学位論文

Search for Long-lived Chargino
via √Gluino Pair Production in pp Collisions
at s = 13 TeV with the ATLAS Detector（ATLAS 実験における重心系エネルギー 13 TeV での陽子陽子衝突によるグルイーノ対生成チャンネルを用いた
長寿命チャージーノ探索）
平成 29 年 12 月博士（理学）申請

東京大学大学院理学系研究科
物理学専攻
小坂井千紘

2

Search for Long-lived Chargino√ via Gluino Pair
Production in pp Collisions at s = 13 TeV with the
ATLAS Detector
Chihiro Kozakai
February 14, 2018

Abstract
Supersymmetry (SUSY) is one of the most promising theories beyond the Standard Model. SUSY
models which predict that the Lightest SUSY Particle (LSP) is the partner of the neutral W boson(wino) are especially attractive because they are compatible with the cosmological observations. Suchmodels also predict that the second lightest SUSY particle is the charged wino whose mass is nearly
degenerated to the neutral wino mass. The charged wino has a long lifetime of about 0.2 ns due tothe degeneracy and therefore the charged wino trajectory may be reconstructed by the inner detectorof the ATLAS detector. The short wino track is a characteristic signature of the charged wino, andno such event signature is expected from the√ SM processes. This thesis presents a search for the
long-lived charged wino in pp collisions at s = 13 TeV at the LHC with the ATLAS detector. The
integrated luminosity of 36.1 fb−1 data is used for this analysis. Gluino pair production followed bygluino decay into a charged or neutral wino and two jets is focused. The search uses pixel tracklets
which is reconstructed from only four hits in the pixel detector. It is the first attempt in the ATLAS
Collaboration to use the tracklets of the pixel detector as a physics object. The observed distributionof the transverse momentum of candidate events is consistent with the background-only hypothesis.
For the wino lifetime of 0.2 ns, the gluino masses less than 1650 GeV are excluded at the chargino
mass less than 460 GeV, which is the lower chargino mass limit from searches for electroweak direct
production of winos. The chargino mass less than 1050 GeV is excluded for the region with the massdiﬀerence between wino and gluino larger than 100 GeV. For the wino lifetime of 1.0 ns, the gluinomass less than 1750 GeV is excluded at the chargino mass of 580 GeV. The chargino mass less than
1200 GeV is excluded for the region with the mass diﬀerence between wino and gluino larger than
100 GeV.

Contents
1

Introduction

92

Physics motivation
2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Remaining issues in SM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Minimal Supersymmetric Standard Model . . . . . . . . . . . . . . . . . . .
2.3.2 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Solutions of SM issues by SUSY . . . . . . . . . . . . . . . . . . . . . . .
2.4 Wino LSP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Anomaly mediated SUSY breaking model . . . . . . . . . . . . . . . . . . .
2.4.2 Pure Gravity Mediation model . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Higgs Anomaly Mediation model . . . . . . . . . . . . . . . . . . . . . . .
2.4.4 Wino LSP phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Production of long-lived charginos in a collider experiment . . . . . . . . . . . . . .
2.6 Summary of current constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3

The LHC and the ATLAS detector
3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Muon spectorometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Luminosity detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Trigger and data acquisition system . . . . . . . . . . . . . . . . . . . . . .

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4

Data and MC samples
4.1 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Simulated samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Pile-up simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Signal Monte Carlo sample . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Background MC samples . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3

4

CONTENTS

5

Object reconstruction and the definition
5.1 Inner Detector tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Tracking parameter definition . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Standard track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Tracklet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Definition of disappearing track . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Topological clustering of calorimeter cells . . . . . . . . . . . . . . . . . . . . . . .
5.4 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Jet energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Jet vertex tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Definition of jet object . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Definition of electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.3 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.4 Definition of photon object . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.3 Definition of muon object . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Overlap removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Missing transverse energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6

Tracklet performance
6.1 Pixel detector condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Data quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Reconstruction eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Transverse momentum resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Signal disappearing track pT distribution . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Tracking parameter comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7

Event Selection and analysis strategy
97
7.1 Kinematic selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.2 ETmiss trigger performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.3 Analysis strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

CONTENTS

5

8Background estimation
8.1 Hadronic background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Control region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.2 Smearing technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Leptonic background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2 Control region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3 Electron Transfer Factor (TF) measurement . . . . . . . . . . . . . . . . . .
8.2.4 Muon TF measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.5 Estimated leptonic background . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Fake background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9

The statistical method to evaluate experimental limits

127

10 Systematic uncertainties
131
10.1 Uncertainties in signal normalization . . . . . . . . . . . . . . . . . . . . . . . . . . 131
10.2 Uncertainty in the background events . . . . . . . . . . . . . . . . . . . . . . . . . 147
11 Result and the interpretation
11.1 Fitting result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2 Exclusion limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12 Conclusion

155

Preface
The ATLAS experiment is executed by thousands of people and this thesis largely relies on their work.
Therefore, my contribution of this thesis is explicitly summarised here. Please refer to the main bodyfor the details.
First, I proposed search in the gluino pair production channel in Run 2 and analyzed for this channel. Thanks to the higher centre of mass energy in the LHC than that in Run 1, the gluino production
becomes a promising production process again. The direct electroweak gaugino production is modelindependent but the production cross section is small. While the gluino pair production sensitivity
depends on mass relation of the gluino mass and the chargino mass, the production cross section islarger. Therefore, gluino production channel may discover heavier chargino earlier than the directelectroweak production. The chargino search in the gluino pair production and the direct electroweak
production is complementary. In addition, the signal acceptance of the gluino pair production is expected to be higher. It is because two gluinos decay accompanies four jets, which leads to high ETmiss
trigger eﬃciency. The large mass diﬀerence between the gluino and the chargino gives larger chargino
boost and higher short track reconstruction eﬃciency. The analysis dedicated to the gluino production
is done by me. I made all the plots in Chapter 7–11. Signal MC preparation is also my work.
Second, I validated the analysis with pixel tracklets. Thanks to the IBL installed from Run 2,
tracking with only four pixel detector hits, pixel tracklet is available. Because this analysis uses
pixel tracklet for the first time in the ATLAS experiment, the performance is studied in detail. The
theoretical prediction of the lifetime of the chargino is 0.2 ns implies that the expected number ofhits of chargino track is few. Therefore, the use of short pixel tracklet is crucial in this analysis.
Furthermore, tracks reconstructed with pixel detector hits and 1 SCT hits is found to have more faketrack backgrounds. Such backgrounds are reduced by using the pixel tracklet alone.
Third, I studied about modification of leptonic background estimation. Tag and probe method isused to determine the number of lepton background as described in Sec. 8.2.3 and 8.2.4. I updated
tag and probe analysis by using calorimeter clusters for electron and MS tracks for muon to keep the
Z → ℓℓ event selection eﬃciency. The background reduction method using the signs of tag lepton
and probe lepton is also developed.
Finally, I contributed to the alignment of the pixel detector as my qualification work to be an
author of the ATLAS Collaboration papers.

7Chapter 1
Introduction
Elementary particle physics experiments have revealed that the Standard Model (SM) can describe
the nature of the quarks and leptons and the three fundamental interactions (electromagnetic, weak
and strong interactions) very well. Searches for new particles expected by the SM is completed
by the discovery of the Higgs boson in July 2012 by the ATLAS and the CMS experiment at the
LHC. However, there are several facts that cannot be explained by the SM. For example, no darkmatter candidate is included in the SM. There should be new physics beyond the Standard Model.
Supersymmetry (SUSY) is one of the promising theories which solves some questions remained in
the SM. SUSY is a theory which assumes symmetry between bosons and fermions. SUSY predicts
that each elementary particle in the SM has its supersymmetric partner.
To discover SUSY direct searches using a high energy collider is the best way to show clear
evidence of a new particle. The Large Hadron Collider(LHC) is the highest energy proton-proton√
collider running at the centre of mass energy of s = 13 TeV. The ATLAS detector is one of thefour detectors at the LHC. It is a multi-purpose detector designed to collect many diﬀerent typesof collision data and to precisely measure the final state of the collisions. The ATLAS detector isdesigned to discover many diﬀerent event topologies induced by new particles produced at the LHC.
Some SUSY models predict that the lightest SUSY particle is the SUSY partner of neutral SU(2)weak gauge boson (wino). Such SUSY models are especially attractive. One of the reasons is that it
is compatible with the cosmological constraints when the LSP wino is the dark-matter. The second
reason is that such models also predict that squarks are O(100–1000) times heavier than top quark,
which is compatible with the Higgs-boson mass of 125 GeV. When the neutral wino is the LSP, thenext lightest SUSY particle is the charged winos. In this case, a theory predicts that the charged winomass almost degenerates with the LSP mass, which leads to the long lifetime of the charged winoof around 0.2 ns. Therefore, if a charged wino is produced at the LHC, it can fly O(6 cm) so that itleaves hits along the track in the ATLAS detector. The decay products of the charged wino decay are
an LSP and a charged pion. The LSP cannot be detected and the pion has a very low momentum to be
detected in the ATLAS detector. The charged wino track would be detected as a disappearing track
inside the inner detector of the ATLAS detector. However, the standard tracking cannot be applied forsuch short tracks because of the severe requirement of number of hits to be at least seven. The new
tracking uses only four pixel detector hits. This is referred to a pixel tracklet in this thesis. Using the
pixel tracklet as a physics object is for the first time in the ATLAS experiment.
9

10

CHAPTER 1. INTRODUCTION

This thesis focuses on chargino production in cascade decays of gluinos which are produced by
the strong interaction. The advantage of this mode is that the strong production of gluinos has larger
cross-section than the direct electroweak production of charginos, and some properties of gluino
decay such as multiple high pT (transverse momentum) jets, large ETmiss (missing transverse energy)
and boosted chargino make the signal acceptance higher.
This thesis is organised as follows. In Chapter 2, theoretical aspects of the interested physics,
phenomenological implication and current experimental results are presented. Chapter 3 summarises
the LHC collider and the ATLAS detector. Chapter 4 describes the data and MC simulated samples.
Then the reconstruction of events in the ATLAS detector is discussed in Chapter 5. In Chapter 6,
pixel tracklet performance is presented in detail because it is of particular importance in this thesis. In
Chapter 7, the event selection procedure and overview of the analysis are discussed. The backgroundestimation is given in Chapter 8. Chapter 9 discusses the statistical method to examine the existenceof the signal events. Systematic uncertainties are summarised in Chapter 10. Then Chapter 11 shows
the results of the statistical analysis applied to the data. Finally, Chapter 12 concludes this thesis.

Chapter 2
Physics motivation
2.1 The Standard Model
Currently the Standard Model (SM) is the best theory to describe most of the experimental results inelementary particle physics. The SM is composed of a gauge theory and the Higgs mechanism. The
gauge theory of SU(3)C ⊗ SU(2)L ⊗ U(1)Y derives strong, weak, and electromagnetic interactions.
The Higgs mechanism gives mass to the elementary particles.
The components of the SM are listed in Fig. 2.1. Fermions (quarks and leptons) compose matter.
Quarks interact via electroweak and strong interactions. Leptons interact by electroweak interaction.
Vector bosons mediate interactions. Namely gluons mediate the strong interaction, photon mediates
the electromagnetic interaction, and W and Z bosons mediate the weak interaction. The Higgs boson, only one scalar boson in the SM, causes spontaneous symmetry breaking and gives mass to theelementary particles.

2.2 Remaining issues in SM
In spite of the success of the SM, it is far from the ultimate theory of everything. Remaining main
issues are:• Absence of gravity– The SM describes only three interactions (strong, weak, and electromagnetic) out of thefour fundamental interactions. Gravity is not included in the SM.
• Absence of the dark-matter– From astrophysical observations [2, 3], the existence of the dark-matter is indicated, but
the particle origin of the dark-matter has never been directly observed. According to thelatest result from Planck satellite [4], the energy in the universe is composed of 4.9 % ofbaryons, 26.7 % of dark-matter and 68.4 % of dark-energy. One of the promising darkmatter models is called as Weakly Interacting Massive Particles (WIMP). WIMP can feelweak interaction, but neither electromagnetic nor strong interactions.
11CHAPTER 2. PHYSICS MOTIVATION

12

Figure 2.1: Table of the SM particles. [1]• Grand unification is not achieved– In the SM, only two interactions, electromagnetic and weak interactions are mixed interms of gauge theories. Since there are still two diﬀerent coupling constants g and g′ (gand e), the two interactions are not really unified but they are mixed. Grand unification assumes that three fundamental interactions, electromagnetic, weak, and strong interaction
are unified at a high energy scale slightly (three order of magnitude in energy) below the
Planck scale.
• Hierarchy problem– Now we have two fundamental energy scales, namely the electroweak scale O(100 GeV)
and the Planck scale O(1019 GeV). It is not understood why these two scales diﬀer somuch. For example, the Higgs-boson mass gives rise to the fine tuning problem. Mass
squared of the Higgs-boson in the SM, m2h , is given by
∫ Λ 4
∑ λ2f
d p
2
2
f
mh ≈ mh0 −
Nc
2
8π
p2
f
(2.1)
∑ λ2f
N f Λ2 ,≈ m2h0 +2 c8πfwhere mh0 is the bare Higgs-boson mass, which is a free parameter in the SM. λ f is
the Yukawa coupling constant, Ncf is the number of colours of fermion f , and Λ is theultraviolet cutoﬀ scale.

2.3. SUPERSYMMETRY

13

mh is measured to be 125.0 GeV [5]. Therefore, if Λ is at the Planck scale, m2h0 /m2h ∼ 1030
is derived. It means fine tuning of 30 orders of magnitude for mh0 is required to cancel
this diﬀerence. It seems unnatural.
• Baryogenesis– The universe is matter dominant and the anti-matter density is very small. The CP violation expected in the matter (quarks and leptons) sector of the SM could have explained thebaryogenesis, but the actual matter dominance cannot be explained by the matter sector
alone.
• Higgs-boson field condensation in vacuum– The Higgs potential is said to break the electroweak gauge symmetry spontaneously. However, the SM does not provide the mechanism that causes it.

2.3 Supersymmetry
2.3.1 Minimal Supersymmetric Standard Model
Supersymmetry (SUSY) is one of the most promising theories to solve some of the above serious
issues of the SM. It extends the SM by introducing boson-fermion symmetry. Here, the simplest
SUSY model, so called the Minimal Supersymmetric Standard Model (MSSM), is discussed.
A list of Particles in the MSSM is summarised in Fig. 2.2. As it shows, the MSSM predicts extra
Higgs bosons (H 0 , A0 , H ± ) and each SM particle has its SUSY partner whose spin diﬀers by 1/2 units
from the SM particle spin. The coupling constants of a SM particle and those of its partner should be
identical. The SUSY partners of quarks and leptons are named as squarks and sleptons, and their spinis 0. The SUSY partners of gauge bosons are named as gauginos, and they are spin 1/2 fermions. The
partners of SU(3), SU(2), U(1) gauge bosons are named as gluino, wino and bino respectively. As analternative expression, gluino, wino, zino, and photino are also used. The SUSY partners of Higgs
bosons are named as higgsinos and their spin is 1/2. Electroweak gauginos (W̃ 0 , W̃ ± , B̃0 ) and higgsinoswith the same electric charge can mix to form mass eigenstates. They are called as charginos (χ̃i ± ,
i=1,2) and neutralinos (χ̃i 0 , i=1,2,3,4). The index i is assigned according to mass ordering. In general,
SUSY partner of fermion is named as sfermion and that of boson is named as bosino.
If supersymmetry is exact, a SUSY particle has the same mass as its SM partner. Since no SUSY
particles with the same mass as the SM partners are discovered, supersymmetry must be broken.
Several SUSY breaking mechanisms are proposed and they form phenomenological models.

2.3.2 R-parity
In the MSSM, the baryon number and the lepton number may not be conserved. However, theirviolations cause proton decay, which is not observed experimentally. To prevent proton decay, Rparity conservation is often assumed. R-parity is defined as
R = (−1)2S +3(B−L) ,(2.2)

CHAPTER 2. PHYSICS MOTIVATION

14

Figure 2.2: Table of the MSSM particles [6].
where S is the spin, B is the baryon number and L is the lepton number. For the SM particles R = 1
and for the SUSY particles R = −1. When R-parity is conserved, the following rules on SUSY
particle phenomenology are derived.
• The SUSY particles are always pair produced.
• The Lightest SUSY Particle (LSP) must be left at the end of decay chains of any SUSY particle
decay.
• The LSP is stable.
In this thesis, R-parity conservation is assumed.

2.3.3

Solutions of SM issues by SUSY

Some of the SM problems discussed in Sec.2.2 are solved by SUSY, and SUSY is a natural extensionof the SM.
• Extension of Poincaré algebra– Anti-commutation of boson-fermion translation algebra Q includes spacetime translation[7].
{}
Qα , Qβ = −2(γµ )αβ Pµ ,(2.3)
where γµ is the γ matrix and Pµ is the four-momentum. Here, Q can be interpreted as factorization of momentum operator. Therefore, SUSY operator localization derives generalcoordinate translation. A gravity theory which uses this property is called as Supergravity,
SUGRA.

2.3. SUPERSYMMETRY

15• Dark-matter– When R-parity is conserved, the LSP is a good candidate of dark-matter. Depending on
models, the LSP is either neutral wino, higgsino, bino, or gravitino. It feels only weak andgravitational interactions.
• Grand unification– The variations of running gauge couplings with energy scale are changed at the scale of
SUSY-particle masses [7]. Fig. 2.3 shows that three couplings are unified at ∼ 1016 GeV
in the MSSM. Therefore, grand unification can be achieved with SUSY.

Figure 2.3: Variation of the gauge couplings as a function of the energy scale. Black dashed lines arefor the SM, red and blue lines are for the MSSM. For blue (red), common threshold is 750 GeV (2.5
TeV) and α3 (mZ ) is 0.117 (0.120). This is cited from Ref. [7]• Hierarchy problem– SUSY predicts that each particle in the SM has a SUSY partner with a half spin diﬀerence.
Therefore, the contribution of the corresponding loop diagrams to Higgs-boson mass cancel each other [8]. However, the cancelation is not perfect due to SUSY breaking. The
Higgs boson mass is calculated asm2h ≈ m2h0 −

∑ λ2f
f

8π2

Ncf (m2f˜ − m2f ) ln Λ2 /m2f˜,(2.4)

where f˜ is SUSY partner of fermion f . The quadratic divergence is moderated to thelogarithmic divergence.

16

CHAPTER 2. PHYSICS MOTIVATION

Given that Higgs boson mass is 125 GeV, it is getting diﬃcult to find models which solve all
the above issues at the same time. In this thesis, model compromising on the hierarchy problem isfocused as discussed in the next section. However, SUSY significantly relaxes the fine tuning problem
compared to the SM.

2.4 Wino LSP model
Naively, the Higgs boson mass of 125 GeV and the Eq. 2.4 imply that sfermion’s mass becomesO(10–100 TeV) [9]. From the cosmological constraints on the dark-mater, the wino-like LSP is oneof favoured scenarios. Three representative promising models with these features are introduced here.
Then, a characteristic signature of these models is discussed.

2.4.1 Anomaly mediated SUSY breaking model
Anomaly Mediated SUSY Breaking model (AMSB) assumes that SUSY breaking is caused by loop
eﬀects [10]. AMSB does not require any additional fields. It means that the eﬀect of AMSB exists
more or less in any SUSY models. SUSY particles acquire mass from anomaly eﬀect. This is one of
the simplest models.
AMSB predicts gaugino (bino, wino, and gluino) mass (M1 , M2 and M3 ) to be()
g21 33M1 =m3/2
16π2 5g2 ()
M2 = 2 2 m3/2
16π
g2 (
)
M3 = 3 2 −3m3/2 ,
16π

(2.5)
(2.6)
(2.7)

where g1 , g2 , and g3 are gauge coupling constants at the weak scale and m3/2 is the gravitino mass at
the grand unified theory (GUT) scale. The mass ratio is M1 : M2 : M3 ≈ 3 : 1 : 8. i.e., wino is theLSP.

2.4. WINO LSP MODEL

17

Mass of squarks and sleptons is
(

)
(
)
m23/2
11 4 3 4
1 2
2
24− sin θW MZ cos 2β + − g1 − g2 + 8g3
2 3502(16π2 )2
(
)
)
(
m23/2
1 1
3
11
Md̃2L = m20 + − + sin θW 2 MZ2 cos 2β + − g41 − g42 + 8g432 3502
(16π2 )2
(
)
m23/2
2
88
Mũ2R = m20 + sin θW 2 MZ2 cos 2β + − g41 + 8g43325
(16π2 )2
(
)
m23/2
1
22 4
2
2
2 2
4
Md̃R = m0 − sin θW MZ cos 2β + − g1 + 8g3325(16π2 )2
(
)
(
)
2
1
99 4 3 4 m3/2
2
2
2
2
MẽL = m0 + − + sin θW MZ cos 2β + − g1 − g22502
(16π2 )2()
2
1 2
99 4 3 4 m3/2
22
Mν˜e = m0 + MZ cos 2β + − g1 − g22502
(16π2 )2()
2
198 4 m3/2
2
2
2 2
MẽR = m0 − sin θW MZ cos 2β + −g,
25 1 (16π2 )2Mũ2L = m20 +

(2.8)
(2.9)
(2.10)(2.11)(2.12)(2.13)(2.14)

where m0 is the universal scalar mass at the unification scale, θW is the Weinberg angle, tan β is theratio of vacuum expectation values of the two Higgs doublets. To avoid sleptons being tachyon, m0
must be larger than O(100 GeV). Thus, masses of squarks and sleptons can be naturally O(10–100
TeV), while gaugino masses can be light enough to be produced at the LHC.

2.4.2 Pure Gravity Mediation model
Pure Gravity Mediation (PGM) SUSY breaking [11] assume that gauginos acquire mass in a similar
way as the AMSB models, and squarks and sleptons acquire masses through supergravity. Gaugino
mass is contributed by additional eﬀects of the Higgs-higgsino loop.
)(
g21 331
M1 =m3/2 + L
16π2 5112
g ()
M2 = 2 2 m3/2 + L
16π
g2
M3 = −3 3 2 m3/2
16π
m2A
|µ|2
L ≡ µ sin 2β 2ln,|µ| − m2A m2A(2.15)(2.16)(2.17)(2.18)

where L is radiative correction due to Higgs-higgsino loop. Due to the contribution of L, gaugino
mass ratio is not fixed like the AMSB case. L is at most O(m3/2 ). Fig. 2.4 shows the relation between

CHAPTER 2. PHYSICS MOTIVATION

18

the gluino mass and the wino mass for some representative values of L/m3/2 . Wino is the LSP in
most of the possible parameter space. In addition, NLO correction decreases the gluino mass [12].
Therefore, eﬀective parameter space with the wino LSP can be larger than the case shown in Fig. 2.4.

3000

2
3
2

L

m

1500

=

L m

32

=

1

B

2000

AMS

mgluino GeV

2500

L

m

2
3

=3
mwino >mbino

1000

500

mwino >mgluino

200

400
600
mwino GeV

800

1000

Figure 2.4: The correlation between the gluino and wino mass in PGM for some given L values.
The solid blue line corresponds to the prediction for purely anomaly mediated gaugino mass, i.e.
L = 0. The blue dashed lines correspond to some representative values of L/m3/2 . In the light shaded
region, the wino mass becomes higher than the bino mass due to large higgsino threshold eﬀects (L ≳ m3/2 ). [13]2.4.3 Higgs Anomaly Mediation model
Higgs Anomaly Mediation assumes that only the Higgs field directly couples to SUSY breaking field[14, 15]. In this model, gauginos acquire mass from anomaly as in AMSB model. Squarks andsleptons acquire mass not only from anomaly eﬀect, but also from the coupling of Higgs field to the
SUSY breaking field.

2.4.4 Wino LSP phenomenology
As discussed above, wino LSP is predicted in several simple models. When the LSP is pure wino,
it is predicted that the Next Lightest SUSY Particle (NLSP) is a charged wino. Hereafter, chargino
means charged wino as the NLSP and neutralino means neutral wino as the LSP. Their mass highly2.5. PRODUCTION OF LONG-LIVED CHARGINOS IN A COLLIDER EXPERIMENT

19

degenerates because their mass diﬀerence comes only from radiative correction. The decay width ofthe chargino is
(
)1
2G2F
m2π 2
2
2
3
cos θC fπ (δm) 1 −,(2.19)
Γ χ˜1 → χ˜1 π =π(δm)2where G F is the Fermi coupling constant, θC is the Cabbibo angle, fπ is the pion decay constant, δm is
mass splitting between the neutralino and the chargino and mπ is the pion mass [16]. Fig. 2.5 shows
the mass splitting calculation as a function of the neutralino mass. The mass splitting is around 160
MeV in a wide range of the chargino mass and then the lifetime is approximately 0.2 ns as shown in
Fig. 2.6. Therefore the chargino has a long lifetime [17]. If a chargino is produced in pp collision,
it typically flies cτχ̃± = 6 cm or longer if boosted. Therefore, it is expected that chargino can leavesome hits in the inner detector. When the mass splitting is 160 MeV, a chargino mainly decays into aneutralino and a charged pion. The neutralino is undetectable and the pion has too low momentum tobe reconstructed. Thus chargino leaves a characteristic signature of disappearing track, which leaves
several hits in the inner part of the tracking detector and no associated hits are left in the outer part of
the tracking detector.
(

±

0 ±

)

Figure 2.5: Charged and neutral wino mass splitting calculation of one-loop (green) and two-loop(red) as a function of neutralino mass [17].

2.5 Production of long-lived charginos in a collider experiment
To produce chargino in a collider experiment, there are two types of production channels. One iselectroweak direct production and the other is production via gluino cascade decay.
The electroweak direct production is pair production of two charginos or one chargino plus one
neutralino. On the other hand, the gluino cascade production is pair production of two gluinos followed by gluino decay into jets and a chargino or a neutralino. The representative diagrams are shownin Fig. 2.8.

CHAPTER 2. PHYSICS MOTIVATION

20

Figure 2.6: Lifetime dependence on mass splitting of charged and neutral wino [18].
The cross-section of the gluino pair production is larger than that of the electroweak direct production. Fig. 2.7 shows the production cross-section of SUSY particles as functions of their mass.
Coloured particles (gluino, squark) have larger cross-sections than gauginos, because the LHC isa hadron collider. However, when the gluino mass is too large to be produced at the LHC, the electroweak production may be the only accessible channel. Two production channels are complementarywith each other. In this thesis, the gluino strong production channel is focused on.

2.6 Summary of current constraint
Here, current constraints from the collider experiments and the WIMP dark-matter searches are summarised.
Collider experiment Long-lived chargino is searched for in ATLAS [20], CMS [21], and LEP
experiments [22]. Fig. 2.9 shows the constraints from ATLAS and LEP experiments with theoreticalprediction of the relation between mass and lifetime and Fig. 2.10 shows the constraint from CMS
experiment. Assuming chargino lifetime to be 0.2 ns, which is the theoretical prediction, the most
severe exclusion limit is the chargino mass of 460 GeV from the disappearing track search in the
ATLAS experiment. The disappearing track search in the ATLAS experiment [20] and this thesis
inherit analysis method applied to the Run 1 data discussed in Ref. [18].
Inclusive gluino search is also performed by ATLAS [23] and CMS [24, 25]. Fig. 2.11 and 2.12
shows exclusion limits by each experiment. Inclusive gluino searches include the model which is2.6. SUMMARY OF CURRENT CONSTRAINT

21√
Figure 2.7: SUSY particle√production cross sections at the LHC [19]. Solid lines are for s= 8 TeV
and dashed lines are for s= 13–14 TeV. Blue lines are for electroweak gaugino pair production,
green lines are for stop pair production, pink lines are for squark pair production, red lines are forgluino pair production and light blue lines are sum of the strong production.

q

π±

p
g̃

p

j

q

g̃
χ̃01
(a) pp → g̃g̃ → qqqqχ˜1 ± χ˜1 0

χ̃01

χ̃01

χ̃±
1

q

p

p

χ̃±
1

χ̃01
π±

q
(b) pp → jχ˜1 ± χ˜1 0

Figure 2.8: Representative chargino production diagrams. (a) Strong production channel. (b) Electroweak production channel.

CHAPTER 2. PHYSICS MOTIVATION22± 0 ∼± ∼∼χ ∼χ , χ χ production±11tanβ = 5, µ > 0

1 11τ∼χ± [ns]

10
4
3
2
1

0.4
0.3
0.2

ATLAS
s=13TeV, 36.1 fb-1

0.1

Observed 95% CL limit (±1 σtheory )Expected 95% CL limit ( ±1 σexp )

0.04
0.03
0.02
0.01

ATLAS (8 TeV, 20.3 fb-1, EW prod.)
Theory (Phys. Lett. B721 (2013) 252)
ALEPH (Phys. Lett. B533 (2002) 223)

100

200

300

400

500

600

700

m∼χ± [GeV]1

Figure 2.9: Chargino exclusion limit of ATLAS and LEP [20]. The red solid line is the observed limit
and red dashed line is the observed limit with signal cross-section shifted by 1 standard deviation. The
black dashed line is expected exclusion limit and the yellow band is its uncertainty. The blue dashedline is the exclusion limit from Run 1 result of the ATLAS and the green shaded region is excluded
by LEP. The gray dashed line is the theoretical prediction of the chargino lifetime as a function of thechargino mass.

2.6. SUMMARY OF CURRENT CONSTRAINT

231τ∼χ± [ns]19.5 fb-1 (8 TeV)

CMS

102

10

tanβ = 5, µ > 0

Expected limit ±2 σ
Expected limit ±1 σ
Expected limit

1

Observed limit

10-1
100

200

300

400

500

600

m∼χ± [GeV]1

Figure 2.10: Chargino exclusion limit of CMS [21]. The black solid line is observed limit, theblack dashed line is expected limit, the green band is 1 standard deviation from expected limit and theyellow band is that of 2 standard deviation.

CHAPTER 2. PHYSICS MOTIVATION

24
focused on in this thesis.
0~~~
gg production, B (g → qq ∼χ )=100%

ATLAS
s = 13 TeV, 36.1 fb-1

1600

1

m∼χ0 [GeV]

1

1800

0-leptons, 2-6 jets

1400

MEff or RJR (Best Expected)
All limits at 95% CL

1200

SUSY

Obs. limit (± 1 σtheory)
Exp. limits (± 1 σexp)
Exp. limits MEff
Exp. limits RJR
0L obs. limit (13 TeV, 3.2 fb -1)

1000

1

m
g~ <

m

600

χ∼ 0

800

400
200
0

500

1000

1500

2000

2500

m~g [GeV]
Figure 2.11: Gluino pair production exclusion limit of ATLAS and LEP [23]. The same definitionof legends is used as in Fig. 2.9. The pink dashed line is expected limit by analysis using MEﬀ whichis the scalar sum of jets pT and missing transverse energy, the green dashed line is expected limit
by analysis using recursive jigsaw reconstruction (RJR) [26, 27, 28] and the blue shaded region is
excluded region by analysis with integrated luminosity of 3.2 fb−1 .

WIMP dark-matter search AMS-02 experiment [29] measured positron flux at the ISS. Fig. 2.13
shows the result. It shows significant excess from expected flux from collisions of cosmic rays. It
is consistent with the positron energy spectrum expected from annihilations of dark-matter with themass of 1 TeV. However, the source of excess may be due to other astrophysical phenomena such aspulsars. This puzzle is under investigation [29].
H.E.S.S. [30] and Fermi [31] experiments set limits of the dark-matter annihilation rate (σ(χ˜1 0 χ˜1 0 →W + W − )3, σ(χ˜1 0 χ˜1 0 → γγ)3 + σ(χ˜1 0 χ˜1 0 → γZ 0 )3 where 3 is speed) as shown in Fig. 2.14 [32].

2.6. SUMMARY OF CURRENT CONSTRAINT

25

1600

CMS Preliminary

Moriond 201735.9 fb-1 (13 TeV)

miss

0
1

m∼χ [GeV]∼
pp → ~g~g, ~g → q q χ01

1400

SUS-16-033 (HT )SUS-16-036 (MT2)

Expected
Observed

1200
1000
800
600
400
200
0

800

1000

1200

1400

1600

1800

2000

2200

m~g [GeV]
Figure 2.12: Gluino pair production exclusion limit of CMS [24, 25]. The blue lines are for analysis
using Hmiss(the magnitude of the vector pT sum) and the green lines are for analysis using MT2 (theTpossible minimum transverse mass of the maximum transverse mass of a pair). The solid lines areobserved limit and dashed lines are expected limit.

Figure 2.13: Positron flux measured by AMS-02 [29]. Red points are data, green line is expectedbackground distribution and brawn line is expected distribution with dark-matter with mass of 1 TeV.

CHAPTER 2. PHYSICS MOTIVATION

26

Thermal
10-22
-21

10

10-25
-24

10

10-26

1

10

2

10-24
-23

ΣΓΓ + ΓZ v Acm3  sE

ΣWW v Acm3  sE

10-23
10-22

10-25
10-27
-26

10

0.5

1.0

1.5
2.0
M2 @TeVD

2.5

3.0(a) Exclusion limit for thermal dark-matter.

W h2 = 0.12
10-22
-21

10

10-25
-24

10

10-26

1

10

2

10-24
-23

ΣΓΓ + ΓZ v Acm3  sE

ΣWW v Acm3  sE

10-23
10-22

10-25
10-27
-26

10

0.5

1.0

1.5
2.0
M2 @TeVD

2.5

3.0(b) Exclusion limit for non-thermal dark-matter.

Figure 2.14: The red dashed line is the annihilation rate of σ(χ˜1 0 χ˜1 0 → W + W − )3 and the red shaded
region is the excluded region by the Fermi experiment. The blue solid line is the annihilation rate ofσ(χ˜1 0 χ˜1 0 → γγ)3 + σ(χ˜1 0 χ˜1 0 → γZ 0 )3 and blue shaded region is the excluded region by H.E.S.S. The
yellow shaded region corresponds to Ωh2 = 0.12 ± 0.006. The black shaded region shows the region
where a thermal wino dark-matter exceeds the observed relic density [32].

Chapter 3
The LHC and the ATLAS detector
3.1 The Large Hadron Collider
The Large Hadron Collider (LHC) is the largest proton-proton collider in the world constructed in theunderground of around the CERN, in the suburbs of Geneva. From 2015, the center of mass energy ofcollision is 13 TeV. Fig. 3.1 shows a schematic view of the LHC and its injection accelerator systems.

Figure 3.1: A schematic view of the LHC. [33]27CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

28

240
220 ATLAS Online, s=13 TeV
200
180
160
140
120
100
80
60
40
20
0
0
5 10 15 20 25 30∫Ldt=42.7 fb-1

2015: <µ> = 13.7
2016: <µ> = 24.9
Total: <µ> = 23.7

2/17 calibration

Delivered Luminosity [pb-1/0.1]

Acceleration of proton beam starts at the LINAC2. The LINAC2 produces bunches of protons withthe energy of 50 MeV. Then the bunches are injected into the Proton Synchrotron Booster (PSB). It
is circular accelerator. The PSB increases the proton energy up to 1.4 GeV and makes the bunch size
smaller. Next accelerator is the Proton Synchrotron (PS). Protons are accelerated up to 26 GeV. The
PS also divides bunch to two or three bunches by radio frequency pulses. Then the proton beam is
injected into the Super Proton Synchrotron (SPS). Proton energy reaches 450 GeV in the SPS. Finally,
proton bunches are sent to the LHC in both directions to acquire energy of 6.5 TeV to make collisions.

35

40

45

50

Mean Number of Interactions per Crossing

Figure 3.2: The mean number of interactions per crossing distribution [34]. The red line filled withgreen is that in 2015, the blue line filled with light blue is that in 2016, and the black line filled withpurple is the total from 2015 to 2016. Run 1 is from 2011 to 2012. Run 2 is from 2015 to 2017. In
this thesis, data obtained in Run 2, in 2015 and 2016, is used.
The performance of the LHC is summarised below. The total number of bunches is 2200. Eachbunch contains 1.1 × 1011 protons. Bunch spacing is 25 ns. The beam crossing angle at the interaction
point is 370 µrad at the start of the Run 2 and improved to 280 µrad in 2016. Fig. 3.2 shows the
distribution of mean number of interactions per crossing. It ranges from 7 to 50 and mean value in the
total duration is 23.7. Peak luminosity is 1.4 × 1034 cm−2 s−1 . The evolution of integrated luminosity
for each year is shown in Fig. 3.3.

3.2 The ATLAS detector
Fig. 3.4 shows an overall picture of the ATLAS (A Toroidal LHC ApparatuS) detector. It has a cylindrical shape with the z-axis corresponding to the beam line. The most inner part of the detector system
is called Inner Detector (ID), which consists of the pixel detector, the SemiConductor Tracker (SCT)
and the Transition Radiation Tracker (TRT). The ID is surrounded by a solenoid magnet providing
a magnetic field of 2 T in the z-axis direction. Calorimeters are located just outside of the solenoid.
The calorimeter consists of the LAr electromagnetic calorimeter and tile calorimeter in the barrel

29

45
40
35
30

ATLAS Online Luminosity
2011 pp2012 pp2015 pp2016 pp2017 pp

s = 7 TeV
s = 8 TeV
s = 13 TeV
s = 13 TeV
s = 13 TeV

25
20
15

initial 2017 calibration

Delivered Luminosity [fb-1]

3.2. THE ATLAS DETECTOR

10
5
0
Jan

Apr

Jul

Oct
Month in Year

Figure 3.3: Integrated luminosity vs time in each year [34]. The green line is that in 2011, the blueline is that in 2012, the red line is that in 2015, the pink line is that in 2016 and the orange line is thatin 2017.

Figure 3.4: Schematic view of the ATLAS detector [35]. It is consists of the pixel detector, the SemiConductor Tracker (SCT), the Transition Radiation Tracker (TRT), solenoid magnet, liquid Argon(LAr) electromagnetic calorimeter, tile calorimeter, LAr hadronic calorimeter, toroid magnets, andmuon chambers.

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

30

region, and LAr calorimeters in the end-cap region. In the most outer region, toroidal magnets andmuon chambers are located. Luminosity detector, Beam Condition Monitor (BCM) and LUminosity
measurement using Cherenkov Integrating Detector (LUCID) are located at the very forward region.
Each component of the ATLAS is reviewed in the following sections.
The coordinate system of the ATLAS detector is as follows; the origin of the coordinate system
is at the centre of the interaction region. z-axis is defined to be the beam line direction as mentioned
above. x-axis points to the center of the LHC. y-axis is set to the vertical upward direction. Polar
angle θ is defined with respect to the z-axis, and azimuthal angle ϕ is measured around z-axis (ϕ = 0
at x-axis). For convenience, pseudorapidity η is often used instead of θ. The definition isθ
2
It is also used to define the angular distance of two objects.
η ≡ − ln tan∆R ≡√(∆η)2 + (∆ϕ)2

(3.1)

(3.2)

3.2.1 Inner Detector

Figure 3.5: Cut-away view of the ATLAS inner detector. [36]
Inner Detector (ID) is used for tracking of charged particles [38, 39, 40]. Fig. 3.5 and 3.6 show
the overview and the cross-section of the ATLAS ID. The whole inner detector is installed inside3.2. THE ATLAS DETECTOR

Figure 3.6: Cross-sectional view of the ATLAS inner detector. [37]

31

32

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

the solenoid coil and magnetic field of 2 T along the z-axis is provided to measure the transverse
momentum of charged particles. The ID is composed of three types of detectors, pixel detector,
SemiConductor Tracker (SCT) and Transition Radiation Tracker (TRT).
The pixel detector is a highly pixelated silicon semiconductor detector. The innermost layer islocated at the radius of 33.5 mm in barrel region. This layer is called Insertable B-Layer (IBL). It was
installed during long shutdown just before Run 2. Most of the pixel detectors are n+ -in-n planar typedetector, but IBL in the high-η region uses the 3D type detector. The planar type has n+ type implants
at the readout side, n-type bulk, and p-n junction at the other side. For the 3D type, n+ doped columns
and p+ doped columns are located vertically to the surface of the module. The voltage is applied to thedirection parallel to the surface. The thickness of planar type is 200 µm and the thickness of 3D typeis 230 µm in IBL. The thickness of the other layers is 250 µm. In barrel region, IBL is at the radiusof 33.5 mm and pixel layers are at radius of 50.5 mm, 88.5 mm, and 122.5 mm covering |η| < 1.9.
In each end-cap region, pixel layers are at z = 495 mm, 580 mm, and 650 mm covering |η| < 2.5
combined with the barrel region. The pixel size is 50 × 250 µm2 (ϕ direction × η direction) for IBL
and 50 × 400 µm2 for the other layer. The typical position resolution is 10 × 66.5 µm2 for IBL and14 × 115 µm2 for the other layer. Ganged pixel distributes in inter-chip regions. Ganged pixel is the
pixel which has shared readout with another pixel. The pixel detector has particular importance on
this thesis.
The SCT is a silicon microstrip detector. A layer of SCT consists of 40 mrad tilted two microstrip
sensor layers. The pitch of the microstrip sensor is 80 µm. SCT layers are at radius of 299 mm, 371
mm, 443 mm, and 514 mm in barrel region. The layers in the end-cap are located at z = 853.8 mm,
934 mm, 1091.5 mm, 1299.9 mm, 1399.7 mm, 1771.4 mm, 2115.2 mm, 2505 mm, and 2720.2 mm
in each end-cap region. The typical position resolution is 17 × 580 µm.
The TRT is a straw tube gaseous detector. The gas is a mixture of Xe, CO2 , and O2 . However,
the gas leakage happened and Ar, CO2 , and O2 gas is used for compensation of Xe gas leakage. It
enables continuous tracking and particle identification between electron and pion. TRT covers from
563 mm to 1066 mm in radius in barrel region and 848 mm < z < 2710 mm in end-cap region. The
typical position resolution is 0.17 mm along ϕ-axis. The position resolution along z-axis is very bad
due to the long straw length of 150 cm at maximum.

3.2.2 CalorimeterAs shown in Fig. 3.7, the ATLAS calorimeter system is composed of liquid Argon (LAr) electromagnetic calorimeter [42] and Tile calorimeter as a hadron calorimeter [43] in the barrel region covering|η| < 1.5. The end-cap regions are covered by LAr electromagnetic end-cap calorimeter (EMEC)
and LAr hadron end-cap calorimeter (HEC) covering 1.4 < |η| < 3.2, and LAr Forward Calorimeter(FCal) in the forward region. Electromagnetic calorimeter is located in the inner part of the calorimeter and measures electron or photon energy. Hadronic calorimeter is outer part of the calorimeter andmeasures hadronic energy.
The LAr calorimeter is operated at −183◦ C. Fig. 3.8 shows the structure of the LAr calorimeter.
It has an accordion-like structure. It can put readout services in outside of the LAr calorimeter. The
absorber of the calorimeter is lead.
The LAr electromagnetic calorimeter has presampler in the innermost layer to observe the initial3.2. THE ATLAS DETECTOR

33

Figure 3.7: Cut-away view of the ATLAS calorimeter. End-cap calorimeter is located both sides ofthe barrel. [41]34

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

development of EM showers for particle identification (γ/π0 , e/π± ). LAr EM calorimeter consists ofthree parts in depth, front(Strip), middle, and back. The cell division granularities of these three parts
are diﬀerent. The front is the most granular part and the back is the coarsest as shown in Fig. 3.8. In
this design, the front part is used to discriminate photons from pions, the middle part measures mostpart of the shower energy, and the back part measures the leak from the EM calorimeter to identify
hadrons from electrons and photons. The total depth ranges from 24 to 34 radiation length (X0 ). The
granularity of the LAr electromagnetic calorimeter is summarised in Table 3.1.
The LAr electromagnetic end-cap calorimeter (EMEC) consists of 2 wheels, each covers 1.4 <|η| < 2.5 and 2.5 < |η| < 3.2. The amplitude of the accordion wave scale increases with the radius.
The cells of the LAr hadronic end-cap calorimeter (HEC) have pointing geometry in azimuth,
but only ”pseudo-pointing” in η in order to prevent particles from sneaking through the detector
boundaries. The perspective view of the HEC is shown in Fig. 3.9. It consists of 2 wheels of outerradius 2.03 m. The absorber copper thickness is 25 mm for the one near the Interaction Point, IP(First wheel), and 50 mm for the other absorbers which are farther from the IP (Second wheel). The
depths of sampling are 1.4 λI and 2.9 λI for the first wheel and 5.7 λI for the second wheel, where λI
is the interaction length.
The Forward Calorimeter (FCal) is located at 4.7 m from the IP. It consists of 3 sections. The firstsection uses copper and the other sections use tungsten for the absorber. The structure is shown in
Fig. 3.11.
Table 3.1: The granularity of the LAr electromagnetic calorimeter (pseudorapidity, azimuth) [42]
η range0 < |η| < 1.4 1.4 < |η| < 1.8 1.8 < |η| < 2.0 2.0 < |η| < 2.5 2.5 < |η| < 3.2
Presampler
0.025 × 0.1
0.025 × 0.1
Sampling 1
0.003 × 0.1
0.003 × 0.1
0.004 × 0.1
0.006 × 0.1
0.1 × 0.1
Sampling 2 0.025 × 0.025 0.025 × 0.025 0.025 × 0.025 0.025 × 0.025
0.1 × 0.1
Sampling 3 0.050 × 0.025 0.050 × 0.025 0.050 × 0.025 0.050 × 0.025
Trigger
0.1 × 0.1
0.1 × 0.1
0.1 × 0.1
0.1 × 0.1
0.2 × 0.2
The tile calorimeter is a sampling calorimeter with steel absorber and scintillator as the sensitive
material, which is read out by wavelength shifting fibres (WLS). The scintillating tiles are set perpendicular to the beam axis. Fig. 3.12 shows the design of the tile calorimeter. Each WLS runs radiallyand is connected to a PMT. It is divided into three parts along the beam axis, a long central barrel
and two extended barrels as shown in Fig. 3.7. At η = 0, tile calorimeter has three layers of readoutsamplings with interaction lengths of 1.4, 3.9 and 1.8. Angular segmentation is ∆ϕ × ∆η = 0.1 × 0.1(0.1 × 0.2 in the third layer).

3.2.3 Muon spectorometer
The Muon Spectrometer (MS) is used for tracking of charged particles in particular muons, which
penetrate the calorimeters [45]. The MS is located just outside of the calorimeters. Fig. 3.13 and3.14 shows cross sections in r-z and x-y planes respectively. Air-core toroid magnets provide magnetic
field to bend charged particles and to measure the momentum. In |η| < 1.0, the magnet consists ofeight coils around hadron calorimeter and provides 3 Tm of bending power. In 1.4 < |η| < 2.7, the3.2. THE ATLAS DETECTOR

Figure 3.8: Structure of the ATLAS electromagnetic calorimeter. [42]

35

36

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

Figure 3.9: Perspective view of one end-cap calorimeters. [42]Figure 3.10: Position of the LAr calorimeters [44].

3.2. THE ATLAS DETECTOR

37

Figure 3.11: The structure of the ATLAS Forward calorimeter [44]. Red region is filled with LAr.

magnet consists of two smaller end-cap magnets at the both ends of the barrel toroid and provides 6
Tm of bending power. In 1.0 < |η| < 1.4, the magnetic field is provided by the combination of barrel
and end-cap coils, thus this region is called as transition region. Fig. 3.15 shows toroid bending power
as a function of η.
In the barrel region, three cylindrical layers containing muon chambers, called stations, are placed.
In the end-cap and the transition region, muon chambers are placed in three stations vertically. Mostof the chambers are Monitored Drift Tubes (MDT). The MDT consists of 30 mm diameter aluminium
tube and tungsten-rhenium (W-Re) wire. The tube is filled with an Ar-CH4 -N2 (91%, 5%, 4%) mixture
gas at 3 bar of absolute pressure. The MDT gives single-wire resolution of 80 µm in z-axis. In large
η region, Cathode Strip Chambers (CSC) are used. The CSC is a multiwire proportional chamber.
The anode wire pitch is 2.54 mm and the cathode readout pitch is 5.08 mm. The gas is a mixture of
Ar-CO2 -CF4 (30%, 50%, 20%). RMS resolution is better than 60 µm.
For trigger, the Resistive Plate Chamber (RPC) on the front side and the back side of the MDT
station covers |η| < 2.4 and the Thin Gap Chamber (TGC) covers the end-cap region. The RPC
is a gas detector with space-time resolution of 1 cm × 1 ns with digital readout. An electric fieldof 4.9 kV/mm is applied in the narrow gap (C2 H2 F4 94.7%, Iso-C4 H1 5%, SF6 0.3%) between two
resistive bakelite plates separated by polycarbonate spacer. The TGC design is similar to multiwire
proportional chamber, but the cathode-anode distance of 2.8 mm is longer than anode wire pitch of 1.8
mm. Quenching gas is a mixture of 55% CO2 and 45% n-pentane. The TGC is operated in saturated
mode.

38

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

Figure 3.12: The Tile Calorimeter design. [43] Double readout means that the scintillation light isread out by a pair of WLS fibres located on both ϕ edge of scintillating tiles.

3.2. THE ATLAS DETECTOR

39

Figure 3.13: r-z cross-section of the MS. [44]3.2.4 Luminosity detector
Beam Condition Monitor (BCM) consists of four 8 × 8 mm2 diamond sensors. The BCM is locatedat 5 cm radius from beam and 1.84 m from the IP on each side at |η| = 4.2. A hit is recorded when thesignal is over the threshold. The Vertical pair (BCMV) and the horizontal pair (BCMH) is read out
separately.
LUminosity measurement using Cherenkov Integrating Detector, LUCID, consists of two arraysof Aluminium tubes operated in a vacuum. It points the IP and surrounds the beam pipe (z ∼17 m)
covering 5.6 < |η| < 6.0. Charged particle emits Cherenkov light in the quartz window and photons
are collected at the end of the tube. Photons are read out by a PMT via quartz fibre bundles.
Both the BCM and the LUCID have no dead time by the Central Trigger Processor (CTP). The
hit patterns are read out at each bunch crossing.
The luminosity measurement method is discussed in Ref. [48]. The bunch luminosity Lb is calculated by
Lb =

µ fr
,
σinel

(3.3)

where µ is the average number of inelastic interactions per bunch crossing, fr is the bunch revolution
frequency, and σinel is the pp inelastic cross-section. The total instantaneous luminosity L is
L=

nb
∑
b=1

Lb = nb ⟨Lb ⟩ = nb⟨µ⟩ fr
,
σinel

(3.4)

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

40

Resistive plate chambers
MDT chambers
Barrel toroidcoils
End-cap
toroidCalorimeters

Inner detector

Figure 3.14: x-y cross-section of the MS. [45]

3.2. THE ATLAS DETECTOR

Figure 3.15: Toroid bending power as a function of η for two ϕ values [44].

Figure 3.16: Schematic figure of the BCM. [46]

41

42

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

Figure 3.17: Schematic figure of the LUCID. [47]

3.2. THE ATLAS DETECTOR

43

where nb is the number of bunch pairs. The bunch luminosity is calculated using the visible average
number of inelastic interactions per bunch crossing µvis = ϵµ, where ϵ is the eﬃciency of interaction
point detection due to the detector and algorithm, the bunch luminosity isµvis fr
,
(3.5)
σvis
where σvis is the visible cross-section defined as σvis ≡ ϵσinel . The BCM and the LUCID measure µvis
using EventOR algorithm described as follows. Assuming the Poisson distribution, the probability ofobserving at least one event is
Lb =

−µvis
PEventOR (µOR,vis ) = NOR /N BC = 1 − e
OR

(3.6)

where NOR is the number of event count by the detector and NBC is the number of bunch crossings in
the same time interval. Therefore,µOR
vis = − ln (1 − NOR /N BC ).

(3.7)

The LUCID can measure up to about 30 interactions per bunch crossing and the BCM can measurelarger interactions per bunch crossing thanks to the lower acceptance. The calibration is done by van
der Meer method [49]. This method determines the bunch luminosity by beam parameters and therelation to µvis .

3.2.5 Trigger and data acquisition system
Because it is impossible to process and store entire event in the ATLAS for each bunch crossing
due to limited data processing capability and storage, the ATLAS uses dedicated trigger to pick up
interesting events.
Fig. 3.18 shows the schematic diagram of the ATLAS Trigger and Data Acquisition system(TDAQ). Trigger system has two levels, Level-1 and High Level Trigger (HLT).
The Level-1 trigger is hardware trigger. Calorimeters are used to measure energies and to identify the objects of electron, photon, tau, jet and Missing Transverse Energy (MET or ETmiss ). Muon
detectors and TileCal are used for muons. If an event passes criteria on pT and the number of objects,
Level-1 trigger is accepted and the detector readout is executed. 100 MHz of raw event rate is reduced
to 100 kHz.
Events which passed the Level-1 trigger are processed in the HLT. Here, oﬄine-like algorithm
which is discussed later in Chap.5 runs using more detector information. Finally, event rate of 1 kHz
is recorded.

44

CHAPTER 3. THE LHC AND THE ATLAS DETECTOR

Figure 3.18: The ATLAS TDAQ system in Run 2. L1topo (trigger using event topology) and Fast
Tracker is under commissioning in 2016. [50]Chapter 4
Data and MC samples
4.1 Data samples√
The data of pp collisions at the centre of mass energy s = 13 TeV were collected by the ATLAS detector from 2015 to 2016. The integrated luminosity of good quality data is 36.1 fb−1 with uncertaintyof 3.2%. The triggers used in this thesis are summarised in Table 4.1. The naming scheme of the above
triggers is HLT (xe as ETmiss , e as electron or mu as muon)(energy threshold in GeV) (measurement
method L1 trigger for ETmiss or identification quality for lepton). The trigger thresholds were changed
with instantaneous luminosity.
For signal search, missing transverse energy (ETmiss ) trigger based on calorimeter is used. The
ETmiss for trigger is calculated from only calorimeter activity.The trigger performance will be discussed
later in Sec. 7.2. For background estimation, single electron and single muon triggers are also used.
Electron trigger uses electromagnetic calorimeter information. Muon trigger uses the RPC and the
TGC in the MS (Sec. 3.2.3).

4.2 Simulated samples
MC samples of signal events are used to simulate signal distribution and to estimate selection eﬃciency. On the other hand, MC samples of standard model events are used only for validation ofanalysis method, not for the evaluation of the number of backgrounds.
√
All samples were generated at the centre of mass energy s = 13 TeV with a single configuration of the detector corresponding to the beginning of the 2015 data taking and are simulated using
GEANT4 [51, 52].

4.2.1 Pile-up simulation
Every sample used in this analysis is overlaid additional minimum bias events on during digitisation. Minimum bias events were generated by Pythia 8.186 [53] with the A2 tune for minimum bias
events [54] and the α s leading-order parton distribution function (PDF) set MSTW2008LO [55]. The
number of pile-up interactions in an event is distributed as observed as for the 2015 to 2016 data.
45

CHAPTER 4. DATA AND MC SAMPLES

46

Table 4.1: List of triggers used in this thesis.
Trigger nameThreshold of object energy (or transverse momentum)
ETmiss triggers
HLT xe70 mht
70 GeVHLT xe90 mht L1XE50
90 GeVHLT xe100 mht L1XE50
100 GeVHLT xe110 mht L1XE50
110 GeVElectron triggers
HLT e24 lhmedium L1EM20VH
24 GeVHLT e24 lhtight nod0 ivarloose
24 GeVHLT e26 lhtight nod0 ivarloose
26 GeV
Muon triggers
HLT mu20 iloose L1MU15
20 GeVHLT mu24 iloose
24 GeVHLT mu24 ivarloose
24 GeVHLT mu26 imedium
26 GeVHLT mu26 ivarmedium
26 GeV
However, the number of pile-up event in MC was scaled by 1.16 on average to correct the diﬀerencein the ratio of the visible cross-section to the inclusive cross-section between data and MC [56].

4.2.2 Signal Monte Carlo sample
Signal model
Gluino pair production with cascade decay into chargino channel is targeted. Typical diagrams of thetarget processes are illustrated in Fig. 4.1.
Here, the simplified model defined in Ref. [57] is used. This model uses eﬀective Lagrangian withminimal number of new particles. Assumed branching ratios of gluino decay modes to g̃ → qqχ̃0 ,g̃ → qqχ̃− and g̃ → qqχ̃+ are all 1/3. Therefore, the branching ratio of Fig. 4.1(a) is 4/9 and thatof Fig. 4.1(b) is 4/9. The rest of the process does not include chargino in decay products. Only thefour light quarks (d,u,c,s) are considered and the heavy quarks (t,b) are not considered for the q. The
chargino proper lifetime follows the exponential function with average proper lifetime. Charginos
were forced to decay into χ˜1 0 + π± in the Geant4 simulation.
The signal topology is characterised by• Four high pT jets
• Large missing transverse momentum (ETmiss ) from neutralinos• One ( or two) high-pT disappearing track(s)4.2. SIMULATED SAMPLES

47

q

q

q
π±

p
g̃

g̃

p

χ̃01
q
(a) pp → g̃g̃ → qqqqχ˜1 ± χ˜1 0

q

π±

p
g̃

χ̃01

χ̃±
1

q

p

g̃

χ̃01

χ̃±
1
χ̃±
1

χ̃01
π±

q

q

(b) pp → g̃g̃ → qqqqχ˜1 ± χ˜1 ±Figure 4.1: Typical diagrams of gluino production processes.
One advantage of this channel is that the larger the mass diﬀerence between gluino and chargino
causes the more Lorentz boost of charginos. Consequently, the flight length of chargino become
longer in the lab frame. Fig. 4.2 shows a normalised distribution of decay radii of charginos in thelab frame for gluino cascade decay with the gluino mass of 1800 GeV, the chargino mass of 500 GeV,and lifetime of 0.2 ns, and also that for the direct electroweak production (see Fig. 2.8(b)) with the
chargino mass of 500 GeV, lifetime of 0.2 ns. Charginos from gluino decay tend to decay at a larger
radius. As discussed later in Sec.5.1.4, our main target is chargino decay at radius between 122 mm
and 300 mm, which is between the outermost layer of the pixel detector and the innermost layer of
the SCT. In this region, the signal from gluino pair decay has twice more eﬃciency than the events ofdirect production as shown in Fig. 4.2.
Another advantage is that the gluino pair production cross-section is larger than that for the directelectroweak gaugino production because gluino is a coloured particle. In addition, depending on therelation of the gluino mass and the chargino mass, the higher chargino mass region may be reachable
in this channel. Thanks to multiple high pT jets, gluino pair production events are triggered by ETmiss
trigger with very high eﬃciency.
Simulation setting
Several benchmark signal points were prepared and used for this analysis. The signal MC samples
were generated using MadGraph5 [58] interfaced to PYTHIA8.212 [53] with A14 NNPDF23LO [59]parton distribution functions (PDFs). These samples were simulated based on the ATLAS detector
configuration of 2015 with Geant4 [51, 52]. Then pile-up events were overlaid at the digitisationlevel.
The mean lifetime of the chargino is set to 0.2 ns or 1.0 ns. Samples were generated for the signal
points over the chargino mass range from 200 to 1800 GeV and the gluino mass range from 700
to 2200 GeV. The mass diﬀerence between chargino and neutralino was fixed to be 160 MeV. The
parameter sets of produced samples are listed in Table 4.2. The dataset size depends on the selection
eﬃciency (see Sec. 7.1) to keep the selected number of events to be O(100).

CHAPTER 4. DATA AND MC SAMPLES

Fraction of charginos

48

Gluino pair production

10−1

Direct production

10−2

10−3

10−4
0

100 200 300 400 500 600 700 800 900 1000
Decay radius [mm]Figure 4.2: Chargino decay radius distribution. The black points show the distribution of gluinocascade decay with the gluino mass of 1600 GeV, the chargino mass of 500 GeV, lifetime of 0.2 ns
from gluino decay and the red points show that for the electroweak direct electroweak production
with the chargino mass of 500 GeV, lifetime of 0.2 ns (red). The radius is measured from the beamline in cylindrical coordinate.

4.2. SIMULATED SAMPLES

49

Signal MC samples with diﬀerent mean lifetimes were obtained by applying event weights so thatthe distribution of the proper lifetime follows that of the requested mean lifetime. The event weight
w is given bynχ˜1 ±
[ (
)]
∏
1
1
τ0
exp −ti−,(4.1)
w(τχ˜1 ± ) =
±
±
τ
τ
τ
χ
˜
χ
˜
0
1
1
i
where nχ˜1 ± is the number of charginos in the event, τ0 is the chargino mean lifetime set in the simulation for the sample, τχ˜1 ± is requested mean life time, ti is the proper lifetime of the i–th chargino.
Signal cross-sections were calculated to the next-to-leading order in the strong coupling constant(NLO) using Prospino2 [60], adding the resummation of soft gluon emission at the next-to-leadinglogarithmic accuracy (NLO+NLL) [61]. An envelope of cross-section predictions calculated from 68% ambiguities in PDF, physics parameters, factorisation scale, and renormalisation scale is used as
the uncertainty.
mg̃ [GeV]
Cross-section [pb]mχ˜1 ± [GeV]
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200

700
3.53

0.2,1.0800
1.49

0.2,1.0
0.2,1.0900
0.677

0.2,1.0
0.2,1.0
0.2,1.0

1000
0.325

0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0

1200
1400
1600
0.0856 0.0253 0.00809
Life times [ns]

1.0
1.0
1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0

1.0
1.0
1.0
1.0
1.0
1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.01800
0.002762000
0.000980

2200
0.000359

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.2,1.0
0.2,1.0
0.2,1.0
0.2,1.0

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.2,1.0
0.2,1.0
0.2,1.0

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

Table 4.2: Summary of MC signal sample√ parameter list for the gluino mass, the chargino masses,
lifetime and their NLO cross-sections at s = 13 TeV for strong production.

4.2.3 Background MC samples
In this section, MC samples of Standard Model processes are introduced. They are used only for
analysis validation and not for the actual background estimation.
Prepared processes are tt, W → eν, W → µν, W → τν, Z → νν, Z → ee, Z → µµ, Z → ττ,and multijet events. tt events were generated by PowhegPythiaEvtGen [62, 53, 63] using P2012
PDF [64]. The data size is equivalent to 131 fb−1 . W → ℓν and Z → νν events were generated by
Sherpa [65] using NNPDF30NNLO PDF [66]. The data size varies depending on the energy scale.

50

CHAPTER 4. DATA AND MC SAMPLES

For small energy scale, the data size is equivalent to 1 fb−1 . For large energy scale, the data size isequivalent to 7 × 104 fb−1 . Z → ℓℓ events were generated by PowhegPythia8EvtGen [62, 53, 63]
using AZNLOCTEQ6L1 PDF. The data size is equivalent to 95 fb−1 . Multijet events were generated
by Pythis8EvtGen [53, 63] using A14NNPDF23LO PDF. The data size varies depending on theenergy scale. For small energy scale, the data size is equivalent to 0.4 fb−1 . For large energy scale,the data size is equivalent to 7 × 1013 fb−1 .

Chapter 5
Object reconstruction and the definition
5.1 Inner Detector tracking
Tracking in the Inner Detector is performed to reconstruct trajectories of charged particles using hits
in the inner detectors (Sec. 3.2.1). First, standard tracking is described and then dedicated tracking of
tracklet for disappearing track reconstruction is discussed.

5.1.1 Tracking parameter definition
A track is represented by 5 parameters. Fig. 5.1 illustrates these parameters. The parameters referto the perigee point, the nearest point of the track to the beam spot in the transverse plane and theprimary vertex (see Sec. 5.2) for the r-z plane. The charge over transverse momentum q/pT , thetransverse impact parameter d0 , the longitudinal impact parameter z0 , the azimuthal angle at perigee
ϕ0 , and the polar angle θ are shown in the Fig. 5.1. Instead of θ, the pseudorapidity η at the perigee
defined by Eq. 3.1 is also used.

5.1.2 Standard track reconstruction
The ATLAS standard tracking is discussed in Ref. [67] and Ref. [68]. There are 2 approaches, naming“inside-out” and “outside-in” tracking.
Reconstruction procedure
Inside-out tracking Hit space points formation is done to translate the pixel cluster or pair of SCT
strip hits to the three dimensional point of the charged particle hit. Then seeding using the pixel andthe SCT hits is performed from the inner layer. The seeding is done with roughly estimated perigee
parameter requirements. Then hit finding from seeds is executed to outer layers by applying window
search to the seed direction. Simplified Kalman filtering and smoothing approach is used to determine
whether a hit is added or rejected to track component candidates. The standard tracking requires atleast 7 hits in silicon detector, the pixel and the SCT detector.
51

52

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

Figure 5.1: Track parameter definition illustration. The transverse plane (left) and the r-z plane(right).The origin is defined by the beam spot in the transverse plane and the origin is defined by the
primary vertex (see Sec. 5.2) in the r-z plane.
Next, ambiguity solving is performed. It is to reject fake tracks and to discriminate overlapping
tracks with shared hits. Ambiguity solving is done by scoring of the track quality. Scoring uses thenumber of hits in each detector, χ2 , log pT , the number of shared hits, the number of holes which is
missing hit layer on which a hit is expected. The treatment of shared hits is optimised for high pileupcase in Run 2 to identify merged cluster eﬃciently. The neural network evaluation of merged cluster
is performed during ambiguity solving to use not only cluster information but also track candidate
information. When a track is qualified, track extension to the TRT detector is performed. Using the
track information in silicon detectors as input, candidate TRT hits associated to the inner track arefound by road finding through track extrapolation and line fit. The candidate TRT hits are evaluatedby track fit and quality scoring for ambiguity solving, but the pixel and the SCT hits are not modified
during TRT extension. Then same ambiguity solving as used for silicon tracking is performed todetermine the final track collection of inside-out tracking.
Outside-in tracking This tracking starts from a global pattern recognition in the TRT. It is doneusing a standard Hough transform mechanism. Here, hits already used in the inside-out tracking is
avoided. Then, the TRT segments are extended into the silicon detectors.

5.1.3 Tracklet reconstruction
Tracklets are short tracks which cannot be reconstructed by standard tracking. Because the ATLAS
standard tracking requires at least 7 silicon hits, shorter disappearing track cannot be reconstructed.

5.1. INNER DETECTOR TRACKING

53

Therefore, another tracking with looser number of hits requirement is performed using the left-overhits after the standard tracking. The tracking algorithm for the tracklet is just same as the standard
tracking but only the left-over hits are used and some parameter requirements are optimised for shortdisappearing tracks. Table 5.1 summarises the diﬀerence between the standard track and the tracklet
reconstruction. The track seeding is done using only pixel hits. SCT seeding is the option that SCT
hits are used or not used for seeding. SCT seeding is not used in tracklet reconstruction to findtracks with pixel hits only eﬃciently. pT,min is the minimum transverse momentum of the track orhits
the tracklet. It is set higher than standard tracking to reject fake tracks and to save CPU time. Nminis the minimum number of hits. Tracklet reconstruction requires only four to allow tracks with pixel
pixel
hits only. Nminis the minimum number of pixel hits. It is set to four in tracklet to reduce fake trackshare
eﬃciently. Nmax is the maximum number of hits shared with other tracks. It is set to 0 in tracklet
not sharedis the minimum number of hits which is not shared withto reduce fake track eﬃciently. Nmin
hits
hole
is the maximum number of missing hits which is
any other tracks. It is set consistent to Nmin . Nmax
pixelholeis maximum
expected to exist on track. It is set to 0 for tracklet to reject fake track eﬃciently. Nmax
number of missing hits in pixel which is expected to exist on track. It is set to 0 for pixel tracklet toreject fake track eﬃciently. Detailed performance of the tracklet will be discussed later in Chap.6.
Table 5.1: Track reconstruction parameter diﬀerence between standard track and tracklet.
Parameter
Standard track (Sec.5.1.2) Tracklet (Sec.5.1.3)
SCT seeding
Used
UnusedpT,min0.1 GeV
5 GeV
hits
Nmin
7
4
pixel
Nmin
0
4
share
Nmax
1
0
not shared
Nmin
6
4
hole
Nmax
3
0
pixelholeNmax
205.1.4 Definition of disappearing track
In this thesis, tracklet with pixel hits only, pixel tracklet, is used as disappearing track candidate. Pixel
tracklet should satisfy the requirements below:(1) The pixel tracklet has pT above 20 GeV and the highest pT of all the isolated standard tracks
and the tracklets in the event.
(2) The pixel tracklet is isolated from any physics objects (jets, electrons, muons, and muon spectrometer tracks); the angular distance R between the tracklet and any jets (electrons and muon,
muon spectrometer tracks) with pT > 50(10, 0)GeV should be greater than 0.4 in the η–ϕ space.
(3) The pixel tracklet is isolated; pcone40/pT < 0.04 where pcone40
is the sum of the pT of all standard
TT
tracks with pT > 1GeV which passed “Loose” track selection criteria in a cone of ∆R < 0.4
around the pixel tracklet.

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

54(4) 0.1 < |η| < 1.9. |η| < 0.1 is rejected because the muon spectrometer is ineﬃcient in this region.
(5) |d0 /σd0 | < 2 and |z0 sin θ| < 0.5 mm.
(6) The pixel tracklet has a good χ2 quality: probability(χ2 , ndf) > 0.1.
(7) The number of hitsSia) NHole= 0. Here, the hole is points on the pixel tracklet where a hit is expected but missing
and Si is silicon detector, pixel and SCT.
Pixel
Pixel
Pixel
= 0. Here, the outlier is a hit near
= 0 and NGangedFlaggedFakeHits= 0 and NSpoiltHitsb) NOutliers
the tracklet but not the component of the tracklet because of the too high χ2 contribution,
spoilt hit is a hit rejected from tracklet component, and ganged flagged fake hit is a hit
which has shared readout with another channel and judged as fake hit during ambiguity
solving. The ganged pixel distributes in inter-chip regions.

c) All the four layers of the pixel detector have at least one hit.
d) NSCT = 0(1) is to identify the most promising signal candidate pixel tracklet. (2) is to reject pixel tracklets
made by standard model particles. (3) is to reject fake tracklets in dense occupancy in a jet. (4) isgeometrical η acceptance of the pixel detector. (5)-(7)a,b) is quality requirements. (5) is requirementthat the pixel tracklet comes from the primary vertex. (6) is a fit quality requirement. (7) a,b) is toensure pixel tracklet quality and c,d) is disappearing condition requirement.

5.2 Vertex
Interaction points in a bunch crossing are reconstructed by standard tracks as vertices [69]. It is
important to distinguish interesting high energy events and pile-up events. The vertices are used to
identify objects from high energy events as discussed later for example in Sec. 5.4.3 It is also used todefine parameters of reconstructed objects.
For the vertex reconstruction, standard tracks which satisfies the following requirements are considered:• pT > 400 MeV• |η| < 2.5• NSihits > 9 (11) if |η| < 1.65 (|η| ≧ 1.65)• At least 1 hits in first 2 pixel layers• A maximum of 1 shared hit (1 shared pixel hit or pair of shared SCT strip hits)
Pixel• NHole=05.3. TOPOLOGICAL CLUSTERING OF CALORIMETER CELLS

55

S CT
• NHole≤1

Vertex reconstruction is done by vertex finding and vertex fitting. First, a set of tracks which fulfill
the requirements above is defined. Then a seed position of the first vertex is set by searching for thevertex with maximum number of tracks in the z coordinate. Next, iteration of the fitting of the tracks
and the seed is performed. During the iteration, a track may be assigned a smaller weight when the
track seems less compatible to the seed vertex and vertex is fitted again. When the vertex position isdetermined, tracks incompatible with the vertex are removed from the fitting and used to reconstructanother vertex. The vertices must have at least 2 associated tracks. This algorithm is repeated until all
the tracks are associated with any vertices or no more vertices can be reconstructed in the remaining
set of tracks. Among reconstructed vertices in an event, a Primary Vertex (PV0 ) is defined by a vertex
with the highest scalar sum of the track transverse momenta.

5.3 Topological clustering of calorimeter cells
An energy deposit in the calorimeters is primarily reconstructed as a topo-cluster [70]. Topo-cluster
EM
formation is based on the cell signal significance ςcell
.
EM
Ecell
σnoise√pile−up 2))2 + (σnoise
σnoise = (σelectronic
noise
EM
ςcell
=

(5.1)
(5.2)

These variables are measured in electromagnetic scale, that is, calibration is optimised for electromagnetic shower.
Topo-cluster formation is performed by the growing-volume algorithm. It starts from a calorimeter
cell with a highly significant seed signal. There are three threshold parameters: primary seed threshold
S=4 is the significance threshold to seed a topo-cluster, threshold for growth control N=2 is thesignificance threshold to add a cell to the seed cluster, and principal cell filter P=0 is the significancethreshold to include the cluster edge cell as follows,EM|>S|ςcell

(5.3)

EM
|>N
|ςcellEM|>P|ςcell

(5.4)
(5.5)

Topo-cluster formation repeats until topologically connected cells satisfying Eq. 5.3 and 5.4 andtheir direct neighbours satisfying Eq. 5.5 are found.
If a cluster has 2 or more local maxima, cluster splitting is performed. The energy in a cell is
divided according to the distances to the centre of the 2 maxima, d1 and d2 . The weights are calculatedasCHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

56

wgeo
cell,1 =EM
Eclus,1
EM
EM
Eclus,1+ rEclus,2

geo
wgeo
cell,2 = 1 − wcell,1

r = exp(d1 − d2 )

(5.6)
(5.7)
(5.8)

The cluster direction and energy are measured by following equation.
∑Ncellηclus =

i=1

EM
wgeo
cell,i |E cell,i |ηcell,i∑Ncelli=1∑Ncellϕclus =

i=1

EM
wgeo
cell,i |E cell,i |ϕcell,i∑Ncell
i=1

EM
Eclus
=

Ncell
∑

EM
wgeo
cell,i |E cell,i |EM
wgeo
cell,i |E cell,i |EM
wgeo
cell,i E cell,i(5.9)(5.10)(5.11)

i=1

where Ncell is the number of cells in the cluster, and wgeo
cell,i is the geometrical signal weights by cluster
splitting as given in Eq. 5.6 and 5.7. The cell direction (ηcell , ϕcell ) is measured from the origin of the
ATLAS detector.
Assuming that the particle is massless, momentum and energy components are
EM
EM
EM
EM
Pclus
= Eclus· (1, sin θclus cos ϕclus , sin θclus sin ϕclus , cos θclus ) = (Eclus, ⃗pclus)(5.12)

where θclus is calculated from ηclus .
There are two calibrations. One is EM calibration. The other calibration categorise topo-cluster
either as an electromagnetic or a hadronic cluster, and the corresponding energy weight is multiplied
for each cluster. This is called local calibration weighting (LCW).

5.4 JetWhen the final state of a collision emits high energy quarks or gluon, hadronisation occurs due tocolour confinement and multiple particles are produced in very short time along the direction of thequark or gluon. In the ATLAS detector, such an object is reconstructed as a set of topo-clusters andcalled as a jet.

5.4.1 Jet reconstruction
Jet reconstruction is performed by the anti-kt algorithm [71]. First, the distance between i-th and j-thentity di j and the distance between i-th entity and beam diB are defined as5.4. JET

57

di j = min(kti−2 , kt−2j )diB = kti−2∆2i j(5.13)

R2(5.14)∆2i j = (yi − y j )2 + (ϕi − ϕ j )2

(5.15)

where kti is the transverse momentum, yi is the rapidity, and ϕi is the azimuthal angle of the i-th entity.
R is a radius parameter set to R = 0.4. The cluster procedure is as follows:
0. The initial entities in the list are all the topo-clusters.
1. Among all di j and diB , the minimum one is identified.
2. If diB is the minimum, an entity i is defined as a stand alone jet and removed from the list.
3. If di j is the minimum, an entity i and entity j are combined to form a new entity and this entity
is included in the list while i and j are removed.
This procedure is continued until all the entities are categorised as stand alone jets.
There are 2 kinds of jets, EM jets and LCW jets depending on which topo-cluster calibration isused, EM one or LCW one.

5.4.2 Jet energy calibration
The Ref. [72] discusses the jet energy calibration method in detail. The origin correction is to correctfour momentum of the jet assuming that the jet comes from the PV. The pile-up correction is tosubtract average energy density in the area of the jet in ∆η × ∆ϕ and also remaining dependence on
the number of reconstructed PVs for in-time pileup and the expected average number of interactions
per bunch crossing for out-of-time pileup. The jet energy scale (JES) and η calibration is applied
based on MC simulation. The global sequential correction (GSC) is performed for the dependence
on the topological properties of the jet. In-situ JES calibration is also applied to correct the diﬀerence
between data and MC simulation.

5.4.3 Jet vertex tagging
Jet Vertex Tagger (JVT) is used to identify and suppress pile-up jets [73]. JVT uses following 2
variables defined for a jet:∑corrJV F =∑∑R pT =

trkl
l pT (PV0 )
∑ ∑

trkl
l pT (PV0 ) +trkl
l pT (PV0 )
pTjet

n≥1

trkl
l pT (PVn )PU )(k·ntrk(5.16)(5.17)

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

58∑
lwhere l ptrk
the scalar pT sum of the tracks associated with the jet and originate from theT (PV0 ) is∑∑PUlprimary vertex PV0 . n≥1 l ptrk
T (PVn ) is the scalar pT sum from pile-up interactions. ntrk is total
PU
number of pile-up tracks and k · ntrk is correction for linear increase of expected pT with k = 0.01.
The JVT likelihood is derived from the ratio of the number of hard-scatter jets and the number of
hard-scatter plus pileup jets.

(a) JVT likelihood value function.

(b) Simulated JVT likelihood distribution of pile-up andhard scatter.

Figure 5.2: (a) The 2-dimensional JVT likelihood function and (b) simulated JVT likelihood distribution of pile-up and hard scatter [73]. Green histogram is for pileup jets and purple histogram is forhard scatter jets.
Fig. 5.2 shows JVT likelihood function and the distribution for pile-up and hard scatter. JVT=-0.1
is assigned to jets with no associated tracks. The JVT working point is set to 0.59. If a jet has JVTlarger than 0.59, it is considered to have originated from PV.

5.4.4 Definition of jet object
In this thesis, jets satisfying the following requirement are used.
• pT > 20 GeV• |η| < 2.8• JVT likelihood > 0.59

5.5. ELECTRON

59

5.5 Electron
The electron is reconstructed using energy deposits in the EM calorimeter and associated tracks in theID [74].

5.5.1 Reconstruction
Seed cluster reconstruction
The EM calorimeter is divided into towers of size ∆ηtower × ∆ϕtower = 0.025 × 0.025. The tower energy
is the sum of energy in longitudinal layers. Then, sliding-window algorithm is applied to search EM
clusters with window size 3 × 5 towers. If the EM cluster fulfills Rη > 0.65 and Rhad < 0.1 (variable
definitions are in Table 5.2), the seed is used.
Electron-track candidate reconstruction
A region of interest (ROI) is defined as a cone with size ∆R = 0.3 around the seed cluster barycenter.
Because electron may lose significant energy in trajectory due to bremsstrahlung, pattern recognition
with at most 30% energy loss at each material surface is performed. If a track seed with pT > 1 GeV
fails to be reconstructed, but it is in one of the EM cluster ROIs, tracking is retried using this patternrecognition scheme.
Tracks are fitted using the ATLAS Global χ2 Track Fitter [75] with pion or electron hypothesis
depending on the hypothesis in the pattern recognition since the electron track may have more kinks
due to large bremsstrahlung. If the fit fails with pion hypothesis, electron hypothesis is also tried.
Track association to the EM cluster
Loose matching of the ID tracks to EM cluster is checked. There are 2 criteria and either of them is required. For track candidates, parameters are re-estimated using Gaussian Sum Fitter (GSF) algorithm[76].
• Criteria 1:– Track with at least 4 silicon hits
* The extrapolated track is within 0.2 (0.05) in ϕ of the EM cluster on the same (opposite) side that the track is bending toward* The extrapolated track is within 0.05 in η of the EM cluster– TRT-only tracks* The extrapolated track is within 0.1 (0.05) in ϕ of the EM cluster on the same (opposite) side that the track is bending toward* No requirement on η.
• Criteria 2:

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

60– Track rescaled to the measured cluster energy* The extrapolated track is within 0.1 (0.05) in ϕ of the EM cluster on the same (opposite) side that the track is bending toward* If the track is not TRT-only track, within 0.05 in η
The object is reconstructed as electron if it satisfies the requirements above.
Electron identification
For electron identification, likelihood-based identification is used. The likelihood function is using
the input variables summarised in Table 5.2. There are 3 working points defined by the likelihood
function values, loose, medium, and tight correspond to the typical identification eﬃciencies of 95 %,90 %, and 80 %.
Fig. 5.3 shows Identification eﬃciency dependence on ET and η for each working point.

(a)

(b)

Figure 5.3: Electron identification eﬃciency plots (a) as a function of ET and (b) as a function of
η. Filled marker is for data and open marker is for MC. Blue is for loose identification, red is for
medium identification, and black is for tight identification. [74]Electron isolation
Track isolation is evaluated by Pvarcone20/pT which is the sum of pT of tracks with pT > 0.4 GeV in
T∆R < (10 GeV/pT ) for pT > 50 GeV and ∆R < 0.2 for pT < 50 GeV. The threshold is defined as theeﬃciency becomes 99 %.

5.5. ELECTRON

Table 5.2: Definition of electron discriminating variables [74].
Type
Description
Hadronic leakage The ratio of ET in the first layer of the hadronic calorimeter to ETof the EM cluster (used in |η| < 0.8 or |η| > 1.37)
The ratio of ET in the hadronic calorimeter to ET of the EM cluster(used in 0.8 < |η| < 1.37)
Back layer of EM Ratio of the energy in the back layer to the total energy in the EM
calorimeter
accordion calorimeter√∑∑∑∑
Middle layer of Lateral shower width,( Ei η2i )/ Ei − (( Ei ηi )/ Ei )2 ,EM calorimeter
where Ei is the energy and ηi is the pseudorapidity of the cell iand the sum is calculated within a window of 3 × 5 cells
The ratio of the energy in 3 × 3(η × ϕ) cells over the energy in 3 × 7
cells centered at the electron cluster position
The ratio of the energy in 3 × 7 cells over the energy in 7 × 7 cells
centered at the electron cluster position
Strip layer of EM Ratio of the energy diﬀerence between the largest and second
calorimeter
largest energy deposits in the cluster over the sum of these energies
The ratio of the energy in the strip layer to the total energy in the
EM accordion calorimeter
Track quality
The number of hits in the innermost pixel layer discriminates
against photon conversions
The number of hits in the pixel detector
The number of total hits in the pixel and SCT detector
Transverse impact parameter with respect to the beam spot
The significance of transverse impact parameter defined as theratio of d0 and its uncertainty
The momentum lost by the track between the perigee and the lastmeasurement point divided by the original momentum
TRT
Likelihood probability based on transition radiation in the TRT
Track-cluster∆η between the cluster position in the strip layer and the extrapomatchinglated track∆ϕ between the cluster position in the middle layer and the extrapolated track, where the track momentum is rescaled to the cluster
energy before extrapolating the track to the middle layer of thecalorimeter

61

Name
Rhad1
Rhad
f3
Wη2

Rϕ
Rη
Eratiof1
nBlayern pixel
nS i
d0
σd 0
∆p/p
TRTPID∆η1∆ϕres

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

62

5.5.2 Definition of electron
In this analysis, object which satisfies likelihood-based loose identification, ET > 10 GeV, and |η| <2.47 is used as the electron. For background estimation, likelihood-based tight identification and track
isolation is also required.

5.6 Photon
Converted and unconverted photons are reconstructed using EM calorimeters and the ID [77, 78].

5.6.1 Reconstruction
Because photon and electron leave similar EM cluster, their reconstruction is performed in parallel.
Clustering and track matching are common with electron reconstruction.
There are three categories of photon, unconverted photon, double-track conversion photon andsingle-track conversion photon. The unconverted photon is a photon which is produced as a final stateparticle and reaches to the calorimeter without conversion. The double-track conversion photon is aphoton which converted into two electrons inside the inner tracker and left two tracks of the electrons.
The single-track conversion is for similar case to double-track conversion photon, but one of the tracks
is not reconstructed due to too low momentum or collinear to the other track. To identify converted
photon, ”double-track” and ”single-track” conversion vertex reconstruction is performed.
Double-track conversion photon
Double-track conversion vertex requires 2 candidate opposite-charged electron-like ID track. Eachtrack is required to fulfill that likelihood probability to be an electron based on TRT detector response
is larger than 10 % (80 %) if the track has (does not have) silicon detector hits. The threshold diﬀerence is due to electron identification ability of the TRT. Tracks are classified by having or not having
silicon hits, Si-track or TRT-track. Such a track pair is reconstructed as converted photon if it satisfies
following requirement:• ∆ cot θ < 0.3(0.5) between the conversion track candidates. However, if TRT-track pair and|η| < 0.6, not applied.
• The closest distance of track pair < 10 mm (50 mm) if (not) Si-tracks pair.
• Defining R sum as the sum of the radii of track helices and dc as the distance between centre ofhelices, -5 mm < R sum −dc < 5 mm for Si-track pair, -50 mm < R sum −dc < 10 mm for TRT-track
pair, or -25 mm < R sum − dc < 10 mm for a Si-track and a TRT-track pair.
• Defining ∆ϕ as diﬀerence of ϕ at the conversion vertex position, ∆ϕ < 0.05(0.2) for (not)Si-track pair5.6. PHOTON

63

Then, conversion vertex position fitting with three degrees of freedom is performed using parameters of track pair and the constraint that they are parallel at the conversion vertex position. The vertex
is required to satisfy the following criteria:• χ2 < 50• The vertex position from beam line Rconversion > 20 mm for Si-tracks pair, Rconversion > 70 mm
for Si-track and TRT-track pair, or Rconversion > 250 mm for TRT-tracks pair. It is to requireconsistency of the track starting point and the conversion vertex point.
• ∆ϕ between vertex position and each track direction of the reconstructed conversion photon< 0.2
Single-track conversion photon
Single-track conversion vertex reconstruction is performed for tracks without hits in the IBL. If electron likelihood probability is larger than 95 % or no TRT hits are included, it is reconstructed as aphoton. Because conversion vertex fitting is impossible, it is assumed that first measurement point is
the conversion vertex position.
Cluster matching
For the photon conversion candidate, cluster matching is performed. For double-track conversion vertex candidate, if track transverse momentum diﬀers from the other track by less than factor of 4, eachtrack is extrapolated to the 2nd sampling layer of the calorimeter, and else if track transverse momentum diﬀers from the other track by more than factor of 4, straight line extrapolation is performed to
the fitted track direction at the conversion vertex as for neutral particle. For single-track conversion
vertex candidate, the track is extrapolated from the last measurement point in the ID.
For Si-tracks and the cluster, |∆η| < 0.05 and |∆ϕ| < 0.05(0.1) is required for double(single)track conversion. For TRT-track and the cluster of single-track candidate, ∆ϕ < 0.02(0.03) on the(opposite) side the track is bending toward or ∆ϕ < 0.02 on both sides if extrapolated as neutral
particle and ∆η < 0.35(0.2) in the barrel (end-cap) TRT or ∆η < 0.35 if extrapolated as neutral
particle. The asymmetry of the threshold is to loosen the constraint in the direction of the expected
conversion pair direction which may bias the cluster position by merging.
If the same cluster is matched to multiple conversion candidate, priority is given as follows:• Double-track candidates are prior to single-track candidates.
• Candidate with more Si-track.
• Smaller conversion vertex radiusCHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

64
Object classification

Finally, candidate objects are determined as either unconverted photon, converted photon, or electron
by following way:
• If EM cluster is not conversion vertex candidate or no track is associated, it is considered as an
unconverted photon candidate.
• If EM cluster matches to the conversion photon candidate, it is considered as converted photon.
An exception is the case that it is categorised as both a double-track candidate and an electron
candidate, with an associated track is common and the track has IBL hits, it is considered as
an electron. The other exception is that associated track is diﬀerent and track pT is larger thanconverted photon candidate pT . In this case it is considered as an electron and converted photon
candidate is removed.
• Single-track converted photon candidate is recovered if it is an electron candidate with pT > 2
GeV, E/p < 10 and no silicon hit is included in the associated track.
• Unconverted photon candidate is recovered from electron candidate if associated track withpT > 2 GeV has no silicon hit or it is not a single-track converted photon candidate and associated track is pT < 2 GeV and E/p > 10. The electron candidate is removed.
The photon energy measurement is done by EM cluster. Cluster size of ∆η × ∆ϕ = 0.075 × 0.123
is used. However, for converted photon in barrel region ∆η × ∆ϕ = 0.125 × 0.123 is used to calculate
the energy.

5.6.2 Identification
The cut-based tight photon identification is applied in this analysis. The threshold changes dependingon η. Used variables are acceptance in η, variables used for electron identification defined in table
5.2 (Rhad1 , Rhad , Rη , Wη2 , Rϕ , Eratio ), shower width calculated from energy deposit in the 3 strips
around the maximum energy deposit, lateral shower width, energy ratio outside the cluster core, anddiﬀerence between the energy associated with the second maximum in the strip layer and the energy
reconstructed in the strip with the minimum value found between the first and second maxima.

5.6.3 Isolation
For photon isolation, calorimeter energy deposit in ∆R < 0.4 excluding the photon energy ETcone40 andtrack isolation pcone20/pT should satisfy the following criteria. ETcone40 < 0.022pT + 2.45 GeV andTpcone20/pT < 0.05 are applied.
T

5.6.4 Definition of photon object
In this analysis, reconstructed photon which satisfies the following criteria is used:5.7. MUON

65

• Tight identification• pT > 25 GeV• |ηclus | < 2.37
• No HV dead region in the calorimeter cell in the EM cluster and none of central 8 strip aremasked in the reconstruction due to large noise.
• Isolation criteria

5.7 Muon
Muon is reconstructed using the ID and muon spectrometer (MS) [79].

5.7.1 Reconstruction
First, tracking is performed independently in the inner detector and the muon spectrometer. Tracking
in the inner detector is the same method as described in Sec.5.1. Tracking in the muon spectrometerstarts from search for hit pattern by the Hough transform [80]. Then, track candidates are reconstructed using track segments which satisfy hit multiplicity and fit quality criteria. The matching of
ID track and MS track is based on their relative positions and angles. At least 2 (1) such segments are
required for a track in barrel and end-cap (transition) region. Overlap removal is done to identify fakehit or shared hit. Finally, the global χ2 fit is applied to examine fit quality after adding consistent hits,
and removing incompatible hits. Hereafter, these tracks are called as MS tracks.
In this analysis, so called combined muon and extrapolated muon are used. Combined muon is amuon reconstructed by a combination of the ID track and MS track. Combined track is reconstructedby global fit using the ID and the MS hits. An MS hit may be removed if it significantly degrades fit
quality. Extrapolated muon is only defined in the region of 2.5 < |η| < 2.7, which is not covered by
the ID. It is reconstructed only by the MS track. Loose compatibility of the track to the IP is required.
Parameters at the IP is estimated by taking an expected energy loss in the calorimeters into account.

5.7.2 Identification
In this analysis, so called “Medium” and “Tight” identification described below is used.
For ID track, following criteria are required for both medium and tight identification:• N pixel ≥ 1• NS CT ≥ 5• NSiholes < 3• At least 10% of the TRT hits originally assigned to the track are included in the final fit

CHAPTER 5. OBJECT RECONSTRUCTION AND THE DEFINITION

66

Medium identification criteria are• N MDT hits ≥ 3• If |η| < 2.5, muon is reconstructed as combined muon.
• If |η| > 0.1, N MDT layer ≥ 2• If |η| < 0.1, N MDT layer ≥ 1 and N MDT holelayer < 1• If 2.5 < |η| < 2.7, N MDT/CS Clayer ≥ 3• q/p significance between ID and MS track < 7
Tight identification criteria are• Muon is reconstructed as combined muon.
• Satisfy medium identification criteria• N MS ≥ 2• χ2 /n.d.f < 8• 2-dimensional cut in q/p significance and ∆pT (ID, MS)/pT (ID) depending on the muon pT

5.7.3 Definition of muon object
In this analysis, objects which satisfy the requirement below is used as reconstructed muon.
• Medium identification quality• pT > 10 GeV• |η| < 2.7
For background estimation, track isolation same as required for electrons is also required. Tight
identification is also used in part of background estimation.

5.8 Overlap removal
Same particle is often reconstructed as multiple objects. Therefore, rejection rules are applied asfollows to determine what the particle is likely. Photon is not considered here but in ETmiss calculation
as described in the next section.
• If associated ID track of a muon candidate and an electron candidate are identical, the electron
candidate is rejected.

5.9. MISSING TRANSVERSE ENERGY

67• If an electron candidate and a jet are in ∆R < 0.2, the jet is rejected.
• If an electron candidate and a jet are in 0.2 < ∆R < 0.4 and the jet is not flagged as pile-up jet,that is, the jet does not satisfy pT < 60 GeV and |η| < 2.4, and JVT < 0.59, electron is rejected.
• If a muon candidate and a jet are ghost-associated (muon track is associated to negligible mo∑≥ 0.7, and the jet
mentum cluster of the jet) or in ∆R < 0.2 with pµT /pTjet ≥ 0.5, pµT / in jet ptrackT
has less than 3 tracks with pT > 500 MeV, the jet is rejected.
• If a muon candidate and a jet are in ∆R < min(0.4, 0.04+10GeV/pmuon) and the jet is not fllagedT
as pile-up jet, muon is rejected.

5.9 Missing transverse energy
If invisible particle like neutrino or undiscovered particle such as neutralino is produced, momentum
imbalance in the transverse plane is expected.
The ETmiss reconstruction is performed using selected calibrated hard objects [81].
miss,so f t
miss, jetmiss,γ
miss,e+ E miss,µE missx(y) = E x(y) + E x(y) + E x(y)x(y) + E x(y)√miss
2miss )2
ET = (E missx ) + (E y(5.18)

ϕmiss = arctan (Eymiss /E missx )(5.20)(5.19)

ftis track-based soft
Each term is a negative vector sum of the momenta of each object. E miss,sox(y)term TST. It is calculated using tracks originate from PV, but not associated with any reconstructedobjects.
The object definition in the ETmiss calculation diﬀers from defined above in some points.

• Primary vertex satisfies impact parameter cut of d0 < 1.5 cm and z0 < 1.5 cm with respect tothe nominal interaction point.
• Electron identification is medium.
• |η| < 1.37 or 1.52 < |η| < 2.47 for electron• |η| < 1.37 or 1.52 < |η| < 2.37 for photon• JVT > 0.64 for jet with |η| < 2.4 and pT < 50GeV. If not satisfied, the ID tracks are used for
the TST.
TST uses tracks not associated with any objects and the tracks in jets which fails to satisfy the lastrequirement above. Tracks are further required to fulfill the criteria below:• ∆R (track, electron/photon cluster) > 0.05
• Not ghost-associated with jets
• Momentum uncertainty is less than 40 %Chapter 6
Tracklet performance
Tracklet is used in the ATLAS physics analysis for the first time. Therefore, detailed performance isdiscussed here.

6.1 Pixel detector condition
6.1.1 Data quality
In 2016, there were some disabled modules in the pixel detector especially in the pixel layer 2. Fig. 6.1
and Fig. 6.2 show examples of disabled module map in a typical run. Typically 46 modules out of
the 676 modules were disabled in layer 2. One reason is that the new readout system installed before
2016 data-taking worked imperfectly. Another reason is that issues like Single Event Upset (SEU) in
the front-end chips of the pixel detector caused data loss.
Fig. 6.3 and Fig. 6.4 show average occupancy per event in a typical run. It is less than 10−3 ,tolerable level. Fig. 6.5 and Fig. 6.6 show distributions of charge deposit. The peak values are 20k
for the IBL and 25k for the pixel.

6.1.2 Alignment
Pixel detector alignment is performed by the method discussed in Ref. [82] with the SCT and the TRTalignment at the same time. There are 6 alignment parameters: translations T x , T y , T z and rotations
R x , Ry , Rz . The alignment parameters are assigned to each alignable structure. The definition ofalignable structure changes with alignment level of granularity. About the pixel detector, alignablestructures are the whole pixel detector and the IBL bowing in the level 1, each pixel and IBL layers
in the level 2, each pixel and IBL staves in the level 2.7 and each pixel and IBL modules in the level
3. The IBL bowing in the level 1 alignment is introduced because it is found that the IBL bowing
happens depending on the temperature. The alignment uses the global χ2 track based algorithm.
The alignment parameters are determined to minimize residual between the cluster position and the
expected hit point from tracking. Fig. 6.7 and Fig. 6.8 show local residual distributions. Coordinatesof local x and local y is defined along each pixel module plane. x corresponding to ϕ direction andy corresponding to η direction. The residual uncertainties are 12×82 µm2 in the IBL and 9×81 µm2
69

70

CHAPTER 6. TRACKLET PERFORMANCE(a) IBL(b) Pixel layer 0

Figure 6.1: Disabled module and synchronization error fraction map. Red modules are disabled.
Value range from 0 to 1 is synchronization error fraction.

6.1. PIXEL DETECTOR CONDITION

71(a) Pixel layer 1(b) Pixel layer 2

Figure 6.2: Disabled module and synchronization error fraction map. Red modules are disabled.
Value range from 0 to 1 is synchronization error fraction.

72

CHAPTER 6. TRACKLET PERFORMANCE(a) IBL(b) Pixel layer 0

Figure 6.3: Average occupancy per event.

6.1. PIXEL DETECTOR CONDITION

73(a) Pixel layer 1(b) Pixel layer 2

Figure 6.4: Average occupancy per event.

74

CHAPTER 6. TRACKLET PERFORMANCE(a) IBL(b) Pixel layer 0

Figure 6.5: Cluster charge distribution on track.

6.1. PIXEL DETECTOR CONDITION

75(a) Pixel layer 1(b) Pixel layer 2

Figure 6.6: Cluster charge distribution on track.

CHAPTER 6. TRACKLET PERFORMANCE76

in the other layers. These values are very close to the detector resolution. However, there is misalignment which cannot be corrected by global χ2 track based algorithm. For example, systematicradius expansion does not change χ2 but cause bias in momentum measurement. Such mis-alignmentis called as a weak mode [83]. The bias is measured using Z → µµ events applying constraints on thereconstructed mass. The result is shown in Fig. 6.9 as a sagitta mean bias function of η, in Fig. 6.10 asa sagitta RMS function of η and Fig. 6.11 as a sagitta mean bias function of η and ϕ. Here, sagitta bias
δ sagitta is defined as bias of q/pT . Unfortunately, this thesis uses data before reprocessing. Therefore,
there is a sagitta bias of around 0.1 TeV−1 . There is ϕ dependence too. Because this measurement
uses the whole inner detector, the sagitta bias of pixel tracklet is roughly estimated to be 10 TeV−1
by scaling measured value with squared arm ratio (the whole ID 1000 mm and the pixel detector 100mm) of about 100.

6.2 Reconstruction eﬃciency
The reconstruction procedure of the tracklet is discussed in Sec. 5.1.3. Reconstruction eﬃciency isestimated by signal chargino MC. Because the eﬃciency highly depends on the number of hits in the
pixel detector and the pixel layers are installed cylindrically, eﬃciency is calculated as a function of
decay radius of the chargino. Fig. 6.13 shows the pixel tracklet reconstruction eﬃciency, the standard
track reconstruction eﬃciency and the chargino decay radius distribution of benchmark signal. Here,any quality cut is not applied both to the standard track and to the pixel tracklet except for the disappearing requirement given in Sec.5.1.4, that is, NSCTHits = 0, NPixelHits ≥ 4 and NContribuedPixelLayers ≥ 4
for the pixel tracklet and geometrical acceptance cut |η| < 1.9 for both the standard track and the
pixel tracklet. Because the chargino decay radius distribution exponentially decreases, the total signal
reconstruction eﬃciency of the standard tracking is too low. On the other hand, the pixel tracklet
reconstruction eﬃciency is significantly better for the chargino decays between the pixel and the SCT
detectors, i.e. 123-299 mm. Therefore, the total signal eﬃciency is much better for the pixel tracklet.
The eﬃciency decrease near decay radius 300 mm is due to decay product pion hits in the SCT areused in tracking and the track is vetoed by the disappearing requirement.
The reconstruction eﬃciency depends on the average number of interactions per bunch crossing.
Fig. 6.14 shows the dependence on average number of interactions. The reconstruction eﬃciency
decreases with the average number of interactions. This is because chargino hits tend to be usedin the standard tracking by mistake when there is many charged particles from pileup events. The
tracklet reconstruction uses only hits which are not used in the standard tracking. Therefore, thereconstruction eﬃciency depends on the number of pileup events.
Disabled modules discussed in Sec. 6.1.1 aﬀect the tracking eﬃciency in data. In MC, disable
modules were not simulated because disabled modules changes run by run. Therefore, the probability
to lose hits by disabled modules is measured using Z → µµ events [85]. Events and muons satisfying
requirement below is selected:• Passed single muon trigger• Tight muon identification• 81 GeV < Mµµ < 101 GeV where Mµµ is mass reconstructed from the pair of muon.

Number of hits

6.2. RECONSTRUCTION EFFICIENCY

7000
6000
5000

77

ATLAS Preliminary

Data 2017µ=0 µm, FWHM/2.35=13 µm

IBL

Data 2016µ=0 µm, FWHM/2.35=12 µm

Z→µ µ Events

Z→µµ MC16µ=0 µm, FWHM/2.35=12 µm

p >15 GeV
T

4000
3000
2000
1000
0

-0.04

-0.02

0

0.02
0.04
Local x residual [mm]Number of hits(a) IBL local x residual

8000
7000
6000

ATLAS Preliminary

Data 2017µ=0 µm, FWHM/2.35=87 µm

IBL

Data 2016µ=0 µm, FWHM/2.35=82 µm

Z→µ µ Events

Z→µµ MC16µ=-4 µm, FWHM/2.35=69 µm

p >15 GeV
T

5000
4000
3000
2000
1000
0

-0.3

-0.2

-0.1

0

0.1
0.2
0.3
Local y residual [mm](b) IBL local y residual

Figure 6.7: Local x and local y residual distribution in the IBL. [84]

CHAPTER 6. TRACKLET PERFORMANCE

Number of hits

78

×103
25

ATLAS Preliminary

Data 2017µ=0 µm, FWHM/2.35=9 µm

Pixel Barrel

Data 2016µ=0 µm, FWHM/2.35=9 µm

20Z→µ µ Events

Z→µµ MC16µ=0 µm, FWHM/2.35=8 µm

p >15 GeV
T

15
10
5
0

-0.04

-0.02

0

0.02
0.04
Local x residual [mm]Number of hits(a) Pixel local x residual

×103
20
18
16

ATLAS Preliminary

Data 2017µ=0 µm, FWHM/2.35=87 µm

Pixel Barrel

Data 2016µ=0 µm, FWHM/2.35=81 µm

Z→µ µ Events

Z→µµ MC16µ=2 µm, FWHM/2.35=70 µm

p >15 GeV
T

14
12
10
8
6
4
2
0

-0.3

-0.2

-0.1

0

0.1
0.2
0.3
Local y residual [mm](b) Pixel local y residual

Figure 6.8: Local x and local y residual distribution in the pixel. [84]

Mean δsagitta [TeV-1]

6.2. RECONSTRUCTION EFFICIENCY

79

0.6
0.4

Reprocessed alignment

ATLAS Preliminary
Data 2016, s = 13 TeV
Z → µµ

Prompt alignment

0.2
0.0

−0.2
−0.4
−0.6
−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5
η

RMS δsagitta [TeV-1]

Figure 6.9: Mean bias of the track sagitta as a function of η. Gray points are prompt alignment andblue points are after reprocessing. [83]

1.0
0.9
0.8

Reprocessed alignment

ATLAS Preliminary
Data 2016, s = 13 TeV
Z → µµ

Prompt alignment

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5
η

Figure 6.10: RMS of the track sagitta as a function of η. Gray points are prompt alignment and blue
points are after reprocessing. [83]

φ

3
2

ATLAS Preliminary
Data 2016, s = 13 TeV
Prompt alignment

1

Mean δsagitta [TeV-1]

CHAPTER 6. TRACKLET PERFORMANCE

80

1

0.5

0

0

−1

−0.5

−2
−3
−2.5 −2 −1.5 −1 −0.5 0

−1
0.5

1 1.5

2

2.5
η

Figure 6.11: Mean bias of the track sagitta as a function of η and ϕ. [83]For selected muons, re-tracking using only the pixel detector hits included in the standard track
associated with the muon is performed. Used number of muons is 6 × 104 . The eﬃciency to hit 4
layers of pixel detectors without failing to leave hit due to disabled modules is measured to be 81.1%.
This eﬀect is considered by scaling the expected number of signals by 0.811 in simulated events.
Using the same procedure, tracklet re-tracking eﬃciency is measured using events with 4 pixel
hits [85]. Fig. 6.12 shows the comparison between data and MC. The reconstruction eﬃciency is
0.9368 ± 0.0008 in data and 0.9484 ± 0.001 in MC. The diﬀerence is 1.2% and this is considered asa signal normalisation uncertainty.

6.3 Transverse momentum resolution
Due to the short arm length of the pixel tracklet, transverse momentum measurement of the pixel
tracklet has significantly worse than that of the standard track.
To estimate the transverse momentum resolution in data, muon tracks in Z → µµ events areused. It is the same procedure as the reconstruction eﬃciency comparison in data and MC as discussed in Sec. 6.2. It can be assumed that standard track has negligible transverse momentum uncertainty compared to the pixel tracklets. Therefore, the pixel tracklet transverse momentum resolution
can be estimated by comparing the transverse momentum of the pixel tracklet (q/ppixelT ) and that ofstandard
the standard track (q/pT) reconstructed for the same muon. Fig. 6.15 shows the distribution of
pixel
standard∆(q/pT ) = q/pT − q/pT
. The distribution is fitted to an empirical function,

6.3. TRANSVERSE MOMENTUM RESOLUTION

81

Pixel

SCT

TRT

1

0.005

0.8

0.004

0.6

Fraction of chargino decays

Fraction of chargino decays [mm-1]

Reconstruction efficiency

Figure 6.12: The pixel tracklet reconstruction uncertainty when there are four pixel hits. The blackline is data and red line is MC. The diﬀerence between data and mc is 1.2%. [85]0.003

Pixel tracklets

0.4

0.002

Standard tracks

0.2

0

0.001

200

400

600

800

1000

0

Decay Radius [mm]Figure 6.13: The pixel tracklet reconstruction eﬃciency in red, the standard track reconstruction
eﬃciency in green, and the chargino decay radius distribution of a benchmark signal point in blue
with right vertical axis. The yellow shaded region shows where detectors are installed.

CHAPTER 6. TRACKLET PERFORMANCE

82

Reconstruction efficiency

Pixel

SCT

TRT

0.8
0.7
0.6
0.5

0 ≤ µ <1010 ≤ µ <1515 ≤ µ <25
25 ≤ µ <3030 ≤ µ <60

0.4
0.3
0.2
0.1
0
0

200

400

600

800

1000

Decay Radius [mm]Figure 6.14: The pixel tracklet reconstruction eﬃciency for various average number of interactions
ranges. Purple is 0 ≤ µ < 10, blue is 10 ≤ µ < 15, light blue is 15 ≤ µ < 25, green is 25 ≤ µ < 30
and yellow is 30 ≤ µ < 60.

6.4. SIGNAL DISAPPEARING TRACK PT DISTRIBUTION∆(q/pT ) − βσexp(α(z + α/2))(z < −α)2f (z) = exp(−z /2)(−α < z < α)
exp(−α(z − α/2)) (z > α)
z =

83

(6.1)

(6.2)

where α is the slope of the tail, β is the mean, and σ is the resolution around the peak. The fitted
parameters are α =1.67, β =-1.72 TeV−1 , and σ =13.2 TeV−1 .
Fig. 6.16 shows muon pT distribution used in Fig. 6.15 both for the standard track and the pixel
tracklet reconstructed from the pixel hits in the standard track. Using the resolution function Eq. 6.2
as a smearing function, smeared pT distribution of the standard track is also shown. This is madeby convoluting standard track pT distribution with the smearing function. The pixel tracklet pT distribution and smeared standard track distribution is consistent. This smearing technique is used inbackground distribution estimation later (Sec. 8.1.2).

6.4 Signal disappearing track pT distribution
Since the pT resolutions of pixel tracklets for data (see Fig. 6.15) and simulated MC muons are so
diﬀerent, smearing of pT is applied to simulated signal MC events to get the signal distribution.
The resolution in data is worse due to diﬃculties in reproducing detector condition in MC such asalignment uncertainty. The smearing is applied to the generator-level pT of charginos which arereconstructed as disappearing tracks. The smeared pT distribution is used as the signal template. The
smearing parameters in Eq. 6.2 is calculated in data and in MC for muon and signal wino. Fig. 6.17
shows the statistical one standard deviation contour of fitting parameter, σ and α of Eq. 6.2 for eachsample. Table 6.1 summarises the fitting parameters. The diﬀerence of muon σ between data andMC can be described by sagitta bias discussed in Sec. 6.1.2. The quadratic sum of σ = 9.0 TeV−1
for muon MC and RMS of sagitta bias 10 TeV−1 is 13.4 TeV−1 , which is consistent to the σ of muon
data. One may concern that sagitta bias just cause momentum bias, but does not smear the momentum.
However, the sagitta bias has η-ϕ dependence as shown in Fig. 6.11. Therefore, considering sagitta
bias as smearing source is reasonable. Fig. 6.16 also shows that this treatment does not aﬀect to thesmearing accuracy. The parameter α changes due to correlation with σ. The reason of the correlationis that the smearing function tail slope is α/σ as a function of ∆(q/pT ). Therefore, if there is no
reason to change the tail slope, α should be proportional to σ. Because the wino sample used for the
search does not include multiple scattering in the detector simulation and MC does not include actual
detector condition, pixel tracklet pT is not used to estimate the signal pT distribution and the signal
pT distribution is obtained by smearing using the smearing function. For signal wino, special sample
with multiple scattering is also used. This special sample is generated for only one signal point due
to limited computing resource. Here, parameters of muon both in data and MC are estimated by thesame method as described in Sec.6.3. On the other hand, the smearing function of wino is obtainedby comparing the pixel tracklet q/pT and the generator-level q/pT . The smearing function of signal
in data is estimated by assuming that parameter ratio of data and MC is common for any particle:

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets / 4 TeV-1

84

−1

10

ATLAS
s=13TeV, 2.0 fb-1

Data
Fit

10−2
10−3
10−4
10−5
−100

−50

0

50
100
-1
∆ (q / p ) [TeV ]T

Figure 6.15: The distribution of the diﬀerence between q/pT of the pixel tracklet and the standard
track in Z → µµ events in data. The solid red line shows the fitting function (Eq. (6.2)). The parametervalues of the function are α =1.67, β =-1.72 TeV−1 , and σ =13.2 TeV−1 . The red band indicates a 1σvariation of the statistical uncertainty. The data are normalised to unit area. [20]

Track(let)s / GeV

6.4. SIGNAL DISAPPEARING TRACK PT DISTRIBUTION

103

85

Standard tracks
Pixel tracklets
Smeared tracks

102

Z → µµ candidates

10
1

10−1
10−2 ATLAS(Smeared tracks) /(Pixel tracklets)

s=13TeV, 2.0 fb-1

2
1.5
1
0.5
0

P t [GeV]
100

1000

10000

p [GeV]T

Figure 6.16: The muon pT distribution used for the resolution measurement. The green points arethat for standard track, the red points are for the pixel tracklet reconstructed from the pixel hits inthe standard track. The blue points are the standard track pT distribution smeared by measured q/pT
resolution as shown in Fig. 6.15. The bottom plot shows the ratio of the pixel tracklet and the smeared
standard track distribution. [20]

CHAPTER 6. TRACKLET PERFORMANCE

86

MC
Data
σχData/σµMC ,
˜1 ± /σχ˜1 ± = σµ

(6.3)

MC
αχData˜1 ± /αχ˜1 ±

(6.4)

=

αµData /αµMC ,σ [TeV-1]

where these parameters are defined in Eq. 6.2 and the upper index shows used sample (data or MC)
and the lower index shows the used particle type. With these assumptions, wino smearing function
parameters for data is estimated from the smearing parameters of muon in MC, muon in data, andWino with multiple scattering in MC. The parameter is shown in Fig. 6.17 and Table 6.1. The uncertainty includes the fitting statistical error of used parameters and diﬀerence between wino MC withand without multiple scattering as systematic uncertainty. This smearing function parameter is used
to estimate the signal pT distribution. For signal events satisfying the SR criteria discussed in Sec.7.1,
the generator-level wino pT corresponding to the disappearing track candidate is convoluted with thesmearing function obtained as discussed above.

14
13
Muon data

12

Muon MC
Wino MC
Wino MC w/ multiple scattering

11

Estimated Wino data

10
9
8
7

0.8

1

1.2

1.4

1.6

1.8
α

Figure 6.17: Smearing function (Eq. 6.2) parameter fitting result statistical 1 σ contour for muonin data (black), muon in MC (light blue), wino in MC (red), and special wino sample with multiple
scattering (orange). The estimated parameter for the wino in data from Eq. 6.3 is also shown as purple
point.

6.5. TRACKING PARAMETER COMPARISON

87

Table 6.1: Summary of the smearing function parameter. Uncertainty is statistical error, but estimatedwino data uncertainty also includes the diﬀerence between the wino MC with and without multiple
scattering as systematic uncertainty.
Sampleσ [TeV−1 ]αMuon data 13.20 ± 0.09
1.67 ± 0.03
Muon MC
9.0 ± 0.3
1.17 ± 0.07
Wino MC8.05 ± 0.04 1.095 ± 0.007
Wino MC with multiple scattering
8.3 ± 0.3
1.00 ± 0.05
Estimated wino data
12.2 ± 1.0
1.42± 0.09

6.5 Tracking parameter comparison
Tracking parameter distributions of tracklets of each origin (chargino, electron, muon, hadron, andfake) in MC is compared in Fig. 6.18-6.26 as described below. Fake means that the track is reconstructed using hits from diﬀerent particles. Here, tracklets which satisfy disappearing condition(NSCT = 0, NContributedPixelLayers = 4) is used. No kinematic event selection is applied. Each distribution
is normalised to the unity.
The pT distribution in Fig. 6.18(a) shows that typical chargino pT is O(100 GeV) but background
distributions monotonically decrease. This is because charginos from gluino decay tend to be boosted.
The η distribution in Fig. 6.18(b) shows that charginos tend to have lower η than background. Peakaround η ∼ 0 in muon distribution is due to ineﬃciency of the Muon Spectrometer (MS) track in thatarea. d0 in Fig. 6.19(b) and d0 /σd0 distribution in Fig. 6.20(a) show that fake distribution is relatively
flat because it is mis-combination of hits from diﬀerent particles. Chargino d0 /σd0 distribution has
a sharp peak at d0 /σd0 = 0, but it is because multiple scattering is not included in chargino simulation. This problem is included in systematic uncertainty as discussed later in Sec.10.1. χ2 /d.o. f. in
Fig. 6.21(a) and fit quality in Fig. 6.21(b) shows that fake backgrounds tend to give bad fit result.
The number of pixel hits is shown in Fig. 6.22(a) and the number of pixel shared hits is shown in
Fig. 6.22(b). More than four pixel hits is due to overlapped modules in a layer to keep hermeticity.
The number of pixel and SCT outliers are shown in Fig. 6.23(a) and Fig. 6.23(b). Chargino has
relatively fewer pixel outliers. The number of pixel spoilt hits is shown in Fig. 6.24(a). Chargino has
relatively few pixel spoilt hits.
Ganged pixel in Fig. 6.25(a), 6.25(b) means pixels which shares a same readout channel withanother pixel. pcone40/pT in Fig. 6.26(a) is the sum of the pT of all standard tracks with pT > 1GeV
T
passed “Loose” track selection criteria in a cone of ∆R < 0.4 around the tracklet divided by pT .
Background has relatively large value because of the existence of other particles near the tracklet
or another track is reconstructed after the scattering of the particle. ETclus40 /pT in Fig. 6.26(b) iscalorimeter energy deposit in ∆R < 0.4 of extended track direction divided by pT . Especially electron
has peak around 1 due to an EM cluster of itself.

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets

88

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6

102

10

3

104
p [GeV]T

Fraction of tracklets(a) pT

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 2.5 − 2 − 1.5 −1 − 0.5

0

0.5

1

1.5

2

2.5
η

(b) η

Figure 6.18: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

Fraction of tracklets

6.5. TRACKING PARAMETER COMPARISON

89

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6

−3

−2

−1

0

1

2

3
φ

Fraction of tracklets

(a) ϕ

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
−200 −150 −100 − 50

0

50

100

150

200

d0 [µ m](b) d0Figure 6.19: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets

90

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 40

− 30

− 20

− 10

0

10

20

30

40

Fraction of tracklets(a) d0 /σd0

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
−500 −400 −300 −200 −100 0

100 200 300 400 500
z0sinθ [µ m](b) z0 sin θ

Figure 6.20: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

Fraction of tracklets

6.5. TRACKING PARAMETER COMPARISON

91

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6

0

1

2

3

4

5

6

7

8

9

10

χ2 / nDoF

Fraction of tracklets(a) χ2 /d.o. f.

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Fit Quality(b) Fit quality

Figure 6.21: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets

92

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6

0

1

2

3

4

5

6

7

number of Pixel hits

Fraction of tracklets(a) Number of Pixel hits

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of Pixel shared hits(b) Number of pixel shared hits

Figure 6.22: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

Fraction of tracklets

6.5. TRACKING PARAMETER COMPARISON

93

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of Pixel outliers

Fraction of tracklets(a) Number of pixel outliers

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of SCT outliers(b) Number of SCT outliers

Figure 6.23: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets

94

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of Pixel spoilt hits(a) Number of pixel spoilt hits

Figure 6.24: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

Fraction of tracklets

6.5. TRACKING PARAMETER COMPARISON

95

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of Ganged flagged fakes

Fraction of tracklets(a) Number of ganged pixels flagged as fake1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6
− 0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

number of Ganged Pixels(b) Number of ganged pixels

Figure 6.25: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

CHAPTER 6. TRACKLET PERFORMANCE

Fraction of tracklets

96

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6 −3
10

10−2

10−1

1
10
cone40p/p
T

T

Fraction of tracklets(a) pcone40/pT
T

1
Chargino

10−1Electron

10

−2

Muon

10−3

Hadron
Fake

10−4
10−5
10−6 −3
10

10−2

10−1

1
10
topo clus40
ET/pT(b) ETclus40 /pT

Figure 6.26: Tracking parameter distribution for each origin in MC. Red: chargino, blue: electron,
light green: muon, green: hadron, yellow: fake.

Chapter 7
Event Selection and analysis strategy
7.1 Kinematic selection
In this section, distributions of kinematic variables for signals and backgrounds are summarised.
As mentioned in Sec.4.2.2, a signal event has multiple high pT jets, large ETmiss , and one or two
disappearing tracks. Because the disappearing track requirement is powerful to distinguish signal
from background, other kinematic selections are designed to keep as much signal events as possible.
The Signal Region (SR) selection criteria are(1) ETmiss trigger(2) Bad jet veto (discussed in Ref. [86] as “BadLoose” for all jets and “BadTight” for leading jet)(3) Lepton veto (definition of electrons and muons are given in Sec.5.5.2,5.7.3. Tau is not vetoed.)(4) ETmiss > 150 GeV(5) 1st leading jet pT > 100 GeV(6) 2nd and 3rd leading jet pT > 50 GeV(7) ∆ϕ(jet, ETmiss ) > 0.4 for leading 3 jets. If there is 4th leading jet with pT > 50 GeV, this cut isalso applied.
(8) At least 1 disappearing track
The trigger and its performance studies are described later in Sec.7.2. Fig. 7.1, 7.2, 7.3 show
kinematic variable distributions of relevant objects in the Signal Region (SR) but excluding selection
criteria about the variable. There are a few sticking out bins in the QCD MC samples due to statisticalfluctuation in the simulation.
The cut flow is summarised in Table 7.1.
97

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Events

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Z→ ee
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Z→ ν ν
W→ e ν
W → µν
W→ τ ν
tt
Data
m ~g =1000 GeV, m ∼ =900 GeVχ±m ~g =1600 GeV, m ∼ =500 GeVχ±m ~g =1800 GeV, m ∼ =200 GeVχ±

100 200 300 400 500 600 700 800 900 1000
1st jet p [GeV]

data/MC

T

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W→ e ν
W → µν
W→ τ ν
tt
Data
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χ±m g~ =1600 GeV, m ∼ =500 GeV
χ±m g~ =1800 GeV, m ∼ =200 GeVχ±

100 200 300 400 500 600 700 800 900 1000
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data/MC

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100

200

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700

800

900

1000

(b) 2nd leading jet pT after applying all the other cuts except for cuts (6)(8)Figure 7.1: The kinematic variable distributions for the various MC background processes in thestacked histogram, the data in the black points and simulated events for the benchmark signals incoloured points. As benchmark signals, (mg̃ , mχ˜1 ± ) =(1000 GeV, 900 GeV) in red, (1600 GeV, 500
GeV) in blue, and (1800 GeV, 200 GeV) in green are shown. The lower plot shows the ratio of data
and MC in black points and MC statistical uncertainty is shown by red shade. Red arrows mean thatthe ratio is out of range.

Events

7.1. KINEMATIC SELECTION

99

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χ±

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(b) ETmiss after applying all the other cuts except for cuts (4)(8)Figure 7.2: The kinematic variable distributions for the various MC background processes in thestacked histogram, the data in the black points and simulated events for the benchmark signals incoloured points. As benchmark signals, (mg̃ , mχ˜1 ± ) =(1000 GeV, 900 GeV) in red, (1600 GeV, 500
GeV) in blue, and (1800 GeV, 200 GeV) in green are shown. The lower plot shows the ratio of data
and MC in black points and MC statistical uncertainty is shown by red shade. Red arrows mean thatthe ratio is out of range.

CHAPTER 7. EVENT SELECTION AND ANALYSIS STRATEGY

data/MC

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QCD
Z→ ee
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W→ e ν
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χ±m g~ =1800 GeV, m ∼ =200 GeV
χ

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9

±

(b) Number of jets with pT > 50 GeV after applying the other cut except for cuts (5)(6)(8)Figure 7.3: The kinematic variable distributions for the various MC background processes in thestacked histogram, the data in the black points and simulated events for the benchmark signals incoloured points. As benchmark signals, (mg̃ , mχ˜1 ± ) =(1000 GeV, 900 GeV) in red, (1600 GeV, 500
GeV) in blue, and (1800 GeV, 200 GeV) in green are shown. The lower plot shows the ratio of data
and MC in black points and MC statistical uncertainty is shown by red shade. Red arrows mean thatthe ratio is out of range.

7.2. ETMISS TRIGGER PERFORMANCE
Selection requirement(1)Trigger(2)Jet cleaning(3)Lepton veto(4)(5)(6)(7)ETmiss and jet requirements
Isolation and pT requirement
Geometrical |η| acceptance
Quality requirement(8)Disappearance condition

101
Observed
434,559,704
288,498,579
275,243,946
537,861
107,381
77,675
1337
35

Expected signal
285
282
278
202
43.6
36.4
13.9
11.0

(eﬃciency)(0.98)(0.97)(0.95)(0.69)(0.15)(0.13)(0.048)(0.038)

Table 7.1: Summary of the selection criteria and the corresponding observed number of events in data
as well as the expected number of signal events in the simulation for a benchmark model, chargino
produced in the strong channel with (mg̃ , mχ˜1 ± , τχ˜1 ± ) =(1600 GeV, 500 GeV, 0.2 ns). Decay branchingratio of g̃ → qqχ˜1 ± is assumed to be 2/3. The expected number of signal events is normalised to36.1 fb−1 . The signal selection eﬃciencies are also shown in parentheses. Selection requirements
below the dashed line are applied to tracks and tracklets.

7.2

ETmiss trigger performance

For the SR event selection, ETmiss trigger is used. The trigger performance is evaluated using W → µν
event candidates with similar jets criteria to SR:• Single muon trigger (HLT mu20 iloose L1MU15 (2015), HLT mu26 ivarmedium (2016), or
HLT mu50 (2015 and 2016), Table.4.1)• Electron veto
• Exactly 1 muon
• Muon pT > 27 GeV• Muon isolation√• 30 GeV < mT < 100 GeV, where mT = 2pµT ETmiss [1 − cos ∆ϕ(µ, ETmiss )] is transverse mass ofmuon and ETmiss expected to be near W boson mass.
• 1st leading jet pT > 100 GeV• 2nd and 3rd leading jet pT > 50 GeV• ∆ϕ(jet, ETmiss (no µ)) > 0.4 for leading 4 jets with pT > 50 GeV, where ETmiss (no µ) means ETmiss
calculated excluding muon contribution.
The trigger eﬃciency is measured by calculating the ratio of the number of events which passed
ETmiss trigger condition and the number of total events which are selected by the above event selection,

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which uses muon trigger. The muon trigger is assumed to be independent of the ETmiss trigger. It isevaluated as a function of ETmiss (no µ) and the 1st leading jet pT . The reason that muon is excluded
from ETmiss is because ETmiss trigger uses calorimeter energy deposit which does not include muon
contribution. The results are shown in Fig. 7.4 and 7.5 for each trigger. To calculate the number of
expected signal events, the eﬃciency obtained as a function of ETmiss and 1st leading jet pT is applied
to scale each simulated signal event instead of applying the trigger requirement. The topologicaldistribution of the data in above selection and the signal may be diﬀerent, but the eﬀect to the signal
eﬃciency is almost negligible because the trigger eﬃciency of the signal is nearly 100%.

7.3 Analysis strategy
The pT distribution of the disappearing track candidate is used to search for the excess from background. The background estimation is performed using only data. It is because the pixel tracklet
reconstruction and the parameter measurement resolution largely depends on detector condition and
it is diﬃcult to simulate in MC. The detail of the background estimation is discussed later in chapter 8.
The examination of the signal existence and determination of the background normalization are doneby likelihood fitting of pT distribution of the disappearing track candidate as described in chapter 9.
Because backgrounds are dominant in low pT , but the signal may be dominant in the high pT region
if signal exists, the low pT region mainly contributes to background normalization fitting.

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Figure 7.4: Trigger eﬃciency dependence on ETmiss and 1st leading jet pT .

CHAPTER 7. EVENT SELECTION AND ANALYSIS STRATEGY

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Figure 7.5: Trigger eﬃciency dependence on ETmiss and 1st leading jet pT .

Chapter 8
Background estimation
Background tracks are categorised into three by the origins of disappearing track candidates. Fig. 8.1
shows the schematic pictures of the three categories: hadron, lepton, and fake. Hadrons may be reconstructed as pixel tracklets when they scatter due to nuclear interaction or decay in the material insideor outside of the pixel detector and reconstruction fails to extend the track to the SCT. Leptons scatteror decay similarly to the case of hadrons, and their tracks also bend oﬀ due to bremsstrahlung. Fake
tracks are induced by the mis-combination of hits from diﬀerent particles. In this section, backgroundestimation methods are described for each category. Hadron background estimation is discussed inSec.8.1, lepton background estimation is discussed in Sec.8.2, and fake background estimation is
discussed in Sec.8.3. Normalization of each background is finally determined by the fitting pT distribution of the disappearing track candidate pixel tracklets as discussed later in Chap. 9.

8.1 Hadronic background8.1.1 Control region
To estimate hadronic background, Hadron Control Region (HCR) is defined as the same as the SR(Sec.7.1) except that a pixel tracklet requirement is replaced by an isolated hadron candidate requirement. The selection criteria are as following:• ETmiss trigger (Sec.7.2)• Bad jet veto (Sec.7.1)• Lepton veto (definition of electrons and muons are given in Sec.5.5.2,5.7.3)• ETmiss > 150 GeV• 1st leading jet pT > 100 GeV• 2nd and 3rd leading jet pT > 50 GeV• ∆ϕ(jet, ETmiss ) > 0.4 for up to four leading jets with pT > 50 GeV
105

Pixel

Pixel

Pixel

SCT

SCT

SCT

CHAPTER 8. BACKGROUND ESTIMATION

106(a) Hadron(b) Lepton(c) Fake

Figure 8.1: Schematic picture of three categories of background disappearing track. (a) Hadron
which decays at the fourth layer of the pixel detector. (b) Lepton which causes bremsstrahlung. (c)Fake tracklet that reconstructed from hits from diﬀerent particles. The black lines denote the detector
layers, the yellow points are hits, the red solid line is the truth trajectory of charged particles, thered dashed line is the truth trajectory of neutral particles, and the blue line is the reconstructed pixel
tracklet. [20]
• 1 hadron track candidate which satisfies requirements below:– The same track selection as the disappearing track candidate selection except for the disappearing condition– NTRT ≥ 15
– NSCT ≥ 6– ETcone20 > 3GeV, where ETcone20 is the calorimeter transverse energy deposited in a cone of∆R < 0.2 around the track excluding the ET of the calorimeter cluster associated with the
track.
∑∑> 0.5, where ∆R<0.4 ETclus is the sum of the cluster transverse energies– ∆R<0.4 ETclus /ptrackTin a cone of ∆R < 0.4 around the track.

It can be assumed that the distribution of the background hadron pT in SR and that of the hadroncandidate pT in HCR is similar because the probability of elastic or inelastic nuclear interaction or
decay do not depend on pT . This assumption is confirmed in MC as shown in Fig. 8.2. Therefore, thepT distribution of the hadron candidate track in HCR is used as that of the hadron background in SR.
Since selected these tracks are good long ones and the resolution of tracking parameter are far better
than that of the short disappearing ones, pT is smeared as described in Sec.6.3.

8.1. HADRONIC BACKGROUND

107

Fraction of tracks

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30

40 50 60 70 80 100
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Figure 8.2: The generator-level pT distribution of the pion in MC. The green points are pion which
does not scatter in the ID and the red points are pion which scattered in the ID. [20]

CHAPTER 8. BACKGROUND ESTIMATION

108

8.1.2 Smearing technique
The function represented as in Eq. 6.2, which is fitted to data as shown in Fig. 6.15, is used for thesmearing. This is called smearing function. Each pT of the hadron candidate track is convoluted
with the smearing function. Fig. 8.3 shows the pT distributions of hadron candidates in HCR and thesmeared one. Cutoﬀ at 50 GeV in the HCR is due to requirement of up to 4 jets with pT > 50 GeV
do not exist in the region of ∆R > 0.4 from the track. The shape of the smeared one is used as theestimated hadronic background. Normalization is determined later by the fitting in the SR.

8.2 Leptonic background8.2.1 Overview
For the leptonic background, electron and muon backgrounds are estimated separately. The control region is defined same as the SR (Sec.7.1) except for that the disappearing track requirement is
replaced to an isolated electron or a muon requirement and lepton veto is removed as explicitly described in Sec.8.2.2. The number of lepton background is estimated using Transfer Factors (TFs). TF
is the ratio of the number of identified electrons (muons) and the number of disappearing tracks fromelectrons (muons). Using the TF, the number of lepton background is estimated as
e(µ)
e(µ)
NSe(µ)
R = NCR × TFdisappearing ,

(8.1)

e(µ)
where NSe(µ)
R is the estimated number of electron (muon) background events, NCR is the number of
events in the control region of electron (muon), and TFe(µ)
disappearing is the TF of electron (muon).
The TF is evaluated by so called the tag and probe method as described explicitly in Sec.8.2.3 for
TFedisappearing and in Sec.8.2.4 for TFµdisappearing . The tag and probe method uses Z → ee(µµ) candidate
events. The tag electron (muon) is identified with tight criteria in the event selection. For a probe
electron (muon), minimal electron (muon) identification criteria are required. Instead of loose criteria
for the probe electron (muon), requirement for reconstructed mass with the tag electron (muon) andthe probe electron (muon) to be Z boson mass is applied to suppress fake probe electron (muon)from non-Z → ee(µµ) events. Once events for the tag and probe method is selected, probe electrons(muons) are used to calculate the TF.
For the electron tag and probe, the probe electron candidate requires topo-cluster and a track in thenear direction. Muon TFµdisappearing is divided into 2 factors: TFµtracklet and TFµMS . This is because probemuon for TFtracklet measurement requires MS track and a track in near direction, but disappearing track
definition (Sec.5.1.4) includes isolation from MS track and therefore TFµdisappearing cannot be exactly
calculated by using the probe muon. TFtracklet is the ratio of number of baseline muon and numberof muon that leaves a pixel tracklet and an MS track. TFMS is the ratio of the number of the muoncandidate with a long track and an MS track and the number of muon candidate with a track longenough but no MS track in near direction.
Finally, the lepton background distribution is estimated by using Eq. 8.1 and then smearing technique (Sec.8.1.2) is applied to account for the pT resolution diﬀerence between the standard track inthe control region and the pixel tracklet in the SR as discussed in Sec.8.2.5.

Events

8.2. LEPTONIC BACKGROUND

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Figure 8.3: The HCR hadron candidate track pT distribution and the smeared one. Various MC
standard model processes are shown in stacked histogram and data is shown in black points. The
lower plot shows the ratio of data and MC in the black points and MC statistical uncertainty is shownby the red shade.

CHAPTER 8. BACKGROUND ESTIMATION110

The detailed lepton background estimation is described below.

8.2.2 Control region
For the leptonic background estimation, an Electron CR (ECR) and a Muon CR (MCR) is definedas the same as the SR (Sec.7.1) except that a pixel tracklet requirement is replaced by an isolated
electron for the ECR or an isolated muon for the MCR requirement.
The ECR is defined by the following requirements.
• ETmiss trigger (Sec.7.2)• Bad jet veto (Sec.7.1)• Muon veto (definition of muons is given in Sec.5.7.3)• ETmiss > 150 GeV (For ETmiss calculation, an electron is ignored)• 1st leading jet pT > 100 GeV• 2nd and 3rd leading jet pT > 50 GeV• ∆ϕ(jet, ETmiss ) > 0.4 for up to four leading jets with pT > 50 GeV• An electron candidate which satisfies requirements below:– The same track selection as the disappearing track candidate selection except for the disappearing condition and the isolation from electron– pT > 16 GeV– Identified as an electron– ∆R > 0.4 from MS track
The MCR is defined by the following requirements.
• ETmiss trigger (Sec.7.2)• Bad jet veto (Sec.7.1)• Electron veto (definition of electrons is given in Sec.5.5.2)• ETmiss > 150 GeV (For ETmiss calculation, muon is ignored)• 1st leading jet pT > 100 GeV• 2nd and 3rd leading jet pT > 50 GeV• ∆ϕ(jet, ETmiss ) > 0.4 for up to 4 leading jets with pT > 50 GeV

8.2. LEPTONIC BACKGROUND

111• A muon candidate which satisfies requirements below:– The same track selection as the disappearing track candidate selection except for the disappearing condition and the isolation from muon and MS track– pT > 16 GeV– Identified as a muon
Fig. 8.4 shows the pT distribution of the lepton candidate tracks in the ECR and the MCR. Discrepancy between data and MC comes from mainly dead module eﬀect of 81.1% in data as mentioned inSec.6.2. The total number of events ratio of data and MC is 75.9 ± 1.0 (stat.)% form ECR and 82.6 ±
0.5 (stat.)% in MCR. Remaining discrepancy is due to systematic uncertainties such as luminosity uncertainty, cross-section uncertainty and lepton identification eﬃciency uncertainty. This dead moduleeﬀect always appears when event selection includes tracking requirements of four pixel contributed
layers.

8.2.3 Electron Transfer Factor (TF) measurement
To measure the TF, tag and probe method is used. The tag and probe method uses Z → ee candidate
events. For the tag electrons, electron identification with tight criteria is required. The probe electronis then searched for in the event requiring minimal electron identification criteria. Instead of theloose criteria on the probe electron, a requirement on reconstructed mass with tag electron and probe
electron to be Z boson mass, |Mee − MZ | < 10 GeV, is applied to suppress fake probe electrons from
non-Z → ee events.
Once the events for tag and probe are selected, probe electrons are categorised into the baseline
electron same as used in the ECR or the electron which become disappearing track candidates. The
TF is the ratio of the numbers of electrons in the above two categories.
Specific event selection criteria are as follows:
Definition of tag electron• Satisfying tight electron criteria (Sec.5.5.2)• The electron fired the single electron trigger (Sec.4.1)• pT > 30 GeV
Definition of probe electron• No electron identification requirement• A topo-cluster with an associated track or tracklet within ∆R < 0.2• The topo-cluster pT > 10 GeV• The topo-cluster |η| < 2.5• The associated ID track satisfies track selection described below.

CHAPTER 8. BACKGROUND ESTIMATION

Events112

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(b) MCR muon candidate track pT

Figure 8.4: The lepton candidate track pT distributions in the ECR and the MCR. Various MC standard
model processes are shown in the stacked histogram and data is shown in the black points. The lower
plot shows the ratio of data and MC in the black points and MC statistic uncertainty is shown by the
red shade.

8.2. LEPTONIC BACKGROUND

113

Event selection• Trigger: single electron trigger for each period. HLT e24 lhmedium L1EM20VH for data 2015,
HLT e24 lhtight nod0 ivarloose or HLT e26 lhtight nod0 ivarloose for data 2016
depending on the instantaneous luminosity. (Sec.4.1)• Bad jet veto (Sec.7.1)• At least one reconstructed primary vertex with a minimum of 2 tracks with pT > 0.4 GeV.
• No identified muons.
• At least one tag electron.
• At least one probe electron.
• |Mee −MZ | < 10 GeV, where Mee is the reconstructed mass from the tag electron four-momentum
and the probe electron calorimeter energy deposit (in order to avoid using ID track information).
Track selection• The same track selection as the disappearing track candidate selection (Sec.5.1.4) except forthe disappearing condition and the isolation from electron• ∆R > 0.4 for any jets (muon, MS track) with pT > 50(10) GeV• Only for the baseline electron (synchronised to the ECR electron):
The track is associated to a reconstructed electron (Sec.5.5.2).
• Only for the disappearing track (synchronised to Sec.5.1.4):– NSCT = 0– Not reconstructed as an electron
Fig. 8.5 shows the reconstructed mass distributions in each category but reconstructed mass requirement |Mee − MZ | < 10 GeV is not applied. As it shows, disappearing track category includes
significant amount of background from jets in W → eν events. According to MC, the purity is 43%.
To estimate the background distribution, sign of the tag electron and the probe electron is used. If an
event is Z → ee, tracks should have opposite charge. If an event is W → eν, there is no favor whether
it is same sign or opposite sign and it is expected to be even probability. It is confirmed by MC within
the statistical uncertainty. Fig. 8.6 (a), (b) shows the reconstructed mass distributions in disappearing
track category divided into the same sign and the opposite sign. Z → ee is separated very well andbackground distributions are very similar. Therefore, background is suppressed by subtracting same
sign distribution from opposite sign distribution. Fig. 8.6 (c) is a subtracted distribution. Backgroundis suppressed very well. This background correction method is applied to other distributions shownin and after this section.

CHAPTER 8. BACKGROUND ESTIMATION

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Events

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Z→ ee
Z→ µµ
Z→ τ τ
Z→ ν ν
tt
W → eν
W → µν
W→ τν
Data

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110

(b) Disappearing track

Figure 8.5: The Mee distributions of each category. Various MC standard model processes are shownin the stacked histogram and data in the black points. Lower plot shows the ratio of data and MC in
the black points and MC statistic uncertainty is shown by the red shade.

1000

115

EventsEvents

8.2. LEPTONIC BACKGROUND

s=13TeV, 36.1 fb -1

QCD
Z→ ee
Z→ µµ
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Z→ ν ν
tt
W → eν
W → µν
W→ τν
Data

800
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Z→ ee
Z→ µµ
Z→ τ τ
Z→ ν ν
tt
W → eν
W → µν
W→ τν
Data

800
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200
70 75 80 85 90 95 100 105 110

70 75 80 85 90 95 100 105 110
Mee [GeV]

data/MC

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Z→ ee
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Data

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(c) Opposite sign - same sign

Figure 8.6: The Mee distributions of (a) the opposite sign events and (b) the same sign events indisappearing track category. (c) is (a) subtracted by (b). Various MC standard model processes areshown in the stacked histogram and data in the black points. The lower plot shows the ratio of data
and MC in the black points and MC statistic uncertainty is shown by the red shade.

CHAPTER 8. BACKGROUND ESTIMATION116

The electron TF is measured as a function of pT and η using the equation
TFdisappearing (pT , η) = Ndisappearing (pT , η)/Nbaseline (pT , η),(8.2)

where Ndisappearing (pT , η) is the number of events in the disappearing track category and Nbaseline (pT , η)is the number of events in the baseline category. pT and η are taken from the probe topo-cluster. To decrease statistical uncertainty, the same |η| bin is combined before calculate the TF assuming the symmetric structure of the ATLAS detector. Fig. 8.7 shows distribution of Nbaseline (pT , η), Ndisappearing (pT , η)and TFdisappearing (pT , η) derived from Eq. 8.2. The cutoﬀ in Fig. 8.7(b) at pT ∼ 50 GeV is due to therequirement of ∆R < 0.4 from any jet with pT > 50 GeV which is mis-identified electron’s energy
deposit as a jet. The cutoﬀ in Fig. 8.7(a) at pT ∼ 10 GeV is due to ineﬃciency of electron identification. To avoid this problematic region, the ECR electron is required pT > 16 GeV. Fig. 8.7(c) is used
to determine normalisation of electron background in the SR.

8.2.4 Muon TF measurement
The muon TF is also measured by the tag and probe method. Here, an MS track is required forthe probe muon. However, the disappearing track definition includes ∆R < 0.4 MS track veto andtherefore probe is impossible to be exactly the same definition as the disappearing track. To resolve
the problem, muon TF is divided into 2 factors: the TFtracklet that a track becomes a pixel tracklet andthe TFMS that the MS track is missing.
TFdisappearing = TFtracklet × TFMS

(8.3)

Both TF is measured by tag and probe. The detailed method is discussed in the following paragraphs.
The TFtracklet measurement
The TFtracklet is measured by the tag and probe method with Z → µµ events. The event selection
criteria are as follows:
Definition of tag muon
• Satisfying tight muon criteria• The muon fired the single muon trigger• pT > 30 GeV
Definition of probe muon
• No muon identification requirement• An MS track with an associated track or tracklet within ∆R < 0.2

2.5

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8.2. LEPTONIC BACKGROUND

2
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(a) Nbaseline (pT , η)

η

105
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− 2.5

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10

102

10

3

(b) Ndisappearing (pT , η)104
p [GeV]

1

T

10−1

2.5
2
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0
− 0.5
−1

10−4

− 1.5
−2
− 2.5

10

2

10

3

4

10
p [GeV]10−5T(c) TFdisappearing

Figure 8.7: Distribution of (a) Nbaseline (pT , η), (b) Ndisappearing (pT , η) . (c) is measured TFdisappearing in
data.

118

CHAPTER 8. BACKGROUND ESTIMATION• The MS track pT > 10 GeV• The MS track |η| < 2.5• The associated ID track satisfies the track selection described below.
Event selection• Trigger: single muon trigger for each period. HLT mu20 iloose L1MU15 for data 2015,
HLT mu24 iloose, HLT mu24 ivarloose or HLT mu26 imedium, or HLT mu26 ivarmedium
for data 2016 depending on the instantaneous luminosity.
• Bad jet veto
• At least one reconstructed primary vertex with a minimum of 2 tracks with pT > 0.4 GeV.
• No identified electrons.
• At least one tag muon.
• At least one probe muon.
• |Mµµ − MZ | < 10 GeV, where Mµµ is reconstructed mass from the tag muon four-momentum
and the probe muon MS track four-momentum (ID track information is not used)
Track selection• The same track selection as the disappearing track candidate selection (Sec.5.1.4) except forthe disappearing condition and the isolation from muon and MS track• ∆R > 0.4 for any jets (electron) with pT > 50(10) GeV• Only for the baseline muon (synchronised to the MCR muon):
The track is associated with the reconstructed muon.
• Only for the pixel tracklet (synchronised to Sec.5.1.4 except for the MS track isolation):
NSCT = 0
Fig. 8.8 shows the reconstructed mass distributions in each category, but the reconstructed massrequirement is not applied. As is done in the electron TF measurement, signs of the tag muon andthe probe muon are used for the background subtraction. That is, the opposite sign events distribution
subtracted by the same sign events distribution is used. The purity before subtraction is 99.9 %according to MC. The background correction method is applied to other distributions shown here
after in this section.
Because the statistics are very poor and dependence on pT is not expected, TFtracklet is measured
as a constant number, not a function.
TFtracklet = Ntracklet /Nbaseline ,(8.4)

8.2. LEPTONIC BACKGROUND

119

Events3×10500

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Z→ ee
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Data

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Data

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(b) Pixel tracklet

Figure 8.8: The Mµµ distributions of each category after background correction. Various MC standard
model processes are shown in the stacked histogram and data in the black points. The lower plotshows the ratio of data and MC in the black points and MC statistic uncertainty is shown by the red
shade.

CHAPTER 8. BACKGROUND ESTIMATION

120

where Ntracklet is the number of events in the pixel track category and Nbaseline is the number of eventsin the baseline category. The measured value is TFtracklet = 3.6(±0.6) × 10−5 .
The TFMS measurement
The measurement of the TFMS uses the tag and probe method, but the event and object selection are
modified from those for the TFtracklet . Categories are divided by existing or missing an MS track.
Specific selection criteria are as follows.
Definition of tag muon Same as that for TFtracklet .
Definition of probe muon
• No muon identification requirement• The same track selection as the disappearing track candidate selection (Sec. 5.1.4) except forthe disappearing condition and the isolation from muon and MS track• NS CT ≥ 6• NT RT ≥ 15
• For the existing category: An MS track exists in ∆R < 0.4• For the missing category: An MS track is absent in ∆R < 0.4
Event selection• The same as that for the TFtracklet except for the Mµµ definition.
• |Mµµ − MZ | < 10 GeV, where Mµµ is reconstructed mass from four-momenta of the tag muonand the probe muon ID track (MS track information is not used)
Fig. 8.9 shows reconstructed mass distributions in each category, but the reconstructed mass requirement is not applied. As is done in the electron TF measurement, the signs of the tag muon and theprobe muon are used for the background correction. The purity before subtraction is 16% according
to MC. That is, the opposite sign events distribution subtracted by the same sign events distribution
is used. The background correction method is applied to other distributions shown here after in thissection.
MS track existence or missing is mostly due to the geometrical eﬀect of the ATLAS detector.
Therefore, it is evaluated as a function of η and ϕ.
TFMS (ϕ, η) = Nmissing (ϕ, η)/Nexisting (ϕ, η),(8.5)

where Nmissing (ϕ, η) is the number of events in missing MS track category and Nexisting (ϕ, η) is the number of events in the existing MS track category. ϕ and η is taken from the probe ID track. Because

8.2. LEPTONIC BACKGROUND

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Data

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Data

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(b) MS track missing

Figure 8.9: The Mµµ distributions of each category after background correction. Various MC standard
model processes are shown in the stacked histogram and data in the black points. The lower plotshows the ratio of data and MC in the black points and MC statistic uncertainty is shown by the red
shade.

CHAPTER 8. BACKGROUND ESTIMATION

122

the statistics are very poor and the ATLAS detector is nearly 8-fold rotational symmetry in ϕ, symmetrical points are combined before calculating the TFMS (ϕ, η). The same |η| bin is also combined.
Fig. 8.10 shows the distribution of Nexisting (ϕ, η), Nmissing (ϕ, η) and TFMS (ϕ, η) derived from Eq. 8.5.
High TFMS (ϕ, η) around |η| ∼ 0 is due to the ineﬃciency of the MS in this area. Significant change at|η| ∼ 1 is because it is barrel toroid magnet edge. Fig. 8.10(c) is used to determine the normalisationof muon background together with the TFtracklet in the SR.

8.2.5 Estimated leptonic background
Using the results in the above sections, the leptonic background is estimated byeNSR(pT , η) = NECR (pT , η) × TFdisappearing (pT , η)

(8.6)

µ
NSR
(pT , ϕ, η) = NMCR (pT , ϕ, η) × TFtracklet × TFMS (ϕ, η)(8.7)

Fig. 8.11 show the electron and the muon pT distribution weighed by the TFs. Then, as is donein Sec.8.1.2, smearing is performed to account for the resolution diﬀerence. Fig. 8.12 shows theestimated electron and muon background distribution.

8.3 Fake background
Fake is a mis-combination of hits from diﬀerent particles. As shown in Fig. 6.20(a), fake tracklet
d0 /σd0 distribution is wide. Therefore, Fake Control Region (FCR) is defined the same as the SR(Sec.7.1) except for that disappearing track d0 /σd0 is required to be large. FCR definition is as follows.
• ETmiss trigger (Sec.7.2)• Bad jet veto (Sec.7.1)• Lepton veto (definition of electrons and muons are given in Sec.5.5.2,5.7.3)• 1st leading jet pT > 100 GeV• 2nd and 3rd leading jet pT > 50 GeV• ∆ϕ(jet, ETmiss ) > 0.4 for up to four leading jets with pT > 50 GeV• 1 fake candidate which satisfies requirements below:– The same track selection as the disappearing track candidate selection except for |d0 |/σd0– |d0 |/σd0 > 10
The distribution of the FCR is fitted by an empirical function,()
f (pT ) = exp −p0 · log(pT ) − p1 · (log(pT ))2 ,(8.8)

where p0 and p1 are free parameters. The FCR distribution and the fit result are shown in Fig. 8.13.

2.5

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φ
(c) TFMS

Figure 8.10: The distribution of (a) Nexisting (ϕ, η) (b) Nmissing (ϕ, η) . (c) is measured TFMS in data after
combining symmetrical bins.

CHAPTER 8. BACKGROUND ESTIMATION

Events124102

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Z→ ee
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tt
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Data

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Events(a) Estimated electron background distribution
s=13TeV, 36.1 fb -1

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(b) Estimated muon background distribution

Figure 8.11: The estimated electron and muon background distributions before smearing. Various
MC standard model processes are shown in the stacked histogram and data in the black points. The
lower plot shows the ratio of data and MC in the black points and MC statistic uncertainty is shownby the red shade.

Events

8.3. FAKE BACKGROUND

125

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Events(a) Estimated electron background distribution
s=13TeV, 36.1 fb -1

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(b) Estimated muon background distribution

Figure 8.12: The estimated electron and muon background distributions after smearing. Various MC
standard model processes are shown in the stacked histogram and data in the black points. The lower
plot shows the ratio of data and MC in the black points and MC statistic uncertainty is shown by the
red shade.

CHAPTER 8. BACKGROUND ESTIMATION

Tracklets

126

103

Data
Fit

-1

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2 Strong production
10 Fake control region

10
1

Data / Fit

10−1
2
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100

1000

10000

Tracklet p [GeV]T
Figure 8.13: The FCR disappearing track distribution and the fit result. The black points are data andthe blue dashed line is fitting result. The blue shaded region is fitting uncertainty. The lower plotshows the ratio between data and fitting result. χ2 = 8.5, number of degrees of freedom = 19.

Chapter 9
The statistical method to evaluate
experimental limits
The final examination whether signal excess is observed or not is performed by unbinned likelihood on
the pT distribution of disappearing tracks in the SR (Sec.7.1) with the estimated signal and background
distributions.
To constrain the number of fake backgrounds, so called ABCD method is used as described in thefollowing. In addition to the SR, Low-ETmiss region (LCR), High-ETmiss Fake Control region (HFCR),
and Low-ETmiss FCR (LFCR) are considered in the likelihood fitting. The LCR definition is the sameas the SR but the ETmiss requirement is replaced to 100 GeV < ETmiss < 150 GeV. The HFCR definitionis the same as the FCR (Sec.8.3) except for that ETmiss requirement 150 GeV < ETmiss is added. The
LFCR definition is the same as the FCR except for that ETmiss requirement 100 GeV < ETmiss < 150
GeV is added. It is assumed that fake background is dominant in the HFCR and the LFCR. Because
ETmiss and |d0 |/σd0 do not correlate as shown in Fig. 9.1, the ratios of the number of fake backgrounds
is assumed to satisfy the equation,
N Sf R /N HFCR
= N LCR/N LFCR
f
f
f

(9.1)

where N Rf is the number of fake backgrounds in the region R (R = SR, HFCR, LCR, or LFCR). This
is included as a constraint in the likelihood. N HFCR
and N LFCR
are the expected number of events in
f
f
SR
LCR
each region and N f and N f are the estimated number of fake backgrounds by fitting with all thebackground components and a signal.

127

CHAPTER 9. THE STATISTICAL METHOD TO EVALUATE EXPERIMENTAL LIMITS

Probability density

128

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103

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Track Pt (GeV)

103

104
Track Pt

102

Probability (a.u.)(a) d0 dependence

10−2
10−3
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10−7
102

(b) ETmiss dependence

Figure 9.1: The fake background distribution dependence on d0 and ETmiss . The diﬀerent color bandshows diﬀerent d0 or ETmiss range. The discrepancy is within the statistical uncertainty. [85]129
The likelihood function is defined as:
LTotal = Lshape × Lsyst

(9.2)
(9.3)

where
e−(ns +nh +ne +nµ +nf ) e−(ns·=nSobsR !
SR

Lshape

SR

×

nobs
∏

SR

SR

SR

LCR +nLCR +nLCR +nLCR +nLCR
e
µ
h
f

SR

)

LCR
nobs
!

(
)
(
)
, αsmearing+ nSh R FhS R pT ; σsmearing[nSs R FsS R pT ; σsmearing, αsmearing
s
s
BG
BG

+nSe R FeS R (pT ) + nSµ R FµS R (pT ) + nSf R Ff (pT ; p0 , p1 )]
LCR

×

nobs
∏

(
(
)
)
smearing[nsLCR FsLCR pT ; σsmearing, αsmearing+ nhLCR FhLCR pT ; σsmearing
,
α
s
s
BG
BG

+neLCR FeLCR (pT ) + nµLCR FµLCR (pT ) + nfLCR Ff (pT ; p0 , p1 )]HFCR() HFCR e−N LFCR ()nLFCRe−N
HFCR nobs
× HFCR · N
× LFCR · N LFCR obs ,nobs !
nobs !
Lsyst = N

nSs R
nsLCR

=
=

rABCD =N (X; ∆X) =(NsS R ; ∆NsS R

)

(

)

(

NµS R ; ∆NµS R

)

×N
×N
)
)
(
)
(
×N NsLCR ; ∆NsLCR × N NeLCR ; ∆NeLCR × N NµLCR ; ∆NµLCR()( smearing)
smearing
smearing
×N σsmearing
;
∆σ
×
N
α
;
∆α
BG
BG
BG
BG
( smearing)( smearing)
smearing
smearing
×N σs
; ∆σs
× N αs; ∆αs×N (rABCD ; ∆rABCD ) × N (p0 ; ∆p0 ) × N (p1 ; ∆p1 ) ,µs × NsS R ,µs × NsLCR ,NfS R /N HFCR
log LCR
Nf /N LFCR
(X−⟨X⟩)21e− 2∆X2 .
√2π∆X(

NeS R ; ∆NeS R

(9.4)

(9.5)
(9.6)
(9.7)
(9.8)
(9.9)

The definitions of the variables are summarised in Table 9.1. Lshape is a likelihood function forthe shape of the pT distribution. It includes Poisson distribution of the number of events in eachregion and parameters in the PDF. Lsyst consists of normal distributions of systematic uncertainty of
the relevant parameters. The detail of the systematic uncertainties will be discussed in Chap.10. The
same relative signal strength µ s in each region is included as a constraint.

130

CHAPTER 9. THE STATISTICAL METHOD TO EVALUATE EXPERIMENTAL LIMITS

Variable
LTotalLshapeLsyst
SR
Fs(h,e,µ,f)
LCR
Fs(h,e,µ,f)pT
RnSs(h,e,µ,f)LCRns(h,e,µ,f)
S R(LCR,HFCR,LFCR)
nobs
⟨X⟩
∆X

N HFCR(LFCR)
σsmearinge,hαsmearinge,hσsmearings
αsmearing
s
p0
p1
SR
Ns(e,µ)LCR
Ns(e,µ)rABCDµsTable 9.1: The definition of likelihood variables.
Definition
Likelihood functions
Total likelihood
Likelihood about pT distribution function
Likelihood about nuisance parameters
Probability density functions
The probability density function of signal (hadron, electron, muon, fake) in
the SR
The probability density function of signal (hadron, electron, muon, fake) inthe LCR
Measured variables
The transverse momentum of the disappearing track candidate pixel tracklet
The observed number of signal (hadron, electron, muon, fake) in the SR
The observed number of signal (hadron, electron, muon, fake) in the LCR
The observed total number of events in the SR (LCR, HFCR, LFCR)
The estimated parameter value (X denotes any nuisance parameters)
Uncertainty of the estimated parameter value (X denotes any nuisance parameters)
Fitting parameter
The expected total number of events in the HFCR (LFCR)
σ in Eq. 6.2 for background
α in Eq. 6.2 for backgroundσ in Eq. 6.2 for signal
α in Eq. 6.2 for signal
p0 in Eq. 8.8
p1 in Eq. 8.8
The expected number of signal (electron, muon estimated in Sec.8.2) in theSR
The expected number of signal (electron, muon estimated in Sec.8.2) in the
LCR
Logarithmic of ratio of right hand side and left hand side of Eq. 9.1. (0 isnominal)Relative signal strength (1 is nominal if signal exists. 0 is nominal if background only.)Chapter 10
Systematic uncertainties
10.1 Uncertainties in signal normalization
The following sources of systematic uncertainties on the signal normalisation are considered:• Theoretical cross-section• Initial and final state radiation (ISR/FSR)• Jet energy scale and resolution (JES/JER)• ETmiss Track Soft Term (TST, Sec.5.9) scale and resolution• Trigger eﬃciency• Pile-up modeling• pT distribution• Track reconstruction eﬃciency and pT resolution• Track |d0 | significance• Integrated luminosity
Contributions of each systematic uncertainty in the signal expectations are summarised in Table 10.1. Details of each uncertainty source are described below.
Theoretical uncertainty in the signal cross-section is evaluated as discussed in Ref. [87]. PDF
uncertainty, choice of the renormalisation scale for α s , and the choice of the factorisation scale areconsidered. The factorisation scale is the energy scale where the parton shower model and perturbative
QCD calculation are connected. The cross-section and the uncertainty depend on the gluino mass.
High-pT jets originating from initial and final state radiations (ISR and FSR) aﬀect the signal
acceptance. The following items are considered.
131

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

132

Source(Theoretical uncertainty)
Cross-section(Uncertainties on the acceptance)
ISR/FSR
JES/JER
TST
Trigger eﬃciency
Pile-up modeling
Track reconstruction eﬃciency
Signal selection eﬃciency
d0 biasLuminosity
Sub-total

Signal pointmg̃ = 1000 GeV, mχ˜1 ± = 900 GeV mg̃ = 1800 GeV, mχ˜1 ± = 500 GeV
±17

±28.1

+14/ − 8.4+3.5/ − 6.6+0.1/ − 2.4< 0.1+0.2/ − 0.2+0.1/ − 0.7+0.2/ − 0.4
< 0.1

±18

+4.5/ − 3.3
±1.2
±6.8
±0.7
±3.2

±9.3

Table 10.1: Summary of systematic uncertainties [%] in the expectation of the number of the signal
events.
• The uncertainty in the choice of renormalisation/factorisation scale is evaluated by changing
the default scale by a factor of 0.5 and 2 in MadGraph5.
• The uncertainty on the CKKW-L merging [88] scale is evaluated by taking the maximum
deviation from the nominal MC sample when varying it by a factor of 0.5 or 2.
• The uncertainty on the parton shower generator tuning is evaluated by Pythia8 A14 NNPDF23LO
tune variations described in Ref. [59]. Among Var1, Var2, Var3a, Var3b, Var3c mentioned in
the reference, only Var3c has non-negligible eﬀect to acceptance. Var3c corresponds to the α svalue tunining.
The uncertainty is evaluated using signal acceptance in the SR (Sec.7.1) without the disappearing
track candidate requirement, i.e. kinematic selection only, because ISR/FSR uncertainty does not affect track selection eﬃciency. Relative uncertainties as a function of the gluino mass and the chargino
mass are shown in Fig. 10.1,10.2,10.3. The resulting uncertainty is assigned by combining them inquadrature (Fig. 10.4) and take the larger one of scale up or scale down. For Fig. 10.4, after combining the uncertainties in quadrature, the sign of the resulting uncertainty is the same as the sign of thelinearly combined uncertainties.
The uncertainty in the JES/JER results in a variation of the signal selection eﬃciency, but does notdirectly aﬀect the pT distribution of chargino tracks. The relative uncertainty from jet η calibration isshown in Fig. 10.5. The JES uncertainty sources are divided into three categories by the strength of thecorrelations among sources. Relative uncertainties as a function of the gluino and the chargino mass
is shown in Fig. 10.6,10.7 and 10.8. JER uncertainty is evaluated by worsening the resolution by 1
standard deviation. Relative uncertainties as a function of the gluino and the chargino mass are shownin Fig. 10.9. The resulting uncertainty is assigned by combining them in quadrature (Fig. 10.10).
The uncertainty on the TST for ETmiss is estimated in a similar way as that of JES/JER. The resolution uncertainty is evaluated by worsening the resolution by 1 standard deviation as is done for

1200

1000

800

600

400

200

1400

1600

1800
800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. -0. 0. -0. -0. -0. -0. 0. 0. 0. 0. 0. 0. 0. -2. -2.
3 0 2 2 2 4 1 8 0 1 4 5 9 2 0 1 6-0 0 0 -0 -0 0 -0 0 0 0 0 0 -1 -1 -1 1
.6 .6 .7 .0 .1 .5 .0 .2 .0 .6 .2 .4 .9 .7 .8 .1

1800

0. 0. 0. 0. 0. -0. 0. -0. 0. -0. 0. 0. 0. 0. -0. -2. 3.
4 8 2 4 1 2 5 4 3 1 2 6 5 2 2 1 2- - - .2 0.3 0.1 0.2 0.5 0.1 0.3 0.3 0.1 0.3 0.1 0.2 0.3 0.2 0.4 9.6

1600

-0

0. -0. 0. -0. 0. -0. 0. -0. 0. -0. -0. -0. -0. 1.
1 1 5 2 0 3 0 7 5 2 5 8 1 0-0 0 -0 -0 0 -0 0 -0 0 0 1 2.8 .5 .7 .6 .4 .1 .0 .1 .7 .2 .1 .0

1400

0. 0. 0. 0. -0. -0. -0. -0. 0. -0. -1. -1. -2. -4.
3 7 0 2 3 1 1 7 2 4 3 2 7 0- - - .2 0.3 0.3 0.3 0.5 0.2 0.5 0.6 1.8 1.2 3.7 0.3

LSP mass [GeV]
1200

-0

200
0. 0. 0. 0. -0. 0. -1. -2. -0. -1.
0 6 2 1 8 2 0 1 3 0

1000-0 0 0 -0 -0 -0 0 -0 -1 -5.1 .9 .5 .6 .3 .2 .5 .4 .5 .1

400

1
1. 0.
1 7
-1 2 -2.4 .9 .0
0. -0. -0. -0. 1. 1. 1. -1.
0 5 5 4 8 9 6 3

600
2.

800

0.
3
-1 -3
.8 .1
-1 0 0.8 .5 .1
-0 -1 -0 -0 1 -0 -3 -5.5 .0 .6 .3 .6 .5 .0 .8

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
133

−4

−6

−8

−10

(a) Scale up

−4

−6

−8

−10

(b) Scale down

Figure 10.1: ISR/FSR variations on the signal acceptance for gluino signals as a function of the gluinomass and the chargino mass: Scale variations.

1200

1000

800

600

400

200

1400

1600

1800
800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. -0. 0. 0. -0. -0. -0. -0. -0. -0. 0. 0. 0. -0. -3. -0.
2 0 5 2 2 5 1 7 4 3 3 2 5 2 3 6 31800-0 0 -0 0 0 -0 0 -0 -0 -0 -0 0 0 0 0 -3 -2.1 .3 .1 .1 .1 .5 .4 .8 .1 .1 .0 .5 .6 .2 .0 .2 .7-0 0 0 0 -0 0 -0 0 0 0 0 0 0 1 3 0.3 .8 .4 .1 .5 .2 .4 .1 .3 .3 .4 .8 .7 .7 .3 .8

1600-0 0 0 -0 -0 0 0 -0 -0 0 -0 1 -1 -2 -2 -8.5 .7 .6 .3 .4 .5 .3 .2 .0 .1 .5 .0 .3 .3 .6 .2

0. 0. 0. -0. -0. -0. -0. 0. 0. -0. -0. -0. -1. 0.
4 4 4 1 1 1 2 2 6 4 4 3 6 3-0 -0 -0 -0 -0 -0 -0 -0 0 -0 2 4.2 .3 .3 .4 .8 .0 .9 .3 .4 .0 .9 .6

1400

0. 0. 0. -0. 0. 0. 0. -0. 0. 0. -0. -1. -0. -5.
1 5 3 2 2 3 5 3 1 1 4 8 8 7200
1. 0. 0. 0. -0. 1. 0. 0. 0. 4.
0 9 6 1 4 0 3 7 9 8

LSP mass [GeV]
1200-0 0 -0 -0 -0 -0 0 0 0 -0 2 -5
.1 .2 .4 .1 .7 .2 .1 .4 .1 .7 .7 .9400

6
2. 11.
2 0-1 2 3.2 .9 .0
-0 -0 -0 -0 0 1 2 4.4 .1 .0 .0 .7 .4 .8 .4

1000

0. 1. 0. 0. -0. -0. 0. -2. -2. -6.
2 4 4 6 6 9 3 3 4 0

600
8.

800

0.
2
-0 2
.8 .2
-0 1 6.6 .8 .5
-0 0 -0 -0 0 1 -2 -7.5 .4 .8 .1 .5 .9 .5 .7

LSP mass [GeV]134

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

−6

−8

−10

(a) Scale up

−4

−6

−8

−10

(b) Scale down

Figure 10.2: ISR/FSR variations on the signal acceptance for gluino signals as a function of the gluinomass and the chargino mass: Parton-jet merging scale variations.

600

800

200

1000

1200

1400

1600

- - - - - - - .3 0.2 0.6 0.1 0.3 0.1 0.4 0.1 0.3 0.3 0.1 0.3 1.5 1.8 2.4 9.4

1800
800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. -0. 0. 0. -0. 0. -0. -0. -0. -0. 0. 0. 0. 0. -0. 4.
3 1 5 4 2 7 3 5 1 2 2 3 5 9 3 6 5

1800

0. 0. 0. 0. 0. -0. -0. -0. -0. -0. -0. 0. -0. -0. -0. -3. -1.
0 5 0 5 4 6 1 5 2 1 2 3 6 5 8 3 2-0- - .3 0.2 0.7 0.0 0.1 0.2 0.0 0.1 0.4 0.2 0.2 0.2 0.8 0.3 1.8 3.6

1600

-0

- - - .2 0.2 0.2 0.3 0.4 0.5 0.2 0.1 0.1 0.8 0.1 0.3 3.0 5.6

-0

1400

0. 0. -0. -0. -0. -0. 0. -0. -0. -0. -1. -1. -3. -7.
1 1 1 2 1 3 0 3 6 8 7 3 8 1-0 -0 -0 0 0 -0 -0 -1 0 0 5 7.2 .1 .1 .4 .0 .2 .8 .4 .8 .6 .2 .2

1200-0 -0 -0 -0 -1 -0 -0 -0 -0 -2 -3.3 .8 .2 .5 .3 .5 .4 .0 .5 .9 .7

LSP mass [GeV]

0. 0. 0. 0. -0. 0. 0. 1. 4. 7.
4 6 3 1 6 5 3 9 0 7

1000

0. -0. 0. 0. -0. -1. -0. -2. -4.
0 3 1 4 3 0 8 1 1-2 -3 -9
.3 .8 .2
-0 -0 -0 -0 -0 -1 -4.3 .5 .7 .1 .2 .1 .5

400
.6
6. 3.
7 7
-0 5 4.8 .3 .9
-0 -0 0 0 0 1 1 5.6 .6 .5 .5 .2 .2 .4 .4

200

.4

400

-2

13

600

.6

800

-5

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
135

−4

−6

−8

−10

(a) Scale up

−4

−6

−8

−10

(b) Scale down

Figure 10.3: ISR/FSR variations on the signal acceptance for gluino signals as a function of the gluinomass and the chargino mass: Parton shower tuning variations.

1200

1000

800

600

400

200

1400

1600

1800
800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. -0. 0. 0. -1. 0. -1. -0. -0. -0. 0. 1. 0. 0. -4. 5.
5 1 7 5 3 0 3 2 4 4 6 6 2 9 5 2 21800

0. 1. 0. 0. 0. -0. 0. -1. -0. -0. -0. 0. 1. -0. -0. -5. -4.
4 0 3 7 4 8 7 0 4 1 3 9 0 5 8 1 4.7 1.0 1.1 0.1 0.5 0.6 0.4 0.2 0.4 0.7 0.5 1.0 2.2 2.5 4.2 3.8

-0

1600

-0 0 0 -0 -0 0 -0 -0 -0 0 -0 1 -2 -2 -3.6 .8 .9 .4 .8 .5 .6 .4 .3 .5 .5 .0 .0 .9 .6

0. 0. 0. 0. 0. -0. 0. -0. 0. -0. -0. -0. 3. 5.
5 5 6 4 4 6 3 7 8 9 6 9 4 7-0 0 -0 -0 -0 -0 -1 -1 1 0 6 8.8 .6 .8 .8 .9 .3 .2 .4 .2 .7 .0 .7

1400

0. 0. 0. -0. -0. -0. 0. -0. -0. -0. -2. -2. -4. -10
4 8 3 4 4 4 5 9 7 9 2 5 7 .0

LSP mass [GeV]
1200-0 -0 -0 -0 -1 -0 -0 -0 1 -3 5
.4 .9 .5 .6 .6 .5 .6 .7 .8 .2 .9200
1. 1. 0. 0. -1. 1. -1. 2. 4. 9.
1 3 7 2 0 2 1 9 1 1

1000

0. 1. 0. 0. -0. -1. 1. -3. -4.
3 7 6 9 7 3 0 1 9400.2
7. 11.
1 7-2 6 6.0 .7 .1
-0 -0 -0 -0 2 2 3 7.7 .8 .7 .6 .0 .6 .5 .1

16

600

.6
-3
.1
-3 -4
.0 .3
-0 -1 -1 -0 1 2 -5
.8 .2 .2 .4 .7 .2 .9

800

-5

LSP mass [GeV]136

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

−6

−8

−10

(a) Scale up combined

−4

−6

−8

−10

(b) Scale down combined

Figure 10.4: Combined ISR/FSR variations on the signal acceptance for gluino signals as a functionof the gluino mass and the chargino mass.

800

600

400

200

1600

1400

1200

1000

1800

0. 0. -0. 0. 0. -0. 0. -0. -0. 0. 0. 0. -0. 0. 0. -0.
4 7 3 6 0 2 2 2 2 0 0 0 3 0 0 4

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

−6

−8

−10

(b) Eta-intercalibration non-closure down

Figure 10.5: JES/JER variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 1. 0. -0. 0. 0.
0 0 0 0 0 0 2 0 5 0 4 5 0 4 0 0

0. 0. -0. -0. -0. 0. 0. 0. 0. 0. -0. -0. -1. 0. 0. 0. 0.
0 2 1 2 1 0 0 0 0 0 2 0 4 3 0 5 6-0 -0 0 0 0 0 0 0 1 0 0 0 -0 0 0 -0
.2 .3 .0 .6 .0 .0 .0 .0 .2 .0 .0 .3 .3 .2 .6 .2

1800

1. 0. -0. 0. -0. 0. 0. 0. -0. 0. 0. 0. -0. 0. 0. -0. 0.
1 0 4 0 1 0 0 0 2 0 0 0 1 0 0 2 0200
0. 3. 0. 0. -0. 0. 0. 0. 0. -0. -0. -0. -0. -0.
2 0 3 0 6 0 0 7 3 7 2 0 5 1

1600

0. 0. 0. -0. -0. 0. -0. 0. 0. 0. -0. 0. -0. 0. -0. -2.
0 0 2 5 5 0 2 0 0 0 0 0 9 2 3 1400

0. 0. -0. 0. 0. -0. -0. 0. 0. 0. -0. 0.
5 0 2 0 2 0 5 0 0 0 1 0

1400

0. 0. 0. 0. 0. 0. 0. -0. 0. -0. -0. 0. -0. -0.
0 0 7 0 9 0 0 5 0 0 0 1 4 7

600-0 0 0 0 0 0 -0 -0 -0 1
.4 .8 .0 .0 .8 .0 .4 .4 .0 .5

LSP mass [GeV]
1200

0. -0. 0. 0. 0. -0. 0. 0. 0. -0. 0. -0.
5 6 0 0 2 1 5 0 0 8 1 2

800

0.
6
0. 0.
4 5
-0
0.
.4
5
-0 0 0 -0 0 0 0 1
.
.
.
.
.
.6 0 7 .2 3 3 2 .2

1000

-1 -0 0 -0 0 -0 0 0 -0 -1.0 .4 .0 .5 .0 .4 .0 .0 .6 .3

-0
.2
-0 0
.4 .0
0. -0. -1.
2 6 3-2 0 -0 0 -0 0 -0 -1.
.1 .2 4 .0 .5 .1 .3 .0

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
137

−4

−6

−8

−10

(a) Eta-intercalibration non-closure up

1000

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600

400

200

1200

1400

1600

1800

0. 0. -0. 0. 0. -0. 0. -0. 0. -0. 1. -0. 0. -0. 1. -0.
0 7 3 6 5 2 1 2 1 5 2 0 1 1 0 7

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

−6

−8

−10

(b) Jet Energy Scale (Grouped nuisance parameter 1) down

Figure 10.6: JES/JER variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]0. -0. -0. -0. 0. -0. -0. 0. 0. 0. -0. 1. 0. 0. -0. -2.
0 2 2 3 0 5 4 2 0 2 7 7 8 0 9 2-0 1 -0 0 -0 0 0 -0 -1 -0 0 -0 -1 -0 -2 -0 -4.2 .4 .3 .0 .7 .0 .0 .6 .0 .5 .2 .5 .3 .1 .5 .4 .3

1800

0. 0. -0. 0. 0. -0. 0. 0. -0. 0. -0. 0. -0. 1. -0. 1. 4.
3 0 1 3 1 0 1 6 9 9 5 6 1 9 4 6 4

0. 1. 0. 0. -0. 0. -1. 0. 0. 0. 0. 0. -1. -2. -1. -8.
0 8 2 2 4 6 0 1 6 3 3 3 4 1 9 3

1600-0 1 0 0 0 0 -0 0 0 0 0 1 0 2 2 6.2 .8 .1 .3 .3 .4 .2 .2 .4 .2 .2 .4 .8 .5 .9 .0-0 -0 0 0 -1 -0 0 1 -0 -0 -0 -0 -1 -2.8 .4 .1 .2 .4 .4 .3 .3 .6 .0 .8 .7 .5 .4

1400

1. -0. 1. -0. -1. 0. -0. -0. 0. 0. 1. 0. 1. 4.
2 3 0 7 0 2 6 1 5 3 6 1 4 8

0. 0. -0. 0. -1. -0. 2. -0. -0. -1. -3. -2.
3 0 6 5 6 2 0 5 0 1 0 2

1200-1 -0 -0 -0 -0 0 0 0 0 1 5 4.4 .1 .2 .3 .0 .6 .9 .5 .0 .7 .5 .9

LSP mass [GeV]-0 -0 0 -0 0 0 -2 -4 -4 -4.4 .0 .4 .5 .0 .2 .7 .2 .3 .0

1000

1. 0. 1. -1. 0. -0. 0. 1. 1. 2.
0 9 2 6 7 5 2 1 6 5

200
.6
-0 -8
.4 .3
0. -1. -9.
2 4 7-0 0 -1 -0 -2 -0 -2 -5.
.3 2 .4 .8 .1 .8 .3 .2

400

2. 2.
3 6
1. 1. 2.
7 2 6
-1 0 0 -0 -0 1 2 0.0 .8 .9 .6 .0 .1 .8 .7

-2

600

1

800

2.

LSP mass [GeV]138

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

−6

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−10

(a) Jet Energy Scale (Grouped nuisance parameter 1) up

800

600

400

200

1600

1400

1200

1000

1800

0. 0. 0. 0. 0. 0. -0. -0. 0. 0. 0. 1. 0. -0. 0. -0.
0 0 0 0 0 0 5 2 0 0 0 5 0 4 3 3800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

−6

−8

−10

(b) Jet Energy Scale (Grouped nuisance parameter 2) down

Figure 10.7: JES/JER variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. 0. 0. 0. 0. 0. -0. 0. 0. -0. 0. -0. 0. 0. -0.
0 0 0 0 3 0 0 2 5 0 4 0 3 0 4 4

0. 0. -0. 0. -0. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0. -0.
0 3 3 0 1 0 0 0 0 0 0 5 0 0 0 0 8

0. 0. 0. 0. 0. 0. -0. 0. 1. 0. 0. 0. -0. -0. -0. -3.
0 0 0 4 0 0 3 3 2 0 0 0 3 2 6 9

1800

0. 0. -0. 0. -0. 0. 0. 0. 0. 0. -0. 0. -0. 0. 0. 0. 1.
6 0 1 4 0 0 0 0 3 0 2 2 8 3 0 3 5200
0. -0. 0. 0. -0. 0. 0. 0. 0. -0. -0. -0. 0. 0.
0 1 0 0 9 0 0 3 0 7 1 2 0 6

1600

0. -0. 0. 0. 0. 0. -0. 0. 0. 0. -0. 0. -0. 0. 0. 0.
0 3 1 2 3 0 2 2 0 0 0 6 3 2 0 0400

0. -0. 0. 0. -1. -0. 0. 0. 0. -0. -1. -0.
5 3 0 0 2 3 0 0 0 6 2 6

1400

0. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0. 0. 0.
0 0 0 0 9 2 0 1 2 3 3 1 0 0

600-0 -0 0 -2 0 0 0 -1 -1 0
.3 .7 .0 .1 .0 .0 .0 .8 .6 .9

LSP mass [GeV]
1200

0. 0. -0. 0. 0. 0. -0. 0. 0. -0. 0. 1.
0 0 2 0 2 2 0 3 4 2 3 3

800

0.
0
-0 -0
.3 .5
0. -0. -1.
0 3 0
0. 0. 0. 0. 0. 0. -0. -1.
0 4 2 2 2 3 3 21000

0. 0. 0. 0. 0. -0. 0. 0. 0. 0.
0 5 0 0 4 4 2 0 5 5

-0
.2
-0 -0
.3 .7
-0 0 0.5 .4 .9
-0 0 0 0 0 0 0 0.3 .0 .0 .0 .3 .0 .1 .5

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
139

−4

−6

−8

−10

(a) Jet Energy Scale (Grouped nuisance parameter 2) up

800

600

400

200

1400

1200

1000

1600

1800

0. -0. 0. 0. 0. 0. -0. -0. 0. -0. 0. 1. 0. -0. 1. -0.
0 4 0 0 3 0 5 2 0 2 0 5 1 4 0 3

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

−6

−8

−10

(b) Jet Energy Scale (Grouped nuisance parameter 3) down

Figure 10.8: JES/JER variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]- - .4 0.3 0.3 0.6 0.2 0.2 0.2 0.2 0.2 0.0 0.4 0.0 0.0 0.0 0.4 0.8-00. 0. -0. 0. -0. -0. 0. 0. -0. 0. 0. -0. -0. 0. 0. 0. -0.
6 2 3 0 2 2 0 0 2 0 0 2 5 0 0 0 3

0. 0. 0. 0. -0. 0. 0. 0. 0. 0. 0. 0. -0. -0. 0. -1.
0 0 2 4 2 0 0 3 2 3 0 0 8 2 3 6

0. -0. 0. 0. 0. -0. 0. 0. -0. -1. -0. -0. -0. -0.
0 1 4 0 0 2 0 9 0 0 4 1 9 9

1800

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 0. -0. -0. 0. -0. 1.
0 5 0 1 2 0 0 0 0 4 2 0 4 0 0 2 8200
0. -0. 0. 0. -1. 0. -0. 0. 0. -0. -0. -0.
2 3 0 0 2 3 4 0 4 8 6 1

1600

0. 1. 0. 0. 0. -0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0 2 0 0 0 4 0 2 0 3 3 5 0 3 0 0400- - - .8 0.3 0.0 0.5 0.0 0.2 1.3 0.3 1.1 0.9

1400

0. 3. 0. -0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0.
6 0 3 4 1 5 0 0 6 3 5 0 0 0

600

-0

LSP mass [GeV]
1200-1 -0 0 0 0 -0 0 0 -0 -0 1 1.4 .3 .0 .0 .0 .2 .7 .0 .4 .2 .5 .5

800

0.
6
-0 -1
.2 .3
0. -0. -0.
1 2 6
0. 0. 0. 1. 0. 0. -0. -0.
0 4 2 3 5 1 1 3

1000

0. -0. 0. -0. 0. -0. -0. -0. -0. -0.
1 4 2 5 0 3 2 4 1 1

-0
.2
0. 0.
3 5
-0 -0 0.5 .1 .5
-2 -0 -0 -1 0 0 -0 0
.5 .4 .1 .4 .0 .0 .1 .0

LSP mass [GeV]140

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

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(a) Jet Energy Scale (Grouped nuisance parameter 3) up

400
200

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

10
8
6
4
2
0
−2

Relative uncertainty [%]0. 4. 0. 0. -0. -0. -0. -0. 0. -1. -0. -0. -0. 0. -1. 0.
1 9 1 2 1 7 5 8 0 1 1 6 1 0 2 0

600

141

0. -0. -0. 0. -0. 0. -0. -0. -0. -0. 0. -0. 0. 0. 0. 0. 0.
8 2 5 8 4 0 9 3 2 5 3 0 6 2 8 3 5

800

4.
7
-1 -8
.7 .0
2. -0. 1.
1 4 0-0 -1 -0 0 1 0 -0 0.
.
.
.9 .0 4 2 6 .2 .7 .4

1000

-1

1200

-0 -1 1 -0 -3 0 -0 2 -0 -0 1 -2
.7 .4 .8 .5 .1 .3 .5 .1 .0 .1 .8 .5

1400- .0 0.3 1.1 0.4 0.0 0.2 1.0 0.4 0.3 0.3 0.2 2.7 3.1 9.3

1600

0. 1. -1. 0. -0. 1. -0. 1. 2. 0. 0. 0. 0. 0. 0. 2.
3 6 1 5 1 4 8 4 9 5 2 9 8 8 9 4

1800

1. 0. 1. -0. 0. 0. -1. -2. 0. 1.
3 3 5 5 4 5 7 5 7 3

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION

−4
−6
−8
−10

(a) Jer Energy Resolution up

Figure 10.9: JES/JER variations on the signal acceptance.
JER. Relative uncertainties as a function of the gluino mass and the chargino mass are shown in
Figure 10.11, 10.12. The resulting uncertainty is assigned by combining them in quadrature (Figure 10.13).
The tracking reconstruction eﬃciency of pixel tracklet is strongly aﬀected by pileup. The uncertainty originating from the pile-up modeling (Sec.4.2) in the simulation is evaluated by weighting
simulated samples using re-scaled average number of interactions from the nominal re-scaling(1/1.16)
to 1.00 and 1.23. The pileup modeling uncertainty is expected to be independent of the gluino and thechargino mass as shown in Fig. 10.14. The average value of 4.5 % is assigned for the uncertainty.
Since the trigger eﬃciency is estimated from data as discussed in Sec.7.2, the uncertainty comesfrom the statistical uncertainty of the trigger eﬃciency curve. This uncertainty is estimated by changing trigger eﬃciency with 1 sigma of the statistical uncertainty and comparing signal acceptance after
SR selection (Sec.7.1) except for the disappearing track requirement.
The modeling of the inner detector material alters the track reconstruction eﬃciency and aﬀects
the signal selection eﬃciency because MC cannot simulate it perfectly. The material eﬀect on reconstruction eﬃciency is estimated by comparing re-tracking eﬃciency with only pixel-detector (thesame procedure as the pT smearing function in Sec. 6.3) in muon data and in MC simulated events.
Signal selection eﬃciency uncertainty is estimated by using Z → µµ as discussed in Sec. 6.2 andcomparing tracking quality cut eﬃciency between data and MC simulated events.
The d0 bias is found in 2016 data. The uncertainty of d0 bias reduces signal acceptance because of
requiring tight d0 significance as the nominal selection value. This bias of pixel tracklet is measured
by tag and probe method in Z → µµ. Then the acceptance change with biased d0 selection of 0.7 %

1200

1000

800

600

400

200

1400

1600

1800

-0 -5 -0 -0 -0 -0 -0 -0 -0 -1 -1 -2 -0 -0 -1 -1.4 .0 .4 .9 .6 .8 .9 .9 .2 .2 .2 .2 .4 .5 .8 .0

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]-0 -4 -0 -0 -0 -0 -0 -0 -0 -1 -1 -2 -0 -0 -1 -2.4 .9 .3 .7 .4 .9 .7 .9 .7 .2 .0 .3 .9 .4 .6 .3-1 -1 -0 -0 -0 -0 -0 -0 -1 -0 -0 -0 -2 -0 -2 -0 -4.0 .4 .8 .8 .8 .2 .9 .6 .1 .7 .4 .8 .1 .3 .6 .7 .5

1800-1 -0 -0 -1 -0 -0 -0 -0 -1 -1 -0 -0 -1 -1 -0 -1 -5.5 .5 .7 .0 .5 .0 .9 .7 .0 .1 .7 .6 .1 .9 .9 .6 .0-0 -2 -1 -0 -0 -1 -1 -1 -3 -0 -0 -1 -1 -2 -2 -9.4 .4 .2 .9 .5 .5 .3 .4 .4 .7 .3 .0 .8 .3 .3 .6-1 -3 -1 -0 -1 -0 -1 -1 -0 -1 -0 -2 -3 -9.4 .0 .2 .5 .7 .5 .1 .8 .8 .4 .9 .8 .6 .6-1 -1 -1 -0 -4 -0 -2 -2 -0 -1 -3 -3.1 .5 .9 .8 .0 .5 .1 .2 .4 .5 .7 .4

1600-0 -2 -1 -0 -0 -1 -0 -1 -2 -0 -0 -1 -1 -2 -3 -6.4 .7 .2 .8 .7 .5 .9 .4 .9 .7 .4 .9 .5 .7 .1 .8

200-1 -1 -1 -2 -0 -0 -3 -5 -4 -4.6 .1 .5 .3 .9 .6 .5 .3 .8 .7

1400-1 -3 -1 -0 -1 -0 -1 -0 -0 -0 -1 -2 -3.7 .0 .7 .9 .7 .6 .2 .7 .8 .6 .7 .7 .4400.9-2 -1 -9
.2 .5 .8
-1 -1 -1 -1 -2 -0 -2 -5.1 .2 .7 .6 .7 .9 .4 .5

800

-1

LSP mass [GeV]
1200-2 -1 -1 -0 -3 -0 -1 -2 -0 -1 -6 -5.1 .6 .8 .6 .2 .7 .4 .2 .6 .9 .0 .8

600
.4

-5

1000

-1 -1 -1 -1 -0 -1 -1 -2 -1 -3.9 .2 .9 .8 .9 .0 .8 .8 .8 .1

-5
.1
-2 -8
.9 .5
-2 -1 -3
.8 .5 .3
-3 -1 -1 -1 -1 -1 -2 -1.5 .4 .1 .6 .7 .1 .9 .4

LSP mass [GeV]142

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

−6

−8

−10

(a) Combined systematics (up)

−4

−6

−8

−10

(b) Combined systematics (down)

Figure 10.10: Combined JES/JER variations on the signal acceptance.

1000

800

600

400

200

1200

1400

1600

1800

0. 0. -0. 1. 0. -0. 0. -0. 0. 0. -0. 0. 0. 0. 0. 0.
4 4 3 2 3 7 8 4 2 0 5 9 3 3 4 3800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

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(b) Soft Track Parpendicular Resolution

Figure 10.11: TST variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. 0. 0. -0. 0. 0. 0. 0. 0. -0. 0. 0. -0. 0. -2.
4 0 0 6 2 0 0 0 0 0 4 2 0 3 0 9

0. 0. -0. 0. 0. 0. 0. -0. -0. 0. 0. 0. 0. 0. 0. 0. 0.
0 0 7 0 1 0 6 2 2 2 0 0 3 3 3 0 4

1800

1. 0. -0. -0. 0. -0. 0. 0. 0. 0. 0. -0. -0. -0. 1. 0. -0.
1 0 7 3 1 3 3 0 5 2 0 1 5 4 1 3 1

0. 0. -0. 0. 0. -0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0 0 1 0 3 2 0 4 0 0 5 2 0 2 6 7

1600-0 0 -0 0 0 0 0 0 -0 0 0 0 0 -0 1 -1
.0 .0 .7 .6 .3 .0 .3 .2 .0 .0 .8 .6 .8 .2 .7 .4

0. 0. 0. 0. -0. 0. 0. 0. 0. -0. -0. 1. 0. -0.
2 0 3 0 9 5 0 4 3 3 3 1 5 7

1400

0. 0. 0. -0. -0. 0. 0. 0. 0. -0. 0. 0. 0. 2.
0 4 2 0 6 2 0 4 8 4 1 4 0 7

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. -0.
0 3 0 0 2 3 2 0 1 0 0 6

1200

0. -0. -0. 0. -1. -0. -1. 0. 0. -0. 0. 0.
5 4 2 5 2 1 1 0 4 0 5 0

LSP mass [GeV]- .6 0.0 0.0 1.6 0.0 0.1 1.2 0.3 1.0 0.5

-0

1000

-0 0 -0 0 -0 -0 -2 0 -0 0
.8 .7 .2 .0 .7 .3 .2 .0 .2 .5

200

0. 0.
4 0
0. -0. -0.
4 1 3-0 0 -1 0 0 0 -0 0
.6 .6 .0 .6 .5 .1 .5 .8

400

1.
0
0. 0.
2 0
0. 0. 0.
0 1 8
0. 0. 0. 0. 1. 0. -0. 0.
0 4 1 4 1 7 3 3

600

8

800

2.

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
143

−4

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(a) Soft Track Pararell Resolution

800

600

400

200

1600

1400

1200

1000

1800

-0 0 0 0 0 0 0 0 -0 0 -0 0 -0 -0 0 -0
.4 .7 .0 .0 .0 .0 .0 .0 .2 .0 .7 .0 .3 .3 .0 .4

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

−4

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(b) Soft Track Scale down

Figure 10.12: TST variations on the signal acceptance.

Relative uncertainty [%]10

Relative uncertainty [%]0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 0. 0.
0 0 0 6 0 0 0 0 0 0 0 0 0 4 0 3

0. 0. -0. 0. 0. 0. 0. 0. -0. 0. 0. 0. -0. 0. 0. 0. 0.
6 0 6 0 0 0 0 0 2 0 0 0 2 0 3 0 30. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0.
0 0 0 0 3 0 3 2 0 0 3 2 3 0 7 7

1800

0. 0. 0. 0. -0. 0. 0. 0. 0. 0. -0. -0. 0. 0. 0. -0. -1.
2 0 0 0 1 0 0 0 3 0 2 3 0 0 0 3 0200
0. 0. 0. 0. -0. 0. 0. 0. 0. 0. 0. 0. 0. 1.
0 0 3 0 6 2 0 4 8 3 1 9 0 4

1600

0. 0. 0. 0. -0. -0. -0. 0. 0. 0. 0. 0. 0. 0. -0. -0.
0 0 1 2 3 2 3 0 0 0 0 0 6 0 3 7400

0. 0. 0. 0. -1. 0. -0. 0. 0. -0. 0. 0.
0 2 0 0 2 0 3 0 4 2 7 0

1400

0. 3. 1. 0. 0. 0. 0. 0. 0. 0. -0. -0. 0. -1.
0 0 0 0 0 3 0 0 0 0 2 3 0 4600-0 0 0 0 -0 0 0 0 0 0.7 .4 .0 .0 .4 .5 .0 .3 .5 .0

LSP mass [GeV]
1200

0. -0. 0. 0. 0. -0. 0. 0. -0. -0. -1. -1.
0 2 0 0 0 1 0 0 4 4 1 1

800

0. 0.
4 0
0. 0. 0.
2 6 3
-0 0 -0 0 0 0 -0.
.
.
.3 6 .1 6 6 .4 .0

1000-0 -0 -0 -2 0 -0 0 -1 -1 -0.3 .7 .4 .1 .4 .7 .0 .6 .3 .7

-0
.1
-0 0
.2 .0
0. -0. -1.
0 1 0
0. 0. 0. 0. 0. -0. -0. -1.
0 0 5 0 8 1 6 0

LSP mass [GeV]144

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−4

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−10

(a) Soft Track Scale up

1400

1200

1000

800

600

400

200
-0 -1 -0 -0 -0 -3.9 .0 .4 .5 .4 .0

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

0. 1. 0. 0. 0. 3.
6 0 3 6 4 0

0. 0. 0. 1. 0. 0.
1 6 5 2 3 6

1. 0. 0. 0. 2. 1.
0 7 8 3 0 7

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]1. 0. 0. 0. 0. 0. 0. 0.
2 3 2 3 6 2 6 3

1.
2

0. 0. 0. 1. 0. 0. 0. 0. 0.
5 4 3 5 4 7 8 4 2

0. 0. 0. 0. 0. 0. 0.
7 6 4 2 4 5 0

0. 1. 0. 0. 1. 0. 3.
7 2 5 4 4 5 1

1600

0.
0

0. 0. 0. 0. 1. 0.
2 4 4 0 2 6

1800-0 -0 -0 -1 -0 -0 -0 -0 -0.6 .7 .3 .3 .4 .7 .8 .4 .3-1 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -1 -0 -1.0 .3 .2 .3 .6 .2 .7 .3 .2 .3 .6 .5 .1 .4 .1-1.1-0 -0 -1 -0 -1 -1.9 .7 .0 .3 .9 .7

1600-0 -0 -0 -0 -0 -0 -0.7 .7 .4 .3 .4 .5 .0

1800

-0
.0

200

-0 -0 -0 -0 -1 -0 -3.6 .8 .5 .4 .2 .5 .1

400

0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 0.
5 5 2 5 7 3 1 0 6 2 3 6

1400-0 -3 -1 -0 -1 -0.2 .0 .0 .0 .0 .6

600

1. 0. 0. 1. 0. 0. 2. 0. 1. 0.
2 8 2 6 8 6 5 4 1 8

LSP mass [GeV]
1200-0 -0 -0 -0 -1 -0 -1 -0 -0 -0 -1 -1.5 .5 .2 .5 .2 .3 .1 .0 .6 .4 .6 .2

800

2.
9
0.
6
0. 0. 0.
5 6 9
0. 1. 1. 1. 1. 0. 0. 0.
7 0 0 0 4 8 6 81000-1 -0 -0 -2 -0 -0 -2 -1 -1 -1.0 .9 .5 .6 .8 .8 .5 .6 .7 .0

-2
.9
-0
.5
-0 -0 -1
.4 .2 .3
-0 -0 -1 -0 -1 -0 -0 -1.
.6 7 .1 .8 .5 .7 .8 .3

LSP mass [GeV]

10.1. UNCERTAINTIES IN SIGNAL NORMALIZATION
145

−4

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(a) TST scale up

−4

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(b) TST scale down

Figure 10.13: Combined TST variations on the signal acceptance.

1400

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1000

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600

400

200

1600

1800

-5 1 4 -5 -7 -1 -0 -3 -2 -7 -5 0 -0 -4 -3 2
.8 .3 .0 .1 .4 .6 .0 .1 .1 .0 .9 .4 .8 .8 .1 .4

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

800 1000 1200 1400 1600 1800 2000 2200~
g mass [GeV]

8

6

4

2

0

−2

10

8

6

4

2

0

−2

Relative uncertainty [%]10

Relative uncertainty [%]6. -3. -5. 4. 8. -1. 2. 3. 3. 8. 7. 1. 2. 3. 4. -9.
4 3 1 1 4 5 9 3 2 6 7 1 0 4 2 8

6. 2. 3. 4. 5. 3. 5. -2. 1. 4. 0. 7. -7. 0. 5. 3. -1.
8 2 0 8 4 8 1 1 4 6 1 8 3 8 8 6 5

1800-2 -4 -2 -2 -3 -3 -4 -0 -0 -2 -2 -6 2 -4 -2 -4 -3.3 .5 .8 .5 .0 .6 .1 .0 .3 .7 .3 .1 .0 .5 .8 .5 .2.0 3.2 2.2 7.4 3.3 6.4 4.1 2.9 0.3 4.4 0.1 0.8 0.8 4.2 7.4 2.9-7

2. 1. -1. 2. 10 1. 5. -1. 6. 3. 2. -1. 11. 7.
8 6 0 4 .1 3 3 0 1 6 6 4 4 2

1600

0. -3. 0. -6. -3. -3. -0. -4. 1. -2. 0. 0. -1. -4. -5. -0.
4 2 3 7 3 9 9 7 7 8 2 5 5 2 7 5200
7. 7. 0. 6. 5. 7. 7. 7. 7. 0. 0. 5.
6 2 3 8 7 1 5 9 8 5 9 3

1400-0 -2 -1 -4 -5 -3 -3 -0 -7 -1 -4 1 -7 -3.0 .0 .7 .6 .9 .0 .9 .8 .0 .3 .2 .4 .7 .7

LSP mass [GeV]
1200-4 -5 0 -4 -5 -5 -3 -4 -4 -2 -1 -6.2 .0 .9 .4 .9 .5 .5 .0 .8 .0 .6 .8

400-0 -1 0 4 2 8 4 4 2 6.8 .3 .7 .2 .7 .7 .9 .4 .4 .5

1000-1 5 0 -6 -1 -7 -1 -4 -3 -6.4 .0 .2 .8 .5 .2 .3 .4 .9 .8

600

3.
6
9. 6.
6 5
6. 3. 2.
2 6 0
7. 2. 5. 9. 3. -0. 4. 5.
3 6 8 0 8 5 8 2

800

-7 -2
.2 .6
-6 -3
.3 .4
-3 -2 -3 -7 -4 -1 -4 -2.0 .9 .6 .9 .3 .5 .1 .7

LSP mass [GeV]146

CHAPTER 10. SYSTEMATIC UNCERTAINTIES

−4

−6

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(a) Pileup scaling up

−4

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(b) Pileup scaling down

Figure 10.14: Pileup modeling variations on the signal acceptance as a function of the gluino massand the chargino mass.

10.2. UNCERTAINTY IN THE BACKGROUND EVENTS

147

is added to the uncertainty.
The uncertainty of the integrated luminosity is ±3.2%.
The uncertainty of the estimated signal pixel tracklet pT resolution function parameter discussed
in Sec.6.4 is included as a nuisance parameter in the likelihood Eq. 9.2. This changes expected signal
pT shape, but not the normalization.

10.2 Uncertainty in the background events
The following sources of systematic uncertainties on the background normalization are considered:• Lepton background normalization• Fake background pT shape• Fake background normalization assumption reliability (Eq. 9.1)
• Smearing function parameters
Because the impact of most of the above items depends on background-event yields which are
estimated in the fitting, their contribution will be shown later in Sec. 11.1, Table 11.2.
The normalization of the hadron background component and fake track background component
are free parameters in the fit while those of the electron and muon background tracks are estimatedwith finite uncertainties. The uncertainty is evaluated from two components. One evaluation is fromthe statistical uncertainty of transfer factors (Sec. 8.2.3,8.2.4) and number of events in the control
region (Sec. 8.2.2). The estimated relative uncertainty is 17% for electron and 482% for muon.
The relative uncertainty for muon is very large, but it does not crucially aﬀect to the fitting because
the estimated number of muon background is almost negligible, far less than 1 event. The otherevaluation is to use transfer factor derived by changing reconstructed mass requirement around the Z
peak to be twice broader from the nominal selection in the tag and probe method in Sec. 8.2.3,8.2.4.
Such transfer factor is expected to have a contribution twice as large from the background eventsand thus the deviation from the result with the nominal transfer factor is assigned to be systematic
uncertainty. Estimated relative uncertainty is 4% for electron and 8% for muon. The quadratic sum of
the two uncertainties by evaluations above is used as the systematic uncertainty of the normalizationof estimated leptonic backgrounds. Finally, the expected number of electron background is 12.1 ± 2.1
and that of muon is 0.06 ± 0.27.
The Eq. 8.8 is used for the pT distribution of fake background. The fitting uncertainty of theparameter is included in the likelihood fitting.
The uncertainty of the assumption of Eq. 9.1 is conservatively set to be 100%. It is included in
the likelihood function (Eq. 9.2) as a constraint on rABCD . Details of the statistical analysis procedureare given in the Chap. 9.
The uncertainty in the smearing parameters is included in the fitting parameter with the constraint
discussed in Sec.6.4. Therefore, the fitting uncertainty is automatically taken in the sensitivity calculation.

Chapter 11
Result and the interpretation
11.1 Fitting result
Unbinned likelihood fit discussed in Chap. 9 is performed with background only hypothesis; µs = 0.
The result is shown in Fig. 11.1 for both the SR (Sec. 7.1) and the Low-ETmiss Control Region LCR
Chap. 9Table 11.1 summarises the observed number of events, the number of background events ofvarious sources obtained by the fitting, null probability p0 , model-independent visible cross-section
limit, and the expected number of signals in the SR above pT > 100 GeV for a benchmark point.
Null probability p0 means the probability that the data becomes more signal-like due to statisticalfluctuation of the background. It is derived by counting the number of data in pT > 100 GeV. As
p0 = 0.4 which means that probability to be more signal-like distribution is 40%, it is consistent
with the background only hypothesis. Hadron background is the most dominant and the electron
background is the next largest sources of background. The number of muon and fake background
events are fitted to be very small. Model-independent visible cross-section upper limit is calculated
from the Poisson distribution taking into account the uncertainty in the background yields in pT > 100
GeV region. It is the cross-section limit of any new particles which is selected by this analysis. Table
11.2 summarises the systematic uncertainty contributions for each source. Systematic uncertainty
related to fake is negligible because the fitting result shows that the number of fake background
events is negligibly small. It should be noted that signal uncertainties are larger than backgrounduncertainties among the fitting uncertainties.

11.2 Exclusion limits
Fitting result is consistent with the background only hypothesis and no evidence of beyond the Standard Model is observed. Therefore, the exclusion limit is set. For the exclusion limit calculation,µ s = 0 constraint is removed. The exclusion limit is set by examining whether the fit including expected signal is consistent with the data with 95 % confidence level. Here, the exclusion limit is set
in the region of the gluino mass vs the chargino mass grid with fixed lifetime, τχ˜1 ± = 0.2 ns or 1.0 ns.
Lifetime of 0.2 ns is the preferable lifetime of the wino-LSP model from the theoretical prediction as
discussed in Sec. 2.4.4. Lifetime of 1.0 ns is the most sensitive lifetime in this analysis, which uses
149

CHAPTER 11. RESULT AND THE INTERPRETATION

1054
Fake tracklet-1
Muon
103 s=13TeV, 36.1 fb
Electronproduction
102 Strong missHadronTotal Background
10 High E T region
Signal101
10−−21
10−3
10−4
10−5
10−6
10−7 (m~g, mχ∼ , τ ∼ ) = (1600 GeV, 500 GeV, 0.20 ns)
χ
10
Data

Data / Fit

Tracklets

150

±

±

1

1

2
1.5
1
0.5
0

100

1000

10000

Data
105
Fake tracklet
104 s=13TeV, 36.1 fb-1
Muon
3
Electron
10 Strong production
Hadron2
missTotal Background
10 Low E T region
Signal
10
1
10−1
10−2
10−3
10−4
10−−5610 (mg~, mχ∼ , τχ∼ ) = (1600 GeV, 500 GeV, 0.20 ns)
10−7

Data / Fit

Tracklets

Tracklet p [GeV]T(a) Signal Region (SR)

2
1.5
1
0.5
0

±

±

1

1

100

1000

10000

Tracklet p [GeV]Tmiss(b) Low-ET control region (LCR)

Figure 11.1: Fitting result of the SR (Sec. 7.1) and the LCR (Chap. 9). The black points are data, theblue line is the fitting result of fake background distribution, the green line is the muon background
distribution, the yellow line is the electron background distribution, the light blue line is the hadronbackground distribution, the gray line is the total background, and the red line is the expected signal
distribution for mg̃ =1600 GeV, mχ˜1 ± =500 GeV, τχ˜1 ± = 0.2 ns normalised by the cross-section and theintegrated luminosity. The shaded region is the uncertainty of the fitting. The lower plots show theratio between data and the fitting result of the total background. The red arrow shows that the data
point is out of range.

11.3. FUTURE PROSPECTS

151

Number of observed events with pT > 100 GeV in SR
2
Number of expected events with pT > 100 GeV in SR
Hadron background1.15± 0.32
Muon background0.03± 0.07
Electron background0.56± 0.10Fake background0.000,02 ± 0.005,20
Total background
1.7
± 0.3
p0 (null probability)
0.4
95%
Observed σvis [fb]
0.12
+0.07
Expected σ95%
[fb]
0.11
−0.04
vis
Number of expected signal events with pT > 100 GeV in SR
5.6
± 0.8
Table 11.1: Fitting result and the observed number of events in the SR above pT > 100 GeV. The
number of expected signal events for mg̃ = 1600 GeV, mχ˜1 ± = 500 GeV, τχ˜1 ± = 0.2 ns and the model
independent visible cross-section limit are also given.
the pixel tracklets.
As shown in Fig. 11.2(a), for chargino lifetime 0.2 ns, the gluino mass of less than 1650 GeV is
excluded if the chargino mass is less than 460 GeV, which is the lower limit of the chargino mass
obtained by the electroweak direct production search [20]. The gluino mass less than 1150 GeV is
excluded for the region with the mass diﬀerence between chargino and gluino larger than 100 GeV.
As shown in Fig. 11.2(b), for chargino lifetime 1.0 ns, the gluino mass less than 1750 GeV is excluded
if the chargino mass is less than 580 GeV, which is the upper limit of the chargino mass obtained by
the electroweak direct production search. The gluino mass less than 1300 GeV is excluded for theregion with the mass diﬀerence between chargino and gluino larger than 100 GeV. The strange shapeat around the gluino mass 1300 GeV and chargino mass 1200 GeV is due to discrete signal points of
the MC.
Fig. 11.3 is the same exclusion limit as Fig. 11.2 but the prediction of mass relation by the
AMSB and the PGM as shown in Fig.2.4 is overlaid. The region between the AMSB line and thembino = mwino line is the allowed for the PGM model. As shown in Fig. 11.3(a), for chargino lifetime
0.2 ns, the gluino mass of less than 1500 GeV is excluded for all the possible PGM parameter phase.
As shown in Fig. 11.3(b), for chargino lifetime 1.0 ns, the gluino mass of less than 1600 GeV is
excluded for all the possible PGM parameter phase.

11.3 Future prospects
The LHC will provide 3 times more data than the data used in this thesis at the end of Run 2 andprovide 30 times more data at the end of High-Luminosity LHC (HL-LHC). Because the production
cross-section of the gluino decreases roughly exponentially with the gluino mass, high integrated
luminosity provides more signal events of high mass gluino. The increase of data also improves

CHAPTER 11. RESULT AND THE INTERPRETATION152

1mχ∼ ± [GeV]

0
±
~~
~
~
gg production, B(g→ qqχ∼ )=67%, B(g→ qq∼
χ )=33%
1

1600
1400
1200

1

Observed 95% CL limit (±1 σtheory )Expected 95% CL limit ( ±1 σexp )ATLAS ( 13TeV, 36.1 fb-1, EW prod. Obs.)m~g=mχ∼ ±1

s=13TeV, 36.1 fb-1
τχ∼ ± = 0.2 ns
1

1000
800
600
400
200

800

1000 1200 1400 1600 1800 2000 2200

m~g [GeV](a) Lifetime τ1800= 0.2 ns

0
±
~~
~
~
gg production, B(g→ qqχ∼ )=67%, B(g→ qq∼
χ )=33%1

1

Observed 95% CL limit (±1 σtheory )Expected 95% CL limit ( ±1 σexp )ATLAS ( 13TeV, 36.1 fb-1, EW prod. Obs.)m~g=mχ∼ ±1600

1mχ∼ ± [GeV]

χ˜1 ±

1

1400

s=13TeV, 36.1 fb-1

1200

τχ∼ ± = 1.0 ns
1

1000
800
600
400
200

800

1000 1200 1400 1600 1800 2000 2200

m~g [GeV](b) Lifetime τχ˜1 ± =1.0 ns

Figure 11.2: The exclusion limits in the phase of the gluino mass vs the chargino mass assuming
chargino lifetime of 0.2 ns (a) and 1.0 ns (b). The red solid line is the observed exclusion limit and the
red broken lines are the exclusion limits for signal cross-section shifted by ± 1 σ deviation. The black
broken line is the expected exclusion limit, and the yellow band is its 1 standard deviation region of
the expected limits. The green line is the exclusion limit set by the electroweak direct production
search.

153

1800

0
±
~~
~
~
gg production, B(g→ qqχ∼ )=67%, B(g→ qq∼
χ )=33%1

1

Observed 95% CL limit (±1 σtheory )Expected 95% CL limit ( ±1 σexp )ATLAS ( 13TeV, 36.1 fb-1, EW prod. Obs.)m~g=mχ∼ ±1600

1mχ∼ ± [GeV]

11.3. FUTURE PROSPECTS

1

1400

s=13TeV, 36.1 fb-1

1200

τχ∼ ± = 0.2 nso1=m win=3
2
L/m 3/
o

m bin

1000
800

=2
L/m 3/2

600

1
L/m3/2=

400
AMSB

200

800

1000 1200 1400 1600 1800 2000 2200

m~g [GeV]

1800

0
±
~~
~
~
gg production, B(g→ qqχ∼ )=67%, B(g→ qq∼
χ )=33%1

1

Observed 95% CL limit (±1 σtheory )Expected 95% CL limit ( ±1 σexp )ATLAS ( 13TeV, 36.1 fb-1, EW prod. Obs.)
mg~=mχ∼ ±1600

1mχ∼ ± [GeV](a) Lifetime τχ˜1 ± = 0.2 ns

1

1400

s=13TeV, 36.1 fb-1

1200

τχ∼ ± = 1.0 nso=m winm bino=3
2
L/m 3/

1

1000
800

=2
L/m 3/2

600

1
L/m3/2=

400
AMSB

200

800

1000 1200 1400 1600 1800 2000 2200

m~g [GeV](b) Lifetime τχ˜1 ±=1.0 ns

Figure 11.3: The exclusion limits in the phase of the gluino mass vs the chargino mass assuming
chargino lifetime of 0.2 ns (a) and 1.0 ns (b) overlaid with the prediction of mass relation by the
AMSB and the PGM (fig. 2.4). The red solid line is the observed exclusion limit and the red brokenlines are the exclusion limits for signal cross-section shifted by ± 1 σ deviation. The black broken lineis the expected exclusion limit, and the yellow band is its 1 standard deviation region of the expected
limits. The green line is the exclusion limit set by the electroweak direct production search. The
blue lines show the prediction of mass relation by the AMSB and the PGM for several representative
parameter values.

154

CHAPTER 11. RESULT AND THE INTERPRETATION
Parameter
Expected signal events
α in signal pT resolution function
σ in signal pT resolution function
log rABCD
α in background pT resolution function
σ in background pT resolution function
p0 parameter of the fake-BG pT function
p1 parameter of the fake-BG pT function
Expected number of electron events
Expected number of muon events

Strong channel [%]
13
0.9
8.8
<0.1
3.7
1.6
<0.1
<0.1
0.2
1.9

Table 11.2: Systematic uncertainty impact on signal exclusion significance. Signal with mg̃ = 1600
GeV, mχ˜1 ± = 500 GeV, τχ˜1 ± = 0.2 ns is used.
statistical fluctuation of background estimation and background estimation precision.
To improve the analysis, one idea is to increase signal acceptance. Development of shorter trackreconstruction will improve the disappearing track acceptance because the decay radius distribution
decreases exponentially as shown in Fig. 4.2. Track reconstruction with only two or three hits is possible options. Using vertex constraints or large dE/dx may also contribute to suppress the backgroundwith shorter tracks.
√ If the SUSY particles are too heavy to produce at the LHC, Future Circular Collider (FCC) withs ∼ 100 TeV is one of the promising future experiments. It is expected that long-lived wino up to amass of 3 TeV can be discovered with the FCC. Because wino-like dark-matter is not consistent withcosmological observation if the mass is larger than 3 TeV, the FCC should discover it if the model iscorrect.

Chapter 12Conclusion√
Search for long-lived chargino via gluino pair production in pp collisions at s = 13 TeV with the
ATLAS detector is presented in this thesis.
This search is based on some attractive supersymmetric models which predict the wino-like lightest SUSY particle (LSP). Wino-like LSP generally derives long-lived charged wino as the second
lightest SUSY particle. Thanks to the long lifetime of the chargino of 0.2 ns, it is possible to reconstruct the short track of chargino itself. Pixel tracklet, which is reconstructed by only 4 hits inthe pixel detector, is used for the first time to detect the track of chargino as disappearing track signature. Gluino pair production channel is targeted in this search. The search is based on unbinned
likelihood fitting of the disappearing track candidate pT distribution. The main background is hadronbackground and the next is electron background.
The result is consistent with the background only hypothesis. Therefore, exclusion limit is set in
the phase of the gluino mass vs the chargino mass grid. For chargino lifetime of 0.2 ns, the gluinomass less than 1650 GeV is excluded along the exclusion limit from the electroweak direct production
search and the gluino mass less than 1150 GeV is excluded for the region with the mass diﬀerence
between chargino and gluino larger than 100 GeV. For chargino lifetime of 1.0 ns, the gluino mass lessthan 1750 GeV is excluded along the exclusion limit from the electroweak direct production searchand the gluino mass less than 1300 GeV is excluded for the region with the mass diﬀerence between
chargino and gluino larger than 100 GeV.
The PGM model specific exclusion limit is also set. For chargino lifetime 0.2 ns, the gluino massof less than 1500 GeV is excluded for all the possible PGM parameter phase. For chargino lifetime
1.0 ns, the gluino mass of less than 1600 GeV is excluded for all the possible PGM parameter phase.

155

Acknowledgments
Firstly, I would like to express my sincere gratitude to my supervisor Prof. Sachio Komamiya. He
gave an opportunity for the research and also important suggestion on my thesis.
I would like to thank my local supervisor at CERN, Prof. Shoji Asai. He gave important suggestion
on the selection of the theme of this thesis and also the direction of the research.
My sincere thanks also goes to Prof. Ryu Sawada. He leads the disappearing track analysis groupand gave me many explicit advices.
I thank Dr. Takashi Yamanaka and Dr. Shimpei Yamamoto. They also leads the disappearing track
analysis group and gave physical and technical help.
I am grateful to Mr. Masahiko Saito, Mr. Toshiaki Kaji, and Mr. Kenta Uchida. They are colleagueof the disappearing analysis. Their study is necessary to complete my thesis.
I would like to thank my colleagues in ICEPP, Prof. Junichi Tanaka, Prof. Yuji Enari, Prof. Yasuyuki Okumura, Prof. Tatsuya Masubuchi, Dr. Tomoyuki Saito and Dr. Takuya Nobe. Discussions
with them inspired many improvements of the analysis.
A special gratitude goes to the group conveners, Prof. Till Eifert, Prof. Iacopo Vivarelli, Prof. Simone Amoroso, Prof. Simon Pagan Griso and Prof. Laura Jeanty. The discussion with them is really
helpful to develop the analysis.
With a special mention to Prof. Heather Gray and Prof. Shih-Chieh Hsu. They are conveners of
tracking CP and alignment and they also gave me good suggestions on tracking issues.
I would like to thank Dr. Yosuke Takubo and Mr. Daiki Yamaguchi. They instruct on pixel detector
data quality monitoring work.
My sincere thanks also goes to Prof. Daniel Jeans and Prof. Yoshio Kamiya. They are supervisorof master period and also gave warm encouragement.
I am grateful to my colleague in Komamiya-lab, Prof. Junping Tian, Mr. Yuya Kano, Mr. Koji
Yamada, Mr. Takaaki Yasui and Mr. Hitoshi Nakanishi for the wonderful life in this lab.
A special gratitude goes to secretariats, Ms. Kuniko Kono, Ms. Masako Shiota, and Ms. Kyoko
Tanaka. They helped my oﬃce works.
I would like to thank Dr. Yusuke Suda, Ms. Miki Nishimura, Ms. Maya Okawa, Mr. Chikuma
Kato and Dr. Shion Chen. We shared tough feeling of Ph.D.
With a special mention to Mr. Sébastien Stoecklin, the landlord of my room in Saint Genis Pouilly.
I could spend wonderful days in the studio.
I am grateful to my physics teacher in high school, Mr. Takashi Kamijo, and the other membersof Tokyo Physics Circle. Their encouragement has driven my enthusiasm in physics research.
Finally, I would like to express my sincere gratitude to my family. I would not complete my thesis
without their support.
157

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