Doctoral Dissertation
博士論文

Search for direct Chargino production
based√ on a disappearing-track signature
at s = 13 TeV with the ATLAS detector(ATLAS 検出器での 13TeV 衝突エネルギー実験データを用いた消失飛跡を特徴としたチャージーノ探索)

A Dissertation Submitted for the Degree of Doctor of Philosophy
April 2019平成 31 年 4 月博士（理学）申請
Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科
物理学専攻
Masahiko Saito齊藤 真彦Abstract
A supersymmetric theory is one of the most well-motivated theories of Beyond the Standard Model. The past observations favour the supersymmetric models where the lightest
charged-supersymmetric particle is nearly mass-degenerate with the lightest neutral-one.
Such models predict a meta-stable charged supersymmetric particle with a lifetime ofO(0.01–0.1) ns, resulting in a characteristic track signature, called disappearing track.
This thesis presents a search for a direct chargino production based on the disappearing
track signature in the ATLAS detector in the proton-proton collisions produced by theLarge Hadron Collider at the centre of mass energy of 13 TeV. The introduction of short
tracks which consist of only four Pixel-sensor hits gives a significant improvement forthe signal acceptance by a factor of seven.
The results with data recorded in 2015–2017 show no significant excess from theStandard Model prediction, resulting in the strong constraints for the pure wino/higgsino
LSP scenarios; the chargino mass up to 490 GeV is excluded in the pure wino LSP scenario, and the chargino mass up to 170 GeV is excluded in the pure higgsino LSP scenario.
The future prospects of disappearing track analysis are also discussed. Although thecurrent LHC does not have a sensitivity to explore the entire chargino-mass parameter
space which is viable from the cosmology, the next-generation collider, Future Circular
Collider, has the suﬃcient potential to discover them.

Contents
1 Introduction
1.1 The problems in the Standard Model . . . . . . . . . . . . . . . . . . . . .
1.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Minimal Supersymmetric Standard Model . . . . . . . . . . . . . . . . . .
1.4 Constraints from past experimental results . . . . . . . . . . . . . . . . . .
1.5 SUSY breaking models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Anomaly mediated SUSY breaking model . . . . . . . . . . . . . .
1.5.2 Pure gravity mediation model . . . . . . . . . . . . . . . . . . . . .
1.5.3 Supergravity mediation model . . . . . . . . . . . . . . . . . . . .
1.6 Phenomenology of the lightest charginos in the pure wino / pure higgsino
scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1 Mass diﬀerence . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Decay width and lifetime . . . . . . . . . . . . . . . . . . . . . . .
1.7 Previous disappearing-track search . . . . . . . . . . . . . . . . . . . . . .
1.8 New tracking technique for long-lived particles . . . . . . . . . . . . . . .
1.9 Contents of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
5
6
7
9
11
11
11
12

2 LHC and ATLAS detector
2.1 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Luminosity detector . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Trigger and data acquisition system . . . . . . . . . . . . . . . . .

20
20
21
21
22
26
29
31
32

3 Data and simulated samples
3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Simulated samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Signal Monte Carlo sample . . . . . . . . . . . . . . . . . . . . . .

33
33
33
33
35
35

1

12
13
14
16
17
19

3.2.2Monte Carlo samples of the Standard Model background . . . . . . 37

4 Object reconstruction
4.1 Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Inside-out track reconstruction . . . . . . . . . . . . . . . . . . . .
4.1.2 Outside-in track reconstruction . . . . . . . . . . . . . . . . . . . .
4.2 Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Electron and photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Missing transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . .

41
41
41
42
43
43
43
44
44

5 Track-reconstruction for disappearing signature
5.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 For meta-stable charginos . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Disappearing tracklet selection . . . . . . . . . . . . . . . . . . . .
5.2.3 Data/MC comparison using high purity tracklets . . . . . . . . . .
5.2.4 Correction of simulated data using observed data . . . . . . . . . .

46
46
48
48
49
53
57

6 Event selection
6.1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Event cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Kinematic selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Disappearing track selection . . . . . . . . . . . . . . . . . . . . . . . . . .

65
65
67
68
71

7 Background estimation
7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Hadron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Lepton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Fake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74
74
75
77
86

8 Extraction of signal yield91
8.1 Unbinned extended maximum likelihood fit . . . . . . . . . . . . . . . . . 91
8.2 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
9 Systematic uncertainties
95
9.1 Common systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . 95
9.2 Signal systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 95
9.3 Background systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . 101
10 Result104
10.1 Shape fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
10.2 Model-independent limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

2

11 Discussion, interpretation and perspective
108
11.1 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
11.1.1 Constraints on the long-lived wino models . . . . . . . . . . . . . . 108
11.1.2 Constraints on the long-lived higgsino models . . . . . . . . . . . . 111
11.2 Future experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
11.2.1 High-Luminosity Large Hadron Collider . . . . . . . . . . . . . . . 113
11.2.2 Future Circular Collider . . . . . . . . . . . . . . . . . . . . . . . . 116
12 Conclusion

119

A Tracklet q/pT distribution and a smearing function

121

3

Chapter 1

Introduction
The discovery of the Higgs boson in 2012 was a milestone on the elementary particle
physics, resulting in the reconfirmation of the validity of the Standard Model. The
Standard Model is, however, not a perfect nor an ultimate theory because it contains
an artificial tuning like the anthropic principle and cannot explain 95% of the energy in
our universe. Importance of the searches for new physics beyond the Standard Model isincreasing since there is still no clear hint indicating new theories close to the ultimate
theory.
One of the most well-motivated theories is a supersymmetric theory, which solves
many problems in the Standard Model. Although the supersymmetric theory has ahuge number of model parameters, the properties of the supersymmetric theory are
expected according to the precise agreements between nature and the Standard Modeland a few unexpected deviations, including the existence of dark matter. One of the wellmotivated scenarios in the supersymmetric theories is the case where superpartners of
the W boson or the Higgs boson is the lightest supersymmetric particle. Such scenarios
can be satisfied with constraints from the Higgs boson mass, dark-matter relic density
and the flavour physics.
Despite the motivation, it is known to be hard to search for such a scenario in
hadron collider experiments within the traditional searches based on only energetic jets,
leptons and the missing transverse momentum due to the lack of energetic particles
from a cascade decay from the supersymmetric particles. On the other hand, instead ofthe energetic signatures, such a model predicts a charged meta-stable supersymmetricparticle with a lifetime of O(0.01–0.1) ns. Since such a lifetime corresponds to the decay
radius of O(1–10) cm, which is smaller than the size of a track detector (tracker) in
the ATLAS detector, the charged supersymmetric particles can be observed as suddenly
disappearing in the tracker after running some macroscopic distances. Such a signature
is called a disappearing track. Since the Standard Model particles do not produce adisappearing track, a requirement for the disappearing track has strong rejection power
for the Standard Model particles.
The past experiments using disappearing track signature did not have adequate signal
acceptance because it was diﬃcult to reconstruct the short tracks comparable with the4typical decay radius (O(1–10) cm) due to the tracker layout. The ATLAS experiment upgraded the tracker in the long-shutdown in 2013–2014, making it possible to reconstruct
shorter tracks with the track length of 12 cm. The shorter tracks and the improvements
in various parts in the analysis including the track reconstruction, measurements of the
tracking performance and the background estimation technique, significantly improve
the sensitivity for the supersymmetric particles.
This chapter briefs the supersymmetric theory and the motivative supersymmetricscenarios at first, then describes the properties of the characteristic signature predictedfrom the motivative scenarios. After showing a limitation of the disappearing track
analysis, a significant advantage of the shorter tracks is discussed. The last section gives
an overview of this thesis.

1.1

The problems in the Standard Model

The Standard Model (SM) of elementary particle physics was theoretically finalised by
the 1970s for the most part, and verified by many experimental results. The last missing
particle in the SM, i.e. Higgs boson, was discovered by both the ATLAS and the CMS
experiments in 2012 [1,2], resulting in the experimental confirmation of the SM. The SM
describes the properties of elementary particles with surprising precision. It is, however,
not a perfect model: the SM has some problems.
The first problem is related to the naturalness of SM parameters. This problem
relates to the Higgs boson. Higgs boson mass is contributed by a radiative correction
from a fermion loop, e.g. top-quark∆m2h ∝

3λ2t 2
Λ ,
4π 2

(1.1)

where λt is a top Yukawa coupling constant and Λ is the cut-oﬀ scale of the SM. The
cut-oﬀ scale is considered to be near the Planck scale ≈ O(1019 ) GeV if the SM is valid
to this energy scale, while the observed Higgs mass is around 125 GeV. Therefore, toaccomplish the observed Higgs mass, the squared of the bare mass must be tuned at
10−34 level. Since this is not natural, this problem is called a naturalness problem.
The second one is related to a grand unification theory (GUT). When considering the
GUT, the strengths of the three fundamental forces (electromagnetic, weak and strong)should be unified at one energy scale, called the GUT scale. However, it was revealed thatthe three gauge coupling constants are not unified at a high energy scale if considering
all contributions only from the SM particles. So GUT is not simply accomplished in theSM.
The third one is the existence of dark matter, which was proposed at first to explain
the inconsistency of the galactic rotation curves. By the great success of the Λ-Cold Dark
Matter model with the precise measurements of cosmic microwave background by the
WMAP/Planck, detailed properties of dark matter in our universe became clear: darkmatter density is five times larger than the baryon density, dark matter does not interact5electromagnetically and strongly, and its velocity should be small. Such a particle does
not exist in the SM.
The existence of Beyond the Standard Model (BSM) is necessary to solve the threeproblems mentioned above, and many kinds of BSMs are proposed.

1.2Supersymmetry

Supersymmetry (SUSY) models are the promising BSM models which can solve these
problems. Supersymmetry is a new symmetry between bosons and fermions. SUSY predicts additional new particles, called the superpartners, which have the same properties
as the SM particles except for the spin. Such particles, however, are rejected experimentally, e.g. no scalar particle with the electron mass, corresponding to the electroncounterpart, has been observed The supersymmetry must be broken, and SUSY particles
are expected to have heavier masses than the SM particles.
Although new particles predicted in the SUSY are not discovered yet, SUSY is awell-motivated model, because the SUSY solves the problems in the SM.

Naturalness
The new symmetry protects the Higgs mass from a quadratic divergence. A contribution
to a radiative correction of the Higgs mass from new scalar particles gives an oppositesigned contribution to the SM fermions, resulting in a cancellation of the quadratic
divergence and relaxation to a logarithmic divergence. Although the Higgs mass is afree parameter in the SM, it can be predicted in the SUSY frameworks as follows
(
(
))
2
2 m4
2
2
m
3g
X
X
1
e
t
m2h ≲ m2Z cos2 2β + 2 2t log t2 + t2 1 −(1.2)
12 me2t
8π mW
mt
met
Xt = At − µ cot β
me2t ∼ mte1 mte2 ,where tan β is the ratio of vacuum expectation value, met , mt , mh , mZ and mW are themasses of superpartner of top-quark, top-quark, Higgs boson, Z boson and W boson,respectively, At is the trilinear coupling of Higgs and a superpartner of top-quark, µ isa mixing parameter of doublet Higgs and g is SU(2) gauge coupling. The second term
is a contribution from a radiative correction, and it is proportional to the logarithm of
the mass scale of a new particle. Even though the Higgs mass depends on some SUSY
parameters, it should be less than around 130 GeV. The observed Higgs mass (125 GeV)
favours the existence of SUSY.

6

Grand Unification
An existence of SUSY particles changes a gauge-coupling renormalisation-group-equations (RGE)
as follows
(
)
bi
Q
−1
−1
αi (Q) − αi (MGUT ) =ln(1.3), (i = 1, 2, 3)
2π
MGUT
(
)
41 19
(b1 , b2 , b3 )SM =
− ,
, 7
10 6
(
)
35
⇒ (b1 , b2 , b3 )MSSM =− , −1, 3 ,(1.4)
5where αi−1 is an inverse gauge coupling, Q is an energy scale and MGUT is an energy
scale of the grand unification. The three coupling constants are unified at one energy
scale ≈ O(1016 ) GeV when assuming TeV-scale SUSY particles as shown in Fig. 1.1.
60
U(1)

50
40
SU(2)
-1
α 30

20
10 SU(3)
0
2

4

6

8

10

12

14

16

18

Log10(Q/GeV)

Figure 1.1: Inverse gauge couplings (α−1 ) as a function of energy scale (Q) (Ref. [3]).
Black dotted lines show ones with considering only the SM particles. Red lines andblue lines show ones with introducing supersymmetric particles mass of 750 GeV and
2.5 TeV, respectively. Three coupling constants are unified at one energy scale thanks
to introduced supersymmetric particles mass of 1–10 TeV.

Dark matter
The lightest SUSY particle (LSP) is a candidate of a dark-matter. The details are
discussed in Sec. 1.4.

1.3

Minimal Supersymmetric Standard Model

SUSY can solve many problems in the SM as shown in Sec. 1.2. This section describes
a minimum supersymmetric extension of the SM, called the Minimal Supersymmetric7

Standard Model (MSSM) as a practical framework to discuss the phenomenology of
SUSY models.
The MSSM contains only one supersymmetric partner for each SM particle as shownin Table 1.1. Superpartners have diﬀerent spins from the SM particles for just by half.
The superpartners of quarks and leptons are called squarks and sleptons, and the superpartners of bosons (Higgs boson, gluon, W boson, B boson) are called higgsino, gluino,
wino and bino, respectively. Especially, superpartners of the gauge bosons are called
gauginos. Although a graviton is an undiscovered particle, its superpartner gravitino
often takes an important role in the phenomenology and cosmology.
Super multiplet
squarks/quarks

sleptons/leptons
Higgs/higgsinos
gluinos/gluons
winos/W-bosons
bino/B-boson

Q
ū
d¯
L
ē
Hu
Hd
g
W
B

spin 0(euL , deL )

u
eR
deR
(e
eL , νeL )eeR(Hu+ , Hu0 )(Hd0 , Hd− )spin 1/2(uL , dL )uR
dR(eL , νL )eR
e u+ , He u0 )(He −)e 0, H
(H
d
d
ge
f0, W
f±
W
f0
B

spin 1(SU (3)C , SU (2)W , U (1)Y )g
W 0, W ±B0( 3, 2, 61 )( 3̄, 1, - 32 )( 3̄, 1, 31 )( 1, 2, - 21 )( 1, 1, 1 )( 1, 2, 21 )( 1, 2, - 21 )( 8, 1, 0 )( 1, 3, 0 )( 1, 1, 0 )Table 1.1: Supermultiplets in the MSSM. A right column shows the representation of
the gauge groups of SU (3)C × SU (2)W × U (1)Y . Only the first generation sparticles areshown.
The MSSM introduces two Higgs doublets because only one Higgs doublet cannot givethe fermion mass for both up- and down- types. So there are two vacuum expectation
values (VEVs) of Higgs doublets (⟨Hu0 ⟩, ⟨Hd0 ⟩). The ratio of two VEVs is a free parameterbut takes an important role in the MSSM, so the ratio is traditionally written using a
mixing angle β as
⟨Hu0 ⟩
tan β =.
(1.5)
⟨Hd0 ⟩
Since bino, wino and higgsino have the same quantum numbers, they mix and form
new mass-eigenstates. Neutral states are called neutralinos, and charged states are called
e W
f0, H
e 0, He 0 ) is given as
charginos. The mass matrix of neutralinos (B,
u
d


MNe

=

M1

0

−mZ sin θW cos βmZ sin θW sin β0M2mZ cos θW cos β−mZ cos θW sin β−mZ sin θW cos βmZ cos θW cos β0−µmZ sin θW sin β−mZ cos θW sin β  , (1.6)−µ0

where M1 and M2 are the mass terms of bino and wino, respectively, µ is a mixing parameter of doublet Higgs, and θW is a Weinberg angle. As shown in the mass
matrix (Eq. 1.6), a component of the mixture depends on the M1 , M2 , µ, Weinberg
8angle (θW ) and tan β. The mixing changes the properties of neutralinos and especiallyis related to dark-matter properties, which is discussed in Sec. 1.4. As a context of thephenomenology, the mass eigenstates are often used. They are written as χ
e01 , χe02 , χe03 , χe04
f±, H
e ± ) is given as
in the order of their masses. A mass matrix of chargino (W
u/d
(
MCe

=

√ M2
2mW sin β√)
2mW cos β
.
µ

(1.7)

The mass-eigenstates are written as χ
e±
e±
1, χ
2 in the order of their masses.
In the MSSM, an R-parity is introduced
R = (−1)3(B−L)+2S ,(1.8)

where B, L and S are the baryon number, the lepton number and the spin. All theSM particles have R = +1, while all the supersymmetric partners have R = -1. The
Lagrangian of the MSSM consists of using R-parity invariant terms because an R-parityviolated term leads to forbidden processes by some experimental facts, e.g. the baryon
number violation which conflicts with the lower limits of the proton lifetime (> 1.6 ×1034 years [4]). Another advantage of the R-parity conservation is that the LSP becomesstable, resulting in a good candidate of dark matter.

1.4

Constraints from past experimental results

The MSSM framework contains large numbers of free parameters. However, it can beconstrained with various experimental results.

Higgs mass
The Higgs mass can be predicted in the SUSY framework, unlike the SM, and themeasured value, 125 GeV, gives a constraint on SUSY parameters. From Eq. 1.2, there
are two possible solutions to explain the Higgs mass. The first solution is that stop
mass (met ) is set to heavy enough (> 10√TeV). The second solution is that the stop
mixing parameter (Xt ) is set to around 6mt̃ with O(1) TeV stop mass. Figure 1.2
shows the relation between the stop mass and the Higgs mass. Although the naturalness
favours that a stop is not far from the electroweak scale, heavy sparticles lead to otheradvantages as discussed later.

Dark-matter relic density
A dark-matter relic density can also constrain on SUSY parameters. There are somecandidates of the LSP (and dark-matter as well) in the MSSM framework with R-parity
conservation. From an observation of how dark matter interacts with normal matter, thecandidates are limited to neutral particles for electromagnetic charge and strong charge,
e wino (Wf ), higgsino (H)e and gravitino (G).
e Since gravitino becomes a hot
i.e. bino (B),dark-matter and it smears out the large structure of the universe, this thesis focuses onneutralinos (bino, wino and higgsino).
9

MSSM Higgs Mass
140

mh @GeVD

130

Xt =

6 mt

mh = 124-126 GeV

120
110
Xt = 0

100
90
200

300

500

700

mt1

Suspect
FeynHiggs

1000

1500 2000

3000

@GeVD

Figure 1.2: The Higgs mass as a function of stop mass [5]. Red lines show the two-loop
calculation using Suspect, and blue lines √show the two-loop calculation using FeynHiggs.
Two upper lines show the case of Xt = 6mt̃ (maximal mixing), and two bottom lines
show the case of Xt = 0. The tan β is set to 20 for all cases.
The relic density of the lightest neutralino can be calculated with the annihilation
cross-section, which is measured by Planck collaboration [6] to be ΩDM h2 = 0.120±0.001.
Assuming a thermal production scenario where the dark-matter density was fixed at
decoupled temperature, the relic abundance of LSP should be smaller than the observed
dark-matter density. When the lightest neutralino is a pure bino, the upper boundof the lightest neutralino mass is highly constrained, and it is almost excluded by LHC
experiments. The upper bounds can be relaxed by assuming an adequate co-annihilation
process, which is realised such as setting a small mass diﬀerence between the bino andthe next-lightest SUSY particles. Such a compressed region is one of the important phasespace in the MSSM [7]. Unlike the bino LSP case, the upper bound of the pure wino
and the pure higgsino is more moderate than the pure bino case due to their large crosssection: the upper bounds are 3 TeV for wino and 1 TeV for higgsino, respectively [7].
Therefore, the pure wino and the pure higgsino with their masses of O(0.1–1) TeV cannaturally be a dark-matter candidate without a tuning of the next-LSP masses.
When the bino and wino masses decouple with the higgsino masses, mass-eigenstates (χ̃)
e Wf /H).
eare nearly equivalent to pure flavour states (B/Flavour changing neutral current and CP violation
In the MSSM framework, non-diagonal terms in mass matrices for squarks and sleptons
are non-zero in general. Such a term leads flavour mixing or CP violating processes,
e.g. the large K 0 ↔ K̄ 0 mixing (∆mK = mKL − mKs ) and lepton flavour violation, e.g.
µ → eγ. However, they should be highly suppressed by some experimental results [8].
Such processes can be suppressed if squarks and sleptons are nearly mass-degenerate or
their masses are heavy (≫O(1) TeV).
10

1.5

SUSY breaking models

Since the MSSM contains a huge number of parameters (124), the parameters are reducedby assuming the SUSY breaking mechanism. Considering the experimental constraints
as discussed in the previous section, this thesis focuses on SUSY breaking models thatpredict
Condition 1.
The LSP is a neutralino which consists of a pure wino state or a pure higgsino
state, and their masses do not lead to the overabundance of the dark-matter relicdensity.
Condition 2.
Squark masses and slepton masses are heavy enough to explain the Higgs massand the current experimental constraints from the flavour physics.
There are three models in which these conditions are satisfied.

1.5.1

Anomaly mediated SUSY breaking model

Anomaly Mediated SUSY Breaking (AMSB) models are a promising scenario to predict
the wino LSP. These models assign a conformal anomaly as a SUSY mediator connecting
the hidden sector to the SM-sector [9], and this is a general breaking mechanism in allother SUSY models.
The mediator creates gaugino masses as following
Mi =

bi 2
g m
(i = 1, 2, 3),
16π 2 i 3/2(1.9)

where gi are gauge coupling constants of the SM gauge groups, m3/2 is the gravitino
mass, and bi are coeﬃcients of RGE (Eq. 1.4) in the MSSM case. From the relation of
the magnitude of bi gi2 values, a wino becomes the LSP. The mediator also contributes tomasses of scalar SUSY particles, and resultant squared of scalar mass becomes negative.
Therefore an artificial scalar-mass term (m0 ) is added as an input model parameters to
avoid a tachyon. These models are described using only four model parameters: m0 ,m3/2 , tan β and sign(µ), which is a sign of higgsino mixing parameter (µ).

1.5.2Pure gravity mediation model

Pure Gravity Mediation (PGM) models [10–12] are an extension of the AMSB models. In
these models, sfermion and higgsino masses are produced from the mediation of gravity
at tree level. Therefore, their masses are comparable to the gravitino mass. On theother hand, due to the lack of the tree-level contribution for gaugino masses, they aremainly produced from one-loop level gravity mediation. Therefore, the gaugino masses
naturally become lighter than squark/slepton masses by a factor of 10−1 –10−2 , resulting
in the satisfaction of the Condition 2. Considering the next-to-leading corrections [13],11the gaugino masses are aﬀected by a sizeable contribution from the higgsino thresholdcorrection due to the large higgsino mass comparable to the gravitino mass as follows,
33 g12
1(m3/2 + L)
2
5 16π
11
g22
M2 =
(m + L)16π 2 3/2
g2
M3 = −3 3 2 m3/2
16π
m2
|µ|2
L = µ sin 2β 2 A 2 ln 2 ,|µ| − mA mA
M1 =(1.10)(1.11)(1.12)(1.13)

where M1 , M2 and M3 are mass terms of bino, wino and gluino, respectively, µ andmA are the higgsino mixing term and the pseudo-scalar Higgs mass, respectively. L
represents a contribution from a higgsino threshold correction. The L parameter is
expected to be of the same order of m3/2 when µ ∼ m3/2 . Although the large L parameter
leads the bino-LSP scenario, a large part of the phase space leads the wino-LSP scenario.

1.5.3

Supergravity mediation modelSupergravity mediation model (SUGRA) assumes that both the sparticle masses andgaugino masses are produced through the mediation of gravity at tree level. This model
uses only five model parameters: a universal sparticle mass at the GUT scale (m0 ), a
universal gaugino mass at the GUT scale (m1/2 ), a universal trilinear coupling (A0 ),tan β and a sign of the µ (sign(µ)). When m0 is set to a large value, Condition 2 issatisfied.
In this case, the gaugino mass relation is diﬀerent from the above two models, because
the mass relation is determined by the RGE of the gaugino mass as follows
M1 : M2 : M3 = g12 : g22 : g32 ≈ 1 : 2 : 6.

(1.14)In the mSUGRA model, the lightest gaugino is a bino, instead of a wino. However, whenm1/2 is large and µ is small, the neutral higgsinos are the LSP. In this case, Condition 1
is satisfied.
A condition of an electroweak symmetry breaking in the MSSM requires to tune theµ-parameter and the Higgs field soft SUSY-breaking terms (mHU and mHD ). If µ is set
to be a large value compared to the electroweak scale, the high-level tuning is needed.
In order to avoid such an unnatural tuning, namely from the view of naturalness, lightµ is favoured.

1.6

Phenomenology of the lightest charginos in the purewino / pure higgsino scenario

As discussed in Sec. 1.5, the wino/higgsino LSP scenario is one of the most important
cases in SUSY frameworks. Verification of the above models is, however, not easy for12the following reasons.
• Masses of gluino and squarks are expected to be large in these cases to explain
the Higgs mass of 125 GeV. Hadron colliders have strengths in the production ofheavy particles having SU(3) charge. However, such heavy strong-particles maybe
not be produced even in the highest proton beam at present.
• For the wino/higgsino direct pair production, no energetic secondary particles
are emitted from heavier SUSY particles. Both the wino and the higgsino are
multiplets of SU(2), and the lightest chargino belongs to the same multiplets as thelightest neutralino due to the little mixing of neutralinos/charginos. Therefore, themass diﬀerence between the lightest neutralino and the lightest chargino becomesquite small not as large to be detected in the detector.
For these reasons, traditional SUSY searches have less sensitivity for the above models.
On the other hand, when the lightest chargino is a pure wino or a pure higgsino, thechargino is highly mass-degenerate with the lightest neutralino mass, resulting in aninteresting signature. In this section, the phenomenology of the wino/higgsino LSP
models is discussed.

1.6.1

Mass diﬀerence

The lightest neutralino is nearly mass-degenerate with the next lightest charginos when
they are pure states of wino or higgsinos. A tiny mass diﬀerence is produced fromradiative correction of the SM particles. The mass diﬀerence with one-loop calculationis represented as [14–16]
(
)
(
)]
g2M [
2
sin θWf m2Z /M 2 + (1 − 2Y )f m2W /M 2 ,
2
8π
∫ 1
[
]
f (z) =
(1 + x) log 1 + z(1 − x)/x2 dx,mχ̃± − mχ̃01
1=(1.15)(1.16)

0where M and Y are the mass and the hypercharge of the lightest chargino respectively,
g is a weak coupling constant, mZ is the Z-boson mass, θW is the Weinberg angle, andthe function f (z) is a loop function. The hypercharge for wino (higgsino) is 0 (1/2).
Eq. 1.15 can be simplified to
 2
)
(
)]
g M[ (
2
 2 f m2W /M 2 − cos θW
f m2Z /M 2 , for wino8πmχ̃± − mχ̃01 =.
(1.17)
2M [
1
( 2
)]

g

2
2

sin θW f mZ /M,
for higgsino
8π 2
The function f (z) becomes 1 when z → 0. The mass diﬀerence of wino (higgsino)
becomes 166 (354) MeV at the limit of M ≫ mZ as shown in Fig. 1.3. A two-loop
calculations for wino case were also done [16, 17] and superimposed in Fig. 1.3 (a).

13

350

170

340
330

160
155

320
∆m+ |rad [MeV]

Heavy wino limit
by Yamada (2009)δm [MeV]

165

310
300
290
280
270

150

two-loop
one-loop
100

260
250

1000
mneutralino [GeV]

200

400

600

800
|µ| [GeV]

1000

1200

1400

(b)

(a)

Figure 1.3: Mass splitting between the lightest chargino and the lightest neutralino asa function of the neutralino mass. (a) For the wino case with two-loop calculation [16].
(b) For the higgsino case with one-loop calculation [18].

1.6.2

Decay width and lifetime

Because of the tiny mass splitting, the decay channels of the lightest charginos are highly000
limited. The possible decaying ways are only into π χ̃ , eν χ̃ and µν χ̃ , and their decay
widths depend on the mass splitting given as [14, 16]√
 2 2( m )2
2G
f

π
π
2
3
F

cos θc ∆m 1 −, for wino

π
∆m
±
0
±
e1(,2) π ) =Γ(eχ1 → χ
(1.18)
√
)2
(
2 2


 GF fπ cos θ2 ∆m3 1 − mπ , for higgsino
c
∆m
 π2
(
)
2G
m

l

 F3 ∆m5 P, for wino
15π
∆m
±
0
±
e1(,2) l νl ) =Γ(eχ1 → χ
(1.19)
(m )
2

G
l

5
F

∆m P
, for higgsino
15π 3
∆m
√
9
15x4
tanh−1 1 − x2 ,P (x) = 1 − x2 − 4x4 + √(1.20)
2
2 1 − x2
where ∆m is the mass diﬀerence between the lightest chargino and the lightest neutralino, mπ and ml are the mass of a pion and a lepton respectively, G2F is the Fermi
coupling constant, fπ is a pion decay constant, and cos θc is a Cabibbo angle.
The relation between the mass diﬀerence and the chargino lifetime is shown in
Fig. 1.4 (a). The lifetime of pure wino (higgsino) is about 0.2 ns (0.023 ns) in therest frame, corresponding to the mean decay length of O(0.1–10) cm. As shown in
Fig. 1.4 (b), a wino or a higgsino decays primarily into a pion which has too low momentum and it is diﬃcult to reconstruct as tracks. Such a particle looks like disappearing
in the detector as shown in Fig. 1.5, remaining only a short track in the tracker, whichis called disappearing track.
14

Figure 1.4: (a) A lifetime of the lightest chargino [19]. (b) A decay branching ratio forthe lightest chargino [19].

ATLAS Simulation

π+

~0
χ
1

~+
χ
1

Figure 1.5: Illustration of the disappearing track signature. A chargino is observed asa few sensor-hits in the tracker shown as red squares. A neutralino does not interact
with the detector, resulting in the missing momentum shown as a white dotted line. A
secondary particle, a pion shown as green curve, can leave energy deposits to each sensor
in the tracker, but it is diﬃcult to reconstruct as a track due to the tiny momentum.

15

1.7

Previous disappearing-track search

The disappearing-track searches were done by both ATLAS [20] and CMS [21] experiments. In these searches, signal events were triggered by initial-state-radiation jets andthe missing transverse momentum toward the opposite side as shown in Fig. 1.6. Thenthe existence of disappearing tracks was required. As discussed above, the expected signal track length was so small that signal acceptance was very low. Figure 1.7 shows theresults in Run 1 analyses in the ATLAS experiment and a Run 2 analysis using 38 fb−1 inthe CMS experiment, where the ATLAS experiment used short tracks whose length waslarger than 30 cm. These analyses had strong discovery potential for long-lived particles(≳5 ns) but did not have adequate sensitivity for particles with motivated lifetimes.

j
p
χ̃01

p

χ̃01

χ̃±
1

π±
Figure 1.6: Diagrams of chargino-neutralino direct production with an association of
one initial-radiation-jet.
The leading reason that the previous analyses had limited sensitivities for motivated
lifetime predicted from the wino/higgsino LSP scenario is that they used the disappearing track signature longer than typical chargino decay lengths (O(1-10) cm). Since
the charginos decay exponentially ( cτ1βγ e−r/cτ βγ ), where βγ is a boost factor, signal acceptance for the disappearing track signature is also exponentially suppressed by theminimum reconstructable track length (R)∫ ∞1 −r/cτacceptance =edr = e−R/cτ ,(1.21)cτ
R
where assuming βγ = 1. Considering winos/higgsinos are expected to be heavy (O(0.1–1) TeV), the straightforward way to increase signal acceptance is to use shorter tracks
than the previous ones.
One diﬃculty for the use of the short tracks is increasing fake tracks which are
accidentally produced from a wrong combination of the hits in the tracker. The fakerate is decreased by using large numbers of hits because of the small probability that16τ∼χ± [ns]

10

1

1

τχ∼± [ns]38.4 fb-1 (13 TeV)

tanβ = 5, µ > 0

102

CMS Preliminary

10
1

ATLAS
s = 8 TeV,∫

L dt = 20.3 fb

1-1

tan β = 5, µ > 0
0
±
Β (∼
χ →∼
χ π±) = 100%1

1

95% CL limit±2 σexperiment±1 σexperimentMedian expected
Observed

Observed 95% CL limit (±1 σtheory)

10-1

Expected 95% CL limit (±1 σexp)
ATLAS ( s = 7 TeV, 4.7 fb-1, EW prod.)
ALEPH (Phys. Lett. B533 223 (2002))∼±‘Stable’ χ

10−1

1

200

100 150 200 250 300 350 400 450 500 550 600

400

600

mχ∼± [GeV]1800m∼χ± [GeV]
1

(a)

(b)

Figure 1.7: Constraints for long-lived particles leaving disappearing track signature. (a)ATLAS Run 1 results [20]. (b) CMS Run 2 results [21].
all hits are consistently aligned. On the contrary, tracks with a small number of hits
tend to be fake. The requirement on the minimum number of hits is determined by atrade-oﬀ between the signal acceptance and the fake rates. The ATLAS Run 1 analysis
used short tracks reconstructed from at least five hits, which consists of three Pixel hits
and two SCT hits1 , as shown in Fig. 1.8, resulting in the track length of larger than
30 cm and low sensitivity for charginos with their decay lengths of O(1–10) cm.

1.8

New tracking technique for long-lived particles

The ATLAS detector was upgraded in the long-shutdown in 2013–2014, and a new layerof the inner tracker was installed at the nearest position to the beam pipe. This enabled
us to reconstruct shorter tracks, called pixel-tracklets, than those used in Run 1 analysis
as shown in Fig. 1.8. Pixel-tracklets consist of four Pixel hits, instead of three Pixel
hits and two SCT hits, resulting in a higher signal acceptance with a comparable faketrack rate due to their short track length of around 12 cm. The use of pixel-tracklets
increases the signal acceptance by a factor of seven compared to Run 1 analysis forthe wino LSP scenario as shown in Fig. 1.9. On the other hand, new tracks require tomodify the background estimation technique because the smaller track length leads tothe worse momentum resolution. This thesis focuses on the significant improvement ofsignal tracks acceptance by the pixel-tracklets and shows the latest results which aremost sensitive to the wino/higgsino LSP scenario, using 80 fb−1 of pp collision data
1

Two SCT hits correspond to a three-dimensional measurement on one SCT layer because SCT
detector is a double-sided strip detector.

17

Figure 1.8: Illustration of tracks in the ATLAS detector. Inner three (four) layers are
the Pixel detector, and the outer four layers are the SCT detectors. The yellow points
represent hits in each layer. A black line shows the normal length track which consistsof full hits in the tracker. A blue line shows a short track used in Run 1 analysis, wherea track is made by three Pixel hits and two SCT hits. A red line shows a new short
track (pixel tracklet), which consists of four Pixel hits. The pixel tracklet reconstruction
became possible thanks to new Pixel-layer shown as red dashed line.

18Signal acceptancecollected by the LHC/ATLAS experiments at√

s = 13 TeV.

0.2
0.18

m∼χ± = 400 GeV, τ ∼χ± = 0.2 ns
1

0.16

1

Previous tracking
New tracking

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

100

200

300

400

500

600

Minimum radius of the available tracks [mm]Figure 1.9: Signal acceptance as a function of the threshold on the chargino decay radius
above which the chargino tracks are assumed to be fully reconstructed. A blue line shows
the signal acceptance for a wino with a mass of 400 GeV and a lifetime of 0.2 ns. A green
region corresponds to the track radius used in the ATLAS Run 1 analysis. A Yellow
region corresponds to the track radius used in this thesis.

1.9

Contents of this thesis

This thesis presents a significant improvement in the search for supersymmetric particles
using data recorded in 2015–2017 with the ATLAS detector. After introducing the ATLAS detector (Chapter 2), data and simulated samples used in this search (Chapter 3)
and object reconstruction technique (Chapter 4), the short-track reconstruction is discussed in Chapter 5. An event selection to reduce background with keeping signal eventsare discussed in Chapter 6. The Chapter 7 discusses the evaluation method of the remaining number of events after the selections by categorising the background sources.
Introducing the statistical procedure for an evaluation of the number of signal events
in Chapter 8 and discussing its systematic uncertainties in Chapter 9, the results areshown in Chapter 10. In the last Chapter 11, the interpretation of the results and future
prospects by a next-generation collider are discussed.

19Chapter 2

LHC and ATLAS detector
2.1

Large Hadron Collider

The Large Hadron Collider (LHC) [22] is a two-ring-superconducting-hadron accelerator
and collider installed in the 27 km tunnel used for Large-Electron-Positron (LEP) machine. It was designed to collide proton beams with a centre of mass energy of 14 TeV
and the peak luminosity of 1034 cm−2 s−1 .
The beam injecting to the LHC is successively accelerated: up to 50 MeV by Linac2,
1.4 GeV by Proton Synchrotron Booster (PSB), 25 GeV by Proton Synchrotron (PS),
450 GeV by Super Proton Synchrotron (SPS) and finally the LHC accelerates the beam
up to 7 TeV.
The LHC uses 1232 main superconducting dipole magnets based on NbTi cables asa bending magnet cooling to 1.9 K in superfluid helium, operating at fields up to 8.33 T
as a designed value. The LHC proton beam consists of 39 batches (bunch-trains), which
are filled 72 bunches with 25 ns spacing, resulting in 2808 bunches in total. The bunch
structure flexibly changes depending on the beam condition as summarised in Table 2.1.
Each bunch has 1.2 × 1011 protons as a designed nominal value, and then luminosity
becomes to 1034 cm−2 s−1 .
√The LHC started a pp run from 2010 to 2012 with s = 7 TeV (2010 and 2011)√
and s = 8 TeV (2012), which is called Run 1. After upgrading the accelerators and√detectors, the LHC restarted the operation from 2015 with s = 13 TeV, called Run 2.
The peak luminosity of the pp collision was designed to 1 × 1034 cm−2 s−1 as nominal
values, and 2.5 × 1034 cm−2 s−1 as ultimate values, while the peak luminosity in Run 2
reached 2.09 × 1034 cm−2 s−1 (Maximum average events per bunch crossing is 79.8) at
2017 run (Table 2.1). The maximum number of bunches was designed as 2808, while
2544 was recorded in 2017.
There are four large experiments using the LHC: ATLAS [23], CMS [24], ALICE [25]and LHCb [26], and each experiment put a detector at the collision points. The ATLAS
detector and the CMS detector are multi-purpose detectors, which aim for a precise
measurement of the SM and a discovery of the BSM particles. ALICE (LHCb) is designed
for a detailed study of nuclear physics (B-physics).
20

ValuesBeam energy [TeV]Luminosity ×103 [cm−2 s−1 ]Number of bunches
Bunch spacing [ns]Design7
1 (2.5)2808
252012 Run
4
0.8
1380
50

Run 2
6.5
2.1
2544
25

Table 2.1: The LHC beam parameters as a designed value, Run 1 value (2012) andRun 2 value.

2.2

ATLAS detector

A Toroidal LHC ApparatuS (ATLAS) is a general-purpose detector designed for coveringmuch of the new phenomena at TeV scale. For detection of rare processes from theenormous amount of hadronic collisions due to the high beam intensity, the detector
is required to be fast and radiation-hard, and to have a high granularity and a large
azimuthal angle coverage. The detector consists of subcomponents: inner detector,
solenoid magnet, calorimeter, toroidal magnet and muon spectrometer. Figure 2.1 showsa layout of the ATLAS detector.

Figure 2.1: Overview of the ATLAS detector [23]. It has 25 m height, 40 m length and7000 tonnes weight.

2.2.1

Coordinate

The ATLAS experiment uses a right-handed Cartesian coordinate system (x, y, z) where
its origin is set at the nominal pp interaction point, the x-axis points to the centre of
the LHC ring, the y-axis points upward, and z-axis directs to beam axis. Additionally,21

a spherical coordinate system (r, θ, ϕ) is used as defined√r =x2 + y 2(r)θ = arctan( zy )
ϕ = arctan
.
x

(2.1)
(2.2)
(2.3)

Hadron collider often uses the transverse observables, such as transverse momentum
pT = p sin θ. It is because the vector sum of the momentum at the transverse plane isconserved, while one at longitudinal planes is not conserved due to the fluctuation ofparton energy in protons. As related to it, particles produced in pp collisions are often
highly boosting along the z-axis. In this case, it is useful to use the rapidity (y) definedas()
E + pz1,(2.4)
y = ln2
E − pzwhere E and pz are the energy and longitudinal momentum, respectively. Since therapidity diﬀerence (∆y) is Lorenz-invariant, it is easy to grasp the event topology at
a mass-frame. Since the rapidity needs the mass information, the pseudorapidity (η),
which is a massless limit of the rapidity, as represented
)
(
θ
(2.5)
η = − ln tan
2
is normally used instead of θ. By using η and ϕ, the angular distance between two
particles is defined as√∆R = (∆η)2 + (∆ϕ)2 .
(2.6)

2.2.2

Inner detector

The ATLAS inner detector consists of three sub-detectors as shown in Fig. 2.2. Pixel
detector is aligned nearest to the beam pipe, and has an advantage to well-measured
the impact parameters. SCT detector covers the radii of 30–50 cm, and can find thecharged tracks together with the Pixel detector. TRT covers an outermost region in the
tracker up to 1 m, and possible to continuously measure the trajectory. Surrounding theinner detector, solenoid magnet provides a uniform magnetic field within the tracker tomeasure the transverse momentum of the charged particles.
In order to reduce the scattering with the material, the amount of material in the
tracker system is kept at low level as shown in Fig. 2.3, and is also precisely measured
using hadronic scattering [27].
Solenoid magnet
One of the aims of the tracker is to measure the momentum of charged particles. By
bending the charged particles with the strong magnetic field, the momentum can beevaluated from the curvature of the tracks. The superconducting solenoid magnet, which
22

Figure 2.2: The layout of the inner detector [27].

Figure 2.3: Radiation length as a function of η for the whole inner detectors [28]23Field (Tesla)surrounds the inner detector, provides a 2 T magnetic field along the beam axis andability of a momentum measurement. The coil of the magnet is made of Al-stabilised
NbTi, and the material thickness is kept at a low level (0.66 X0 radiation length) inorder to avoid a decrease of calorimeter performance.
The magnetic fields (Bz , BR and Bϕ ) are measured with the accuracy of less than
1 mT using 3D Hall cards as shown in Fig. 2.4.
2
1.5

Bz at R=1.058 m
Br at R=1.058 m

1

Bz at R=0.538 m
Br at R=0.538 m
Bz at R=0.118 m

0.5

Br at R=0.118 m

0
-0.5
-3

-2

-1

0

1

2

3
z (m)

Figure 2.4: Measured magnetic field provided by the solenoid magnet as a function of z
at three radii [23].

Pixel detector
The Pixel detector consists of four barrel-layers placed at radii of 33.5 mm, 50.5 mm,
88.5 mm and 122.5 mm, and three end-cap layers placed at z-positions of 495 mm,
580 mm and 650 mm. The barrel layers cover up to |η| = 1.9, and the end-cap layers
covers up to |η| = 2.5. The innermost barrel layer, called Insertable B-Layer (IBL) [28],
was installed after Run 1 in order to improve the tracking performance, then used from2015. The total radiation length in the Pixel detector is shown in Fig. 2.5.
The sensor consists of a 250 µm thick n-bulk with 47232 (144 columns × 328 rows)
readout pixels on the n+ -implanted side. Most of the pixels have the pitch of 50 ×
400 µm2 , the remaining ones have longer pitches of 50 × 600 µm2 , and the pixels in the
IBL have smaller pitches of 50 × 250 µm2 . Due to the technical requirement, some pixels
near the edge of the frond-end chips share the one readout with the other pixels, which
are called ganged-pixels. Although the sharing readout leads to ghost sensor hits, theambiguity of the ganged-pixels can be resolved using consistency with other pixel hits
at track reconstruction steps.
The charge deposit at each pixel (IBL) is measured as 8 (4)-bit dynamic range
information by counting the number of clocks where the signal is above a threshold,which is called Time-over-Threshold (ToT). The ToT information of each pixel is usedin the determination of the position passed by the charged particles.
24

The spatial resolution at each layer is 10 µm (r-ϕ) in both barrel and end-cap layers,
115 µm (z) in the barrel layers, and 115 µm (r) in the end-cap layers.

Figure 2.5: Radiation length as a function of η for the whole Pixel detectors [28]Semiconductor tracker
The semiconductor tracker (SCT) consists of micro-strip silicon sensors and surrounds
Pixel detectors. SCT consists of four barrel-layers placed at radii of 299 mm, 371 mm,
443 mm and 514 mm covering up to |η| = 1.1, and two end-caps containing nine disks
placed at z-position between 854 mm and 2720 mm covering up to |η| = 2.5. The sensors
are single-sided p-in-n sensors with 80 µm pitch, and two strip sensors are piled as apair. Each sensor in a pair is integrated with rotating by ±20 mrad each other, resulting
in a capability to measure the passed position along the strip orientation. The spatial
resolution is 17 µm in r-ϕ plane and 580 µm in the z (r)-direction for a barrel (end-cap)
layers.
Transition Radiation tracker
The transition radiation tracker (TRT) is a gas straw-tube detector using transition
radiation for particle identification. The drift tubes are made by multi-layer polyimide
film with coated by graphite-polyimide, aluminium and polyurethane, and are filled with
Xe-based gas mixture. Drifting electrons are collected by anode made of a tungsten wire
plated with gold, and the operational drift-time accuracy is 130 µm. The straw tubes
are of 4 mm diameter and align with a mean spacing of 7 mm. A transition radiatormaterial is a 19 µm-diameter polypropylene fibre for a barrel sector and a 15 µm thickpolypropylene radiator foil separated by a polypropylene net for an end-cap sector,
surrounding the straws.

25

The TRT barrel sector is located at radii from 554 mm to 1082 mm and covering up
to |η| = 1.0, and the end-cap sectors covers up to |η| = 2.0. The barrel sector contains 73
layers of straws for the radius direction, and the end-cap sectors contain 160 straw planes
along to beam-axis. Charged tracks traverse at least 36 straws in the barrel or end-cap
region, on the other hand, the tracks passing barrel-end-cap transition region (0.8 < |η|< 1.0) traverse the smaller number of straws of at least 22 straws due to the gap between
the barrel and the end-cap modules.
Since there are two mechanisms producing two diﬀerent amount of energy deposit (ionisation and transition radiation), two diﬀerent thresholds are used for recording the timeover thresholds. Higher thresholds are used to separate electrons and other particles.
Electrons emit higher energies as the transition radiation because of the large γ factor (p/m).
Electrons traversing the straw leave longer time over thresholds for the higher threshold,resulting in strong discriminants for the separation of electrons and other particles, especially pions.

2.2.3

Calorimeter

ATLAS has two types of sampling calorimeters for electromagnetic and hadronic measurements with a full ϕ-symmetry. Figure 2.6 shows the layout of the ATLAS calorimetersystem. Most parts of the calorimeter use liquid argon (LAr) as the active matter because it has a good linearity, a stability of response over time and radiation-hardness,while the barrel hadron calorimeter uses scintillating tiles as the active material becauseof the low cost.

Figure 2.6: The layout of the ATLAS calorimeter [23].

26Electromagnetic calorimeter
The electromagnetic (EM) calorimeter aims to measure the energies of electrons andphotons with a precise resolution. There are two structures: the barrel EM calorimeterand the end-cap EM calorimeters, that cover central region (|η| < 1.475) and forward
region (1.375 < |η| < 3.2), respectively. The detectors have an accordion-shaped structure to provide complete ϕ symmetry, are filled with liquid-argon as active matter anduse lead as an absorber. Radiation length is shown in Fig. 2.7.
The each EM calorimeter consists of three layers. The first layer is finely segmented
in η (∆η =0.003 for barrel, ∆η =0.003–0.006 for end-cap). This layer is designed fora good separation of the γ/π 0 . This layer is prepared in only a small η region (|η| <2.5). The second layer has a large radiation length (16 X0 at η =0) and collects large
fractions of the energy. The granularity of the cell is ∆η × ∆ϕ = 0.025 × 0.025. The
third layer collects the tail of the shower, and the granularity in η is twice coarser than
the second layer. A transition region (1.35 < |η| < 1.5) does not have the third layer.
Additionally a presampler, thin liquid-argon layer, is placed in front of the first layer:
all η coverage for barrel region and 1.5 < |η| < 1.8 for end-cap. This layer enables toestimate the energy loss before the calorimeter and improve the energy resolution of theelectromagnetic calorimeter.
Energy resolution measured using electron/positron test-beam as a function of energy
in the range from 10 GeV to 245 GeV at η = 0.687 is
σ(E)
10%
=√
⊕ 0.17%,E
E(GeV)

(2.7)

40
35

X0

X0

and linearity (Eobs /Ebeam ) is within ± 0.1% in the energy range from 15 GeV to 180 GeV.
Layer 3Layer 2
Layer 1
Before accordion

40
35

30

Layer 3Layer 2
Layer 1
Before accordion

30

25

25

20

20

15

15

10

10

5
0
0

45

5
0.2

0.4

0.6

0.8

1

0

1.2
1.4
Pseudorapidity

(a)

1.6

1.8

2

2.2

2.4

2.6

2.8
3
3.2
Pseudorapidity(b)

Figure 2.7: Radiation length in the electromagnetic calorimeter as a function of η for(a) barrel region and (b) end-cap region [23].

27Hadronic calorimeter
The hadronic calorimeter consists of three types of sub-detectors: the tile calorimeter,
the liquid-argon hadronic end-cap calorimeter and the liquid-argon forward calorimeter.
Interaction length of the hadronic calorimeter is shown in Fig. 2.8.
Tile calorimeter is located outside the EM calorimeter in the barrel region (|η| < 1.0),
and in the extended barrel region (0.8 < |η| < 1.7). It is a sampling calorimeter using
steel as the absorber and scintillating tiles as active material. Each barrel consists of 64
modules of ∆ϕ ∼0.1, and each module forms periodic structure with a ratio of 4.7:1 forsteel plates and scintillating tiles. Interaction length is about 7.4 λ. A fractional energy
resolution for pions at |η| = 0.35 is
σ(E)
56%
⊕ 6%.
=√
E
E(GeV)(2.8)

The hadronic end-cap calorimeter (HEC) is located behind the end-cap EM calorimeter, covering 1.5 < |η| < 3.2. It is a sampling calorimeter using copper as absorberand filled with liquid-argon as active material. The material was chosen for radiation
hardness. HEC consists of two wheels in each side, and each wheels consists of 32 modules. The thickness of copper plates of the rear wheels is double of the front wheels,
resulting in smaller sampling fractions than the front wheels. A readout cell size of each
module is ∆η × ∆ϕ = 0.1 × 0.1 for |η| < 2.5 and 0.2 × 0.2 for larger |η|. An energy
resolution using the electromagnetic end-cap calorimeter and the HEC using π − (π + )test-beam in 2002 isσ(E)
85 (82)%=√.
E
E(GeV)(2.9)

The forward calorimeter (FCal) is located at forward region, with a coverage over|η| < 4.9. It consists of three modules. The first module (FCal1) is optimised forelectromagnetic measurements and made of copper to optimise the resolution. Other
two modules (FCal2 and FCal3) are optimised for hadronic interactions and made oftungsten to minimise the lateral spread of hadronic showers. All modules use LAr as
active matter. A shielding plug is installed behind FCal3 to suppress backgrounds in themuon system. The thickness of the FCal is approximately 10 λ. An energy resolution
measured by test-beam in 2003 for electrons is
σ(E)
29%
⊕ 4%,
=√
E
E(GeV)(2.10)

70%
σ(E)
=√
⊕ 3%.
E
E(GeV)(2.11)

and for pions

28

Interaction lengths

20
18
16
14
12
10

HEC3
Tile3

HEC2

6 Tile2

HEC1

8

4 Tile1
2

0
0

0.5

1.5

FCal2

HEC0

EM calo
1

FCal3

2

2.5

FCal1
3

3.5

4
4.5
5
Pseudorapidity

Figure 2.8: Interaction length in the calorimeter as a function of η [23].

2.2.4

Muon system

The muon system consists of four sub-detectors: Two are for triggering and others arefor precision tracking as shown in Fig. 2.9. There is a gap at |η| ≈ 0 due to the serviceof the solenoid magnet, the calorimeter and the inner detector. The maximum gap is
1–2 m, corresponding to |η| < 0.08 for high pT muons. Therefore, a muon passing tothis gap cannot be reconstructed as a muon spectrometer track.
Muon pT is measured by bending the muon using the air-core toroid magnets locating
inner of the muon spectrometers.
Toroidal magnet
Magnets for muon tracking consists of one barrel toroid and two end-cap toroid magnets, which consist of eight coils made of Al-stabilised Nb/Ti/Cu and surrounding thecalorimeters as shown in Fig. 2.10 (a). They are aligned to cover whole η region up to|η| < 2.7. A magnetic field∫ is optimised to bend any muons in the acceptance, and theintegrated field strength ( Bdl) is 1.5 T·m to 5.5 T·m for barrel region and 1 T·m to
7.5 T·m for end-cap region, while transition regions (1.4 < |η| < 1.6) has lower bending
power as shown in Fig. 2.10 (b).
Precision tracking
Monitored drift tube (MDT) is the main part of the muon system for precise muontracking. MDT consists of three layers (r = 5 m, 7.5 m and 10 m) for barrel, andfour layers (|z| = 7.4 m, 10.8 m, 14 m and 21.5 m) for end-cap region, covering |η| <2.7 except for the innermost layer in the end-cap region. Each MDT chamber has two
multi-layers, which consists of three or four tubes, and has four optical rays to monitor
alignment of the tubes. Tubes are made of a pressurised aluminium drift tube with a
29

8
6
4
2

Transition region∫B dl (T ⋅ m)

Figure 2.9: A layout of the muon system [23]. The three letters in each layer refer tobarrel (B), end-cap (E), inner (I), middle (M), outer(O), large (L) and small (S).

Barrel region

φ=π/8

End-cap
region

φ=0

0
-2
0

0.5

1

1.5

2

2.5

|η|

(b)

(a)

Figure 2.10: (a) Magnet systems of the ATLAS detector. Outer red components are
toroidal magnets [23]. (b) A magnetic field of toroidal magnets [23].

30diameter of 30 mm, Ar/CO2 gas and gold-plated tungsten-rhenium anode wire. Eachtube is aligned along ϕ for both barrel and end-cap, then have a good resolution 35 µm
for z-position.
MDTs in the first layer of end-caps in a high η region (2 < |η| < 2.7) are replaced
by Cathode strip chamber (CSC) in order to withstand a high counting rate. CSC
on each end-cap side consists of eight big chambers and eight small chambers whichcontain four CSC planes. CSC is multiwire proportional chambers having two oriented
cathodes. One cathode is segmented perpendicular (bending plane) to the wires, andother is parallel (non-bending plane) to the wires with coarser pitches, resulting in spatial
resolution of 40 µm for r, and 5 mm for ϕ.
Triggering
Resistive plate chamber (RPC) is a gas parallel electrode-place detector. Two plates areparallel to each other at a distance of 2 mm with electric field of 4.9 kV/mm, then thesignal is read out via two orthogonal sets of strips for η and ϕ with a pitch of 23–35 mm,
resulting in spatial resolution of 10 mm for z, 10 mm for ϕ and good time resolution of
1.5 ns. Information about ϕ position is also used in the precise tracking with MDT’s
precise r-position information. RPC consists of three layers: two layers sandwich thesecond layer of MDT, and one layer is located outer the third layer of MDT, and covering|η| < 1.05.
Thin gap chamber (TGC) is a multi-wire proportional chamber with small wire-tocathode distance (thin gap) and highly quenching gas mixture of CO2 and n-C5 H12 ,leading to a good time resolution of 4 ns. The r-position is measured by wire groups,
while the ϕ-position is measured by the radial strips. For a requirement on a good
granularity at a high η region, the size of wire groups varies as a function of η, resulting
in a good granularity of 2–3 mrad from the interaction point. TGC consists of four layers:
the one layer (triplet) is in front of the second MDT wheel and two layers (doublets) arebehind the second MDT wheel, while the fourth layer (doublet) is in front of the first
MDT wheel, covering 1.05 < |η| < 2.4. TGCs give complemental information about the
non-bending plane alternative to MDTs.

2.2.5

Luminosity detector

Luminosity measurement using Cerenkov Integrating Detector-2 (LUCID-2) [29] is aluminosity detector installed in 2014 as an upgraded detector from LUCID. LUCID-2
modules are installed at both end-cap sides, and each module consists of 16+4 photomultipliers: 16 photomultipliers with thin quartz windows as Cherenkov medium arearranged around the beam-pipe with a distance of 13 cm from the beam line and 17 m
away from the interaction point, and other four photomultipliers using quartz fibres as
Cherenkov medium are put 1.5 m away from the LUCID detector. The calibration andmonitoring the gain stability was done using 207 Bi sources, LED or LASER signals.

31

The average luminosity is calculated from
Lave =

fLHC · nb · µvis,
σ vis

(2.12)

where fLHC is the LHC revolution frequency (11 kHz), nb is the number of colliding
bunches (∼2500), µvis is a visible number of interactions in a bunch and σ vis is thevisible cross-section. The luminosity can be determined by measuring µvis and σ vis . µvis
is measured by counting the number of signals above threshold in 60 seconds, assumingthat the hit-counts follow a Poisson distribution, while absolute σ vis is determined invan der Meer (vdM) fills [30] profiling beam densities [31].

2.2.6

Trigger and data acquisition system

The Trigger and Data Acquisition (TDAQ) system consists of two subsystems: the firstlevel trigger (L1) and the high-level trigger (HLT) [32].
L1 is a hardware-based trigger and filters the event from 40 MHz to 100 kHz. A
central trigger processor in L1 decides the accept/reject using the information from thetwo logics (L1Calo and L1Muon), which handle the output of the calorimeter and themuon spectrometer respectively, then sends the accept-flag and Region-of-Interest (RoI)
information to HLT. L1Calo trigger aims to identify electron/photon, hadronic-τ , jets
and the missing transverse momentum. To eﬃciently and fast identify high energy
objects, L1Calo segments the calorimeter cells into (η × ϕ) ≈ (0.1 × 0.1) blocks, called
trigger-tower, and calculate the energy, coordinate, object type and isolation based on
the energy deposit in each trigger-tower. L1Muon trigger aims to identify high pTmuons from the interaction point and detects them by requiring a coincidence of hits inthe diﬀerent layers in RPC and TGC within the requiring curvature.
HLT is a software-based trigger and filters the event from 100 kHz to 1 kHz. Unlike
the L1 trigger, HLT can use full information in the detector, that is fine granularity
segmentation in the calorimeter, precise tracking in the muon spectrometer and thetracking information from the inner detector within RoI region, as a similar level as theoﬄine reconstruction. The events accepted by the HLT are transferred to permanentstorage and are applied a time-consuming object-reconstruction algorithm for physics
analyses.

32

Chapter 3

Data and simulated samples
3.1

Data

This analysis is based on the pp collision data collected with the ATLAS detector at the√
LHC at s = 13 TeV from 3rd June 2015 to 26th November 2017. Data quality wasmonitored at all times, then the data where the detector did not work at their desired
performance were filtered out from the data for physics analyses.

3.1.1

Luminosity

The instantaneous luminosity was grown year by year as shown in Fig. 3.1. The peakluminosity in three years is 2.09 × 1034 cm−2 s−1 , which nearly reaches designed ultimate
values (2.5 × 1034 cm−2 s−1 ). The combined integrated luminosity in 2015–2017 being
satisfied with good quality requirements mentioned above is 79.8 fb−1 , and the uncertainty is 2.0%. It is derived, following a methodology similar to that detailed in Ref. [31],from calibrations of the luminosity scale using x-y beam-separation scans performed inAugust 2015, May 2016 and July 2017.

3.1.2

Pile-up

When instantaneous luminosity increases, the number of pp interactions per bunch crossing also increases. Since the rate of the target process is generally rare, most of the pp
interactions are not of interest, and they are called pile-up. Figure 3.2 shows a distribution of the number of pp interactions per bunch crossing in the data in 2015–2017.
The mean number of interactions per crossing in 2017 data is much higher than theprevious two years due to the high instantaneous luminosity operation. High luminosity operation increases the production rate of target signals, while degrades the physics
performance, especially tracking performance. The quantitative eﬀects are discussed inSec. 5. The bump around µ = 60 is due to luminosity levelling, which aims to avoid
that instantaneous luminosity exceeds 1.5 × 1034 cm−2 s−1 and that the serious pile-up
aﬀects the trigger rate.

33

ATLAS Online Luminosity
2011 pp2012 pp2015 pp2016 pp2017 pp2018 pp60
50

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

40
30
Initial 2018 calibration

Delivered Luminosity [fb-1]

70

20
10
0
Jan

Apr

Jul

Oct
Month in Year350

∫Ldt=86.3 fb-1

ATLAS Online, 13 TeV

2015: <µ> = 13.4
2016: <µ> = 25.1
2017: <µ> = 37.8
Total: <µ> = 31.9

300
250
200
150
100

2/18 calibration

Recorded Luminosity [pb-1/0.1]

Figure 3.1: Cumulative luminosity in each year as a function of time.

50
0
0

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing

Figure 3.2: The luminosity-weighted distribution of the mean number of interactions per
bunch crossing for 2015–2017 pp collision data.

34

3.2

Simulated samples

To validate the analysis method, Monte Carlo (MC) simulated samples are used. Samples
were produced in some stages. At first, target elementary processes were created by event
generators, which calculate a matrix element in pp collisions, then hadronic particles were
simulated to reproduce parton showering and hadronisation. Second, a realistic responseof the detector was simulated with Geant4 [33–35], which simulates interactions ofparticles in processed events. In order to emulate pile-up eﬀects correctly, minimum bias
events were overlaid to each simulated samples, where minimum bias events were added
to not only the same bunch crossing but also before and after the bunch crossing in order
to emulate the eﬀects from interactions in other bunch crossings. Overlaid minimum
bias events were generated using Pythia 8.210 [36] and EvtGen (v1.2.0) [37] with
NNPDF2.3 LO PDF set [38] with A3 tune [39]. The number of overlaid minimum bias
events in each bunch crossing was roughly set to match the observed pile-up distribution,and they were precisely tuned by applying an event-weight at the analysis step. After
digitisation of Geant4 simulation outputs, the particle reconstruction algorithms as
described in Sec. 4 were applied for simulation samples as with the observed data. In
order to minimise a diﬀerence between observed data and MC simulated samples, several
corrections are applied to MC.
This section summarises the details of the event generator, parton showering and thehadronisation of the simulated samples.

3.2.1

Signal Monte Carlo sample

A mass spectrum of wino LSP models was calculated using the ISASUSY ver.7.80 [40]assuming minimal AMSB model with tan β=5, the sign of the higgsino mixing term (sign(µ))
set to be positive and the universal scalar mass set to m0 = 5 TeV. Gravitino mass (m3/2 )was selected to become charged wino mass to 91 GeV, 200 GeV, 300 GeV, 400 GeV,
500 GeV, 600 GeV, 700 GeV, 800 GeV and 900 GeV. For a mass spectrum of higgsino
LSP models, charged higgsino masses were set to be 95 GeV, 100 GeV, 120 GeV, 140 GeV,
160 GeV and 200 GeV as a model parameter, and the neutral higgsino masses are set
to appropriate values from the theory [14, 41]. Masses of other particles were set to be
40 TeV to be decoupled from the other particles. The signal samples were generated withup to two extra partons in the matrix element using MadGraph5 aMC@NLO 2.6.2 [42]at leading order (LO) interfaced to Pythia 8.230 [36] for parton showering and hadronisation. The NNPDF2.3 LO [38] parton distribution function (PDF) set was used with
A14 tune [43]. A decay from chargino to neutralino was simulated in the Geant4. The
decay branching ratio of charginos were set to±0Br(χ̃1 → χ̃1 π) = 100.0 (95.5)%±0Br(χ̃1 → χ̃1 eνe ) = 0.0 (3.0)%±0Br(χ̃1 → χ̃1 µνµ ) = 0.0 (1.5)%,35

where the values in parenthesis are for higgsinos. A secondary particle from chargino
decay has quite a small momentum and is hard to be reconstructed as the tracks inthe current tracking configuration. The signal acceptance is not aﬀected from the decaybranch. The eﬀects from the diﬀerence of branching ratio between wino and higgsino
were confirmed to be negligible by comparing both samples.
In order to reduce the meaningless events in the simulated samples, which are nevermiss were dropped before
triggered and left in the analysis dataset, events with low ET
missGeant4 simulation. A threshold of ET for the drop of events was set to 60 (50) GeV forwino (higgsino). The typical filter eﬃciencies were 20–50% for their mass. The thresholds
miss selection in kinematical selection (Sec. 6) andare much lower than a threshold of ET
the events dropped by this filter were confirmed not to pass kinematical selection.
Cross-sections were calculated using Resummino 2.0 [44–48] at NLO +NLL level.
Figure 3.3 shows calculated cross-sections and uncertainties using CTEQ6.6 and MSTW2008
PDF sets at each chargino mass points. The final cross-sections and the uncertainties
used in this analysis were evaluated from above two cross-sections from diﬀerence pdf
sets as described at Ref. [49]. The central values were set to a centre of two uncertainties band, and the uncertainties were set to a diﬀerence between the central values
and a maximum/minimum of uncertainty band as shown in Fig. 3.3, and summarisedin Tables 3.1 and 3.2. For higgsinos, there are two neutralinos having the same mass
because of the assumption of the decouple limit (µ ≪ M1 , M2 ). The same production
− 0
+ 0
− 0
+ 0
cross-sections as χ̃1 χ̃2 and χ̃1 χ̃2 are assigned to χ̃1 χ̃1 and χ̃1 χ̃1 , respectively.
The lifetime of charginos strongly reflects from the signal model property and tightly
relates with the signal acceptance in this analysis. It is necessary to precisely evaluate
the signal discovery sensitivity as a function of the lifetimes. It is not eﬃcient to produce
chargino samples with precisely binning of the lifetime, because in most cases, a chargino
in small lifetime samples is not reconstructed as tracks, then it is out of acceptance. In
order to keep statistical uncertainties at a suﬃciently low level, the chargino samples
were produced by setting the lifetime to be large enough to keep signal acceptance, andthen special weights were applied to be normalised samples to the correct pdf as follows
w(τχ̃± ) =1

f (τ ) =f (τχ̃± )1

f (τM C )
(
)
1
t
exp −
,
τ
τ

(3.1)
(3.2)

where t is a proper time of charginos for each event in simulated samples, τχ̃± is a1
lifetime of a target chargino and τM C is a lifetime in produced simulated samples. When
there were two charginos, the events were applied to each weight respectively (w =w(τχ̃± ,1 ) · w(τχ̃± ,2 )). Lifetime of the produced samples are 0.2 ns, 1.0 ns, 4.0 ns and11
10.0 ns for wino and only 0.3 ns for higgsino. Since target lifetime for higgsino models
are quite small, only one higgsino sample with small lifetime was created for each masspoints. In order to emulate the signal samples with not-produced lifetime values (e.g.
0.4 ns), some samples with the same masses were merged, then treated as one samples,
where the number of merged samples was limited to be at most two samples whose36

lifetime is near the target signal to avoid a large statistical error from large extrapolation
weights.

3.2.2

Monte Carlo samples of the Standard Model backgroundThe simulated samples of the SM processes are used for validation of method, a fraction ofremaining background components and some systematic uncertainties related to tracking
properties. This analysis uses weak boson process (pp → W , Z, W W , W Z and ZZ),
t-quark production process (pp → t, tW and tt̄) and multi-jet events (pp → jet + jet).
The cross-section of each process is summarised in Table 3.3.
Weak boson production
Weak boson production samples, containing W , Z and V V , were generated by
Sherpa v2.2 [50] with NNPDF3.0 NNLO [51] PDF set, including parton showering and hadronisation. Each process was calculated at diﬀerent accuracy for thenumber of additional partons as summarised in Table 3.4.
Cross-sections of single boson processes (W and Z) were calculated at NNLO accuracy in αs using FEWZ [52]. Cross-sections of di-boson processes were calculatedusing Sherpa with the accuracy level of each production.
t-quark production
tt̄ and single-t production with s-channel and W -boson-associated channel weregenerated by Powheg-Box 2 [53–56] with NNPDF3.0 NLO PDF set at NLO withhdump parameter set to 1.5 mtop , interfaced to Pythia 8.230 with NNPDF2.3 LOwith A14 tune. B-hadron decay was controlled by EvtGen (v1.6.0) [37] instead ofPythia. Single-t production with t-channel was generated with a similar condition
to other t samples except using NNPDF3.04f [51] PDF set to set to four-flavour
scheme and except using MadSpin [57] for t-quark decay to correctly model theirspins.
The cross-section of the tt̄ process was calculated at the NNLO+NNLL soft gluon
resummation using Top++v2.0 [58] assuming mt = 172.5 GeV. A cross-section of
single-t W -associated channel was calculated at approximate NNLO (NLO+NNLL) [59].
Cross-sections of single-t s/t-channels were calculated at NLO using Hathor v2.1 [60][61].
Multi-jet events production
Multi-jet process and the cross-sections were generated by Pythia 8.186 replacing
B-hadron decay by EvtGen (v1.2.0) with NNPDF2.3 LO with A14 tune.

37

Cross section [pb]10

χ+χ- CTEQ6.6

χ+χ- MSTW2008

χ+χ- , final

χ+χ0 CTEQ6.6

χ+χ0 MSTW2008

χ+χ0, final

χ- χ0 CTEQ6.6

χ- χ0 MSTW2008

χ- χ0, final

1 1
1 1
1 1

1 1
1 1
1 1

1 1
1 1
1 1

1
10−1
10−2
10−3
100 200 300 400 500 600 700 800 900
Wino mass [GeV]Cross section [pb](a)χ+χ- CTEQ6.6

χ+χ- MSTW2008

χ+χ- , final

χ+χ0 CTEQ6.6

χ+χ0 MSTW2008

χ+χ0, final

χ- χ0 CTEQ6.6

χ- χ0 MSTW2008

χ- χ0, final

1 1
1 2
1 2

1 1
1 2
1 2

1 1
1 2
1 2

1

10−1

100 120140 160

180 200

220 240

Higgsino mass [GeV](b)

Figure 3.3: Calculated cross-section of chargino pair production. Left two points in eachmass points are calculated with CTEQ6.6 (left) and MSTW2008 (centre) pdf set. Right
points in each figures are final nominal value and uncertainties used in this analysis. (a)Wino LSP case. (b) Higgsino LSP case.

38

χ̃±
1 mass [GeV]
91
91
91
200
200
200
300
300
300
400
400
400
500
500
500
600
600
600
700
700
700
800
800
800
900
900
900

Process
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
− 0
χ̃1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
+ 0
χ̃1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
− 0
χ̃1 χ̃1
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃1
0
χ̃−
1 χ̃1

σNLO+NLL [pb]
16.5
19.6
12.5
0.89
1.15
0.62
0.184
0.252
0.122
0.056
0.080
0.035
0.021
0.031
0.01260.00880.01350.00520.00410.00640.00230.00200.00320.00110.00100.00170.00056

Rel. unc.
2.6%
2.0%
4.1%
4.0%
3.4%
5.5%
4.9%
4.4%
6.3%
5.6%
5.4%
7.0%
6.3%
6.2%
7.6%
6.8%
6.8%
8.2%
7.3%
7.3%
8.9%
7.7%
7.7%
9.5%
8.2%
8.0%
10.3%

Table 3.1: Cross-section for wino direct pair production.

39

χ̃±
1 mass [GeV]
95
95
95
100
100
100
120
120
120
140
140
140
160
160
160
200
200
200

Process
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃2
0
χ̃−
1 χ̃2
± ∓
χ̃1 χ̃1
0
χ̃+
1 χ̃2
0
χ̃−
1 χ̃2
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃2
0
χ̃−
1 χ̃2
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃2
− 0
χ̃1 χ̃2
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃2
0
χ̃−
1 χ̃2
∓
χ̃±
1 χ̃1
0
χ̃+
1 χ̃2
0
χ̃−
1 χ̃2

σNLO+NLL [pb]
3.6
4.2
2.6
2.9
3.4
2.2
1.57
1.79
1.09
0.91
1.04
0.61
0.56
0.65
0.37
0.25
0.29
0.16

Rel. unc.
2.9%
2.1%
4.2%
3.0%
2.2%
4.3%
3.2%
2.4%
4.6%
3.5%
2.7%
4.9%
3.7%
2.9%
5.1%
4.1%
3.4%
5.5%

Table 3.2: Cross-section for higgsino direct pair production.
ProcessW
ZZ
tt̄
single t, s-channel
single t, Wt-channel
single t, t-channel
VV
Loop-induced V V
EW V V jj
Multi-jet inelastic

Decay
ℓν
ℓℓ
νν
inclusive
leptonic
inclusive
leptonic
inclusive
inclusive
inclusive
inclusive

Order
NNLO
NNLO
NNLO
NNLO+NNLL
NLO
NLO+NNLL
NLO
NLO
LO
LO
LO

Cross-section
60 nb
6.3 nb11 nb
832 pb
3.4 pb72 pb
70 pb
100 pb
2.4 pb0.24 pb
77 mb

Table 3.3: Cross-sections of the SM processes.
Process
V (W and Z)
V +jj (VBF)VV
Loop-induced V V
EW V V jj
t quark
Multi-jets

Generator (PDF)
Shower/Hadronisation (PDF)
Sherpa (NNPDF3.0 NNLO)
Sherpa (NNPDF3.0 NNLO)
Sherpa (NNPDF3.0 NNLO)
Sherpa (NNPDF3.0 NNLO)
Sherpa (NNPDF3.0 NNLO)
Powheg (NNPDF3.0 NLO, (4f))
Pythia 8 (NNPDF2.3 LO, A14 tune)
Pythia 8 (NNPDF2.3 LO, A14 tune)

accuracy
NLO(0,1,2p), LO(3,4p)
LO(0,1,2p)
NLO(0,1p), LO(2,3p)
LO(0,1p)
LO(0p)NLO
NLO

Table 3.4: Summary of the generator configuration of the SM processes.
40

Chapter 4

Object reconstruction
This section discusses the way of the reconstruction of physics objects used in this analysis, which are tracks, vertices, jets, electrons/photons, muons and a missing transverse
momentum.

4.1

Track

Passing through a sensor of the inner tracker, a charged particle leaves an energy depositin each sensor. By connecting the several energy deposits, called “hits”, a trajectory of
the charged particle can be reconstructed. A reconstructed trajectory is called a track.
Tracks have many information about the charged particles: a momentum, a direction
and an impact parameter. Tracks have better momentum resolution, pointing resolution
and a separation power from pile-up than calorimeter information.
There are two tracking strategies [62]: Inside-out and Outside-in. Most of the tracks
are reconstructed in the former one, while the latter strategy recovers charged particles
produced in flight from the interation points.

4.1.1

Inside-out track reconstruction

Inside-out strategy consists of four steps: the space-point creation, the seed-track creation, the ambiguity resolver and the TRT extension. In the earlier three steps, thetracks are created using only the silicon detector (Pixel and SCT). Then, the tracks are
extrapolated to TRT detectors and merge the associated TRT hits.
Space-point creation
First, neighbouring silicon-sensor hits are merged into a cluster in order to determine a three-dimensional position of a charged particle passing across the sensors byusing a connected component analysis (CCA) technique [63]. The cluster having
a three-dimensional position is called a space-point. The position of each pixel
sensor on a module is known, it is, therefore, straight forward to calculate a threedimensional position. On the other hand, the space-points of SCT sensors, which
are strip-type sensors, are constructed from the binded strips.
41

In a dense environment, clusters from two charged particles are close each other andoften merged as one space-point. In the case that the one space-point is shared bymultiple tracks, the neural-network technique ( [64–66]) is used in order to identify
the split of the space-point and to estimate the position and the uncertainty foreach sub-clusters.
Seed-track creation
A seed-track is built by the combination of at least three space-points requiring
several constraints on track parameters to reduce the number of seed-track candidates. Here three space-points are sequentially selected from only the SCT detector,
only the Pixel detector and both Pixel and SCT detector, then an additional one
space-point on the trajectory is required in order to reduce fake seed-tracks [67].
A seed-track is extrapolated using a combinatorial Kalman filter [68] and incorporates the space-points on the trajectory. In order to improve the purity of track
candidates, merged hits are required to be consistent with the track trajectory.
Ambiguity resolver
The track candidates still contain many fake-tracks. In order not to consume
unnecessary compute resources, the fake tracks are suppressed by the following
strategy. First, track candidates are re-fitted with the detail material information.
Although the fit-quality evaluated in the re-fitting provides a means of identifying
fake tracks, the selection by only this variable is not suﬃcient for a reduction of faketracks. As a second step, the goodness of track-candidates are evaluated by scoring
the track-candidates using likelihood technique, which uses the several variables
related to the tracks, e.g. the momentum, fit-quality, the number of associatedhits and the number of holes1 . After scoring all track-candidates, seed-tracks aresequentially regarded as track objects in the order of the score, where a shared hit
is defined by checking if the hit in the track-candidate is used in the already-defined
track objects. If the number of shared hits of a track-candidate is more than one,the track-candidate is rejected.
TRT extension
After the track reconstruction only with silicon hits, TRT hits are added to thetracks. By extrapolating the track to TRT detectors, the near TRT hits are added as TRT-hits candidates. Here in order to reduce the bad extrapolation withwrongly assigned TRT hits, a track without the extrapolation is kept if the scoreof it is higher than the extrapolated track.

4.1.2

Outside-in track reconstruction

Inside-out algorithm can reconstruct most of the charged particles from the interaction
points. However, it assumes that charged particles leave the suﬃcient number of siliconhits, therefore it cannot work in the cases that silicon hits are intrinsically missing: e.g.
1

A hole is defined as a missing expected hit on the trajectory42for the secondary particles from meta-stable particles and photon conversion. In orderto reconstruct such tracks, TRT segments are used for seeding instead of hits in silicondetectors. Since the TRT detector consists of straw tubes, the space-points, which havethree-dimensional position information, cannot be defined. Therefore, in the TRT case,the two-dimensional-planes, r-ϕ for a barrel region and r-z plane for an end-cap region,
are used for the seed finding, then trajectory patterns are detected by using Houghtransformation technique [69].
After finding the patterns, they are re-fitted using drift time, then they are extrapolated into silicon detectors to find the associated silicon hits.

4.2

VertexA position of a pp interaction, called vertex, is reconstructed using tracks. Especially, thehardest vertex, which has the highest sum of squared momenta of associated tracks in allvertices, is called primary vertex. The vertex reconstruction [70–72] consists of seeding
and fitting. A vertex seed is selected as the mode of z coordinate of the reconstructed
tracks. Then, the vertex position is determined by an adaptive vertex fitting algorithmwith an annealing procedure [73]. After iterative fitting with the vertex compatibility,
the incompatible tracks with the vertex are removed. Until all tracks are assigned toany vertices, the procedure is repeated.

4.3

Jet

After a quark or a gluon is produced, it hadronises and is observed as a group of
hadronic particles, which is called jet. Jets are reconstructed mainly from the calorimeter
information.
First, the cells in the calorimeter are merged using the topological clustering algorithm [74], where the used cells are required to have significant energies above a noise
threshold. Second, jets are reconstructed using the anti-kT algorithms [75] with radiusparameter R = 0.4 as implemented in the FastJet package [76]. Jets are reconstructed
as the electromagnetic scale. In order to match the jet energy to the truth-level scale,jets are calibrated [77] with pileup mitigation [78].

4.4Electron and photon

First, a cluster of calorimeter cells is formed by the topological clustering algorithms
as described in [74] as well as a jet case. Then tracks associated to the cluster are
searched for. If associated tracks which come from an interaction point is found, thecluster is identified as an electron. The detail of cluster-track matching in electronreconstruction is given in Ref. [79]. Tracks associated with electrons are re-fitted using
Gaussian Sum Filter [80] that treats the bremsstrahlung more appropriately. Then the
supercluster algorithm [81] is performed to merge the neighbourhood clusters in order to43

catch the radiated bremsstrahlung photons. If there are no associated tracks, the cluster
is identified as an unconverted photon. And if there are associated tracks identified as
coming from a photon conversion, the cluster is identified as a converted photon. The
detail of photons reconstruction is given in Ref. [82, 83]. In this analysis, photons aremiss calculation. Electron and photon energy calibration is described
used only in the ET
in Ref. [84].
Reconstructed electrons contain the fake electron which does not come from the trueelectron. To reject such fake electrons, four identification criteria (VeryLoose, Loose,Medium and Tight) are defined, where electrons in a later criterion must pass an earlier
criterion, and the earlier former criterion has higher eﬃciency and lower fake reduction.
Using likelihood techniques based on the several variables, true electrons are discriminated from fake electrons as described in Ref. [85]. This analysis uses electrons labelled as“Loose” unless otherwise noted because electrons are required to be tightly vetoed. The
electron and photon identification eﬃciencies are summarised in Ref. [86] and Ref. [83],respectively.

4.5

Muon

A muon is reconstructed using an inner-detector track (ID-track) and a muon-spectrometer
track (MS-track). An MS-track is reconstructed at each sub-detector as a segment.
Then, extending the segments, the track-candidate is created.
A muon is reconstructed based on various algorithms. Four muon types are defined
as follows. (1) Combined muons are formed using hits from both the ID-tracks andMS-tracks. (2) Segment-tagged muons are formed using ID-tracks and muon segment in
the MDT or CSC chambers. (3) Calorimeter-tagged muons are formed using ID-tracks
and an energy deposit in the calorimeter compatible with the muons. (4) Extrapolatedmuons are formed using only MS-tracks. This analysis uses only Combined muons.
Muon reconstruction performance in Run 2 is summarised in Ref. [87].
As well as electrons, to reduce fake muons, muon-identification criteria (Ref. [87])are applied. There are three identification criteria (Loose, Medium and Tight) as withelectron identification criteria. These qualities are defined based on the muon types, q/p
significance, momentum balance between ID-tracks and MS-tracks, χ2 /ndf in the fit andthe number of hits in muon spectrometer. This analysis uses “Medium” quality unlessotherwise noted.

4.6

Missing transverse momentum

miss ) is a sum of the momenta of undetectable particles.
Missing transverse momentum (ETmiss
The SM particles observed as ET are only neutrinos. On the other hand, some new
miss , e.g. neutralino, so E miss has good separation power between
BSM particles create ET
Tthe SM and the BSM.
miss is reconstructed using all objects described above (hard objects) and the otherET

44

contribution (soft objects) [88, 89] as follow∑ # jet∑ #»∑ # µ»∑ # γ» # »»#»ET = −
pT −
peT −
pT −
pT − ETsoft ,
jets

muons

electrons(4.1)

photons

where overlaps between diﬀerent objects are resolved by the appropriate treatments foreach objects in order to avoid the double-counting the same momentum (e.g. electron
and jets).
The soft term is aiming for the low pT particle contribution. The soft term is calculated using inner-detector tracks which are not associated with the hard objects asfollows∑ # »# »ETsoft =ptrack
,(4.2)
Ttrackswhere tracks are required to have a good quality and comes from the primary vertex
in order to reject fake-tracks and pileup tracks. These requirements make the soft term
pileup-tolerant.

45

Chapter 5

Track-reconstruction fordisappearing signature
The standard ATLAS tracking algorithm is designed to reconstruct trajectories of stablecharged particles. The track reconstruction is the most time-consuming part of thereconstruction-algorithm chain. The fewer requirements on the number of Pixel hits inthe track reconstruction increase the number of unphysical tracks, which results in ahigher demand for compute resources. Moreover, the typical charged particles measured in the ATLAS detector have long lifetimes enough to fly through the inner detector. Therefore, the standard track-reconstruction algorithm requires a long trajectoryand is not suitable for the particles targeted in this search due to the quite low trackreconstruction eﬃciency. The new special track reconstruction, which is called “Pixel
tracklet” reconstruction, is designed to be enabled to reconstruct meta-stable charginoswith lifetimes considered in this search. Hereafter, a track reconstructed by the pixel
tracklet reconstruction is called a “pixel tracklet” or just “tracklet”, and a track reconstructed by the standard track-reconstruction algorithms described in Sec. 4.1 is called
a “standard track”.

5.1

Algorithm

The algorithms of the pixel tracklets are based on the standard tracking described inSec. 4.1. The main diﬀerences between the standard track reconstruction and the pixel
tracklet reconstruction are the parameters and the type of used hits in the track reconstruction. A summary of the diﬀerences in the configuration between two trackreconstructions is shown in Table 5.1, where “hole”-hit is defined as a missing expected
hit on the trajectory, and “shared”-hit is defined as a hit which is also used by othertracks. The number of required hits in the pixel tracklet reconstruction is only four, andthis is a much looser requirement than the standard track reconstruction which requires
seven hits. As mentioned above, a track-reconstruction with the small number of hitsleads many combinatorial-fake tracks, resulting in an enormous consumption of computeresources. In order to reduce fake tracks and the number of patterns for seed tracks,
46

tight requirements, which are no hole hits, no shared hits and higher pT , are required atseed-track finding algorithms. This requirement keeps the compute resources at a levelof less than a few percent of the standard track reconstruction.
In order to reduce the compute time, the special tracking algorithm uses only leftover hits which are not used in the standard tracks. This limitation can realise aneﬃcient reduction of seed-tracks and remove an overlapping with tracks reconstructedin the standard tracking.
Figure 5.1 shows a distribution of the number of Pixel and SCT hits associated witha standard track or a pixel tracklet. The pixel tracklet tracking algorithm recovers short
tracks having less than seven silicon hits. A peak around seven hits is due to fake tracks.
The standard track reconstruction requires at least seven hits, and this is tighter thanpixel tracklet tracking. However, since requirements on the hit quality are looser thanpixel tracklets, fake tracks can pass the quality check.
Tracking variables
Transverse momentum
N of hits
N of holes
N of shared hits|η|SeedingStandard tracks≥ 500 MeV
≥7
≤2
≤1
≤ 2.7
Pixel + SCT

Pixel tracklet≥ 5 GeV
≥4
=0
=0
≤ 2.2
unassociated Pixel hits

Tracks (a.u.)

Table 5.1: A summary of tracking configuration for the standard track reconstruction
and the pixel tracklet reconstruction.

910

s = 13 TeV, 79.8 fb-1
2015-2017 Datap > 5 GeV
T

108

107
Standard tracks
Pixel tracklets

106
0

2

4

6

8

10 12 14 16 18 20
Number of silicon sensor hits

Figure 5.1: The number of hits in silicon sensors. A black line shows the standard tracks,
and a red line shows pixel tracklets.

47

5.2

Performance

The tracking performance has to be carefully checked because pixel tracklets are strongly
aﬀected by unexpected detector conditions. This section describes the performance ofthe tracklet reconstruction as follows.
1. A performance for chargino samples is performed in Sec. 5.2.1 to check the signal
acceptance by this tracking.
2. Tracklet selection criteria are examined in Sec. 5.2.2, that reduce fake tracks andpopulate tracklets originating from a particular kind of particles.
3. A tracklet performance in the observed data is performed in Sec. 5.2.3, wheretracklets are produced with a special configuration to enhance high purity tracklets.
4. Additional tracklet modellings are performed using observed data in Sec. 5.2.4.

5.2.1

For meta-stable charginos

As signal samples, wino and higgsino simulated samples are used. All chargino samples
are combined regardless of their masses and lifetimes to reduce statistical uncertainties.
In order to ensure that a reconstructed track is produced using the hits by a chargino,
it is required the chargino track association, which is defined that the ∆ R between a
tracklet and a generator-level particle is smaller than 0.01.
The tracklet reconstruction eﬃciency as a function of the decay radius vs η and z
are shown in Fig. 5.2 (a) and (b), respectively. Most tracklets come from the charginos
decaying between the fourth Pixel-layers (r = 123 mm) and the second SCT-layers (r= 370 mm). A low-eﬃciency region above |η| > 1.9 corresponds to a gap between thebarrel and the end-cap of the Pixel detector. A tracklet reconstructed using hits in
end-cap layers has a diﬀerent track performance, especially pT , from one reconstructedusing only barrel layers. Therefore, this analysis uses only tracklets with |η| < 1.9. Thisrequirement secondarily contributes to a reduction of background because the forward
region has a larger amount of material than the central region.
Figure 5.3 (a) shows a comparison of the track reconstruction eﬃciency as a functionof decay radius between the standard tracks, pixel tracklets and pixel tracklets requiring no SCT hits (SCT veto). The standard track has little eﬃciency when chargino
decays before the SCT detector (at 300 mm). On the other hand, the pixel tracklet
has a significant reconstruction eﬃciency in the region. After vetoing SCT hits, thereconstruction eﬃciency reduces, because sometimes hits originating from a chargino
decay product (pion, electron or muon) or background SCT hits are assigned to thetracklet. Since these tracks have bad tracking properties, they cannot be used in theanalysis. Such tracks with the wrong combination have a pile-up dependence as shownin Fig. 5.3 (b), because high pile-up circumstance increases fake tracks in the standard
tracks and the fake tracks accidentally use Pixel hits originating from a chargino, resulting in ineﬃciency in the pixel tracklet reconstruction. This issue is expected to be

48

500

Decay radius [mm]Decay radius [mm]solved by using all clusters in the reconstruction step. Since a study of a pile-up tolerant
tracking needs quite much compute resources, it was not implemented in this study.
Tracking parameter distributions as the diﬀerence between tracks and associatedgenerator-level particles are shown in Fig. 5.4. Five parameters (q/pT , θ, ϕ, transverse
impact parameter (d0 ) and longitudinal impact parameter (z0 ) 1 ) and pT at the closet
points with the beam spot (perigee) are shown with three type tracks (the standard
tracks, pixel tracklets and pixel tracklets with SCT veto). Resolutions of θ and z0 of
pixel tracklets are compatible with tracks in the standard track reconstruction. On theother hand, resolutions of pT , d0 and ϕ of pixel tracklets are much worse than tracks in thestandard track reconstruction due to the small number of associated hits and the small
track length of pixel tracklets, which are related to track curvature uncertainty. Notably,a bad resolution of q/pT of pixel tracklets gives a large impact to the analysis because
the track momentum is used for a separation between the signal and the background,and used as the final discriminant. Further study using observed data is discussed
in Sec. 5.2.4. A tail in the ∆ q/pT distribution of inclusive pixel tracklets is due to
tracklets with SCT hits. These tracks largely have wrong hits as mentioned in the above
paragraph, that leads wrong pT observation.
0.7

450
400

0.6

350
0.5

300
250

0.4

200

0.3

150

500
450

0.7

400

0.6

350

0.5

300
250

0.4

200

0.3

150

0.2

100

0.2

100

50
0
−2.5 −2 −1.5 −1 −0.5 0

0.5

1 1.5

2

2.5

0.1

0.1

50

0

0
0
−1000−800−600−400−200 0 200 400 600 8001000

Chargino ηz [mm](a)(b)

Figure 5.2: Pixel tracklet reconstruction eﬃciency as a function of chargino decay radiusvs (a) chargino η and (b) z-position of chargino decay. Black dash lines show the layer
positions of the silicon detectors.

5.2.2

Disappearing tracklet selection

As mentioned in Sec. 5.1, a large fraction of pixel tracklets are fake tracks which havean unphysical origin.

1
In this thesis, the transverse impact parameter (d0 ) is defined as the distance of the closest approachin the transverse plane between a track and the beam line. The longitudinal impact parameter (z0 ) isdefined as the z-coordinate distance between the primary vertex and the point where the d0 is defined.

49

0.8

Reconstruction efficiency

Reconstruction efficiency

Pixel

1

SCT

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

0.6
0.4
0.2
0
0

1

Meta-stable chargino samples|η| < 2.2, 130 mm < decay radius < 280 mm
Pixel tracklets
Pixel tracklets (SCT veto)

0.8
0.6
0.4
0.2

100

200

300

400

0
0

500

10

Decay radius [mm]

20

30

40

50

60

70

80

Average interactions per crossing

(a)

(b)

Figure 5.3: (a) Track reconstruction eﬃciency as a function of chargino decay radius.
(b) Track reconstruction eﬃciency when a chargino decays between the fourth Pixellayer and the first SCT-layer as a function of average number of pp interactions per
bunch crossing (pile-up). A standard track is shown as green squares. A pixel tracklet isshown as orange circles. A pixel tracklet with SCT veto is shown as red triangles. The
diﬀerence between the inclusive pixel tracklet and the tracklet with SCT veto is due towrong association of SCT hits.
Figures 5.5–5.7 show distribution of track variables of pixel tracklets after applying
minimum track selections as follows
1. Kinematic selection is applied to extract signal-like kinematic topology. Details
are shown in Sec. 6.3.
2. A tracklet pT is required to be larger than 20 GeV
3. A tracklet |d0 significance| (≡ |d0 /err(d0 )|) is smaller than 5
4. A tracklet |z0 sin θ| is smaller than 500 µm,
where a tracklet which has at least one wrong associated hit is labelled as “wrong comb.”.
Moreover, truth matching criteria mentioned before are applied for charginos. As shownin the figures, there are many fake tracks, and a reduction of these tracks is necessary.
In this subsection, tracklet selection criteria are discussed. By applying the tracklet
selection, most of fakes can be reduced, and tracklets having physical origin remain.
At least four Pixel hits
Pixel tracklet reconstruction algorithm requires that the number of clusters is morethan or equal to four. However, after precise fitting, a cluster can be labelled as an
outlier. An outlier hit is not used in a fitting, and then a pixel tracklet can look
like a three-layer track. Such a situation happens when a particle passes throughan overlap region of barrel layers because a pixel tracklet has two hits in one layer
50

1Arbitrary unit

Arbitrary unit

10

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

1
10−1

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

−1

10

10−2
−2

10

10−3
10−3
10−4
−100 −80 −60 −40 −20 0−0.2 −0.15 −0.1 −0.05

20 40 60 80 100

00.05 0.1 0.15 0.2∆ q/p [/TeV]

d0 [mm]T(b)
Arbitrary unit

Arbitrary unit

(a)
10
1
−1

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

10

2

10

10
1

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

10−1

10−2

10−2

10−3

10−3
10−4

10−4

10−5

−5

10
−0.5 −0.4 −0.3 −0.2 −0.1 0

10−6−10 −8 −6 −4 −2

0.1 0.2 0.3 0.4 0.5

02

z0 sinθ [mm]

10
1

6

8

10

(d)
Arbitrary unit

Arbitrary unit

(c)
102

4

∆ θ × 103 [radian]Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

10−1

Meta-stable chargino samples|η| < 2.2
Pixel tracklets
Pixel tracklets (SCT veto)Standard tracks

10−2

10−2
10−3
10−4
10−5
10−6
−10 −8 −6 −4 −2

0

2

4

6

8

10−3
−100 −80 −60 −40 −20 0

10

20 40 60 80 100∆ p [GeV]∆ φ × 103 [radian]

T

(e)

(f)

Figure 5.4: Track parameters at perigee. (a) ∆q/pT between the track and the generatorlevel particle. (b) d0 . (c) z0 sin θ. (d) ∆θ between the track and the generator-levelparticle. (e) ∆ϕ between the track and the generator-level particle. (f) ∆pT between
the track and the generator-level particle. The standard tracks are shown as green
squares. The pixel tracklets are shown as yellow circles. The pixel tracklets with SCT
veto are shown as red triangles.

51

in this case. A performance of three-layer tracks is diﬀerent from typical pixel
tracklets (four-layer tracks). In this analysis, in order to avoid these tracks, it isrequired that the number of pixel layers associated with hits of the tracklet is morethan or equal to four shown in Fig. 5.5 (c). This requirement ensures that a pixel
tracklet has an expected track length and the performance will be under control.
All hits having good properties
There are three bad hit types labelled in the track reconstruction stage as definedin Table 5.2. In order to reduce fake background further, a tracklet is removed
when it has any bad hits: fake ganged-hits (Fig. 5.5 (e)), spoilt hits (Fig. 5.5 (f))
and outlier hits (Fig. 5.5 (d)).
LabelOutlier hit
Spoilt hit
Fake ganged-hit

Definition
Far from the track (χ2 >9)Having a large position uncertainty
Ganged-pixels (Sec. 2.2.2) identified as fake in ambiguity solving
Table 5.2: Definitions of bad types of hits

Isolation
The rate of fake pixel tracklets is correlated to the occupancy of the Pixel detector. Jets contain many charged particles and increase the hit occupancy locally.
Therefore, fake pixel tracklets are easily created around high pT jets.
A chargino is isolated from other particles in most cases. Pixel tracklets are required to be isolated from other objects for a reduction of fake tracks. The isolation
is evaluated using ∆R between a tracklet and other particles as follows• minimum ∆R(tracklet, jets (pT > 50 GeV)) > 0.4 (Fig. 5.6 (a))• minimum ∆R(tracklet, electrons) > 0.4• minimum ∆R(tracklet, muons) > 0.4• minimum ∆R(tracklet, muon spectrometer tracks) > 0.4 (Fig. 5.6 (b))
Additionally, in order to further reduce fake pixel tracklet from jets, a track isolation is required as pcone40< 0.04 pT , where pcone40
is defined as a scalar sum ofTTtrack pT with ∆R(tracklet, standard tracks) < 0.4, where used standard tracks are
required to have pT higher than 1 GeV and |z0 sin θ| less than 3 mm (Fig. 5.6 (c)).
Impact parameterAll particles except secondary particles from meta-stable particles have small impact parameter. On the other hand, fake tracks usually have large impact parameters because fake tracks have no origin particles produced around a primaryvertex. This analysis requires that two variables related to the impact parameterare small.
52• An absolute value of a significance of transverse impact parameter (d0 significance= d0 /σd0 ) is less than 1.5 (Fig. 5.6 (d)).
• An absolute value of longitudinal impact parameter (z0 sin θ) is less than
0.5 mm (Fig. 5.6 (e)).
Fit quality
Fitting quality is a useful index for detecting fake tracklets. Here χ2 -probability,
defined as an upper integration of the χ2 distribution, is used. The tracklets whoseχ2 -probability is less than 0.1 are rejected (Fig. 5.6 (f)).
Geometrical acceptance
Pixel tracklets are reconstructed with a range between η = -2.2 and η = 2.2.
Outer region over 1.9 in |η| is not an active region of TRT. Additionally, there isa transition region of pixel barrel and end cap shown in Fig. 5.2 and the material
budget is higher. The muon spectrometer has low eﬃciency in the inner region (|η|< 0.1). The use of tracks in the small |η| region leads an increase of pixel tracklet
background from muons. By the above condition, it is required that the absoluteη of pixel tracklets is larger than 0.1 and less than 1.9 (Fig. 5.7 (a)).
Disappearance condition
In order to ensure a pixel tracklet disappears in the tracker, it is required that the
pixel tracklet has no SCT hits (Fig. 5.7 (b)) and no TRT hits (Fig. 5.7 (c)).

5.2.3

Data/MC comparison using high purity tracklets

In Sec. 5.2.2, data/MC comparisons of fake-dominant tracklets are performed to ensurethat track selections eﬃciently reduce fake tracks. The data/MC comparisons are performed for high purity tracklets, which contain less fake tracks. It is necessary to checkthe validity of MC simulated samples using not-fake-like tracks. It is diﬃcult to populate tracklet samples, in data, originating from a particle decaying to un-reconstructableparticles, like charginos. This issue is solved by using an artificial re-tracking technique.
The artificial pixel tracklet is created by using only hits in the pixel detector, no matter
whether there are hits in the SCT or TRT detector. By doing this, all tracks, including
the standard tracks, are reconstructed as pixel tracklets. Reconstructed tracklets by thismethod implicitly requires that there are at least four Pixel-hits. Therefore, the casethat a hit associated with signal particles is missing cannot be included in this way. Sucha case is assessed in Sec. 5.2.4.
Muons are good candidates to compare the track performance because it is easy to
extract high purity muon track samples. Since artificial re-tracking technique requires alarge number of compute resources, a limited number of data samples are used for thisstudy, where the samples are selected to cover the whole run time in 2015–2017.
Here high purity muon tracks from Z → µµ events are triggered by the single isolated
muon trigger, then extracted by requiring two muons whose reconstructed mass (Mµµ )of within the range of 10 GeV of the Z boson mass, where the leading muon pT is larger53

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Count

Count
4

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

10
3

10

3

10

2

10

2

10

Ratio

Ratio

10
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

30 40 50

100

200

300

1000
p [GeV]

0

1

2

3

4

5

6
7
8
number of Pixel hits

T

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

(b)

t,t t
VV
Zll
data

Count

Count

(a)

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

6

10

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

10

4

10

3

10
3

10

2

10

10

2

10

Ratio

Ratio

1
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0

1

2

3

4
5
6
7
8
number of contributed Pixel layers

0

0.5

1

1.5

2

6

10

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

t,t t
VV
Zll
data

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

t,t t
VV
Zll
data

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

4

10

10

3

10

2

10

3

2

10

10

Ratio

10

Ratio

3.5
4
4.5
5
number of Pixel outliers

6

10

10

1.4
1.2

1
1.4
1.2

1

1

0.8

0.8

0.6

0.6

0

3

(d)
Count

Count

(c)

2.5

0.5

1

1.5

2

2.5
3
3.5
4
4.5
5
number of fake ganged-pixel hits

(e)

0

54

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
number of Pixel spoilt hits(f)Figure 5.5: Data/MC comparison for pixel tracklets. (a) pT (b) the number of Pixel hits(c) the number of Pixel layers associated with the hits (d) the number of Pixel outlier
hits (e) the number of fake ganged-pixel hits (f) the number of Pixel spoilt hits510

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

t,t t
VV
Zll
data

1

Count

Count

6

10

6

10

10

10

4

10

10

3

10

2

10

1

1

3

2

10

Ratio

10
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
∆ R Jet

0

0.1

0.2

0.3

0.4

6

10

5

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

0.5

0.6

0.7

0.8 0.9
1∆ R MSTrack(b)

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

t,t t
VV
Zll
data

1

Count

Count

(a)

10

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

t,t t
VV
Zll
data

4

10

Ratio

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec

5

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec

4

1

10

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

t,t t
VV
Zll
data

1

4

10

3

10

3

10

2

10

2

10
10

10

Ratio

Ratio

1
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0.001
0.002

0.01 0.02

0.1 0.2

1

−5

2 34
10
pcone40 / p
T

−4

−3

−2

−1

5

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

1

2

3
4
5
d0 significance

(d)

t,t t
VV
Zll
data

4

Count

Count

(c)

10

0

T

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

10

3

10

3

10

2

10

10
2

Ratio

Ratio

10
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−500 −400 −300 −200 −100

0

(e)

100

200

300 400 500
z 0sinθ [µ m]

0

55

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.91
χ2-probability(f)Figure 5.6: Data/MC comparison for pixel tracklets. (a) ∆R(tracklet, jets) (b)∆R(tracklet, muon spectrometer tracks) (c) pcone40/ pT (d) d0 significance (e) z0 sin θTwrt primary vertex (f) χ2 -probability

1Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

t,t t
VV
Zll
data

1

Count

Count

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec

6

10

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

10

3

10

3

10

2

10

10

1.4

1
1.4

Ratio

Ratio

2

10

1.2

1.2

1

1

0.8

0.8

0.6

−2.5

0.6

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5
η

0

2

4

8

10

12
14
number of SCT hits

(b)
Count

(a)

6

6

10

5

10

s =13TeV, 79.8 fb-1m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

t,t t
VV
Zll
data

1

Wrong comb.
Signal x1000
multi-jet
Zν ν
Wlν

4

10

3

10

2

10

10

Ratio

1
1.4
1.2
1
0.8
0.6

0

5

10

15

20

25

30

35
40
45
50
number of TRT hits(c)Figure 5.7: Data/MC comparison for pixel tracklets. (a) η (b) the number of SCT hits(c) the number of TRT hits

56

than 25 GeV and the sub-leading muon pT > 20 GeV. Additionally, in order to increasea purity, the events are required to not have electrons and that an artificial pixel tracklet
overlaps with the muon track coming from the standard tracking (∆R(tracklet, muon)< 0.2)
Figures 5.8 and 5.9 are comparison plots where disappearing track selections areapplied except the related selection with its variable. As shown in these figures, thetracklet performance of MC samples is well-modelled. Since the diﬀerence in pT resolution and impact parameters are sensitive in this analysis, additional treatments areapplied. Systematic uncertainties related to track selection eﬃciency is discussed inSec. 9.

5.2.4

Correction of simulated data using observed data

Due to a mismodelling in simulated data, a correction for a mismodelling in a simulationis necessary. This subsection describes a mismodelling in q/pT and the number of Pixelhits.
pT resolution of pixel tracklets
The modelling of pT and its control are important because this analysis use tracklet pT as
the final discriminant and pixel tracklets are strongly aﬀected by the detector condition
and misalignment due to the small number of associated hits.
The pT is calculated from the curvature of the tracks, and the curvature resolution isapproximately proportional to the resolution of a sagitta, which is a maximum distance
between the track and a straight line connecting the edges of the track. Sagitta resolution
is approximately proportional to the inverse of the pT as follows
sagitta[m] ∼0.3 B[T](L[m])2,
8 pT [GeV](5.1)

where L is a track length and B is a magnetic field strength (2 T for ATLAS solenoid).
The position resolution of each space points is correlated with a charge over pT resolution.
Therefore in order to control pT , a q/pT resolution is measured from observed data thenthe generator-level pT in simulated samples is smeared using the resolution function
instead of directly using the reconstructed pT of simulation samples. The measured
q/pT resolution is called “smearing function” because it is used to smear the generatorlevel pT .
The measurements of ∆q/pT between a tracklet and an associated standard trackis performed with both data and MC samples for the diﬀerent pT slices. The artificial
re-tracking technique discussed in the Sec. 5.2.3 is applied for both samples. The artificial re-tracking technique requires the existence of the standard tracks, resulting in a
potential bias from a missing event where a charged particle is not reconstructed as thestandard tracks. However, the eﬀect is negligible (< 5 × 10−3 ) because the probability ofsuch events is small (<1%) and, moreover, the behaviour of pT resolution of such event
is equivalent to the one of events having the standard tracks in most cases (>95%).
57

Arbitrary unit

Arbitrary unit

Observed data
Simulations = 13 TeV

10−1

Observed data
Simulations = 13 TeV

10−1

Ratio

Ratio

10−2

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

102

10
p [GeV]

−2

3

−1.5

−1

−0.5

0

0.5

1

1.5

T

1

(b)
Arbitrary unit

Arbitrary unit(a)Observed data
Simulations = 13 TeV

2
η

10−1

Observed data
Simulations = 13 TeV

1

10−1
10−2
10−2

10−3

Ratio

Ratio

10−3

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0

1

2

3

4

5
6
7
8
9
10
The number of contributed Pixel hits

0

0.5

1

1.5

2

Observed data
Simulations = 13 TeV

1

3
3.5
4
4.5
5
The number of pixel outliers(d)Arbitrary unit

Arbitrary unit

(c)

2.5

1

Observed data
Simulations = 13 TeV

10−1

10−1
10−2
10−2

10−3
10−4
Ratio

Ratio

10−3
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0

0.6

0.5

1

1.5

2

2.5
3
3.5
4
4.5
5
The number of fake ganged pixels

0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
The number of pixel spoilt hits

58
(e)

(f)

Figure 5.8: Data/MC comparison with muon tracks. Disappearing track selections areapplied except the related selection with its variable. (a) pT (b) η (c) The number of
Pixel-layers associated with the hits (d) The number of Pixel outlier hits (e) The numberof fake ganged-pixel hits (f) The number of Pixel spoilt hits

Arbitrary unit

Arbitrary unit

Observed data
Simulations = 13 TeV

1

1
Observed data
Simulations = 13 TeV

10−1

10−2

10−1

10−3
10−4
Ratio

Ratio

10−2

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0

−5

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
pcone40 / p
T

−4

−3

−2

−1

1

2

3
4
5
d0 significance(b)
Arbitrary unit

Arbitrary unit

(a)

1

0

T

Observed data
Simulations = 13 TeV

10−1

Observed data
Simulations = 13 TeV

10−1

10−2
10−3

10−2

Ratio

Ratio

10−4
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−0.5 −0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3 0.4 0.5
z0 sinθ [mm]

0

(c)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.91
χ2 probability(d)Figure 5.9: Data/MC comparison with muon tracks. Disappearing track selections areapplied except the related selection with its variable. (a) pcone40/ pT (b) d0 significanceT(c) z0 sin θ wrt primary vertex (d) χ2 -probability

59

Probability

The event missing the standard tracks is caused by a scatter with material because the
SCT detector and the TRT detector cover the full η range of the pixel tracklet (0.1 <|η| < 1.9) as shown in Fig. 2.2. In such events, 95% of particles, which are reconstructed as pixel tracklet but fail to reconstruct the standard track, are derived from being
scattered by material between the fourth Pixel-layer and the first SCT-layer as shown in
Fig. 5.10. Since the scatter occurs after creating four Pixel hits used in a pixel tracklet,
their positions are not aﬀected by the scatter. Because of using the unbiased four Pixel
hits, pT resolution is equivalent to the measurements based on the artificial re-tracking
technique. Therefore, the smearing function is well-modelling a pT resolution of the pixel
tracklet.

10− 2

10

−3

10− 4

0

50

100

150

200

250

300

350
400
Scattering radius [mm]Figure 5.10: The probability of identifying an electron as a disappearing pixel tracklet
as a function of the scattering radius. The fourth Pixel-layers and the first SCT-layers
are placed at z-positions of 123 mm and 299 mm, respectively. Since each layer is not
an ideal cylindrical but tilted, a part of sensors is widely placed around the designed
positions.
In order to extract high purity lepton tracks from data samples, Z → ee and Z → µµ
events are selected by applying similar selection to the selection in Sec. 5.2.3. Additionally, the disappearing track selection except for lepton veto and the pT requirements is
applied to extract tracklets with the same conditions as the analysis. For MC samples,
special simulated samples, where only one particle is produced in the interaction pointwith no pileup, are used to obtain the high purity tracks.
The ∆ q/pT distribution with a fit for high pT particles are shown in Fig. 5.11 for
the Z → ee and Z → µµ comparison in the data and for the muon and pion comparisonin the simulated samples. Others are shown in Appendix A. In the fit, a double-sided

60

Crystal-ball function is used.
− z)−nA · (B( 2 )f (z) =
exp −z /2
A · (B + z)−n(z < −α),(−α < z < α),(z > α)(5.2)∆(q/pT ) − βσ ()( n )n
α2
exp −
A =
α
2
n
B =
− α,
α
z =

where α, β, σ and n are parameters representing the slope of the tail part, the mean of
the core part, the resolution of the core part and the index of the tail power function,
respectively. After the fit, the best fit n is very large sometimes. When n is infinity, atail part of this function becomes exponential as follows(z < −α)exp(α(z + α/2))2
f (z) =
(5.3)
exp(−z /2)(−α < z < α),exp(−α(z − α/2)) (z > α)z =∆(q/pT ) − β.
σ

In case that n is consistent with infinity, Eq. 5.3 is used instead.
Fig. 5.12 shows the pT dependence of the fitting parameters of the smearing functions. Basically, the resolution in data is worse than that in MC. This is expected dueto the misalignment. Electrons with low momenta are more strongly aﬀected multiplescattering eﬀects than other heavier particles. The muons and pions have similar properties because their masses are similar. But pions have a wider tail in the high pT region
as shown in Fig. 5.12 (c). These eﬀects are taken into account in the analysis.
Summarised above, the ∆q/pT distribution measured from observed data is used tosmear the signal chargino pT and to estimate tracklet pT from the standard track pT
distributions in observed data. For muons and electrons, the distributions measured in
Z → ee events and Z → µµ events are applied respectively. For hadrons and charginos,
the distribution measured from Z → µµ events is used instead of measurements of
the hadrons and charginos in observed data. The additional tail eﬀect (n) which isobserved in simulation is added to the distribution for hadron and electron with 100%
uncertainties.
Eﬀects from Pixel dead modules
Some fraction of pixel sensors is not functional due to synchronisation errors or the otherproblems in the modules. A modelling of the status of Pixel modules is not perfect inthe simulation. Since this analysis requires for tracks to have at least four Pixel hits, the
61

10−1

Observed data
Z → ll events

10−1

Zee
Z µµ

50 GeV < p < 200 GeV

10−2

Pion
Muon

10−3

10−3

10−4

Zµ µ events
σ = 12.6 ± 0.1
α = 1.78 ± 0.04
Zee events
σ = 13.2 ± 0.1
α = 1.79 ± 0.04

10−4

10−5
Ratio

10−5

Ratio

T

10−2

T

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−100 −80

50 GeV < p < 200 GeV

−60

−40

−20

0

20

40

−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

T

20

40

60
80 100∆ q/p [/TeV]
T

(a)

(b)

Figure 5.11: ∆ q/pT distribution passed disappearing track selection. (a) The comparison of Z → ee and Z → µµ events in observed data. (b) The comparison of muon andpion events in the simulated samples.
dead modules change the signal acceptance. Therefore this eﬀect should be consideredusing observed data.
The artificial re-tracking method discussed before does not work in this case because
it requires suﬃcient Pixel hits originating from a charged particle. In order to measure
the eﬃciency of Pixel hits requirements, high purity muon tracks reconstructed by thestandard track reconstruction is used. The high purity muons are extracted by selecting
Z → µµ events. Then, in order to reduce fake tracks, additional track selections are
required as follows
1. pT > 15 GeV
2. The number of Pixel hits is more than one
3. The number of SCT hits is more than four
4. The number of TRT hits is more than five
The selection eﬃciency of a requirement on at least four contributed Pixel-layers isshown in Fig. 5.13 (a) and (b). Some eﬀects from dead modules are not reflected MC as
shown in the figures. Figure 5.13 (c) shows a ratio of data to MC which is used to scale
the signal samples in the final steps in this analysis.

62ασ [TeV-1]

22

3.5

Pion
Muon
Data (Zee)
Data (Zµµ)

20
18

4
Pion
Muon
Data (Zee)
Data (Zµµ)

3

16

2.5

14

2

12

1.5

10

1

8

0.5

6
0 20 40 60 80 100120140160180200

00 20 40 60 80 100120140160180200

p [GeV]p [GeV]

T

T

(b)
1/n

(a)
0.5
Pion
Muon
Data (Zee)
Data (Zµµ)

0.4
0.3
0.2
0.1

0
0 20 40 60 80 100120140160180200
p [GeV]T(c)

Figure 5.12: Parameters of the smearing function as function of particle pT . Black open
circles show a Z → µµ events in data. Yellow open circles show a Z → ee events indata. Black squares show a muon in simulated samples. Blue triangles show a pion insimulated samples. (a) A resolution of the core part (σ). (b) A slope of the tail part (α).
(c) An additional slope of the tail part (n).

63

0.8

φ

0.9
2

0.7

1

1

3

0.8
0.7

1

0.6
0

0.6

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0

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0.3
0.2

−2

0.3
0.2

−2

0.1
−3
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2ηEfficiency

0.9
2

Efficiency

φ

1

3

0.1
−3
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
η

0

2

3

1.8
2

1.6

Data / MC

(b)
φ

(a)

0

1.4

1

1.2
0

1
0.8

−1

0.6
0.4

−2

0.2
−3
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
η

0

(c)

Figure 5.13: Data/MC comparison with muon tracks. Selection eﬃciency of the numberof Pixel-layers associated with the tracks. (a) Data (b) MC (c) Data/MC

64

Chapter 6

Event selection
There are two chargino production modes. One is the electroweak direct production ofa chargino-pair or a chargino-neutralino pair. The other is a cascade decay from otherheavier particles, e.g. gluino. In the latter case, the masses of heavier particles should
be light enough to be produced in the LHC at 13 TeV for this search to have sensitivity.
Although, some models (e.g. PGM models with some tuning parameters) predict heavier
particles which are possible to be produced at the LHC energy, current limits on gluino isstrict. In the former case, the production cross-section depends on only the chargino andneutralino masses. The electroweak direct production is more inclusive than the strong
production. This thesis focuses on the electroweak direct production as illustrated inFig. 6.1 (a).
When the mass diﬀerence between chargino and neutralino is quite small, it is diﬃcult
to detect the secondary particles. This analysis requires initial-state-radiation (ISR) jets
as illustrated in Fig. 6.1 (b) to trigger the events. The chargino prouduction is often
accompanied by ISR jets due to high-Q2 required to produce charginos. The existenceof high energy ISR jets and undetectable chargino/neutralino leads an observation ofmiss in the situation of no leptons. The large E miss signature is characteristic
large ETT
miss is muchcompared to a large momentum jet signature, and a trigger threshold of ET
miss is used as a physics-object forless than a threshold of a single jet trigger. The ET
triggering the events instead of jets.

6.1

Triggermiss trigger [32, 90]. Trigger thresholds and algorithms
Events were triggered by a ET
missin the ET calculation were changed depending on the instantaneous luminosity since
miss trigger rate highly depends on the pile-up. For 2015–2016 data, the events
the ET
miss threshold of 50 GeV in the level-1 trigger, then they were
were triggered by the ET
missmiss intriggered by the ET threshold of 70–110 GeV in the high-level-trigger, where ET
the high-level-trigger was calculated by the missing HT (MHT) algorithm [32], where themiss calculation.
calibrated anti-kT jets with a radius parameter of 0.4 were used for the ET
For 2017 data, due to the serious pile-up condition, the events were triggered by the

65

j

p
χ̃01

p
χ̃01

p

χ̃01

χ̃±
1

p

χ̃01

χ̃±
1

π±

π±

(a)

(b)

Figure 6.1: Feynman diagrams of (a) chargino-neutralino direct production (b) charginoneutralino direct production with an association of one ISR jet.
miss threshold of 55 GeV in level-1 trigger, then they were triggered in the high-levelET
miss threshold of 110 GeV which was calculated by the pile-up fit (pufit)
trigger by the ET
miss calculation, and pileup
algorithm [32], where topological clusters were used for the ET
were subtracted by the average of the low-pT segmented calorimeter clusters in theevents.
A trigger performance is not perfectly modelled in the simulation. In order to reduce
the systematic uncertainties, the trigger eﬃciency is directly measured from observed
miss is calculated from only calorimeter energy
data using W → µν events. The trigger ET
miss . Similarly, signal charginos
deposits, leading that muon momentum are treated as ET
missare treated as ET because they do not leave their energies in the calorimeter and themuon spectrometer. Therefore, it is possible to measure the trigger eﬃciency in a similar
topology to signals.
W → µν events are triggered by the single isolated muon, then are extracted byrequiring

1. exact one muon identified as “Tight” quality and pT > 27 GeV
2. no electrons
3. 30 GeV < mT < 100 GeV, where transverse mass (mT ) is defined as√[]
miss 1 − cos ∆ϕ(muon, E miss )mT = 2pmuon
ET
T
T

(6.1)

4. pT of the highest-pT jet (leading jet) > 140 GeV
miss ) > 1.0, where ∆ϕ(jets, E miss ) is defined as a minimum ∆ϕ between
5. ∆ϕ(jets, ETT
missET and each of the up to four highest-pT jets.

66

Missing E (no muon) [GeV]

Efficiency

The last two requirements are to match the kinematical topology with the events after akinematic selection as discussed in Sec. 6.3. By using W → µν events extracted by thismiss trigger
selection, a trigger eﬃciency is estimated as a ratio of events which passes ET
miss .
to all events as a function of ET
The observed trigger eﬃciency is shown in Fig. 6.2 (a) with all trigger menus usedmiss resolution, the turn-on is mild, and the actualin this analysis. Due to a finite ET
thresholds do not match exactly to the trigger names. However, most of the events with
miss > 200 GeV pass all the E miss triggers. Jet activities slightly aﬀect thethe oﬄine ETTmiss trigger eﬃciency, although the E miss trigger should depend on only E miss ideally.
ET
T
T
miss and leading jet p as
In order to consider this eﬀect, a two-dimensional map of ET
Tshown in Fig. 6.2 (b) is applied to signal simulated samples.

1
HLT_xe70_mht

0.8

HLT_xe90_mht_L1XE50
HLT_xe100_mht_L1XE50
HLT_xe110_mht_L1XE50

0.6

Data, HLT_xe110_pufit_L1XE55

0.9
250

0.8
0.7

200

0.6

T

HLT_xe110_pufit_L1XE55

300

Data

0.4

150

0.5
0.4

100

0.2

50

0
0

0

0.3
0.2
0.1

100

200

300

400

500

150

200

250

Missing E (no muon) [GeV]

300

350

400

0

Leading jet p [GeV]

T

T

(a)

(b)

miss trigger eﬃciency measured from W → µν events. (a) Trigger eﬃciency
Figure 6.2: ET
miss . Data points are coloured by E miss thresholds andas a function of the oﬄine ETTmissmiss trigger
trigger ET reconstruction algorithms in the L1 and the HLT trigger. (b) ET
miss and the leading
eﬃciency in 2017 data as a function of a magnitude of the oﬄine ET
jet pT . A weak dependence on the jet pT is observed.

6.2

Event cleaning

Events which are not triggered by a hard pp scattering are removed by the following
criteria.
Non-collision background vetoNon-collision background events mainly come from beam scattering before collision
point [91,92]. When a part of beams is scattered at the forward region of the beampipe, some energetic particle can travel through the detector and leave large energy
in the calorimeter without tracks from the nominal interaction point. Such an event
appears to have jets and a small number of tracks.

67

Two cleaning criteria (“Loose” and “Tight”) as described in Ref. [93] are applied tojets in this analysis. First, all jets with pT higher than 20 GeV are required to pass
the “Loose” jet cleaning criteria. If any jets do not pass these cleaning criteria, theevent is rejected. The “Loose” cleaning rejects bad jets clearly identified as comingfrom non-collision background. Second, a leading jet is required to pass the “Tight”
jet cleaning criteria. “Tight” criteria use precise inner-detector track information,so an η of a leading jet is required to be within the coverage of the inner tracker (|η|< 2.4). If the leading jet is not satisfied with the both requirements, the event isdiscarded.
An eﬀect of this cleaning is shown in Fig. 6.3. Events from non-collision backgrounds peak around ϕ = 0 and π are suppressed by the cleaning criteria.
Bad muon veto
A muon can have an anomalously large momentum with a large momentum error
by a mis-reconstruction of a track or a mis-combination of an inner-detector track
and a muon-spectrometer track. In order to reject such a muon, a muon is requiredthat the relative curvature error (σq/p /(q/p)) is smaller than 0.2 and smaller than
σq/p /(q/p) of an inner-detector track and a muon-spectrometer track.
miss ,
Additionally, in order to reduce bad events where fake muons create large ET
the following value :miss,muon}{ETmiss,muon
miss
)
−
ϕ(E
)
cos
ϕ(E
T
T
miss
ET

(6.2)

miss,muonis required to be less than 0.5, where ET
is defined as follows∑ # µ»#»ET miss,muon = −
pT .

(6.3)

muons

6.3

Kinematic selection

A kinematical topology of the target signal is characterised by the high pT jets, the large
miss and no leptons as shown in Fig. 6.1 (b). Kinematical selections are applied toET
reduce the SM processes as follows.
Lepton veto
If an event has a lepton (an electron or a muon) whose transverse momentum
is higher than 10 GeV, the event is rejected. The lepton veto reduces eventsfrom W → ℓν, Z → ℓℓ and t-quark production. Since a lepton leaves a trackin the inner detector, a lepton failing identification criteria becomes one of themain backgrounds in this analysis. Properties of the background and a way ofbackground estimation are discussed in Sec. 7.3.

68

t,tt
VV
Zll
Signaldata

s =13TeV, 79.8 fb-1

710m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

Count

Count

8

10

multi-jet
Zνν
Wτν
Weν
W µν

s =13TeV, 79.8 fb-1

610m∼χ± = 500 GeV, τ∼χ± = 0.2 nsec
1

1

t,tt
VV
Zll
Signaldata

multi-jet
Zνν
Wτν
Weν
W µν

1

2
3
Missing E φ

5

6

10

10

5

10

4

10

4

10

3

10
3

10

2

10

2

10

10

Ratio

Ratio

10
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−3

−2

−1

0

1

−3

2
3
Missing E φ

−2

−1

0

T

T

(a)

(b)

miss ϕ distribution (a) before applying the non-collision background vetoFigure 6.3: ET(b) after applying the non-collision background veto

missEnergetic jet and ET
miss are required to be larger thanThe leading jet pT and the magnitude of ET
150 GeV and 200 GeV, respectively. The use of two diﬀerent thresholds helps
to extract signal events eﬃciently. Additionally, it is required that the minmiss and each of the up to four highest-p jets with p >imum ∆ϕ between ET
T
T
miss produced from the SM processes))
islargerthan
1.0.
E
50 GeV (∆ϕ(jets, EmissTT
not emitting neutrinos is mostly created by jet mismeasurement, resulting in a
miss . Therefore, the above selection strongly resmall distance between a jet and ET
duces the SM processes not having neutrinos (multi-jets, t-quark production withno lepton).

Figure 6.4 shows distributions of kinematical variables used in the kinematic selection
where the selection related to the plotting variable is not applied. The multi-jet event
is not well modelled as shown in Fig. 6.4 (b). However, the multi-jet events are tightly
miss and the minimum ∆ϕ selection as shown in Fig. 6.4 (b) and (c),reduced by the ET
and do not remain after the kinematic selection.
Table 6.1 shows the cut-flow comparison between the observed data, the SM background in the simulated samples and the signal process in the simulated samples. Thereis a discrepancy in the amount of the observed data and simulated samples before thelepton veto because of the mismodelling of the multi-jet process. However, a reasonable
miss
agreement in the amount of observed data and simulated samples is seen after ET
selection. The number of events which pass the kinematic selection is well modelled.
miss distribution after the kinematical selection is shown in Fig. 6.5. E miss distriETTbution obtained from the simulated data is in good agreement with that of the observed69s =13TeV, 79.8 fb
7

10

t,tt
VV
Zll
Signaldata-1mχ∼± = 500 GeV, τχ∼± = 0.2 nsec
1

1

6

10

Count

Count

8

10

multi-jet
Zνν
Wτν
Weν
W µν

10

10

9

10

8

10

t,tt
VV
Zll
Signaldata

s =13TeV, 79.8 fb-1
mχ∼± = 500 GeV, τχ∼± = 0.2 nsec
1

1

7

10

multi-jet
Zνν
Wτν
Weν
W µν

6

10

5

10

4

10

3

10

5

10

4

10

3

10
2

10

2

10
10

10
1

Ratio

Ratio

1
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

30 40 50

100

200

300

1000
1st jet p [GeV]

30 40 50

100

200

300

T

T

t,tt
VV
Zll
Signaldata8s =13TeV, 79.8 fb-1

7

10mχ∼± = 500 GeV, τχ∼± = 0.2 nsec
1

(b)

1

Count

Count

(a)

10

1000
Missing E [GeV]

multi-jet
Zνν
Wτν
Weν
W µν

9

10

8

10

t,tt
VV
Zll
Signaldata

s =13TeV, 79.8 fb-1
mχ∼± = 500 GeV, τχ∼± = 0.2 nsec

7

1

1

10

multi-jet
Zνν
Wτν
Weν
W µν

6

10

6

10

5

5

10

10

4

4

10

10

3

10

3

10

2

10

2

10

10
1

Ratio

Ratio

10

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0

0.6

0.5

1

1.5
2
2.5
3
50GeV,50GeV,50GeV,50GeV∆ φ (jet,Missing E )

0

1

2

3

4

5

T

(c)

6

7

8
9
10
Number of leptons(d)Figure 6.4: Kinematic distribution after all kinematic selections except for the selection
related with the plotting variable. Multi-jets samples with the leading generator-level jet
pT smaller than 60 GeV are removed to reduce large statistical fluctuation. (a) Leading
miss (c) minimum ∆ϕ (jets, E miss ) (d) The number of leptons
jet pT (b) ET
T

70

Requirement
Observed
Trigger
Event cleaning
Lepton veto
miss
ET > 200 GeV
Leading jet pT > 150 GeV
jet−Emiss
T

∆ϕmin

> 1.0

Number of events
SM background (MC) Signal (m=500 GeV)

5.98×108
4.15×108
3.92×108
3.76×106
3.20×106(8.58 ± 0.08)×108(7.18 ± 0.07)×108(6.91 ± 0.07)×108(3.99 ± 0.15)×106(3.30 ± 0.03)×106

990 ± 7919 ± 6917 ± 6463 ± 5421 ± 4

1.97×106(1.89 ± 0.02)×106

394 ± 4

Table 6.1: Summary of selection eﬃciency of the observed data, the SM backgroundin MC simulation and signal process in MC simulation. Multi-jets samples with theleading generator-level jet pT smaller than 60 GeV are removed to reduce large statisticalfluctuation. Simulated samples are normalized to 79.8 fb−1 .
data. Table 6.2 shows the fraction of the SM background processes after the kinematic
selection. The main remaining process is Z → νν and W → τ ν after the kinematic
selection.
Processes

Kinematic selection

All selection

W → eν
W → µν
W → τν
Z → νν
Z → ℓℓDi-bosont-quark
Multi-jets(6.7 ± 0.3) %(8.6 ± 0.1) %(21.9 ± 0.3) %(52.2 ± 0.6) %(0.5 ± 0.0) %(1.7 ± 0.0) %(5.1 ± 0.1) %(3.4 ± 1.1) %(34.6 ± 9.2)%(0.2 ± 0.1)%(44.6 ± 9.4)%(4.5 ± 1.6)%(0.4 ± 0.5)%(2.4 ± 0.7)%(13.2 ± 3.0)%(0.0 ± 0.0)%

Table 6.2: The fraction of the SM process (a) after the kinematic selection and (b) after
all the selection.

6.4

Disappearing track selection

A tracklet selection described in Sec. 5.2.2 is applied to events after applying the kinematic selection. A category for the events which pass both the kinematic selection
and the disappearing track selection is called “signal region”. A cut-flow is shown in
Table 6.3. Requiring a track satisfied with the disappearance condition reduces bothsignal events and background events due to the signal acceptance and the no disappearing tracks in the SM processes, respectively. On the other hand, other requirements
on tracklets, especially the impact parameter requirement and the quality requirement,

71

Count

8

10

7

10

t,tt
VV
Zll
Signaldata

s =13TeV, 79.8 fb-1
mχ∼± = 500 GeV, τχ∼± = 0.2 nsec
1

1

6

10

multi-jet
Zνν
Wτν
Weν
W µν

5

10

4

10

3

10

2

10

Ratio

10
1
1.4
1.2
1
0.8
0.6

300

400

500

600

700 800
1000
Missing E [GeV]T

miss distribution after kinematical selection. As signal samples, wino LSP
Figure 6.5: ETmodels with a mass of 500 GeV and a lifetime of 0.2 ns are used. The data are shown inblack points. Signal distributions are shown in red lines. The Standard Model processes
are shown in diﬀerent colours.

72reject a large fraction of backgrounds compared to the signals, because most of the
tracklets in the events after the kinematic selection are fake tracklets.
Table 6.2 shows a fraction of background components. After only the kinematic
selection, a dominant background is Z → νν process. On the other hand, after the track
requirements, a dominant background is W → τ ν process, and the next largest fraction
comes from W → eν process. A jet derived from a quark and a gluon is highly rejectedby the tracklet selection. A source of tracklet background is leptons (electron, muon andtau) coming from a W production process.
Requirement
Kinematic selection
Disappearance condition
Geometrical acceptanceOverlap removal
Isolation
Impact parameter
Quality

Observed

Number of events
SM background (MC) Signal (m=500 GeV)

1.97×106
3.89×104
2.84×104
2.38×104
1.79×104
114
79(1.889 ± 0.022)×106(3.066 ± 0.035)×104(2.245 ± 0.030)×104(1.823 ± 0.028)×104(1.402 ± 0.021)×104
128 ± 2489 ± 16394 ± 427.4 ± 1.1
24.3 ± 1.0
22.8 ± 1.0
21.3 ± 0.9
18.0 ± 0.9
16.9 ± 0.8

Table 6.3: A cut-flow of tracklet selection after applying kinematic selections. A chargino
sample with a mass of 500 GeV and a lifetime of 0.2 ns is used as signal samples. The
Pixel dead module correction is not applied here.

73

Chapter 7

Background estimation
7.1

Overview

This analysis extracts the signal event yield by fitting with tracklet pT shapes. This isbecause the tracklet pT shapes are clearly diﬀerent between the signal events and thebackground events. A background estimation based on only MC samples would be notreliable due to the mismodellings of the event generation and the detector description
including material budget. In this analysis, the background estimation is based on datadriven technique, where most of the background estimation is done using only observeddata.
A tracklet pT shape of a background diﬀers among the cause and the origin. Background components are as follows
1. Charged particles hardly scattered by material of the tracker, which is called“Scattered” background. This origin can be further separated as follows(a) Charged hadrons (electrons) inelastically-scattering (causing bremsstrahlung)then lost hits expected to be along the direction of the seed-tracks.
(b) Muons failing reconstructions of tracks in both the inner detector and themuon spectrometer.
2. Tracklets which are formed from hits originating from two or more particles (called“Fake” background)
The scattered hadron backgrounds have nearly the same pT shape as the particles
which are not scattered by material. The pT shape is estimated using the tracks originating from each background source which does not scatter. Tracklet pT shape of the
lepton backgrounds is constructed by evaluating the probability that a lepton leaves adisappearing pixel tracklet. The probability is determined by using a high purity lepton
from Z-boson. Although the estimation of the pT shape of the scattered backgrounds isbased on the pT distribution of the source particles, the estimation of the pT distribution of the fake backgrounds is hard to be constructed from the pT shape of the source
74particles because the wrong-hit combination causes a wrong pT measurement. The pT
shape of the fake backgrounds is estimated by extrapolating it from a fake-backgroundenriched region.
The isolation with jets is required in a disappearing track selection. Applying thisrequirement reduces high pT tracks from hadrons and electrons to a negligible level ata very high pT region. However, due to the poor pT resolution of tracklets, high pT
tracklets, which originate from a low pT particle, may remain in the signal region. Thiseﬀect is evaluated by using the smearing function as discussed in Sec. 5.2.4.
The pT shape fitting without any constraints on the background event yield hasless discovery sensitivity because the structure of the pT shapes is smeared by the poor
tracklet pT resolution. This analysis evaluates the yields for each a background sourcefrom background enhanced samples in addition to the pT shapes.
In this section, estimations of the pT shape and the yield of each background sources
are described.

7.2

HadronWhen a hadron interacts with material of the tracker, the hadron changes the direction
or decays into other particles, and the outer hits produced by secondary charged particles
are not able to be associated in the tracking algorithm, then the trajectory looks like
disappearing and pass the disappearance condition. Since the scattered probability does
not depend on the pT shown in Fig. 7.1, the tracklet pT distribution of the scatteredhadrons is obtained by smearing the track pT distribution of non-scattered hadrons
without any pT -dependent scaling.
In order to extract the pT distribution of non-scattered hadrons in a similar condition
to tracklets in the signal region, a similar track selection to the disappearing track
selection is applied except for the requirements on the number of SCT hits, the numberof TRT hits and adding a requirement on the calorimeter energy deposit as follows
1. The number of SCT hits is more than 6
2. The number of TRT hits is more than 15
3. ETclus40 /pT > 0.3,
where ETclus40 is defined as the sum of calorimeter cluster energy associated with the
track within a cone of ∆R=0.4. The first and the second requirements are to ensurethat a track is not hardly scattered by the material and the track is not a fake. The third
requirement on the energy deposit is required in order to suppress muon contamination
shown in Fig. 7.2.
The pT distribution of non-scattered hadrons extracted by applying all the requirements described above is shown in Fig. 7.3 (a). Due to the poor tracklet pT resolution,
the template used in a fitting in the signal region is emulated by smearing the pT distribution with the resolution function measured in observed data as described in Sec. 5.2.4.

75

Scattering Probability

Arbitrary unit

All
Scattering

105

104

×10−3
72
70
68
66
64

Scattering before SCT layers|η| < 1.9

20 30 40 50 60 70 80 90 100

20 30 40 50 60 70 80 90 100

pion p [GeV]pion p [GeV]

T

T

(a)

(b)

Figure 7.1: (a) Pion pT distribution in the simulated samples. All pions are shown as
black points, and pions scattering before SCT detector are shown as red points. (b)Scattering probability as a function of pion pT . The scattering probability in this pT
scale is independent of its energy.

s =13TeV, 79.8 fb-1

multi-jet
Zνν
Wτν
Weν
W µν

t,tt
VV
Zll
data

4

10

5

10

s =13TeV, 79.8 fb-1

multi-jet
Zνν
Wτν
Weν
W µν

t,tt
VV
Zll
data

4

10

3

3

10

10

2

10
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10

10

1

Ratio

Ratio

10

1.4
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1.4
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1

1

0.8

0.8

0.6

0.6

20

30

40

50

60

70

80

−3

90
100
p [GeV]

10

10−2

10−1

T

1

topo clus40

ET

10
/p
T

(b) ETclus40 /pT(a) Track pT

Figure 7.2: (a) Track pT and (b) ETclus40 /pT before a requirement on the large energy
deposit. Dark green filled histograms are W → τ ν, and light green filled histograms are
W → µν. Although a dominant background is W → τ ν, other tracks from W → µν
process leaking from the lepton veto remains in high pT regions.

76

Figure 7.3 (b) is a smeared pT distribution. Small electron contamination around 70–
90 GeV is negligible after smearing due to the poor pT resolution.

5

multi-jet
Zνν
Wτν
Weν
W µν

10

s =13TeV, 79.8 fb-1

t,tt
VV
Zll
data

4

10

multi-jet
Zνν
Wτν
Weν
W µν

5

10

s =13TeV, 79.8 fb-1

t,tt
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Zll
data

4

10

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Ratio

1

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20

0.6

30

40

50

60

70

80

90
100
p [GeV]

102

T

3

10

104
Smeared p [GeV]T(a) Before smearing(b) After smearing

Figure 7.3: Track pT after requiring that ETclus40 /pT is larger than 0.3. Muon candidates are rejected by the calorimeter requirement. (a) Track pT before applying the pT
smearing. (b) Track pT after applying the pT smearing.
The bulk of the pion pT shape is not changed by the calorimeter energy requirement
because its threshold is small. However, the calorimeter requirement changes the tailfraction as shown in Fig. 7.4 (a) because the existence of high-energy calorimeter-clusters
associated with a track enhances the existence of a high-energy jet which vetos the
track due to the requirement on the isolation between the jet and the track. Thisdiﬀerence disappears after smearing pT due to the poor tracklet pT resolution as shownin Fig. 7.4 (b).
A yield of the hadron background is eﬀectively normalised at the low pT region in thefitting. Since the number of low pT tracklets is much larger than the high pT tracklets asshown in Figure 7.3 (b) and most of the tracklets originating from signal charginos havehigh pT , the number of high pT hadron tracklets can be evaluated with small statisticaluncertainties.

7.3

LeptonOnly electrons and muons are referred to as leptons here. Leptons can be clearly identified because they leave their characteristic signatures in the detector. Although theyleave clear signatures, they may leave disappearing track signature and the leptonidentification fails because of missing the standard track originating from them. Using
the benefit of leptons being easy to control, the number of lepton backgrounds in the sig77

Arbitrary unit

Arbitrary unit

All long tracks
Eclus40/ p > 0.3
T

104

T

103

All long tracks
Eclus40/ p > 0.3
T
T

104

103
102
102
10

NSCT ≥ 6, NTRT ≥ 15
|η| < 1.9

NSCT ≥ 6, NTRT ≥ 15
|η| < 1.9

20 30 40 50 60 70 80 90 100

103104pion p [GeV]102pion p [GeV]
T

T

(a)

(b)

Figure 7.4: Pion pT distribution (a) with and (b) without the requirement on calorimeter.
nal region is estimated using the probability of a lepton being identified as a disappearing
track.
Electrons and muons behave quite diﬀerently. Electrons leave their signs at thecalorimeter. On the other hand, muons leave little energies in the calorimeter and leave
tracks in the muon spectrometer. Due to the diﬀerence, two components are separately
treated and evaluated.
The number and pT shape of leptons in the signal region (NSR (pT )) is estimated byconverting the number and the pT shape in the one-lepton region (control region) as thefollowing formula∑
NSR (pT ) =P(pT , ηi , ϕj )NCR (pT , ηi , ϕj ),(7.1)
ηi ,ϕjwhere the first term, P, is a transfer factor from the one-lepton events to zero-lepton
events. It is defined as the ratio of the probability of the lepton having the pixel tracklets
to the probability of the lepton having the standard tracks. The transfer factor isevaluated as a function of pT , η and ϕ. The second term, NCR is the number of leptons
identified using the standard tracks in the one-lepton control region. Two terms are
separately discussed in following sections.

Extraction of events with exactly one lepton
In order to extract a similar kinematical topology to the signal region, almost the samekinematical selection as in the signal region is used. The diﬀerences from the normal
kinematical selection are the requirement on exactly one lepton instead of the lepton veto
miss definition. Alternative E miss is calculated by excluding
and the use of alternative ETT78

the lepton term to emulate the case that the lepton is identified as a disappearing track.
In the case of an electron failing a lepton identification, the electron energy contribution
is added to the jet term because the electron deposits sizable energy in the calorimeter.
On the other hand, in the muon case, since the corresponding jet term is quite small,miss is quite diﬀerent from the original one. This diﬀerence causes
the alternative ETa diﬀerence in the kinematical distribution between electrons and muons as shown in
Fig. 7.5 (a) and (b).
Events in the exactly one lepton region are triggered by single isolated-lepton triggers [32, 90, 94, 95]. For the electron trigger, it is required that the pT of an electron ishigher than 22 GeV in the Level-1 trigger and 26 GeV in the High-Level-Trigger, and theelectron satisfies the “Tight” quality criteria and is isolated. For selecting muon events,
it is required that the pT of a muon is higher than 15 or 20 GeV in the Level-1 trigger
and 22–26 GeV in the High-Level-Trigger, and the muon is isolated.
A lepton is required to have an isolated inner-detector track satisfying the disappearing track selection except for some conditions
1. pT is greater than 15 GeV instead of 5 GeV
2. the number of TRT hits is more than 5 instead of the TRT veto3. No requirement on the SCT hits is applied
4. No requirement on isolation with jets is applied.
Figure 7.5 (c) and (d) show lepton pT distributions in the lepton control regions. The
miss definition mentioned above
diﬀerence between electrons and muons comes from the ET
and the diﬀerence in calorimeter energy deposit. A diﬀerence of normalisation between
data and MC in Fig. 7.5 comes from a Pixel dead module as discussed in Sec. 5.2.4
because the scale factor is not applied here.

An estimation of the transfer factor from good leptons to disappearing
tracks
The first term of Eq. 7.1 is measured using Z → ℓℓ events. In order to ensure thatdisappearing tracks come from leptons, the events are required to contain the following
signatures
1. One lepton identified as high purity leptons (named as “tag” lepton)(a) pT > 30 GeV(b) |η| < 2.5(c) |η| < 1.37 and 1.52 < |η| for electrons(d) Identified as “Tight” quality as described in Sec. 4.
2. One isolated track associated with characteristic signature used in lepton reconstruction steps (named as “probe” lepton)
79

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(d)

miss distribution in electron control region (b) E missFigure 7.5: One lepton events (a) ETT
distribution in muon control region (c) Electron pT distribution in electron control region(d) Muon pT distribution in muon control region

80(a) For electron case, a track is associated with an electromagnetic calorimetercluster with the pT higher than 10 GeV and |η| smaller than 2.5.
(b) For muon case, a track is associated with a muon-spectrometer track with thepT higher than 10 GeV and |η| smaller than 2.5.
3. An event has the above two objects and the mass reconstructed from tag lepton
and probe lepton is within a narrow mass window around the Z mass.
(a) |Mtag,probe − MZ | < 10 GeV, where Mtag,probe is a reconstructed mass from a
tag lepton and a probe lepton.
(b) ∆ϕ(tag, probe) > 0.1
The events are selected by using single-isolated-lepton triggers. In order to extract the
only clean Z → ℓℓ events, the events having more than two diﬀerent lepton flavours are
rejected.
By using high purity lepton objects extracted here, a ratio of the probability of probe
lepton having an associated tracklet to that of the probe lepton having an associatedstandard track is evaluated. In order to use tracks with a similar condition with thedisappearing track candidates, the associated standard tracks and the associated pixel
tracklets are required to pass track selections as follows
1. pT > 15 GeV
2. Isolation with jets are applied only for pixel tracklet selection
3. No diﬀerent flavour leptonic objects around the tracks(a) ∆R(track, muons) > 0.4 for electrons(b) ∆R(track, MS-tracks) > 0.4 for electrons(c) ∆R(track, electrons) > 0.4 for muons
4. ∆R(tracks, probe) < 0.2
5. The number of TRT hits is more than 5 for standard track selection
6. No hits in SCT and TRT for pixel-tracklet selection
Figure 7.6 show the di-lepton mass (Mtag,probe ) distribution with a requirement on
tracks associated with the probe lepton. A diﬀerence between data and MC simulation
comes from the mismodelling of Pixel detector condition discussed in Sec. 5.2.4. Mostof the events around the Z-mass peak are produced by Z → ℓℓ events, and the contamination from other particles is small enough to be neglected. The small mismodellingaround the Z-mass peak comes from the absence of the energy calibration, which isused for reconstructed lepton, for the energy of EM calorimeter and MS tracks. As
this mismodelling does not aﬀect the purity of lepton events very much, no additionalcorrections of EM clusters and MS tracks are applied.
81

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110
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Zµ µ Mass [GeV](d)Figure 7.6: Di-lepton mass distribution with a large mass window (|Mtag,probe − MZ | <30 GeV). (a) Z → ee associated with the long standard tracks (b) Z → ee associatedwith pixel tracklets (c) Z → µµ associated with the long standard tracks (d) Z → µµ
associated with pixel tracklets

82

2.5

Zee probe η

Zee probe η

The transfer factor is calculated as the ratio of the number of events having pixel
tracklets to those having the standard tracks as a function of pT and η. Figure 7.7
shows the transfer factor for electrons. Electrons leave large fractions of energies in thecalorimeter. Therefore high pT electrons do not pass the disappearing track selection
due to the isolation requirement with jets. An η dependence in the transfer factors isdue to the material budget of the inner tracker shown in Fig. 2.3. Figure 7.8 shows thetransfer factor for muons. The pT dependencies of muon are diﬀerent because muons do
not leave their energies in the calorimeter like electrons. Since muons are heavier thanelectrons and produce bremsstrahlung less frequently, the transfer factor for muons issmaller than electrons.

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0 10 20 30 40 50 60 70 80 90 100
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T

Zee probe η

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(b)
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1e-021e-02 9e-034e-03

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4e-034e-03 3e-037e-04

20

30

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9e-06

40

50

60

70 80 90 100

Zee probe p [GeV]T(c)

Figure 7.7: (a) The number of electrons associated with the long standard tracks asfunction of pT -η. (b) The number of electrons associated with the pixel tracklets asfunction of pT -η. (c) The ratio of the number of electrons having pixel tracklets to thosehaving the standard tracks (transfer factor) as function of pT -η.

83

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40

2
10−4

1.5
1
0.5
0

20

50 60 70 80

100

10−5
200

Zµµ probe p [GeV]T(c)

Figure 7.8: (a) The number of muons associated with the long standard tracks as functionof pT -η. (b) The number of muons associated with the pixel tracklets as function of pT -η.
(c) The ratio of the number of muons having pixel tracklets to those having the standard
tracks (transfer factor) as function of pT -η.

84

Tag and Probe method for estimation of MSTracks
In the disappearing track selection, a veto of muon-spectrometer tracks is required.
Therefore, as the transfer factor of muons, the eﬀects should be added in addition to thetransfer factor of MS-tracks. For the estimation of the MS-track transfer factor, Z → µµ
events are used. The ratio of the probability of a lepton not having a muon-spectrometer
track to that of a lepton having a muon-spectrometer track is evaluated.
1. One lepton identified as high purity leptons (named as “tag” lepton)(a) pT > 20 GeV(b) |η| < 2.5(c) Identified as “Tight”
2. One isolated inner-detector tracks (named as “probe” lepton)(a) pT > 15 GeV(b) |η| < 2.5(c) Normal disappearing track condition, except an isolation with muons and
SCT veto
3. An event has the above two objects and the mass reconstructed from tag lepton
and probe lepton is within a narrow mass window around the Z mass.
(a) |Mtag,probe − MZ | < 10 GeV(b) ∆ϕ(tag, probe) > 0.1(c) No electrons
And events need to be triggered by the isolated single muon trigger.
For MS tracks, the following selections are required.
1. pT > 5 GeV
2. ∆R(probe inner-detector track, MS-track) < 0.2
Figure 7.9 shows the mass distribution in this selection. As shown in Fig. 7.9 (b),high purity Z → µµ events are selected.
Figure 7.10 shows the transfer factor as a function of η and ϕ of muon probes. Unlike
the inner detector, the muon spectrometer is not uniform in ϕ as shown in Fig. 7.10 (c).
A peak around η = 0 is due to the inactive region of the muon spectrometer. This region
is not used in this search.

Template for the signal region
Figure 7.11 show the two-dimensional distribution of electrons as a function of pT and η
and that of muons as a function of η and ϕ after applying each transfer factor. The pT
templates after applying the smearing method to the lepton pT in the one-lepton control
region shown in Fig. 7.5 (c) and (d) are shown in Fig. 7.12. As shown in Fig. 7.12,
W → ℓν events are dominant backgrounds.
85

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7.4

Fake

Fake tracklets are formed from a wrong combination of hits. In this case, tracklets
have almost a random pT and d0 significance distribution. Since there is no correlation
between them, tracklets with large d0 significance are used as a control sample.
Figure 7.13 shows a d0 significance distribution after an application of all selection
miss selection (E miss > 120 GeV) and except for the d significance selection,with loose ET
0
T
where one-wrong-combination is defined as one of the hits in tracks does not come fromthe same particle and multi-wrong-combination is defined as two or more hits in tracks
do not come from the same particle. The diﬀerence in the d0 significance between data
and MC is due to misalignment in the detector and other imperfection in the modellingof the simulation. Most of the tracklets having d0 significance larger than 10 come froma wrong combination of hits.
To extract the pT template for the fake background, large d0 significance (> 10) is
required. Figure 7.14 shows the pT distribution in the fake control region, where an
empirical function
2f (pT ) = eA log pT +B(log pT )(7.2)
is used to fit data. This function is a quadratic function for a log-log axis, and able tomodel the pT shape in the fake control region.
The yield of fake tracklet background in the signal region is evaluated using theso-called ABCD method. When there is no correlation between a variable a and b, thedouble ratio
N (a ∈ A, b ∈ B) N (a ∈ A, b ∈ B ′ )rABCD =/,
(7.3)
N (a ∈ A′ , b ∈ B) N (a ∈ A′ , b ∈ B ′ )86

Zµ µ probe ηZµ µ probe η

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Zµµ probe φ(c)Figure 7.10: (a) The number of the standard tracks associated with MS tracks as functionof ϕ-η. (b) The number of the standard tracks not associated with MS tracks as functionof ϕ-η. (c) The ratio of the number of the standard tracks associated with MS-tracks tothose not associated with MS-tracks (transfer factor of MS-tracks) as function of ϕ-η.

87

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Muon φElectron p [GeV]
T

(a)

(b)

Figure 7.11: (a) Two dimensional distribution of electrons as a function of pT and ηafter applying transfer factor. (b) Two dimensional distribution of muons as a functionof η and ϕ after applying transfer factor.

310

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p [GeV]
T

(a)

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Figure 7.12: pT template after pT smearing (a) for electron (b) for muon. Black points
are observed data. Filled histograms are MC simulated samples. The same smearing
function, which is measured from observe data, is applied for both observed data andMC simulated samples.

88s =13TeV, 79.8 fb-1

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top
Other SMdata

Multi wrong comb.
One wrong comb.
Zν ν
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|d significance|0

miss selecFigure 7.13: |d0 significance| distribution after all selection with loose ET
miss > 120 GeV) and except for d significance selection. Black point showstion (ET0observed data, and filled histograms show the SM simulated process. Light grey anddark grey histograms show fake tracklets.

where N (a ∈ A, b ∈ B) represents the number of events where variable a is satisfied
with the condition A and variable b is satisfied with the condition B, is expected to
be unity typically. The number of events in the interesting region (N (a ∈ A, b ∈ B))
is evaluated from the other three regions. The d0 significance value of a pixel tracklet
miss value, because track information of the pixel tracklet isdoes not depend on the ET
miss
not used in the ET calculation. The number of fake tracks in the signal region can beevaluated by the formula
Nsmall d0 ,large Emiss = Nsmall d0 ,low Emiss ×TT

Nlarge d0 ,large Emiss
T

Nlarge d0 ,low Emiss

,

(7.4)

T

miss and large E miss region are defined as 120 GeV < E miss < 200 GeV
where low ETTTmiss , respectively, and small d and large d regions are defined as
and 200 GeV < ET00
|d0 significance| < 1.5 and |d0 significance| > 10, respectively.
miss . The p
Figure 7.15 shows a dependence on d0 significance and ET
T shape is
missindependent of the ET and d0 significance within an uncertainty of the fit function.

89

Tracklets / GeV

10−2

Fit
Data

10−3

f(p ) = exp( A log p + B (log p )2)T

TTχ2/Ndf = 0.39

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10−72
Tracklet p [GeV]

1.5

T

1
0.5
0

102

10

3

104
Tracklet p [GeV]T

Tracks / GeV

Tracks / GeV

Figure 7.14: The transverse momentum of tracklets in the fake control region. Observed
data are shown as black points. The fit function is shown as a blue line and the blue
band is the 1-σ uncertainty.
s=13TeV, 79.8 fb -1
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miss

120 GeV < ET

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< 120 GeV

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10 < |d significance| < 50
0

5 < |d significance| < 10
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30

100

200

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1000 2000
10000
Track p [GeV]

Track p [GeV]

T

T

(a)

(b)

miss requirement with
Figure 7.15: Dependence of the fake-tracklet pT on (a) the ET
miss requirement.
d0 significance > 10 and (b) the d0 significance requirement with no ET

90

Chapter 8

Extraction of signal yield
A signal yield is extracted by using an unbinned extended maximum likelihood technique.
A likelihood function consists of sub-terms about the total number in the signal region,
pT shape and systematic uncertainties. A pT shape for signal charginos is constructedusing a generator-level pT distribution of the charginos which pass the event selection,then the pT distribution is smeared using the smearing function as discussed in Sec. 5.2.4.
pT shapes for background is already discussed in Chapter 7. In order to constrain themiss region (E miss > 200 GeV) and low E miss region (120 GeV
fake track events, the high ET
TTmiss < 200 GeV) are fit simultaneously.
< ET

8.1

Unbinned extended maximum likelihood fit

The likelihood function (L) for the tracklet pT in an ensemble of observed events isdefined as
∏
R
R
R
R
R
L(µs , nH , nL , θ, rf | p⃗T ) ≡P(nR
obs |µs ns + nh + ne + nµ + nf )R∈{H,L}×∏

Lshape (p⃗T ; µs , nR , θ)R∈{H,L}×∏

Lsys (nR ),R∈{H,L}× Lsys (θ),× Lsys,fake (nH , nL , rf ).

(8.1)

The first term is an extended term and constrains the sum of the number of each
H(L)
H(L)
H(L)
H(L)
H(L)
components by the observed number of events, where nobs , ns , nh , ne , nµH(L)and nfare the number of total observed events, signal events for a given model,
hadron track events, electron track events, muon track events and fake track events inmiss region. The function
the signal region, respectively. “H (L)” represents high (low) ET

91

of P(n|µ) represents the Poisson distribution
P(n|µ) =µn e−µ.
n!

(8.2)

The second term is a shape term and evaluates the probability of the observed pTfor each event. The variables, nH (L) and θ, are the number of events for each source
and the systematic uncertainties for the pT template, respectively, as follows
H H H H H
nH ≡ {nHs , nh , ne , nµ , nf , nFakeCR }(8.3){nLs , nLh , nLe , nLµ , nLf , nLFakeCR }

(8.4)

L

n

≡

θ ≡ {θ⃗s , θ⃗h , θ⃗µ , θ⃗e , θ⃗f }θ⃗s ≡ {σssmear , αssmear }θ⃗h ≡ {σhsmear , αhsmear , νhsmear }{}θ⃗µ ≡ σµsmear , αµsmearθ⃗e ≡ {σesmear , αesmear , νesmear }
{
}
fit
θ⃗f ≡
pfit
,
p
,
0
1

(8.5)
(8.6)
(8.7)
(8.8)
(8.9)
(8.10)

where the parameters θ⃗h , θ⃗µ , θ⃗e , θ⃗s and θ⃗f are nuisance parameters used to include uncertainties in the hadron smearing function, muon smearing function, electron smearing
function, signal smearing function and fake background pT -spectra, respectively. The
formulation of Lshape is given as
Lshape (p⃗T ; µs , n, θ) =n∏
obs

µs ns Fs (pT ; θ⃗s ) +µs n s +∑⃗c∈{h,e,µ,f } nc Fc (pT ; θc )∑c∈{h,e,µ,f } nc,

(8.11)

where Fs , Fh , Fe , Fµ and Ff are the probability density functions of signals, hadrons,
electrons, muons and fake tracks, respectively.
The third term is for systematic uncertainties of the number of events of signal,
electron and muon components. The formulation of Lsyst is given as∏2
2
2
Lsyst (n) = BiN (ns | nexp
N (nc | nexp
(8.12)s , σd,ns , σu,ns ) ×
c , σnc ),c∈{e,µ}where the function of N (x | µ, σ 2 ) and BiN (x | µ, σd2 , σu2 ) represent a normal distribution
and an asymmetric Gaussian distribution)(
1(x − µ)22
N (x | µ, σ ) = √(8.13)
exp −
2
2σ 2
2πσ

(
)
2
exp − (x−µ)
x<µ
2
2σd )
(
BiN (x | µ, σd2 , σu2 ) =,(8.14)
2
exp − (x−µ)
other
2
2σ
u

92

where µ is the expected mean and σ is the uncertainty. The uncertainties are summarised
in Sec. 9.
The fourth term is for systematic uncertainties for a pT smearing function and theformulation is given as∏
Lsyst (θ) =N (σcsmear | σcsmear,exp , σσ2csmear )c∈{s,e,h,µ}∏×N (αcsmear | αcsmear,exp , σα2 smear)cc∈{s,e,h,µ}×∏

N (νcsmear | νcsmear,exp , σν2csmear ),(8.15)c∈{e,h}The last term is for systematic uncertainties related with a fake tracklet. rf represents
a logarithmic ratio for the number in the ABCD method as follow( H H)
nf /nFakeCR
rf = log rABCD = log(8.16).
nLf /nLFakeCR
H(L)

where nfakeCR is the number of the fake events in the fake control region. This term
should be zero-consistent when the ABCD method ideally works. The formulation of
Lsyst,fake is given as
Lsyst,fake (nH , nL , rf ) = N (rf | rfexp , σr2f )
)
)
(
(
L,obs
L
H
×
P
n
|n
×P nH,obs|n
FakeCR FakeCR , (8.17)
FakeCR FakeCR
As the probability density function of fake tracks, the polynomial function is used as
miss signal region and the low E miss control region are fit
described in Sec. 7.4. The high ET
Tsimultaneously, so the correlation between parameters are automatically incorporated.

8.2

Hypothesis testing

In order to claim a discovery or to set exclusion limits, test statistic is defined as follows
q̃0 = −2 ln λ̃(0)(µ̂ ≥ 0)q̃µ = −2 ln λ̃(µ) (0≤ µ̂ ≤ µ)
ˆL(µ, θ̂(µ))(µ̂ ≥0),λ̃(µ) =
L(µ̂, θ̂)(8.18)(8.19)(8.20)

ˆ
where θ̂ is a θ which maximises L for given µ. µ̂ and θ̂ are µ and θ which maximise L,
respectively. For the test of a discovery or an exclusion, the p-values, which is definedas cumulative distribution∫ ∞p0 ≡(8.21)f (q̃0 | 0)dq̃0q̃ obs

pµ ≡

∫ 0∞

obs
q̃µ

f (q̃µ | µ)dq̃µ93(8.22)

are generally used. When p-values are less than the traditional threshold (e.g. 0.05 (95%),
1.3×10−3 (3-σ discovery), 2.9×10−7 (5-σ discovery)), one can claim the discovery or the
exclusion.
For a limit setting, in order to avoid claiming a limit for which this analysis does nothave sensitivity due to negative background fluctuations, this analysis uses CLs [96] asdefinedCLs (µ) =ps+b
1 − pb

(8.23)∫ ∞CLs+b (µ) = ps+b =CLb (µ) = 1 − pb =f (q̃µ | µ) dq̃µ

obs
q̃µ
∫ ∞

obs
q̃µ

f (q̃µ | 0) dq̃µ .

(8.24)(8.25)For the exclusion limit setting, 95% CLs , where CLs is less than 5%, is used. In orderto minimise the calculation time of p-value, the calculation is done using asymptotic
formulas [97], where it is assumed that the test statistic can be approximated to q̃µ ≈ µ−µ̂
σ2
by Wald’s theorem [98]. The parameters used in the approximation are determined using
Asimov dataset which is constructed to satisfy all parameters set to be their expectedvalues.

94

Chapter 9

Systematic uncertainties
There are three types of uncertainties: for common uncertainties aﬀecting both signal
and background processes, uncertainties relevant only for signal or background processes.
As common systematic uncertainties, there are smearing-function-related uncertainties,
which change the pT templates. The smearing-function-related uncertainties are evaluated for each a particle. Signal systematic uncertainties are assessed as a normalisation
uncertainty. As a background systematic uncertainty, an uncertainty of the method of
the fake normalisation estimation is considered.

9.1

Common systematic uncertainty

Smearing function
Since the smearing function is directly measured from observed data, the MC
simulation uncertainties are not necessary to be considered. However, a time dependence was observed as shown in Fig. 9.1. The maximum diﬀerence between
all period and all pT bins is assigned as the uncertainty. For muons, 7.3% and17.1% are assigned for σ and α, respectively. For electrons, 8.5% and 21.2% areassigned for σ and α, respectively. For n parameter for electrons and pions, 100%
uncertainties are assigned. For signals, the maximum diﬀerence between all period
for the highest pT bins, 6.32% and 10.1%, are assigned for σ and α, respectively.

9.2

Signal systematic uncertainty

In this section, signal-related uncertainties are discussed. Theoretical cross-section uncertainties are already discussed in Sec. 3.2.1.
Generator modelling
Since this analysis requires high pT jets in the kinematical selection, a modellingof ISR jets aﬀects the signal kinematical acceptance. In order to evaluate thegenerator uncertainties, the generator tunes in the event generation are varied, and95

σ [TeV-1]

24Zµµ, p = (50, 200) GeV
T
Zµµ, p = (40, 50) GeV
T
Zµµ, p = (30, 40) GeV
T
Zµµ, p = (25, 30) GeV
T
Zµµ, p = (20, 25) GeV

22

Zee, p = (50, 200) GeV
T
Zee, p = (40, 50) GeV
T
Zee, p = (30, 40) GeV
T
Zee, p = (25, 30) GeV
T
Zee, p = (20, 25) GeV

T

20

T

18
16
14
12
10
04/15

07/15

10/15

12/15

04/16

07/16

09/16

12/16

04/17

07/17

09/17

12/17

04/18

Date [month/year]

α

(a)
4
Zµµ, p = (50, 200) GeV
T
Zµµ, p = (40, 50) GeV
T
Zµµ, p = (30, 40) GeV
T
Zµµ, p = (25, 30) GeV
T
Zµµ, p = (20, 25) GeV

3.5

Zee, p = (50, 200) GeV
T
Zee, p = (40, 50) GeV
T
Zee, p = (30, 40) GeV
T
Zee, p = (25, 30) GeV
T
Zee, p = (20, 25) GeV

T

T

3
2.5
2
1.5
1
04/15

07/15

10/15

12/15

04/16

07/16

09/16

12/16

04/17

07/17

09/17

12/17

04/18

Date [month/year](b)

Figure 9.1: Time dependence of smearing function parameters, (a) σ and (b) α, observed
from observed data for muons (labelled as Z → µµ) and for electrons (labelled as Z → ee)
separated in ranges of pT . The resolution σ becomes worse as the integrated luminosity
increases.

96the change in the kinematical acceptance at the generator-level between samples
are assigned to the uncertainty. Three variations are considered as follows• Renormalisation scale and factorisation scale are varied by factors of 0.5 and
2.0 from the default ones (M 2 + p2T ).
• CKKW-L merging scale [36,99], which determines the process (matrix-element
or parton-shower) of additional partons, is varied by factors of 0.5 and 2.0
from the default one (1/4 of chargino mass).
• Parameters in the parton shower tuning [43] are varied by the uncertainties.
Although there are five variation sets, only one set related to ISR αs has a
non-negligible eﬀect.
Figure 9.2 shows the relative changes by variation as a function of chargino mass.
Because the lifetime variation does not change the generator-level kinematical acceptance within the considered lifetime range, common uncertainties are used for
all chargino lifetimes. Figure 9.2 (g) and (h) show combined systematic uncertainties from the event modelling in the event-generator. These uncertainties are
assigned to each signal mass points.
Jet energy scale/resolution
Although jet energy scale and resolution are calibrated, there is a small discrepancy
between data and MC simulation. The uncertainties of jet energy scale and resolution are sensitive to this analysis because of the use of high pT jet to select signal
events. The impact is evaluated by comparing the kinematical acceptance withvarying jet performance by their uncertainties discussed in Ref. [77]. This analysis
uses a strongly-reduced nuisance-parameter set, where several eﬀects of parameters
are combined, because of a negligible impact from the correlation between errorsof the parameters. The impacts from the jet energy scale are 2–3%, and ones fromjet energy resolution are less than 1%.
missETmiss is reconstructed using all hard objects and the soft term as described inETmiss from the jet uncertainties are contained in the evaluation
Sec. 4.6. Eﬀects to ET
of jet energy scale and resolution uncertainties as discussed above. The uncertainties related to the soft term is evaluated by comparing the observed data to three
diﬀerent MC-generators as described in Ref. [89]. These eﬀects on this analysis
are evaluated by comparing the kinematical acceptance varying the uncertainties.
The impact is less than 1%.

Trigger eﬃciency
Since trigger eﬃciency is directly evaluated from observed data, the only statisticaluncertainty of the measurement is considered as the systematic uncertainty, and
it is found to be negligible.

97

15

Relative systematic uncertainties [%]Relative systematic uncertainties [%]

20
up
down

Pythia Var3c
Wino

10
5
0
−5
−10
−15
−20

100

200

300

400

500

600

700

15

up
down

Pythia Var3c
Higgsino

10
5
0
−5
−10
−15

800

100

120

140

160

Chargino mass [GeV]

up
down

Jet matching scale
Wino

10
0
−10
−20
100

200

300

400

500

600

700

20

up
down

Jet matching scale
Higgsino

10
0
−10
−20

800

100

120

140

160

Chargino mass [GeV]

Relative systematic uncertainties [%]Relative systematic uncertainties [%]

4
2
0
−2
−4
−6
100

200

300

400

500

600

700

10

up
down

Factorization/Renormalization Scale
Higgsino

5
0
−5
−10

800

100

120

140

160

Chargino mass [GeV]

Relative systematic uncertainties [%]Relative systematic uncertainties [%]

up
down

20
10
0
−10
−20
−30
200

300

400

500

600

700

800

30

up
down

Combined
Higgsino

20
10
0
−10
−20
−30
100

Chargino mass [GeV](g) Combined

200(f) R/F Scale

Combined
Wino

100

180

Chargino mass [GeV](e) R/F Scale30200(d) CKKW-L merging scale

up
down

Factorization/Renormalization Scale
Wino

180

Chargino mass [GeV](c) CKKW-L merging scale
6200(b) ISR αs (VAR3c)
Relative systematic uncertainties [%]Relative systematic uncertainties [%](a) ISR αs (VAR3c)20

180

Chargino mass [GeV]

120

140

160

180

200

Chargino mass [GeV]98(h) Combined

Figure 9.2: Uncertainties related to the event modelling in the event-generator. (a)Pythia parton shower generator tuning for wino samples (b) Pythia parton shower generator tuning for higgsino samples (c) Jet merging scale for wino samples (d) Jet merging
scale for higgsino samples (e) Factorisation/Renormalisation scale for wino samples (f)Factorisation/Renormalisation scale for higgsino samples (g) Combined uncertainties forwino samples (h) Combined uncertainties for higgsino samples

0.03

Tracklet efficiency

Arbitrary unit

Pile-up
Pile-up distribution uncertainties are assigned to cover the discrepancy in the average interaction per bunch crossing (⟨µ⟩) between MC simulation and observed
data derived from the visible cross-section measurements as shown in Fig. 9.3 (a),where the nominal variation corresponds to the scale-factor to match the Pile-up
distribution in MC with observed data. The impact on the signal kinematicalacceptance is less than 0.5%. On the other hand, the eﬀect on the track reconstruction is higher as shown in Fig. 5.3, so the eﬀects on the tracking eﬃciency
from the ⟨µ⟩ scale factor (µSF ) uncertainties are also evaluated. Due to the smallereﬀects on the kinematical acceptance than the track reconstruction, the impacts
are evaluated independently on the chargino mass and lifetime. Moreover, no kinematic selection is applied to increase statistics. Figure 9.3 (b) shows a tracklet
reconstruction and selection eﬃciency as a function of decay radius with pile-up
variations. The change in signal acceptance is less than 2.3%, which is assigned as
the pile-up systematic uncertainty.

Down (µ = 1/1.07)
SF
Nominal (µ = 1/1.03)SFUp(µ = 1/0.99)

0.025

SF

0.02

Down ( µ = 1/1.07)
SF
Nominal ( µ = 1/1.03)SFUp(µ = 1/0.99)

0.4
0.35

SF

0.3
0.25
0.2

0.015

0.15
0.1

0.01

Meta-stable chargino samples|η| < 1.9

0.05
Ratio

0.005

0
1.04
1.02
1

0
0

10

20

30

40

50

0.98

60

0.96

50

Mean number of Interactions per Crossing

(a)

100

150

200

250

300

350

400
450
500
Decay radius [mm](b)

Figure 9.3: Tracklet reconstruction and selection eﬃciency with pile-up variations.
Track reconstruction eﬃciency / selection eﬃciency
Since a detector modelling is not perfect, it is necessary to incorporate the possible
diﬀerence in the tracking reconstruction and selection eﬃciency in observed data
and MC simulation. The uncertainties in the track reconstruction eﬃciency andthe selection eﬃciency are evaluated by comparing the tracklet in the observed data
and MC simulation using artificial pixel tracklets in Z → µµ events discussed in
section 5.2.3. Figure 9.4 shows the comparison of tracklet reconstruction eﬃciency
between the observed data and MC simulation. The maximum diﬀerence of 2.8%, isassigned to the reconstruction eﬃciency uncertainty. Figure 9.5 and Table 9.1 show
a comparison of track selection eﬃciency at each selection criteria. The maximum
eﬀect comes from the isolation requirement, which comes from the mismodellingin the number of tracks. The maximum diﬀerence of 4.2 % is assigned to the track
selection eﬃciency uncertainties.
99

Reconstruction efficiency

1
0.98
0.96
0.94
0.92
0.9
0.88

Observed data
Simulation

0.86

Ratio

0.84
1.04
1.02
1
0.98
0.96

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

η

Track selection efficiency

Figure 9.4: Data/MC comparison of reconstruction eﬃciency for muon tracks.

1.05
Observed data
Simulation

1
0.95
0.9
0.85
0.8
0.75
0.7
0.6

Data
1
0.906
0.898
0.898
0.898
0.896
0.895
0.855
0.828
0.828
0.809
0.808
0.670

Isolation

d0significanceOverlap removal

z 0sinθNo spoilt hits

χ2-probability

No Pixel outliers

No hole hits

No gangged fake

Innermost layer hits

N of Pixel hits

All

1.04
1.02
1
0.98
0.96
0.1 < η < 1.9

Ratio

0.65

selection
All
0.1 < η < 1.9
N of Pixel hits
Innermost layer hits
No hole hits
No ganged fake
No Pixel outliers
No spoilt hits
χ2 -probability
z0 sin θ
d0 significanceOverlap removal
Isolation

Figure 9.5: Data/MC comparison of selection ef- Table 9.1: Cut-flow of relative
selection eﬃciency.
ficiency for muon tracks.

100

MC
1
0.909
0.905
0.905
0.905
0.904
0.903
0.862
0.829
0.828
0.816
0.815
0.699

d0 significance mean

d0 significance bias
A shift of transverse impact parameter is observed as shown in Fig. 9.6, wheremuon tracklets are extracted by the same selection used for the measurementsof the smearing function discussed in section 5.2.4 except for the d0 significancerequirement. The mean value of d0 significance is shifted from negative to positiveat the first technical shutdown in 2016, and their bias is disappeared from 2017.
The eﬀects of this bias are summarised in Tables 9.2 and 9.3. This shift is observedin about half of the total luminosity. Therefore the half eﬃciency loss by a shiftof the d0 significance by 0.4 is subtracted from the total signal selection eﬃciency
and the same uncertainty of the same amount is assigned.
0.5
2015

0.4

2016

2017

0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
01/04

02/07

01/10

31/12

01/04

01/07

30/09

30/12

01/04

01/07

30/09

31/12
Date [dd/mm]

Figure 9.6: History of d0 significance (d0 /σd0 ) of pixel tracklets. A shift from a negative
bias to positive bias in June 2016 corresponds to the first technical shutdown in 2016.
Mass (GeV)
Loss

91
-1.8%

200
-2.0%

300
-2.5%

400
-2.8%

500
-2.6%

600
-2.7%

700
-2.7%

800
-2.9%

900
-3.1%

Table 9.2: Signal selection loss by a shift of the d0 significance by 0.4 for wino samples.
Mass (GeV)
Loss

95
-2.7%

100
-2.2%

120
-2.4%

140
-2.4%

160
-2.2%

200
-2.1%

Table 9.3: Signal selection loss by a shift of the d0 significance by 0.4 for higgsino samples.
Integrated luminosity
As discussed in the section 3.1.1, 2.0% is assigned to the uncertainty of the integrated luminosity.
Tables 9.4 and 9.5 summarise all the considered uncertainties.

9.3

Background systematic uncertainty

This analysis relies on the data-driven method. Uncertainties in the object reconstruction are negligible compared to fitting uncertainties coming from the statistical uncer101

Source(Theoretical uncertainty)+ −Cross-section(χ̃1 χ̃1 )+ 0
Cross-section(χ̃1 χ̃1 )− 0
Cross-section(χ̃1 χ̃1 )(Uncertainties on the acceptance)
Scale+PS+PDF
JES
JER
TST
Trigger eﬃciency
Pile-up modeling
Tracklet reconstruction eﬃciency
Signal selection eﬃciency
d0 biasLuminosity
Sub-total

91

200

Chargino mass (GeV)
300
400
500
600

700

800

±2.6
±2.0
±4.1

±4.0
±3.4
±5.5

±4.9
±4.4
±6.3

±5.6
±5.4
±7.0

±6.3
±6.2
±7.6

±6.8
±6.8
±8.2

±7.3
±7.3
±8.9

±7.7
±7.7
±9.5

+25.1
−6.7
+3.2
−3.1
+0.8
−0.0
+0.7
−1.1
+0.0
−0.1

+11.9
−8.3
+2.6
−2.4
+0.3
−0.0
+0.4
−0.6
+0.0
−0.1

+8.5
−8.5
+2.0
−1.8
+0.2
−0.0
+0.2
−0.4
+0.0
−0.1

+6.8
−9.9
+1.8
−1.6
+0.4
−0.0
+0.2
−0.3
+0.0
−0.2

+9.5
−4.9
+1.8
−2.0
+0.1
−0.0
+0.1
−0.2
+0.0
−0.2

+9.8
−9.6
+1.4
−1.9
+0.0
−0.2
+0.2
−0.2
+0.0
−0.2

+10.1
−7.0
+1.3
−0.9
+0.0
−0.4
+0.2
−0.2
+0.0
−0.2

+4.3
−15.3
+1.4
−1.9
+0.0
−0.2
+0.1
−0.3
+0.0
−0.3

±0.9

±1.0

±1.4

±1.6

+26.0
−9.6

+13.6
−10.5

+11.8
−9.3

+7.6
−16.6

+2.1%/ − 2.3%
±2.8%
±4.2%
±1.3 ±1.4 ±1.3 ±1.4
±2.0%

+10.6
−10.6

+9.3
−11.7

+11.4
−8.0

+11.6
−11.5

Table 9.4: Summary of systematic uncertainties [%] in the expectation of signal eventsin wino case.

Source(Theoretical uncertainty)+ −Cross-section(χ̃1 χ̃1 )+ 0
Cross-section(χ̃1 χ̃1 )− 0
Cross-section(χ̃1 χ̃1 )(Uncertainties on the acceptance)
Scale+PS+PDF
JES
JER
TST
Trigger eﬃciency
Pile-up modeling
Tracklet reconstruction eﬃciency
Signal selection eﬃciency
d0 biasLuminosity
Sub-total

95

Chargino mass (GeV)
100
120
140
160

200

±2.9
±2.1
±4.2

±3.0
±2.2
±4.3

±3.2
±2.4
±4.6

±3.5
±2.7
±4.9

±3.7
±2.9
±5.1

±4.1
±3.4
±5.5

+26.1
−0.9
+3.1
−3.6
+0.0
−0.2
+0.7
−1.3
+0.0
−0.1

+19.4
−4.4
+2.9
−2.8
+0.5
−0.0
+0.7
−1.0
+0.0
−0.1

+12.7
−6.2
+3.3
−2.6
+0.5
−0.0
+0.7
−0.8
+0.0
−0.1

+9.5
−7.8
+2.9
−2.4
+0.0
−0.0
+0.5
−0.7
+0.0
−0.1

+14.4
−4.3
+2.7
−2.2
+0.4
−0.0
+0.5
−0.0
+0.0
−0.1

+10.8
−6.5
+2.1
−2.0
+0.0
−0.1
+0.3
−0.4
+0.0
−0.1

±1.4
+27.0
−7.0

+2.1%/ − 2.3%
±2.8%
±4.2%
±1.1 ±1.2 ±1.2 ±1.1
±2.0%

+20.5
−0.8

+14.5
−9.1

+11.6
−10.2

+15.8
−7.7

±1.1
+12.5
−9.1

Table 9.5: Summary of systematic uncertainties [%] in the expectation of signal eventsin higgsino case.

102

tainties in the background control regions. The uncertainties related to the number of
lepton backgrounds in the signal region, the number of fake tracklets in the control region, pT shape function of fake tracklets and smearing function are incorporated in theprocedure for signal extraction.

±

Data / BG

1

2
1.5
1
0.5
0

Data
Fake tracklet
Muon
HadronElectron
Total Background
SignalTracklets

104-1
103 s=13TeV, 79.8 fb
EW
production
102 Low E missregion
T
10
1
10−1
10−2
10−3
10−4 (m∼χ , τ∼ ) = (500 GeV, 0.20 ns)

103 s=13TeV, 79.8 fb-1
102 EW production
missHigh E T region
10
1

±

χ

1

100

Data
Fake tracklet
Muon
HadronElectron
Total Background
Signal

10−1
10−2
10−3
10−4 (m∼ , τ∼ ) = (500 GeV, 0.20 ns)
χ
χ
10−25

Data / BG

Tracklets

Log ABCD ratio
The number of fake background events is estimated using the ABCD method,where it is assumed that a distribution of a d0 significance of a fake tracklet is
miss . The validity is evaluated by setting a pseudo signal
independent on the ET
region, where no signal remains, by using customised d0 significance requirement,
2 < |d0 significance| < 5, as shown in Fig. 9.7. Here hadron and muon templates
estimated using normal d0 significance requirements (|d0 significance| < 1.5) areused, and hadron template is substituted for the electron template. The fit isdone without any ABCD ratio constraints. By the fitting, the evaluated value is
rf = 0.29 ± 0.41. Since this is a consistent value with zero, the ABCD method isvalid within the statistical uncertainties. This observed value is used as a constraint
on rf in the signal extraction.

1000

10000

1.5
1
0.5
0

±

±

1

1

100

1000

Tracklet p [GeV]

10000

Tracklet p [GeV]

T

T

(a)

(b)

miss
Figure 9.7: Fit result using the tracklets with 2 < |d0 significance| < 5. (a) Low ET
miss
miss
miss
region (120 GeV < ET < 200 GeV) (b) High ET region (200 GeV < ET )103

Chapter 10

Result10.1

Shape fitting

A null-hypothesis test described in Sec. 8.2 is applied to the events which pass the event
selection (Chapter 6) using pT templates (Chapter 7) assuming only the Standard Model.
Figure 10.1 show pT distributions of observed tracklets with the expected signal andbackground pT templates after the background-only fitting. Templates for the signals
are not used in the fitting, but shown in the figures as setting signal strength (µ) to 1.
Table 10.1 is a summary of fitting parameters. The parameters which are constrainedin the control region are not changed significantly before and after the fitting, and theobserved numbers of events in each a source are consistent with the expected number. A
p-value for background-only hypothesis (p0 ) for a wino model with the mass of 500 GeV
and the lifetime of 0.2 ns is 0.36, and that for a higgsino model with the mass of 160 GeV
and the lifetime of 0.04 ns is 0.37. There is no significant deviations from the SM
prediction are found. Table 10.2 is a summary of background component in the highpT (pT > 100 GeV) region. The observed number of high pT tracklets are consistent
with the expected numbers within the uncertainties. The number of the four backgroundsources in the high pT region are comparable to each other, and the fake background isdominant contribution.
The CLs for an exclusion limit is calculated for a wino model with the mass of
500 GeV and the lifetime of 0.2 ns and a higgsino model with the mass of 160 GeV andthe lifetime of 0.04 ns. The observed cross-section 95% CLs upper limit for the winomodel is 70 fb, and expected one is 69+29−20 fb. The observed cross-section 95% CLs upper
limit for the higgsino model is 1.6 pb, and expected one is 1.6+0.7−0.5 pb. A visible crosssection is defined as a signal yield in the signal region with normalised by the integrated
luminosity. The observed visible cross-section 95% CLs upper limit for the wino modelis 0.18 fb, and expected one is 0.18+0.07−0.05 . The observed visible cross-section 95% CLs
upper limit for the higgsino model is 0.17 fb, and expected one is 0.17+0.08−0.05 .

104

Data
Fake tracklet
Muon
Electron
HadronTotal Background
Signal-1

s=13TeV, 79.8 fb
103 EW production
miss
2 Low E T region

10
10

104

Tracklets

Tracklets

104

10
1

1
−1

10

10−1

10−2

10−2

Data / BG

1

2
1.5
1
0.5
0

10−3

(mχ∼±, τ∼χ±) = (500 GeV, 0.20 ns)

100(mχ∼±, τ∼χ±) = (500 GeV, 0.20 ns)
1

1

Data / BG

10−3

Data
Fake tracklet
Muon
Electron
HadronTotal Background
Signal-1
10 s=13TeV, 79.8 fb
EW production
region102 High E miss
T

3

1000

10000

2
1.5
1
0.5
0

1

100

1000

Tracklet p [GeV]

10000

Tracklet p [GeV]

T

T

(a)

(b)

Figure 10.1: The pT distributions of the observed disappearing track candidates for (a)miss selection and (b) High E miss selection are shown as black points. The coloured
Low ETT
lines show the expected pT distribution of signal (red, µ=1), fake background (blue),electron background (yellow), muon background (green), hadron background (light blue)
and the total backgrounds (gray), which are determined by the background-only fitting.
The signal strength (µ) is set to 1, but the signal template is not used in the fitting.

105Source
HadronElectron
Muon
Fake
Total
HadronElectron
Muon
Fake
Total
Fake
Fake
pfake
0
pfake
1
rf
smearingσhαhsmearingνhsmearing
σµsmearing
αµsmearing
σesmearing
αesmearingνesmearing

RegionHigh METHigh METHigh METHigh METHigh MET
Low MET
Low MET
Low MET
Low MET
Low MET
Fake CR, High METFake CR, Low MET

Without fit
28.7 ± 5.9
1.9 ± 0.2
82.1 ± 16.7
2.1 ± 0.2
0.29 ± 0.41
0 ± 0.07
0 ± 0.17
0 ± 1.00
0 ± 0.07
0 ± 0.170 ± 0.08
0 ± 0.21
0 ± 1.00

With fit
37.6 ± 11.2
28.9 ± 5.9
1.9 ± 0.2
10.3 ± 5.8
78.7 ± 8.8
44.4 ± 23.1
83.5 ± 16.8
2.1 ± 0.2
18.8 ± 9.3
148.8 ± 12.2
32.0 ± 5.8
79.0 ± 8.8
1.00 ± 0.24
0.071 ± 0.024
0.30 ± 0.37
-0.01 ± 0.07
0.03 ± 0.17
-0.20 ± 0.96
-0.00 ± 0.07
0.00 ± 0.17
-0.09 ± 0.09
-0.01 ± 0.23
-0.00 ± 1.00

Observed

79

149
32
79

Table 10.1: The fitting parameters without and with the background-only fitting. The
top 12 rows show the number of each background source, and other bottom rows show
the parameters for the pT templates. The expected numbers of the events are consistent
with the observed events shown in the rightest column.

106RegionObserved
Expected BG
SourceHadronElectron
Muon
Fake

Number (Fraction)
miss
miss
High ET
Low ET
715
7.0 ± 1.6
12.0 ± 2.6
1.8 ± 0.6 (25.9 ± 11.3 %)1.1 ± 0.2 (15.6 ± 5.0 %)0.9 ± 0.1 (12.6 ± 3.2 %)3.2 ± 1.8 (46.0 ± 16.3 %)2.1 ± 1.1 (17.5 ± 11.1 %)3.1 ± 0.6 (26.0 ± 7.9 %)0.9 ± 0.1 ( 7.1 ± 1.8 %)5.9 ± 3.0 (49.4 ± 15.2 %)Table 10.2: The number of events having high pT (pT > 100 GeV) tracklets and thefraction of the background sources. The observed numbers of events are consistent with
miss region.
the expected ones for both low and high ET

10.2

Model-independent limit

The result in Sec. 10.1 depends on the given signal pT distribution. This section showsa model-independent result. The observed number of events having the high pT tracklet
is compared to the expected number which is estimated by fitting with the backgroundmiss region.
only hypothesis with blinding of events having the high pT tracklet in high ET
The blind threshold is set to 75 GeV, 100 GeV, 200 GeV and 300 GeV. The numberof expected backgrounds, the number of observed events and p-value (p0 ) are shown in
Table 10.3. The discovery p-value (p0 ) ranges from 0.11 to 1.00. There is no significant
excess.
The 95% CL upper limit for a visible cross-section is also shown in Table 10.3. Byusing the visible cross-section, the exclusion limit for other BSM models predicting adisappearing track can be evaluated.
ThresholdObserved events
Expected BG
p0
95%
σvis
[fb]

75 GeV129.2 ± 2.0
0.25
0.14

100 GeV76.9 ± 1.7
0.51
0.10

200 GeV6
3.0 ± 0.8
0.11
0.11

300 GeV2
2.3 ± 0.7
1.00
0.06

miss signal
Table 10.3: The observed number of events in the high tracklet pT and high ET
region and the expected number estimated by the fitting except for the high tracklet
miss signal region. The model-independent discovery p-value (p ) and thepT and high ET
095%
model-independent visible cross-section upper limit (σvis) are shown for each tracklet
pT threshold.

107

Chapter 11

Discussion, interpretation andperspective
11.1

Interpretation

11.1.1

Constraints on the long-lived wino models

Exclusion limits for a wino LSP model with signal strength (µsig ) of unity are evaluatedas a function of chargino mass and chargino lifetime. As discussed in Chapter 8, the yieldand the pT shape of signal events are evaluated using MC simulation for each mass pointwith the lifetime re-weighting technique (Eq. 3.2). Figure 11.1 (a) shows an expected
number of signal events in the signal region as a function of the chargino mass andchargino lifetime. Figure 11.1 (b) shows a signal acceptance × eﬃciency as a function of
the chargino mass and chargino lifetime. Signals with their lifetime of 1 ns have higher
acceptance × eﬃciency than others because the pixel tracklets are sensitive to the signals
decaying between the fourth Pixel-layers (r = 123 mm) and the first SCT-layers (r =299 mm), corresponding to the cτ of 0.4 ns to 1.0 ns. Figure 11.2 (a) shows exclusion
limits at 95% CLs in the chargino mass and lifetime plane. The upper exclusion limit forthe predicted lifetime is set at 490 GeV by this analysis. This analysis has low sensitivity
for very short lifetimes (< 0.02 ns) and long lifetimes (> 0.85 ns) compared to the LEP
results and the ATLAS/CMS previous results, respectively, because of the diﬀerence ofthe track length. This analysis is the most sensitive for model-favoured lifetime of 0.2 ns.
Figure 11.2 (b) shows exclusion limits in the chargino mass and mass splitting plane.
The mass splitting is computed using a relation between the wino mass splitting andlifetime described in Sec. 1.6.2. This analysis has better sensitivity than LEP for themass splitting smaller than 290 MeV.
Figure 11.3 (a) and (b) show constraints for AMSB parameters with tan β = 5 and 10,
respectively. The relation between the wino mass and AMSB parameters are calculatedusing SOFTSUSY 4.1.5. The Higgs mass is also calculated using SOFTSUSY without
three–loop correction. This analysis excludes m3/2 up to 150 TeV, and some parameters
are satisfied with observed Higgs mass.

108

102

1
0.4
0.3
0.2

10

0.1

1
0.04
0.03
0.02
0.01
100

200

300

400

500

10−1

600

± 0 ∼± ∼∼χ ∼χ , χ χ productionmχ∼± [GeV]11tanβ = 5, µ > 0

1 1

10−1

4
3
2

s=13TeV, 79.8 fb-1

10−2

1

10−3

0.4
0.3
0.2

10−4

0.1

10−5

0.04
0.03
0.02

10−6

0.01
100

200

300

400

500

1

Total acceptance × efficiency

s=13TeV, 79.8 fb-1

4
3
2

10

1

103

τ∼χ± [ns]tanβ = 5, µ > 0

1 1

1τχ∼± [ns]1

The number of signal events in Signal Region

±

1

±

± 0 ∼± ∼∼χ ∼χ , χ χ production

10

10−7

600

mχ∼± [GeV]
1

(a)

(b)

Figure 11.1: (a) The number of signal events in the signal region (b) The signal acceptance × eﬃciency as a function of chargino mass and chargino lifetime.
±1

tanβ = 5, µ > 0

1 1

1τχ∼± [ns]

1

0

±

1

tanβ = 5, µ > 0
s=13TeV, 79.8 fb-1

280

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

1

4
3
2

∼
χ ∼
χ ,∼
χ∼
χ production
300 1 1 1 1±m∼χ± - m∼χ0 [MeV]± 0 ∼± ∼∼χ ∼χ , χ χ production±

10

ATLAS (8 TeV, 20.3 fb-1, EW prod. Obs.)
CMS (13 TeV, 38.4 fb-1, EW prod. Obs.)
Theory (Phys. Lett. B721 (2013) 252)±
LEP2 ∼
χ excluded

260

1

1

240
0.4
0.3
0.2

220
200

0.1

s=13TeV, 79.8 fb-1
180

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

0.04
0.03
0.02

ATLAS (8 TeV, 20.3 fb-1, EW prod. Obs.)
CMS (13 TeV, 38.4 fb-1, EW prod. Obs.)
Theory (Phys. Lett. B721 (2013) 252)±
LEP2 ∼
χ excluded

160

1

0.01

100

200

300

400

500

600

700

140

800

m∼χ± [GeV]

100

200

300

400

1

500

600

700

800

m∼χ± [GeV]
1

(a)

(b)

Figure 11.2: Exclusion limit on (a) the chargino mass and the chargino lifetime (b) the
chargino mass and mass splitting between the chargino and the neutralino. Observed
exclusion limit is shown as a red curve. The dotted orange line around observed limits
shows the cross-section uncertainties discussed in Sec. 3.2.1. The expected sensitivity isshown as a black dotted line, and the 1 sigma fluctuation is represented as a yellow band.
Grey chained line in (a) ((b)) shows a relation between wino mass and wino lifetime (masssplitting) calculated with up to two–loop. LEP (Ref. [100]), ATLAS (Ref. [20]) and CMS
results (Ref. [21]) are shown as a grey band, a blue line and a green line, respectively.
109

m3/2 [TeV]

M

250

hig

gs

150

Ge

V

Tachyonic Particle
No EWSB / Slepton LSP

150
=1

5G
= 11

gs

M hig

M higgs

20

100

V

Ge

eV

100

gs

V

Ge

110 Ge

15

=1

50

M hig

Mhiggs =50

23

Observed 95 % CL limit
ATLAS (8 TeV, 20.3 fb-1, EW prod. Obs.)

200

Tachyonic Particle
No EWSB / Slepton LSP

=1

V

GeV

200

125 Ge125

Observed 95 % CL limit
ATLAS (8 TeV, 20.3 fb-1, EW prod. Obs.)tanβ = 10, µ > 0

300
Mhiggs =higgs =

eV

0G

250

M

= 12

Mhiggs = 123 GeV

M higgs

m3/2 [TeV]tanβ = 5, µ > 0

300

V

5

10

15

20
25
m0 [TeV]2(a) tan β = 5

4

6

8

10

12

14 16
m0 [TeV](b) tan β = 10

Figure 11.3: Constraints in the m3/2 − m0 plane. New constraint from this analysis isrepresented by the red line. Blue line is ATLAS Run 1 results (Ref. [20]). Small m0 andlarge m3/2 regions are forbidden due to the existence of tachyonic particles. Large m0
and small m3/2 regions are forbidden due to slepton LSP or no electroweak symmetry
breaking. Orange chains show a contour of the Higgs mass. The exclusion lines near
the boundaries on the forbidden regions are not plotted due to the diﬃculties of theextrapolation.

110

1400

1

m∼χ± [GeV]

In the pure gravity mediation model, the gluino can be light enough to be detectedin LHC experiments. Figure 11.4 shows constraints on the gluino and chargino masses.
In the case of AMSB-like (L=0), the gluino is too heavy to be produced in the LHC.
On the other hand, there are some viable parameter regions where gluino is light to be
produced in the LHC. As shown in this figure, inclusive gluino search with hadronic jetsin the final states (Ref. [101]) is more sensitive than this analysis when L equals to about
1.

1200

m~g < m∼χ±1
mB~ < mW~
Observed 95 % CL limit

ATLAS (13 TeV, 36.1 fb-1, 0 lepton. Obs.)

1000
=2

800

/2

L/m 3

600

L/m 3/2=1

400
L/m3/2

200
0
500

1000

1500

2000

MSB)
= 0 (A

2500

3000

m~g [GeV]

Figure 11.4: Constraints on the gluino mass – chargino mass plane. Excluded parameters
are shown as blue shade. A result in zero lepton analysis (Ref. [101]) is shown as a
black line. Dark grey and light grey shade represent model-disfavour regions where thegluino mass is lighter than the chargino mass and where the bino mass is lighter thanwino mass, respectively. The black lines represent a relation between gluino mass andchargino mass with diﬀerent L parameters in the pure gravity mediation model, where
the relation (Eqs. 1.10–1.13) is used.

11.1.2

Constraints on the long-lived higgsino models

Figure 11.5 (a) and (b) show the exclusion limits for higgsino models. This analysis
excludes the higgsino masses up to 170 GeV for the predicted lifetime. It is more sensitive
than LEP for the mass splitting smaller than 330 MeV.
Figure 11.6 shows constraints on higgsino mass and bino and wino masses in the
MSSM. Here mass splitting between the lightest chargino and the lightest neutralino iscomputed using the radiative correction and chargino/neutralino mixing. For a simple
setup, bino mass and wino mass are assigned to common mass. For a light bino andwino mass case, this analysis has a higher exclusion sensitivity than LEP for bino/winomass larger than 40 TeV. For a lighter bino and wino case, this analysis is not sensitivefor higgsinos.
111

± 0 ∼± ∼0 ∼± ∼∼χ ∼χ , χ χ , χ χ production± 0 ∼± ∼0 ∼± ∼∼χ ∼χ , χ χ , χ χ production

1

2

1 1

m∼χ± - m∼χ0 [MeV]11τ∼χ± [ns]

±

1

±

0.3

1

Observed 95% CL limit (±1 σtheory )∼± excludedχ
1
Expected 95% CL limit (±1 σexp )Theoretical line for pure higgsino±
LEP2 ∼
χ1 excluded

0.1

1

1

1

320
300
280
260

0.05

240

0.04

Observed 95% CL limit (±1 σtheory )±∼χ1 excluded
Expected 95% CL limit (±1 σexp )Theoretical line for pure higgsino±
LEP2 ∼
χ1 excluded

220

0.03
200
100

120

140

1 1

s=13TeV, 79.8 fb-1

340

0.07

0.02

2

1

s=13TeV, 79.8 fb-1

0.2

360

160

180

180

200

mχ∼± [GeV]

100

120

140

1

160

180

200

mχ∼± [GeV]
1

(a)

(b)

Figure 11.5: Constraints of higgsino models on (a) chargino mass and chargino lifetime (b) chargino mass and mass splitting between chargino and neutralino. Observed
exclusion limit is shown as a red curve, and a red-shaded region represents excluded
parameters. The dotted orange line around observed limits shows the cross-section uncertainties discussed in Sec. 3.2.1. The expected sensitivity is shown as a black dotted
line, and the 1 sigma fluctuation is represented as a yellow band. Grey chained line in(a) ((b)) shows a relation between higgsino mass and higgsino lifetime (mass splitting)calculated with up to one–loop, where naive systematics uncertainty for higgsino the2ory (∆2−loop δm = ( α4π )2 πmt ∼ 3.9MeV) is assigned as a gray hatch. LEP result [100] isshown as a grey band.

112

± 0 ∼ ± ∼ 0 ∼ ±∼∼χ ∼χ , χ χ , χ χ production

mw~ = m~b [TeV]

±

104

1

1

1

2

1 1

Observed 95 % CL limit

LEP2 ∼
χ excluded±

1

M1 = M2

103

102

90 100 110 120 130 140 150 160 170 180

m~h [GeV]

Figure 11.6: Constraints on the higgsino mass – bino/wino mass plane. Excluded parameters are shown as a red-shaded region. LEP result [100] is shown as a grey band.

11.2

Future experiments

In case the energy or the luminosity of the LHC is not suﬃcient to discover new physics,
more powerful collider would be needed. This section focuses on future hadron colliders.

11.2.1High-Luminosity Large Hadron Collider

After the Run 3, where 300 fb−1 of data will be collected, the LHC is planned to be
upgraded for high luminosity run, which is called High-Luminosity LHC (HL-LHC).
The HL-LHC will deliver 3000 fb−1 of collisions in 10 years, and the high luminosity
experiments will be run with a higher pile-up of 200. In parallel to the upgrade of the
LHC machine, the ATLAS detector will be upgraded to be tolerant to the harsh pile-up
condition. Especially, the inner tracker will be replaced because high radiation would
cause serious damage to the performance of the inner tracker located at the nearest
position to the beam pipe. The new tracker, called “Inner Tracker” (ITk) [102], isshown in Fig. 11.7. All sub-detectors consist of silicon sensors, and the position of layers
is very much diﬀerent from the current layout Fig. 2.2.
The discovery potential of winos/higgsinos is evaluated assuming the latest ITk layout, the centre of mass energy of 14 TeV, µ = 200 and the integrated luminosity of3000 fb−1 [103]. The analysis strategy follows the ATLAS Run 2 analysis. The strategy
miss ,
of a kinematic selection is the same with the current analysis: no lepton, large ET
misshigh pT jet and large ∆ϕ(jets,ET ). The thresholds are optimised to maximise a discovery sensitivity at the 3000 fb−1 . The short tracks, which has at least four hits, areused as well as the Run 2 analysis.
The kinematic properties of both the signal charginos and the SM processes are113

evaluated using the generator-level variables, then smearing them by the parametrised
detector functions [104]. The signal tracking acceptance and the tracklet backgroundrate are evaluated by Geant4 simulation and the track reconstruction algorithm basedon the current ATLAS algorithm as discussed in Sec. 4.1 with a tune of a configuration.
Figure 11.8 shows the signal track reconstruction eﬃciencies with the ITk layout
and the current ATLAS layout, respectively. The fourth layer of the ITk is locatedfarther than the current ATLAS fourth layer, resulting in lower signal acceptance thanthe current ATLAS tracker. On the other hand, the reconstruction eﬃciency at the
maximum point is better than the Run 2 because of a lower rate of the assignment ofwrong hits thanks to the sensor pitches and the layout. Tracklet pT resolution is also
evaluated with the Geant4 simulation, and is applied to the generator-level chargino
pT .
The expected number of backgrounds is evaluated based on the estimated yields ofbackground components in an ATLAS analysis (Ref. [105]). The number of scatteredbackground is obtained with scaling the ATLAS results by the ratio of material budget.
The number of fake backgrounds is obtained with scaling the ATLAS result by theratio of the number of tracks in the fake dominant region. Since the number of faketracks exponentially increases as a function of the number of hits, the fake track events
dominate the background in the HL-LHC.
Figure 11.9 shows a discovery sensitivity for the wino LSP scenario and the higgsino
LSP scenario. The HL-LHC has the potential to access the wino for up to about 850 GeV
and the higgsino up to about 250 GeV.

Figure 11.7: Illustration of the ITk layout [102]. Pixel sensors are shown as red lines.
Strip sensors are shown as blue lines.

114

Reconstruction Efficiency

1
0.8
ATLAS Simulation
ITk Inclined Duals, ⟨µ⟩ = 200
Pure wino LSP scenario, |η| < 2.2

0.6

Tracks + Tracklets
TracksTracklets
Tracks + Tracklets, Run 2
Tracks, Run 2

0.4
0.2

Tracklets, Run 2

0

200

400

600

800

1000

Chargino decay radius [mm]Figure 11.8: A signal reconstruction eﬃciency as a function of the chargino decay radius [102]. Solid lines are ones for the ITk. Dotted lines are ones for the current ATLAS
layout. Red lines show pixel tracklets.

1

1

∼0 χ
∼± , χ
∼± χ
∼,χ
∼± χ
∼0 production, tanβ = 5, µ > 0χPure Wino

1

Disappearing Track Analysis

ATLAS Simulation Preliminarys=14 TeV, 3000 fb-1, µ = 200
All limits at 95% CL106τ [ps]

τ [ps]

±

1

±

∼± χ
∼,χ
∼± χ
∼0 production, tanβ = 5, µ > 0
χ

107

107

2

1

1

1

1

Pure Higgsino

1

Disappearing Track Analysis

ATLAS Simulation Preliminarys=14 TeV, 3000 fb-1, µ = 200
All limits at 95% CL

106

105

105

104

104

103

103

102

102
Expected Limit (±1 σexp)
5σ discovery
TheoryRun 2 Limit (arXiv:1712.02118)

10
1
200

400

600

800

1000

Expected Limit (±1 σexp)
5σ discovery
TheoryRun 2 Limit (ATL-PHYS-PUB-2017-019)

10
1

1200
1400
m(χ±) [GeV]

100

200

300

400

500

1

600

700

800
m(χ±) [GeV]
1

(a)

(b)

Figure 11.9: Expected sensitivities with the ITk layouts with 3000 fb−1 [103] (a) for purewino (b) for pure higgsino. Yellow bands show the exclusion limits at the HL-LHC. Bluelines show the discovery limits at the HL-LHC. Red regions show the ATLAS Run 2
exclusion limits with 36.1 fb−1 .

115

11.2.2

Future Circular Collider

CERN is considering the construction of a next-generation collider, the so-called Future
Circular Collider (FCC) [106]. FCC would be constructed near the LHC, and the tunnel
is designed to have 100 km circumference. The FCC could have three operating modes.
FCC-ee is an electron-positron collider and would be operated at the centre of massenergy of 91 GeV to 365 GeV. The main aim of the FCC-ee is precision measurementsof the Standard Model. The FCC-ee would produce huge numbers of Z bosons, W W
pairs, Higgs bosons and tt̄ pairs depending on the centre of mass energy. FCC-hh is
a hadron collider like the LHC and would be operated at the centre of mass energy of
100 TeV with 16 T bending magnets. The FCC-hh program can access new physics at
O(10) TeV. FCC-eh is an electron-proton collider and would be operated with a 50 TeV
proton beam and a 60 GeV electron beam. The FCC-eh can measure the quark/gluon
structure in proton with great accuracy.
From the view of WIMP dark matter, the FCC-hh has the highest sensitivity among
three options, the discovery potential is therefore evaluated [107]. Figure 11.10 (a)shows the number of signal chargino decays and the reference FCC-hh inner tracker inthe conceptual design report [106]. In this study, an optimised layout is also consideredas shown in Fig. 11.10 (b), which has an additional silicon layer and the positions of theinner five layers are optimised.
The signal acceptance is evaluated assuming that all signal tracks can be reconstructed if the signal chargino passes through at least five silicon layers in the tracker. The
backgrounds from the scattered-sources are evaluated by scaling the ATLAS Run 2 result by the ratio of material budget. The fake background is evaluated using Geant4
simulation and a simple tracking algorithm as described in Ref. [107]. Pile-up collisions
are produced by Pythia with two diﬀerent models of soft QCD processes: only nondiﬀractive processes and a mixture of diﬀractive and non-diﬀractive processes. Since thefake rate depends on η as shown in Fig. 11.11 (a), tracks with small η (|η| < 1) are usedin this study. The fake rate strongly depends on the pile-up, the QCD process and thenumber of hits in the track as shown in Fig. 11.11 (b). In order to suppress the faketracklet rate, this analysis requires at least five hits for all tracks, which is a diﬀerent
condition from the ATLAS analysis.
Recently, the fast timing silicon detectors are being developed. Such detectors canmeasure the particles arrival time with O(10) ps. Since fake tracks are formed from
uncorrelated hits, e.g. originating from diﬀerent collision points, the relation of thetiming between the hits in the track is not consistent to be a track originating froma single particle. About 96% of fake tracks can be removed by checking the hit time
assuming 50 ps time resolution at each pixel sensor.
The strategy of the kinematic selection is the same with Run 2 analysis: no lepton,
miss . A kinematic selection is optimised for 3 TeV wino and 1 TeVhigh pT jet and large ET
higgsino assuming the integrated luminosity of 3 ab−1 . Figure 11.12 shows a discovery
sensitivity in the FCC-hh. The diﬀerence between the soft QCD processes in pile-up
collisions is assigned to uncertainties as represented as error bands. The sensitivities
strongly depend on the tracker layout. The FCC-hh with the optimised tracker layout
116

107

-1

102

106

400
105

350
10

300

3

104

250
10

200

4

103

150

102

100

10

50
0
−2000 −1500 −1000 −500

107

-1

102

105

350
10

103

104

200
150

10

102
10

1

0
−2000 −1500 −1000 −500

2000

5

10

50

6

1500

3

104

100

1000

106

400

250

5

500

450

FCC-hh, s = 100 TeV, 30 ab
Alternative layout (#3)

300

10

0

500

Number of chargino decays

450

FCC-hh, s = 100 TeV, 30 ab
Default layout (#1)

Radius [mm]500

Number of chargino decays

Radius [mm]has potential to discover charginos with masses predicted from the relic density of dark
matter.
p
The time measurements can determine the velocity, and mass (m = βγ). So after the
discovery of the new particles, this could determine the mass and the model parameters,that is discussed in the article [108].

6

10

1
0

z [mm]

500

1000

1500

2000

z [mm](a)(b)

Figure 11.10: (a) Reference layout in the FCC conceptual design report. (b) Optimisedlayout for disappearing track analysis. Red lines show positions of silicon detectors. The
dotted black lines correspond to |η| = 1.

117

Chargino, mχ∼± = 3 TeV
1Fake tracks

FCC-hh, s = 100 TeV

0.025
0.02
0.015
0.01
0.005
0
−5

−4

−3

−2

−1

0

1

2

3

4

5

Fake background rate per bunch crossing

Arbitrary unit

0.03

Track η10−24-layer-tracks
non-diffractive−3

Default layout (#1)
Alternative layout (#3)

10

10−4
4-layer-tracks
non-diffractive + diffractive

10−5

Default layout (#1)

−610

5-layer-tracks
non-diffractive
Default layout (#1)
Alternative layout (#3)

10−7
10−8

200

300

400 500

1000

2000

Average number of interactions per bunch crossing

(a)

(b)

Figure 11.11: (a) Fake track rate as a function of η. Black points show fake track
rate. (b) Fake track rate as a function of pileup. Black circles show a fake rate using
default layout (Fig. 11.10 (a)). Red triangles show a fake rate using optimised layout (Fig. 11.10 (b)). The blue diamond shows a fake rate estimated including diﬀractive
process. The open symbols represent a fake rate usinig four-layer-tracks. The filled
symbols represent a fake rate usinig five-layer-tracks.

Default layout (#1), <µ > = 200
Alternative layout (#3), <µ > = 200
Default layout (#1), <µ > = 500
Alternative layout (#3), <µ > = 500

FCC-hh

20
18
16
14
12
10
8
6
4
2
0

s = 100 TeV, 30 ab-1

Wino
hit

Nlayer = 5, Time-fit

2500

3000

3500

Default layout (#1), <µ > = 200
Alternative layout (#3), <µ > = 200
Default layout (#1), <µ > = 500
Alternative layout (#3), <µ > = 500

FCC-hhDiscovery significanceDiscovery significances = 100 TeV, 30 ab-1

4000

20
18
16
14
12
10
8
6
4
2
0

Higgsino
hit

Nlayer = 5, Time-fit

800

1000

Chargino mass [GeV]

1200

1400

Chargino mass [GeV]

(a)

(b)

Figure 11.12: Discovery sensitivities (a) for pure winos (b) for pure higgsinos. Blackgraphs show the sensitivities using default layout. Red graphs show the one using optimised layout. Solid one is for µ = 200, and hatched one is for µ = 500.

118

Chapter 12Conclusion
This thesis presents a search for heavy meta-stable charged particles at a centre of massenergy of 13 TeV. Such new particles are predicted from well-motivated models in the
supersymmetric theory, while their typical lifetimes (0.2 ns and 0.04 ns) are too short
to reconstruct with conventional tracking techniques in the ATLAS experiment. The
introduction of pixel-tracklets, which are quite short, makes it possible to access suchcharginos.
The analysis is designed to maximise the signal acceptance of short-lived charginos byusing the pixel-tracklets. Focusing on the direct chargino and neutralino pair production
makes the search inclusive, namely independent of heavier supersymmetric particles. The
properties of short tracks are measured from mostly observed data. The backgroundestimation is based on the pT spectrum fitting; templates used in the fit are derived
from observed data.
This analysis uses the data recorded by the ATLAS detector in 2015–2017 withan integrated luminosity of 80 fb−1 . No significant excess from the Standard Model
prediction is found in the signal enhanced region. This result gives a new constraint for
new particles: 490 GeV for the pure-wino LSP model and 170 GeV for the pure-higgsino
LSP model.
There is still room to allow the existence of the heavier charginos because wino (higgsino)mass up to 3 (1) TeV is motivated from the observed value of the dark-matter relicdensity. Next-generation colliders, the High-Luminosity LHC and the Future Circular
Collider, have potential to discover such charginos.

119Acknowledgements
First of all, I would like to thank my supervisor, Prof. Shoji Asai, for his suggestion fora subject and a direction of my research in more than five years. I learnt the mind of ascientist from his attitude, passion and deep knowledge into physics. My first step as a
researcher could not be productive without his advice and help.
I am also grateful to Prof. Ryu Sawada for his support of my research. I could notsmoothly proceed with my research in the collaboration without his great assistance.
His deep understanding of a physics analysis and software always guided me to better
solutions.
I would like to thank Prof. Junichi Tanaka and Prof. Koji Terashi. A discussion
about future perspectives and technologies on this field excited and motivated me. I’mlooking forward to expanding these studies more in the near future.
I would like to thank Prof. Takashi Yamanaka and Prof. Shimpei Yamamoto for
their supports in my early stage. They supported me in my early career, especiallyduring the master course. Their support formed the basis of this research and indicatedthe direction to the current position.
I am grateful to all the professors and staﬀs, Prof. Masaya Ishino, Prof. Yasuyuki
Okumura, Prof. Yuji Enari, Prof. Tatsuya Masubuchi, Prof. Tomoyuki Saito and Prof.
Takuya Nobe, for all their support. Discussions in weekly meetings and much chat in acoﬀee break were suggestive and productive. I was very impressed by their hard workand vitality.
I am grateful to my colleagues at the University of Tokyo and ATLAS-Japan. Withoutthem, I could not have such a fruitful life in these five years and a special stay in CERN.
Lastly, I would like to express my deepest gratitude for my family.

120

Appendix A

Tracklet q/pT distribution and asmearing function∆q/pT distributions of MC simulation samples for a electron, a muon and a pion are
shown in Fig. A.1 for each pT slices. A tracklet originating from a low pT electron
has poor resolution than others due to the small mass. A tracklet originating from ahigh pT electron and a chargino has good resolution than others. Since these particle
leave a large energy deposit to each pixel sensor, the hit position can be measured more
precisely. This eﬀect is not observed in observed data as shown in Fig. A.2 because another eﬀect, e.g. misalignment, dominantly contributes to the resolution.

121

10−1

10−1

15 GeV < p < 20 GeV
T

20 GeV < p < 25 GeV
TElectron
Pion
Muon

Electron
Pion
Muon

10−2

−2

10

10−3

10−4

Ratio

Ratio

10−3

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−100 −80

−60

−40

−20

0

20

40

−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

20

40

T

T

(a)
10−1

60
80 100∆ q/p [/TeV]

(b)

10−1

25 GeV < p < 30 GeV
T

Electron
Pion
Muon

10−2

10−2

10−3

10−3

30 GeV < p < 40 GeV
T

Electron
Pion
Muon

10−4

10−4

Ratio

Ratio

10−5
1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−100 −80

−60

−40

−20

0

20

40

−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

20

40

T

T

(c)

10−1

60
80 100∆ q/p [/TeV]

(d)

10−1

SignalElectronPion
Muon

40 GeV < p < 50 GeV
T

10−2

SignalElectronPion
Muon

50 GeV < p < 200 GeV
T

10−2
10−3

10−3

10−4
−4

10

10−5

10−6

Ratio

Ratio

10−5

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

−100 −80

0.6

−60

−40

−20

0

20

40

−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

T

20

40

60
80 100∆ q/p [/TeV]
T

122
(e)

(f)

Figure A.1: ∆q/pT distribution for MC simulated samples with fit functions for particle
pT slices: (a) 15 GeV < pT < 20 GeV (b) 20 GeV < pT < 25 GeV (c) 25 GeV < pT <30 GeV (d) 30 GeV < pT < 40 GeV (e) 40 GeV < pT < 50 GeV (f) 50 GeV < pT <200 GeV. A black square shows a muon. A blue triangle shows a pion. A yellow circle
shows a electron. A red triangle shows a charginos.

10−1

Observed data
Z → ll events

10−1

Zee
Z µµ

20 GeV < p < 25 GeV

Zee
Z µµ

25 GeV < p < 30 GeV

T

T

10−2

10−2

10−3

10−3

Zµ µ events
σ = 14.2 ± 0.3
α = 1.80 ± 0.13
Zee events
σ = 19.5 ± 0.1
α = 2.38 ± 0.13

1.4
1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−100 −80

−60

−40

−20

0

20

40

Zµ µ events
σ = 13.6 ± 0.2
α = 1.91 ± 0.09
Zee events
σ = 16.3 ± 0.1
α = 2.05 ± 0.07

10−4
Ratio

10−4
Ratio

Observed data
Z → ll events−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

20

40

T

T

(a)

10−1

(b)

Observed data
Z → ll events

10−1

Zee
Z µµ

30 GeV < p < 40 GeV

10−2

10−2

10−3

10−3
Zµ µ events
σ = 13.4 ± 0.1
α = 1.90 ± 0.05
Zee events
σ = 15.0 ± 0.1
α = 2.02 ± 0.04

Ratio

Ratio

1.2

1.4
1.2

1

1

0.8

0.8

0.6

0.6

−40

−20

0

20

40

Zµ µ events
σ = 13.0 ± 0.1
α = 1.79 ± 0.04
Zee events
σ = 13.8 ± 0.1
α = 1.93 ± 0.05

10−5

1.4

−60

Zee
Z µµ

T

10−4

10−5

−100 −80

Observed data
Z → ll events
40 GeV < p < 50 GeV

T

10−4

60
80 100∆ q/p [/TeV]−100 −80

60
80 100∆ q/p [/TeV]

−60

−40

−20

0

T

20

40

60
80 100∆ q/p [/TeV]
T

(c)

(d)

10−1

Observed data
Z → ll events

Zee
Z µµ

50 GeV < p < 200 GeV
T

10−2
10−3
Zµ µ events
σ = 12.6 ± 0.1
α = 1.78 ± 0.04
Zee events
σ = 13.2 ± 0.1
α = 1.79 ± 0.04

10−4

Ratio

10−5
1.4
1.2
1
0.8
0.6

−100 −80

−60

−40

−20

0

20

40

60
80 100∆ q/p [/TeV]
T

123
(e)

Figure A.2: ∆q/pT distribution for observed data with fit functions for particle pT slices:(a) 20 GeV < pT < 25 GeV (b) 25 GeV < pT < 30 GeV (c) 30 GeV < pT < 40 GeV (d)40 GeV < pT < 50 GeV (e) 50 GeV < pT < 200 GeV. A black circle shows a Z → µµ
process. A yellow circle shows a Z → ee process.

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