φ [rad]Region 0+1

Region 2+3

Region 4+5

Region 6+7

Region 8+9

Region 10

Region 11

0.45
0.4

Region 0+1

Region 2+3

0.35

Region 4+5

Region 6+7

0.3

Region 8+9

Region 10

Region 11

0.25
0.2

0.15

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−3

−2

−1

0

1

Track Δη

Arbitrary Unit(c) Track Δη

2

3

Track Δφ [rad](d) Track Δφ

10
1
10−1

Region 0+1

Region 2+3

Region 4+5

Region 6+7

Region 8+9

Region 10

Region 11

10−2
10−3
10−4
10−5
0

2

4

6

8

10 12 14 16 18 20
Track p [GeV]T(e) Track pT

Figure 5.24: The properties η, φ, Δη, Δφ, pT of tracks in the track templates for eachregion (Δ means with respect to the PV-DV direction). Several adjacent radial regions
are merged because it is too dense to show 12 histograms overlaid. The central dips inΔφ distributions come from a requirement that only tracks with d0 > 2 mm are used forsecondary vertexing.

74

Crossing Factor

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

0.004
0.0035s = 13 TeV, L = 32.7 fb-1

0.003
0.0025

Crossing Factor

0.002
0.00150.001
0.0005
0
0

50

100

150

200

250

300

R [mm]

Figure 5.25: Crossing factor for the twelve radial region for 2016 data. The factors arecalculated by normalising the model to data in the control region, for vertices with three
tracks and mass larger than 10 GeV. The error bars represent the statistical uncertainties.

The ﬁrst part constructs a mass template for each radial region by looping over all seedvertices and then sampling a random track from the track template of the corresponding
region. This is done for all n-track multiplicities of the seed vertices. For the second
step, a simple method is used to estimate the probability of having a randomly crossing
track, denoted as a crossing factor. The 3-track control region is used, i.e. the (2+1)track mDV template is normalised to ﬁt the high-mass region (mDV > 10 GeV) of the
3-track DV spectrum of the data. The extracted crossing fractions are shown in Fig. 5.25
for all radial regions. The resulting invariant mass spectra, after applying the crossing
fraction, are able to reproduce the shape of the high-mass distribution from data in the
CR (3-track DVs) as shown in Fig. 5.26 and 5.27.
Applying the crossing fractions to models of (3+1)-track (or higher track) DVs mass
spectra, the number of 4-track (or higher track) DVs from random crossing tracks canbe estimated. The estimated number of vertices from random crossing tracks with themass of mDV > 10 GeV integrated over all regions is summarised in Tab. 5.4. Tab. 5.4
contains the estimations of hadronic interaction and merged vertices as well.
The background estimation method (including the crossing fractions) is validated
in the two VRs. The two following sections discuss the details of validation of the
background estimation.

5.7.4

Validation of the Background Estimation

The crossing factors are estimated in the 3-track control region. The number of 5 (ormore track) DVs in the signal region can be estimated by applying the crossing factors
to the templates of 4+1 (or 5+1, ...) track DVs and integrating them over the mass
range above 10 GeV. However, the method itself needs to be validated before going into
the signal region. Although it is a straightforward to use 4-track DVs as a validation
region, this region could suﬀer from signiﬁcant signal contamination and thus cannot be
used for the validation without additional requirements. Here, two sets of requirements
are used to create validation regions. The ﬁrst set of requirements are an upper limit
miss and a relative azimuthal angle between jets and E miss . This low-E miss VR is
on ET
T
T
denoted as “VRLM”. The second region is made up of vertices in regions dominated by
the detector materials and is denoted as “VRM”. This region is enriched in hadronic

75

Number of Vertices / 0.2 GeV

310

ATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 0 < R < 22 mm
Observed 3-track vertices

10

Predicted (2+1)-track vertices

1
10− 1
10− 2

1.5
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0.5
0

10

20

30

40

50

60

70

80

90

100

ATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 22 < R < 25 mm

10Observed 3-track vertices

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Predicted (2+1)-track vertices

10− 1
10− 2

Data/Model

Data/Model

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Number of Vertices / 0.2 GeVATLAS Preliminary-1

s = 13 TeV, L = 32.7 fb , 25 < R < 29 mm

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10− 1

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10Observed 3-track vertices

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−1

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Data/Model

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90

(b) around Beam pipe (22 < R < 25 mm)

1.5
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80

90

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mDV [GeV]

mDV [GeV](c) inside IBL (25 < R < 29) mm)(d) around IBL (29 < R < 38 mm)

10Number of Vertices / 0.2 GeV

3ATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 38 < R < 46 mm
Observed 3-track vertices

10

Predicted (2+1)-track vertices

1
10− 1
−2

10

Data/Model

Data/Model

Number of Vertices / 0.2 GeV

Data/Model

Number of Vertices / 0.2 GeV(a) inside Beam pipe (R < 22 mm)
102

80

mDV [GeV]

1.5
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80

90

100

mDV [GeV]

3

ATLAS Preliminary

10s = 13 TeV, L = 32.7 fb-1, 46 < R < 73 mm

2

10Observed 3-track vertices

10
Predicted (2+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

mDV [GeV](e) inside B-Layer (38 < R < 46 mm)(f) around B-layer (46 < R < 73 mm)

Figure 5.26: 3-track mDV distributions of 2016 data for regions 0–5. The modelled
distributions are normalised to data by use of the high-mass range e.g. mDV > 10 GeV.
The modelled vertices reproduce the high-mass shape distribution of the data.

76

Number of Vertices / 0.2 GeVATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 73 < R < 84 mm

10

Observed 3-track vertices
Predicted (2+1)-track vertices

1
10− 1
−2

10

1.5
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20

30

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60

70

80

90

3

10

ATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 84 < R < 111 mm

100

Observed 3-track vertices

10

Predicted (2+1)-track vertices

1
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Data/Model

Data/Model

Number of Vertices / 0.2 GeV

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1.5
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mDV [GeV]

Number of Vertices / 0.2 GeV

3ATLAS Preliminary102

s = 13 TeV, L = 32.7 fb-1, 111 < R < 120 mm
Observed 3-track vertices

10

Predicted (2+1)-track vertices

1
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10

1.5
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100

s = 13 TeV, L = 32.7 fb-1, 120 < R < 145 mm

2

10Observed 3-track vertices

10
Predicted (2+1)-track vertices

1
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70

Number of Vertices / 0.2 GeVATLAS Preliminarys = 13 TeV, L = 32.7 fb-1, 145 < R < 180 mm
Observed 3-track vertices
Predicted (2+1)-track vertices

1
10− 1
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10

1.5
1
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(d) around Layer-2 (120 < R < 145 mm)

Data/Model

Number of Vertices / 0.2 GeV

Data/Model

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mDV [GeV](c) inside Layer-2 (111 < R < 120 mm)

102

100

ATLAS Preliminary

310mDV [GeV]

1090(b) around Layer-1 (84 < R < 111 mm)

Data/Model

Data/Model

Number of Vertices / 0.2 GeV(a) inside Layer-1 (73 < R < 84) mm
1080

mDV [GeV]

100mDV [GeV]

3

10

ATLAS Preliminarys = 13 TeV, L = 32.7 fb-1, 180 < R < 300 mm

102

Observed 3-track vertices

10

Predicted (2+1)-track vertices

1
10− 1
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1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

mDV [GeV](e) inside octagonal support (145 < R < 180mm)(f) inside 1st SCT Layer (180 < R < 300 mm)

Figure 5.27: 3-track mDV distributions of 2016 data for regions 6–11. The modelled
distributions are normalised to data by use of the high-mass range e.g. mDV > 10 GeV.
The modelled vertices reproduce the high-mass shape distribution of the data. The error
bars in the mass distributions and the grey bands in the bottom ratio distributions show
the statistical uncertainties.

77

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Table 5.4: Total number of estimated background vertices with a mass mDV > 10 GeV
in the control, validation and signal regions, using the 2016 full integrated luminosityof 32.7 fb−1 . The numbers shown are obtained before applied the event-level transfer
factors.
Control and Validation Regions
3 Track DV
4 Track DV(2 + 1) Track(3 + 1) Track (2 + 2) Track
Pure 4 Track
Estimation 3093 (Normalisation)
12.6 ± 0.3
3.64 ± 3.64
0.3 ± 0.9Signal Region (before applying event-level transfer factor)
5 Track DV(4+1) Track(2+3) Track Pure 5 Track
Estimation
1.3 ± 0.07
0.01 ± 0.01
0.9 ± 2.8
6 Track DV
7 ≥ Track DV(5+1) Track
Pure 6 Track (i + 1) Track Pure 7 ≥ Track
Estimation
0.37 ± 0.03
0.18 ± 0.58
0.37 ± 0.03
1±3interactions by inverting the material veto requirement. In this region, it is expected
to collect the DVs from instrumental eﬀects more eﬃciently than the signal DVs oflong-lived particles. Assuming that the number of vertices arising from random crossing
tracks can be factorised into the product of the crossing factor and the number of “seed”
vertices, an increase of the hadronic interaction vertices leads to a linear increase of thevertices from random crossing tracks. Therefore the VRM region allows for validationof the methodology used for the random-track crossing estimate with large statistics. In
this sense, the VRM is complementary to the VRLM.
miss Validation Region - VRLM
Low-ET

Since non-negligible amounts of signal events would contaminate a simple 4-track data
samples, a region with additional requirements for reducing the fraction of signal events is
miss would eliminate signal events with large
used for validation. An upper limit on the ET
missmass diﬀerence between a gluino and the lightest neutralino to a large extent. The ET
cut is not eﬀective for signal events in small mass diﬀerence scenarios due to the small
miss . Instead an additional requirement is placed on the minimum
amount of intrinsic ET
miss and the reconstructed jets in theazimuthal angle between the oﬄine calibrated ET
event, Δφmin . Much of the background for this analysis originates from QCD multi-jet
miss , and thus theevents. The energies of jets are occasionally mis-measured yielding ET
Δφmin of such events is peaked at 0 and ±π. On the other hand, signal events with
miss are more likely to obtain larger values of Δφsmall intrinsic ET
min . For this analysis,
this variable is calculated using all jets with pT > 30 GeV which passed the baseline jet
miss and Δφselection described in Section 5.5.6. Distributions of the ET
min are shown fordata and various signals in Fig. 5.28 where the discrimination powers can be seen.
In order for a validation in VRLM to be valid in the SR as well, it must be shown thatmiss and Δφthe DV properties are uncorrelated with both of ET
min . The distributions formiss and Δφthe DV mass and track multiplicity are shown in slices of ET
min in Fig. 5.29.
The tails of the distributions are normalised to the same integral. These plots show only
miss and Δφa tiny dependence on ET
min . Therefore, it should be reasonable to test themiss and Δφbackground estimation method using a part of data with selections on ET
min .
78

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Data
gg 1400 100 1 ns
gg 1400 600 1 ns
gg 1400 800 1 ns
gg 1400 1270 1 ns
gg 1400 1320 1 ns
gg 1400 1350 1 ns
gg 1400 1370 1 ns

102
10
1

Data
gg 1400 100 1 ns
gg 1400 600 1 ns
gg 1400 800 1 ns
gg 1400 1270 1 ns
gg 1400 1320 1 ns
gg 1400 1350 1 ns
gg 1400 1370 1 ns

1

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100 200 300 400 500 600 700 800 900 1000

0

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2

2.5

Offline Missing E [GeV]

3

3.5

4

4.5

5

min Δφ(Jet[all], MET)

T

a.u.

a.u.

Figure 5.28: Normalised distributions are shown for data and various signals.

104
10

Data 0-100 GeV

Data 200-300 GeV

Data 300-400 GeV

Data 300-400 GeV

10402074 0-100 GeV

10402074 0-100 GeV

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mDV [GeV]

miss (top)Figure 5.29: The properties of the DV candidates are shown as a function of ET
and Δφmin (bottom). DV mass (right) and track multiplicity (left) are shown. The
track multiplicity plots are normalised to the area above 3 and the mass distributions
are normalised to the area above 3 GeV.

79

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS  -.%).#
)*!$*!&%
* &$!%123$!%123

 -#,0#"3

 

3+*0!%.(&$("!)*(!+*!&%)

 
 &$'()*!$*,!* * 


!%#'&'+#*(!&%

!%#'&'+#*(!&%

Figure 5.30: A qualitative diagram of the VRLM design is shown.

Since the correlation between DV properties and these variables is negligible, theestimation of 4-track DV in VRLM can be derived by scaling the estimation of 4-track
DV in an original VR (16.5 ± 3.8 as shown in Tab. 5.4). The eﬃciency of passing themiss < 150 GeV and ΔφVRLM requirements of ET
min < 0.75 is measured in the 3track control region to be 1854/3066 = 60.47%. The 4-track estimate in VRLM is then
(16.5 ± 3.8) × 60.47% = 10.0 ± 2.3 events expected. The observed number of 4-track
DVs in VRLM is 9 and these are consistent. A diagram summarising how the region isdeﬁned and where the various quantities are measured is shown in Fig. 5.30.
The levels of signal contamination expected in this region are shown in Fig. 5.31 forvarious gluino masses, neutralino masses and lifetimes. For the signal scenarios withmg̃  O(1) TeV that were not excluded by Run-1 results, signal contamination for thisregion is at most ∼ 10% level although signal events were rather dominated before theselections.
Material-dominated Validation Region - VRM
When the material veto requirement is inverted, i.e. only vertices in the dense materialdominated regions are selected, the contributions from hadronic interactions increase
dramatically. Just like the DVs from in-ﬂight decays, these vertices can also be crossed
by a random track. The amount of vertices with randomly crossing tracks is proportional
to not only the track density but also the number of seed vertices. As the acceptancehas been highly reduced, the contribution from the signal vertices to that region aregoing to be reduced also, allowing to obtain a region with high statistics but with low
signal contamination. Figures 5.32 and 5.33 show 3-track mDV distributions of 2016 data
along with the predictions from the random-track model using the inverted material vetorequirement. One can see that the predictions agree well with data in the material-rich
80MC τ=0.01 ns
MC τ=0.04 ns

106
105
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2016, s=13 TeV, Simulation∫L dt=3. fb-1

MC τ=0.10 ns
MC τ=0.40 ns
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MC τ=10.00 ns

102

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CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

2500

ATLAS
s = 8 TeV, 20.3 fb-1

2000 Split SUSY Model

Expected limit (± 1 σexp)
Observed limit (± 1 σSUSY)theory∼ (100 GeV) ][~g → g/qq χ
01

95% CL limit

1500

MC τ=50.00 ns
Data

10
1

1000

10−1
10−2
10−3 500

500

1000

1500

2000

1

102

10

m~g [GeV](a)103cτ [mm](b)

Figure 5.31: (a) Signal yields are shown (markers) as a function of R-Hadron lifetime(shape) and gluino mass (x-axis). Those signal models with a 100 GeV LSP are shownin black. For reference, the yield in VRLM in data is shown in the dashed black line.
For the signal scenarios with mg̃ > 1000 GeV that were not excluded by Run-1 results,
signal contamination for this region is at most ∼ 10% level. (b) For convenience, theRun-1 exclusion limits are shown for models with a 100 GeV LSP [32].

regions as well. Region 0, 6 and 10 (see Fig. 5.21) are excluded in the plots because thevolume vetoed by material map in those regions is tiny.
In addition, Fig. 5.34 and 5.35 show the same distributions for 4-track DVs. The
high-mass tails are well modelled by the orange mass templates.
Summary of the observed and expected numbers of 4-track DVs with mDV > 10 GeV
in the regions with inverted material veto is shown in Fig. 5.36(a). The agreement
between data and estimation is good in this region. The observed number of DVs thereis 177. The expected number of DVs from randomly crossing tracks is 137.4±2.9 (stat.)±29.8 (syst.). The diﬀerence between these numbers could be explained by contributionof hadronic interactions as in the following paragraph.
Figure 5.36(b) shows the summation of the 4-track mDV distributions. The number of
DVs from hadronic interaction is estimated by ﬁtting this using an exponential functionand extrapolating it to mDV > 10 GeV. The estimated number of DVs from hadronicinteractions is 16 ± 1 (stat.). The sum of these numbers are consistent with the observed
number of DVs and the background estimation method has been validated in VRM.
Signal contamination in this VR is evaluated in Fig. 5.37. The event yields of signal
samples which are not excluded yet (mg̃  1 TeV) are below 10% level of the event yieldof data, irrespective of the LSP mass and the gluino lifetime.

5.7.5

Systematic Uncertainties on Background Estimation Methods

Hadronic Interaction
The validity of the exponential assumption used in the estimation of hadronic interaction is tested in a truth-level study using the Geant4-based simulation of hadronicinteractions. Using Pythia8 dijet samples, the truth-level mass distributions of hadronic interactions are studied in bins of vertex track multiplicity. When ﬁtting the mass
distribution to an exponential in the range 5-10 GeV and extrapolating to the region for81

Number of Vertices / 0.2 GeV

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mDV [GeV](c) around IBL (29 < R < 38 mm)

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104

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mDV [GeV](d) inside B-Layer (38 < R < 46 mm)

5

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s = 13 TeV, L = 32.7 fb-1, 46 < R < 73 mm

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102
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mDV [GeV](e) around B-layer (46 < R < 73 mm)

Figure 5.32: 3-track mDV distributions of 2016 data with inverted material veto requirement for regions 1–5. The modelled distributions are normalised to data by use of thehigh-mass range e.g. mDV > 10 GeV. The model reproduces shape of the distributionof the data at high mass well.

82

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mDV [GeV](c) around Layer-2 (120 < R < 145 mm)(d) inside 1st SCT Layer (180 < R < 300 mm)

Figure 5.33: 3-track mDV distributions of 2016 data with inverted material veto requirement for regions 7-9 and 11. The modelled distributions are normalised to data by use of
the high-mass range e.g. mDV > 10 GeV. The model reproduces the shape of the highmass region of the distribution for the data well. The error bars in the mass distributions
and the grey bands in the bottom ratio distributions show statistical uncertainties only.

83

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3

10

s = 13 TeV, L = 32.7 fb-1, 25 < R < 29 mm

102

Observed 4-track vertices

10
Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

mDV [GeV]

Number of Vertices / 0.2 GeV

104
3

s = 13 TeV, L = 32.7 fb-1, 29 < R < 38 mm

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

mDV [GeV]

Number of Vertices / 0.2 GeV

100

3

10

s = 13 TeV, L = 32.7 fb-1, 38 < R < 46 mm

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

mDV [GeV](c) around IBL (29 < R < 38 mm)

Data/Model90(b) inside IBL (25 < R < 29) mm)

Data/Model

Data/Model

Number of Vertices / 0.2 GeV(a) around Beam pipe (22 < R < 25 mm)

1080

mDV [GeV](d) inside B-Layer (38 < R < 46 mm)

104
s = 13 TeV, L = 32.7 fb-1, 46 < R < 73 mm

3

10

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

mDV [GeV](e) around B-layer (46 < R < 73 mm)

Figure 5.34: 4-track mDV distributions of 2016 data with inverted material veto requirement for regions 1–5. The modelled distributions are normalised to data by use of thehigh-mass range e.g. mDV > 10 GeV. The model reproduces the shape of the high-mass
region of the distribution for the data well.

84

Number of Vertices / 0.2 GeV

104
3

10

s = 13 TeV, L = 32.7 fb-1, 84 < R < 111 mm

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

102
s = 13 TeV, L = 32.7 fb-1, 111 < R < 120 mm

10

100

Observed 4-track vertices

1

Predicted (3+1)-track vertices

−1

10

10− 2

Data/Model

Data/Model

Number of Vertices / 0.2 GeV

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1.5
1
0.5
0

10

20

30

40

50

60

70

80

mDV [GeV]

Number of Vertices / 0.2 GeV

3

s = 13 TeV, L = 32.7 fb-1, 120 < R < 145 mm

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

70

80

90

100

(b) inside Layer-2 (111 < R < 120 mm)

Data/Model

Data/Model

Number of Vertices / 0.2 GeV(a) around Layer-1 (84 < R < 111 mm)
1090mDV [GeV]

100

3

10

s = 13 TeV, L = 32.7 fb-1, 180 < R < 300 mm

102

Observed 4-track vertices

10

Predicted (3+1)-track vertices

1
10− 1
10− 2

1.5
1
0.5
0

10

20

30

40

50

60

mDV [GeV]

70

80

90

100

mDV [GeV](c) around Layer-2 (120 < R < 145 mm)(d) inside 1st SCT Layer (180 < R < 300 mm)

Number of Vertices

Figure 5.35: 4-track mDV distributions of 2016 data with inverted material veto requirement for regions 7-9 and 11. The modelled distributions are normalised to data by useof the high-mass range e.g. mDV > 10 GeV. The model predictions match the shapeof the high-mass region of the distribution for the data well. The error bars in themass distributions and the grey bands in the bottom ratio distributions show statisticaluncertainties only.

105

240
220
s = 13 TeV, L = 3. fb-1

200
180

Observed

160

Predicted (Stat.)104

Predicted (Syst.)

140

103

120
100

102

80
60
40

10

20
0
0

50

100

150

200

250

300

0

2

4

6

8

10

R [mm]

(a)

12

14

16

18

20

Invariant Mass [GeV](b)

Figure 5.36: (a) Summary of the observed and expected numbers of 4-track DVs withmass above 10 GeV in the regions with inverted material veto. Region 0, 6 and 10 are
excluded in this ﬁgure because too tiny volume is vetoed by material map there. (b)The summation of the 4-track mDV distributions in Figure 5.34 and 5.35. The red line
represents a ﬁtted exponential function.

85

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Figure 5.37: Yields of data and R-hadron pair production events in the additional VR
with inverted material veto requirement. The horizontal dashed line represents the yieldof data. The black markers show event yield of each sample with the lightest neutralinomass of 100 GeV. The green markers show event yield of each sample but the lightest
neutralino mass is not 100 GeV. For the signal scenarios with mg̃ > 1000 GeV that were
not excluded by Run-1 results, signal contamination for this region is at most ∼ 10%
level.
mDV > 10 GeV, a deviation of approximitely 300% is seen between the integral of theﬁt function and the truth level distribution. As a result, an additional 300% uncertainty
is added to the estimate of hadronic interactions. With this additional uncertainty, thehadronic interaction estimates become 0.3 ± 0.9 for 4-track DVs, 0.9 ± 2.8 for 5-track
DVs, 0.18 ± 0.58 for 6-track DVs and 1 ± 3 for ≥ 7-track DVs. The details of this study
can be found in Appendix A.
Random Crossing Track
The crossing fractions are derived using the number of vertices with the mass above
10 GeV to normalise the mass spectra of model to that of data for all the twelve regions.
However, if the shape of model distribution does not perfectly agree with data, an uncertainty on the model will enter into the background estimation. The eﬀects can be
estimated by varying the mass interval ±5 GeV used to estimate the crossing fractions.
This gives an estimate of how stable the crossing fraction is and an uncertainty of the
shape of the model as shown in Fig. 5.38. The systematic uncertainties on the ﬁnal
estimates are summarised in the next section.

5.8

Results

5.8.1

Total Background Estimate and Event-Selection Transfer Factor

The output of the background estimation techniques, the total number of vertices, integrating over all regions for vertices with a mass larger than 10 GeV, is shown in Tab. 5.5.

86

Crossing Factor

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

0.004
0.0035

Crossing Factor (M > 5 GeV)

0.003

Crossing Factor (M > 10 GeV)
Crossing Factor (M > 15 GeV)

0.00250.002
0.0015
0.001

Ratio

0.0005

1.5
1
0.5
0

50

100

150

200

250

300

R [mm]
Figure 5.38: Crossing factors which are derived from diﬀerent mDV intervals for ﬁtting
mass template to data in each region in 2016. Black dots show the crossing factors innominal setting (using data points in mDV > 10 GeV for ﬁtting, red dots are those with
mDV > 5 GeV cut, and green dots are those with mDV > 15 GeV cut.

The SR was blinded until the background estimation became convincing. These estimates represent the expected number of selected vertices (i.e. not number of events) basedon the CR selections as deﬁned in Tab. 5.2.
In order to obtain an estimate for the number of events in the signal region, twoconversions must be made. One must account for diﬀerence of the acceptances between
the CR selections and the SR selections used for the signal region events. Multiplying
the estimate by the ratio of the yields for the two selections accounts for this eﬀect.
The second consideration is the conversion from a vertex-level estimate to an eventlevel estimate for the sake of interpretations. This is, ideally, the ratio of the numberof vertices observed in the SR selections to the number of events observed in the SR
selections. Unfortunately, this was not accessible when the signal region was blinded, so
a proxy is used: the ratio of the number of vertices in the CR selections to the numberof events in the CR selections. The degree to which this is an appropriate proxy will betaken as a systematic.
The steps above are summarised in Eq. (5.3).
 DV −1
NFEvent
NF ullEvent
DVull= NBase × Event ×
NSR
NBase
NFEventull DV −1
Event
N ull
NBase
DV
≈ NBase× FEvent
×
,
(5.3)
Event
NBase
NBase
where N Event and N DV are the number of events and DVs after certain selections,
respectively. The subscript Base indicates that the number is one after the CR selections
and the subscript Full indicates that the number is the one after the SR selections except87CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

Table 5.5: Total number of estimated background vertices with a mass mDV > 10 GeV forthe vertex selections used in the control, validation, and signal regions. The (n + 1)-trackcontributions are estimated using the accidental-crossing factor method (Section 5.7.3),
the (n + 2)-track contribution is obtained from merged vertices (Section 5.7.2), and thepure n-track estimation is evaluated using the hadronic interactions (Section 5.7.1). The
control region yield is normalised to data. Also shown are the estimated background
event yields in the pre-selection region with at least 5 tracks. The predicted backgroundyield in the full signal region appears in the bottom row, and includes the transfer factors
shown.
Vertex Selection

Sub-RegionCR, 3-track

3093 (Normalised)vrlm(3 + 1)-track(2 + 2)-track
Pure 4-track
Sub-total
Selection eﬀ. corr.
Total

12.6 ± 0.3 ± 1.1
3.64 ± 3.64
0.3 ± 0.9
16.5 ± 3.9( . . . × [56 ± 6]% )
9±2

vrm

(3 + 1)-track
Pure 4-track
Total

137.4 ± 2.9 ± 29.8
16 ± 47
153 ± 55.7

5-tracks(4 + 1)-track(2 + 3)-track
Pure 5-track
Total

1.3 ± 0.07 ± 0.12
0.01 ± 0.01
0.9 ± 2.8
2.2 ± 2.8

6-tracks(5 + 1)-track
Pure 6-track
Total

0.37 ± 0.03 ± 0.04
0.18 ± 0.58
0.55 ± 0.58

≥ 7-tracks(n + 1)-track
Pure ≥ 7-track
Total

0.37 ± 0.03 ± 0.04
1±3
1.4 ± 34.2 ± 4.1

Total

Full SR event& Vertex selection

Estimated(2 + 1)-track

VRs, 4-track

SR-like, ≥5-track

Background component

Event selection transfer factor
Vertex-to-event transfer factor( . . . × [5.08 ± 2.56] × 10−3 )( . . . × [1.0 ± 0.16] )0.02 ± 0.02

Total

88

Double Ratio

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

4
2trk-DVs(cut)/2trk-DVs(base)
Events(cut)/Events(base)

3.5
3

5HTXLUHat least 1 DV

3trk-DVs(cut)/3trk-DVs(base)
Events(cut)/Events(base)4trk-DVs(cut)/4trk-DVs(base)
Events(cut)/Events(base)

2.5≥ 5trk-DVs(cut)/ ≥ 5trk-DVs(base)
Events(cut)/Events(base)

2
1.5
1
0.5
0

Base

Trigger

Filter

MET250Figure 5.39: Cut ﬂow showing how the number of displaced vertices per event changes
with applied selections. The horizontal axis shows the cut level and the vertical axis
shows the double ratio of the number of DVs and events after the full selections to thoseafter the base (CR) cuts. If there is no correlations between the number of DVs andevents, the double ratio would lie on unity. The discrepancies from unity are taken as
systematic uncertainty of the event selection transfer factor.

for the cuts on mDV and the number of associated tracks (see Tab. 5.2). The second
factor in Eq. (5.3) is found to be 5.08 × 10−3 (±0.02 × 10−3 [stat.]). The third factor
is found to be 1.0. The degree to which the approximation in Eq. (5.3) is valid can bequantiﬁed by studying the double ratio
Event
DV
NFDV
NFDV
ull /NBase
ull /NF ull=.
DV /N Event
Event
NBase
NFEventBaseull /NBase(5.4)

This double ratio as a function of the cut level is shown in Fig. 5.39 for diﬀerent DV
track multiplicities. The deviation from unity suggests that a 50% uncertainty accounts
for the degree to which the assumption holds. An additional uncertainty comes fromthe dependence of the third factor in Eq. (5.3) on the properties of the reconstructed
DVs. The number of vertices per event as a function of the mass and track multiplicityof the vertices in the CR is shown in Fig. 5.40. It is shown that the number of DVs per
event is 1.0 for DVs with any masses and at least 3 associated tracks. For 2-track DVs,
the value varies up to 1.16. This 0.16 diﬀerence is taken as the systematic uncertainty
conservatively. This gives a total scaling factor of 5.08 × 10−3 ± 2.56 × 10−3 .
With this, the ﬁnal nominal estimate for the number of events in the signal region is
EventsNSR= [4.2 ± 4.1] × [ 5.08 × 10−3 ± 2.56 × 10−3 ]= 0.02 ± 0.02

(5.5)

Table 5.6 summarises the estimates described above and the observed numbers. Figure 5.41 shows the two-dimensional distribution of mDV and track multiplicity for DVs
in events that pass all signal region event selection criteria. Drawn numbers correspond to
89

1.25

6
5.5
5

1.2

4.5

NDV per Event

NTrack > y

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

1.15

4
3.5
3

1.1

2.5
1.05

2
1.5
1
0

2

4

6

8

10

12

1

mDV > x GeV

Figure 5.40: Number of DVs per event as a function of DV mass and track multiplicity.
The dark blue region with NTrack > 2 indicates that the bin entries are unity there.

Table 5.6: The observed results for the control, validation, and signal regions are shown
along with the background expectations for the 32.7 fb−1 of data collected in 2016.
Vertex Selection

Sub-Region

Estimated

CR, 3-track

VRs, 4-track

SR-like, ≥5-track

Full SR event& vertex selection

Observed
3093

vrlm
vrm

9±2
153 ± 56

9
177

5-tracks

2.2 ± 2.8

1

6-tracks

0.55 ± 0.58

1≥7-tracks

1.4 ± 3.0

3

Total

4.2 ± 4.1

5

Total

0.02 ± 0.02

090mDV [GeV]

CHAPTER 5. THE DISPLACED VERTEX ANALYSIS

5
4

2

10

1

12
5
31

1

44

1

83
155

10

1

382

2

796

3

1465

8

2152

3

10−1

2797

6

3465

13

4135

15

1

1

4788

10

6

3

3346

14

7

1482

14

1

778

22

1

3

2

4

10−2

1

5 6 7 8 910

20
30 40 50
Number of Tracks

Figure 5.41: The two-dimensional distribution of mDV and track multiplicity for DVs inevents that pass all signal region event selection criteria. Drawn numbers correspond tothe observations in data, while the colour-representation shows an example distribution
for an R-hadron signal MC sample with (mg̃ , mχ̃01 , τg̃ ) = (2000 [GeV], 100 [GeV], 1 [ns])as a reference. The red lines represent the boundary of the signal region requirements.
the observations in data, while the colour-representation shows an example distribution
for an R-hadron signal MC sample with (mg̃ , mχ̃01 , τg̃ ) = (2000 [GeV], 100 [GeV], 1 [ns])as a reference. The red lines represent the boundary of the signal region requirements.
The number of observed events in the signal region is 0 in the dataset used in thisanalysis. The observations are consistent with all the estimates of background events
within the uncertainties. Given the results, limit setting on parameter space of a SplitSUSY model will be discussed in the next chapter.

91

Chapter 6

Interpretation in Supersymmetry
6.1

Introduction

The ATLAS and CMS experiments have tested many models of physics beyond theStandard Model. The Minimal Supersymmetric Standard Model (MSSM) is one of themain targets of the experiments. Despite their enthusiastic eﬀorts, no evidence of new
physics has been observed and a wide range of parameter space has been excluded.
In setting limits in the parameter space, there are two main conceptual approaches
to statistics: Frequentism and Bayesianism. In the classical Frequentist approach, data
are regarded as a repeatable random sample and there is a frequency. Probability isinterpreted as the limit of a relative frequency in an inﬁnite number of trials given acertain hypothesis. In the latter Bayesian approach, data are rather ﬁxed and one canconsider probability of a hypothesis. Probability is then interpreted as a degree of belief
in the reliability of the hypothesis in a Bayesian view. It is arbitrary to choose one of
the approaches, or to make use of the hybrid of them. In this analysis, the Bayesian approach is adopted for estimation of credible interval of parameters of interest. Statistical
tools needed for this purpose is provided by the RooStats toolkit [116, 117], which wasdeveloped originally within the BaBar collaboration [118]. The 95% credible intervals
are calculated by integrating the posterior distribution from its mode downwards until
the interval has a 95% of whole probability contents. For the integration, a conventional
Markov-Chain Monte Carlo (MCMC) method is used in this analysis. A Markov Chainis constructed with the Metropolis-Hastings algorithm [119, 120].
The target signature is a pair production of long-lived gluinos which both form Rhadrons and decay to a pair of quarks and the lightest neutralino via squark exchange
expected in a Split-SUSY model. When the mass of squarks are ﬁxed at a certain
value (10 TeV in this dissertation), parameters of interest are just the gluino mass (mg̃ ),neutralino mass (mχ̃ 01 ) and gluino lifetime (τ ). Although each MC sample is generated ina conﬁguration of ﬁxed parameters, the eﬀective gluino lifetime of a sample is varied byapplying a proper weight. A method of the lifetime reweighting is described in Section 6.2
and a summary of systematic uncertainties on the signal eﬃciency is given in Section 6.3.
Given these information and the analysis results shown in Section 5.8.1, several limit plots
are illustrated and discussed in Section 6.4.

92

Event-level efficiency

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

1

2016, s=137H9, Simulation

0.8

reweighting method, τ=1 ns
simulated lifetime τim~g=2000 GeV, m∼ 0=100 GeV
χ1

0.6
0.4
0.2
0
1

10

102

103

104
cτ [mm]Figure 6.1: Closure test for the eﬃciency re-weighting procedure. A sample generated
with τ = 1 ns (cτ  300 mm) is re-weighted to give the blue curve (statistical uncertainty
considered only). This is compared with several samples with the same mass spectrum
but generated at diﬀerent τ = 0.01, 0.04, 0.1, 1, 10, 30 and 50 ns, (corresponding tocτ = 3.0, 12.0, 30.0, 300, 3000, 9000 and 15000 mm), which are represented as the redpoints. The ﬁgure shows the closure of the weighting treatment to within statisticaluncertainty in all the points considered.

6.2

Lifetime Reweighting

Signal MC samples used in this analysis have ﬁxed values of the average lifetime τ of thelong-lived particle. In order to evaluate the eﬃciencies for any values of τ , a simple reweighting method is used. Each event that passes the selection cuts (i.e. event-level cuts
and at least one DV passing all vertex selection criteria) is re-weighted by the probability
that both true long-lived particles would have been decayed with the given lifetime at
the decay positions in the particular event. The weight assigned for a given value of theaverage lifetime of a MC sample τMC and given true decay times ttrue
and ttrue
is,
1
2


 true true
t2
τMC 2
t1
ttrue
ttrue
true true1
2
w(t1 , t2 ) =
exp
,
(6.1)
exp
−
−
τtargetτMCτtargetτMCτtargetin order to reproduce a sample with lifetime of τtarget .
Figure 6.1 shows a comparison between the eﬃciency-vs-lifetime curve from this reweighting method, for an R-hadron sample with 2 TeV gluino and 100 GeV neutralino
at 1 ns, and diﬀerent samples simulated with diﬀerent lifetimes: 0.01 ns, 0.04 ns, 0.1 ns,
10 ns, 30 ns and 50 ns. The method shows validity of this reweighting method within
the statistical uncertainty.

6.3

Systematic Uncertainties on the Signal Eﬃciency

Eﬃciency-vs-lifetime relations can be derived with the lifetime reweighting method foreach parameter point. One must take account of additional “systematic” uncertainties
on the signal eﬃciencies. Three dominant sources of systematic uncertainties on tracking/vertexing performance, ISR/FSR modelling or pileup reweighting, are discussed inthis section.
93

Events / ( 3 MeV )Events / ( 3 MeV )CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

35000
30000
25000

Simulation, dijet JZ6W
Decay Length ∈ [5,10] mm|η| < 1mK Range: 351.5-648.5 GeV
S
σ: 6.50 (σ1: 5.15 σ2: 12.05)
χ2/dof: 2.68
Num KS: 106105 ± 364

20000
15000
10000
5000
0
350

400

450

500

550

600

650

22000
-1
20000
s = 13 TeV, Ldt= 6.8 fb
Decay Length ∈ [5,10] mm
18000 mK Range: 351.5-648.5 GeV|η| < 116000 σ2: 7.14 (σ1: 5.32 σ2: 13.68)
χ /dof: 2.77
14000 Num KS: 72365 ± 283
12000
10000
8000
6000
4000
2000
0
350
400
450
500
550
600
650

∫

S

Particle Mass (MeV)(a)

Particle Mass (MeV)(b)

Figure 6.2: An example of the double Gaussian ﬁt used to count the number of signal
KS0 on the barrel for the decay length interval 5-10 mm, for MC (a) and data (b). The
green line corresponds to the background-function, the red line is the ﬁt for the signal
while the blue lines are the combined ﬁt. Using a simultaneous ﬁt, the number of KS0
candidates are extracted.

6.3.1

Tracking/Vertexing Performance

To estimate the systematic uncertainty from the track reconstruction eﬃciency on thevertex reconstruction, the ratio of KS0 yields are compared for a few intervals of decay
radii. A deviation from unity for this ratio can be used to approximate the uncertainty
in the track reconstruction eﬃciency in MC. From the maximum discrepancy a trackkilling factor is derived which is then applied to MC and the vertexing algorithm isre-run, to estimate the eﬀect on the vertex reconstruction eﬃciency. The eﬃciency-vs-cτ
and eﬃciency-vs-R estimates are then made for the signal samples with the track-killing
fraction applied.
The data selected for this study has been obtained from the DRAW RPVLL 2016 data
sample described in section 5.2.1, in particular runs between 297447 and 303201 corresponding to 6.8 fb−1 . The MC samples used are dijet samples produced with Pythia8.
The number of KS0 candidates found in each interval of decay length, 5-10 mm, 1015 mm, 15-25 mm and 25-40 mm, are counted using a ﬁt. The ﬁt function for thiscounting is a combination of a double Gaussian for the signal and a polynomial function
for the background. Figure 6.2 show the ﬁt for MC and data in the barrel region and forthe interval 5-10 mm.
Since the KS0 production rate is not known in MC and data, the samples are individually normalised to the amount of KS0 seen at the smallest decay lengths. The maximum
i /Data0
discrepancy is then taken as the maximum deviation of the double ratio Data
M Ci /M C0 .
Figure 6.3 shows the ﬁnal result with the ratio for the barrel region (|η| < 1) and theendcap region (|η| ≥ 1), the maximum discrepancy is taken to be 10% in the barrel and
20% in the endcap. The ineﬃciency to reconstruct KS0 as a function of the ineﬃciency
in tracking can be calculated as following:(1 − KS ) = 2 · (1 − trk ) − (1 − trk )2(6.2)

The track-killing factor is estimated to the ﬁrst order as half the value of the maximum
94

1.6

Double Ratio Data/MC

Double Ratio Data/MC

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

1.5
1.4

∫

s=13 TeV, Ldt=6.8 fb

1.3

-1

|η| < 1

1.2
1.1
1

1.6
1.5
1.4

1

0.8

0.8

0.7

0.7
15

20

25

30

35

40

|η| ≥ 1

1.1
0.9

10

-1

1.2

0.9

0.6
5

∫

s=13 TeV, Ldt=6.8 fb

1.3

0.6
5

10

15

20

25

30

35

40

Ks proper decay length [mm]Ks proper decay length [mm]

(a)

(b)

Figure 6.3: Double ratio of number of KS0 found in MC and data individually normalised
to the number found at the smallest interval, for the barrel region (left) and endcap(right). The maximum deviation from one is taken as an conservative estimate of thesystematic uncertainty from the tracking eﬃciency.

deviation from one yielding 5% for |η| < 1 and 10% for |η| ≥ 1. The signal MC samples
are then re-reconstructed, using these values to randomly remove a fraction of tracks
before the vertexing step. The analysis is repeated on these “Track-Killed” samples, andthe diﬀerence between the “Nominal” and “Track-Killed” eﬃciency-vs-lifetime curves istaken as a systematic uncertainty. Figure 6.4 shows the track killing factor eﬀect overthe vertex reconstruction eﬃciency as a function of the radial position of the displaced
vertex for a couple of signal samples. The eﬀect of tracking systematic varies between
1-10% depending on diﬀerent grid points.

6.3.2

ISR and FSR Modelling

Initial State Radiation (ISR) and Final State Radiation (FSR) have a direct eﬀect on thesignal eﬃciency. Pythia6 samples are used in this analysis in order to use the speciﬁcpackage for modelling interaction of R-hadron. However, it is known that Pythia6 has
a problem in terms of modelling of ISR and FSR. As mg5 amcnlo simulate a moreaccurate description of radiative eﬀects, our Pythia6 samples are re-weighted to reproduce the distribution of pT (g̃g̃) from equivalent mg5 amcnlo samples. The diﬀerence
between the two generators is then used as a conservative estimate of the uncertainty
on the modelling of the radiations. Several mg5 amcnlo samples are compared to signal Pythia samples. To estimate the systematic uncertainties, the vector sum of thepT of the gluino-gluino system in both the Pythia and the mg5 amcnlo samples arecompared as can be seen in the left plot of Fig. 6.5 for a gluino mass of 1400 GeV. Thisshows that Pythia predicts less radiation. The right ﬁgure shows a weight function
extracted by taking the ratio of the left plot (done separately for all mass points). The
event weights are then applied to the Pythia6 R-hadron signal MC events in the nominal processing. The eﬀect of ISR/FSR systematic varies between diﬀerent mass points
miss from theand goes up to 30%. The eﬃciency for samples with smaller amount of ET
neutralino are more sensitive to the uncertainty on the ISR/FSR modelling.

95

1.6
1.4
1.2

εMC/0.6 mm

εMC/0.6 mm

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

Simulation, s=137H9m~g=2000 GeV, m∼ 0=100 GeV, τ=1 ns
χ1nominalkilling factor applied

1

1.6
1.4
1.2

χ1

0.8

0.6

0.6

0.4

0.4

0.2

0.2
50

100

150

200

250

m~g=2000 GeV, m∼ 0=1970 GeV, τ=1 ns
nominalkilling factor applied

1

0.8

0
0

Simulation, s=137H9

0
0

300

50

100

150

rMC
[mm]
DV

200

250

300

rMC
[mm]
DV

Weight (Madgraph/Pythia)

Figure 6.4: Vertex reconstruction eﬃciency for two MC signal samples, 402735 (left) and
402739 (right). The blue markers shows the eﬃciency distribution without the trackkilling factor and the red markers are with the track-killing factor applied.

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

102
103
p of Gluino-Gluino system [GeV]
T

(a)

(b)

Figure 6.5: (a) A vector summation of the transverse momentum for the gluino-gluino
system with 1400 GeV R-hadron for samples of Pythia in green and a mg5 amcnlo(MadGraph) in red. (b) A weight computed taking the ratio of the both samples.

96

Absolute Uncertainty [%]Relative Uncertainty

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

1.8
1.6
1.4

Gluino 1200 GeV, ΔM 1100 GeV
Statistical Error
Total Systematics
ISR
PRW
JET
MET
TRK

1.2
1
0.8

20
18

Gluino 1200 GeV, ΔM 1100 GeV
Statistical Error
Total Systematics
ISR
PRW
JET
MET
TRK

16
14
12
10
8

0.6

6

0.4

4

0.2
0
1

22

2
10

102

103

104
cτ [mm]

0
1

10

102

103

104
cτ [mm]Figure 6.6: Contributions to the uncertainty on eﬃciency vs lifetime for a sample with
1200 GeV gluino and 100 GeV LSP. The left plots are the relative uncertainties and theright plots are the absolute uncertainties.

6.3.3

Pileup Re-weighting

The standard ATLAS pileup re-weighting tool is used to weight the distribution of μfor MC samples to match that for data. The μ represents the average number of pp
interactions per bunch crossing. In this procedure, the event weights are obtained fromthe distributions of the μ observed in data. It varies this ±1σ around the mean value, μ ,of the μ-distribution in order to obtain distributions for the up and down variations. The
re-weighting procedure is applied using those distributions, taking the yield diﬀerenceswith respect to the nominal μ-distribution as systematic of the pileup re-weighting.

6.3.4

Summary of Uncertainties on the Signal Eﬃciency

Figure 6.6 shows the diﬀerent contributions to the uncertainty on the eﬃciency-vs-cτ .
The dominant uncertainty at small lifetimes is statistical, as a result of our re-weighting
procedure (only events with DVs decaying at small cttrue have signiﬁcant contributions).
Each simulated R-hadron signals sample has only 10k events. The breakdown of thediﬀerent contributions to the uncertainty is summarised in Tab. 6.7.
Since many of the systematic uncertainties (such as that associated with changing thescale factor for the pileup re-weighting) are evaluated by looking at the diﬀerence between
the “nominal” eﬃciency-vs-cτ and the eﬃciency-vs-cτ curve after some change (e.g. ISR
weight variation), there is a statistical component to these systematic uncertainties,
again, particularly at very small or very large lifetimes where individual events can havelarge weights.
In addition to the statistical uncertainty which dominates at small lifetimes, the ISRrelated uncertainty is also large in some cases, as a larger boost arising from the recoil
miss cuts. At
against an ISR jet can increase the fraction of events passing the jet or ET
large lifetimes, the uncertainty associated with the lifetime re-weighting can also be seenin Fig. 6.6.
Figure 6.8 shows the eﬃciency-vs-proper-decay-length distribution for a certain Rhadron sample. All considered systematic uncertainties are included.

97

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

ISR_Py2MG_SF_removed
Tracking efficiency
PRW_DATASF__1up
PRW_DATASF__1down
MET_SoftTrk_ScaleUp
MET_SoftTrk_ScaleDown
MET_SoftTrk_ResoPerp
MET_SoftTrk_ResoPara
JET_JvtEfficiency__1up
JET_JvtEfficiency__1down
JET_JER_SINGLE_NP__1up
JET_GroupedNP_3__1down
JET_GroupedNP_3__1up
JET_GroupedNP_2__1down
JET_GroupedNP_2__1up
JET_GroupedNP_1__1down
JET_GroupedNP_1__1up
JET_EtaIntercalibration_NonClosure__1down
JET_EtaIntercalibration_NonClosure__1up
Nominal−0.3

ISR_Py2MG_SF_removed
Tracking efficiency
PRW_DATASF__1up
PRW_DATASF__1down
MET_SoftTrk_ScaleUp
MET_SoftTrk_ScaleDown
MET_SoftTrk_ResoPerp
MET_SoftTrk_ResoPara
JET_JvtEfficiency__1up
JET_JvtEfficiency__1down
JET_JER_SINGLE_NP__1up
JET_GroupedNP_3__1down
JET_GroupedNP_3__1up
JET_GroupedNP_2__1down
JET_GroupedNP_2__1up
JET_GroupedNP_1__1down
JET_GroupedNP_1__1up
JET_EtaIntercalibration_NonClosure__1down
JET_EtaIntercalibration_NonClosure__1up

m~g = 1200 GeVmχ∼0 = 100 GeV

s = 13 TeV

10

τ = 1ns

Split-SUSY Model, g
χ1~ →qq ∼

−0.2

−0.1

0
(N

shifted0.1

Nominal

0.2

−0.3

0.3

m~g = 1200 GeVmχ∼0 = 1070 GeV

s = 13 TeV

10

τ = 1ns

Split-SUSY Model, g
χ1~ →qq ∼

−0.2

- Nnominal) / N

−0.1

0
(N

nominalshifted

0.1

0.2

0.3

- Nnominal) / N

nominalEvent-Level Efficiency [%]Figure 6.7: Pulls of the number of events passing the whole selections between nominaland shifted 1σ of each systematic source. The left plot is of a signal sample with gluinomass of 1200 GeV, the LSP mass of 100 GeV, R-hadron life time of 1 ns, while the rightplot is of that with gluino mass of 1200 GeV, the LSP mass of 1070 GeV, R-hadron life
time of 1 ns. Since the eﬃciency of a compressed scenario is signiﬁcantly gained by ISR
eﬀect, the dominant uncertainty source is ISR weighting from Pythia to MadGraph.

10080
M_g 1200 dM 110060
M_g 1200 dM 130

40
20
0
1

102

10

103

104
cτ [mm]Figure 6.8: Eﬃciency vs proper decay length for the qq R-hadron samples with 1200 GeV
gluino and 100 GeV or 1070 GeV neutralinos. All systematic corrections and uncertainties are included.

98

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

6.4

Exclusion Limits

Table 6.1 shows the number of events in data remaining after each of the selection cuts.
No events containing a massive displaced vertex with high track multiplicity have been
Table 6.1: Cut ﬂow table for 2016 data.

Initial Events
Good Runs List
Event cleaning
Primary vertex
NCB veto
MET Trigger
MET Filter
Oﬄine MET cut
Base DV selection
Full DV selection

Reco DVs
Event cuts
Fiducial acceptance
DV displacement
Fit quality
Material veto
Disabled module
DV nTrk
DV mass

Event Selection Cuts
Number of Events Relative Eﬃciency [%]75439504
100
73374312
97.3
73019704
99.5
73018496
100.04780144865.52858025659.8
285562510.0294614
10.3
45734
15.5
0
0.0
Vertex Selection Cuts
Number of DVs Relative Eﬃciency [%]41243944
100
1541400.37
13008784.4
12988699.8128491
98.9
53621
41.7
51876
96.7
6
1.2·10−20
0.0Overall Eﬃciency [%]
100
97.3
96.8
96.8
63.4
37.9
3.8
0.39
6.1·10−2
0.0Overall Eﬃciency [%]
100
0.37
0.32
0.31
0.31
0.13
0.13
1.5·10−5
0.0√
observed in the ATLAS dataset recoded in 2016 at s = 13 TeV corresponding to theintegral luminosity of 32.7 fb−1 . The estimated number of background DVs is 0.02 ± 0.02
as shown in Section 5.8.1. The results are interpreted in the context of the Split-SUSY
models (see Section 2.2.3). Given the values discussed so far, upper limits are set forthe production cross section σprod of a pair of gluinos which form R-hadrons and decay
into two quarks each. The mean expected number of events passing the selections N isformulated as:(6.3)
N = L · σprod · (cτ ),where , L is the integrated luminosity,  is the event selection acceptance. The integrated
luminosity used in this analysis is corresponding to 32.7 fb−1 . Its relative uncertainty
is 3.4%. It is derived from a preliminary calibration of the luminosity scale using x–y
beam-separation scans [121] performed in May 2016.
Figure 6.9 shows upper limits on the cross section for the decay, g̃ → q q̄ χ̃01 , for severalmg̃ values as a function of cτ . The left ﬁgure has a ﬁxed value for mχ̃01 = 100 GeV while
the right ﬁgure has a ﬁxed Δm = mg̃ − mχ̃01 = 100 GeV. The horizontal grey dashed lines
in the plot represent the theoretically given cross section for the gluino pair production,
pp → g̃g̃, with squarks decoupled. The mass of squarks are assumed to be 10 TeV
here. The grey bands represent the uncertainties of the cross sections. Parameter spacesurrounded by the grey line and the limit curve is excluded at 95% conﬁdence level.
99

104
m~g = 1400 GeV

103

s = 13 TeV, 32.7 fb-1

m~g = 2000 GeV
Observed
Expectedm∼χ = 100 GeV
0102
1400 GeV gluino production

102000 GeV gluino production

1

Upper limit on cross section [fb]Upper limit on cross section [fb]CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

104
m~g = 1400 GeV
310

s = 13 TeV, 32.7 fb-1

m~g = 2000 GeV
Observed
Expected

Δm = 100 GeV

1021400 GeV gluino production

102000 GeV gluino production

1

10−1
10−2

10−1

1

10−2

10

10−1

τ [ns](a)1

10
τ [ns](b)

Figure 6.9: Upper limit on cross-section vs decay length for the samples considered at
ﬁxed 100 GeV neutralino mass (a) and at ﬁxed Δm = 100 GeV (b).

The maximum sensitivity is achieved around cτ = O(10-100) mm where the Pixel
detector is placed. At the lower lifetime, long-lived particles likely to decay at the radiusless than 4 mm from primary vertex. Such vertices are not selected by the vertex selection
criteria as shown in Section 5.6.2. On the other hand, at the higher lifetime, long-lived
particles likely to decay outside of the ﬁducial volume of r < 300 mm and |z| < 300 mm(see Section 5.6.1). Even if particles decay within the ﬁducial volume, the vertices might
not be eﬃciently reconstructed due to relatively smaller tracking eﬃciency in a region
outer than the outermost Pixel layer (Pixel Layer-2) placed around r ≈ 122.5 mm. For
miss activity is also small, so that the event selection
the small Δm case (Fig. 6.9(b)), the ET
eﬃciency is not as high as large Δm scenario (Fig. 6.9(a)). These facts make the limit
curves in Fig. 6.9 as they are.
The 2D exclusion contours in Fig. 6.10 and Fig. 6.11 interpret the results in the mg̃ -cτ
and mg̃ -mχ̃0 planes, respectively. For the large Δm scenario with the ﬁxed neutralinomass of 100 GeV, the exclusion limit reaches ∼ 2400 GeV. A signiﬁcant gain by ∼800 GeV is achieved with respect to the previous search [32]. In addition, it is the ﬁrst
time to set the exclusion limit for scenarios with smaller Δm between a gluino and thelightest neutralino in the ATLAS experiment. The limit is set around 1600 GeV at the
maximum.
Figure 6.11 shows the 2D exclusion contour in a plane of mg̃ –mχ̃01 with τ = 1 ns.
One can see that this analysis has sensitivity in a compressed region where mg̃ –mχ̃01 is
missless than O(100) GeV. It is diﬃcult for typical SUSY search, such as multi-jets+ET
channel, to search this region due to lack of hard objects. It can be said that this analysis
is complementary to the other SUSY searches.
Figure 6.12 shows constraints on the gluino mass-vs-lifetime plane for a Split-SUSY
model with the gluino R-hadron decaying into light quarks and the lightest neutralinowith mass of 100 GeV for several searches. There are the displaced vertices result,miss result on the plot. It is shown
stopped gluino result, Pixel dE/dx result and jets+ETthat the displaced vertices search has better sensitivity than others when the gluino
lifetime is approximately between 0.01 ns and 10 ns.

100

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

mg~ [GeV]

Expected limit (±1 σexp)

s=13 TeV, L = 32.7 fb-11

3000

0
~
g → qq ∼χ @ m∼ 0 = 100 GeV
1χ

Observed limit (± 1 σSUSY)theorymg~ [GeV]

3000

4000

Expected limit (± 1 σexp)

2500

s=13 TeV, L = 32.7 fb-11
0~
g → qq ∼χ @ Δm = 100 GeV

Observed limit (± 1 σSUSY)theory

1

1

2000
2000

1500
1000

1000
−2 −1.5−1 −0.5

0

0.5

1

500

1.5

−2 −1.5−1 −0.50

0.5log (τ /ns)

1

1.5log (τ /ns)

10

10

104
s = 13 TeV, L = 32.7 fb-1

m g~ = 1400 GeV
m g~ = 2000 GeV
Observed
Expectedτ = 1 ns

1

103

3000

m∼χ0 [GeV]

Upper limit on cross section [fb]Figure 6.10: Excluded region in the gluino mass-vs-lifetime at ﬁxed neutralino mass
100 GeV (left), and at ﬁxed Δm = 100 GeV (right).

Expected limit (± 1 σexp)

s=13 TeV, L = 32.7 fb-11
0~
g → qq ∼χ @ τ = 1 ns

2000

102

Observed limit (± 1 σSUSY)theory1

1400 GeV gluino-pairr production

10
~

1000

2000 GeV gluino-pairo-pa productiono-p1

m ∼χ0 1

≤ mg

10−1
500

1000

1500

2000
mχ∼0 [GeV]
1

1000

1500

2000

2500
m~g [GeV]

Figure 6.11: (Left) Upper limit on cross-section vs mχ̃01 for the samples with mg̃ = 1400
or 2000 GeV. (Right) Excluded region in the gluino-vs-neutralino mass plane at ﬁxed
gluino lifetime τ = 1 ns.

101

CHAPTER 6. INTERPRETATION IN SUPERSYMMETRY

Lower limit on m ~g [GeV]0~g R-hadron → g/qq ∼χ ; m ∼χ0 = 100 GeV
1Status: March 2017

1

-1

2800

Displaced vertices ATLAS-CONF-2017-026 (33 fb , s=13 TeV))

2600

Jets+ET

Expected
Observed-1

Stopped gluino Phys. Rev. D88, 112003 (5.0,23 fb , s=7,8 TeV)
miss

-1

ATLAS-CONF-2017-022 (36 fb ,s=13 TeV)-1

Pixel dE/dx Phys. Rev. D93, 112015 (3.2 fb , s=13 TeV)

2400

95% CL limits
not included
σSUSY
theory-1Stable charged arXiv:1606.05129 (3.2 fb , s=13 TeV)

2200
2000
1800
1600
1400
1200

600

Stable800

Prompt

1000

10−2

10−1

1

10

(r for η=0, βγ =1) Beampipe Inner Detector Calo MS

10−3

10−2

10−1

1

10

103

102
102

104 τ [ns]103104cτ [m]

Figure 6.12: Constraints on the gluino mass-vs-lifetime plane for a Split-SUSY modelwith the gluino R-hadron decaying into light quarks and the lightest neutralino withmass of 100 GeV.

102

Chapter 7

Conclusion
The Standard Model of particle physics is generally regarded to be an incomplete theory
because of several shortcomings such as absence of dark matter, instability of the Higgs
potential or the fact that the strong force has not been uniﬁed with the electroweak
interaction yet. A number of extensions of the Standard Model has been suggested toprovide explanations to the unsolved problems. One of the most promising extensions of
the Standard Model is the supersymmetry (SUSY). A large number of SUSY searches
have been conducted typically using hard objects arising from a primary vertex as probes.
However, such searches do not have adequate sensitivity to long-lived particles which
decay at a distance from the interaction point.
Given the observed Higgs mass of ∼ 125 GeV, the mass of squarks is naively expected
to be much heavier than O(1) TeV that is basically beyond the reach of the LHC. A
Split-SUSY model matches this situation and it often predicts a gluino, supersymmetricpartner of gluon, to be long-lived. A long-lived gluino has colour charge so that it
hadronizes and forms into R-hadron state. If the mass diﬀerence between a gluino andthe lightest neutralino is as small as  100 GeV, the gaugino co-annihilation mechanism
would work to explain the observed relic density of dark matter as well.
In this dissertation, a search for direct production of long-lived gluino pairs whichforms R-hadrons in ﬁnal states with massive displaced vertices (DVs) with high trackmultiplicity and missing transverse momentum was presented. Proton-proton collision
data from the 2016 data taking period were analysed, corresponding to an integrated√
luminosity of 32.7 fb−1 collected at s = 13 TeV by the ATLAS detector at the LHC.
The following decay modes of the gluino was assumed to have 100% branching ratio:g̃ → q q̄ χ̃01

(7.1)

This analysis is aimed at scenarios with large mass-splitting between a gluino and neutralino as well as those with a smaller mass diﬀerence which have less acceptance becauseof non-energetic activities of visible particles.
Backgrounds arising from Standard Model particles are completely negligible when
DVs are required to be massive and have high track-multiplicity. Some experimentallyinduced backgrounds, such as vertices from hadronic interaction, merged by vertexingalgorithm and randomly crossed by a track, are dominant. The methods to estimate
the merged vertices and random crossing tracks are based on those used in the analysisof the LHC run-1 data. A method to estimate the hadronic interaction and a way tovalidate the estimation of random crossing tracks were newly developed in this analysis.
miss was developed in order toFurthermore, a new ﬁlter based on the calorimeter-level ET
improve the sensitivity to small mass diﬀerence scenarios.
103CHAPTER 7. CONCLUSION

The event counts observed after all event and vertex selections were found to be zero.
This is compatible with the expected number of background events 0.02 ± 0.02. The
results were, therefore, interpreted in terms of upper limits for diﬀerent assumptions ofgluino and neutralino masses and R-hadron lifetime. A large portion of parameter space
has been excluded at 95% conﬁdence level. The exclusion limit of gluino mass was set
up to 2400 GeV. There is a signiﬁcant gain compared to the previous Run1 limit whichwere set at 1600 GeV. In addition, a wide range of parameter space with a small massdiﬀerence between gluino and neutralino has been excluded up to ∼ 1600 GeV. It is theﬁrst time for the ATLAS to set a limit on this compressed scenario. Since this searchis almost background free, sensitivity to new physics is nearly proportional to statistics.
Further improvement of sensitivity is expected as the data taking proceeds.

104Appendix A

Hadronic interactions
Section 5.7.1 describes the method used to estimate the number of vertices produced byhadronic interactions which relies on the assumption that the low-mass component of the
distribution (given a number of tracks in the vertex) follows an exponential function. Thishypothesis is tested in this appendix by using an enriched region of hadronic interaction
vertices and studying their mass distributions.

A.1

Hadronic interactions in material-dominated detector
regions

An enriched hadronic interaction vertices is obtained by using the “Base” vertex selection but the material veto inverted. Figure A.1 shows the invariant mass distributions of
the vertices reconstructed in that region; an exponential function has been ﬁtted around
5 GeV, after the low mass peak. It can be observed that for the low track multiplicity there is a visible deviation from the exponential curves, which dilutes whenever the
track multiplicity is increased. That contribution is supposed to come from the randomcrossing tracks.
The random crossing probability is highly correlated with the track density, i.e. theprobability to attach a random track to a vertex increases whenever more tracks arepresent. Therefore, the random crossing tracks contribution in the tails of the distributions at Fig. A.1 can be checked by splitting the sample in high-track density events,
i.e. high number of interactions per bunch crossing (μ); and low-track density events,
i.e. low-μ. Figure A.2(a) shows several μ slices of 3-track DV mass distribution which
passed the “Base” vertex selection but inverting material veto requirement.
The plot strongly supports that the high-tail mass distribution is produced by randomcrossing tracks vertices, given that the non-exponential components decrease as μ value
decreases. Therefore, this sustains the factorization of the mass spectrum into a low
mass peak which falls oﬀ exponentially, and a non-exponential tail from random crossing
tracks vertices.
Figure A.2(b) shows that the fraction of the number of DVs with mass above 10 GeV
for each μ slice in Fig. A.2(a). The x position of each point represents average μ of eachslice. Fitting function is simple exponential function exp(p0 + p1 · μ). The ﬁtting results
are p0 = −8.95 ± 0.81 and p1 = 0.13 ± 0.03. The y-intercept is 1.3 × 10−4 . This means
that, even if contribution from hadronic interaction does not perfectly follow exponentialfunction, its non-exponential component should be O(10−4 ) of all DVs for 3-track DVs.
Such component is consistent with zero in the statistical region of the nominal regions
105

APPENDIX A. HADRONIC INTERACTIONS

105
104
104
103
103

102

102

10

10

1

0

2

4

6

8

10

12

14

16

18

20

0

2

4

6

8

10

Invariant Mass [GeV]

12

14

16

18

20

Invariant Mass [GeV](a) 4-track DVs(b) 5-track DVs

103
3

10

102

102

10

10

1

1
0

2

4

6

8

10

12

14

16

18

20

0

2

4

6

8

10

12

Invariant Mass [GeV]

14

16

18

20

Invariant Mass [GeV](d) ≥7-track DVs(c) 6-track DVs

1

Fraction of N DVs with m > 10 GeV

Arbitrary Unit

Figure A.1: The invariant mass distributions of vertices with more than 3 tracks after“Base” vertex selection but material veto is inverted. Red solid lines are ﬁtted exponential functions and Red dashed lines are extrapolation of them.

5 ≤ μ ≤ 12
13 ≤ μ ≤ 20
21 ≤ μ ≤ 28
29 ≤ μ ≤ 36
37 ≤ μ ≤ 44

10−1

10−2

10−3

10−1

10−2

10−3

10−4

−4

10

0

5

10

15

20

25

30

0

5

10

15

20

25

(a)

30

35

40

45
μ

Invariant Mass [GeV](b)

Figure A.2: (a) The μ slices of 3-track DV mass distribution of SUSY15 data samples in2016. The DVs passed the base selection but inverting material veto requirement. Nonexponential components in the mass spectra decrease as μ value decreases. (b) Fractionof the number of DVs with mass above 10 GeV for each μ slice. The x position of eachpoints represents average μ of each slice. Fitting function is simple exponential function
exp(p0 + p1 · μ). The ﬁtting results are p0 = −8.95 ± 0.81 and p1 = 0.13 ± 0.03.
106All Particles
Charged Particles
Ch. w/ Pion Mass

40

105

Vertices

a.u.

107
106
105
104
103
102
10
1
10−1
10−2
10−3
10−4
10−5
10−6
10−7
10−80

Radial Distance [mm]

APPENDIX A. HADRONIC INTERACTIONS

38

104

36
34

103

32
30

102

28
26

10

24
5

10 15 20 25 30 35

40

22Vertex Mass [GeV]

10 20 30 40 50 60 70 80

1

Truth Vertex Mass [GeV]

(a)

(b)

Figure A.3: The truth vertex masses are shown in (a) for various selections placed on theoutgoing particles from Geant4-simulated interactions. The vertex mass as a functionof radial distance from the interaction point is shown in (b) showing the materials thatmake up the various layers of material close to the interaction point.
(where material veto requirement is not inverted).

A.2

Geant4 studies

A study was performed using Pythia8 dijet MC sample. Truth vertices which werecreated by interactions simulated in Geant4 were selected. For these interactions, avertex mass is calculated in several ways.
1. Using all outgoing truth particles from the truth vertex
2. Using only ﬁnal-state charged particles with pT above 1 GeV
3. Using only ﬁnal-state charged particles with pT above 1 GeV using an assumptionof the charged pion mass to simulate the reco-level vertex reconstruction
A plot of these deﬁnitions inclusive in vertex particle multiplicity can be found in
Fig. A.3(a), normalised to the integral above 10 GeV. The shape of the fully inclusive
distribution is indicative of the complex nature of the Geant4 simulation attempting
to describe the interactions with heavy elements in the detector material. This inclusive
distribution as a function of mass and radial distance shows clearly in Figure A.3(b) that
there are features as expected. The largely Be-9 beam pipe at 25 mm is clearly visible,
as is the C-12 structures in the IBL support and IBL modules. A clear contribution isseen at the IBL radius of Si-28 interactions.
When using only ﬁnal-state charged particles with pT above 1 GeV with an assumed
charged pion mass, reconstructable truth-level vertices can be built. These vertices arethen binned in particle multiplicity (using the above deﬁnition). The distributions of
the masses of these vertices are then ﬁt to an exponential distribution in the region of107

APPENDIX A. HADRONIC INTERACTIONS

5-10 GeV. This ﬁt is then extrapolated into the region above 10 GeV in vertex mass.
The disagreement between the integral of the ﬁt function above 10 GeV and that of thetruth distribution is seen to be ∼ 300%. Distributions and ﬁts can be seen in Fig. A.4.

108

a.u.

105
104
103
102
10
1
10−1
10−2
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10−80

a.u.

APPENDIX A. HADRONIC INTERACTIONS

Ch. w/ Pion Mass5

10 15 20 25 30 35

40

104
103
102
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Ch. w/ Pion Mass

5

a.u.

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Ch. w/ Pion Mass5

10 15 20 25 30 35

40

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5

5

10 15 20 25 30 35

40Vertex Mass (7-Track) [GeV]

10 15 20 25 30 35

40Vertex Mass (6-Track) [GeV]
a.u.

a.u.

Ch. w/ Pion Mass

40

Ch. w/ Pion Mass

Vertex Mass (5-Track) [GeV]
103
102
10
1
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10 15 20 25 30 35

Vertex Mass (4-Track) [GeV]a.u.

Vertex Mass (3-Track) [GeV]

103
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1

10−1
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10 15 20 25 30 35

40Vertex Mass (8-Track) [GeV]

Figure A.4: The distributions of reconstructable mass for truth-level vertices is shownbinned in the number of reconstructable charged particles. The region between 5-10 GeV
is ﬁt to an exponential for comparison in the region above 10 GeV to the truth distribution.

109

APPENDIX A. HADRONIC INTERACTIONS

110

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List of Figures
1.1
2.1
2.2

2.3
2.4
2.5
2.6
2.7
3.1
3.2

3.3
3.4
3.5
3.6
3.7
3.8

3.9

Overlap between the questions and ideas discussed in the conference ofPlanning the Future of U.S. Particle Physics (Snowmass 2013) [21].
An overview of the properties of the particles in the Standard Model.
Summary of several Standard Model total and ﬁducial production crosssection measurements, compared to the corresponding theoretical expectations.
The scalar mass scale in Split Supersymmetry as a function of tan β for a
Higgs mass ﬁxed at 125.5 GeV for no and maximal stop mixing.
A schematic of the comoving number density of a stable species as it
evolves through the process of thermal freeze-out.
Feynman diagram of transition of bino (B̃) into gluino (g̃) via quark scattering.
Contour for the mass diﬀerence ΔM which makes the thermal relic abundance of bino DM equal to the observed DM density ΩDM h2 = 0.12.
Decay length of the gluino cτg̃100 TeV with the squark mass m̃ = 100 TeV
in coloured (almost horizontal) lines
The accelerator complex at CERN, showing the ﬂow of beam accelerationfrom the injectors to the LHC.
The peak instantaneous luminosity delivered to ATLAS during stablebeams for pp collisions at 13 TeV centre-of-mass energy is shown for each
LHC ﬁll as a function of time in 2016 [47].
The luminosity-weighted distribution of the mean number of interactions
per crossing for the 2016 pp collision data recorded [47].
Sectional view of the ATLAS detector [48].
The r–z cross section of a schematic diagram of the ATLAS inner detector
for Run 2.
Computer generated cut-away view of the ATLAS inner detector. [50]Cut-away view of the Pixel, part of the ATLAS inner detector [56].
(a) Sketch of a barrel module where the diﬀerent layers are clearly visible
with the ganging of electrodes in φ. The granularity in η and φ of thecells of each of the three layers and of the trigger towers is also shown. (b)Schematic showing how the mechanical assembly and the optical readoutof the tile calorimeter are integrated together. The various components of
the optical readout, namely the tiles, the ﬁbres and the photomultipliers,
are shown. [5]The yz cross section of a schematic diagram of the ATLAS muon spectrometers [5].

119

9
13

14
18
19
20
21
22
24

25
26
27
28
29
30

32
33

LIST OF FIGURES

3.10 Standard Model cross sections and corresponding event rates as a functionof collider energy, with 125 GeV Higgs [60].
3.11 The setup of the ATLAS trigger and data acquisition system for Run
2 [61]. The event and data rates are also given.
4.1
4.2
4.3
4.4

4.5
4.6
5.1

5.2

5.3
5.4

5.5
5.6

5.7
5.8
5.9

Schematic diagram of the standard inside-out tracking ﬂow in the ATLAS
experiment.
Space point seeds in the ATLAS inner detector barrel for a tt̄ event [62].
Simpliﬁed model of the ambiguity solving process, illustrated in the SCT
Barrel [62].
The tt̄ event for the two possible TRT hit associations (only the barrel
measurements): the brighter coloured hits show the extensions that originate from following the space point seeded tracks into the TRT, thesilicon space point objects are also shown in the same colour.
Schematic diagram of the standard outside-in tracking ﬂow in the ATLAS
experiment.
Schematic illustration of fake tracks rejection.

34
35
37
38
39

40
41
43

Feynman diagram representing production of long-lived gluinos in a Split
SUSY model, which form R-hadrons and give rise to displaced decays withhadronic ﬁnal states.
48
Cumulative luminosity as a function of time delivered to (green), recorded
by ATLAS (yellow) during stable beams for pp collisions at 13 TeV centreof-mass energy in 2016 [47].
48
Illustrations of three sources of background which may result in massive
non-signal displaced vertices with high track multiplicities.
51
Schematic ﬂow of data format conversion adopted in this analysis. The
dashed arrows represent the standard processes in ATLAS and the solids
arrows represent speciﬁc operations. DRAW RPVLL and DAOD SUSY15 in theparentheses are names of data formats used in this analysis.
53
Turn-on curve of HLT xe110 mht L1XE50 trigger for a certain MC signal(red) and 2016 data from Period F (black).
54
miss cut at 250 GeV for MC
Eﬃciencies of ﬁlter and oﬄine calibrated ET
samples of R-hadrons (a) with trackless jets requirement and (b) without
miss threshold istrackless jets requirement but the topocluster-based ET
raised to 180 GeV. The vertical axis shows the mass diﬀerence between
gluino and the lightest neutralino and the horizontal axis shows gluinomass. In case of Δm = Mg̃ − 100 GeV, the lightest neutralino mass is
ﬁxed at 100 GeV. It is shown that the eﬃciencies for small Δm scenarios
are signiﬁcantly improved by removing trackless jets requirement.
55
Schematic illustration of the LHC cleaning system.
57
Distribution in the plane transverse to the beam pipe of CSC muon segments 58
miss for the data. Left: all events passing
Distributions of the φ of the ET
the DRAW+SUSY15 selection (black), all events passing the event-level
miss > 250 GeV cut (blue), and after also requiring
selection including the ET
a good DV passing all but the ntracks and mDV cuts (red). Right: theevents passing the last selection on the left but separated for periods A-J(blue) and K-L (black).
58

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LIST OF FIGURES

miss for one run signiﬁcantly contaminated by
5.10 The φ distribution of the ET
non-collision background before (green histogram) and after (blue mark59ers) requiring fmax < 0.7 for the leading jet.
5.11 Two-dimensional distributions for the two variables proposed to use for
the NCB veto, for (a) data and (b) an example signal MC sample.
60
miss φ distributions (a) for events passing the event-level selection
5.12 The ET
with and without the NCB veto described in the text and (b) the same
selection but also requiring the presence of a vertex with at least three
tracks.
60
miss5.13 (a) Turn-on curve of the topocluster-based ET (MET LocHadTopo) cut.
(b) Turn-on curve of eﬃciency for events passing the xe110 2016 triggers
and MET LocHadTopo > 180 GeV cut in a MC signal and 2016 data of
Period F.
63
5.14 Validation of the new material map. Two-dimensional maps of the numberof vertices which do not pass the material veto, projected in the (a) x–y
plane and (b) r–z plane.
645.15 Two-dimensional maps of the number of vertices in the 2016 DAOD SUSY15
data (a) before material veto and (b) after veto. The number of vertices
signiﬁcantly is reduced thanks to the veto in regions where detector materials are placed.
65
5.16 (a) Two-dimensional map of the number of vertices within the region of|zDV | < 20 mm and rDV > 30 mm in x–y plane. (b) The same map as(a) but the disabled module veto is applied. The presence of ineﬃcientmodules explains some ineﬃcient regions where are not vetoed.
66
5.17 The normalised two-dimensional distribution of mDV and track multiplicity for DVs in events that pass all signal region event selection criteria forsignal MC with the gluino mass of 2000 GeV, the neutralino mass of 100
GeV and the gluino lifetime of 1ns. The red lines represent the boundaryof the signal region requirements.
66
5.18 The invariant mass distributions of vertices with more than 3 tracks after
basic vertex selections. Red solid lines are ﬁtted exponential functions and
Red dashed lines are extrapolation of them.
67
5.19 (a) Three-dimensional distance and (b) z distance between vertex pairs
before weighting. The black points show the distance between the twotrack vertices in the same event. The red points show a model calculated
from the distance between two-track vertices in diﬀerent events. The
invariant mass for the combination of the two vertices is required to be> 10 GeV.
69
5.20 (a) Three-dimensional distance between two-track vertex pairs, after weighting. The right histogram (b) is a close-up view of the left histogram.
(c) Three-dimensional distance between two-track and three-track vertices
pairs, after weighting. (d) A close-up view of the 3D distance between twotrack and three-track vertices, after weighting. The black points show the
distance between the vertex pairs in the same event. The blue lines showa model calculated from the distance between vertex pairs in diﬀerent
events. The value of the model at less than 1 mm gives the estimate forthe number of high-mass four-track or ﬁve-track vertices from this method. 70
5.21 The properties of the displaced vertices changes as a function of rDV ,depending on the track properties.
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LIST OF FIGURES

5.22 Schematic ﬂow of the method for estimation of random crossing tracks.
5.23 Schematic drawing showing the two steps of the random-track association
method. In the vertex labeled (1) the relative azimuthal angle Δφ (marked
with the curved red arrow) to the PV-DV direction (green dashed arrow)for each track in a DV which are ﬁlled into the track templates, andtemplates of η and pT are built up in the same way. The vertex labeled(2) shows how the random track generated from the track templates areadded to the (n − 1)-track seed vertex to construct an n-track DV. A
mass template is constructed by repeating the process many times. The
concentric circles represent a simpliﬁcation of a radial region of the ﬁducial
volume.
5.24 The properties η, φ, Δη, Δφ, pT of tracks in the track templates for eachregion (Δ means with respect to the PV-DV direction). Several adjacentradial regions are merged because it is too dense to show 12 histograms
overlaid. The central dips in Δφ distributions come from a requirementthat only tracks with d0 > 2 mm are used for secondary vertexing.
5.25 Crossing factor for the twelve radial region for 2016 data. The factors
are calculated by normalising the model to data in the control region, forvertices with three tracks and mass larger than 10 GeV. The error bars
represent the statistical uncertainties.
5.26 3-track mDV distributions of 2016 data for regions 0–5. The modelled
distributions are normalised to data by use of the high-mass range e.g.
mDV > 10 GeV. The modelled vertices reproduce the high-mass shape
distribution of the data.
5.27 3-track mDV distributions of 2016 data for regions 6–11. The modelled
distributions are normalised to data by use of the high-mass range e.g.
mDV > 10 GeV. The modelled vertices reproduce the high-mass shape
distribution of the data. The error bars in the mass distributions and thegrey bands in the bottom ratio distributions show the statistical uncertainties.
5.28 Normalised distributions are shown for data and various signals.
miss5.29 The properties of the DV candidates are shown as a function of ET(top) and Δφmin (bottom). DV mass (right) and track multiplicity (left)
are shown. The track multiplicity plots are normalised to the area above
3 and the mass distributions are normalised to the area above 3 GeV.
5.30 A qualitative diagram of the VRLM design is shown.
5.31 (a) Signal yields are shown (markers) as a function of R-Hadron lifetime(shape) and gluino mass (x-axis). Those signal models with a 100 GeV
LSP are shown in black. For reference, the yield in VRLM in data is shownin the dashed black line. For the signal scenarios with mg̃ > 1000 GeV
that were not excluded by Run-1 results, signal contamination for thisregion is at most ∼ 10% level. (b) For convenience, the Run-1 exclusion
limits are shown for models with a 100 GeV LSP [32].
5.32 3-track mDV distributions of 2016 data with inverted material veto requirement for regions 1–5. The modelled distributions are normalised todata by use of the high-mass range e.g. mDV > 10 GeV. The model
reproduces shape of the distribution of the data at high mass well.

122

72

73

74

75

76

77
79

79
80

81

82

LIST OF FIGURES

5.33 3-track mDV distributions of 2016 data with inverted material veto requirement for regions 7-9 and 11. The modelled distributions are normalised
to data by use of the high-mass range e.g. mDV > 10 GeV. The model
reproduces the shape of the high-mass region of the distribution for thedata well. The error bars in the mass distributions and the grey bands inthe bottom ratio distributions show statistical uncertainties only.
83
5.34 4-track mDV distributions of 2016 data with inverted material veto requirement for regions 1–5. The modelled distributions are normalised todata by use of the high-mass range e.g. mDV > 10 GeV. The model
reproduces the shape of the high-mass region of the distribution for thedata well.
84
5.35 4-track mDV distributions of 2016 data with inverted material veto requirement for regions 7-9 and 11. The modelled distributions are normalised
to data by use of the high-mass range e.g. mDV > 10 GeV. The model
predictions match the shape of the high-mass region of the distribution
for the data well. The error bars in the mass distributions and the grey
bands in the bottom ratio distributions show statistical uncertainties only. 85
5.36 (a) Summary of the observed and expected numbers of 4-track DVs withmass above 10 GeV in the regions with inverted material veto. Region 0,
6 and 10 are excluded in this ﬁgure because too tiny volume is vetoed bymaterial map there. (b) The summation of the 4-track mDV distributionsin Figure 5.34 and 5.35. The red line represents a ﬁtted exponential function. 85
5.37 Yields of data and R-hadron pair production events in the additional
VR with inverted material veto requirement. The horizontal dashed line
represents the yield of data. The black markers show event yield of eachsample with the lightest neutralino mass of 100 GeV. The green markers
show event yield of each sample but the lightest neutralino mass is not
100 GeV. For the signal scenarios with mg̃ > 1000 GeV that were notexcluded by Run-1 results, signal contamination for this region is at most
∼ 10% level.
86
5.38 Crossing factors which are derived from diﬀerent mDV intervals for ﬁtting
mass template to data in each region in 2016. Black dots show the crossing
factors in nominal setting (using data points in mDV > 10 GeV for ﬁtting,
red dots are those with mDV > 5 GeV cut, and green dots are those with
87
mDV > 15 GeV cut.
5.39 Cut ﬂow showing how the number of displaced vertices per event changes
with applied selections.
89
5.40 Number of DVs per event as a function of DV mass and track multiplicity. 90
5.41 The two-dimensional distribution of mDV and track multiplicity for DVs
in events that pass all signal region event selection criteria.
91
6.1

Closure test for the eﬃciency re-weighting procedure. A sample generated with τ = 1 ns (cτ  300 mm) is re-weighted to give the blue curve(statistical uncertainty considered only). This is compared with several
samples with the same mass spectrum but generated at diﬀerent τ = 0.01,
0.04, 0.1, 1, 10, 30 and 50 ns, (corresponding to cτ = 3.0, 12.0, 30.0, 300,
3000, 9000 and 15000 mm), which are represented as the red points. The
ﬁgure shows the closure of the weighting treatment to within statisticaluncertainty in all the points considered.
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LIST OF FIGURES

6.2

An example of the double Gaussian ﬁt used to count the number of signal
KS0 on the barrel for the decay length interval 5-10 mm, for MC (a) anddata (b). The green line corresponds to the background-function, the redline is the ﬁt for the signal while the blue lines are the combined ﬁt. Using
94
a simultaneous ﬁt, the number of KS0 candidates are extracted.
6.3 Double ratio of number of KS0 found in MC and data individually normalised to the number found at the smallest interval, for the barrel region(left) and endcap (right). The maximum deviation from one is taken as
an conservative estimate of the systematic uncertainty from the tracking
eﬃciency.
95
6.4 Vertex reconstruction eﬃciency for two MC signal samples, 402735 (left)
and 402739 (right). The blue markers shows the eﬃciency distribution
without the track-killing factor and the red markers are with the trackkilling factor applied.
96
6.5 (a) A vector summation of the transverse momentum for the gluino-gluino
system with 1400 GeV R-hadron for samples of Pythia in green and a
mg5 amcnlo (MadGraph) in red. (b) A weight computed taking the ratioof the both samples.
96
6.6 Contributions to the uncertainty on eﬃciency vs lifetime for a sample with
1200 GeV gluino and 100 GeV LSP.
97
6.7 Pulls of the number of events passing the whole selections between nominaland shifted 1σ of each systematic source.
98
6.8 Eﬃciency vs proper decay length for the qq R-hadron samples with 1200 GeV
gluino and 100 GeV or 1070 GeV neutralinos. All systematic corrections
and uncertainties are included.
98
6.9 Upper limit on cross-section vs decay length for the samples considered at
ﬁxed 100 GeV neutralino mass (a) and at ﬁxed Δm = 100 GeV (b).
100
6.10 Excluded region in the gluino mass-vs-lifetime at ﬁxed neutralino mass
100 GeV (left), and at ﬁxed Δm = 100 GeV (right).
101
6.11 (Left) Upper limit on cross-section vs mχ̃01 for the samples with mg̃ = 1400
or 2000 GeV. (Right) Excluded region in the gluino-vs-neutralino massplane at ﬁxed gluino lifetime τ = 1 ns.
101
6.12 Constraints on the gluino mass-vs-lifetime plane for a Split-SUSY modelwith the gluino R-hadron decaying into light quarks and the lightest neutralino with mass of 100 GeV.
102
A.1 The invariant mass distributions of vertices with more than 3 tracks after“Base” vertex selection but material veto is inverted. Red solid lines are
ﬁtted exponential functions and Red dashed lines are extrapolation of them.106
A.2 (a) The μ slices of 3-track DV mass distribution of SUSY15 data samples
in 2016. The DVs passed the base selection but inverting material vetorequirement. Non-exponential components in the mass spectra decreaseas μ value decreases. (b) Fraction of the number of DVs with mass above
10 GeV for each μ slice. The x position of each points represents average μof each slice. Fitting function is simple exponential function exp(p0 +p1 ·μ).
106
The ﬁtting results are p0 = −8.95 ± 0.81 and p1 = 0.13 ± 0.03.

124

LIST OF FIGURES

A.3 The truth vertex masses are shown in (a) for various selections placed on
the outgoing particles from Geant4-simulated interactions. The vertex
mass as a function of radial distance from the interaction point is shownin (b) showing the materials that make up the various layers of material
close to the interaction point.
A.4 The distributions of reconstructable mass for truth-level vertices is shownbinned in the number of reconstructable charged particles. The region
between 5-10 GeV is ﬁt to an exponential for comparison in the region
above 10 GeV to the truth distribution.

125

107

109

List of Tables
2.1

Fields in the MSSM and the SU (3) ⊗ SU (2) ⊗ U (1) quantum numbers.

15

3.1
3.2

Nominal design parameters of the LHC as a proton-proton collider [6].
Position and number information of the Pixel and IBL [51].

23
31

4.1

Track characteristics that lead to beneﬁts or penalties in the ATLAS silicon detector track score [62].
Cuts applied in the diﬀerent tracking algorithms.

39
42

4.2
5.1

5.2

5.3
5.4

5.5

5.6

6.1

Data taking periods and the corresponding amount of the integrated luminosity for the 2016 dataset after the application of data quality requirements. Runs in period H were recorded with the beam condition of low
μ for forward physics. Runs in period J were taken with β ∗ = 2.5 km forthe measurement of elastic pp-scattering by the “Absolute Luminosity For
ATLAS” (ALFA) detector.
Deﬁnitions of the control, validation and signal regions in the analysis. The
validation and signal regions are deﬁned by the control region requirements
and some additional selections.
Approximations of uniform shapes augmented by the oﬀsets created by
the decoupling of the beam pipe from the ATLAS cavern.
Total number of estimated background vertices with a mass mDV > 10 GeV
in the control, validation and signal regions, using the 2016 full integrated
luminosity of 32.7 fb−1 . The numbers shown are obtained before applied
the event-level transfer factors.
Total number of estimated background vertices with a mass mDV > 10 GeV
for the vertex selections used in the control, validation, and signal regions.
The (n+1)-track contributions are estimated using the accidental-crossing
factor method (Section 5.7.3), the (n + 2)-track contribution is obtained
from merged vertices (Section 5.7.2), and the pure n-track estimation isevaluated using the hadronic interactions (Section 5.7.1). The control region yield is normalised to data. Also shown are the estimated background
event yields in the pre-selection region with at least 5 tracks. The predicted background yield in the full signal region appears in the bottomrow, and includes the transfer factors shown.
The observed results for the control, validation, and signal regions areshown along with the background expectations for the 32.7 fb−1 of datacollected in 2016.
Cut ﬂow table for 2016 data.

49

52
64

78

88

90
99

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