学位論文

Search for supersymmetry in the final state with multiple jets,
missing transverse momentum and one isolated lepton,√ using−1
20.3 fb of data recorded by the ATLAS detector at s = 8 TeVATLAS 検出器を用いた重心系エネルギー 8 TeV における
1 本のレプトンを終状態に持つ超対称性事象の探索

平成 25 年 12 月博士 (理学)申請

東京大学大学院理学系研究科
物理学専攻
佐々木雄一

Abstract
Supersymmetry is one of the most attracting theories beyond the Standard Model. In
the context of R-parity conserving supersymmetry model, the supersymmetric particles areproduced in pairs and the lightest supersymmetric particle (LSP) is stable. Large gluino andsquark production cross-sections are expected at the proton-proton collisions. Once gluinos
and squarks are produced, they decay through a cascade of multiple stages to the final stateswith the LSP. The LSP is only weakly interacting and escapes detection, resulting in large
missing transverse momentum ETmiss . The decay also accompanies many hadronic jets andseveral leptons, which often give a distinct signature from the Standard Model processes.
This thesis presents a general search for supersymmetry in final states with jets, missing
transverse momentum and one isolated electron or muon, using 20.3 fb−1 of proton-proton√
collision data at s = 8 TeV recorded by the ATLAS detector at the LHC in 2012.
One of the notorious backgrounds in proton-proton colliders is QCD multi-jet, which
has an overwhelming cross-section, can be suppressed by requiring an isolated electron or
muon. Therefore, leptonic analysis is an ideal way to search for new physics with small
cross-sections at the LHC. Based on a topology selection of one lepton, large ETmiss andmultiple jets, three signal regions are introduced to cover general supersymmetric event
topologies.
Since no excess over the Standard Model expectation is found in the Signal Regions, theresults are interpreted as mass limits in several models. In a minimal supergravity model, agluino mass up to 1200 GeV is excluded, and a squark mass is excluded up to 1500 GeV. The
result is also interpreted in a simplified model and an upper limit on the cross-section times
branching fraction is set on the gluino pair-production cross-section σ (g̃-g̃) and branching
fraction Br (g̃ → qqW (∗) χ̃01 ), which isσ (g̃-g̃) × Br (g̃ → qqW (∗) χ̃01 )2 < 20 fb
This limit is a good approximation independent of the gluino decay pattern except for someextreme mass spectra.

2

Contents
1 The Standard Model and Supersymmetry
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Elementary particles in the Standard Model . . . . . . . . . . . . . . . . . . . .
1.2.2 Electroweak theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Problems of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Grand unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Hierarchy problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 SUSY breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Particles in MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.4 Minimal supergravity model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.5 Discovery of the Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . .

5
5
5
5
5
6
7
7
8
9
11
11
12
15
16
17

2 LHC and ATLAS detector
2.1 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Calorimeter system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7 Luminosity detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
19
21
21
21
22
23
25
25
27

3 Object reconstruction and definition
3.1 Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Jet finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Pileup suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 b-tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.7 Object definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Cluster reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Track-to-cluster matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Further improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Hard electron definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Soft electron definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Standalone muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28
28
28
28
28
29
29
29
31
32
32
32
33
33
33
35
35
36
36

1

3.4.2 Inner detector muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 STACO muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Segment-tagged muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Hard muon definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 Soft muon definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.7 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kinematic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Event cleanings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
37
37
37
38
38
40
40
40
42
43

4 Data and Monte Carlo simulation
4.1 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Luminosity measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The Standard Model samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Standard Model processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Signal samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Signal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 MSUGRA/CMSSM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Simplified models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47
47
47
48
49
51
51
51
52

5 Signal Region optimization
5.1 Event topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 W+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 tt¯ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Kinematic variables for signal region optimization . . . . . . . . . . . . . . . .
5.2 Signal Region Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55
55
55
55
56
56
59

6 Background estimation
6.1 Multi-jet background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 W+jet and tt¯ backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Validation Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 tt¯ correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 W+jets correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.5 Fitting in the Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.6 Data/MC comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Other backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65
65
65
65
66
66
75
78
79
79

7 Uncertainties
7.1 Instrumental uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Jet Energy Scale (JES) uncertainty . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 Jet Energy Resolution (JER) uncertainty . . . . . . . . . . . . . . . . . . . . . .
7.1.3 Lepton energy scale, resolution, and trigger/reconstruction eﬃciency uncertainties
7.1.4 ETmiss resolution uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.5 Pile-up uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.6 b-tagging eﬃciency uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . .

81
81
81
81
82
82
82
82

3.5
3.6
3.7
3.8

2

7.2

7.3

Theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 tt¯ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 W+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Single Top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.4 Z+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.5 tt¯+V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.6 Dibosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.7 QCD multi-jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 Cross-section uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Acceptance uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83
83
83
84
84
84
85
85
85
85
85

8 Results
88
8.1 Un-blinding the Signal Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.2 Limit calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.3 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.3.1 MSUGRA/CMSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.3.2 Simplified models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9 Conclusion

102

Bibliography

105

A Higgs mechanism
111
A.1 Electroweak theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.2 Gauge theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.3 Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B Details of Signal Region optimization
115
B.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
B.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C Matrix-Method
121
C.1 Lepton misidentification rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
C.2 Lepton identification eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
C.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D Fit results for the Control Regions

126

E Fit results for the Validation Regions

128

F ETmiss and mT for the events in the SRs

132

G Fit results for the Signal Regions

135

H Profile-likelihood and CL s
138
H.1 Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
H.2 Profile-likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
H.2.1 Constraints and approximations . . . . . . . . . . . . . . . . . . . . . . . . . . 139

3

H.3 CL s method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
I

Tile Calorimeter calibration using scrapping muon
142
I.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
I.1.1 Tile calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
I.1.2 Muon spectrometer system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
I.1.3 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
I.1.4 Scraping beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
I.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
I.2.1 Muon track selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
I.2.2 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
I.2.3 Calorimeter response and further selection criteria . . . . . . . . . . . . . . . . 144
I.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
I.3.1 Uniformity of calorimeter cell response . . . . . . . . . . . . . . . . . . . . . . 146
I.3.2 Inter-calibration of radial layers . . . . . . . . . . . . . . . . . . . . . . . . . . 146
I.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4

1 The Standard Model and Supersymmetry
1.1 Introduction
The Standard Model (SM) is a quite successful model to describe the phenomena below the electroweakenergy scale of O(100) GeV with great accuracy. On the other hand, once we consider higher energy up
to the Grand Unified Theory (GUT, ΛGUT ∼1016 GeV) or The Planck scale (Mpl =1.22 × 1019 GeV), there
arise some problems the SM cannot explain.
One natural question is “why the electroweak energy scale and the GUT or Planck scales are so
separated by a significant order?”, which is called “hierarchy problem”. The hierarchy problem gives
rise to a problem on the Higgs mass, whose bare mass receives large radiative corrections of an orderof the fundamental scale. To yield the physical Higgs mass at the electroweak scale, a large degree ofcancellation between bare mass and quantum corrections is needed (naturalness problem). The longsought Higgs boson, the final missing ingredient in the Standard Model, was discovered at the LHC in2012 [1]. The mass of the Higgs boson was measured to be ∼126 GeV, which is an interesting challenge
to naturalness and the discovery of supersymmetric particles at the LHC. The WMAP [2] experiment
made a valuable measurement of the fraction of ingredients of the universe. The results suggest that
more than 85 % of the total matter in the universe is made of “Dark Matter” (DM), for which the Standard
Model does not have an appropriate candidate. Gravity is also a problem which is not described within
the framework of the SM. Supersymmetry is one of the solutions aiming to solve the problems mentioned
above. The brilliant solution of supersymmetry will be discussed in Section 1.4 after introducing the SMin the next Section.

1.2 The Standard Model
The Standard Model consists of two theories: electroweak theory and Quantum ChromoDynamics (QCD).
Electroweak theory is particularly interesting because it introduces the Higgs mechanism, which also
plays an important role in supersymmetry theories. We start from introducing elementary particles andforces in the Standard Model, then describe electroweak theory. QCD theory is explained later mainly
from the experimental aspect.
1.2.1 Elementary particles in the Standard ModelIn the framework of the Standard Model, matter consists of quarks and leptons, which are collectivelyreferred to as fermions. There are six types of quarks (up, down, charm, strange, top and bottom) and six
leptons (electron, muon, tau and their paired neutrinos). As shown in Fig. 1, they are classified into threegroups, called generations. An anti-particle accompanies for each fermion with the same mass but the
opposite quantum numbers, such as charge. All fermions have spin 12 .
There are the particles which intermediates forces between fermions, which are called gauge bosons.
A photon conveys the electromagnetic force, W ± and Z 0 bosons intermediate the weak force and a gluon
conveys the strong force. All these bosons have spin 1. The remaining force, gravity, is not included in
the framework of the Standard Model.
1.2.2 Electroweak theory
Detailed description of electroweak theory and the Higgs mechanism are documented in Appendix A, so
only a simple overview and several important notations are introduced here.
The weak force couples through weak isospin, which obeys SU(2) symmetry (to avoid confusion,
we add a subscript L in the following). The left-handed fermions are put into SU(2)L doublets, such as

5

(

)
(
)
uL
νL
and
. Here the subscript means that the fermions are left-handed. The doublets are denoteddLeL
by capital letters, such as L for leptons and Q for quarks. A right-handed fermion forms SU(2)L singlet
and represented by a small letter with subscript R, for example, eR (electron), uR (up quark). Then we
introduce U(1) symmetry, which is proportional to Hypercharge Y. Gauge theory give birth to electromagnetic and the weak interactions at the same time from U(1)Y ×SU(2)L symmetry. In the frameworkof gauge theory, the gauge bosons are prohibited to have explicit mass terms, which is opposed to experimental results. This problem is solved by the Higgs mechanism. The Higgs mechanism introducesa SU(2)L complex scalar doublet φ with an unstable potential. As a result of Spontaneous Symmetry
Breaking (SSB), a new stable vacuum is chosen where the massive bosons arise. The expectation valueof the Higgs field after SSB hφi is called Vacuum Expectation Value or VEV. Fermion masses are also
explained in gauge theory through Yukawa coupling constant y.

Figure 1: Particles in the Standard Model.

1.2.3 QCD
Quantum Chromo Dynamics (QCD) describes the strong interactions of quarks and gluinos. The theory
has “Chromo” in its name because the theory is based on SU(3)C symmetry and fundamental representation 3 seems to behave like three colors. A quark (anti-quark) obeys 3 (3̄) representation. A 8 representation generated in 3 ⊗ 3̄ = 8 ⊕ 1 is assigned to a gluon. Another diﬃculty of QCD is that the strengthof its coupling constant αS is too strong to perform perturbative calculations. As a result, first or second
order perturbation doesn’t give suﬃcient accuracy, which weakens the prediction power.
A complete overview of QCD goes far beyond the scope of this thesis, therefore, only important
conclusions necessary in the analysis are summarized.
Asymptotic freedom :In renormalization group theory, the running of coupling constant is evaluated by β-function. In
the lowest non-trivial order, β-function for SU(3) theory with the number of generation ngen is
6

given as

ngen )α2 (β1 (α) =
−11 +
,
2π
3

(1)

g
where α represents the coupling constant, α = 4π
. For QCD, ngen is 3, which results in a negativevalue for the β-function. A negative β-function means that the coupling constant becomes weakerat higher energy. This feature makes perturbative calculations possible in hard collisions at the
LHC energy scale, while the calculations of low energy phenomenon around ΛQCD ∼ O(1) GeV
become diﬃcult, because the coupling constant diverges near ΛQCD , which breaks the perturbation. This behavior is problematic for jet shower simulation since jet shower is made up of many
productions of light hadrons at the energy scale of O(1) GeV. To cope with the problem, Monte
Carlo generators stop jet evolution at some energy scale and the existing quarks are forced to bechanged into hadrons. This technical trick is called “Hadronization”.
2

Even at high energy, the coupling constant αS depends strongly on the energy scale comparedwith weak or electromagnetic coupling constants. As a result, the choice of the energy scale atwhich αS is evaluated becomes important. In Monte Carlo simulation, the energy scale, called
renormalization scale, is determined by an empirical formula. Therefore impact of the choice isevaluated by varying the energy scale and taken into the uncertainty.
Confinement :QCD predicts a very strong forces between two colored particles. Contrary to electromagnetic
forces, it becomes stronger when they are separated farther. As a result of this behavior, there
exists a distance at which the potential energy exceeds quark masses, and beyond the distance,
creation of a new particle pair is favored in the light of the total energy. The distance is smaller
than the diameter of proton, so it is impossible to see an isolated colored particle, which is often
said as colored particles are “confined”.
As a result, a few number of quarks and gluinos produced in a collision consequently pair-create alot of particles as they get separated, forming a shower-shape jet. This process is called “fragmentation”.

1.3 Problems of the Standard Model
Although the Standard Model describes a wide range of phenomena, there exist several exceptions whichcannot be explained in the Standard Model. The followings are such interesting phenomena. They’reimportant because they might lead to the theories beyond the Standard Model.
1.3.1 Grand unification
In the grand unification theory, electromagnetic, weak and strong forces are thought to stem out from one
force at the GUT scale. If it is correct, the coupling constants for these three forces should be the same
strength at the GUT scale. In renormalization theory, the energy dependence of coupling constant αi isevaluated by
( )
1
1
bi
Q
−
= − ln
,
(2)
2
2
2π
Q0
αi (Q)αi (Q0 )where Q0 is the energy scale at which the coupling constant αi is measured (usually mZ is chosen) and Q
is the energy scale at which αi is evaluated. In the Standard Model, bi is
 

 4 

 1 
 3  b1   0 
 10 






 b2  =  − 22  + ngen  4  + nHiggs  1  ,
(3)
bSM
=
i
  3  34 
 6 
b3
−11
0
3
7

where ngen is the number of generations and nHiggs is the number of Higgs doublets, which are 3 and1, respectively. Parameters in the parentheses are the function of number of particles appearing in loop
calculations. The running of coupling constants are evaluated as plotted in Fig. 2 (left). The three lines
do not intersect at one point.
On the other hand, in Minimal Supersymmetric Standard Model (MSSM), which will be introduced
later, the coeﬃcients bi are modified because of newly introduced particles. bi , then, becomes,
 3 

 

 
 10  2  b1   0 






 b2  =  −6  + ngen  2  + nHiggs  1  .
(4)
bMSSM
=
i
 2 

 

 
−9
2
b3
0
Note that the number of Higgs fields nHiggs is 2 in MSSM. If supersymmetry exists at the mass scale ofaround O(1) TeV, the three coupling constants cross around Q = O(1016 ) GeV and the grand unification
occurs as shown in Fig. 2 (right).

Figure 2: First order evolution of the tree coupling constants in the Standard Model using MZ andαS (MZ ) from DELPHI data (left) and the second order evolution of the tree coupling constants in MSSM
assuming SUSY mass scale MSUSY of around 1 TeV (right) [3].

1.3.2 Hierarchy problem
Masses of the SM particles are all below the electromagnetic scale, i.e. O(100) GeV, while the Planckscale is MPl ∼ 1016 GeV, where gravity finally becomes as strong as the other three forces. The unnatural
splitting between these energy scales are called “hierarchy problem”.
Another problem, which is also called “hierarchy problem”, occurs for the Higgs mass. In the leading order, the Higgs mass is O(100) GeV (see Appendix A.3), however, once we include higher ordercorrections, the one-loop diagram containing a Dirac fermion f with mass m f , shown in Fig. 3 (left)
also contributes. If the Higgs field couples to f through a term −λ f H f¯ f , then the Feynman diagram in
Fig. 3 (left) yields a correction of|λ f |2∆m2H = − 2 Λ2UV + ...,
(5)8π
where ∆UV is ultraviolet energy cutoﬀ used to regulate the loop integral, or it can be interpreted as theenergy scale to which the SM is valid. If there is no new physics beyond the SM up to the Planck scale,then the Higgs mass diverges quadratically.
Let’s assume a heavy complex scalar particle S with mass mS that couples to the Higgs through aterm −λS |H|2 |S |2 , the Feynman diagram in Fig. 3 (right) gives a correction of∆m2H =λS[Λ2 − 2m2S ln(ΛUV /mS ) + ...].
16π2 UV
8(6)

As shown later, two scalar particles are newly introduced for each of the SM fermion in the supersymmetry framework. If these scalar particles have coupling constants satisfying λS = |λ f |2 , the first termsof Eq. 5 and Eq. 6 cancel each other and the problematic quadrature divergence does not occur any more.
This cancellation mechanism is the primary motivation of introducing supersymmetry.
1.3.3 Dark matter
WMAP [2] measured the contents of the universe in a great accuracy:Ωb h2= 0.0227 ± 0.0006,
2Ωcdm h =0.110 ± 0.006,ΩΛ=
0.74 ± 0.03,(7)

where h is a dimensionless parameter defined from the Hubble constant H0 ,H0 = 100 h km s−1 Mpc−1 .

(8)All the values on the right-hand-side in Eq. 7 are the fractions with respect to the critical density of theuniverse ρc , which isρc c2 = 5.4 ± 0.5 GeV · m−3 .
(9)Ωb h2 is the fraction of Baryonic matter, Ωcdm h2 is the fraction of cold Dark Matter and ΩΛ represents thedark energy. The coldness (or slowness) of dark matter is important for formation of complex structurein the universe, such as galaxy. Assuming a hot dark matter with a relativistic speed, the structure getssmoothed and no star is formed. The dark matter should have the following properties:• To explain the contents of current universe, dark matter should be stable over the lifetime of theuniverse.
• The charge of dark matter should be zero, therefore electromagnetic force cannot or only weaklyinteract with dark matter.
• To be a cold dark matter, it should be heavy. A quantitative limit comes from a comparison withthe mass and the energy scale at which dark matter decoupled from heat-equilibrium in the early
universe.
There’s no particle which satisfies above conditions in the framework of the Standard Model.
Weakly Interacting Massive Particles (WIMPs) is one of the candidates. WIMPs have masses roughly
between 10 GeV and a few TeV, and an interaction cross-sections of the weak force. As shown later,
the lightest supersymmetry particle (LSP) cannot decay further in R-parity conserving supersymmetry
models and becomes a good dark matter candidate satisfying above requirements.

9

S

f
H
H

Figure 3: Example diagrams showing 1-loop radiative corrections which contribute to mh . The loop of a
Dirac fermion f (left) with a coupling constant λ f and the one of a scalar particle S (right) with a coupling
constant λS .

10

1.4 Supersymmetry
As discussed in the previous section, the Standard Model contains some problems and there must be a
new physics beyond the SM. Pursuing the theory of everything, many theorists have proposed solutionsin the last several decades. Supersymmetry introduces “superpartners” of the SM particles which havediﬀerent spin by 12 . Since fermions and bosons have spin 21 and spin 0, respectively, supersymmetry isoften referred to as symmetry between fermion and boson.
There exist several supersymmetry models with diﬀerent particle contents. We focus on the simplest
model, Minimal Supersymmetric Standard Model (MSSM), which contains the minimal extension of theStandard Model particles.
1.4.1 SUSY breaking
Although the basic concept of supersymmetry is simple, recalling the fact that the superpartner with exact
the same mass has not yet been observed, supersymmetry must be “broken” in a sense that supersymmetric particles are much heavier than the SM partners. We see how the SUSY breaking is introduced in
the MSSM framework below1 .
We start from introducing the most general form of SUSY breaking Lagrangian [4], which is
(
)
1
LMSSM
=
M
g̃g̃
+
M
W̃
W̃
+
M
B̃
B̃
+
c.c.
3
2
1
2 (
soft
)
− ū˜ au Q̃Hu − d̄˜ad Q̃Hd − ē˜ ae L̃Hd + c.c.
.
(10)−Q̃† m2Q̃ Q̃ − L̃† m2L̃ L̃ − ū˜ m2ū˜ ū˜ † − d̄˜m2˜d̄˜† − ē˜ m2ē˜ ē˜ †d̄−m2Hu Hu∗ Hu − m2Hd Hd∗ Hd − (bHu Hd + c.c.)
The terms in the Lagrangian are chosen so that the resultant SUSY breaking does not introduce thequadrature divergence again. The first line gives masses to the superpartners of gauge bosons. M3 , M2
and M1 correspond to the masses of gluino g̃, wino W̃ and bino B̃, respectively. The second line contains(scalar)3 type interactions (trilinear coupling). ū˜ , d̄˜, ē˜ are the vector of right-handed up-type squarks,
down-type squarks and sleptons. Each component of the vector represents a particle in three generations.
Q̃, L̃ are similar vectors but of left-handed particles, each of which is a weak isospin doublet as in Eq. 108.
Hu , Hd are the Higgs potentials which couple to up-type and down-type fermions. Finally, au , ad , ae arecomplex 3 × 3 matrices in family space with dimension of mass. These terms resemble the fermion massterm in Eq.108 and actually the terms are in one-to-one correspondence with the Yukawa couplings,
au = Au0 yu , ad = Ad0 yd , ae = Ae0 ye ,(11)where, yX is called Yukawa matrix in which the Yukawa couplings are contained as the components.
The third line consists of squark and slepton mass terms. Each of m2Q̃ , m2L̃ , m2ū˜ , m2˜, m2ē˜ is a 3 × 3 matrixd̄
in family space that can have complex entries. However, from the experimental limits on the flavorchanging neutral current and CP-violation, the squark and slepton mass matrices are required to beflavor-blinded, which is realized when the mass matrices are proportional to the identity matrix 1 before
renormalization group evolution:
m2Q̃ = m2Q̃ 1, m2ū˜ = m2ū˜ 1, m2˜ = m2˜1,d̄d̄
m2L̃ = m2L̃ 1, m2ē˜ = m2ē˜ 1.

(12)Finally, in the last line of Eq. 10 we have supersymmetry breaking contributions to the Higgs potential.
m2Hu , m2Hd are the contributions to the up-type and down-type Higgs masses.
1
The discussion is closely related to the content of the next section, so one should refer the Section 1.4.2 when an undefinedparticle or parameter appears in the text.

11

The original SUSY breaking Lagrangian contains many free parameters, especially as the components of matrices. However, introducing the assumptions such as Eq. 11 and Eq. 12, 124 parameters in
the original Lagrangian are reduced to a few parameters.
1.4.2 Particles in MSSM
Next, we look into the particles introduced in MSSM and their properties. Figure 4 illustrates the correspondence between the SM particles and their superpartners in MSSM.

Figure 4: Illustrations of the SM particles and their corresponding superpartners in the framework of
MSSM.

Higgs and Higgsino :In the MSSM framework, two Higgs doublets with weak hypercharges of Y = +1/2 and Y = −1/2
are introduced. The former one, denoted as Hu , gives masses to up-type fermions, while thelatter one, Hd , couples to down-type fermions. Each of them is composed of neutral and charged
components,
( + )
( 0 )
Hd
Hu
Hu =
, Hd =
.
(13)
Hu0
Hd−
Inserting the components into the SUSY Lagrangian, we obtain a potential related to the Higgs
boson
V=

(|µ|2 + m2Hu )(|Hu0 |2 + |Hu+ |2 ) + (|µ|2 + m2Hd )(|Hd0 |2 + |Hd+ |2 )+ |b(Hu+ Hd− − Hu0 Hd0 + c.c.|
1 2+(g + g02 ))(|Hu0 |2 + |Hu+ |2 − |Hd0 |2 − |Hd0 |2 − |Hd− |2 )28
1 2 + 0∗g |Hu Hd + Hu0 Hd−∗ |2 ,
+
2
12

(14)
(15)
(16)
(17)

where g, g0 are the gauge coupling constants and the terms proportional to µ come from the Higgs
interaction terms in the SUSY Lagrangian. We perform the same calculation of SSB as in the
Higgs mechanism in the Standard Model, i.e. find the minimum of potential V and expand thepotential about the minimum. Using SU(2)L and U(1)Y symmetries, we can set Hu+ = Hd− = 0.
Also, the vacuum expectation values of the two remaining Higgs fields, hHu0 i and hHd0 i, can be set
to real and positive. We require that the VEVs are compatible with the observed phenomenologyof electroweak symmetry breaking. Let us write
vu = hHu0 i, vd = hHd0 i.

(18)Then, the quadrature sum of these two terms corresponds to v in the Standard Model,
v2 = v2u + v2d .

(19)

vu
.
vd

(20)

The ratio of the VEVs is written astan β =The original Higgs doublets have eight freedom in total. Three of them are eaten by three electroweak bosons and five freedoms remain as physical Higgs fields. They consist of two CP-evennatural scalar bosons h0 and H 0 , one CP-odd natural scalar boson A0 and a charge +1 scalar boson H + and its conjugate charge -1 scalar boson H − . The mass of each Higgs field is given as
m2A0
m2h0 ,H 0m2H ±= 2|µ|2 + m2Hu + m2Hd ,
√


)2
(

1  2
2
2
2
2
2
2
=
mA0 − mZ + 4mZ mA0 sin (2β) ,mA0 + mZ ∓2
= m2A0 + m2W .

(21)
(22)
(23)

|µ| is obtained by the following relation:|m2H − m2Hu |m2Z = √ d
− m2Hu − m2Hd − 2|µ|2 .
1 − sin2 (2β)(24)

Note that these Higgs masses are obtained at tree-level calculations. The radiative correction to
the Higgs mass will be discussed in Section 1.4.5.
The superpartners of the Higgs bosons are called Higgsinos. The superpartners for the neutralcomponents are denoted as H̃u and H̃d , and those of the charged components are H̃ + and H̃ − ,respectively. The mass of Higgsinos is given by µ.
Gluino :The superpartners of gluon is called gluino g̃. The mass of gluinos is represented as M3 as shownin Eq 10.
Wino and Bino :The superpartners of electroweak gauge bosons are called wino W̃ and bino B̃ (they are collectivelyreferred to as electroweak gauginos). The masses of winos and bino are given by M2 and M1 ,respectively.
The higgsinos and electroweak gauginos mix with each other because of the eﬀects of electroweak
symmetry breaking. Neutral higgsinos and neutral gauginos combine to form four mass eigenstates13()
called neutralinos. In the gauge-eigenstates basis Ψ0 = B̃, W̃ 0 , H̃d0 , H̃u0 , the neutralino mass partof the Lagrangian is1(25)
Lneutralino mass = (Ψ0 )T MÑ Ψ0 + c.c.,
2
where


M1
0
−cβ sW mZ sβ sW mZ 



0
M2
cβ cW mZ −sβ cW mZ 
(26)
MÑ = 
 .
0
−µ

 −cβ sW mZ −cβ cW mZ
sβ sW mZ −sβ cW mZ−µ
0Here we introduced abbreviations: sW = sin θW , cW = cos θW , sβ = sin β and cβ = cos β.
The charged Higgsinos and winos mix in a similar way to form two mass eigenstates with charge± ), the chargino mass
±1, which are called charginos. In the gauge-eigenstate basis Ψ± = (W̃ ± , H̃u/dterms in the Lagrangian are
1
Lchargino mass = − (Ψ± )T MÑ Ψ± + c.c.
2
with

(
MÑ =

√ M2
2sβ mW√)2sβ mW
.
µ

(27)

(28)

We denote the neutralino and chargino mass eigenstates as χ̃0i (i = 1, 2, 3, 4) and χ̃±i (i = 1, 2). The
labels are assigned so that mχ̃0 < mχ̃0 < mχ̃0 < mχ̃0 and mχ̃±1 < mχ̃±2 .
1

2

3

4

Squark and Slepton :Squarks q̃ are the superpartners of quarks. They have the same quantum numbers of the corresponding quarks except for spin and mass. They behave in the same way as their partners undergauge interactions. The superpartners of left-handed and right-handed quarks are written as q̃L andq̃R . However, since sparticles do not have helicities, the handedness does not refer to its helicity
but just specifies its quantum numbers. So, for example, only a left-handed squark q̃L couples
to W bosons while a right-handed squark q̃R doesn’t. With this notation, gauge interactions are
consistent with their SM partners.
Similarly, sleptons l˜ are the superpartners of leptons. These superparticles also have the same
quantum numbers as their SM partners except for spin and mass.
The masses of the first and second generation squarks and sleptons are calculated as follow assuming they have the same mass m0 at the GUT scale,
m2d̃
L
m2ũL
m2ũR
m2d̃
R
m2ẽL
m2ν̃e
m2ẽR

= m20
= m20
= m20
= m20
= m20
= m20
= m20

+K3
+K3
+K3
+K3
+
+
+

1
+K2 + 36
K1
1
+K2 + 36 K1+ 49 K1+ 19 K1+K2 + 14 K1+K2 + 14 K1+K1+∆d̃L ,+∆ũL ,+∆ũR ,+∆d̃R ,+∆ẽL ,+∆ν̃ ,+∆ẽR ,

(29)

K3 , K2 and K1 represent the contributions obtained during the renormalization group evolution,
which are related to SU(3)C , SU(2)L and U(1)Y forces, respectively. Since left-handed squarks,d̃L , ũL , feel all three forces, all the term contributes to their masses. Right-handed squarks, ũR , d̃R ,do not couple to SU(2)L force, therefore K2 term doesn’t contribute. Left-handed sleptons, ũR , d̃R ,14

do not interact with SU(3)C as they don’t have color charges. Right-handed slepton, ẽR , is thelightest among these particles since it feels only U(1)Y force through hypercharge Y.
The last term ∆X represents a small contribution from the electroweak symmetry breaking [4]. We
focus on the heavy particles for which this contribution is negligible.
Assuming the coupling constant unification occurs at Q0 = 2 × 1016 GeV and fermion masses are
unified at that energy scale, the following values are obtained at the electroweak scale:
K1 ∼ 0.15m21/2 , K2 ∼ 0.5m21/2 , K3 ∼ (4.5 − 6.5)m21/2 ,(30)

where m1/2 is the unified mass of gauginos at the GUT scale.
Due to strong Yukawa couplings, masses of third generation squarks and sleptons take diﬀerent
forms. Here we take stop t˜ for example but the same discussion hold for sbottom and stau as well.
Left- and right-handed stops are mixed by the interactions with the Higgs potential and the soft
breaking term. We consider the terms which contributes to the following mass Lagrangian:
(
)
(
)
t˜L
∗
∗
2
Lstop masses = − t˜L t˜R mt˜
.
(31)
t˜R
First, a contribution of the form y2t Hu0∗ t˜∗L t˜L and y2t Hu0∗ t˜R∗ t˜R (the diagrams are shown in Fig. 5) contribute to the diagonal terms. At the VEV, yt Hu is equal to top mass, therefore this contribution
gives a mass term proportional to the top mass mt . Second, the diagram shown in Fig. 6 contributes
to the oﬀ-diagonal term. This interaction is represented as −µ∗ yt (v cos β)t˜R∗ t˜L + c.c.. The final contribution comes from the soft breaking term which is represented as at (v sin β)t˜L t˜R∗ + c.c.. This term
contributes to the oﬀ-diagonal term as it mixes left- and right-handed stops.
Adding up these terms, we obtain the mass matrix of stops m2t˜ ,
(
m2t˜

=

m2Q3 + m2t + ∆ũLv(a∗t sin β − µyt cos β)v(a∗t sin β − µyt cos β)m2ū3 + m2t + ∆ũR

)
.

(32)

In a similar way, one can obtain the mass matrix of sbottom in the gauge-eigenstate basis of (b̃L , b̃R )with the right-handed squark mass of
m2Q3 + ∆d̃Lv(a∗b cos β − µyb sin β) 2mb̃ = (33) ,v(a∗b cos β − µ∗ yb sin β)m2d̄ + ∆d̃R
3and the stau mass matrix in the gauge-eigenstate basis of (τ̃L , τ̃R ) is()
m2L3 + ∆ẽLv(a∗τ cos β − µyτ sin β)
2
.
mτ̃ =
m2ē3 + ∆ẽRv(a∗τ cos β − µ∗ yτ sin β)(34)

The mass eigenstates are denoted as t˜1 , t˜2 , b̃1 , b̃2 , and τ̃1 , τ̃2 . The subscripts are defined so thatmX̃1 < mX̃2 . The masses of third generation fermions at the electroweak scale, mQ3 , mū3 , md̄3 , mL3 ,and mē3 , are summarized in Eq. (6.5.41)-(6.5.45) in Ref. [4].
1.4.3 R-parity
In MSSM, one needs to introduce a new symmetry in order to forbid the term which induces the baryon
and lepton number violations. It is called R-parity PR and written as
PR = (−1)3(B−L)+2s ,
15

(35)

Hu0

Hu0∗

Hu0

Hu0∗

t̃L

t̃∗L

t̃R

t̃∗R

Figure 5: Interactions with the form of (scalar)4 . The coupling constant is proportional to y2t .

Hd0∗

t̃∗R

t̃L

Figure 6: Interaction with the form of (scalar)3 . The coupling constant is proportional to µ∗ yt .

where B and L are the baryon and lepton numbers, and s denotes the spin. PR takes +1 for the SMparticles and −1 for the SUSY partners. Models that violate R-parity are also possible if the resultant
violations are well below experimental limits, but in this thesis only the R-parity conserving models are
considered. As a result of R-parity conservation, SUSY particles must be produced in pairs and they
decay to stable Lightest SUSY Particles (LSP).
1.4.4 Minimal supergravity model
The original 124 free parameters in the SUSY breaking Lagrangian are reduced down to a few parametersby the assumptions from experimental requirements such as Eq. 11 and Eq. 12. The number of parameters
can be further reduced by introducing SUSY-breaking models.
The breaking is assumed to originate in the hidden sector, which is the collection of unobserved hypothetical particles that do not directly interact via the Standard Model gauge bosons, and the breaking effect is transferred to the MSSM sector by a specific mechanism. In Minimal Supergravity model (MSUGRA)or Constrained Supersymmetry model (CMSSM), gravity is thought to be the messenger that mediates
the breaking. The parameters in MSUGRA/CMSSM model is reduced to 4 and one sign, which makes
the model highly predictive.
m0 : All masses of squarks and sleptons are assumed to be universal at the GUT scale, which is represented by m0 .
m1/2 : All masses of gauginos are assumed to be universal at the GUT scale, which is represented by
m1/2 . The following relationship holds for gaugino masses,
M1
M2
M3= 2 = 2 = m1/2 .
5 02
g
gS
3g
16

(36)

At the electroweak scale, they are
M1 ∼ 0.4m1/2 ,M2 ∼ 0.8m1/2 ,M3 ∼ 2.4m1/2 .

(37)

A0 : All trilinear couplings (Eq. 11) are common in this model.
tan β: The ratio of VEVs of two Higgs bosons as defined in Eq. 20.
sign(µ): The sign of µ. The absolute value is determined through Eq. 24.
In most of the parameter space, there are two possible LSP candidates: χ̃01 and τ̃±1 . However, τ̃±1 isusually forbidden as LSP should be neutral to be a dark matter candidate.
1.4.5 Discovery of the Higgs boson
The primary motivation of supersymmetry is to solve the quadrature divergence of the Higgs mass.
This, in turn, sets limits on SUSY parameters [5]. Considering the recent results of the Higgs decaybranches [6], the light neutral Higgs h0 seems to have quite the same properties of the SM Higgs boson,which happens when h0 is much lighter than the other Higgs particles. This configuration is referred toas “decoupling limit”. In this limit, the Higgs mass with one-loop order correction is written as2Xt2 
3 m4t  mt˜ Xt2 222 ,+ 2 1 −(38)
mh ∼ mZ cos 2β +ln(4π)2 v2  m2t
mt˜
12m2t˜where Xt = At − µ cot β, which is the oﬀ-diagonal term of stop mass matrix in Eq. 32. Figure 7 shows
the contours of mh as a function of stop mass mt˜ and the stop mixing parameter Xt for tan β = 20. The
red/blue bands show the Higgs mass range mh = 124-126 GeV obtained by two diﬀerent programs. The
dotted lines show the degree of fine-tuning ∆, which is defined as the maximum sensitivity to fundamental
parameters pi ,∂ ln m2h.
(39)∆ ≡ maxi∂pi√
The smallest fine-tuning is obtained when |Xt | = 6mt˜, which is referred to as “maximal mixing”. The
parameters of MSUGRA/CMSSM sample used in the analysis are chosen so that this maximal mixing isrealized. In this configuration, one of the stop masses becomes 20-30% lighter than the masses without
mixing. As a result, stops are more likely to appear in decay chains, which increase the complexity ofevents.
The Higgs mass is also aﬀected by a gluino mass through 2-loop order corrections [7, 8], which sets
an limit on a gluino mass M3 :(log(Λ/TeV)
M3 <∼ 900 GeV sin β
3

)−1 (

(
)− 1
mh ) ∆−1 2,
120 GeV 20 %(40)

where Λ denotes the SUSY breaking scale. Allowing 10% fine-tuning, one finds the gluino mass should
be below about 1.3 TeV. Although the limit varies depending on the fine-tuning condition, we safely
expect that the gluino mass lies at O(1) TeV and inside the LHC energy scale.

17Figure 7: Contours of mh in MSSM as a function of a common stop mass mt˜ and the stop maxing
parameter Xt for tan β = 20. The red/blue bands show the Higgs mass range mh = 124-126 GeV obtainedby two diﬀerent programs. The dotted lines show the degree of “fine-tuning”. This plot is cited from
Ref. [5].

182 LHC and ATLAS detector
2.1 Large Hadron Collider
The Large Hadron Collider (LHC) [9] was constructed to collide two proton beams with an unprecedented center-of-mass energy of 14 TeV and a luminosity of 1034 cm−2 s−1 aiming at an investigation ofelectroweak symmetry breaking and searches for the Higgs boson as well as physics beyond the Standard
Model. During the data taking period in 2012, the accelerator was operating at a center-of-mass energyof 8 TeV with a peak luminosity of 7.73 × 1033 cm−2 s−1 . Figure 8 shows the peak luminosity recorded
by ATLAS in 2012.
The beam circulating in the LHC ring is clustered to small chunks, called bunch, with a few cm inlength and the transverse size of O(10) µm, containing approximately 1 × 1011 protons per bunch. The
bunches make collisions at the center of the detectors every 50 ns, which is twice lower rate than theoriginal design. This is due to the beam instability observed during the run and will be cured in the next
data taking phase, giving the designed collision rate of 25 ns or 40 MHz. Table 1 summarizes the proton
beam parameters of the LHC.

Proton Energy [GeV]
Number of Protons in a bunch
Number of Bunches in the ring
Peak luminosity [cm−2 sec−1 ]Bunch spacing [ns]Designed Parameters7000
1.15 × 1011
2808
1.0 × 1034
25

Current Parameters
4000
1 × 1011
1380
7.73 × 1033
50

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

Table 1: Designed LHC beam parameters and the ones in 2012 data taking period.

10

ATLAS Online Luminositys = 8 TeVLHC Stable Beams
Peak Lumi: 7.73 × 10 cm-2 s-1
33

8
6
4
2
0
26/03

06/06

18/08

30/10
11/01
Day in 2012

Figure 8: Peak luminosity recorded by the ATLAS detector per day in 2012.
The LHC is installed in the tunnel where LEP machine was originally placed. Total length of thetunnel is 26.7 km and the whole part lies about 100 m below the ground surface. The LHC uses super19

conducting magnets to bend 4 TeV beams. The original proton is produced from hydrogen gas by stripping the electron, then the proton is accelerated by LINAC2 to 50 MeV. The proton is fed to Proton Synchrotron Booster (BOOSTER) to obtain 1.4 GeV, and passed to the following accelerator, called Proton
Synchrotron (PS), which accelerates the proton to 450 GeV, and finally, the 450 GeV proton is injectedto the LHC. The LHC accelerates the proton to the target energy of the experiment.
There are four big experiments running in the LHC. ATLAS and CMS [10] are general-purpose detectors designed for studying Higgs boson and the physics beyond standard Model. LHCb [11] experimentstudies B-physics, and ALICE [12] is dedicated to heavy ion collisions. Figure 9 shows the schematic
overview of the LHC and four experiments.

Figure 9: A schematic overview of LHC.

20

2.2 ATLAS detector
The ATLAS2 experiment [13, 14, 15] is a general-purpose detector placed at the LHC. It is designed to
study various types of physics signatures, which allows to discover the Higgs boson, extra dimensions
and also supersymmetry. As opposed to CMS detector, which is also targeting new physics, the ALTAS
detector is designed as huge as possible so as to measure the tracks precisely by making the most of thedetector length or to minimize the escaping shower energy from the calorimeter. As a result, the ATLAS
detector is 44 m along the beam axis and 22 m in diameter.
2.2.1 Coordinate system
The x-axis is defined as the direction of the center of LHC ring, and the y-axis points to the opposite
direction from the center of the earth. A right-handed coordinate system is used in the ATLAS, therefore
the z-axis points along the beam axis. A-side is defined as the part of ATLAS detector with positive z,
and C-side is the opposite. Azimuthal angle φ and polar angle θ are defined in a usual way of the righthanded coordinate, so φ is the angle around the beam axis, starting from the direction of x-axis, and θ isthe polar angle from z-axis.
Pseudo-rapidity η is defined using θ(θ)η = − ln tan.
(41)
2
Pseudo-rapidity η is an approximation of the following rapidity y at the mass-less limit()
1
E + pzy = ln,2
E − pz(42)

where E is the energy of a given particle and pz is the transverse momentum. Here, “transverse” isdefined with respect to z-axis. The distance of given two objects ∆R is often used, which is defined as
the square-sum of η and φ distances,√∆R =∆η2 + ∆φ2 .

(43)

2.2.2 Magnet system
The ATLAS magnet system consists of four super-conducting magnets. One solenoid magnet is immersed inside the detector and two toroidal magnets placed at the end-cap of A and C-sides. The last big
toroidal magnet is placed outermost of the detector around the barrel.
The solenoid magnet is aligned to the beam axis and provides a 2 Tesla axial magnetic field. The
magnetic field bends the tracks of charged particles in the inner detector, which allows to measure themomentum from the sagitta of tracks. A 5.8 m length solenoid is placed just inside of LAr calorimeter,
which measures the energy of electron, photon and jets, so the material thickness is minimized as muchas possible. A single layer coil made of Al-stabilized NbTi conductor is placed in the inner wall of the
LAr calorimeter. The inner and outer diameters of the solenoid magnet is 2.46 m and 2.56 m, whichcorresponds to ∼0.66 radiation length at normal incidence. The return flux of the magnet is guided by
the hadronic calorimeter to minimize the leakage to the muon spectrometer.
One barrel toroidal and two end-cap toroidal magnets produce toroidal magnetic field of approximately 0.5 Tesla and 1 Tesla for the muon spectrometers in the barrel and in the end-cap regions, respectively. Figure 10 shows the schematic view of all the magnetic systems. The barrel toroid consists ofeight coils encased in individual racetrack-shaped, stainless-steel vacuum vessels. The overall size of the
2

ATLAS is an acronym of A Toroidal LHC ApparatuS21

barrel toroid system is 25.3 m in length along the beam axis, with the inner and outer diameters of 9.4 m
and 20.1 m. Each end-cap toroid consists of a single cold mass build up from eight flat, square coil units
and eight keystone wedges, bolted together into a rigid structure. Both of the end-cap and barrel toroids
are build up with the same materials and coil structures: pure Al-stabilized Nb/Ti/Cu conductor with apancake-shape in section.

Figure 10: Schematic overview of the magnet system of ATLAS.

2.2.3 Tracking system
In the ATLAS detector, “tracking system” usually means the inner detectors (ID) without including outermost muon spectrometer (MS). The inner detectors consist of three diﬀerent detectors as shown in
Fig.11:
Pixel detector : The pixel detector locates the innermost layer, only 5 cm away from the beam. It consists of 1744 silicon pixel modules and each has pixel sensors of 50 × 400 µm along φ and z-axis.
The intrinsic resolution in the barrel is 10 µm (r − φ) and 115 µm (z), and, in the end-cap disks, it
is 10 µm (r − φ) and 115 µm (r).
Silicon micro-strip detector (SCT): Silicon micro-strip detector is often called as SCT, which is theabbreviation of Semiconductor Tracker. One SCT module consists of one pairs of 6.4 cm-lengthlayers on which single-sided silicon micro-strip sensors are placed. Each micro-strip sensor layer
has strip sensors with a mean pitch of 80 µm. Two strip layers are glued slightly oﬀ-aligned by ±20m radian around the geometrical center as shown in Fig. 12, which gives the detector a sensitivity
to the z-position of hits.
Transition Radiation Tracker (TRT) : TRT locates the outside of SCT system, which consists of 4 mmdiameter straw tubes. The straw tube is filled with Xe gas (70 %) and some CO2 , O2 gas (27 % and
3 %, respectively) as quencher gas. Each straw tube has a thin wire at the center and a high voltage
is applied between the wire and tube. The gaps of the straw tubes are stuﬀed with fibers made ofpolypropylene or polyethylene.
TRT detects the passage of a charged particles in two ways. One is by detecting the ionizationof gas, and one is by detecting the transition radiation which is produced when a charged particle
22

passes the polymer fibers. Since transition radiation is emitted only from electrons and drops
large energy when absorbed by gas, TRT is able to discriminate electrons from the other charged
particles by setting an appropriate energy threshold.

Figure 11: Schematic overviews of tracking system. Left plot shows the cross-section and right plot
gives the bird-eye view.

Figure 12: Illustration of SCT.

2.2.4 Calorimeter system
The ATLAS calorimeters cover the range of |η| < 4.9. Fine granularity electromagnetic (EM) calorimeters are used for the precise measurement of electrons and photons. Hadron calorimeters are made withrather coarser granularity but are suﬃcient for their primary purpose, jet reconstruction. Figure 13 shows
the ATLAS calorimeter system and more details of Tile calorimeter are documented in Appendix I.

23

Figure 13: Schematic overview of ATLAS Calorimeter system.

EM calorimeter EM calorimeter is divided into barrel part (|η| < 1.475) and two end-cap parts (1.375 <|η| < 3.2). EM calorimeter is Lead-LAr detector with accordion-shaped kapton electrodes and leadabsorber plates over its full coverage. Figure 14 shows a sketch of EM calorimeter in the barrel
region. EM calorimeter is constructed from three layers in radial direction. Additional pre-sampler
detector is placed in |η| < 1.8, which consists of an active LAr layer of 1.1 cm (0.5 cm) thick in thebarrel (end-cap) region. It is used to correct the energy loss in upstream material.
Tile calorimeter Tile calorimeter is placed outside of EM calorimeter in the barrel region. The central
barrel part covers |η| < 1.0 and two extended barrels cover 0.8 < |η| < 1.7. Tile calorimetercollects shower energy using 14 mm thick steel plates as absorber and 3 mm thick scintillatingtiles as active material. It is longitudinally segmented in three layers approximately 1.5, 4.1 and
1.8 interaction length thick for the barrel and 1.5, 2.6 and 3.3 interaction length for the extended
barrel. Two sides of the scintillating tiles are read out by wavelength shifting fibers into two
separate photo-multiplier tubes.
LAr hadronic end-cap calorimeter Hadronic end-cap calorimeter (HEC) consists of two independent
wheels in each end-cap behind the end-cap EM calorimeter. To reduce the drop in material density
in the transition part between the end-cap and the forward calorimeter around |η| = 3.1, HEC
extends out to |η| = 3.2. Also HEC covers up to |η| < 1.5 in the barrel region and slightly overlaps
with the barrel tile calorimeter which covers |η| < 1.7. Each wheel has four layers. The innermost
layer is built from 25 mm parallel copper plates, while the outer layers use 50 mm copper plates,interleaved with 8.5 mm LAr gaps as the active medium.
LAr forward calorimeter Forward calorimeter (FCal) is integrated into the end-cap cryostat covering
the range of 3.1 < |η| < 4.9. FCal is approximately 10 interaction lengths deep and consists ofthree modules in each end-cap. The first module is made of copper optimized for electromagnetic
measurements. The other two are made of tungsten for hadronic interaction measurements. Liquidargon is used as the sensitive medium. In order to reduce the amount of neutrons reflected into theinner detector cavity, the front face of the FCal is recessed by about 1.2 m with respect to the EM
calorimeter front face.
24

Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
TriggerTower∆η = 0
.1

2X0

47
0

mm

η=0

16X0
TriggerTow∆ϕ = 0er
.09

82

m

m

4.3X0

15

00

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

Square cells in
Layer 2∆ϕ = 0

.0245

ϕ
37.5m

∆η = 0

.025

m/8 =
4
∆η = 0 .69 mm.0031
Strip cells in Layer 1

ηFigure 14: Expanded view of EM calorimeter. The magenta square shows the minimum unit size of EM
calorimeter.

2.2.5 Muon system
The ATLAS muon system measures muon momentum using the magnetic deflection of muon tracks inthe super-conducting air-core toroid magnets. Over the range of |η| < 1.4, magnetic field is provided by
the barrel toroid. For 1.6 < |η| < 2.7, muon tracks are bent by the two end-cap magnets inserted into
both ends of the barrel toroid. Between these regions, 1.4 < |η| < 1.6, the magnetic field is provided by a
combination of barrel and end-cap magnets. Four types of muon chambers are used for the measurementof muon hit positions. Figure 15 shows the layout of the muon system.
Monitored Drift Tubes (MDT) measure the track properties precisely in the range of |η| < 2.7 (|η| <2.0 for the innermost plane). These chambers consist of three or four layers of drift tubes, which achieve
an average resolution of 80 µm per tube or about 3 µm per chamber. In the center of the detector (|η| ∼ 0),
a gap in chamber coverage is left open for service. Cathode Strip Chambers (CSC), which are multiwire proportional chambers with cathodes segmented into strips, are used in the innermost plane of
2.0 < |η| < 2.7 for additional precise track measurement. The resolution of chamber is 40 µm in thebending plane and about 5 mm in the transverse plane.
The muon trigger system consists of Resistive Plate Chambers (RPC) and Thin Gap Chambers (TGC)
covering |η| < 1.05 and 1.05 < |η| < 2.4, respectively. RPC consist of three concentric cylindrical layers
around the beam axis, referred to as trigger stations. Each station further consists of two independent
detector layers, each measuring η and φ. TGC are multi-wire proportional chambers with the wireto-wire distance of 1.8 mm. TGC are also used to determine azimuthal positions to complement themeasurement of MDT in the bending direction.
2.2.6 Trigger system
The ATLAS experiment is designed to receive data at 40 MHz but the data acquisition system can only
commit data to permanent storage at the rate of a few hundred Hz. To select “interesting” events from thelarge number of incoming events, trigger system are made up of three layers, Level1 (L1), Level2 (L2)and event filter (EF). L1 trigger searches for high transverse momentum muons, electrons, photons, jets,
τ-leptons decaying into hadrons, large missing and total transverse energy. In each event, L1 trigger
25

Figure 15: Overview of Muon Spectrometer system.

defines one or more Regions-of-Interest (RoI) which is the geometrical coordinate in η and φ where aninteresting feature is found. The maximum acceptable L1 rate is 75 kHz and the L1 decision must reachthe front-end electronics within 2.5 µs after the bunch-crossing to tell the front-end electronics whether
the event stored in the buﬀer should be read or discarded. L2 trigger is seeded by the RoI information
provided by L1 trigger. Taking longer time to process data, L2 trigger analyses the events in more detailfor further reduction of trigger rate. L2 trigger is designed to reduce the trigger rate to approximately
3.5 kHz within an event processing time of about 40 ms in average. EF trigger reduces the event rate toroughly 200 Hz, reconstructing the objects with almost the same definitions as the oﬄine analyses anddetermine the event to be stored.

Figure 16: Cut-away view of LUCID detector.

26

2.2.7 Luminosity detectors
There prepared several methods and detectors to measure the luminosity in ATLAS. LUCID (Luminosity
measurement using a Cerenkov Integrating Detectors) is one of such detectors. LUCID are locatedon each side of the interaction point (IP) at a distance of 17 m, covering the pseudo-rapidity range of
5.6 < |η| < 6.0. LUCID are made of aluminum tubes filled with C4 F10 gas and surrounds the beam-pipe
as shown in Fig. 16 (top left). By counting the Cerenkov photons radiated by the high energy charged
particles along the beam axis, which are produced by inelastic collisions of protons, it measures theintegrated luminosity and provide online monitoring of the instantaneous luminosity and beam conditions. Four Beam Current Transformers (BCT) placed per LHC ring [16] directly measure the beam
current. Four BDT consists of two DC current transformers (DCCT) and two fast beam current transformers (FBCT). FBCT has a higher time resolution enough to measure the charge in each bunch separately, while CDDT can measure only the averaged beam current. The luminosity is estimated using thebeam profile information, which will be discussed in Section 4.1.1.

27

3 Object reconstruction and definition
Leptonic supersymmetry search employs many types of objects, such as jets, electrons, muons and missing transverse momentum, whose definitions are discussed in this section. The object definitions used in
the analysis are all following the ATLAS-default recommendations.

3.1 Track
Tracks are primarily used to determine the point of proton-proton collision, which is called Primary
Vertex (PV). One bunch crossing usually contains one hard and several pile-up collisions, which accompanies many outgoing objects. The primary vertex candidate with the largest track pT sum is chosen as
the Primary Vertex of hard collision. A distance from the Primary Vertex is a good quantity to classify
an object to hard collision products or not. Heavy flavor hadrons with long life time often make vertices
away from a Primary Vertex, which are called Secondary Vertex. Secondary Vertex is identified in trackreconstruction procedure and used to tag b-jets. Reconstructed tracks are also used in the following object definitions of electron, muon and jets. Tracks with pT >0.4 GeV and |η| < 2.5 are reconstructed asbaseline tracks.

3.2 JetParticle in a jet create showers in the calorimeter, which are called “clusters”. Jet reconstruction procedure starts from finding clusters, then determines the cluster types by their shape information and apply
appropriate energy calibrations. The clusters are summed up to form jets and, finally, calibrated again sothat the jet energy matches to that of the original parton.
3.2.1 Clustering
Clusters are reconstructed by Topo-cluster algorithm [17]. Clustering starts with finding one “seed cell”
which is defined as a cell with at least four times higher energy than noise level σNoise . Here σNoise isdefined as root-mean-square of the noise distribution. The adjacent cells with energy Ecell are added up
to the seed cell if Ecell > σNoise is satisfied, forming a cluster. This process is repeated to sum up all thecells until there are no more adjacent cells with Ecell > 2σNoise . Finally, one layer of the neighborhood
cells are included to the cluster to sum up the shower leakage. No energy threshold is considered in thelast step. Center of cluster is calculated by the weighted average of cells.
3.2.2 Classification
The raw cluster energy is called EM-scale energy, which is calibrated to gives a good estimation forelectromagnetic shower. For hadronic shower, EM-scale energy is not correct due to the missing energy
carried out by neutrons and neutrinos. Hadronic clusters need to be calibrated to compensate the missing
energy. Clusters are classified to EM-like, Hadron-like or unknown, based on the following variables:
FEM : Fraction of the energy deposit in EM calorimeter over the total energy, i.e. F = EEM /Etotal .
λ : Cluster barycenter depth in the calorimeter.
ρ : Average cell density weighted by cell energy.
Cluster energies are then multiplied by a calibration constant estimated using Monte Carlo. Calibration
constants includes the following corrections to compensate instrumental eﬀects:

28

Out-Of-Cluster correction : Some fraction of the shower energy escapes from the active region at its
tail. This correction is applied to recover the lost energy.
Dead material correction : This correction compensates the energy deposit outside of the active regions of LAr and Tile calorimeters. Also the lost energy in upstream materials, such as the innerdetector, magnetic coils and cryostat walls are recovered.
3.2.3 Jet finding
Calibrated clusters are then summed up to form jets [18] using anti-kT algorithm [19] with a distanceparameter R = 0.4. Anti-kT algorithm is infrared safe to all orders in perturbative QCD [20] and also
robust against pile-up as it starts summing constituents up from higher momentum. In the algorithm, twotypes of distances are defined:
2p

2p

di j = min(kti , kt j ) ·(yi − y j )2 + (φi − φ j )2
,
R2

2p

diB = kti ,

(44)
(45)

where p is the parameter which governs the relative power of energy versus geometrical scales. p = −1
is chosen in anti-kT algorithm, thus it has a prefix of “anti-”. i, j runs over all cluster objects. The pairof clusters which has the minimum di j are summed up to make a new object. After including the new
object into the list of clusters and removing the original two objects, all di j and diB are recalculated. This
procedure continues until one of diB becomes the smallest than the others. Then object i is removed fromthe object list, classified as a jet. This process continues until all clusters are removed from the list.
3.2.4 Calibration
A method called Jet Energy Scale (JES) calibration [21] is applied to jets. Calibration constants are
determined as a function of pT and η using Monte Carlo so that pT of reconstructed jet matches to thecorresponding true parton pT .
As a confirmation of the calibration, diﬀerences between data and Monte Carlo simulation are assessed using in-situ techniques exploiting the transverse momentum balance between a jet and a wellmeasured reference object. First, the pT balance between a central and a forward jet in the events having only two jets is selected to check the equality of jet response in large η region. After removing η
dependence, pT of a photon or Z boson decaying to electrons or muons is used as a reference to checkthe calibration within |η| < 1.2. Finally, the events in which low-pT jets are recoiled against a high pT jet
are used to check the jet response in TeV regime. In this measurement, the low-pT jets are limited within|η| < 2.8 while the leading jet is required to be within |η| < 1.2.
The residual of Jet Energy Scale calibration evaluated by the combination of these in-situ techniques
is shown in Fig. 17, together with statistical and systematic uncertainties. All the measurements show
consistent results and the maximum discrepancy is 3% in pT >1 TeV. The total uncertainty is 3% at the
maximum. Including additional uncertainties due to pile-up and flavor response, a fractional uncertainty<2.5% is obtained for central jets with pT > 100 GeV as shown in Fig. 18 (left). The plot on the rightshows the η dependence of JES uncertainty for jet with pT = 40 GeV.
3.2.5 Pileup suppression
Low pT particles from multiple soft collisions (pile-up) increase the calorimeter activity and shift jet
energies. To remove the energy shift, a pile-up correction has been developed based on the idea thatnoise (pile-up) has a lower energy density than signal jets [22]. “Median pT density” ρ, is defined as29

MC/ Response

ATLAS Preliminarys = 8 TeV, |η | < 0.8

anti-kt R = 0.4, LCW+JES
Data 2012

1.08
1.06
1.04

Data

Response

1.1

1.02
1
0.98
0.96

γ +jetZ +jetMultijet

0.94
0.92
0.9

Total in situ uncertainty
Statistical component

2×102

102

20 30 40

3

10
p jet [GeV]
T

0.1
0.09
0.08

anti-kt R = 0.4, LCW+JES + in situ correction

ATLAS Preliminary

Data 2012, s = 8 TeV
η = 0.0

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pileup, average 2012 conditions

0.07
0.06
0.05
0.04

Fractional JES uncertainty

Fractional JES uncertainty

Figure 17: Residual of JES calibration obtained from the combination of the in-situ techniques withstatistical and systematic uncertainties. This plot is cited from Ref. [21].
0.1
0.09
0.08

0.04

0.02

0.01

0.01
102

2×102

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pileup, average 2012 conditions

0.05

0.03

30 40

jet

p T = 40 GeV

0.06

0.02

20

ATLAS Preliminary

Data 2012, s = 8 TeV

0.07

0.03

0

anti-kt R = 0.4, LCW+JES + in situ correction

0

103
2×103
p jet
[GeV]
T

-4

-3

-2

-1

0

1

2

3

4
η

Figure 18: JES and additional uncertainties due to pile-up, flavor response and composition for central
jets (left) and for jets with pT =40 GeV (right). These plots are cited from Ref. [21].

jetthe median of pT /Ajet of all the jets. Here, Ajet is the geometrical area of a jet which is determined jet
by jet by adding up all the clusters involved. The number of pile-up jets is much larger than jets froma hard collision, therefore the median is mainly determined by pile-up jets without a significant bias.
Figure 19 (left) illustrates that ρ increases with the number of primary vertex per bunch crossing NPV . ρprovides a direct estimate of the global pile-up activity in any given event, while Ajet provides an estimateof a jet’s sensitivity to pileup. By multiplying these two quantities, an estimate of the eﬀects of pile-up is
obtained. Subtracting this estimate from the original jet pT permits to reduce the dependence on pile-up:
jet,corrpT

jet= pT − ρ × Ajet .
jet,corr(46)

Figure 19 (right) shows the root-mean-square of (pT− ptrueT ) as a function of the average number ofpileup interactions per bunch crossing hµi. The impact of pile-up on jet pT is evident from the linear riseobserved in the uncorrected points. Compared to the previous oﬀset correction method [23] based on hµi
and NPV used in 2011, the jet area method further mitigates the degradation in jet pT resolution.

30

20 ≤ 〈µ〉 < 21

0.1

NPV = 6

NPV = 10

NPV = 14

NPV = 18

Pythia Dijet 2012, s = 8 TeVLCW TopoClusters

0.08

13
12
11

0.04

7

0.02

6
10

15

20

uncorrectedf(〈µ 〉, NPV) correction
ρ×A correction

98

5

Pythia Dijet s=8 TeV
anti-k t LCW R=0.6
20 ≤ ptrue < 30 GeVT|η| < 2.4

10

0.06

0
0

ATLAS Simulation

T

0.12

T

ATLAS Simulation

RMS(preco - ptrue) [GeV]

Normalised entries

0.14

14

5

25
30
ρ [GeV]5

10 15 20 25

30 35 40〈µ 〉Figure 19: (Left) ρ distribution for four representative values of the reconstructed Primary Vertex multiplicity NPV . (Right) Root-mean-square width of the distributions of (preco− ptrueTT ) for anti-kT (R=0.6)
jets. These plots are cited from Ref. [22].

3.2.6 b-tagging
Several tagging algorithms have been invented for better b-tagging eﬃciency. A method based on neuralnetwork, MV1, which combines the inputs from IP3D, SV1 and JetFitter, is used to improve purity andeﬃciency.
IP3D [24] is the tagging algorithm using the likelihood technique in which input variables are compared with pre-defined distributions for both b- and light-jet hypotheses, obtained from Monte Carlosimulation. The signed transverse impact parameter significance and the longitudinal impact parametersignificance, along with their correlation, are used as the input parameters.
SV1 [24] is also an algorithm based on the likelihood technique, but using reconstructed Secondary
Vertex information. It uses ∆R between a jet and a b-hadron, and the number of two-track vertices. Also,
the combined two-dimensional information of the Secondary Vertex mass and the energy fraction of theSecondary Vertex with respect to the total tracks are employed.
These methods have a drawback of giving a bad tagging eﬃciency in case a long-lived hadron isemitted from the decay as these methods assume only one Secondary Vertex. JetFitter [25] takes the
decay of long-lived hadrons into consideration under the assumption that the long-lived hadron decays
occur on the flight axis of the initial b-hadron. The separation between b-, c- and light-jets is performed
based on the likelihood method.
MV1 algorithm combines the results from these methods using a neural-network. As the tagging
eﬃciency is not critical in our analysis, we use a moderate working point at which 60% of b-jets aretagged. At this working point, light-jet rejection factor of 577, c-jet rejection factor of 8 and tau-jet
rejection factor of 23 are obtained, respectively3 . The discrepancy of the tagging eﬃciency between data
and Monte Carlo is corrected by applying a scale factor.

3

The rejection factor is defined as the number of jets out of which one jet is mis-tagged as a b-jet.

31

3.2.7 Object definition
Jet candidates defined in the previous section may contain “fake” jets. Here we apply further cleanings
to define sets of genuine jets that are used in the analysis. Fake jets, such as cosmic muons, noise in thedetector electronics and the particles not originating from the proton collision, are eliminated as follow.
• Pulse shapes of calorimeters are monitored for all jets. If the shape diﬀers from the usual one, thejet may be a noise and is judged as a fake jet.
• The baseline voltage of LAr electronics takes some time to settle to the usual level after incomingof a jet. Instability of baseline voltage makes negative energy cells and if the total negative energy
is sizable, the jet is tagged as a fake jet.
• The energy fraction of a radial layer in the total jet energy should be smaller than a specific threshold. If one layer has a significant fraction of the energy, it may be a fake jet produced by a scrapping
particle, flying into the detector parallel to the beam axis.
Next, electron showers, which are also reconstructed as jets, are removed. Jet within ∆R < 0.2 frompreselected electrons (defined in Table 4 for Hard electron and Table 5 for Soft electron) are removed.
Finally, we define four types of jets: signal jets, b-jets, ETmiss jets and overlap removal jets. Signal
jets are the ones on which our kinematic selections are applied. b-tagging is checked for signal jets with
60% eﬃciency working point to define b-jets. ETmiss jets are the collection of jets with |η| < 2.5 andpT >20 GeV, which are defined to calculate ETmiss 4 . Overlap removal jets are defined to be used in the
lepton isolation check, which will be discussed in Section 3.3.4. Table 2 summarizes their definitions.
Cut
Jet Type
Acceptanceoverlap removal
pT > 20 GeV
No limit on |η|Overlap
Other–

ETmissValue/description
signalb-jet
pT > 30 GeV|η| < 2.5
∆R(jet, e) > 0.2
MV1 with 60% eﬃciency working point

Table 2: Summary of the jet selection criteria.

3.3 Electron
Electron reconstruction [26] starts from clustering electromagnetic calorimeter cells and then the cluster
is matched to an inner detector track. As jets contain many tracks and calorimeter activities, raw electron
candidates contain many “fake” electrons from jets, which are rejected by requiring additional quality
selections such as Bremsstrahlung radiations in TRT and the absence of hadronic activity. Then we
define several sets of electrons which are used in the following analysis.
3.3.1 Cluster reconstruction
Electron reconstruction begins with forming a seed cluster. A method called sliding window algorithm [17] with a window size of 3 × 5 in η × φ middle layer cell units (0.025 × 0.025), finds a seedcluster with energy above 2.5 GeV.
4
Note that clusters between 2.5 < |η| < 4.9 are included in ETmiss calculation as Soft term, which will be mentioned in
Section 3.5.

32

3.3.2 Track-to-cluster matching
Reconstructed tracks are matched to seed clusters by extrapolating to the second layer of calorimeter.
The impact point are then compared to the corresponding seed cluster position. If several tracks match
to the same cluster, the tracks that have SCT hits are preferred and the one with the smallest ∆R to theseed cluster survives. After track-to-cluster matching, cluster energy is recomputed with 3 × 7 (5 × 5)
sliding window in the barrel (end-cap). Finally, four-momentum is computed using the track and cluster
information. Energy information is taken from the cluster and the direction is taken from the track when
there are more than 3 hits in TRT and silicon tracker, otherwise the cluster η and φ are used.
3.3.3 Further improvements
Reconstructed electrons are then checked if they pass a set of identification selections to obtain a maximum rejection of fake electrons. Three identification criteria are defined: Loose++, Medium++ andTight++, as listed in Table 3. All electrons are required to pass Medium++ condition in both Soft andHard lepton analyses.
Medium++ electron, for example, requires the absence of hadron activities at the tail of showers.
Also it checks whether Bremsstrahlung radiations occurred in TRT, which gives an useful information
to discriminate electrons from other heavier particles, such as pion. Tight++ selection further requires
a consistency between the track momentum and cluster energy, which reduces an accidental match of
tracks and clusters.
3.3.4 Hard electron definition
If one finds an electron nearby a jet, the electron is likely to be the decay product of a hadron in thejet. Such “fake leptons” should be rejected to reduce the QCD multi-jet background. Therefore, if anelectron is close to the overlap removal jet (defined in Section 3.2.7) within ∆R < 0.4, the electron isvetoed.
Then the following types of electrons are defined: ETmiss electron, preselected electron, crack electron,
loose electron and signal electron. ETmiss electrons are used in ETmiss calculation in Section 3.5. The
electrons with pT >10 GeV and |η| < 2.47 are taken into ETmiss calculation. Preselected electrons are usedfor vetoing the events with a second lepton. As will be discussed in Section 5, a second lepton increases
full-leptonic decay of tt¯ background and leads to a sensitivity loss. To veto such events, preselected
electrons are defined as loose as possible. Crack electrons are defined as the electrons falling into thecrack region of the calorimeter (1.37 < |η| < 1.52), where the barrel and endcap calorimeters intersect.
A large correction is needed for an electron to compensate the energy loss in the crack region, which
introduces a huge uncertainty on the reconstructed energy. As crack electrons worsen ETmiss resolution
and increases backgrounds in our signal region, we veto the events with at least one crack electron. Looseelectrons are defined to make a fake-enriched region to estimate the QCD multi-jet background (detailwill be discussed in Section 6.1). In the electron channel, the leading lepton should pass signal electron
selection. Signal electron selection is designed to reduce the QCD multi-jet background by requiring
Tight++ quality selection. In addition, the following track isolation is required:ptcone20/pT < 0.10,(47)

where ptcone20 is the sum of track momentum within ∆R < 0.2 from the electron track (the electron
track itself is not included). Fake electrons stemmed from jets may accompany many charged hadron
tracks, therefore, this condition greatly reduce fake electrons. To further reduce the fake electrons fromheavy flavor hadrons, the radial distance between the track and Primary Vertex d0PV is required to besmaller than 1 mm. Also the distance along the beam axis zPV
0 should be smaller than 2 mm, which
33

Type
Hadronic leakage
Middle layerof EM calorimeter

Strip layer of
EM calorimeter

Track-cluster matching
Track quality

Third layer of
EM calorimeter
Track quality
TRT

Track-cluster matching
TRT
Conversions

Description
Loose++
Ratio of ET in the first sampling of thehadronic calorimeter to ET of the EM cluster.
Ratio in η of cell energies in 3 × 7 versus 7 × 7 cells.
Ratio in φ of cell energies in 3 × 3 versus 3 × 7 cells.
Lateralof the shower.
√ width∑∑∑∑Lateral shower width, ( Ei η2i )/( Ei ) − (( Ei ηi )/( Ei ))2 ,where Wi is the energy and ηi is the pseudo-rapidity of cell i and the sum is
calculated within a window of 3 × 5 cells.
√∑∑
Shower width, ( Ei (i − imax )2 )/( Ei ), where i runs over all strips ina window of ∆η × ∆φ ∼ 0.0625 × 0.2, corresponding typically to 20 strips
in η, and imax is the index of the highest-energy strip.
The ratio of the diﬀerence between the largest and second largest energy
deposits in the cluster over the sum of these energies.
∆η between the cluster position in the strip layer and the extrapolated track.
The number of hits in the pixel detector.
The number of total hits in the pixel and SCT detectors.
Medium++ ( in addition to Loose++ conditions )Ratio of the energy in the third layer to the total energy.
The number of hits in Blayer (discriminates against photon conversions).
Transverse impact parameter.
Ratio of the number of high-threshold hits to the total number of hits
in the TRT.
Tight++ ( in addition to Medium++ conditions )∆φ between the cluster position in the middle layer and the extrapolated track.
Ratio of the cluster energy to the extrapolated track.
Total number of hits in the TRT.
Veto electron candidates matched to reconstructed photon conversions.
Table 3: Summary of the electron selection criteria.

34

Cut
Electron TypeAcceptancePreselected

Value/description
Crack
Loose

ETmisspT > 10 GeV|η| < 2.47
1.37 < |η| < 1.52
Medium++∆R(e, jet) > 0.4––––

QualityOverlap Removal
Isolation
Impact Parameter

SignalpT > 25 GeV|η| < 2.47
Tight++∆R(e, jet) > 0.4
ptcone20/pT < 0.10
d0PV ≤1 mm|zPV
0 | ≤2 mmTable 4: Summary of the hard electron selection criteria.
CutElectron TypeAcceptance

Value/description
Preselected
Crack
Loose
SignalpT > 7 GeV
10 GeV < pT < 25 GeV|η| < 2.47
1.37 < |η| < 1.52
|η| < 2.47
Medium++∆R(e, jet) > 0.4–∆R(e, jet) > 0.4–
ptcone30/pT < 0.16–
|d0PV /σ(d0PV )| ≤5–|zPV0 sin θ| < 0.4 mm
ETmiss

QualityOverlap Removal
Isolation
Impact Parameter

Table 5: Summary of the soft electron selection criteria.
ensures that the electron comes from a hard collision, not from pile-up. Table 4 gives the summary ofthese electron definitions.
3.3.5 Soft electron definition
In the soft lepton analysis, electrons from pT >10 GeV are used to define signal and loose electrons, while
the other electrons start from pT >7 GeV. In addition, the following items are modified for signal electron
to obtain better eﬃciency and background rejection.
• Medium++ criteria,• ptcone30/p`T < 0.16,• |zPV
0 sin θ| < 0.4 mm,• |d0PV sin θ/σ(d0PV )| < 5.
Here, z0 is the track distance from the primary vertex along the beam axis, and θ is the polar angle of the
track direction. σ(d0PV ) is the uncertainty of d0PV . ptcone30 is defined as the sum of track momentum in∆R < 0.3 from the electron. Table 5 summarizes soft electron definitions.
3.3.6 Performance
The overall electron eﬃciency consists of a reconstruction (Section 3.3.1-3.3.2) eﬃciency and an identification (Section 3.3.3) eﬃciency.
35

Efficiency

Reconstruction Efficiency

Figure 20 (left) shows the electron reconstruction eﬃciency as a function of transverse energy ET ,measured with tag-and-probe method [27] using 2012 dataset. The eﬃciency in 2012 is higher than 97%
for ET > 10 GeV and is well reproduced by Monte Carlo simulation within the uncertainty. The rightplot of Fig. 20 (right) shows the electron identification eﬃciencies as a function of ET . For Medium++and Tight++ lepton selections, a 2% level discrepancy is observed. Therefore, the eﬃciency is correctedin the analysis but the uncertainty associating with the correction is well below 2%, thus negligible.

1.05
1 η<2.47

ATLAS
Preliminary

1
0.95
0.9
0.85

0.95

0.8

0.9

0.75
Reconstruction and track quality efficiency

0.85

2011 data s=7 TeV
2011 MC

0.8

2012 data s=8 TeV∫ L dt = 4.7 fb

0.7

-1

∫ L dt = 20.7 fb

0.65

-1

0.6

2012 MC

0.75

20

30

40

50

60

70

80

|η| < 2.47
Loose
Loose, MC
Multilepton
2012
Multilepton, MC
ATLAS Preliminary Medium
Medium, MC-1
L dt = 20.3 fb
Tight
Tight, MCs = 8 TeV Z→ ee∫

10 20 30 40 50 60 70 80 90 100
ET [GeV]

Cluster ET [GeV]

Figure 20: (Left) Eﬃciency of electron reconstruction is shown as a function of transverse energy ET
for the electrons in the central part of the detector with |η| < 2.47 for data (filled markers) and MC (openmarkers) for 2011 (triangles) and 2012 (circles) datasets. The total (statistical and systematic) uncertainty
is displayed as the error bars. (Right) Identification eﬃciency of electrons from Z → ee decay for Loose,
Multi-lepton, Medium and Tight selections are shown as a function of ET for |η| < 2.47. These plots arecited from Ref. [27].

3.4 Muon
Muon tracks are reconstructed separately by two detectors: Muon Spectrometer and Inner Detector. The
information of these two tracks are then combined to improve quality using STACO [28] or Segmenttagged muon algorithms. Further improvements of purity is achieved by requiring good hits for trackers.
3.4.1 Standalone muons
The muons reconstructed by the outermost muon detector (called Muon Spectrometer or MS) are historically called standalone muon since Muon Spectrometer is designed to detect muons independently of theother parts of the detector. The standalone algorithm first builds track segments in each of the three muon
stations and then links the segments to form tracks. In STACO algorithm, an algorithm called Muonboy [29] is used to form spectrometer tracks from these segments. Segment-tagged muon algorithm uses
the raw segment information to identify muon tracks, combined with the inner tracker information.
3.4.2 Inner detector muons
Inner detector tracks reconstructed in Section 3.1 are used to define inner detector muons. These tracks
contain the tracks from pile-up, electron and fake tracks. Therefore Muon Spectrometer information
36

should be combined to select pure muon tracks.
3.4.3 STACO muonsMatch chi-square χ2match is defined as the diﬀerence between the standalone muon track and the innerdetector track vectors weighted by their combined covariance matrix:
χ2match = (TMS − TID )T (CMS + CID )−1 (TMS − TID ) .

(48)

Here T denotes a vector of track parameters and C is the covariance matrix. The subscript ID refers to
the inner detector and MS to the muon spectrometer. The pair having the best χ2match is chosen for the
combination. Then the combined muon track vector is given by
(
) (
)
−1 −1
−1
T = C−1
C−1
ID + CMSID TID + CMS TMS .

(49)

ID information dominates the measurement up to pT =80 GeV in the barrel and pT =20 GeV in the endcap. For higher pT ( <∼ 100 GeV), the ID and MS measurements have similar weight while the MS dominates in pT >
100
GeV.
∼
3.4.4 Segment-tagged muons
Segment-tagged muon reconstruction starts from Inner Detector tracks, extrapolates them to the inner
station of Muon Spectrometer, and tries to match them to the segments not yet associated to the muonsreconstructed by STACO algorithm. Segment-tagged muon algorithm provides an eﬃciency improvement for low pT muons.
3.4.5 Hard muon definition
Both STACO and Segment-tagged muons are combined to increase the reconstruction eﬃciency over awide pT range. To improve purity, the following hit qualities are required for the candidate muons.
• The number of hits in the pixel detector should be larger than 1. If, after the reconstruction, thepixel sensor which is passed by the track is found to be malfunctioning, the number of hits isincreased by the number of such malfunctioning sensors to increase eﬃciency.
• Similarly, the number of SCT hits are requested to be greater than 6. Again, the number of malfunctioning SCT sensors are added up to the number.
• If more than 3 holes are found in Pixel and SCT detectors along the extrapolated track, the track
quality is judged as bad.
• If the muon passes a working innermost pixel sensor, a hit should be recorded in that sensor.
• If |η| < 1.9, the number of TRT hits should be larger than 5 and the outlier tubes near the track
should not exceed more than 10% of the total TRT hits.
• If |η| ≥ 1.9 and the number of TRT hits is larger than 5, the outlier tubes near the track should notexceed more than 10% of the total TRT hits.
To reject fake muons from hadron decays, muons within ∆R < 0.4 from an overlap removal jet (definedin Section 3.2.7) is vetoed.

37

Then the following muons are defined: ETmiss muon, loose muon, preselected muon and signal muon.
The usages for these muons are the same as electrons in the previous section. The isolation condition of
signal muon is diﬀerent from that of electron, which is
ptcone20 < 1.8 GeV,(50)

where ptcone20 is the sum pT of all tracks within ∆R < 0.2. The definitions are summarized in Table 6.
3.4.6 Soft muon definition
Most of the definitions are the same as those of Hard Muon. Here we see only the diﬀerences. First,
pT thresholds are changed to 6 GeV for all muons. In addition, signal muon is requested to pass thefollowing isolation conditions• ptcone30 < 1.2 GeV,
• |zPV
0 sin θ| < 0.4 mm,• |d0PV /σ(d0PV )| ≤3.
zPV
0 is the track distance from the primary vertex along the beam axis and θ is the polar angle of the track.
d0PV is the radial distance between the track and the Primary Vertex. σ(d0PV ) is the uncertainty of d0PV .
Table 7 gives the summary of soft muon definition.
3.4.7 Performance
Figures 21 show the muon eﬃciency as a function of pT (left) and η (right). The muons reconstructedby both STACO and Segment-tagged algorithms are combined. The eﬃciency is larger than 98% for
pT > 20 GeV, and the discrepancy between data and Monte Carlo is well below 1%. The discrepancy iscorrected by introducing a correction factor, but the impact is negligible.
1

1

0.9

0.95

0.8
0.9

MC, CB+ST muons

30

40

50

60

70

80

30

40

50

60

70

80

0.5

90

100

90

100

Data/MC

Data/MC∫-12012 Data, Chain 1

0.6

Data, CB+ST muons

L dt = 20.7 fb

ATLAS Preliminary

pT > 20 GeV

2012 Data, Chain 1

0.85
0.8
1.0220
1
0.98
20

0.7

ATLAS Preliminary

0.1 < |η| < 2.5

-2.5
1.02
1
0.98
-2.5

Data, CB+ST muons∫

L dt = 20.7 fb-1

MC, CB+ST muons

-2

-1.5

-1 -0.5

0

0.5

1

1.5

2

2.5

-2

-1.5

-1 -0.5

0

0.5

1

1.5

2

2.5
η

pT [GeV]Figure 21: Reconstruction eﬃciency for STACO and Segment-tagged muons as a function of pT (left)
and |η| (right). The bottom panel shows the ratio between data and Monte Carlo. These plots are citedfrom Ref. [30].

38

Cut
Muon TypeAcceptanceOverlap Removal
Isolation

Value/description
Preselected
Loose
SignalpT > 10 GeV
pT > 25 GeV|η| < 2.4
∆R(µ, jet) > 0.4–
ptcone20 < 1.8 GeV
ETmissTable 6: Summary of the hard muon selection criteria.

Cut
Muon TypeAcceptanceOverlap Removal
Isolation
Impact Parameter

Preselected

Value/description
Loose
SignalpT > 6 GeV|η| < 2.4
∆R(µ, jet) > 0.4
ptcone30 < 1.2 GeV|zPV
0 sin θ| < 0.4 mm|d0PV /σ(d0PV )| ≤3

ETmiss–––Table 7: Summary of the soft muon selection criteria.

393.5 Missing transverse momentum
ETmiss is defined as the missing momentum in the transverse plane calculated from all objects reconstructed in the previous sections. Namely, ETmiss is calculated as follow,
Emiss
= −
T
−
−

∑

ElectronElectron pT∑

Muon
Muon pT∑

Jet
Jet pT∑
Soft−
Soft ET,(51)

where,
Electron : ETmiss electrons defined in Table 4 (Hard Lepton) or Table 5 (Soft Lepton) are included.
Muon : ETmiss muons defined in Table 6 (Hard Lepton) or Table 7 (Soft Lepton) are used.
Jet : ETmiss jets defined in Table 2 are included. Hadronic τ-jets are also classified to this term. The jets
jetwith pT <20 GeV are included in the soft term.
Soft : Soft term consists of the Topo-Clusters and tracks within |η| < 4.9 not associated to any physics
objects.
ETmiss (scalar) is defined as the norm of Emiss
T ,ETmiss = |Emiss
T |.

(52)

3.5.1 Performance
Figure 22 shows the ETmiss distribution in Z 0 → µµ events [31]. As Z 0 → µµ events do not have an
escaping neutrino in the final state, it provides a good environment to investigate ETmiss resolution, whichis the most diﬃcult quantity to be reproduced in Monte Carlo due to the detector response and thecontribution from pile-up. As can be seen from the plot, the agreement between data and Monte Carlo isquite well.
The pile-up dependence of the ETmiss resolution is shown in Fig. 23. The black filled (hollow) points
show the ETmiss resolution of data (Monte Carlo) as a function of the number of primary vertex per a bunch
crossing NPV . In high pile-up condition (NPV >∼ 15), the Monte Carlo has a slightly lower resolution by
1-2 GeV. However, since we require a large ETmiss (>150 GeV at least), the diﬀerence is small enough tobe neglected.

3.6 Kinematic variables
In the analysis phase, interesting events are selected by putting thresholds on several kinematic selections, which are designed to pick up typical characteristics of the supersymmetry events. Based on thereconstructed objects in the previous sections, the following kinematic variables are defined:p`T : Transverse momentum of the leading lepton is represented as p`T . In the electron (muon) channel,
the signal lepton defined in Table 4 (Table 6) (Hard Lepton) or Table 5 (Table 7) (Soft Lepton) is
used.

40

Events / 2 GeV

6

fb ATLAS Preliminary∫sLdt=20= 8 TeV

10

-1

5

10

Data 2012
MC Z → µµ
MC ttbar
MC WZ
MC ZZ
MC WW

104
3

10

102
10

Data / MC

1
1.60
1.4
1.2
1
0.8
0.6

50

100

150

200

250

0

50

100

150

200

250

Emiss
[GeV]
T

Resolution [GeV],EmissEmissxyFigure 22: ETmiss distribution after requiring two muons. The black points show 2012 data, the othercolored histograms show the various Standard Model processes. This plot is cited from Ref. [31].

30
25

ATLAS Preliminary
Data 2012 default
Data 2012 Pile-up suppression
MC default
MC Pile-up suppression

Z → µµs = 8 TeV

20

∫ Ldt=20 fb

-1

15
10
0

5

10

15

20

25
Npv

Figure 23: ETmiss resolution as a function of the number of primary vertex per a bunch crossing NPV , measured in Z 0 → µµ events. The black filled (hollow) circles show the data (Monte Carlo) with the default
pile-up correction. The red filled (hollow) squares show the ones with STVF pile-up corrections (notused in the analysis) [31].

41

jet

jet

pT : Transverse momentum of a jet is represented as pT . Jets are sorted by their transverse momentum
and indices are specified from the hardest jet, for example the transverse momentum of the leading
jet1
jet2
and the next leading jets are expressed as pT and pT . Signal jets defined in Table 2 are used.
X : The number of jets with transverse momentum larger than X GeV is denoted as N X . The signal
Njet
jet
jets defined in Table 2 are used.

mT : Transverse mass mT is defined as
mT =

√

(
)
2ETmiss p`T 1 − cos ∆φ(ETmiss , lep) ,(53)

where ∆φ(ETmiss , lep) is the opening angle of ETmiss and the lepton. mT has a clear cut-oﬀ for the
events with only one missing object. For example, mT ≤ mW holds for W+jets production and thecut-oﬀ is called Jacobian peak. No clear peak appears for the events with more than two missing
objects, such as a supersymmetry event with two LSPs, therefore mT is a good variable to suppress
W+jets and semi-leptonic tt¯ backgrounds.
meﬀ : Eﬀective mass meﬀ is defined asmeﬀ = p`T + ETmiss +

∑

jet

pT ,

(54)

jet
jet

where “jet” runs over all the signal jets with pT >30 GeV. meﬀ is the sum of transverse momentumof all objects reconstructed in the detector and represents the energy scale of a collision. Forsupersymmetric particles, meﬀ is known to be roughly proportional to the initial particle masses.

3.7 Event cleanings
The ATLAS detector is a complex of several sub-detectors, which then consist of multiple cells andelectronics. A good working eﬃciency was achieved during 2012 data taking period, however, there
exists some period in which one of the sub-detector was malfunctioning. The data in such period isremoved by selecting only good “LumiBlocks”, which is the smallest time chunk (∼ O(1) minute) indata recording. Also a set of flags are defined to find event-by-event electronics failures. The events
without any failure flag are used for the further analysis. In addition, the following items are checked toreject bad quality events:• To make sure that a hard collision occurs in the bunch crossing, a Primary Vertex with at least
5 tracks is required. If no such Primary Vertex is found in the event, the event is rejected.
• If a crack electron (defined in Table 4, 5) is found in the event, the event is vetoed as it has a bad
ETmiss quality.
• In addition to the detector problems, the cosmic muon makes unphysical ETmiss thus becomes abackground of supersymmetry search. To remove such events, we veto the cosmic muon events
based on the muon trajectory distance from the Primary Vertex. The cosmic muon is defined as
the preselected muons with one of the following conditions,– |zPV0 | > 1.0 mm,– d0PV > 0.2 mm.
• Finally, to veto the events with a possible fake ETmiss due to other detector problems, the following
fake ETmiss veto is applied:42

– If one of the jets passes the following criteria, then the event is judged as having a fake ETmiss
thus vetoed:jet∗ pT >40 GeV,
∗ Bcorr
jet > 0.05,∗ ∆φ(ETmiss , jet) < 0.3.
Bcorr
jet is a variable to estimate the possible energy loss due to a malfunctioning of the calorimeter cells in a jet. The estimation is based on the geometrical shape of jets and if a cell has
significantly small energy for the position in the jet, then the diﬀerence between the measured
and the expected cell energy is counted as missing energy. Bcorr
jet is the fraction of the total
missing energies with respect to the total jet energy.
– During 2012 data taking period, a specific region of Hadron Endcap calorimeter (-1.85<η<1.55, -0.7363<φ<0.) is turned oﬀ due to a malfunction of the electronic circuit. Since thedetector collects only a part of jet energies, jet reconstruction itself is not aﬀected by thisproblem, but reconstructed energies are inevitably underestimated, which makes large fakeETmiss . To remove such events, a fake ETmiss estimation algorithm has been invented. The
jetmethod loops over the jets with pT >20 GeV which are pointing the problematic region. Ifsuch a jet exists in the event, the size of fake missing momentum ETmiss (fake) is estimated by
the following set of equations,pcorr= pT ·
T

1 − Bcorrcell
1 − Bcorr
jet,ETmiss (fake) = pcorr
T − pT ,

(55)
(56)

where pT is the reconstructed transverse momentum of the jet, Bcorr
is the fraction of thecellenergy which is assigned to the bad calorimeter cells estimated from the average of theneighboring cells. The correction based on Bcorr
is applied to all jets in default, however,cell
it is designed to work well only for a small hole-like malfunction. Since the geometrical sizeof the LAr failure is too large to be corrected by Bcorr, the correction is replaced by the one
cell
based on Bcorr
,
which
can
be
adopted
to
a
large
size
of malfunction. pcorr
is the corrected
T
jet
miss
transverse momentum, and by subtracting the original jet pT , ET (fake) is estimated.
In principle, we can correct the fake ETmiss by adding ETmiss (fake) to the original ETmiss , but to beconservative, we rather veto the events. If ETmiss (fake) passes both of the following conditions,ETmiss (fake) is judged to have a non-negligible contribution, thus the event is vetoed.
ETmiss (fake) > 10 GeV,
ETmiss (fake)/ETmiss> 0.1.

(57)(58)

3.8 Triggers
Three diﬀerent triggers are employed to select hard electron, muon, and soft lepton events. Due tooverwhelming QCD multi-jet backgrounds, a trigger which directly tags a soft lepton cannot be used,
but alternatively we use a ETmiss trigger to select soft lepton events. Also for the hard lepton triggers,
not only a lepton trigger but also additional conditions are required so as to reduce the trigger rate. It is
important to check if the trigger eﬃciencies are suﬃcient enough for the kinematic selections requiredin the following analysis.

43Electron trigger : Electron trigger fires when an electron is found in an event. But it is suﬀered fromthe mis-firings from fake electrons and the trigger rate is overwhelmed by them. We require large
ETmiss at trigger level to reduce the background.
A trigger called EF e24vh medium1 EFxe35 tclcw tags the events which have• at least one medium++ quality electron with p`T >25 GeV,
• ETmiss larger than 80 GeV.
EF e24vh medium1 EFxe35 tclcw has a few % eﬃciency loss for large lepton pT . To compensate the eﬃciency loss, EF e60 medium1 is added in the trigger menu, which fires for the electronwith pT >60 GeV.
Figure 24 shows the electron trigger eﬃciency as a function of oﬄine ETmiss (corresponding toETmiss defined in Section 3.5). ETmiss used in the trigger decision is diﬀerent from the oﬄine ETmiss :the trigger ETmiss is based on a diﬀerent calibration scheme and muons are not added up whencalculating momentum balance. As a result, a slight topology dependence is expected. The difference between tt¯ (red) and W+jets (blue) gives the rough size of the topology dependence. To
select a similar topology as our Signal Regions, the following kinematic selections are applied:
jet3
jet1
mT >60 GeV, pT >80 GeV, pT >40 GeV and exactly 1 electron. The eﬃciency calculation is performed based on a method in which the events are selected by an orthogonal trigger and the trial
trigger is tested on those events to measure the eﬃciency.
Number of events passing both the trial and orthogonal triggers
Number of events passing the orthogonal trigger(59)
For the orthogonal trigger, an isolated electron trigger is used here.

Trigger eﬃciency (trial trigger) =Trigger Efficiency

The trigger eﬃciency becomes fully eﬃcient for ETmiss >80 GeV and the diﬀerence between data
and Monte Carlo (tt¯, W+jets) is below 1%, thus negligible.

1.2

1

0.8

0.6

Data
tt
W+jets

0.4

0.2

0
0

20

40

60

80

100

120

140

160

180

200
220
miss
ET [GeV]Figure 24: Trigger eﬃciency of EF e24vh medium1 EFxe35 tclcw as a function of ETmiss .

44

Muon trigger : Muon trigger fires when a muon is found in an event. The muon trigger is also suffered from fake muons from QCD multi-jet background. To reduce fake trigger rate, we use a
ETmiss +muon+jet trigger: EF mu24 j65 a4tchad EFxe40 tclcw, which selects the events with• at least one muon with pT >25 GeV,
• ETmiss larger than 120 GeV,
jet

• at least one jet with pT >80 GeV.

1.2

Trigger Efficiency

Trigger Efficiency

Figures 25 show the eﬃciency plots, which are measured in the same way as the Electron case with
an isolated muon trigger being used for the orthogonal trigger. The left plot shows ETmiss dependence and the right plot shows jet pT dependence. For the left plot, exactly 1 muon, mT >60 GeV,
jet3
jet1
pT >80 GeV and pT >40 GeV are required, while for the right plot, exactly 1 muon, mT >60 GeV
and ETmiss >150 GeV are required. The trigger is fully eﬃcient after requiring ETmiss >120 GeV andjet1
pT >100 GeV, where the diﬀerence between data and Monte Carlo is below 1%.

1

1.2

1

0.8

0.8

0.6

0.6

Data
tt
W+jets

0.4

0.2

0
0

20

40

60

80

100

120

140

160

180

Data
tt
W+jets

0.4

0.2

0

200
220
miss
ET [GeV]

20

40

60

80

100

120

140

160

180

200
jet1
p [GeV]T

Figure 25: Trigger eﬃciencies of EF mu24vh j65 a4tchad EFxe40 tclcw as functions of ETmiss (left)jetand pT (right).
ETmiss trigger : Lepton pT thresholds of the lepton triggers are too high to tag events in the soft lepton
analysis. Instead, triggers based on ETmiss are used. Two diﬀerent triggers are combined since thelowest un-prescaled triggers were changed during 2012 data taking period, which are summarizedin Table. 8. Since EF xe80T tclcw loose trigger does not use the first three bunches in a bunchtrain, the luminosity becomes slightly lower for the trigger. The loss is 10%, so a scaling factor of
0.9 is multiplied to the first 2.1 fb−1 of data, leading to an luminosity of 1.9 fb−1 . As a result, theintegrated luminosity for the soft lepton analysis becomes 20.1 fb−1 .
For both of the triggers, the eﬃciencies reach to a plateau after requiring the following condition,• ETmiss larger than 200 GeV.
Since no serious discrepancy is observed between data and Monte Carlo above this threshold andno significant topology dependence is found, no further corrections or the uncertainty is introduced
for this trigger.
Figure 26 shows the trigger eﬃciency curve of EF xe80 tclcw loose with the following condijet1
jet3
tions: exactly 1 electron, mT >60 GeV, pT >80 GeV and pT >40 GeV. An isolated electron trigger is used for the orthogonal trigger.
The triggers mentioned above are summarized in Table 9.
45

Trigger Efficiency

1.2

1

0.8

0.6

Data
tt
W+jets

0.4

0.2

0
0

50

100

150

200

250

300
miss
ET [GeV]Figure 26: Trigger eﬃciencies of EF xe80 tclcw loose as a function of ETmiss .

Trigger
EF xe80T tclcw loose
EF xe80 tclcw loose

delivered lumi.
2.1 fb−1
18.2 fb−1

rescaled lumi.
1.9 fb−1
18.2 fb−1

Table 8: The lowest un-prescaled triggers and their delivered and rescaled luminosities.

ChannelElectron

Trigger
EF e24vh medium1 EFxe35 tclcw
or EF e60 medium1

Luminosity
20.3 fb−1

Muon

EF mu24 j65 a4tchad EFxe40 tclcw

20.3 fb−1

Soft Lepton

EF xe80T tclcw looseor EF xe80 tclcw loose

20.1 fb−1

Comments
Fully eﬃcient with :Electron pT >25 GeV
ETmiss >80 GeV
Fully eﬃcient with :Muon pT >25 GeV
ETmiss >120 GeV
jet
at least 1jet with pT >80 GeV
Fully eﬃcient with :ETmiss >200 GeV.

Table 9: Summary of the triggers. The “Comments” show the minimum oﬄine selection needed in theanalysis.

46

4 Data and Monte Carlo simulation
4.1 Data samples

Total Integrated Luminosity fb-1

This thesis uses the data recorded by the ATLAS detector in proton-proton collision at the center-of√
mass energy of s = 8 TeV. These events were collected from April 5th to December 6th in 2012. The
data taken in the period yields a total integrated luminosity of 21.3 fb−1 . To assure a good data quality,
all detectors are required to be turned on and working without a fatal problem. The detector condition
is recorded for each LumiBlockand the LumiBlocks flagged as problematic are eliminated, leaving an∫
integrated luminosity of L dt = 20.3 ± 0.6 (2.8%) fb−1 . Figure 27 shows the LHC delivered, ALTAS
recorded, and good-for-physics integrated luminosities.
25
ATLAS Preliminarys = 8 TeV

20

LHC Delivered
ATLAS Recorded
Good for Physics

15

Total Delivered: 22.8 fb -1
Total Recorded: 21.3 fb -1
Good for Physics: 20.3 fb-1

10
5
0
1/4

1/6

1/8

1/10
1/12
Day in 2012

Figure 27: LHC delivered (green), ATLAS recorded (yellow), and good-for-physics (blue) luminosities.
The x-axis shows the date in 2012.

4.1.1 Luminosity measurement
The ATLAS detector has several algorithms and sub-detectors [32] to monitor the luminosity. They
mostly count the number of reference events µvis and calculate the luminosity using the cross-section of
the event σvis asµvis nb fr
L=
.
(60)
σvis
The unknown parameter σvis is calibrated beforehand by an absolute luminosity measurement, van derMeer (vdM) scan. vdM scan, or often referred to as beam separation scan, measures spacial protondensity profile of bunches by shifting the impact oﬀset between two colliding beams. Also the absolute
number of protons in a bunch is measured by monitoring the beam current at the same time. With theseinformation, the absolute luminosity is calculated asL=nb fr n1 n2,2πΣ x Σy(61)

where n1 , n2 are the number of protons contained in two colliding bunches and Σ x , Σy are the root-meansquare of transverse proton distribution.
By equating Eq. 60 and Eq. 61, σvis is obtained as,
σvis = µvis

2πΣ x Σy
.
n1 n2

47

(62)

Here we have only measurable values in the equation and hence σvis is determined.

4.2 The Standard Model samples
Monte Carlo samples are produced by Monte Carlo generators and then processed with detector simulations using GEANT4 [33]. Energy deposit of particles in the active detector material is converted into
detector outputs, emulating the real detector. The generated events are processed through trigger simulation and reconstructed with the same software as real data.
Monte Carlo generators produce events in two steps [34]: Matrix-Element and Parton-Shower calculations. The former step evaluates Feynman-diagram at the Leading-Order (LO) or at the Next-toLeading-Order (NLO) to determine the kinematics of the outgoing partons (quark and gluon). The strong
coupling constant αS used in Matrix-Element calculation strongly depends on the energy scale of thehard process, called “renormalization scale”. In Monte Carlo generators, the energy scale is determinedby an empirical formula depends on physics processes. The uncertainty of the arbitrariness is evaluatedand included in the systematic uncertainty.
Though Matrix-Element calculation is precise, it has a drawback of the processing time, especiallywhen the number of outgoing partons increases. In addition, the perturbation theory of QCD process
becomes a bad approximation in low energy scale near ΛQCD ∼ 1 GeV. Therefore Matrix-Element
calculation is used to evaluate only hard processes and the following evaluation is performed by PartonShower algorithm. Parton-Shower algorithm uses collinear approximation to evaluate the emission probability of additional partons. For example, the diﬀerential cross-section of a gluon emission from aquark dσ(q → q + g) is approximated asdσ(q → q + g) ∼ αS σ0dθ2dz P ji (z),
θ2

(63)

where σ0 is the cross-section without the gluino emission, θ is the opening angle of the emission. P ji (z)is i → j splitting function, which describes the distribution of the fraction z of energy of i carried by j.
In case of q → q + g, the splitting function is
Pqg (z) =]1[ 2z + (1 − z2 ) .
2(64)

The partons emitted from Matrix-Element and Parton-Shower algorithms have an inevitable overlap.
When two partons are overlapped, the parton from Matrix-Element is prioritized because Matrix-Element
calculation is more accurate. This procedure is called matching. Two diﬀerent methods are proposedto perform matching [35]: MLM and CKKW. MLM matching is based on geometrical separation ofpartons to remove the double count. On the other hand, CKKW matching decides the rejection based onkT -measure [36, 37].
The momentum distribution of incoming partons in proton is given by Parton Distribution Function (PDF). PDF measured in the other colliders with lower center-of-mass energy is evolved by DGLAP
equation [38, 39, 40] to the LHC energy. The energy scale at which PDF is evaluated is called “factorization scale”. Factorization scale is determined event by event using an empirical formula. The
arbitrariness is evaluated and taken into systematics (detail will be discussed in Section 7.2).
The outgoing partons are often oﬀ-shell5 , therefore they need to emit additional partons to back totheir physical (on-shell) states. The emission is called Final State Radiation (FSR). The same radiation
is emitted before the hard process, called Initial State Radiation (ISR). The entire process is kicked backby the sum momentum of ISR and FSR, therefore their contributions make a visible impact not only on
5

The degree of oﬀshellness is sometimes refereed to as “virtuality”.

48

jets but also on the momentum of objects such as supersymmetry particles and electroweak bosons. Most
part of ISR and FSR are simulated in Parton-Shower algorithm.
The cross-section of proton-proton collision (including both elastic and inelastic interactions) is
O(100) m barn at 8 TeV, so more than 1 proton pairs may interact in one bunch crossing, which are referred to as pile-up. Pile-up events are generated with PYTHIA8 [41] with AM2 tune [42] and the LO
PDF set MSTW2008LO [43, 44, 45]. The impact of pile-up is a small eﬃciency loss in lepton identification, energy shift in jets and resultant resolution deterioration in ETmiss . To treat all these eﬀects, thepile-up events are superimposed to the hard collision events before starting object reconstruction. The
average number of interactions per bunch crossing hµi in Monte Carlo are controlled so that it reproduces
the distribution of data.
4.2.1 Standard Model processes
The Standard Model processes are background candidates for supersymmetry searches. Especially, if aprocess accompanies a lepton, large ETmiss and high pT jets, it contaminates to our signal region. Two
major such backgrounds are W+jets and tt¯ productions. Event topologies for these processes will be
discussed in Section 5.1. The following processes also contribute to the background and are included in
the background estimation, however the impact is small compared with tt¯ and W+jets.
Single top : Decay of a top-quark accompanies a lepton, a neutrino and jets. However, since the production cross-section is small compared with tt¯ production, Single Top production does not become adominant background.
Dibosons : WW, WZ, ZZ productions are collectively-referred to as Diboson production and somefractions of them decay into leptonic final states. However, due to small cross-sections and soft
event topologies, the processes does not play an important role in background estimation.
tt¯+V : tt¯ production accompanied by an electroweak boson W, Z is denoted as tt¯+V. The cross-section
for these productions is O(10−3 ) times smaller than tt¯ production, therefore negligible.
Z+jets : Z → ll decay becomes a background if one of the leptons is not identified. However, theproduction cross-section of this process is about 10 times smaller than W+jets and also ETmiss is
so small because it doesn’t have a neutrino in the final state. Therefore, the contribution of thisprocess cannot be large.
Table 10 shows the Standard Model processes included in the analysis. Detail configurations ofMonte Carlo generation are discussed below.
W/Z+jets :W/Z+jets processes are generated with Sherpa [46] using NLO PDF sets CT10 [47]. MatrixElement calculates up to 4 partons and additional partons are emulated by Parton-Shower algorithm implemented in Sherpa. To obtain correct production fractions of c- and b-quarks, thesequarks are treated as massive particles in Matrix-Element calculation.
Reference cross-sections are calculated by DYNNLO [48, 49] implemented with LO MSTW2008
PDF sets [43, 44, 45]. In the cross-section calculation for Z+jets, mll > 60 GeV is applied toremove low mass Drell-Yan process. Inclusive cross-sections for W ± → l± ν and Z 0 → l± l∓ processes are 12.2 nb and 1.15 nb, respectively. Cross-section uncertainty of Z+jet is taken from thecomparison of generator level cross-section (LO) and NNLO calculation using DYNNLO, which
gives 12% diﬀerence. Similar uncertainty estimation is applied to W+jets and gives the same size.

49

tt¯ :
tt¯ process is generated at NLO by Powheg [50] generator with LO PDF sets CTEQ6L1 [51].
Parton-Shower emulation is performed by Pythia6.4 [52]. All the partons except for the objects
produced in hard process are collectively-referred to as underlying event. The latest underlyingevent tune called Perugia 2011C tune [53] is used for this production.
Cross-section for tt¯ production are evaluated at NNLO, which is 252.89+13.30
pb for top quark mass
−14.52of 172.5 GeV/c2 [54]. The error cited here is the quadrature sum of the scale dependence and PDF
uncertainties. Scale uncertainty is evaluated by varying renormalization and factorization scales
by a factor of 2 or 1/2 independently. For PDF uncertainty, PDF4LHC prescription [55] is applied.
Single Top :Single Top consists of three diﬀerent production processes. For all of these processes, CTEQ6L1 [51]
LO PDF set is used and Parton-Shower is simulated by Pythia6.4 [52] with Perugia tune 2011C [53].
The cross-section is calculated using NNLO PDF set MSTW2008 [43, 44, 45].
• t-channel
AcerMC [56] is used to generate events. Cross-section is calculated at NNLL level [57],which is 87.76+3.44−1.91 pb.
• s-channel
Powheg [50] is used to generate events. Cross-section is calculated at NNLL level [58], whichis 5.61 ± 0.22 pb.
• Wt-channel
Powheg [50] is used for event generations. Cross-section is calculated at NNLL level [59],which is 22.37 ± 1.52 pb. Wt-channel production has an overlap with tt¯ since they have thesame final states t + (W + b). The overlap is removed by Diagonal Removal (DR) method [60,61] and an uncertainty is introduced to punish the arbitrariness of this choice (the size of
uncertainty is evaluated in Section 7.2.3).
Dibosons :Diboson production is generated by Sherpa [46] with LO PDF sets CT10 [47]. Matrix-Element
calculates up to 3 partons. A lepton pT cut of p`T >5 GeV and an invariant mass cut of mll >0.1 GeV are applied.
NLO cross-section is calculated by MCFM [62], giving 5.88 pb (for WW → llνν), 10.33 pb (for
WZ → lllν) and 9.69 pb (for ZZ → llll). Uncertainties are taken from the diﬀerence between the
NLO and LO calculations, which gives about 50%. Other dibosons productions having hadronic
final states are also included, whose cross-section is 33.8 pb in total at LO.
tt¯+V :
tt¯+V production is generated by MadGraph [63] with Pythia for Parton-Shower emulation and
CTEQ6L1 [51] LO PDF sets. Up to 2 partons are calculated with Matrix-Element.
NLO cross section calculations have been performed for tt¯+W in Ref. [64] and for both tt¯+Wand tt¯+Z in Ref. [65]. PDF uncertainty and renormalization/factorization scale uncertainties arereported in the references, which are 8% and 21%, respectively. However, to be conservative, thediﬀerence between NLO and LO cross-section is referred as the uncertainty (30%). The crosssections are 0.232 pb (for tt¯+W) and 0.2057 pb (for tt¯+Z).

50

Process
W+jets (W ± → l± ν)Z+jets (Z ± → l± l∓ )tt¯Single Top (t-channel)
Single Top (s-channel)
Single Top (Wt-channel)
Dibosons (WW → llνν)Dibosons (WZ → lllν)Dibosons (ZZ → llll)
Dibosons (Others)
tt¯+W
tt¯+Z

Cross-section [pb] (the order of the perturbation)
12.2 × 103 ± 12% (NNLO)
1.15 × 103 ± 12% (NNLO)
252.89+13.30(NNLO)−14.52+3.44
87.76−1.91 (NNLL)
5.61 ± 0.22 (NNLL)
22.37 ± 1.52 (NNLL)
5.88 ± 50% (NLO)
10.33 ± 50% (NLO)
9.69 ± 50% (NLO)
33.8 ± 50% (LO)0.232 ± 30% (NLO)
0.206 ± 30% (NLO)

Generator
SherpaSherpaPowheg+Pythia
AcerMC+Pythia
Powheg+Pythia
Powheg+Pythia (DR)
SherpaSherpaSherpaSherpaMadGraph+Pythia
MadGraph+Pythia

Table 10: Summary of the Monte Carlo generators and the cross-sections.

4.3 Signal samples
4.3.1 Signal models
The supersymmetry models and their configurations in event generations are summarized in this section.
We consider the following models:• MSUGRA/CMSSM models• Simplified models
MSUGRA/CMSSM model is based on a physical scenario of gravity mediated SUSY breaking as discussed in Section 1.4.4, while Simplified model [66] is constructed without assuming any SUSY breaking
model but sets sparticle masses by hand to produce various mass hierarchy just in case the SUSY breaking is occurred in an unexpected scenario.
4.3.2 MSUGRA/CMSSM modelMSUGRA/CMSSM model is defined by 5 parameters (details are in Section 1.4.4):
m0 , m1/2 , tan β, A0 , sign(µ).

(65)

In sample production, m0 and m1/2 are scanned in the ranges of m0 =200-6000 GeV and m1/2 =4001000 GeV. The grid points are generated every 50 GeV in both m0 and m1/2 , with some additional points
for the low mass regions and no points for the regions where no sensitivity is expected. In order to becompatible with the discovery of Higgs with mh =126 GeV [67], A0 and tan β are adopted to A0 = −2m0
and tan β = 30 (see Section 1.4.5). The sign of µ is set to be positive. The generated points are displayedin Fig. 28. Top plot shows production cross-sections obtained with NLL-fast [68] and Prospino [69].
The relative uncertainty of the cross-section is shown in the bottom, which includes PDF, normalizationand factorization scales and strong coupling uncertainties (see Section 7.3.1 for detail). SUSY-HIT [70]interfaced to SOFTSUSY [71] and SDECAY [72] is used to calculate the sparticle mass spectra and decay tables, and to guarantee consistent electroweak symmetry breaking. For each point 40 k events are
generated with HERWIG++ generator [73] with UEEE3/CTEQ6L1 PDF sets [51]. Only the processes withcolored sparticle production are generated. Note that MSUGRA/CMSSM samples treat all the particle
51

masses and their decays correctly, therefore the decay chains may include, for example, the decays via
third generation squarks, second or third lightest neutralinos, and so on.
4.3.3 Simplified models
Simplified models starts from direct pair-production of gluinos or squarks. The gluino (squark) decays
into two (one) quarks and a chargino, and the chargino subsequently decays to a W boson and a neutralino LSP. Figures 29 show the decay diagram of gluino-gluino (left) and squark-squark (right) simplified models. The masses of gluino (squark), chargino and LSP are free parameters, however, we reduce
the parameters into two in order to visualize in two dimensional plane.
First way is to set chargino mass mχ̃±1 to the halfway of gluino mass mg̃ (or squark mass mq̃ ) and LSP
mass mχ̃0 :1
mg̃/q̃ + mχ̃01
mχ̃±1 =.
(66)
2
This grid is referred to as “Half-x” in the following. Gluino (or squark) mass and LSP mass are left as
free parameters.
The other way is to fix LSP mass and vary chargino mass. The LSP mass is set to 60 GeV, whichis slightly higher than the lowest model-independent limit obtained in DELPHI experiment[74], and thegluino (squark) and chargino masses are taken as free parameters. For better visualization and interpretation, the chargino mass is not used directly but the following x is defined insteadx=mχ̃±1 − mχ̃01

mg̃/q̃ − mχ̃0

.

(67)

1

This grid spanned by gluino (squark) mass and x is referred to as “Grid-x”. Table 11 summaries the signal
models.
In the case of squark production, only left-handed first- and second-generation squarks are considered. These simplified model grids are all generated using MadGraph [63] and Pythia6 [52], and the
NLO+NLL cross-sections are calculated using NLL-fast [68]. In total 60 k events are generated per
point for Half-x grids, 30 k per point for Grid-x. In the case of gluino-gluino Half-x grid, the number of
events generated per point increases up to 80 k near the diagonal, where mg̃ is close to mχ̃0 .
1

Signal ModelMSUGRA/CMSSM
Simplified Model g̃-g̃, Half-xq̃-q̃, Half-xg̃-g̃, Grid-xq̃-q̃, Grid-x

Comments
Minimum Supergravity model compatible with mh = 126 GeV.
Pair produced gluinos (squarks) decays into LSP
via a chargino. x is fixed at 1/2. mχ̃0 is a free parameter.
1Pair produced gluinos (squarks) decays into LSP
via a chargino. mχ̃0 is fixed at 60 GeV. x is a free parameter.
1

Table 11: Summary of the signal models.

52

1

900
800

10-1

Cross section [pb]m1/2 [GeV]

1000

700
600

10-2

500
400

10-3

300
200
1000

2000

3000

4000

5000

6000

10-4

1
1000
0.9
900

0.8

800

0.7

700

0.6

600

0.5

Rel. uncert. on the cross section

m1/2 [GeV]

m0 [GeV]

0.4

500

0.3
400
0.2
300

0.1

200
1000

2000

3000

4000

5000

6000

0

m0 [GeV]Figure 28: Cross-section (top) and its relative uncertainty (bottom) of MSUGRA/CMSSM model. tan β
is 30, A0 is −2m0 and sign(µ) is positive.

53

σNLO+NLL [pb]σNLO+NLL [pb]Figure 29: Representative diagrams of the Simplified models. On the left (right), the production of agluino (squark) pair followed by chargino decay is shown.

103
102
10

102

10

1

1
10-1
-1

10

10-2
10-2
-3

10

-3

10

10-4

200

400

600

800

1000

1200

10-4

1400
m~g [GeV]

200

400

600

800

1000

1200
m~q [GeV]

Figure 30: (Left) production cross sections are shown as a function of gluino masses for gluino pair
production in the context of Simplified Model. The associated uncertainties are also shown as the error
bars. (Right) the same plot for the squark pair-production.

54

5 Signal Region optimization
We optimize our Signal Regions so that a good signal and background separation is realized and theresultant sensitivity is maximized over a wide range of signals. First, we investigate event topologies
of both background and signals. Important variables to be optimized are introduced in this part. The
diﬃculty of the optimization is in the correlations between the variables. A complete optimization considering the correlation is performed as the next step, which will be discussed in Section 5.2 and also in
Appendix B.

5.1 Event topology
Event topologies are determined by two parts: production and decay. We overview event topologies ofsupersymmetry signals and our major backgrounds, tt¯ and W+jets, mainly in these two viewpoints. The
distributions of kinematic variables are then reviewed.
5.1.1 Signals
Examples of signal production diagrams are shown in Fig. 31. All sparticles should be produced inpairs due to the R-parity conservation. We focus on gluino and squark productions in this thesis. A
gluino decays into a quark and a squark if it is kinematically possible: g̃ → qq̃. A squark then decays
into a quark and an electroweak gaugino, q̃ → qχ̃. If the gluino decay g̃ → qq̃ is not allowed, thesesuccessive decays occur via a oﬀ-shell squark: g̃ → qq̃∗ → qqχ̃. In the Simplified model assumingg̃-g̃ production, the squark mass is set heavier than the gluino mass, therefore a gluino always decays
in three-body mode. The type of the electroweak gaugino χ̃ produced in the squark decay is determinedby the mass hierarchy of electroweak gauginos or the mixing of them. The lightest chargino χ̃±1 and thesecond lightest neutralino χ̃02 play the role in the decay chain in most cases. A chargino χ̃±1 then decays
into a W boson and a LSP: χ̃±1 → W ± + χ̃01 . Similarly, a second lightest neutralino decays into a Z bosonand a LSP: χ̃02 → Z 0 + χ̃01 . Simplified models literary simplify the decay chain and assumes only one-step
decay via a chargino: q̃ (g̃) → q(q) χ̃±1 → q(q) W ± χ̃01 . W bosons in the decay chain may emit leptons,
which we use to tag the events. Another possible lepton source is from a slepton decay, l˜± → l± + χ̃01 ,however, this doesn’t dominate in our parameter space and signal models. Figure 32 summarizes the
decays we discussed here.
The production process of the Simplified models is limited to only q̃-q̃ or g̃-g̃, while the initial particles of MSUGRA/CMSSM model are the mixture of q̃-q̃ g̃-g̃ and q̃-g̃. Fractions for these contributions
are plotted in Fig. 33. Gluino mass becomes lighter than squark mass in large m0 region, which explains
the dominance of g̃-g̃ production in that region. On the other hand, low m0 regime is dominated byq̃-q̃ or q̃-g̃ productions with roughly equal contributions. As discussed in Section 1.4.5, one of the stops
becomes much lighter than first or second generation squarks for the current configuration, thus the production or decay involving stops become dominant. The upshot is the increase in the number of jets,
which pushes up the entire sensitivity.
5.1.2 W+jets
W+jets events are produced by a pair-annihilation of a quark and its anti-quark: q + q̄ → W ± . The
anti-quark is provided from sea-quarks or from the splitting of gluon as shown in Fig. 34. Additional
jets may accompany as ISR. Since each vertex accompanies one αS , the production cross-section fails
constantly as the number of jets.
W boson immediately decays into two fermions. The fraction of leptonic decay W + → l+ ν is 11% foreach lepton flavor. Since only one invisible particle ν emits in the leptonic decay, the transverse mass mT

55

g

g
g

q̃

ū

g̃

g

q̃

q̃
g

g̃

g

q̃

q̃

u

Figure 31: Feynman diagrams which contribute to gluino and squark productions.

qg̃

W ± /Z 0q0χ̃±
1 /χ̃2q̃χ̃01

Figure 32: Schematic diagram of successive decays starting from a gluino. The squark may be virtual depending on the mass hierarchy. In the Simplified model assuming gluino pair-production, thesquark mass is set heavier than the gluino, therefore a gluino is always decay in three-body mode. In
MSUGRA/CMSSM model, another electroweak gaugino may appear in the decay chain, while in the
Simplified model all the decays are assumed to happen in one-step via a chargino. As the “maximum
mixing” configuration is applied for MSUGRA/CMSSM model, one of stops is much lighter than firstor second generation squarks. Therefore, the squark appears in the decay chain is most likely a stop.

has a clear cut-oﬀ, called Jacobian peak. After requiring mT > mW = 80.4 GeV, there remain only two
possibilities for W+jets to pass the selection: (1) W boson is highly oﬀ-shell, (2) ETmiss is mis-measured
due to its resolution. Signal regions are defined so that mT  mW , where the first type of background
dominates.
5.1.3 tt¯
tt¯ events are produced mainly from a gluon pair as shown in Fig. 35. Top decays via a W boson, t → b+W,
and a usual W boson decay follows both leptonically and hadronically. As a result, the final states areclassified into three modes: full-hadronic decay (tt¯ → bb̄ + qq̄qq̄ the branching fraction is 49%), semileptonic decay (tt¯ → bb̄ + qq̄lν : 41%), and full-leptonic decay (tt¯ → bb̄ + lνlν : 10%). A semi-leptonic
decay, tt¯ → bb̄ + qq̄lν , has one neutrino and one lepton in the final state, therefore the event topology
is similar to that of W+jets except for the number of jets. For example, mT selection of mT > mW
eﬀectively reduces this background. On the other hand, mT distributes without a clear cut-oﬀ for fullleptonic decay tt¯ → bb̄ + lνlν. Its decay topology resembles the decay of supersymmetric particles,
which has two missing LSPs. Full-leptonic decays can be reduced by vetoing events with more than two
leptons.
5.1.4 Kinematic variables for signal region optimization
A signal region is defined by a set of thresholds on kinematic variables. We look into these kinematic
variables to find appropriate thresholds, comparing the shapes of signals and backgrounds. In the course

56

900

0.8
800
0.7
700

0.6

600

1000

0.9

900

0.8
800
0.7
700

0.6

600

0.5
0.4

500

1

~~
Fraction of q-q production

0.9

m1/2 [GeV]

1~~
Fraction of g-g production

m1/2 [GeV]

1000

0.5
0.4

500

0.3

0.3

400

400
0.2

300

0.2
300

0.1

200

500

1000

1500

2000

2500

3000

3500
m0 [GeV]

0

200

0.1
500

1000

1500

2000

2500

3000

3500
m0 [GeV]0

Figure 33: (Left) Fraction of g̃-g̃ contribution compared with the total colored particle production. (right),
the same fraction of q̃-q̃ contribution. The fraction of q̃-g̃ production can be calculated by subtracting thefractions from 1.

u

W+

u
W+

u

d
g

g

d

d

Figure 34: Feynman diagrams which contribute to W+jet productions.

of the discussion, we classify the signal models into three groups and define corresponding signal regions.
p`T : Transverse momentum of lepton p`T varies significantly for on-shell and oﬀ-shell W bosons. Figure 36 shows p`T distributions for Half-x grid of the Simplified Model with mg̃ ∼600 GeV. ∆M isdefined as the mass diﬀerence between chargino and LSP, i.e. ∆M ≡ mχ̃±1 − mχ̃0 . The lepton pT
1
distributes broadly around 40 GeV when ∆M is larger than the mass of W boson and on-shell decay χ±1 → W ± + χ̃01 occurs. On the other hand, if ∆M is smaller than W boson mass, the decay
occurs through a three body decay via a oﬀ-shell W boson, χ±1 → W ±∗ + χ̃01 → l± ν + χ̃01 , and thelepton pT becomes soft as it is emitted via a three body decay.
We introduce a dedicated signal region which is optimized for such degenerate signals by selectinga soft lepton. An upper threshold on lepton pT (25 GeV) is introduced so as to be orthogonal to the

g

g
g

t̄

ū
g

t̄

t

t
g

t

g

t

u

Figure 35: Feynman diagrams which contribute to tt¯ productions.

57t̄Hard Lepton Signal Regions.
Leptons from QCD multi-jet events have a soft transverse momentum, therefore Soft lepton analysis suﬀers from QCD multi-jet contribution. In the course of optimization, a selection on thegeometrical separation between lepton and jets, min ∆R(lepton, jet) > 1.0, eﬀectively removes the
jet

A.U.

background (Fig. 37). We apply this selection in the Soft lepton analysis.

∆ M=25GeV

0.3∆ M=40GeV
0.25∆ M=120GeV

0.2∆ M=200GeV

0.15

0.1

0.05

0
0

10

20

30

40

50

60

70

80
90
100
Lepton p [GeV]T

Figure 36: Lepton pT distributions of several signal points taken from Half-x grid of the Simplified
Model with mg̃ ∼600 GeV. ∆M is the mass diﬀerence between chargino and LSP, i.e. ∆M ≡ mχ̃±1 − mχ̃0 .
1ETmiss > 200 GeV is applied.

Njet : The number of jets further divides the hard lepton signal region. Figure 38 (left) shows the numberof jet distribution of g̃-g̃ and q̃-q̃ signals on top of the background distributions. A clear diﬀerencein the number of jets between the signals is observed, which is because each gluino decay has one
additional quark than in a squark decay. We divide the hard lepton signal region into two, Tight
40 ≥ 5 and Loose SR with N 40 ≥ 3, focusing g̃-g̃ and q̃-q̃ productions, respectively.
SR with Njet
jet
We require the Soft Signal Region to cover not only the soft lepton topology, in which the massdiﬀerence between chargino and LSP is small, but also the case with small mass splitting between
gluino (squark) and LSP. In such a case, the number of jets passing a specific pT threshold becomes
small as shown in Fig. 38 (right). Therefore, the threshold of the number of jets are set to 3 for jetswith pT >30 GeV.
mT : Transverse mass mT is a good variable to suppress W+jets and semi-leptonic tt¯ backgrounds. Figure 39 show mT distributions for Hard (left) and Soft (right) lepton analyses. Number of jet selections and ETmiss selections are applied as mentioned in the caption. A clear Jacobian peak isobserved in both cases. mT distributions in the soft lepton plots suggest to put thresholds as low
as possible to keep reasonable signal yields, for example at 100 GeV. For the hard lepton case,the slopes of signals become similar as that of background at around mT ∼ 150 GeV, therefore athreshold is optimized here.
ETmiss : Missing transverse momentum distributions are shown in Fig 40. SUSY events have hard ETmiss
distributions, while the background distributions decrease constantly. Optimization should be performed by considering not only the signal to background ratio but rather the “sensitivity” that58∫ Ldt=20.3fb , s=8TeV

50000

-1

40000

tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

30000

20000

Ratio

10000

2
1
00

0.5

1

1.5

2
2.5
3
min ∆ R(lep,jet) [rad]Figure 37: min ∆R(Leading Lepton, Jet) distribution after requiring 1 soft lepton and at least one jet withJet

pT >20 GeV.

aﬀects to the final limits. We will optimize the thresholds in the next section with a more sophisticated method.
meﬀ : Eﬀective mass meﬀ is known to be sensitive to heavy particle productions since it is roughly
proportional to the masses of colored particles initially produced. Figure 41 shows the correlationof the initial particle masses and the means of their meﬀ distributions. Black points represent
signal points taken from Grid-x (mχ̃0 is fixed at 60 GeV), which show a clear linear correlation.
1
However, signal points of Half-x grids (varying mχ̃0 ), which are shown in red, distribute broader
1
and the correlation seems week. This feature suggests that meﬀ has a good correlation with theinitial particle mass for light LSP cases. meﬀ becomes smaller than the original particles masses
for heavy LSP case, because a significant fraction of the energy is consumed to create heavy LSPs.
Since it is diﬃcult to set an universal threshold on meﬀ , we use meﬀ as a final discriminating
variable and perform a fit on the shape. For reference, meﬀ distributions are shown in Fig. 42.

5.2 Signal Region Optimization
We introduced three signal regions, Tight, Loose and Soft, in the previous section. The thresholds on
lepton pT , the number of jets and mT are readily determined, however, ETmiss and meﬀ show no clear
structure at which the thresholds should be optimized.
The kinematic variables have strong correlations. For example, Njet have a positive correlation withmeﬀ because meﬀ includes pT sum of jets as its ingredients, thus the best optimized threshold of meﬀ
should change depending on the Njet selection. An ideal way of optimization is to try all possible combinations of selections and find the best set. We perform a complete scan over thresholds, which is
documented in Appendix B. The resultant Signal Regions are summarized in Table 12.
The expected exclusion regions are shown in Figs. 43 and 44. Tight, Loose and Soft SRs are combined and binning of meﬀ is taken into the calculation. Black lines show a mean expected limit andyellow bands show ±1σ uncertainties. The uncertainty includes both statistical errors and a systematic
uncertainty of 30%. Profile-Likelihood method is used in the calculation. For reference, a separate limit
obtained by each SR is superimposed in magenta (Tight SR), blue (Loose SR) and green (Soft SR) line.
59

108

∫Ldt=20.3fb , s=8TeV
-1

107

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

7

10

106
5

10
Events104
103∫Ldt=20.3fb , s=8TeV-1tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

106
105
104
103

Events

109

102

102

10

10
1

1
10-1

10-1

10-2

10-2
10-3
0

-3

10

0

2

4

6

8

10

12

14

16

18

20

N40
jet

2

4

6

8

10

12

14

16

18

20
N30
jet

Figure 38: Number of jets distributions after requiring: (left) 1 hard lepton, one jet with pT >80 GeV
and ETmiss >100 GeV; (right) soft 1 lepton and ETmiss >200 GeV. For signal samples, q̃-q̃ productions
with (mq̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and g̃-g̃ productions with1(mg̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line
1
shows a degenerate point with (mg̃ , mχ̃±1 , mχ̃0 ) =(650,625,600).
1

106

∫

106
-1

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

105
Events/5GeV

104
103
102

105

103
102
10
1

1

10-1

10-1

10-2
50

100

150

200

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

104

10

10-20

∫Ldt=20.3fb , s=8TeV-1

Ldt=20.3fb , s=8TeV

Events/5GeV

107

10-30

250
300
mT [GeV]

50

100

150

200

250
300
mT [GeV]Figure 39: mT distributions after requiring: (left) 1 hard lepton, ETmiss >150 GeV and threejets with pT >40 GeV, in which the leading jets should be harder than pT >80 GeV; (right) soft
1 lepton, ETmiss >200 GeV, and three jets with pT >30 GeV. For signal samples, q̃-q̃ productions with(mq̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and g̃-g̃ productions with1(mg̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line
1
shows a degenerate point with (mg̃ , mχ̃±1 , mχ̃0 ) =(650,625,600).
1

60

106

∫

106
-1

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

5

10

4

10
Events/25GeV∫Ldt=20.3fb , s=8TeV-1

Ldt=20.3fb , s=8TeV

103
102

105

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

104
103

Events/25GeV

107

102

10

10
1

1
10-1

10-1

10-2

10-2

-3
10100
200 300 400 500 600 700 800 900 1000
[GeV]
Emiss
T

-3
10200

300

400

500

600

700

800 900 1000
[GeV]
Emiss
T

Figure 40: ETmiss distributions after requiring: (left) 1 hard lepton and three jets with pT >40 GeV, in which
the leading jets should be harder than pT >80 GeV; (right) soft 1 lepton and three jets with pT >30 GeV. For
signal samples, q̃-q̃ productions with (mq̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark cyan) and (800,160,60) (light1cyan), and g̃-g̃ productions with (mg̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark magenta) and (800,160,60) (light1
magenta) are plotted. Blue line shows a degenerate point with (mg̃ , mχ̃±1 , mχ̃0 ) =(650,625,600).

meff mean [GeV]

1

2500

2000

1500

1000

500
200

400

600

800

1000

1200
1400
1600
Initial Particle Mass [GeV]

Figure 41: Signal points in the Simplified Models with g̃-g̃ and q̃-q̃ productions are shown. x-axis
represents mg̃ or mq̃ and y-axis shows the mean of the meﬀ distribution. Black points show Gridx (mχ̃0 =60 GeV) and red points show Half-x grid. See Section 4.3.3 for their definitions.
1

61

107

∫

107
-1

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

106
5

Events/200GeV

10

4

10

103

106

tt
W+jetsZ+jetsSingle Top
Dibosonstt+V~q-~q (800,560,60)~q-~q (800,160,60)~g-~g (800,560,60)~g-~g (800,160,60)~g-~g (650,625,600)

105
104
103
102

102
10

10

1

1

10-1

10-1

10-20

∫Ldt=20.3fb , s=8TeV-1

Ldt=20.3fb , s=8TeV

Events/200GeV

108

500

1000

1500

10-20

2000
2500
meff [GeV]

500

1000

1500

2000
2500
meff [GeV]

Figure 42: meﬀ distributions after requiring: (left) 1 hard lepton and three jets with 40 GeV, in which theleading jets should be harder than 80 GeV; (right) soft 1 lepton and three jets with pT >30 GeV. For signal
samples, q̃-q̃ productions with (mq̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark cyan) and (800,160,60) (light cyan),
1and g̃-g̃ productions with (mg̃ , mχ̃±1 , mχ̃0 ) =(800,560,60) (dark magenta) and (800,160,60) (light magenta)
1
are plotted. Blue line shows a degenerate point with (mg̃ , mχ̃±1 , mχ̃0 ) =(650,625,600).
1

Variable
Leading lepton pT

Loose SR
Preselections>25 GeV

Next leading lepton pT<10 GeV

Number of jets
Leading jet pT
mT
ETmissmincl30
eﬀ

Tight SR

Soft SR[10 GeV, 25 GeV] (Electron),[6 GeV, 25 GeV] (Muon)<7 GeV (Electron),<6 GeV (Muon)

Signal Region specific selections
40 ≥5
40 <5
Njet
3≤ Njet>120 GeV> 80 GeV>150 GeV>120 GeV>350 GeV>250 GeV
BinnedBinned[800,1200,1600, [450,700,950,
2000,2400]
1200,1450]
and >2400 GeV and >1450 GeV
Table 12: Optimized signal regions.

62

30 ≥3
Njet
>100 GeV>100 GeV>300 GeV
Binned[450,700,950,
1200,1450]
and >1450 GeV

These lines clearly show where they have good sensitivities. q̃-q̃ production grid in Fig. 43 shows thatTight and Loose Signal Regions have similar sensitivity, cooperatively increasing the combined sensitivity. In the diagonal region of g̃-g̃ grid in Fig. 44, Soft Signal Region mainly drives the limit. The
combined limits in the other regions are basically driven by the Tight Signal Region.

63∼0,m =60GeV
~
∼0χ
g-~
g → qqqqWW χ∼0∼0,m =60GeV
~
∼0χ
q-~
q → qqqqWW χ
∼0
1 1

1

Expected limit (± 1 σexp)

1

Obs. Limit (2011)
Tight SRAll limits at 95% C.L.

-1

Expected limit (± 1 σexp)
Obs. Limit (2011)
Tight SR1

χ1

∫ L dt = 20.3fb , s = 8TeV

1.2

q

-1

1.4

1

All limits at 95% C.L.

1

∫ L dt = 20.3fb , s = 8TeV

1.2

g

1.4

χ

1

χ

1

1

(m∼± - mχ∼0 ) / (m~ - mχ∼0 )χ

1(m∼± - mχ∼0 ) / (m~ - mχ∼0 )1 1

Loose SR

0.8

Loose SR

0.8

Soft SR

0.6

0.6

0.4

0.4

0.2

0.2

0

400

600

800

1000

1200

0

1400
m~g [GeV]Soft SR

400

600

800

1000

1200

1400
m~q [GeV]

Figure 43: The expected limits are shown for Simplified Models (Grid-x) of g̃-g̃ (left) and q̃-q̃ (right) pair
production. mχ̃0 is fixed at 60 GeV and x = (mχ̃±1 − mχ̃0 )/(mg̃/q̃ − mχ̃0 ) is taken as y-axes. The black line1
1
1
shows an expected limit and the yellow band corresponds to the uncertainty of the limit. The decomposed
limits obtained by three separate Signal Regions are also shown in magenta (Tight SR), blue (Loose SR)
and green (Soft SR) lines.

∼0, x=1/2~∼0χ
g-~
g → qqqqWW χ∼0, x=1/2~∼0χ
q-~
q → qqqqWW χ
1 1

Expected limit (± 1 σexp)

All limits at 95% C.L.

800

Obs. Limit (2011)m ∼χ 1700

Loose SR

600

Expected limit (± 1 σexp)

All limits at 95% C.L.
0

Tight SR~<mg

∫ L dt = 20.3fb , s = 8TeV
-1

900
800

Obs. Limit (2011)0m ∼χ 1

700

1000

1

∫ L dt = 20.3fb , s = 8TeV
-1900mχ∼0 [GeV]1mχ∼0 [GeV]

1 1

1000

Tight SR~<mq

Loose SR

600

Soft SR

Soft SR

500

500

400

400

300

300

200

200

100

100
400

600

800

1000

1200

1400
m~g [GeV]

400

600

800

1000

1200

1400
m~q [GeV]

Figure 44: The expected limits are shown for Simplified Models (Half-x) of g̃-g̃ (left) and q̃-q̃ (right) pair
production. x = (mχ̃±1 − mχ̃0 )/(mg̃/q̃ − mχ̃0 ) is fixed at 1/2 and mχ̃0 is taken as y-axes. The black line shows
1
1
1
an expected limit and the yellow band corresponds to the uncertainty of the limit. The decomposed limits
obtained by three separate Signal Regions are also shown in magenta (Tight SR), blue (Loose SR) andgreen (Soft SR) lines.

64

6 Background estimation
6.1 Multi-jet background
QCD multi-jet events are a notorious background in the LHC due to its large cross-section. A largepart of QCD multi-jet events do not accompany leptons, hence the lepton requirement greatly reduces
the background. However, a small fraction of QCD multi-jet events accompany a lepton due to thefollowing reasons:• π0 decays into two photons. A e+ e− pair is created when one of the photons hits the first layer ofpixel tracker (photon conversion).
• Some fraction of heavy flavor hadrons decay into final states with leptons. Since most of such
leptons are collinear to the jets, they are rejected by overlap removal (as discussed in Section 3.3.4).
The remaining leptons that are emitted far from jets contaminate our signal region.
• π± track is mis-identified as a fake electron if the track accidentally matches to a calorimeter cluster
produced by charge exchange π0 production followed by its decay, π0 → γγ.
Large cross-section of QCD multi-jets obviously exceeds our computing capacity for Monte Carlosimulation. Hence, we estimate QCD multi-jets background using data itself with a method called
Matrix-Method. Matrix-Method estimates the shape and yield of QCD multi-jets from the diﬀerence
between fake-enriched and fake-suppressed distributions. Details of Matrix-Method are documented inAppendix C. Missing transverse momentum of QCD multi-jet events mainly originates from ETmiss mismeasurement and typically quite small. Since we require at least ETmiss >150 GeV for all regions, the
QCD multi-jet component falls into one of the minor backgrounds.

6.2 W+jet and tt¯ backgrounds
W+jets is a sub-dominant background as it satisfies the baseline topology of our analysis: ETmiss , lepton and multiple jets. The cross-section of W+jets is also quite large compared with the other backgrounds (except for QCD multi-jets). tt¯ has rather smaller cross-section, but the decay topology resembles supersymmetric events, which makes tt¯ the most dominant background in many supersymmetry
searches. These two backgrounds contribute more than 75% of the backgrounds in the Signal Regions.
Thus a dedicated estimation is applied for these backgrounds.
6.2.1 Control Regions
Monte Carlo simulation is employed to estimate W+jets and tt¯ backgrounds. But Monte Carlo simulation
is not so accurate to calculate the processes with multi-jets. The number of jet distribution is not reproduced in most of the generators used in the ATLAS analyses. The discrepancy often amounts to O(10)%level, which is quite large compared with the other systematics. To reduce the uncertainty, W+jets andtt¯ Monte Carlos are normalized to data in a dedicated “Control Region” (CR), in which the same jet
selection is required as in the Signal Regions, and a normalization factor (or often called as scale factor)
absorbs the data-MC discrepancy. In addition, the Control Region is set closer to the Signal Region inETmiss -mT plane to avoid making a big extrapolation over ETmiss and mT . Table 13 shows the kinematic
selections of Control Regions corresponding to the Loose, Tight and Soft Signal Regions. The regions
are illustrated on ETmiss -mT plane in Fig. 45.
One important issue on defining Control Region is signal contamination. Assuming the existenceof supersymmetry signals, especially the ones with large cross-sections, the signal “contaminates” theControl Regions and the number of observed events is increased. Once signal contamination occurs, the65normalization factors of backgrounds are overestimated, which leads to a larger background estimationin the Signal Region, spoiling discovery sensitivity.
Figure 46 show the fraction of signal contamination in the Control Regions for Simplified models.
Plots on the left column show g̃-g̃ production of Half-x grid, in which a chargino mass is set to a halfway
of gluino and LSP masses, and the right plots show g̃-g̃ production of Grid-x with varying chargino
mass (see Table 11 for summary). The results for Tight, Loose and Soft Control Regions are placed from
top to bottom. W+jets and tt¯ Control Regions, also electron and muon channels are all combined. The
contour lines show contaminations of signals in the Control Regions, which are defined as
Signal Contamination =

NSig
,
NBkg

(68)

where NSig and NBkg are numbers of signal and backgrounds in the Control Region. The signal contamination around the expected sensitivity limits is estimated at about 20% in the worst case, Which issmall enough for our analysis. In limit calculation, the normalization factors and signal yields are all
fitted simultaneously, taking signal contamination into account. So the limit is always correct even witha heavy signal contamination. Only drawback is a loss of sensitivity.
Variable

Number of jets
Leading jet pT
mT
ETmissmincl30
eﬀ

Tight CR
Loose CR
Pre-selections
Same as the SRs
Specific selections
40 ≥5
40 <5
Njet
3≤ Njet>120 GeV>80 GeV
80-150 GeV
80-120 GeV
250-350 GeV 150-250 GeV>800 GeV>800 GeVSoft CR

30 ≥3
Njet>100 GeV
60-100 GeV
200-300 GeV>500 GeV

Table 13: Kinematic selections defining the Control Regions.

6.2.2 Validation Regions
W+jets and tt¯ samples are extrapolated to the Signal Regions along ETmiss and mT as illustrated in Fig. 45.
Two Validation Regions (VR) are defined to validate the extrapolation for each Signal Region. The
Validation Regions are defined with the same lepton selections, jet requirements and meﬀ selection as theControl Regions, but one of mT and ETmiss is set to the same as the Signal Region. Figure 45 illustrates the
Validation Regions on mT -ETmiss plane. The Validation Region with higher ETmiss selection is denoted as
VR (ETmiss ), while the one with higher mT selection is written as VR (mT ). Tables 14 and 15 summarize
the kinematic selections of the Validation Regions for mT and ETmiss , respectively.
Signal contamination is serious for the Validation Regions because they are set so close to the Signal
Regions. However, if no significant discrepancy is observed both in the Signal and Validation Regions,the correctness of background estimation and the absence of signal are simultaneously concluded.
6.2.3 tt¯ correction
Since supersymmetry searches look into extreme phase spaces such as many jets and large meﬀ , wheregeneral-purpose event generators are not fully tuned, we introduce corrections before using them for66

Variable

Number of jets
Leading jet pT
mT
ETmissmincl30
eﬀ

Tight VR (mT ) Loose VR (mT )Preselections
Same as the SRs
Specific selections
40 ≥5
40 <5
Njet
3≤ Njet>120 GeV>80 GeV>150 GeV>120 GeV
250-350 GeV
150-250 GeV>800 GeV>800 GeVSoft VR (mT )

30 ≥3
Njet
>100 GeV>100 GeV
200-300 GeV>500 GeV

Table 14: Kinematic selections defining the Validation Regions to check the extrapolation on mT .

Variable

Number of jets
Leading jet pT
mT
ETmissmincl30
eﬀ

Tight VR (ETmiss ) Loose VR (ETmiss )Preselections
Same as the SRs
Specific selections
40
40 <5
Njet ≥5
3≤ Njet>120 GeV>80 GeV
80-150 GeV
80-120 GeV>350 GeV>250 GeV>800 GeV>800 GeVSoft VR (ETmiss )

30 ≥3
Njet
>100 GeV
60-100 GeV>300 GeV>500 GeV

Table 15: Kinematic selections defining the Validation Regions to check the extrapolation on ETmiss .

67

300
250

meff>800GeV
3 ≤ Njet < 540

200

VR(mT)

mT [GeV]

Loose CR/VR/SR

SR

CR

VR(ET

150
100

miss

)

50
0
0

50

100

150

200

250

300

350

400

450 500
Emiss
[GeV]
T

300
250

meff>800GeV
Njet ≥ 5
40

200

VR(mT)

mT [GeV]

Tight CR/VR/SR

SR

CR

VR(ET

150
miss

100

)

50
0
0

50

100

150

200

250

300

350

400

450 500
Emiss
[GeV]
T

mT [GeV]

Soft CR/VR/SR
300
250

meff>500GeV
Njet ≥ 3

200

VR(mT)

30

SR

CR

VR(ET

150
100
miss

)

50
0
0

50

100

150

200

250

300

350

400

450 500
Emiss
[GeV]
T

Figure 45: Control, Validation and Signal Region are shown on ETmiss -mT plane. Tight, Loose and Softregions are placed from top to bottom.
68

1000
00

800

00
00
0

600
00
00

400

200

03

LSP mass [GeV]

400

1

0

1
1
2

00

0

600
00
00

400

00

0

200 0 0 0 7

00
0

00

0

15
6
54
16
15
32
7
10
10
101
4
37
4
32
8
133
45
7
22
14
7
59
0

400

0

0

00

00

0

600
00
13

400

200

09

0

2
7

0
014
3
22
00
20
0
1
0
37
25
00
0
0
52
35
115
0
5
136
103
91
15
0
2
0
2
0
10
0
7
14
24
564
186
5
79
0
4
0

400

0
1

0

0
0

0
0

0

800

0

x

80

0.8

0
0
0

0
0
0

0
0
0

0
0
0

0
0
0
0

0
0
0
0

0
0
0
0

0

0
0

0
0

0
0

0
0

14
1

0

400

2
1

1
1
0

600

0
0
0

17
9

76

0
10

2
3
2
1

1
2
0
1

0
0
0
0
0

2

0
0
0
0
0

0
0

0.7

359

0

60

0.6

0

50

0.5

40

0.4

0

30

0.3 0

0

0
0
0

0
0
0

0
0
0

0
0
0

0
0
0

20

0.2 0

10

0.10

0

1200
1400
Gluino mass [GeV]

200

0
0
0
0

0
0
0
0

0
0

0
0

0
0

2

23

400

10
6

5
3

600

1
1
1

0
1
1
1

800

0

100
90
80
70
60

0
0
0

50

0

0

0

0
0
0

0
0
0

[%]

0

0

40

0
0
0

0

1000

0

0

0

0

0

0

0

0
0

0

0
0
0

0
0

0

0

0

0

0
0

0

4

0

0

0

8
3

0

0

2

26

0

0

7

30

23

0

0
0
0
0

0
0

0

10

1200
1400
Gluino mass [GeV]

0
1

19

20

0

0

0

0

30

0

0
0
0

0

2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

24

0
0

0

1
55

40

0

0
0
0
0

0

50

0

0

0

0
4

60
0

0

0

11

70

0

0
0

80

0

0
0
0
0

0

3

90

0

0

0

1000

0
0
0
0

100

0

0

0
0
0

[%]

0

0

0

800

0

0

0

0

0

0

0
0

0

0
0
0

0

0

0

0

10

0

0

0

0

20

0

0

0

4

0

0

0

2

6
2

0

0

0

10

6

42

0

1000

0

1200
1400
Gluino mass [GeV]

0

1

48
0

0

0

0

0

0
0
0

5

0

0

0

0

0

0

30

0

0
0
0
0

0

10

25

0
0

0

1
1

0
0

0

2

0

0

1

0

0

6
0

0

0
1

2

0.9

0

0

0
1

0

0

0

0

0
0
0
0

0

34

0
0

0

1

0

1

0
0
0

0

0
1

0

600

0

0
0

3

1
1
0

0

1
0

0

0

0

16

453

0

0

0

2

3
2
1

0

23

21

90

70

0

0
0

4

0

3

200

100

0

0

0

0

2

0

0

0

1
51

0.10

0

0

1

1000

0
0
0
0

40

0
0

0
5

423

0

0

0

0.2 37

0

0

2

20

100

0

0

0

1

2

0.3 75

0
0

0

46

0

0

0

1

4

0
0

0

30

1

0

0
0

0

7
5
2

50

0

1

9

60
0

0

[%]
0

0

0

0

0

0.4

0
0

0

0

40

0
0
0
1

6

5

0

0

0

0

0.5

0

1200
1400
Gluino mass [GeV]

0

00

50

0

1000

1000

00

0.6

47

0

800

800

60

1
1
1
1

17

0

00

0.7

10

0

0

14
11
5

70

0
0

0

2

20

80

0

0

0

1

800

2

45

0
0

1

600

0

0
0

1
3

70

16

0

0

0

1

0.8

10
8

3
2
3
3

35

0

0
0

1

80

11
11

8
0

0

0
0

2

0.9

0

0

0
1

5

90

0
0

0

1
3

8
26

11

0
0

0
0

4

1

7

7

0
0

0

1

600

0
0

0

0

0

1
3

400

23
11

2
0

0

0
0

0

1

20

32

90

0

0

0

2

100

0
0

1

3

47
19

0

0

7

60
65
33

0

[%]

0
0

6

41

0

0

2

37

116

0
0

0
0

75

0

1

5

30

69

43

0

0

88

50

0

0

0
0

11

2

0
0

1

1

150

126

45
165

0
0

0

0

0
0

18

242

0

0

0
0
0
0

0
0

0

13

0

0

0

0

100

0

0

0
0
0
0

0
0

4

162

200

0

0

0

0

0.10

0
0
0
0

0
0

[%]
0

0

0

0

0.2 2

0

0

0
0

20

0
0
0

0

1

79

32

0

0

0

0

0.3 478

0

1200
1400
Gluino mass [GeV]

00

00

30

0
0
0
0

0

179

121

1000

0

2

0
0
0
0

8

187

1

0

00

0.4

0

5

800

800

40

10

0
1

00

0.5

1

3

4

1

23
373

1

2

7

3

0
0
0
0

2

296

1

4

1
1

168

136
0

1

7

0

13

74

98

50

0

1
3

1122

0
0

1000

LSP mass [GeV]

0
1

3

8
24

370

0
0

0

1
5

600

0

0

2

7

0.6

2
1
3
3

58

1
2

8
12

60

414

83
110

5
6
9
10

504

0

5

20
9
28
00
27
16
7
0 27 11
80
0
38
18
117
31
96
00
162
82
17
33
56
407
0
126
123
11
424
34
147
322
172
368
65
9
30
170
197
368
134
165
26
125
249
158
0
470
113
247
68
16
272
178
137

0.7

0
0

1

3

13
6

0
1

5

70

448

16
15
31
36

35
0

1

7

0.8

0

2

9

80

42
51

0

1

1

0.9
1266

0

0
0

1

90
0

0

3

3

0
0

0

0

0

337
0

0

0

2
0

100

x

00

[%]
0
0

0

x

LSP mass [GeV]

00
0

0

0
0
0
0

0

0

0

0

0
0

0

0

0

0

0

0

0
0
0

0
0
0

0
0
0

0
0
0

1200
1400
Gluino mass [GeV]

30
20
10
0

Figure 46: Signal contamination are shown for several signal models. Plots on the left column show g̃-g̃
production of Half-x grid and the right plots show g̃-g̃ production of Grid-x (see Table 11 for summary).
The results for Tight, Loose and Soft Control Regions are placed from top to bottom. W+jets and tt¯Control Regions, also electron and muon channels are all combined. The z-axes show the contaminationof signals in the Control Regions.

69

background estimation. One is the normalization as discussed in Section 6.2.1, which reduces the uncertainty on the number of jets by requiring the same jet selections between the Control and Signal Regions.
This method is called as semi data-driven method since it reduces the dependence on Monte Carlo by
using data. The extrapolation from a Control Region to Signal Region relies on Monte Carlo shape,
which is not completely correct for extreme phase spaces. Therefore, we correct the shape using data
after enhancing background components. We start from the primary background in our Signal Regions,i.e. tt¯.

∫ Ldt=20.3fb , s=8TeV-1

102
Events/100GeV

103
Events/100GeV∫ Ldt=20.3fb , s=8TeV

Data(2013)tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

-1

104

102
10
1

Data(2013)tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

10

1

10-1

10-2

10-2

2

2

Ratio

Ratio

10-1

1
00

500

1000

1500

2000
2500
[GeV]
mincl30
eff

104

1
00

∫ Ldt=20.3fb , s=8TeV-1

Events/100GeV

103
102

500

1000

1500

2000
2500
[GeV]
mincl30eff

Data(2013)tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

10
1
10-1

Ratio

10-2

2
1
00

500

1000

1500

2000
2500
[GeV]
mincl30
eff

Figure 47: Data-MC comparison for meﬀ . The right, left and bottom plots show Tight, Loose and Softregions, respectively. In order to show the events in a wide phase space, upper limits for mT and ETmissjet
are eliminated. To enhance tt¯ events, at least one b-tagged jet with pT >40 GeV is required in the leading
three jets.

Figures 47 show the meﬀ distributions after applying Loose (left), Tight (right) and Soft (bottom) Control Region selections. In order to show a wide phase space, upper limits for mT and ETmiss are eliminated.
At least one b-tagged jet is required in the leading three jets with pT >40 GeV to enhance tt¯ events. Enhancements of number of events in simulated data for large meﬀ are observed, which is also clearly70visible in the ratio plot in the bottom panels. The discrepancy is purely a background issue because thenumber of possible signal events is much smaller than the discrepancy observed here. Also note that tt¯is dominant over the other backgrounds, which ensures tt¯ is responsible for the slopes. ETmiss and mT are
also examined, but they seem quite fine without any significant deviations. The extrapolation from theControl Regions to Signal or Validation Regions basically goes along ETmiss and mT , therefore the final
results are not aﬀected much by the meﬀ slope in principle. However, the kinematic selections introduce
implicit biases on the population of events in meﬀ , which indirectly spoils the extrapolation from Control
to Signal Regions.
Several items are checked before applying corrections, so as to confirm that the slopes are not caused
by instrumental problems but come from the generator:• Pile-up jets contribute to meﬀ and its uncertainty may impact the slope. This is checked by comparing meﬀ with several pile-up suppression options for jets. No big diﬀerence is found.
• JES uncertainty (see Section 3.2.4) causes a shift on jet energies. But JES uncertainty is found to
be too small to cover such a big discrepancy.
• Since at least one b-tagged jet is required in the plots, b-tagging eﬃciency and its uncertainty havean impact on the meﬀ shape. To make sure that b-tagging is not the cause of the slope, b-tagging isremoved and mT >150 GeV is applied to ensure the dominance of tt¯ events. The meﬀ slope persists
even with this selection criteria, which implies that b-tagging is nothing to do with the slope.
These items ensure that the problem is in the event generator, not in the instrumental side. Considering
the fact that the significant slope is observed only in meﬀ , not in ETmiss and mT , the kinematics of tt¯ systemseems well reproduced in the generator, but rather additional jets may have a problem. Figure 48 gives a
confirmation of this hypothesis. HTISR defined below is plotted after requiring two b-tagged jets (b-jet1,
b-jet2),i∑b−jet1b−jet2HTISR =
piT − (pT
+ pT
).
(69)
jets,pT >40 GeV

For tt¯ events, this variable gives the pT sum of ISR, excluding the contribution from tt¯ decay. In addition
to two b-jets requirement, the following kinematic selections are applied to enrich leptonic decay samplesof tt¯ events: ETmiss >40 GeV, two diﬀerent flavor leptons and the invariant mass of the leptons should
exceeds 100 GeV. The Monte Carlo clearly shows a slope-like discrepancy from data, which leads us toconclude that ISR are poorly reproduced by the generator.
tt¯ events are generated at Next-to-Leading order Matrix-Element calculation for the core process andthe additional jets (ISR) are emulated by Parton-Shower algorithm. As discussed in Section 4.2, PartonShower algorithm is based on the collinear approximation, therefore has a larger uncertainty. The size ofthe impact caused by this uncertainty is illustrated in Fig. 49. The following items are modified within
the uncertainties provided from the ATLAS generator group [75, 42] to produce the systematic samples
compared here.
• Parton-Shower algorithm stops ISR radiation when the incoming quark or gluon obtain a large virtuality and then passes the parton to Matrix-Element calculation. The maximum virtuality threshold is varied within the uncertainty.
• ΛQCD for radiations from ISR parton is varied within its uncertainty.
• Renormalization scale (see Section 4.2) is varied.

71∫ Ldt=20.3fb , s=8TeV

Data

-1

105

tt
W+jetsZ+jetsSingle Top

4

10
Events/50GeV

103

Dibosons
tt+V

102
10
1
10-1
10-2
10-3

Ratio

10-4
10-5
2

1
00

200

400

600

800

1000
1200
HISR
T [GeV]

Figure 48: HTISR after requiring two diﬀerent flavor leptons, ETmiss >40 GeV, di-lepton invariant mass mll >100 GeV and two b-tagged jets.

A O(10)% level discrepancy is observed in HTISR , which could explain the discrepancy observed in meﬀ .
We define a simple 1-dimensional shape correction as a function of meﬀ . We can ensure to remove
the meﬀ slope by this correction, however, for ETmiss and mT , which are used in the extrapolation from theControl Regions to the Signal Regions, are not considered in the correction. Therefore, a systematic error
should be included to cover a possible discrepancy introduced by the correction, which will be discussed
later.
A first order polynomial function with an upper threshold is defined as follow,{
p0 + p1 · meﬀ(meﬀ < Ethres )f (meﬀ ) =(70)
p0 + p1 · Ethres (meﬀ ≥ Ethres ),where p0 and p1 are the parameters which will be determined in the fitting. Ethres is the threshold beyond
which the fitting function is fixed as a constant. This is required because there are no enough events inlarge meﬀ region thus the fitting does not make sense any more. We do not make a guess for such region,
but use the final value we’re sure. Based on available statistics, Ethres is defined for each region. Then, afitting is performed on meﬀ to determine the parameters. The same kinematics as the Control Region isrequired without mT and ETmiss upper thresholds, but the events passing the Signal Region selections are
all vetoed to be blinded to signal events.
Figure 50 shows the fitted results of meﬀ for the Loose Region. Fitted distribution of ETmiss is also
shown on the right. The black points show data and the gray line shows the other backgrounds except
for tt¯. The blue line shows the total backgrounds including the original tt¯ without any correction and the
red line shows the ones with the slope correction. The bottom panel shows the ratios with respect to the
red line. For reference, a first order polynomial fit for the remaining slope in the corrected backgrounds
is shown as a green line. The original slope is clearly eliminated by the correction in all meﬀ range.
The ETmiss plot does not show significant change on the slope, but shows a small improvement in theagreement between data and Monte Carlo. In the same way, the meﬀ slope is corrected in the Tight andSoft regions.

72

1

10-1

10-2

Ratio

10-3

1.5
1
0.5 0

100

200

300

400

500
600
HISR
T [GeV]

Figure 49: HTISR distributions of two diﬀerent parton shower tunes. The Red (blue) line represents theconfiguration for less (more) parton shower emission. HTISR is defined in Eq. 69. No kinematic selection
is applied. The variations are symmetrized.

1

10

1

3

10

Slope = -5.44e-05 ± 7.68e-05( Original = -2.45e-04 ± 5.77e-05 )3

Slope = 3.00e-05 ± 4.65e-04( Original = -5.60e-04 ± 3.62e-04 )χ2/NDF=0.9

Events/10GeV

Events/100GeV

χ2/NDF=1.4

102

102

10

10

1.5

Ratio

Ratio

1

1
0.5 0

500

1000

1500

2000

1.5
1
0.5 0

2500
meff [GeV]

50

100

150

200

250

300

350

400

450
500
Emiss
[GeV]
T

Figure 50: Fit results are shown for the Loose Region, meﬀ is on the left and ETmiss is on the right.
The black points show data, the gray line shows the other backgrounds except for tt¯. The blue line
shows the backgrounds with the original tt¯ without any correction, and the red line shows the ones
with the slope correction. The bottom panel shows the ratios with respect to the red lines, i.e. thecorrected backgrounds. For reference, a first order polynomial fit for the remaining slope in the correctedbackgrounds is shown as a green line.

Table 16 shows the fitted parameters obtained in Loose, Tight and Soft Regions. For Tight Region,a loosened kinematic selections are used to increase the statistics, keeping the same number of jets: thejet5thresholds for pT , mT and ETmiss are lowered to 30 GeV, 60 GeV and 200 GeV, respectively. p1 values
are all around ∼ -40 %/TeV, which implies that the slope correction does not depend on the jet topologies
strongly in our target phase-spaces. The slight topology dependency is explained by a diﬀerence in ISR
contributions due to diﬀerent jet selections. p0 is chosen so that the correction function f (meﬀ ) gives 1 at
meﬀ = 500 GeV.

73

Region
Tight
Loose
Soft

Ethres [TeV]
1.5
1.2
1.2

p1 [%/TeV]-24 ± 13-42.6 ± 7.5-56.4 ± 9.8

Table 16: Fit results for meﬀ corrections for tt¯. Ethres is the end-point of the slope correction and p1 is theslope-correcting parameter.
As this meﬀ correction is not an ideal way of correction but rather an ad-hoc solution, there exists
a possibility of some variable being strained in a wrong way, which should be included as a systematic
error. As shown later in Section 6.2.6, the kinematic distributions of ETmiss and mT in the Validation Regions do not show such strains, or rather the correction seems to fix the small slopes found in the original
distributions (This is also visible in ETmiss distribution in Fig. 50 on the right.). So, at least concerning
the extrapolation from Control to Validation Regions, there is no need to introduce a punishment forthe strain. However, a possibility of having a strain in the extrapolation to the Signal Regions cannot
be excluded as data and Monte Carlo comparison in the Signal Region is not possible due to signal
contamination.
To assign an uncertainty in the Signal Regions, first we evaluate the kinematic selection dependency
jetof p1 by varying Ethres , ETmiss , mT , Njet and pT . The largest variation originates in Njet selection and theother contributions are found to be small. The Control and Signal Regions basically share common jet
selections, but the number of jets distributions may diﬀer by the other kinematic biases. The diﬀerence isfound to be well smaller than 2 jets in all regions, therefore we take the variations of p1 values obtainedin Tight and Loose regions and assign an uncertainty of 50%.
Table 17 summarizes the impacts of the correction on the transfer factor along ETmiss and mT . They are
estimated by calculating the ratio of the transfer factors with and without the correction. As the numerator
and denominator have the same events in common, no statistical error is assigned. In average, the impact
on mT transfer factors seem much smaller than those of ETmiss . The largest variation is 27% for the ETmiss
transfer factor of Soft region, which is mainly because the meﬀ selection of Soft Regions is wider thanthe other regions. As we assume a 50% error for slope correction, an uncertainty of 14% (= 27% × 50%)
is assigned for the transfer factor. The uncertainties for the other corrections are also applied in the sameway.
Region
Tight
Loose
Soft

mT
+0.2%
+0.2%
-6.6%

ImpactETmiss-7.8%-5.0%-20.7%

Total
-7.6%
-4.8%
-27.3%

Table 17: Impacts of slope corrections. The impact is defined as the size of change in the transfer factor
from the Control to Validation Regions with and without the slope correction.

746.2.4 W+jets correction∫ Ldt=20.3fb , s=8TeV-1

108

Data(2013)tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

-1

10

106
105

Data(2013)tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V

104
103
102
10
1

1
00

∫ Ldt=20.3fb , s=8TeV

7Events/250GeV

108
107
106
105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
2

Ratio

Ratio

Events/25GeV

W+jets events are generated at Leading-Order in Matrix-Element evaluation. Compared with Next-toLeading-Order calculation, Leading-Order calculation has a large dependency on renormalization scale.
A mis-modeling in αS would lead to a wrong estimation of jet activity. Since W boson is kicked backagainst the sum of jets momentum, the momentum of W boson might also be wrongly predicted. As aresult, the decay products of W boson, a lepton and a neutrino, also have wrong momentum. A problem
arises here because the transfer factor from Control Regions to Signal Regions are mainly determined by
the extrapolation on ETmiss , the momentum of the neutrino.
Figures 51 show ETmiss (left) and meﬀ (right) distributions in a W+jets enriched region, where 1 lepton,
jet1
ETmiss >100 GeV and pT >80 GeV are required. If the event has a b-tagged jet, then the event is vetoed
to reduce tt¯ contribution. A clear discrepancy is observed in the ratio plots in both of the distributions.
The slope is also observed with diﬀerent kinematic selections. To cure the slope, we introduce a slope
correction function for W+jets in a similar way as the tt¯ correction.

10-1
2

1
00

100 200 300 400 500 600 700 800 900 1000
Emiss
[GeV]
T

500

1000

1500

2000
2500
meff [GeV]

Figure 51:
ETmiss (left) and meﬀ (right) distributions after requiring 1 lepton, ETmiss >100 GeV andjet1
pT >80 GeV. The event with a b-tagged jet is vetoed to reduce tt¯ contribution.
Before introducing a correction, one need to confirm that the slope is caused by a mis-modeling of
the generator, not by instrumental problems nor mis-calibrations. Z 0 → ll events are selected and aquantity that is calculated purely from leptons is investigated so as to exclude JES uncertainty, which is
the largest and dominant uncertainty in the ATLAS detector, Figure 52 (left) show pllT distribution after
requiring the following conditions:• Two same-favor leptons.
• The leptons should have the opposite charges to each other.
• The di-lepton invariant mass mll should be matched to the Z boson mass :66 GeV < mll < 116 GeV.
This analysis is free from JES uncertainty as no jet condition is required. The uncertainty on lepton
energy scale, lepton energy resolution and lepton eﬃciency are all at O(1)% level, thus negligible. Notethat the same generator is used to produce Z+jets and W+jets, hence the insights obtained from Z+jets
75

is applicable to W+jets. A clear slope is observed in pllT distribution, which means the transverse momentum of Z 0 boson is not fully reproduced by the generator. This conclusion encourages us to invent a
correction function and apply it to W+jets events.
The following HTISR is defined to see if ISR are well described for Z 0 → ll,i∑

HTISR =

piT .

(71)

jets,pT >30 GeV

The right plot of Fig. 52 shows HTISR distribution, which clearly shows a discrepancy. Therefore ISR
description seems to have a problem.
As we observed two large discrepancies in pllT and HTISR , one can propose two correction functions:first one is a method based on the transverse momentum of the boson and the second is the one based on
ISR activity. A detailed study shows that the latter choice seems better to correct all kinematic variables.

8

10

106

-1

Data

109

tt
W+jetsZ+jetsSingle Top

-1

107

Dibosons
tt+V

5

10

104
103
102

103
10

-1

10

1

-2

10-1
1.5

1
0.5 0

100 200 300 400 500 600 700 800 900 1000pll [GeV]
T

tt+V

104

1

1

tt
W+jetsZ+jetsSingle Top

105

102

10
1.5

Data

Dibosons

106

10

0.5 0

∫ Ldt=20.3fb , s=8TeV

108

Ratio

Ratio

Events/25GeV

107∫ Ldt=20.3fb , s=8TeV

Events/200GeV

109

200 400 600 800 1000 1200 1400 1600 1800 2000
HISR
T [GeV]

Figure 52: (Left) pllT distribution after requiring two same-flavor leptons with opposite charges. An
invariant mass selection of 66 GeV < mll < 116 GeV is applied to obtain a good purity of Z+jets events.
No jet is required, thus no JES uncertainty concerns. (Right) HTISR is plotted with the same selection.
The following correction is introduced as a function of meﬀ ,{p0 + p1 · meﬀ(meﬀ < Ethres )f (meﬀ ) =p0 + p1 · Ethres (meﬀ ≥ Ethres ),(72)

where p0 and p1 are the parameters which will be determined in the fitting. Ethres is the threshold beyond
which the fitting function is fixed to a constant. For Soft and Loose Regions, the same selections of jets
are applied as the Control Regions, while for Tight Region the thresholds on the leading jet pT and thefifth leading jet pT are loosened to 80 GeV and 30 GeV to enhance the number of events. The soft lepton
requirement (p`T < 25 GeV) kills lots of W+jets events, thus the lepton selection is replaced to that ofHard Lepton analysis. As the lepton pT has only a small contribution to meﬀ , this modification should
not make a big bias in the results.
Table 18 shows the fitted parameters for the Tight, Loose and Soft Regions. The fitted p1 values are
all around ∼ -35 %/TeV within the uncertainty, which suggests the slope correction does not depend on
the jet topologies strongly in our target phase-spaces. The fitted result for the Loose region is shown on
76

the right plot of Fig. 53 and also ETmiss distribution after applying the same correction is shown on theright. The slope of meﬀ is eliminated and also ETmiss becomes flat after the correction. This tendency
is also true for Tight and Soft Regions. p0 is chosen so that the correction function f (meﬀ ) gives 1 at
meﬀ = 500 GeV.
The uncertainty of the correction is assigned following the same way as tt¯. As shown in Table 18, an
uncertainty of ∼40% is taken from the diﬀerence between p1 values in Tight and Loose regions. Table 19
summarizes the impacts of correction on the transfer factor along ETmiss and mT . As the numerator
and denominator have the same events in common, no statistical error is assigned. In average, theimpact on the mT transfer factors seem much smaller than those of ETmiss . The worst systematic error is
8% (= 20.2% × 40%) for the ETmiss transfer factor of the Tight Region and the others are much smaller. A
similar correction on Z+jets shows that the meﬀ correction fixes the discrepancy in pllT almost completely,
which means that, for W+jets, ETmiss is also fixed because it is determined by boson pT .
The plots after applying the corrections on tt¯ and W+jets are shown in Fig. 54. The combined selections of the Control and Validation Regions are used to choose the events (details will be discussed in
Section 6.2.6). The magenta lines show the total backgrounds before applying tt¯ and W+jets corrections.
Since the similar meﬀ regions are already selected, the impact of the slope correction does not look sosignificant, but we see the agreement is improved with the corrections.
1

10

1

3

Slope = -5.44e-05 ± 7.68e-05( Original = -2.45e-04 ± 5.77e-05 )

10

3

10

2

Slope = 3.00e-05 ± 4.65e-04( Original = -5.60e-04 ± 3.62e-04 )χ /NDF=1.4

χ2/NDF=0.9

Events/10GeV

Events/100GeV

2

102

10

10

1.5

Ratio

Ratio

1

1
0.5 0

500

1000

1500

2000

1.5
1
0.5 0

2500
meff [GeV]

50

100

150

200

250

300

350

400

450
500
Emiss
[GeV]
T

Figure 53: Fit results are shown for the Loose region, meﬀ is on the left and ETmiss is on the right. Black
points show the data, the gray line shows the other backgrounds except for W+jets. The blue line shows
the backgrounds with the original W+jets without any correction, and the red line shows the ones withthe slope correction on W+jets sample. The bottom panel shows the ratios with respect to the red lines.
For reference, the green line shows a first order polynomial fit for the remaining slope in the correctedbackgrounds.

Region
Tight
Loose
Soft

Ethres [TeV]
1.5
1.2
1.2

p1 [%/TeV]-48.4 ± 9.0-34.7 ± 6.3-30.7 ± 5.4

Table 18: Fit results for meﬀ corrections for W+jets.

77Region
Tight
Loose
Soft

mT
-0.2%
-0.2%
-0.2%

ImpactETmissTotal-20.0% -20.2%
-3.1%
-3.3%
-10.0% -10.2%

Table 19: Impacts of the slope correction. The impact is defined as the amount of the changes in thetransfer factor from the Control to Validation Regions with and without correction.
6.2.5 Fitting in the Control Regions
Tables 29-31 (in Appendix D) show the fitted results for Tight, Loose and Soft Control Regions. The
errors include all the statistical and systematic errors. Note that the errors have correlations, thus thetotal size of errors diﬀers from the ones obtained by a simple square-sum. As discussed in the firstpart of this section, normalization factors are expected to diﬀer for each jet selections. Therefore threepairs of parameters are prepared for Tight, Loose and Soft regions, each for W+jets and tt¯. In total, six
normalization factors are determined in the fitting. Table 20 summarizes the fitted scale factors. The
normalization factors are consistent with 1 within the uncertainties. The errors are mainly composed ofstatistical error and JES uncertainty with roughly the same contributions. JES uncertainty is absorbed by
the normalization factors here, resulting in a great reduction in the Signal Regions. Third error sourceis b-tagging uncertainty, but the contribution is two (Loose, Soft) or five (Tight) times smaller than JES
uncertainty.
Region
Tight
Loose
Soft

Scale Factortt¯
W+jets
0.67±0.32 0.76±0.61
0.95±0.22 0.83±0.16
1.09±0.23 0.77±0.19

Table 20: Scale factors obtained in the fitting.

78

6.2.6 Data/MC comparison
Figures 54 show ETmiss (left) and mT (right) distributions for Tight, Loose and Soft Regions. For ETmissplots, the Control Region (CR) selections without the upper limit on ETmiss are applied to examine theentire ETmiss range. The region is equal to the sum of phase spaces spanned by CR and VR (ETmiss ).
Similarly, for mT plots, the Control Region selections without the upper limit on mT are applied, which isequal to the phase space spanned by CR and VR (mT ). Here the error band includes JES uncertainty andstatistical uncertainty of Monte Carlo. The background, which is dominated by tt¯ and W+jets, describes
the data points quite well within the uncertainties. No specific trend is observed in the plots, which
confirms that ETmiss and mT shapes are correctly reproduced, therefore the extrapolation from the Control
Regions to the Validation Regions should also be correctly described.
Tables 32-37 (in Appendix E) give quantitative validations of the correctness, which show the numberof observed and expected events in the Validation Regions. The observed numbers are all consistent withthe background expectations within the errors, which contain statistical and systematic errors. Note that
uncertainties mainly come from the normalization uncertainties in the Control Regions.
These results confirm that the extrapolation along ETmiss and mT are correctly described. As the entire
extrapolation from the Control to Signal Regions are composed of two steps of extrapolations along ETmiss
and mT , these validations make sure that our analysis should predict the background events well even in
the Signal Regions.

6.3 Other backgrounds
In addition to tt¯, W+jets and QCD multi-jets, the following components are included as the backgrounds:• Dibosons (WW, WZ, ZZ productions with additional jets)• Single top production• tt¯+V (V = W, Z)• Z+jets
They are all estimated by using Monte Carlo with the nominal cross-sections, which are summarizedin Table 10. They are not normalized in the Control Regions, thus the uncertainties on cross-section
and acceptance into the Signal Regions directly aﬀect the yield estimation. The uncertainties for thesebackgrounds are discussed in Section 7.2.

79∫ Ldt=20.3fb , s=8TeV

Datatt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

102
10
1

2

Ratio

10-2

2
1
300

350

400

∫ Ldt=20.3fb , s=8TeV

3

10

10
1

2

Ratio

10-1

2
1
400

∫ Ldt=20.3fb , s=8TeV

450
500
Emiss
[GeV]
T

Data
tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

-1

105
104

Data
tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

-1

1
080

100

120

140

∫ Ldt=20.3fb , s=8TeV
-1

105
104
Events/20GeV

350∫ Ldt=20.3fb , s=8TeV

3

10

102
10

180
200
mT [GeV]

10

10-2

300

160

102

1

250

140

103

10-1

200

120

104

102

0150

100

105

Data
tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

-1

1
080

450
500
Emiss
[GeV]
T

10
Events/25GeV

1

10-2

4

Ratio

10

10-1

105

Events/25GeV

102

10-1

0250

Data
tt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

-1

103

Events/10GeV

Ratio

Events/50GeV

103∫ Ldt=20.3fb , s=8TeV

104

Events/20GeV

-1

104

103

160

180
200
mT [GeV]Datatt
W+jetsZ+jetsQCD
Single Top
Dibosons
tt+V
Without Reweighting

102
10
1
10-1

1

10-2

2

Ratio

Ratio

10-1

1
0200

250

300

350

400

10-3
2

1
060

450
500
Emiss
[GeV]
T

80

100

120

140

160
mT [GeV]Figure 54: ETmiss (Left) and mT (Right) distributions of Tight (Top), Loose (middle) and Soft (bottom)
Regions. For ETmiss plots, the Control Region selections without the upper limit on ETmiss is required.
Similarly, for mT plot, the Control Regions without the upper limit on mT is applied. The bottom panels
show the ratio of data divided by the Monte Carlo. The normalization factors which are determined in
the Control Regions are applied here. The error band includes JES uncertainty and statistical uncertaintyof Monte Carlo. The magenta line shows the kinematic distributions without the corrections.
80

7 Uncertainties
7.1 Instrumental uncertainties
The ATLAS detector has been calibrated during two years’ data-taking period, but there still remain
inevitable uncertainties in the calibration, such as the uncertainty associating with Jet Energy Scale.
These uncertainties and their impacts on the background estimation are discussed here. Note that theexact impact in the Signal Region is only determined after fitting as discussed in Section 8.1. So here we
only show the rough size of impacts. The exact size of the uncertainties will be discussed after fitting.
Instrumental uncertainties are evaluated for all backgrounds and signals.
7.1.1 Jet Energy Scale (JES) uncertainty
As documented in Section 3.2.4, jet calibration is made up of several steps, starting from a single pion
calibration to in-situ calibrations. All the nuisance parameters introduced in the calibrations are summed
up quadratically and taken into the analysis. Figures 55 show eﬀects of JES uncertainty on mT and the
40 distributions using tt¯ sample. Only minimal kinematic selections are applied in thenumber of jets Njet
jet3

jet1

plots: pT >80 GeV, pT >40 GeV, mT >80 GeV, ETmiss >150 GeV, and meﬀ >500 GeV. The large shift inthe entire scale comes form the cumulative impacts of the kinematic selections, which is absorbed after
normalizing Monte Carlo in the Control Regions. The remaining shape diﬀerence is considered as theuncertainty on transfer factor, which is about 10%.

∫ Ldt=20.3fb , s=8TeV

105

-1

∫ Ldt=20.3fb , s=8TeV
-1

tt

tt

4

10

JES up

JES up3

10

JES down

JES down

2

EventsEvents/10GeV

104

103

10

10
1

102

10-1

1.2

Ratio

Ratio

10-2

1
0.880

100

120

140

160

180

200

220 240mT [GeV]

1.5
1
4

6

8

10
12
The number of jets

Figure 55: mT (left) and the number of jets (right) comparisons with positive (cyan) and negative (magenta) JES uncertainties. Only tt¯ sample is shown.

7.1.2 Jet Energy Resolution (JER) uncertainty
Uncertainty on jet energy resolution is also considered, which is propagated to ETmiss , making an impact
in the steep slope after the Jacobian peak in mT as shown in Fig. 56. However, as we set Control Regions
close to Signal Regions, overall diﬀerence is absorbed by the normalization factors, leaving only O(1)%uncertainty in the final results.

81∫ Ldt=20.3fb , s=8TeV-1

Events/10GeV

104

tt

JER

103

Ratio

102

1.2
1
0.880

100

120

140

160

180

200

220 240mT [GeV]Figure 56: mT comparison with JER uncertainty. Only tt¯ sample is shown.

7.1.3 Lepton energy scale, resolution, and trigger/reconstruction eﬃciency uncertainties
The energy scale and resolution, and also the trigger/reconstruction eﬃciencies of leptons are calibrated
mainly using Z → ll events. Errors on these calibrations are much smaller compared with JES uncertainty, in addition, normalization in the Control Region reduces the uncertainties quite a lot. Even before
the normalization, the impacts are as small as 2% in the worst case, so neglected in the fitting.
7.1.4

ETmiss resolution uncertainties

The uncertainties of jets and leptons mentioned above are all propagated to ETmiss . As shown in Eq. 51, theuncertainty on ETmiss (Soft) is the last remaining term to be evaluated. Both the energy scale and resolutionof the term are varied within the uncertainties, only to find that both of the uncertainties are well below
3%, thus not included in the fitting.
7.1.5 Pile-up uncertainties
The current pile-up simulation does not completely reproduce the number of primary vertex per a collision NPV . Monte Carlo rather predicts 10% lower NPV than that of data. We evaluate the impact of thisdiscrepancy by shifting NPV by ±10%. Since our analysis requires a large ETmiss , the impact is only <2%level, thus not included in the fitting.
7.1.6 b-tagging eﬃciency uncertainty
b-tagging is used to separate W+jets and tt¯, so the uncertainty directly aﬀects the normalization scales
in the Control Regions. b-tagging uncertainty is divided into three components by the flavor of jets: b-,c- and light-jets. The quadrature sum of the uncertainties is taken into the systematic error, which yields
about 10% for tt¯ in most of the kinematic selections. On the other hand, the uncertainty of mis-tagging
is also studied for W+jets, giving a similar size of uncertainty.

82

7.2 Theoretical uncertainties
7.2.1 tt¯
As discussed in Section 6.2.3, there observed a clear mis-modeling in Parton-Shower. We invented acorrection function to fix the mis-modeling and obtained a good agreement. The uncertainty of thiscorrection is 14% in the worst case for the Tight Signal Region.
On top of Parton-Shower uncertainty, the kinematics of tt¯ system, which is mainly determined in
Matrix-Element calculation, has extra uncertainties. We introduce the following uncertainties to cover a
possible mis-modeling of tt¯ system.
Renormalization and Factorization scales :Generators have an inevitable uncertainty of the energy scale at which the strong coupling constant αS is calculated, which is called renormalization scale. Another important energy scale isfactorization scale, at which PDF is evaluated. The impact of the uncertainties of these scales arestudied by comparing systematic samples with the nominal sample. Here, the systematic samples
are the ones produced with the diﬀerent parameter configurations. For these scale uncertainties,
each of the scale is varied by factors of 0.5 or 2.0. In general, Next-to-Leading-Order generators
are robust to these scale uncertainties, therefore, only a small impact is expected.
Figures 57 show the ETmiss and mT distributions of the systematic samples. Due to a poor statisticsof the systematic samples, no kinematic selection is applied. The largest slope is observed in theETmiss distribution of renormalization systematic samples. A 5% of systematic error safely covers
the uncertainty of the transfer factor for all regions. The slope in mT is not so large, especially interms of the transfer factor. No statistically significant variation is observed in meﬀ .
PDF :A study 6 shows that total PDF uncertainty is smaller than 3%, thus it is eliminated from the fit. The
reason of the smallness is explained by the fact that tt¯ is relatively light compared with the protonenergies in the LHC, therefore the bulk regime of the parton momentum fraction x contributes tothe production, where the uncertainty is small.

7.2.2 W+jets
As discussed in the last part of Section 6.2.4, the slope correction introduces an uncertainty. The largest
uncertainty is observed in the Tight Region, giving 8% for the transfer factor. PDF uncertainty is evaluated using Eq. 73, whose contribution is found to be below 3%, thus neglected. Other generator uncertainties are also studied by systematic samples produced with Alpgen. First, renormalization and∑factorization scales Q are varied between 0.5 and 2.0. An empirical formula, Q2 = m2W + j (m2j + p2T, j ) ( jruns over all jets) is used to set Q in default, which is also varied to Q2 = m2W and Q2 = m2W + p2T,W for
further uncertainty estimation. But no significant impact in the transfer factor is found.

6

PDF used in tt¯ generation has 20 pairs of uncertainties coming from the experimental errors. The eﬀect of these uncertainties on the transfer factor Ω is obtained by calculating the transfer factor for each of these variations ω (once up (+) and once
down (-)) while keeping the other parameters fixed. This gives an asymmetric PDF uncertainty:√∑{Ωup = √ i [max(ωup − ω0 , ωdown − ω0 , 0)]2∑
(73)
2
Ωdown =i [max(ω0 − ωup , ω0 − ωdown , 0)]
where i is the index of PDF uncertainties.

83Nominal
Renorm. up
Renorm. down
Factor. up
Factor. down

106

NominalRenorm. up
Renorm. down
Factor. up
Factor. down

107
106
105

105

104
103
102

1.1

Ratio

Ratio

104

1
0.9 0

50

100

150

1.1
1
0.9 0

200
250
mT [GeV]50 100 150 200 250 300 350 400 450 500
Emiss
[GeV]
T

Figure 57: mT (left) and ETmiss (right) distributions of renormalization and factorization scale systematic
samples. No kinematic selections is applied.

7.2.3 Single Top
Background estimation of SingleTop is evaluated fully depending on Monte Carlo and its cross-section.
Therefore, the theory uncertainties of SingleTop become important. Note that the SingleTop is one of
the minor backgrounds, so a large uncertainty doesn’t necessarily lead to loss of sensitivity. In fact,
a comparison study with various fraction (from 20% up to 70%) of systematic errors doesn’t give any
significant diﬀerence in the fit results.
A generator comparison between MC@NLO and Powheg samples and the Parton-Shower variation using Pythia and Jimmy give ∼10% errors at most.
W+t channel includes diagrams which share the same final states with tt¯ [60, 61]. Such diagrams
are already subtracted in event generation, however, as the subtraction method is not well-defined, there
proposed two diﬀerent subtraction algorithms: Diagram Subtraction (DS) and Diagram Removal (DR)7 . As two algorithms give diﬀerent SingleTop yields, we take the diﬀerence into the systematics, whichamounts to 70%.
7.2.4 Z+jets
Though its large cross-section, Z+jets is one of the minor backgrounds once after requiring 1-lepton andtight ETmiss cuts. Z+jets is normalized by its theoretical cross-section, whose uncertainty is 12%. To beconservative, we use a 30% uncertainty in the fitting.
7.2.5 tt¯+VFor tt¯+V sample, two generator comparison and cross-section uncertainties are considered. A comparison between Alpgen and MadGraph shows that the diﬀerence is quite small (∼5%) in all kinematic
regions. A 30% of uncertainty is assigned considering the cross-section error, which is taken from thediﬀerence between LO and NLO calculations. Note that the uncertainty safely covers PDF and renormalization/factorization scale uncertainties.
7

The nominal sample uses Diagram Removal method for the subtraction.

84

7.2.6 Dibosons
An uncertainty of 50% is applied, which comes from the cross-section uncertainty taken from the diﬀerence between LO and NLO cross-sections. A 50% uncertainty is suﬃcient to cover the other errors suchas PDF and scale uncertainties.
7.2.7 QCD multi-jet
The uncertainty on QCD multi-jets estimation is dominated by the statistical error of data. As discussed
in Section 6.1, QCD multi-jet background is evaluated by comparing the event numbers in fake-enriched
and fake-suppressed regions. But even in the fake-enriched region, the event number is quite small after
applying a large ETmiss selection. Uncertainties on fake and real are also included but have negligible
impacts.

7.3 Signal uncertainties
The dominant uncertainty sources of signals are the cross-sections and acceptances in the Signal Regions,which are separately evaluated in the following. Also the instrumental uncertainties are included in thefitting, however, the contributions are much smaller than these theoretical uncertainties.
7.3.1 Cross-section uncertainty
There are several theoretical uncertainties that have an impact on the cross-section. The quadrature sumof uncertainties is shown in Fig. 28 for MSUGRA/CMSSM sample. Uncertainties of the Simplified
Model are shown in Fig. 30 as the vertical error bars. They include the following uncertainties.
Scale uncertainty :Renormalization and factorization scales are both set to the mass of the initial particles Q whencalculating the cross-section (for squark-gluino production, the mean mass is taken, i.e. Q =(mg̃ + mq̃ )/2). This choice gives rise to an uncertainty and the diﬀerence between the ones with
µ = 2Q and µ = Q/2 are taken into account.
PDF uncertainty :PDF uncertainty is estimated using the same method as described in Section 7.2.1.
αS uncertainty :Determination of PDF parameters has an overall uncertainty for the choice of αS [76]. Two diﬀerent cases are tested, and the variations on cross-sections is taken as uncertainty.
These uncertainties are separately evaluated using two PDF sets: CTEQ6.6M [77] and MSTW2008NLO [43,44, 45], and the combination that gives the maximum variation are taken into account. Table 21 shows
the size of these uncertainties for some representative points. PDF uncertainty gives a large error for highmass gluino productions, which is because a large parton momentum fraction x is required for gluons to
produce massive gluinos. On the other hand, squark production has relatively small uncertainty from
PDF because it can use valence quarks.
7.3.2 Acceptance uncertainty
Signal acceptance is defined as the fraction of events passing the signal region selection. Generator
uncertainty also aﬀects the signal acceptance. The following uncertainties are taken into account.

85

SignalUncertainty [%]Parameter [GeV]
Production Scale PDF αSMSUGRA/CMSSM(m0 , m1/2 )=(1000,650)
g̃-g̃
9
51
13
(m0 , m1/2 )=(4000,450)
g̃-g̃
11
29
8
q̃-q̃
19
41
7
Simplified Modelmg̃ =1200
g̃-g̃
11
25
7
mg̃ =800
g̃-g̃
10
17
6
mq̃ =1200
q̃-q̃
11
18
6
mq̃ =800
q̃-q̃
11
12
4

4

(up-down)/(up+down) [%](up-down)/(up+down) [%]Table 21: Decomposition of the signal uncertainty for some representative points. The relative sizeof the error is shown. Note that the gluino and squark masses are 1.5 (1.2) TeV and 1.6 (3.1) TeV for
the MSUGRA/CMSSM points with (m0 , m1/2 )=(1000,650) ((m0 , m1/2 )=(4000,450)), respectively. q̃-q̃
uncertainties for the former point are not shown as it gives only negligible contribution.

m(~q)=500 GeVm(~q)=300 GeV

2

0

2

m(~
q)=500 GeV

0m(~q)=300 GeV

-2

-4

-2
-6
-4
-8
-6

-8
0

-10

50

100

150

200

250

300

350

-12
0

~400 ∼± 450m(q) - m(χ) [GeV]
1

50

100

150

200

250

300

350

~400 ∼± 450m(q) - m(χ) [GeV]
1

Figure 58: ISR uncertainty obtained for the Simplified model with q̃-q̃ production. The mass diﬀerence
between q̃ and χ̃±1 are taken as the x-axis. The y-axis shows the uncertainty defined in Eq. 74. The
uncertainties given in Eq. 75 are shown in black lines. Two mass points with mq̃ =300 GeV (purple) and30 ≥ 3; (right) at
500 GeV (blue) are shown. The kinematic selections are: (left) at least 1 lepton and Njet
40 ≥ 5.
least 1 lepton and Njet

86

ISR uncertainty : Energy scale at which αS is evaluated for ISR is varied from the nominal value to 0.5
or 2.0.
Scale uncertainty : This item is the same as the one mentioned in the previous section, but only the
impact on acceptance is evaluated.
FSR uncertainty : ΛQCD value used for FSR is varied by ±50% from its nominal.
Jet matching uncertainty : Jet matching scale at which the partons from Matrix-Element and PartonShower algorithms are separated is varied by a factor of 0.5 and 2.0.
PDF uncertainty : This uncertainty is the same as the one mentioned in the previous section, but only
the impact on acceptance is evaluated.
Among these uncertainties, ISR uncertainty gives the largest impact on signal acceptance and the others
are much smaller. Therefore we evaluate ISR uncertainty in the following and take it into the systematic
uncertainty.
jet
The primary impact of ISR uncertainty appears in the number of jets passing pT >40 GeV (Tight andjet
Loose) or pT >30 GeV(Soft). In Simplified models, 2 jets (q̃-q̃ grid) and 4 jets (g̃-g̃ grid) are expectedfrom decay chains, therefore, ISR uncertainty is more critical for q̃-q̃ grid. The size of ISR uncertainty
is shown as a function of mass splitting between q̃ and χ̃±1 as it impacts jet pT distribution. Two different samples (up/down) are generated with extreme ISR uncertainty configurations. The uncertainty is
calculated as follow from the number of events in the signal region Nup/down ,uncertainty =Nup − Ndown,
Nup + Ndown(74)

Figure 58 show the uncertainties as a function the mass diﬀerence between q̃ and χ̃±1 . At least 1 lepton
30 ≥ 3 (left) and N 40 ≥ 5 (right). No otheris required. In addition, two jet selections are tested: Njet
jetselection is required in the plots to obtain enough statistics. The uncertainty is larger for low mass
splitting especially below 50 GeV, which is because the jet from q̃ decay becomes as soft as the jet pT
threshold and ISR becomes more important. Two diﬀerent squark mass points are plotted but they show
similar tendencies. The following uncertainties are considered:{(4 + 6e−0.01 x ) (Tight)
ISR uncertainty [%] =(75)(1 + 5e−0.01 x ) (Loose, Soft),
where x is the mass diﬀerence between q̃ (g̃) and χ̃±1 in a unit of GeV. ISR uncertainty is quadratically
added to the cross-section uncertainty in the fitting.

87

8 Results
As discussed in Section 6, dominant backgrounds, tt¯ and W+jets, are normalized in the Control Regions
to reduce generator uncertainties. In addition, meﬀ slope correction is applied to correct the mis-modelingof ISR uncertainty. Two Validation Regions are prepared to justifies the extrapolations along ETmiss andmT , and both of them show good agreements. Since the background estimation in the Signal Region iscomposed of these two extrapolations, we expect that backgrounds in the Signal Region are also correctly
estimated. These observations encourage us to un-blind the Signal Regions to search for an excess indata. If there is no signal-like excess, we calculate the mass limits using a binned likelihood method onmeﬀ .

8.1 Un-blinding the Signal Regions
Table 22 (Tight SR), 23 (Loose SR) and 24 (Soft SR) show the observed event numbers in the Signal
Regions with the expected number of background events. Lepton flavors are separated for Hard Lepton
channels, while they are combined for Soft Lepton channel due to some technical reasons. In all the Signal Regions and channels, the number of observed events are consistent with the expected backgrounds
within the errors. The errors cited as “bkg events” consider both statistical and systematic errors. All
correlations among the errors are taken into account, therefore, the total size of the errors may become
smaller than its components8 .
Table 38 (Tight SR), 39 (Loose SR) and 40 (Soft SR) (in Appendix G) give the raw size of errors
assigned to systematic error sources. The largest systematic error comes from JES uncertainty, which
is 10-15% for Loose and Soft Signal Regions. For Tight Signal Region, it becomes as large as 30%
due to stringent kinematic selections. The scale factors of tt¯ and W+jets are also dominant sources of
the uncertainties, which is determined in the normalization in the Control Regions. JES uncertainty isstrongly anti-correlated with normalization uncertainties of tt¯ and W+jets, therefore the total systematic
error is much smaller. In other words, JES uncertainty is absorbed by the scale factors by normalizing in
the Control Regions.
√
Expected size of the fluctuation of observed events is denoted as Nexp . Since we set stringent cuts
to maximize the sensitivity, the number of remaining events are quite small. For the Tight Signal Region,
we expect only 11.8 events in total, therefore a large statistical error (±3.4) is assigned.
Figures 59 show meﬀ plots in Tight (left), Loose (right) and Soft (bottom) Signal Regions. Several
signals taken from around the exclusion limits are piled up on top of the background distributions. The
same binning is used as the ones used in fitting. Both electron and muon channels are combined. Tight
Signal Region is dominated by large statistical errors both for data and Monte Carlo. The data points are
all consistent with the Monte Carlo expectations within the uncertainties.
The Loose Signal Region has smaller statistical errors, but the data points are still consistent with theMonte Carlo expectations. A slight downward tendency is actually seen in the ratio plot although it isinside the uncertainty band. An orthogonal region is defined by inverting mT selection to 60 GeV < mT <120 GeV to check the origin of this tendency, however, meﬀ distribution in the region seems quite flat
without any specific structure. Therefore the downward slope is concluded to be a statistical fluctuation.
Overall distribution in the Soft Signal Region is consistent with the expectations. The leftmost bin
has a slight excess in data though the statistical error is quite severe. This excess is checked further byloosening one of ETmiss or mT selection to ETmiss >200 GeV or mT >60 GeV and see the meﬀ distributions
8
For example, the uncertainty of b-tagging eﬃciency directly changes the fraction of the events classified to tt¯ control
region and W+jets Control Regions as they are separated by requiring at least one b-tagged jet. As a result, the yields of these
two backgrounds are anti-correlated through b-tagging uncertainty. If we take the uncertainty of one component, it may looklarge. However, once they are summed up in Signal Region or Validation Regions, then the yield changes compensate eachother, leading to a smaller uncertainty.

88

with finer bin width. The results show no significant structure therefore we conclude the excess is notcaused by a specific problem but just a statistical fluctuation.
The ETmiss and mT distributions of the events in these signal regions are shown in Appendix F.

89

Tight SR (El)Tight SR (Mu)84bkg events

6.52 ± 1.17

5.31 ± 1.03

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

3.83 ± 1.23
0.89 ± 0.57
0.00 ± 0.00
0.78 ± 0.43
0.48 ± 0.37
0.37 ± 0.10
0.16+0.21−0.16

3.44 ± 1.04
0.67 ± 0.43
0.06 ± 0.04
0.18+0.28−0.18
0.64 ± 0.46
0.33 ± 0.09
0.00 ± 0.02

channelObserved events

Table 22: Background fit results for the Tight SR (El) and Tight SR (Mu) for an integrated luminosityof 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.

Loose SR (El)

Loose SR (Mu)

179

132

bkg events

166.60 ± 20.35

161.12 ± 18.56

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

93.34 ± 19.77
43.76 ± 5.93
0.85 ± 0.27
11.29 ± 5.87
11.77 ± 8.32
4.13 ± 0.36
1.46+1.92−1.46

86.31 ± 18.05
43.15 ± 6.01
3.75 ± 1.17
12.13 ± 6.24
9.41 ± 6.66
3.38 ± 0.22
2.99 ± 2.10

channelObserved events

Table 23: Background fit results for the Loose SR (El) and Loose SR (Mu) for an integrated luminosityof 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.

Soft SR (El+Mu)

channelObserved events

40

bkg events

35.37 ± 4.57

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

16.65 ± 3.63
12.08 ± 1.21
0.16 ± 0.15
1.42 ± 0.73
2.93 ± 2.07
0.71 ± 0.06
1.43+1.55−1.43

Table 24: Background fit results for the Soft SR (El+Mu) for an integrated luminosity of 20.3 fb−1 . The
errors shown are the statistical plus systematic uncertainties.

90

14

300

∫ Ldt=20.3fb , s=8TeV
-1

-1

tt
W+jetsZ+jets

12

250

QCD
Single Top

10

Events/250GeV

Events/400GeV∫ Ldt=20.3fb , s=8TeV

Data

Dibosonstt+V~g-~g (1200,660,60)~g-~
g (985,705,425)

8
6

Data
tt
W+jetsZ+jetsQCD
Single Top

200

Dibosonstt+V~q-~q (600,360,60)~q-~q (425,305,185)

150
100

4
50

2

0
Ratio

Ratio

0

2
1
0 800 1000 1200 1400 1600 1800 2000 2200 2400

10meff [GeV]30

2∫ Ldt=20.3fb , s=8TeV-1

25500 600 700 800 900 1000 1100 1200 1300 1400
meff [GeV]

Datatt
W+jetsZ+jetsEvents/250GeV

QCD
Single Top

20

Dibosonstt+V~g-~g (665,625,585)

15
10
5

Ratio

0

2
1
0

500 600 700 800 900 1000 1100 1200 1300 1400
meff [GeV]

Figure 59: meﬀ distributions in Tight (left), Loose (right) and Soft (bottom) Signal Regions. Signals
taken from around the exclusion limits are piled up on top of the background distributions. For
Tight SR, gluino pair productions with (mg̃ ,mχ̃±1 ,mχ̃0 )=(1200 GeV, 660 GeV, 60 GeV) (magenta) and1(mg̃ ,mχ̃±1 ,mχ̃0 )=(985 GeV, 705 GeV, 425 GeV) (cyan) are shown. For Loose SR, squark pair produc1
tions with (mq̃ ,mχ̃±1 ,mχ̃0 )=(600 GeV, 360 GeV, 60 GeV) (magenta) and (mq̃ ,mχ̃±1 ,mχ̃0 )=(425 GeV, 305 GeV,
1
1
185 GeV) (cyan) are shown. For Soft SR, gluino pair production with (mg̃ ,mχ̃±1 ,mχ̃0 )=(665 GeV, 625 GeV,
1
585 GeV) is shown in magenta. The last bin includes the overflow events.

918.2 Limit calculation
As no signal-like excess is found in the Signal Regions, the results are interpreted as mass limits on
two signal models. Limit calculation is based on Profile-Likelihood method (details are documented inAppendix. H). Likelihood function is composed of three parts,
L (µ) =

LTight (µ, θTight , λW
, λtt¯ )Tight Tighttt¯
× LLoose (µ, θLoose , λW
Loose , λLoose )(76)

× LSoft (µ, θSoft , λW
, λtt¯ ),Soft Softtt¯
where θX is a vector containing all the nuisance parameters in region X, λW
X and λX are scale factors
for W+jets and tt¯. µ is a signal strength, which is defined as the ratio of a given (or fitted) signal yieldover the nominal signal yield. All nuisance parameters and scale factors are defined separately for eachregion. Signal strength µ is the only common parameter over the regions. Figure 60 gives a schematic
illustration of the structure. Since each likelihood function looks like a tower in the illustration, they arecalled as “Tight-tower”, “Loose-tower” and “Soft-tower”, respectively.
A detailed structure of one of the likelihood functions is given astt¯
LX (µ, θX , λW
X , λX ) =∏i
SRbinsSR,iW SR,itt¯ SR,i
Pois(µsSR,i
X (θ) + λX wX (θ) + λX tX (θ); nX )W WR
tt¯ WRWR× Pois(µsWR
X (θ) + λX wX (θ) + λX tX (θ); nX )W TR
tt¯ TRTR× Pois(µsTR
X (θ) + λX wX (θ) + λX tX (θ); nX )(77)

× Lconstrain(θ).
X
The right-hand-side in the first line gives a Poisson probability for the observed number of events in asignal region of i-th bin, and the terms in the second and third line are the ones for W+jets and tt¯ Control
Regions. Here, wYX (θ) and tYX (θ) are the number of W+jets and tt¯ backgrounds in Y-region of X-tower (asSignal Regions are divided into bins, bin index i is superscripted). Similarly, the number of observed
events in Y-region of X-tower is represented as nYX . The last term is a product of all constraining terms.
The constraining term consists of two parts: MC statistical error terms and systematic error terms.
The former ones are responsible for statistical errors of Monte Carlo samples in each bin. The latter ones
are to constrain the nuisance parameters of uncertainties such as JES, JER, etc. If a constrain is weak
for a given systematic error and the corresponding nuisance parameter is able to move around freely, theerror on signal strength µ also becomes larger. A larger error on signal strength µ means that a signal
model is diﬃcult to be classified to “with-signal” or “without-signal” hypotheses, thus the sensitivity
becomes weaker.
Signal contamination in the Control Regions is correctly taken into account in this configuration.
Therefore, even when a signal with a large cross-section would exist and contaminate to the Control
Regions severely, we could still obtain a correct signal strength.
The Signal Regions are all divided into bins along meﬀ . The Poisson probability in the bin that has
the largest signal to background separation dominates the entire probability, which is equal to setting an
optimized meﬀ threshold for each signal model. As a result, the Signal Regions are sensitive for various
signal models with diﬀerent meﬀ shapes.
Limits are then calculated using the likelihood function. A 95% confidence level (C.L.) is usedthroughout the analysis. Since the uncertainties on signal cross-sections and acceptances are not something to be fitted nor something to worsen the sensitivity, the uncertainties are excluded from fitting andthe impact is explicitly shown in limit plots.

92

signalSignal Strength

Soft
Tower

Loose
Tower

Tight
Tower

SR

SR

SR

WR
TR

WR
TR

WR
TR

JES
...

JES
...

JES
...

Figure 60: Illustration of fit setup. Signal strength is common among the towers, while each tower has
its own systematics and normalization factors, separately.

938.3 Interpretation
8.3.1 MSUGRA/CMSSM
Figure 61 shows the observed (red) and expected (black) mass limits in the MSUGRA/CMSSM modelwith tan β = 30, A0 = −2m0 and µ > 0. Estimation error, including systematic and statistical uncertainties, is shown as the yellow band. Uncertainties related to signal cross-sections and acceptances areshown as the dotted red lines. Gluino and squark mass lines are also shown. The purple lines indicate
the Higgs mass9 . In all of the parameter space, sensitivity is driven by the Tight Signal Region because
the MSUGRA/CMSSM model tends to have hard event kinematics.
The parameters used in the sample production are chosen so as to maximize the compatibility with
the Higgs mass of 126 GeV [1]. Recent experimental results show that the branching fractions of the
Higgs boson are consistent with the Standard Model Higgs boson [6], which is realized at maximummixing scenario in MSSM framework (see also Section 1.4.5). The scenario requires a large mixing
between left- and right-handed stops, making one of the stops much lighter than the other squarks. As
a result, stops are more likely to appear in decay chains, which increases the number of jets and also
signal acceptances. A larger probability of lepton emission is expected from top decays, which also
increases the events passing 1-lepton selection. Hence, a search requiring 1-lepton and multi-jet suits forthe maximal-mixing configuration.
Since a squark mass becomes so heavy in high m0 region, the region is dominated by g̃-g̃ production
as shown in Fig. 33. A gluino then decays into two quarks and one chargino via three-body decay,g̃ → qqχ̃±1 (here we take a case which has the dominant contribution to 1-lepton analysis), and thewino decays into a LSP, χ̃±1 → W ± χ̃01 . The supersymmetry particles appear in the decay chain are allgauginos 10 . As seen in Eq. 37, gaugino masses are (almost) independent of m0 , so the event topology
does not change along the gluino mass contour, resulting in a constant signal acceptance. Production
cross-section is also independent of m0 because squarks are too heavy to be produced and only g̃-g̃
production occurs, therefore the analysis keeps the same sensitivity along the mass contour. A gluinomass up to 1200 GeV is excluded in high m0 region in Fig. 61, which is expected to continue beyond theright edge of the plot.
A squark mass up to 1500 GeV is excluded except for m0 < 500 GeV. The limit line does not
simply follow the squark mass contour and loose sensitivity in the low m0 and high m1/2 region, whichis explained by the following reasons: (1) As shown in Fig. 33, not only q̃-q̃ but also q̃-g̃ production
occurs at around m0 ∼ 1000 GeV. Sensitivity is pushed up a lot by this contribution because a decay
chain starting from g̃-q̃ has a large signal acceptance due to large number of jets. This production issuppressed in higher m1/2 region, which leads to the sensitivity loss. (2) Since LSP mass is proportional
to m1/2 , a heavy LSP is expected in the high m1/2 region. In general, meﬀ becomes soft for heavy LSPs
since some fraction of energy is consumed to create heavy LSPs and smaller fraction of energy is left forvisible objects. This also means that visible objects tends to be softer overall. As a result of these twocontributions, small signal yields are expected in high m1/2 and low m0 region, therefore we loose thesensitivity.

910

The Higgs mass contours run parallel to the squark mass contours as the Higgs mass is determined mainly by a stop mass.
The Higgsino masses are about 1 TeV for this model, therefore they does not appear in the decay chains.

94m1/2 [GeV]MSUGRA/CMSSM: tanβ=30, A =-2m0, µ>0
0

800

SUSY

750

∫

L dt = 20.3fb , s = 8TeV

Observed limit (± 1 σtheory)

700

All limits at 95% C.L.

Expected limit (± 1 σexp)-1

Stau LSP

V)

~
g (12

e
H(126G

550

eV)

)

600

H(125G

H(124GeV650~
g (1400GeV)

00Ge

500

V)

450

~
g (80

350
300

0GeV

0

~
q (4000GeV)eV)~q (1500G

400
)

1000

2000

3000

4000

5000

6000
m0 [GeV]Figure 61: Observed and expected mass limits for the MSUGRA/CMSSM model with tan β = 30,
A0 = −2m0 and µ > 0.

95

8.3.2 Simplified models
Figure 62 shows the observed (red) and expected (black) mass limits in the Simplified model assuming
gluino pair productions and a LSP mass of 60 GeV. The x-axis shows gluino mass and the y-axis represents x ≡ (mχ̃±1 − mχ̃0 )/(mg̃ − mχ̃0 ). Estimation error, including systematic and statistical uncertainties, is1
1
shown by the yellow band. The magenta, blue and green lines show separate limits of the Tight, Looseand Soft Signal Regions. Combined limit is basically driven by the Tight Signal Region, which is because a gluino pair production generally accompanies a large number of jets. The Loose Signal Region
has a good sensitivity in high x regime, where gluino and chargino masses become degenerate. In mostof x range (0.3<x<0.8), a gluino mass up to 1200 GeV is excluded. This is an improvement of 300 GeV
from the previous limit [78] shown in the light blue area. For a severe condition of x>0.1, a gluino mass
up to 1000 GeV is excluded.
Sensitivity loss in high x region for mg̃ >1000 GeV is caused by softer jet pT spectra, thus the numberof jet condition of the Tight Signal Region becomes hard to be satisfied. Instead, the Loose Signal Region
gains sensitivity, though not enough to fully compensate the sensitivity loss of the Tight Signal Region.
On the other hand, in low x region around mg̃ = 1000 GeV, a chargino χ̃±1 tends to have a largetransverse momentum compared with the chargino mass, hence the decay products of the chargino,
especially a lepton and a LSP, have a smaller opening angle. Resultant softer mT leads to the sensitivity
loss. This tendency is also seen in Fig. 39, where the signals with low-x (light magenta and light cyan)seem to have softer mT distributions than those of high-x signals (dark magenta and dark cyan).
Figure 63 shows mass limits in the Simplified model assuming gluino pair productions with varying
gluino and LSP masses. A chargino mass is set halfway between them. The x-axis shows gluino mass andthe y-axis represents LSP mass. In the region where gluinos are much heavier than LSPs, the sensitivity
is solely driven by the Tight Signal Region. When gluino and LSP degenerates and the mass splitting
comes down to 100 GeV, the Tight Signal Regions looses the sensitivity due to an acceptance loss at the
lepton selection. The Soft Signal Region covers the degenerate region until the mass diﬀerence becomes
30 GeV. Below the mass diﬀerence, we loose the sensitivity completely because the lepton emitted fromdecay often fall below our lowest lepton threshold, 6 GeV. Since no lepton is reconstructed in such a
region, it should be covered by 0-lepton analysis [79].
A LSP mass up to 500 GeV is excluded in a wide range below mg̃ =1000 GeV. Assuming a chargino χ̃±1
is produced at rest and W mass is negligible compared with LSP mass, the following equation gives arough estimation of the LSP momentum: m 0 2 mχ̃±1  χ̃  
LSP
p
∼
(78)
1 −  1   .
2
mχ̃±1
pLSP
is suppressed by the second term as LSP mass increases, which results in softer ETmiss . AnotherT
impact of heavy LSP appears in meﬀ , which becomes smaller for heavy LSPs because some fraction of
the energy is consumed to create heavy LSPs. We perform a binned fit on meﬀ to cope with such signals,
however, low meﬀ region is suﬀered from a large background thus we loose sensitivity. The sensitivity
loss in mχ̃0 >500 GeV is mainly explained by these two reasons.
1

Figure 64 shows mass limits in the Simplified model assuming squark pair productions and a fixed
LSP mass of 60 GeV. The y-axis represents x ≡ (mχ̃±1 − mχ̃0 )/(mq̃ − mχ̃0 ). Both the Tight and Loose Signal
1
1Regions equally contributes to the combined limit. The observed limit reaches to 750 GeV, which is lower
than the gluino limit because: (1) the cross-section of squark pair production is about 10 times lower thanthat of gluino around mq̃ =mg̃ =750 GeV (see Fig. 30). (2) the acceptance of squark pair production islower because the decay chain starting from squark has a smaller number of jets.

96For x > 0.2, mq̃ < 700 GeV is excluded. The sensitivity loss in low-x region is explained in a similar
way as gluino pair-production case.
Finally, Fig. 63 shows mass limits in the Simplified model assuming squark pair productions withvarying gluino and LSP masses. A chargino mass is set halfway between them. Both the Tight and the
Loose Signal Regions equally contribute to the combined limit. The Soft Signal Region recovers thesensitivity in the degenerate region around mq̃ =300 GeV. The combined limit exclude a LSP mass up to
200 GeV for mq̃ <750 GeV.

97

∼0,m =60GeV
~
∼0χ
g-~
g → qqqqWW χ
∼0
χ

1

1

(m∼± - mχ∼0 ) / (m~ - mχ∼0 )1 1∫ L dt = 20.3fb , s = 8TeV

1.2

All limits at 95% C.L.

g

1.4

SUSY

Observed limit (± 1 σtheory)-1

Expected limit (± 1 σexp)

Tight SRχ1

1

Obs. Limit (2011)1

Loose SR

0.8

Soft SR

0.6
0.4
0.2
0

400

600

800

1000

1200

1400
m~g [GeV]

Figure 62: Observed and expected mass limits on mg̃ and x = (mχ̃±1 − mχ̃0 )/(mg̃ − mχ̃0 ) for the Simplified
1
1
Model with g̃-g̃ production. mχ̃0 is fixed at 60 GeV. The black line and the yellow band show the expected1
limit and its uncertainty (±1σ). The solid red line shows the observed limit obtained by combining
all the Signal Regions. The dotted red lines specify the impact of signal cross-section and acceptanceuncertainties. The magenta, blue and green lines show separate limits of the Tight, Loose and Soft Signal
Regions. The light blue area shows the previous limit [78] for reference.
∼0, x=1/2~∼0χ
g-~
g → qqqqWW χ1mχ∼0 [GeV]

1 1

1000
SUSY

∫ L dt = 20.3fb , s = 8TeV

Observed limit (± 1 σtheory)

-1

900

Expected limit (± 1 σexp)

All limits at 95% C.L.

800

Obs. Limit (2011)
0

∼χ 1
<m

700

Tight SR~mg

Loose SR

600

Soft SR

500
400
300
200
100
400

600

800

1000

1200

1400
m~g [GeV]

Figure 63: Observed and expected mass limits on mg̃ and mχ̃0 for the Simplified Model with g̃-g̃ produc1
tion. x = (mχ̃±1 − mχ̃0 )/(mg̃ − mχ̃0 ) is fixed at 1/2. The black line and the yellow band show the expected11limit and its uncertainty (±1σ). The solid red line shows the observed limit obtained by combining all
the Signal Regions. The dotted red lines specify the impact of signal cross-section and acceptance uncertainties. The magenta, blue and green lines show separate limits of the Tight, Loose and Soft Signal
Regions. The light blue area shows the previous limit [78] for reference.

98∼0,m =60GeV
~
∼0χ
q-~
q → qqqqWW χ
∼0
χ

1

1

(m∼± - mχ∼0 ) / (m~ - mχ∼0 )1 1∫ L dt = 20.3fb , s = 8TeV

1.2

All limits at 95% C.L.

q

1.4

SUSY

Observed limit (± 1 σtheory)-1

Expected limit (± 1 σexp)

Tight SRχ1

1

Obs. Limit (2011)1

Loose SR

0.8

Soft SR

0.6
0.4
0.2
0

400

600

800

1000

1200

1400
m~q [GeV]

Figure 64: Observed and expected mass limits on mq̃ and x = (mχ̃±1 − mχ̃0 )/(mq̃ − mχ̃0 ) for the Simplified
1
1
Model with q̃-q̃ production. mχ̃0 is fixed at 60 GeV. The black line and the yellow band show the expected1
limit and its uncertainty (±1σ). The solid red line shows the observed limit obtained by combining
all the Signal Regions. The dotted red lines specify the impact of signal cross-section and acceptanceuncertainties. The magenta, blue and green lines show separate limits of the Tight, Loose and Soft Signal
Regions. The light blue area shows the previous limit [78] for reference.
∼0, x=1/2~∼0χ
q-~
q → qqqqWW χ1mχ∼0 [GeV]

1 1

1000
SUSY

∫ L dt = 20.3fb , s = 8TeV

Observed limit (± 1 σtheory)

-1

900

Expected limit (± 1 σexp)

All limits at 95% C.L.

800

Obs. Limit (2011)
0

∼χ 1
<m

700

Tight SR~mq

Loose SR

600

Soft SR

500
400
300
200
100
400

600

800

1000

1200

1400
m~q [GeV]

Figure 65: Observed and expected mass limits on mq̃ and mχ̃0 for the Simplified Model with q̃-q̃ produc1
tion. x = (mχ̃±1 − mχ̃0 )/(mq̃ − mχ̃0 ) is fixed at 1/2. The black line and the yellow band show the expected11limit and its uncertainty (±1σ). The solid red line shows the observed limit obtained by combining all
the Signal Regions. The dotted red lines specify the impact of signal cross-section and acceptance uncertainties. The magenta, blue and green lines show separate limits of the Tight, Loose and Soft Signal
Regions. The light blue area shows the previous limit [78] for reference.

998.4 Discussion
We have looked through four types of simplified models in the previous section. Particularly interesting
signals are g̃-g̃ productions because gluino mass is expected to lie at O(1) TeV as discussed in Section 1.4.5. Therefore, we concentrate on the Simplified models starting from g̃-g̃ productions and set amodel independent limit on gluino pair production cross-section in the following.
MSUGRA/CMSSM models have complicated decay chains, taking all the possible decays via electroweak gausinos into consideration, which increases a probability of having a lepton and many jets inthe final states. Also, one of stops becomes 20-30% lighter than the other squarks in the maximal-mixing
scenario thus more jets are expected in the final state. In contrast, Simplified models assume the simplest
decay chains without taking in such eﬀects, hence the limits obtained in Simplified models are in generalconservative compared with the other physical scenarios. For example, the gluino mass limit obtained in
MSUGRA/CMSSM model is better than the ones obtained in the Simplified model assuming gluino pair
productions.
The maximum mass limit obtained in Simplified models is mg̃ >1200 GeV, but for more generality,
we take mg̃ >1000 GeV as our gluino mass limit. The gluino mass of 1000 GeV seems mostly excludedin Figs. 62 and 63, however, there also exists some regions which are not yet excluded. We repeat theinterpretations discussed in the previous section in the light of mg̃ =1000 GeV to summarize the applicable
scope of our gluino mass limit.
First, the lepton acceptance has an impact on the sensitivity. As far as an on-shell W boson is emitted
in a chargino decay, the lepton pT does not strongly depend on the particle masses as shown in Fig. 36.
When chargino and LSP are degenerate and only oﬀ-shell W is allowed, the lepton pT becomes softer thus
most of the lepton cannot pass the Hard Lepton pT threshold of 25 GeV. The Soft Lepton selection is quite
powerful to recover the lepton acceptance as shown in Fig. 36. This is also seen in the diagonal region in
Fig. 63, where the Tight Signal Region looses sensitivity once the mass splitting between chargino and
LSP gets below the mass of W boson. The Soft Signal Region keeps a good sensitivity even below thelimit, until the mass diﬀerence becomes smaller than 15 GeV. In case of more degenerate signals, which
do not emit any detectable leptons, 0-lepton analysis takes the place of Soft Lepton analysis.
Other regions are almost solely covered by the Tight Signal Region. The stringent ETmiss thresholdof the Tight Signal Region (ETmiss >350 GeV) is the next possibility of sensitivity loss. The sensitivity
drop for mχ̃0 >500 GeV in Fig. 63 is mainly caused by this feature. In most of models, gluino mass is
1much heavier than electroweak gauginos therefore x is expected to be small. Since ETmiss is roughly
proportional to the mass diﬀerence between chargino and LSP, the signal models assuming a chargino
mass halfway between gluino and LSP gives a harder ETmiss distribution than usual models. So the Half-x
Simplified model gives optimistic cases. But even in such cases, LSP mass heavier than 500 GeV is not
excluded in our analysis, which puts an important exception on our limit. In addition, meﬀ becomes small
for a heavy LSP mass scenario because some fraction of the total energy is consumed to create heavy
LSPs, leaving a small fraction of energy for visible particles, therefore we loose sensitivity further.
The low x regime in Fig. 62 is not excluded, which is explained by the soft mT tendency due to thesmall opening angle between LSP and lepton (this tendency is clearly seen in Fig. 39). At mg̃ =1000 GeV,
the sensitivity is lost around x = 0.1, where mχ̃±1 is 154 GeV and mχ̃0 is 60 GeV. Only an energy of 94 GeV
1
is available to produce and boost a W boson, thus the W boson is emitted almost the same direction as
its parent chargino. The mass splitting between the gluino and chargino, on the other hand, is 846 GeV,
therefore the chargino has a large momentum compared with the W boson, resulting in a small opening
angle between the lepton and LSP. Such a case is also an exception of our limit.

100Then, we set a model-independent cross-section limit for g̃-g̃ productions. This limit can be interpreted in any models as far as they contain g̃-g̃ productions. Simplified Models assume 100% branching
fraction for g̃ → qqW (∗) χ̃01 . In general SUSY models, the decay branch is suppressed due to several
competitive decays, thus the cross-section limit is presented including the branching fraction Br (g̃ →qqW (∗) χ̃01 ). Requiring that both of the gluinos decay via charginos, the mass limit mg̃ >1000 GeV isinterpreted as the cross-section upper limit ofσ (g̃-g̃) × Br (g̃ → qqW (∗) χ̃01 )2 < 20 fb.
This limit is a good approximation independent of the gluino decay pattern except for the following
extreme cases:• The mass diﬀerence between the chargino and LSP is smaller than 15 GeV.
• The mass of LSP is larger than 500 GeV for mg̃ =1000 GeV.
• The mass diﬀerence between chargino and LSP is small compared with the mass diﬀerence between gluino and chargino. For mg̃ =1000 GeV and mχ̃0 =60 GeV, a chargino lighter than mχ̃±1 =150 GeV
1cannot be excluded.

101

9 Conclusion
Supersymmetry is one of the most attracting theories beyond the Standard Model. In the context of
R-parity conserving supersymmetry model, the supersymmetric particles are produced in pairs and thelightest supersymmetric particle (LSP) is stable. Large gluino and squark production cross-sections are
expected at the proton-proton collisions. Once gluinos and squarks are produced, they decay througha cascade of multiple stages to the final states with the LSP. The LSP is only weakly interacting andescapes detection, resulting in large missing transverse momentum ETmiss . The decay also accompanies
many hadronic jets and several leptons, which often give a distinct signature from the Standard Model
processes.
A general search for supersymmetry in final states with jets, missing transverse momentum and one√
isolated electron or muon, using 20.3 fb−1 of proton-proton collision data at s = 8 TeV recorded by the
ATLAS detector at the LHC in 2012 is presented in this thesis.
One of the notorious backgrounds in proton-proton colliders is QCD multi-jet, which has an overwhelming cross-section, can be suppressed by requiring an isolated lepton (electron or muon). Therefore,
leptonic analysis is an ideal way to search for new physics with small cross-sections at the LHC. Basedon a topology selection of one lepton, large ETmiss and multiple jets, three signal regions are introduced tocover a wide range of signals in terms of diﬀerent production processes and degenerate particle spectra.
They are optimized based on the characteristic kinematic shapes of signals and further tuned using a fullscan over all combinations of thresholds.
Tight Signal Region is optimized to be sensitive to the signals starting from gluino pair productions
with a suﬃciently large mass splitting between chargino and LSP. Loose Signal Region is designed tocover light squark pair productions, where small number of jets are expected. And finally, Soft Signal
Region is defined to be sensitive to the degenerate region where the mass splitting between chargino and
LSP is smaller than the mass of W boson.
The QCD multi-jet background is estimated in a data-driven way using Matrix-Method. The otherbackgrounds are estimated based on Monte Carlo simulations. Dominant background components, tt¯
and W+jets, are normalized in Control Regions, which are designed to select the events having similar
topologies to the events in Signal Region to cancel generator uncertainties. Mis-modelings in ISR emulation are further corrected based on data. As a result, our background estimation gives suﬃciently good
agreements to data, which is confirmed in dedicated Validation Regions and makes the analysis morereliable.
No excess over the Standard Model expectation is found in the Signal Regions, therefore the results
are interpreted as mass limits in two models. In the MSUGRA/CMSSM model with tan β = 30, A0 =−2 m0 and µ > 0, a gluino mass up to 1200 GeV is excluded at 95% C.L. for all range of universal
scalar mass m0 and universal gaugino mass m1/2 , and a squark mass is excluded up to 1500 GeV withan exception of m0 < 500 GeV. In the Simplified models with the chargino mass halfway between themasses of the gluino/squark and LSP, gluinos (squarks) are excluded for masses below approximately
1200 (750) GeV for low values of the LSP mass. For the LSP mass of 500 GeV, gluino masses are
excluded up to 1000 GeV. In the Simplified model with a fixed LSP mass and varying chargino andgluino/squark masses, gluino (squark) below approximately 1200 (750) GeV are excluded for a wide
range of chargino masses.
The mass limit of mg̃ >1000 GeV is interpreted as an upper limit on the cross-section times branching
fraction on the gluino pair-production cross-section σ (g̃-g̃) and branching fraction Br (g̃ → qqW (∗) χ̃01 ),which isσ (g̃-g̃) × Br (g̃ → qqW (∗) χ̃01 )2 < 20 fb.
This limit is a good approximation independent of the gluino decay pattern except for the following

102extreme cases:• The mass diﬀerence between the chargino and LSP is smaller than 15 GeV.
• The mass of LSP is larger than 500 GeV for mg̃ =1000 GeV.
• The mass diﬀerence between chargino and LSP is small compared with the mass diﬀerence between gluino and chargino. For mg̃ =1000 GeV and mχ̃0 =60 GeV, a chargino lighter than mχ̃±1 =150 GeV
1cannot be excluded.

103

Acknowledgements
I am really grateful to my supervisor, Prof. Shoji Asai, for helpful suggestions both for my analysis andfor my private life. His positive attitude towards new physics always encourages me.
I would like to thank Prof. Naoko Kanaya. The discussion with her is always useful to unveil thestructure of problems and gives me clues to the solutions.
I appreciate Dr. Shimpei Yamamoto and Prof. Junichi Tanaka for useful suggestions and for maintaining the computing resources in CERN.
I would appreciate Dr. Yosuke Kataoka and Dr. Takashi Yamanaka for their deep understanding of
the ATLAS detector and Athena framework. They always give me clear suggestions when I encounter
problems.
I am also thankful to all the professors, staﬀs, and students of analysis group in ICEPP, the University of Tokyo for fruitful discussions and supports during my stay at CERN. I would like to thankProf. Tatsuo Kawamoto, Prof. Tomio Kobayashi, Prof. Koji Terashi, Dr. Tatsuya Masubuchi, Dr. Koji
Nakamura, Dr. Taiki Yamamura, Dr. Yuji Enari, Dr. Keita Hanawa, Ginga Akimoto, Dr. Yuya Azuma,
Dr. Hiroshi Yamaguchi, Shingo Kazama, Keisuke Yoshihara, Youhei Yamaguchi, Youichi Ninomiya,
Masahiro Morinaga, Maya Okawa, and Yuki Kawanishi.
I would like to appreciate the members of analysis group at CERN: Dr. Aleksej Koutsman, Prof. Max
Baak, Prof. Marie-Helene Genest, Dr. Zachary Louis Marshall, Ms. Jeanette Miriam Lorentz, Dr. Evgeny
Khramov, Dr. Pedro Salvador Urrejola Pereira, Ms. Marija Vranjes Milosavljevic, Mr. Adrian Chitan,
Ms. Kuwertz Emma Sian and Ms. Tudorache Valentina.
I am thankful to all members of the ATLAS collaboration and the LHC experts. Without their eﬀorts,
my work would not be completed.
I appreciate Prof. Claudio Santoni for useful discussion for the tile calorimeter calibration.
Finally, I would like to thank my family for supporting my life.

104

References[1] ATLAS Collaboration Collaboration, Combined measurements of the mass and signal strength of
the Higgs-like boson with the ATLAS detector using up to 25 fb−1 of proton-proton collision data,
Tech. Rep. ATLAS-CONF-2013-014, CERN, Geneva, 2013.
[2] E. Komatsu et al., Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations:Cosmological Interpretation, The Astrophysical Journal Supplement Series 192 (2011) no. 2, 18.
[3] U. Amaldi, W. de Boer, and H. Fürstenau, Comparison of grand unified theories with electroweak
and strong coupling constants measured at LEP, Physics Letters B 260 (1991) no. 3-4, 447–455.
[4] S. P. Martin, A Supersymmetry primer, arXiv:hep-ph/9709356 [hep-ph].
[5] L. Hall, D. Pinner, and J. Ruderman, A natural SUSY Higgs near 125 GeV, Journal of HighEnergy Physics 2012 (2012) no. 4, 1–25.
[6] ATLAS Collaboration, Combined coupling measurements of the Higgs-like boson with the ATLAS
detector using up to 25 fb−1 of proton-proton collision data, Tech. Rep. ATLAS-CONF-2013-034,
CERN, Geneva, Mar, 2013.
[7] L. Randall and M. Reece, Single-scale natural SUSY, Journal of High Energy Physics 2013 (2013)
no. 8, 1–31.
[8] M. Papucci, J. Ruderman, and A. Weiler, Natural SUSY endures, Journal of High Energy Physics
2012 (2012) no. 9, 1–45.
[9] L. Evans and P. Bryant, LHC Machine, Journal of Instrumentation 3 (2008) no. 08, S08001.
[10] CMS Collaboration, CMS technical proposal, tech. rep., CERN, CERN-LHCC-894-38, 1994.
[11] LHCb Collaboration, LHCb technical proposal, tech. rep., CERN, CERN-LHCC-98-004, 1994.
[12] ALICE Collaboration, ALICE: Technical proposal for a Large Ion collider Experiment at the
CERN LHC, tech. rep., CERN, CERN-LHCC-95-71, 1997.
[13] ATLAS Collaboration, ATLAS detector and physics performance : Technical Design Report, 1,
ATLAS-TDR-014, CERN-LHCC-99-014, 1999.
[14] ATLAS Collaboration, ATLAS detector and physics performance : Technical Design Report, 2,
ATLAS-TDR-015, CERN-LHCC-99-015, 1999.
[15] ATLAS Collaboration, T. A. collaboration, ATLAS Experiment at the CERN Large Hadron
Collider, JINST 3 (2008) S08003.
[16] G. Andres et al., LHC Bunch Current Normalisation for the April-May 2010 Luminosity
Calibration Measurements, CERN-ATS-Note-2011-004, 2011.
[17] W. L. et al., Calorimeter Clustering Algorithms: Description and Performance,
ATL-LARG-PUB-2008-002, 2008.
[18] M. Cacciari and G. P. Salam, Dspelling the N 3 myth for the kt jet-finder, Phys. Lett. B 641 (2006)
57–61.

105

[19] M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, Journal of HighEnergy Physics 2008 (2008) no. 04, 063.
[20] G. C. Blazey, J. R. Dittmann, S. D. Ellis, V. D. Elvira, K. Frame, S. Grinstein, R. Hirosky,
R. Piegaia, H. Schellman, R. Snihur, V. Sorin, and D. Zeppenfeld, Run II Jet Physics: Proceedingsof the Run II QCD and Weak Boson Physics Workshop, ArXiv High Energy Physics - Experimente-prints (2000) , hep-ex/0005012.
[21] ATLAS Collaboration, G. Aad et al., Jet energy measurement with the ATLAS detector in√proton-proton collisions at s = 7 TeV, Eur.Phys.J. C73 (2013) 2304, arXiv:1112.6426[hep-ex].
[22] M. Cacciari and G. P. Salam, Pileup subtraction using jet areas, Physics Letters B 659 (2008)
no. 1 - 2, 119 – 126.
[23] ATLAS Collaboration Collaboration, Pile-up corrections for jets from proton-proton collisions at√
s = 7 TeV in ATLAS in 2011, Tech. Rep. ATLAS-CONF-2012-064, CERN, Geneva, Jul, 2012.
[24] ATLAS Collaboration, Commissioning of the ATLAS high-performance b-tagging algorithms inthe 7 TeV collision data, ATLAS-CONF-2011-102, 2011.
[25] G. Piacquadio and C. Weiser, A new inclusive secondary vertex algorithm for b-jet tagging in
ATLAS, IEEE Transactions on Nuclear Science 57 (2010) no. 2, 760.
[26] ATLAS Collaboration, Expected electron performance in the ATLAS experiment,
ATL-PHYS-PUB-2011-006, 2011.
[27] ATLAS Collaboration, Electron performance measurements with the ATLAS detector using the2010 LHC proton-proton collision data, The European Physical Journal C 72 (2012) no. 3, 1–46.
[28] ATLAS Collaboration, G. Aad et al., Expected Performance of the ATLAS Experiment - Detector,
Trigger and Physics, arXiv:0901.0512 [hep-ex].
[29] S. Hassani, L. Chevalier, E. Lancon, J. Laporte, R. Nicolaidou, et al., A muon identification andcombined reconstruction procedure for the ATLAS detector at the LHC using the (MUONBOY,STACO, MuTag) reconstruction packages, Nucl.Instrum.Meth. A572 (2007) 77–79.
[30] Preliminary results on the muon reconstruction eﬃciency, momentum resolution, and momentum
scale in ATLAS 2012 pp collision data, Tech. Rep. ATLAS-CONF-2013-088, CERN, Geneva,
Aug, 2013.
[31] ATLAS Collaboration, Performance of Missing Transverse Momentum Reconstruction in ATLAS√
with 2011 Proton-Proton Collisions at s = 7 TeV, ATLAS-CONF-2012-101, 2012.
√[32] ATLAS Collaboration, Improved luminosity determination in pp collisions at s = 7 TeV using
the ATLAS detector at the LHC, The European Physical Journal C 73 (2013) no. 8, 1–39.
[33] GEANT4 Collaboration, S. Agostinelli et al., GEANT4: A Simulation toolkit, Nucl.Instrum.Meth.
A506 (2003) 250–303.
[34] A. Buckley et al., General-purpose event generators for LHC physics, Physics Reports 504 (2011)no. 5, 145 – 233.

106

[35] J. Alwall et al., Comparative study of various algorithms for the merging of parton showers andmatrix elements in hadronic collisions, The European Physical Journal C 53 (2008) no. 3,
473–500.
[36] F. Krauss, Matrix Elements and Parton Showers in Hadronic Interactions, Journal of High Energy
Physics 2002 (2002) no. 08, 015.
[37] S. Catani, F. Krauss, B. R. Webber, and R. Kuhn, QCD Matrix Elements + Parton Showers,
Journal of High Energy Physics 2001 (2001) no. 11, 063.
[38] V. Gribov and L. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov.J.Nucl.Phys. 15(1972) 438–450.
[39] G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl.Phys. B126 (1977) 298.
[40] Y. L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+ eAnnihilation by Perturbation Theory in Quantum Chromodynamics., Sov.Phys.JETP 46 (1977)
641–653.
[41] T. Sjostrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1, Computer Physics
Communications 178 (2008) no. 11, 852 – 867.
[42] ATLAS Collaboration, Further ATLAS tunes of Pythia6 and Pythia8, ATL-PHYS-PUB-2011-014,
2011.
[43] A. Martin, W. Stirling, R. Thorne, and G. Watt, Parton distributions for the LHC, The European
Physical Journal C 63 (2009) no. 2, 189–285.
[44] A. Martin, W. Stirling, R. Thorne, and G. Watt, Uncertainties on αS in global PDF analyses andimplications forpredicted hadronic cross secions, The European Physical Journal C 64 (2009)
no. 4, 653–680.
[45] A. Martin, W. Stirling, R. Thorne, and G. Watt, Heavy-quark mass dependence in global PDF
analyses and 3- and 4-flavour parton distributions, The European Physical Journal C 70 (2010)
no. 1-2, 51–72.
[46] T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, et al., Event generation withSHERPA 1.1, JHEP 0902 (2009) 007, arXiv:0811.4622 [hep-ph].
[47] H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky, J. Pumplin, and C.-P. Yuan, New parton
distributions for collider physics, Phys. Rev. D 82 (2010) 074024.
[48] S. Catani and M. Grazzini, Next-to-Next-to-Leading-Order Subtraction Formalism in Hadron
Collisions and its Application to Higgs-Boson Production at the Large Hadron Collider, Phys.
Rev. Lett. 98 (2007) 222002.
[49] S. Catani, L. Cieri, G. Ferrera, D. de Florian, and M. Grazzini, Vector Boson Production at
Hadron Colliders: A Fully Exclusive QCD Calculation at Next-to-Next-to-Leading Order, Phys.
Rev. Lett. 103 (2009) 082001.
[50] S. Frixione, P. Nason, and G. Ridolfi, A Positive-weight next-to-leading-order Monte Carlo forheavy flavour hadroproduction, JHEP 0709 (2007) 126, arXiv:0707.3088 [hep-ph].

107

[51] D. Stump, J. Huston, J. Pumplin, W.-K. Tung, H.-L. Lai, S. Kuhlmann, and J. F. Owens, Inclusive
jet production, parton distributions, and the search for new physics, Journal of High Energy
Physics 2003 (2003) no. 10, 046.
[52] S. M. T. Sjostrand and P. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026,
arXiv:hep-ph/0603175.
[53] P. Z. Skands, Tuning Monte Carlo generators: The Perugia tunes, Phys. Rev. D 82 (2010) 074018.
[54] M. Aliev, H. Lacker, U. Langenfeld, S. Moch, P. Uwer, and M. Wiedermann, HATHOR ―HAdronic Top and Heavy quarks crOss section calculatoR, Computer Physics Communications
182 (2011) no. 4, 1034 – 1046.
[55] M. Botje, J. Butterworth, A. Cooper-Sarkar, A. de Roeck, J. Feltesse, et al., The PDF4LHC
Working Group Interim Recommendations, arXiv:1101.0538 [hep-ph].
[56] B. P. Kersevan and E. Richter-Was, The Monte Carlo event generator AcerMC versions 2.0 to 3.8
with interfaces to PYTHIA 6.4, HERWIG 6.5 and ARIADNE 4.1, Computer Physics
Communications 184 (2013) no. 3, 919 – 985.
[57] N. Kidonakis, Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel
single top quark production, Phys. Rev. D 83 (2011) 091503.
[58] N. Kidonakis, Next-to-next-to-leading logarithm resummation for s-channel single top quark
production, Phys. Rev. D 81 (2010) 054028.
[59] N. Kidonakis, Two-loop soft anomalous dimensions for single top quark associated production
with a W − or H − , Phys. Rev. D 82 (2010) 054018.
[60] S. Frixione, E. Laenen, P. Motylinski, B. Webber, and C. D. White, Single-top hadroproduction inassociation with a W boson, arXiv:0805.3067 [hep-ex].
[61] E. Re, Single-top Wt-channel production matched with parton showers using the POWHEG
method, arXiv:1009.2450 [hep-ex].
[62] J. Campbell and R. K. Ellis, Radiative corrections to Zbb production, Phys. Rev. D 62 (2000)
114012.
[63] J. Alwall et al., MadGraph/MadEvent v4: The New Web Generation, JHEP 09 (2007) 028,
arXiv:0706.2334 [hep-ph].
[64] J. M. Campbell and R. K. Ellis, tt¯W ± production and decay at NLO, JHEP 1207 (2012) 052,
arXiv:1204.5678 [hep-ph].
[65] M. Garzelli, A. Kardos, C. Papadopoulos, and Z. Trcsnyi, tt¯W ± + tt¯Z hadroproduction at NLO
accuracy in QCD with Parton Shower and Hadronization eﬀects, Journal of High Energy Physics
2012 (2012) no. 11, 1–21.
[66] D. Alves et al., Simplified models for LHC new physics searches, Journal of Physics G: Nuclear
and Particle Physics 39 (2012) no. 10, 105005.
[67] ATLAS Collaboration, Observation of a new particle in the search for the Standard Model Higgs
boson with the ATLAS detector at the LHC, Physics Letters B 716 (2012) no. 1, 1 – 29.

108

[68] W. Beenakker, S. Brensing, M. Krämer, A. Kulesza, E. Laenen, L. Motyka, and I. Niessen, Squarkand gluino hadroproduction, Int. J. Mod. Phys. A26 (2011) 2637–2664.
[69] W. Beenakker, R. Hopker, M. Spira, and P. Zerwas, Squark and gluino production at hadroncolliders, Nucl. Phys. B492 (1997) 51.
[70] A. Djouadi, M. Muhlleitner, and M. Spira, Decays of supersymmetric particles: The Program
SUSY-HIT (SUspect-SdecaY-Hdecay-InTerface), Acta Phys. Polon. B38 (2007) 635–644,
arXiv:hep-ph/0609292.
[71] B. C. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys.
Commun. 143 (2002) 305–331, arXiv:hep-ph/0104145.
[72] M. Muhlleitner, A. Djouadi, and Y. Mambrini, SDECAY: A Fortran code for the decays of thesupersymmetric particles in the MSSM, Comput. Phys. Commun. 168 (2005) 46–70,
arXiv:hep-ph/0311167.
[73] M. B. et al., Herwig++ Physics and Manual, Eur. Phys. J. C58 (2008) 639.
[74] DELPHI Collaboration, Searches for supersymmetric particles in e+ e- collisions up to 208 GeV
and interpretation of the results within the MSSM, The European Physical Journal C - Particles
and Fields 31 (2003) no. 4, 421–479.
[75] ATLAS Collaboration, ATLAS tunes of Pythia6 and Pythia8 for MC11,
ATL-PHYS-PUB-2011-009, 2011.
[76] H.-L. Lai, J. Huston, Z. Li, P. Nadolsky, J. Pumplin, et al., Uncertainty induced by QCD couplingin the CTEQ global analysis of parton distributions, Phys.Rev. D82 (2010) 054021,
arXiv:1004.4624 [hep-ph].
[77] P. M. Nadolsky, H.-L. Lai, Q.-H. Cao, J. Huston, J. Pumplin, et al., Implications of CTEQ global
analysis for collider observables, Phys.Rev. D78 (2008) 013004, arXiv:0802.0007 [hep-ph].
√[78] ATLAS Collaboration, Further search for supersymmetry at s=7 TeV in final states with jets,
missing transverse momentum, and isolated leptons with the ATLAS detector, Phys. Rev. D 86
(2012) 092002.
[79] Search for squarks and gluinos with the ATLAS detector in final states with jets and missing√
transverse momentum and 20.3 fb−1 of s = 8 TeV proton-proton collision data, Tech. Rep.
ATLAS-CONF-2013-047, CERN, Geneva, May, 2013.
[80] ATLAS Collaboration, Electron performance measurements with the ATLAS detector using the2010 LHC proton-proton collision data, The European Physical Journal C 72 (2012) no. 3, 1–46.
[81] G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Asymptotic formulae for likelihood-based tests of
new physics, The European Physical Journal C 71 (2011) no. 2, 1–19.
[82] ATLAS Collaboration, ATLAS muon spectrometer: Technical Design Report. Technical Design
Report ATLAS. CERN, Geneva, 1997. distribution.
[83] ATLAS Collaboration, ATLAS magnet system: Technical Design Report, 1. Technical Design
Report ATLAS. CERN, Geneva, 1997.
[84] J. Allison et al., Geant4 developments and applications, Nuclear Science, IEEE Transactions on
53 (2006) no. 1, 270–278.
109

[85] E. Lund, L. Bugge, I. Gavrilenko, and A. Strandlie, Track parameter propagation through theapplication of a new adaptive Runge-Kutta-Nystroem method in the ATLAS experiment, JINST 4(2009) P04001.
[86] ATLAS Collaboration, Testbeam studies of production modules of the ATLAS Tile Calorimeter,
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment 606 (2009) no. 3, 362 – 394.

110

A Higgs mechanism
A.1 Electroweak theory
Considering a W boson decay such as W + → l+L + νL , or its transposition l−L + W + → νL , in which theleft-handed down-type lepton is converted to the left-handed neutrino (up-type), one presumes the correspondence between W boson and the raising operator of SU(2)L . Here using the Pauli spin matrix (τi ,i = 0, 1, 2), raising (lowering) operator (τ+(−) ) is defined as τ± = 12 (τ1 ± iτ2 ). The interaction of 0-th Paulimatrix might be then presumed to be the counterpart of Z 0 boson, however, the past experiments showthat Z 0 boson interacts not only left-handed but also right-handed fermions. Therefore, the counterpartof 0-th Pauli matrix, W 0 , must be mixed with another interaction. A U(1) interaction is introduced forthis purpose (subscript Y is assigned), which is blind to SU(2)L charge but proportional to weak hypercharge Y. We define weak hypercharge Y for each particle so that electromagnetic charge Q (in a unit ofe) and the eigenvalue of the weak charge T 0 satisfy the following relation:Y.
2

Q = T0 +(79)

The interaction Lagrangian, then, consists of three vector fields Wµi coupled with strength g to weakisospin current Jµi , together with a single vector field Bµ coupled to weak hypercharge current jYµ , withstrength conventionally taken to be g0 /2. The Lagrangian is constructed as
Lint = −ig(J i )µ Wµi − i

g0 Y µ( j ) Bµ .
2(80)

Since no physical correspondence is observed for Wµ0 and Bµ , they must mix in such a way that to giveZ 0 boson and a photon A0 .
{ 0Aµ = Bµ cos θW + Wµ0 sin θW(81)
Zµ0 = −Bµ sin θW + Wµ0 cos θWwhere θW is called Weinberg angle.
Considering Eq. 79-81, the following relation holds,µ
Lint = −ie jEMµ A −iwhere,g
J NC Z µ ,cos θW µjEM=
Jµ0 + 12 jYµ
µ
NC
0
Jµ
= Jµ − sin2 θW jEM
µ

(82)

(83)

Electromagnetic and weak forces are united in this picture, therefore, this theory is called electroweak
theory.

A.2 Gauge theory
Gauge theory derives the interactions between fermions and gauge bosons from symmetries. In theprevious section, we’ve already seen that electroweak theory consists of SU(2)L and U(1)Y symmetries.
In this section, we discuss the concept in more detail.
We start from considering the following transformation
Ψ(x) → eiα(x) Ψ(x),(84)

where Ψ(x) is a Dirac field and α(x) is a phase parameter depending on space and time in a completely
arbitrary way. The following Lagrangian is required to be invariant under the transformation,
L = iΨ̄γµ ∂µ Ψ − mΨ̄Ψ.
111

(85)

This is not attainable when α is a function of space-time, because the partial derivative gives rise to an
extra term as∂µ Ψ → eiα(x) ∂µ Ψ + ieiα(x) Ψ∂µ α(x).
(86)
To remove the last term, we introduce a modified derivative, Dµ or “covariant derivative”, so that theterm is invariant under the transformation
Dµ Ψ → eiα(x) Dµ Ψ.

(87)

We must introduce a vector field Aµ with transformation properties such that the unwanted term is canceled. This can be accomplished by the construction,Dµ = ∂µ − ieAµ ,(88)

where Aµ transforms as,

1
Aµ → Aµ + ∂µ α(x).
(89)
eBy replacing ∂µ by Dµ , the Lagrangian obtains the invariance to the arbitrary phase transformation.
The Lagrangian is thenL = iΨ̄γµ Dµ Ψ − mΨ̄Ψ
µ

(90)
µ

= Ψ̄(iγ ∂µ − m)Ψ + eΨ̄γ ΨAµ .

(91)

The first term in the last line is the kinematic term of the Dirac particle and the second term represents
the interaction of a photon Aµ and the Dirac particle with an electric charge of −e.
The same procedure is applicable to weak isospin symmetry SU(2)L , which gives the weak interaction Lagrangian. However, it is known that a trivial mass term breaks the gauge invariance. This is easily
understood for U(1)Y symmetry case as follow,
1
1
1
1
1
− m2 Aµ Aµ → − m2 (Aµ + ∂µ α)(Aµ + ∂µ α) , − m2 Aµ Aµ .
2
2
e
e
2

(92)

This fact casts a shadow on the gauge theory of weak force because weak bosons are known as
massive particles, therefore a special mechanism should be introduced to bear mass without adding atrivial mass term.

A.3 Higgs mechanism
The Higgs mechanism introduces an SU(2)L doublet of complex scalar fields:)(
1
φ1 + iφ2,
φ= √2 φ3 + iφ4(93)

and considers the Lagrangian
L = (∂µ φ)† (∂µ φ) − µ2 φ† φ − λ(φ† φ)2 ,(94)

where µ2 < 0 and λ > 0. The first term represents the kinematic energy followed by a negative massterm and a four-point interaction term. The latter two terms are interpreted as a potential of φ field anddenoted as V(φ).
To keep the Lagrangian invariant under SU(2)L transformation,
φ → φ0 = eiαa τa /2 φ,
112

(95)

the partial derivative ∂µ is replaced by the covariant derivative,
Dµ = ∂µ + ig

τa a
W .
2 µ

(96)

Here we introduced three gauge fields of SU(2)L , Wµa (x), with a = 0, 1, 2. For an infinitesimal gaugetransformation of α (here the three components are represented in the form of vector), the gauge fields,
Wµ , transform as,
1
Wµ → Wµ − ∂ µ α − α × Wµ .
(97)
g
The potential V(φ) is not stable at φ = 0 because of the negative mass term. The minimal of thepotential is realized when the following relation is satisfied:φ† φ =)1( 2µ2
φ1 + φ22 + φ23 + φ24 = − .
2
2λ

(98)

φ† φ is invariant under SU(2)L transformation, therefore we can choose
φ1 = φ2 = φ4 = 0, φ23 = −µ2≡ v2 ,
λwithout loosing generality. v is called vacuum expectation value and often abbreviated as VEV.
We now expand φ(x) about this particular vacuum:( )10
φ0 ≡ √.
2 v
A small variation around φ0 along the real axis gives a new particle field, Higgs particle H(x),
(
)
1
0
.
φ(x) = √2 v + H(x)

(99)

(100)

(101)

This choice seems arbitrary, however, due to the gauge symmetry, we can always choose the direction
along the real axis. By expanding the potential V(φ) around φ0 , we get the term proportional to H 2 ,which gives a positive Higgs mass of√
mH = 2v2 λ.
(102)
The goal of the Higgs mechanism is to make electroweak bosons massive without introducing a trivial mass term. Now one specific vacuum point φ0 is chosen as a stable state (Spontaneous Symmetry
Breaking: SSB), and the quadrature of electroweak boson fields appears though the covariant derivative (Eq. 96). The mass term, including all the electroweak gauge symmetries, is then represented asfollow:() 2 ()2) ( g2 −gg0 ) ( W 0µ )
τa a
1
g0
1( 0
+ −µ
−ig Wµ − i Bµ φ0 = vg Wµ W + Wµ , Bµ(103)
Bµ−gg0 g02
2
2
2
8
The boson masses are, then,
1
vg,
2 √
1
m(Z 0 ) =v g2 + g02 ,2
m(A0 ) = 0.

m(W ± ) =

113

(104)
(105)
(106)

Massless bosons have only two degrees of freedom, while massive bosons have three. The additional
degree is provided from the three components in the original scalar doublet, φ1 , φ2 , φ4 . The remaining
one degree of freedom is observed as the physical Higgs particle, H(x).
In the framework of the Higgs mechanism, fermion mass is also obtained though the vacuum expectation value. For an electron case, the mass Lagrangian is
)
(
(107)
Lelectron mass = −ye L̄φ0 eR + ēR φ†0 L
ye v= − √ ēe,
(108)
2
)
(
νL
, eR
where L is the weak isospin doublet for left-handed leptons of the first generation, L =eLis the right-handed electron and ye is a constant called Yukawa coupling. The Yukawa coupling ye isdetermined by the following mass relation,ye v
me = √ .
2(109)

The Higgs mechanism doesn’t predict fermion mass, however, several implications, such as the proportional coupling strength to the fermion mass, can be inferred.

114

B Details of Signal Region optimization
B.1 Setup
As discussed in the text, an ideal way of optimization is to test all the possible combinations of selections
and find the best set. Therefore we perform a sensitivity scan over all combinations of thresholds listed
in Table 25. In total 12960 (Hard Lepton) and 10800 (Soft Lepton) trial signal regions C are defined
uniformly in the phase space spanned by the kinematic variables. The numbers of events of signal andbackground are then converted into Score ΨCQ , which is defined as
1 ∑median[Z0 |S i0 , C + BC0 ],N(Q) i
Q

ΨCQ =

(110)

where Q is the collection of signals in which the selection C is optimized and N(Q) is the number ofthe signals. Typical tendencies over the signal collections can be obtained by taking the average of thescores.
median[Z0 |S C + BC ] ∼√2((S C + BC ) ln(1 + S C /BC ) − S C ),(111)

where S C (BC ) is the number of signal (background) events after applying cut C. median[Z0 |S C + BC ]gives an approximate sensitivity based on Profile-likelihood method (detail is given in Section H). To
take uncertainties ∆S C , ∆BC into account, the following event numbers are used in Eq. 110
S C → S C0 = S C − ∆S C ,

(112)

BC →

(113)

BC0 = BC + ∆BC .

This configuration gives the most conservative sensitivity. The size of the uncertainties are set to 30%
for both signal and background. Since signal regions are dominated by statistical errors, the optimization
is not aﬀected if we use 50% for the uncertainty.
One practical diﬃculty occurs when one of the background samples lefts no event after a harsh cut,which gives unphysical optimization results. To avoid this problem, the minimum number of events is
set for the major background samples: W+jets and tt¯. Since tt¯ events are generated plenty enough, theminimum number is set to 0, while that of W+jets is set to 2.5 events.
Before scanning the cuts, the following conditions are applied as pre-selections:Hard Lepton pre-selection :• Exactly 1 signal lepton,• No crack electron.
Soft Lepton pre-selection :• Exactly 1 soft signal lepton,• No crack electron,• min ∆R(lep, jet) > 1.0.
jet

Table 26 shows the signal models and parameter spaces used to define Q for each signal region.
The parameter spaces are chosen so that the signals with representative topologies are selected. Notethat Hard Lepton SR (Tight, Loose) and Soft SR are defined orthogonally by the diﬀerent lepton pT
selections, while Tight and Loose SRs may have an overlap. The overlap is resolved by requiring an
upper limit on the number of jets in Loose Signal Region in the final limit calculation, but it is notconsidered in the optimization procedure.
115

Variable

Trial thresholds
Hard Lepton
40
Njet ≥[3, 4, 5, 6]

#jets
jet1

pT
jet2
pT
mT
ETmissmeﬀ[80, 120, 160, 200, 240]
[40, 70, 100, 130, 160, 190]
[100, 150, 200]
[200, 250, 300, 350, 400, 450]
[400, 800, 1200, 1600, 2000, 2400]

Soft Lepton
30 ≥[3, 4, 5, 6]
Njet[30, 60, 90, 120, 150]
[30, 60, 90, 120, 150]
[100, 120, 150]
[200, 250, 300, 350, 400, 450]
[400, 800, 1200, 1600, 2000, 2400]

Table 25: List of the kinematic variables and their trial thresholds.

Signal Region
Tight
Loose

Soft

Signal Model
Simplified Modelg̃-g̃ production
Simplified Modelq̃-q̃ production
Simplified Modelg̃-g̃ production

Parameter spacemχ̃0 =60 GeV
1mg̃ =1000-1300 GeVmχ̃0 =60 GeV
1mq̃ =450-600 GeV
x <0.3mχ̃0 >60 GeV
1mg̃ =500-800 GeV(mg̃ -mχ̃0 )<200 GeV
1

Table 26: Combination of Signal model and the parameter space which defines Q for each signal region.
x ≡ (mχ̃±1 − mχ̃0 )/(mg̃/q̃ − mχ̃0 ).
1

1

116

B.2 Results
The top panels of Fig. 66-68 show the Score ΦC distributions for Tight, Loose and Soft SRs, respectively.
The scores are classified to low (blue), middle (purple) high (orange) groups. The thresholds of thesegroups are chosen so that clear tendencies are seen with meaningful statistics. Our goal is to withdraw
the characteristics of the selections classified to high score group. To visualize the characteristics, distributions of the thresholds are shown in the bottom panels of Fig. 66-68. They are all normalized sothat the largest bin is always 1, and the colors correspond to the ones in the score distributions in the top
panel.
40 histogram of Fig. 66 as an example. The orange broken line shows a histogram of the
We take Njet
thresholds classified as high-scored group. The histogram peaks at N 40
jets = 5, which means the highscored selections tend to favor the number of jets larger than five. This is an expected result as we foundin Section 5.1.4. With a close look at the histograms, we get the following insights:
Tight SR :jet1
• The number of jets N jet ≥5 is favored. The leading jet favors pT >120 GeV, while histogramof the next leading jet is constantly decreasing, which means the lower pT threshold is favoredfor the next leading jet.
• Tight mT selection is clearly favored. Although it cannot be read from the plot, mT >150 GeV
is favored in the high-scored group.
• Large meﬀ is favored due to heavy initial particles.
• High score group has a peak around 350 GeV. We then take ETmiss >350 GeV for the Tight SR.
Loose SR :• Small number of jets is favored. Thus the number of jets N jet ≥3 is chosen for the Loose SR.
• mT >120 GeV is favored.
• ETmiss >250GeV is clearly favored.
Soft SR :• High-scored group tend to favor lower values for the number of jets, the transverse momentum of the next leading jets, mT and meﬀ .
jet1

• pT

favors a moderate threshold. Here we use 100 GeV for the threshold.

• ETmiss plot peaks at around 300-400 GeV. We then require ETmiss >300 GeV.
Note that these observations are consistent with our findings in Section 5.1.4. The optimized results are
summarized in Table 12.

117

Number of Selections

102

10

0.2

0.4

0.6

0.8

1

1.2

1.4
Score

jet

N40

1
0.5
0

3

3.5

4

4.5

5

5.5

6

T

p

jet1

1
0.5
0

80

100

120

140

40

60

80

160

180

200

220

240

T

p

jet2

1
0.5
0

100

120

140

160

180

mT

1
0.5
0
100

105

110

115

120

125

130

135

140

145

150

600

800

1000

1200

1400

1600

1800

2000

2200

2400

mincl30
eff

1
0.5
0400

Emiss
T

1
0.5
0200

250

300

350

400

450

Figure 66: Plots used in the optimization of Tight SR are shown. (Top) Score distribution obtained in
the full threshold scan, separated by three colors, blue is for the low score, purple for the middle score,and orange for the high score. (Bottom) The distributions of the thresholds are shown. x-axes show
the minimum thresholds applied to the kinematic variables. The colors on top panel correspond to thehistograms in the bottom panel.

118

Number of Selections

103

102

10

1

10-1
0

1

2

3

4

5

6

7
Score

jet

N40

1
0.5
0

3

3.5

4

4.5

5

5.5

6

T

p

jet1

1
0.5
0

80

100

120

140

40

60

80

160

180

200

220

240

T

p

jet2

1
0.5
0

100

120

140

160

180

mT

1
0.5
0
100

105

110

115

120

125

130

135

140

145

150

600

800

1000

1200

1400

1600

1800

2000

2200

2400

mincl30
eff

1
0.5
0400

Emiss
T

1
0.5
0200

250

300

350

400

450

Figure 67: Plots used in the optimization of Loose SR are shown. (Top) Score distribution obtained in
the full threshold scan, separated by three colors, blue is for the low score, purple for the middle score,and orange for the high score. (Bottom) The distributions of the thresholds are shown. x-axes show
the minimum thresholds applied to the kinematic variables. The colors on top panel correspond to thehistograms in the bottom panel.

119Number of Selections

103

102

10

1

10-1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8
Score

jet

N30

1
0.5
0

3

3.5

4

4.5

5

5.5

6

T

p

jet1

1
0.5
0

40

60

80

100

120

140

40

60

80

100

120

140

T

p

jet2

1
0.5
0

mT

1
0.5
0
100

105

110

115

120

125

130

135

140

145

150

600

800

1000

1200

1400

1600

1800

2000

2200

2400

mincl30
eff

1
0.5
0400

Emiss
T

1
0.5
0200

250

300

350

400

450

Figure 68: Plots used in the optimization of Soft SR are shown. (Top) Score distribution obtained in
the full threshold scan, separated by three colors, blue is for the low score, purple for the middle score,and orange for the high score. (Bottom) The distributions of the thresholds are shown. x-axes show
the minimum thresholds applied to the kinematic variables. The colors on top panel correspond to thehistograms in the bottom panel.

120

C Matrix-Method
Matrix-Method estimates the shape and yield of QCD multi-jets from the diﬀerence between fakeenriched and fake-suppressed distributions. Fake-enriched region is defined by loosening the lepton
isolation to “Loose” conditions. Fake-suppressed region is defined by selecting “Signal” leptons. For
simplicity, we call these two leptons as Loose and Tight leptons. The diﬀerence between Loose andTight lepton definitions are summarized in Table 27 (electron) and 28 (muon). Their exact definitions
are documented in Tables 4, 5 (electron), 6, 7 (muon). We also abbreviate QCD multi-jet events as fakeevents.
items
Identification criteria
Track isolation
Transverse IP
Longitudinal IP

Hard Lepton
Medium++→Tight++
ptcone20/pT < 0.10
d0PV ≤1 mm|zPV
0 | ≤2 mm

Soft Lepton
ptcone30/pT < 0.16
|d0PV /σ(d0PV )| ≤5PV|z0 × sin(θ)| ≤0.4 mm

Table 27: Isolation conditions which defines Tight electron from Loose one.
items
Track isolation
Transverse IP
Longitudinal IP

Hard Lepton
ptcone20 < 1.8 GeV-Soft Lepton
ptcone30< 1.2 GeV|d0PV /σ(d0PV )| ≤3PV|z0 × sin(θ)| ≤0.4 mm

Table 28: Isolation conditions which defines Tight muon from Loose one.
The events with 1 Loose lepton are selected to define the population, and the number of events whose
lepton passes also Tight lepton selection is denoted as Npass , while the number of the failing events is
Nfail . Two eﬃciencies are defined for both real and fake leptons, based on the fraction of events passing
Tight lepton selection out of Loose lepton events,
N

Tight

N

Tight

real
fake
real = N Loose, fake = N Loose
.
real

(114)

fake

Then we consider the following relations,{
Npass =
fake · Nfake +real · Nreal,
Nfail = (1 − fake ) · Nfake + (1 − real ) · Nreal(115)

where Nreal and Nfake are the number of real and fake lepton events. The number of fake events passing
Tight
Tight lepton selection Nfake is obtained by solving Eq. 115,
Tight

Nfake = fake ·real · Nfail − (1 − real ) · Npass.
real − fake

(116)

Tight

Nfake gives the evaluation of QCD multi-jets that passes our Signal lepton selections.

C.1 Lepton misidentification rate
fake is evaluated in a dedicated Control Region (Multi-jets control region) using data. The multi-jet
Control Region is defined as follow:
121• ETmiss <30 GeV and mT <40 GeV.
• Exactly one Loose lepton. The lepton is also required to be separated from the overlap removal
jets (defined in Table 2) by ∆R > 0.4.
• At least one jet with pT >60 GeV.
The last item is applied so as to select the events with a topology close to our target kinematic selections.
However, fake is found to be robust against the jet pT and the number of jets.
Then fake is calculated by dividing the number of fake events surviving Tight lepton selection by the
total number of fake events passing Loose lepton selection. Real leptons from W+jets and Z+jets are
removed by using Monte Carlo, taking 20% of cross-section uncertainty into systematic errors. The following three regions are introduced to measure fake under b-tagged, b-vetoed and b-inclusive conditions.
Heavy Flavor enriched region At least one b-tagged jet is required.
Light Flavor enriched region No b-tagged jet is allowed.
Inclusive region Do no apply any requirements on b-tagged jets.
fake measured in Heavy Flavor (Light Flavor) enriched region is used in tt¯ (W+jets) Control Regions.
fake obtained in Inclusive region is used in the Validation and Signal Regions, where no b-jet selection
is required.
Figures 70 show fake for Hard (left) and Soft (right) electron selections in Inclusive region. Similarly,
Fig. 71 show fake for muons. Hard Lepton results are on the left column and soft lepton ones are on
the right. For better visualization, the graphs with diﬀerent η selections are superimposed with shifts
within the pT ranges. The gray vertical lines show the pT bins. The error bars include the systematic
errors from 20% uncertainty of W/Z+jets subtractions and the statistical uncertainties. Note that only
pT <25 (>25) GeV is used in Soft (Hard) lepton plots. fake measured in Heavy and Light flavor enriched
regions show similar values, with the diﬀerence of 5% at most.

C.2 Lepton identification eﬃciency
Isolation eﬃciencies for real leptons real are estimated by using tag-and-probe method [80] on Z 0 → ll
events. Control sample is selected by requiring the following conditions:• At least one electron (muon) which has pT >10 (6) GeV and fires a lepton trigger.
• Exactly two opposite sign and same flavor leptons which satisfy Loose lepton criteria (defined inTable 4, 5, 6, 7).
• Two leptons are well-separated from the overlap removal jets with ∆R > 0.4.
• The invariant mass of the two leptons must satisfy 80 GeV < mll < 100 GeV.
The mll and opposite sign selections ensure that the leptons are real leptons coming from Z 0 → ll.
Then one of the leptons is tested if it passes Tight lepton selection. Isolation eﬃciency real is calculatedby dividing the number of events passing Tight lepton selection by the total event numbers. Since thenumerator and denominator are not statistically independent, the following formula is used to calculate
correct statistical errors,√real (1 − real )stat∆real
=
.
(117)
Loose
Nreal
The diﬀerence in the values measured in data and Monte Carlo is taken as systematic errors. Figure 72
and 73 show real for electron and muon, respectively. No b-jet selections is applied. The error bars
include both systematic and statistical errors.
122C.3 Validation
To validate the methodology of Matrix-Method and the parameters obtained above, QCD multi-jet estimation is compared with data.Figure 69 shows the mT distributions after requiring 1 electron and at least
1 jet with pT >80 GeV. The yield and shape of QCD multi-jet component are correctly estimated within
the uncertainty band shown as the shaded area.

∫ Ldt=20.3fb , s=8TeV

Data(2013)
QCD
tt
W+jetsZ+jetsSingle Top
Dibosons
tt+V

-1

70000
60000
50000
40000
30000
20000

Ratio

10000
0
2

1
00

10

20

30

40

50

60

70

80

90 100mT [GeV]Figure 69: mT distribution for the electron channel after requiring 1 electron and at least 1 jet with
pT >80 GeV.

123

1.2

1.2
0.00<|η|<1.00

0.00<|η|<1.00

1

1

0.8

1.37<|η|<1.52

0.6

1.52<|η|<2.01

1.00<|η|<1.37

∈fake

∈fake

1.00<|η|<1.37

2.01<|η|<2.19

0.4

0.8

1.37<|η|<1.52

0.6

1.52<|η|<2.01

2.01<|η|<2.19

0.4

2.19<|η|<2.37

2.19<|η|<2.37

0.2

0.2
2.37<|η|<2.47

0
6 7 8 9 1020

2.37<|η|<2.47

0

2×102

102

30
40 50 60 70
p [GeV]6 7 8 9 10

T

20

2×102

102

30
40 50 60 70
p [GeV]T

Figure 70: fake of the electrons are plotted as a function of p`T for various η ranges. No b-jet requirement
is applied. Hard (Soft) Lepton result is shown on the left (right). For better visualization, the graphs with
diﬀerent η selections are superimposed with shifts within the pT ranges.

1.2

1.2
0.00<|η|<1.00

0.00<|η|<1.00

1

1

0.8

1.00<|η|<1.50

∈fake

∈fake

0.8

0.6

1.00<|η|<1.50

0.6

1.50<|η|<2.01

1.50<|η|<2.01

0.4

0.4

0.2

0.2

2.01<|η|<2.47

06

7 8 9 102030
p [GeV]40

50

60 70 80

2.01<|η|<2.47

0

102

6

T

7 8 9 102030
p [GeV]40

50

60 70 80

102

T

Figure 71: fake of the muons are plotted as a function of p`T for various η ranges. Hard (Soft) Lepton
result is shown on the left (right). For better visualization, the graphs with diﬀerent η selections aresuperimposed with shifts within the pT ranges.

124

1.2

1.2

0.00<|η|<0.80
0.80<|η|<1.37

10.00<|η|<0.80
0.80<|η|<1.37

1

1.37<|η|<1.52

1.37<|η|<1.52

1.52<|η|<1.80

0.8

1.52<|η|<1.80

0.8

2.00<|η|<2.10

0.6

1.80<|η|<2.00

∈real

∈real

1.80<|η|<2.00

2.00<|η|<2.10

0.6

2.10<|η|<2.20

0.4

2.10<|η|<2.20

0.4

2.20<|η|<2.30

2.20<|η|<2.30

2.30<|η|<2.40

0.2

2.30<|η|<2.40

0.2

2.40<|η|<2.45

2.40<|η|<2.45

2.45<|η|<2.50

0
6 7 8 910

20

30

40 50 60
p [GeV]102

2.45<|η|<2.50

02×102 3×102

6 7 8 910

20

30

T

40 50 60
p [GeV]102

2×102 3×102

T

Figure 72: real of electrons are plotted as a function of p`T for various η ranges. Hard (Soft) Lepton resultis shown on the left (right). For better visualization, the graphs are superimposed with shifts within thepT ranges.

1.2

1.2
0.00<|η|<0.80

0.00<|η|<0.80

1

1
0.80<|η|<1.37

1.37<|η|<1.52

0.6

0.4

0.80<|η|<1.37

0.8

∈real

∈real

0.8

1.37<|η|<1.52

0.6

0.4

1.52<|η|<2.00

0.2

1.52<|η|<2.00

0.2
2.00<|η|<2.50

0
6 7 8 910

20

30

40 50 60
p [GeV]102

2.00<|η|<2.50

02×102 3×102

6 7 8 910

T

20

30

40 50 60
p [GeV]102

2×102 3×102

T

Figure 73: real of muons are plotted as a function of p`T for various η ranges. Hard (Soft) Lepton resultis shown on the left (right). For better visualization, the graphs are superimposed with shifts within thepT ranges.

125

D Fit results for the Control Regions
Tables 29-31 show the fit results for the Loose, Tight and Soft Validation Regions. No signal is assumed
in the fitting. For detail, see the descriptions in Section 6.2.5.

126Tight WR (El)Tight WR (Mu)Tight TR (El)Tight TR (Mu)

27

36

18

22

bkg events

30.48 ± 4.51

32.32 ± 4.21

21.42 ± 3.61

18.24 ± 2.81tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

15.53 ± 4.96
10.87 ± 6.73
0.01+0.02−0.01
1.78 ± 0.95
1.61 ± 1.21
0.47 ± 0.11
0.20+0.27−0.20

13.70 ± 4.52
10.47 ± 6.36
0.12+0.12−0.12
4.53 ± 3.14
1.60 ± 1.34
0.32 ± 0.10
1.58 ± 1.34

17.31 ± 4.45
1.21 ± 0.76
0.00 ± 0.00
0.15+0.64−0.15
2.17 ± 1.60
0.49 ± 0.18
0.10+0.16−0.10

14.44 ± 3.70
1.16 ± 0.79
0.00 ± 0.00
0.00 ± 0.00
2.16 ± 1.82
0.43 ± 0.09
0.05+0.23−0.05

channelObserved events

Table 29: Background fit results for the Tight WR (El), Tight WR (Mu), Tight TR (El) and Tight
TR (Mu) for an integrated luminosity of 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.
Loose WR (El)

Loose WR (Mu)

Loose TR (El)

Loose TR (Mu)

363

303

183

144

bkg events

354.83 ± 13.82

310.67 ± 13.18

177.00 ± 10.33

150.61 ± 8.31

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

84.40 ± 23.39
221.41 ± 28.36
0.54 ± 0.19
31.21 ± 14.41
16.40 ± 11.16
0.72 ± 0.11
0.15+1.86−0.15

69.97 ± 20.10
203.98 ± 26.14
4.41 ± 1.55
17.17 ± 8.01
10.90 ± 7.46
0.61 ± 0.08
3.63+3.78−3.63

126.56 ± 21.08
20.51 ± 3.87
0.03 ± 0.01
6.36 ± 3.03
22.45 ± 15.12
1.07 ± 0.10
0.02+0.78−0.02

103.03 ± 17.07
17.02 ± 3.11
0.79 ± 0.35
8.18 ± 4.06
18.99 ± 12.69
0.90 ± 0.07
1.70+1.88−1.70

channelObserved events

Table 30: Background fit results for the Loose WR (El), Loose WR (Mu), Loose TR (El) and Loose
TR (Mu) for an integrated luminosity of 20.3 fb−1 . The errors shown are the statistical plus systematic
uncertainties.
Soft WR (El+Mu)

Soft TR (El+Mu)

2328

730

bkg events

2327.92 ± 50.26

729.99 ± 27.82

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

389.78 ± 82.87
1724.14 ± 128.66
14.95 ± 5.65
119.32 ± 61.58
58.23 ± 40.93
1.88 ± 0.27
19.62+38.35−19.62530.96 ± 60.65
107.21 ± 15.06
1.58 ± 0.49
15.09 ± 7.55
62.13 ± 43.26
2.64 ± 0.31
10.38+15.16−10.38channelObserved events

Table 31: Background fit results for the Soft WR (El+Mu) and Soft TR (El+Mu) for an integrated
luminosity of 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.

127

E Fit results for the Validation Regions
Tables 32-37 show the expect and observed event numbers in the Loose, Tight and Soft Validation Regions. Each region has two Validation Regions. One is to check the extrapolation along mT , called
VR (mT ), while the other one is to check the extrapolation along ETmiss , called VR (ETmiss ). The extrapolations on tt¯ and W+jets background are separately checked by requiring or vetoing a b-tagged jet, denoted
as TR or WR. For detail, see the descriptions in Section 6.2.6.

128channel
Observed events

VR (mT ; WR, El)

Tight
VR (mT ; WR, Mu)
VR (mT ; TR, El)

VR (mT ; TR, Mu)

7

5

6

10

bkg events

7.93 ± 1.89

6.91 ± 1.70

6.73 ± 1.68

6.58 ± 1.48

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

5.22 ± 1.86
0.65 ± 0.43
0.01+0.27−0.01
0.87 ± 0.47
0.80 ± 0.59
0.37 ± 0.09
0.00+0.05−0.00

4.49 ± 1.60
1.16 ± 0.81
0.02+0.08−0.02
0.56 ± 0.40
0.42 ± 0.39
0.25 ± 0.08
0.00 ± 0.03

5.52 ± 1.74
0.14 ± 0.12
0.01 ± 0.00
0.00 ± 0.00
0.62 ± 0.47
0.43 ± 0.08
0.00 ± 0.02

5.52 ± 1.49
0.16 ± 0.16
0.00 ± 0.00
0.08 ± 0.07
0.39 ± 0.29
0.42 ± 0.08
0.00 ± 0.06

Table 32:
Background fit results for the Tight VR (mT ; WR, El), Tight VR (mT ; WR, Mu), Tight
VR (mT ; TR, El) and Tight VR (mT ; TR, Mu) for an integrated luminosity of 20.3 fb−1 . The errors shown
are the statistical plus systematic uncertainties.

channelObserved events

VR (ETmiss ; WR, El)

Tight
VR (ETmiss ; WR, Mu)
VR (ETmiss ; TR, El)

VR (ETmiss ; TR, Mu)

13

9

2

3

bkg events

9.52 ± 1.89

7.37 ± 1.76

4.95 ± 1.33

3.84 ± 0.87

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

4.25 ± 1.42
3.52 ± 2.14
0.10 ± 0.03
0.74 ± 0.40
0.76 ± 0.63
0.15 ± 0.08
0.00 ± 0.03

2.87 ± 1.10
3.07 ± 1.89
0.07+0.35−0.07
0.71 ± 0.49
0.57+0.78−0.57
0.08 ± 0.03
0.00 ± 0.03

3.64 ± 1.00
0.29 ± 0.25
0.00 ± 0.00
0.10 ± 0.06
0.74+0.85−0.74
0.16 ± 0.07
0.02+0.03−0.02

2.61 ± 0.72
0.43 ± 0.29
0.00 ± 0.00
0.00+0.00−0.00
0.66 ± 0.59
0.13 ± 0.06
0.00 ± 0.03

Table 33: Background fit results for the Tight VR (ETmiss ; WR, El), Tight VR (ETmiss ; WR, Mu), Tight
VR (ETmiss ; TR, El) and Tight VR (ETmiss ; TR, Mu) for an integrated luminosity of 20.3 fb−1 . The errors
shown are the statistical plus systematic uncertainties.

129

channel
Observed events

VR (mT ; WR, El)

Loose
VR (mT ; WR, Mu)
VR (mT ; TR, El)

VR (mT ; TR, Mu)

114

89

95

92

bkg events

110.99 ± 13.72

114.16 ± 13.57

96.61 ± 14.99

82.01 ± 12.85

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

39.35 ± 12.27
50.49 ± 7.34
2.94 ± 0.92
10.96 ± 5.54
4.64 ± 3.40
0.80 ± 0.14
1.77+2.16−1.77

36.84 ± 11.47
50.07 ± 7.79
6.88 ± 2.10
9.38 ± 4.87
4.48 ± 3.26
0.72 ± 0.10
5.78 ± 4.07

74.51 ± 13.47
6.36 ± 1.33
0.57 ± 0.20
2.61 ± 1.32
10.05 ± 7.10
1.62 ± 0.15
0.90+1.34−0.90

62.54 ± 11.54
4.98 ± 0.89
0.95 ± 0.31
1.82 ± 0.95
8.76 ± 6.18
1.26 ± 0.10
1.70+2.22−1.70

Table 34: Background fit results for the Loose VR (mT ; WR, El), Loose VR (mT ; WR, Mu), Loose
VR (mT ; TR, El) and Loose VR (mT ; TR, Mu) for an integrated luminosity of 20.3 fb−1 . The errors shown
are the statistical plus systematic uncertainties.

channelObserved events

VR (ETmiss ; WR, El)

Loose
VR (ETmiss ; WR, Mu)
VR (ETmiss ; TR, El)

VR (ETmiss ; TR, Mu)

179

187

73

70

bkg events

199.82 ± 19.70

182.66 ± 20.03

76.45 ± 11.75

61.03 ± 9.73

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

32.32 ± 9.15
140.15 ± 18.66
0.25 ± 0.08
18.69 ± 10.01
7.33 ± 5.34
0.41 ± 0.07
0.66+1.51−0.66

25.97 ± 7.30
126.31 ± 17.20
2.59 ± 0.81
18.34 ± 10.32
6.96 ± 5.11
0.28 ± 0.03
2.22+3.11−2.22

49.56 ± 9.19
10.96 ± 2.02
0.00 ± 0.00
5.84 ± 3.06
9.08 ± 6.54
0.65 ± 0.07
0.36+0.67−0.36

37.50 ± 6.83
10.33 ± 1.92
0.19 ± 0.07
2.83 ± 1.48
9.21 ± 6.60
0.51 ± 0.05
0.47+0.87−0.47

Table 35: Background fit results for the Loose VR (ETmiss ; WR, El), Loose VR (ETmiss ; WR, Mu), Loose
VR (ETmiss ; TR, El) and Loose VR (ETmiss ; TR, Mu) for an integrated luminosity of 20.3 fb−1 . The errors
shown are the statistical plus systematic uncertainties.

130

Soft
VR (mT ; WR, El+Mu)

VR (mT ; TR, El+Mu)

79

71

bkg events

90.47 ± 9.49

68.36 ± 8.10

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

38.14 ± 8.68
35.31 ± 2.46
1.65 ± 0.51
4.21 ± 2.31
3.14 ± 2.35
0.53 ± 0.06
7.49 ± 2.90

52.30 ± 7.00
4.04 ± 0.53
0.04 ± 0.02
2.65 ± 1.36
4.13 ± 2.97
0.85 ± 0.10
4.34 ± 2.69

channelObserved events

Table 36: Background fit results for the Soft VR (mT ; WR, El+Mu) and Soft VR (mT ; TR, El+Mu) for
an integrated luminosity of 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.

Soft
VR (ETmiss ; WR, El+Mu)

VR (ETmiss ; TR, El+Mu)

381

75

bkg events

390.54 ± 26.95

89.61 ± 11.94

tt¯ events
W+jets events
Z+jets events
Dibosons events
Single Top events
tt¯+V events
QCD events

40.16 ± 10.15
317.02 ± 28.35
2.76 ± 0.97
19.61 ± 10.71
6.64 ± 4.86
0.41 ± 0.07
3.93+7.78−3.93

50.85 ± 8.46
19.73 ± 3.11
0.12 ± 0.05
5.88 ± 3.15
9.73 ± 6.94
0.66 ± 0.09
2.63+3.52−2.63

channelObserved events

Table 37: Background fit results for the Soft VR (ETmiss ; WR, El+Mu) and Soft VR (ETmiss ; TR, El+Mu)
for an integrated luminosity of 20.3 fb−1 . The errors shown are the statistical plus systematic uncertainties.

131

F

ETmiss and mT for the events in the SRs

ETmiss and mT distributions of the events left in the Signal Regions are shown in Fig. 74 and Fig. 75,
respectively. The overflow events are included in the last bin. Several signals taken from around theexclusion limits are piled up on top of the background distributions.

132

400

∫ Ldt=20.3fb , s=8TeV
-1

18
16
Events/100GeV∫ Ldt=20.3fb , s=8TeV
-1

Data

14

tt
W+jetsZ+jets350

QCD
Single Top

300
Events/100GeV

20

Dibosons

12

tt+V
~
g-~
g (1200,660,60)~g-~
g (985,705,425)

10
8

Data
tt
W+jetsZ+jetsQCD
Single Top
Dibosons

250

tt+V
~
q-~
q (600,360,60)~q-~q (425,305,185)

200
150

6
100
4
50

2

0
Ratio

Ratio

0

2
1
0

300

400

500

600

700

1
0

800
Emiss
[GeV]
T

50

2

200

∫ Ldt=20.3fb , s=8TeV
-1

45

400

500

600

700
Emiss
[GeV]
T

Data
tt
W+jets40
Events/100GeV

300

Z+jetsQCD

35Single Top
Dibosons

30

tt+V
~
g-~
g (665,625,585)

25
20
15
10
5

Ratio

0

2
1
0 200

300

400

500

600

700
800
Emiss
[GeV]
T

Figure 74: ETmiss distributions in Tight (left), Loose (right) and Soft (bottom) Signal Regions. Signals taken from around the exclusion limits are piled up on top of the background distributions. For
Tight SR, gluino pair productions with (mg̃ ,mχ̃±1 ,mχ̃0 )=(1200 GeV, 660 GeV, 60 GeV) (magenta) and1(mg̃ ,mχ̃±1 ,mχ̃0 )=(985 GeV, 705 GeV, 425 GeV) (cyan) are shown. For Loose SR, squark pair produc1
tions with (mq̃ ,mχ̃±1 ,mχ̃0 )=(600 GeV, 360 GeV, 60 GeV) (magenta) and (mq̃ ,mχ̃±1 ,mχ̃0 )=(425 GeV, 305 GeV,
1
1
185 GeV) (cyan) are shown. For Soft SR, gluino pair production with (mg̃ ,mχ̃±1 ,mχ̃0 )=(665 GeV, 625 GeV,
1
585 GeV) is shown in magenta. The last bin includes the overflow events.

133

120

∫ Ldt=20.3fb , s=8TeV
-1

14

-1

tt
W+jetsZ+jets12

Datatt
W+jetsZ+jets100

QCD
Single Top

10

QCD
Single Top

Events/50GeV

Events/100GeV∫ Ldt=20.3fb , s=8TeV

Data

Dibosonstt+V~g-~g (1200,660,60)~g-~
g (985,705,425)

8
6

80

Dibosonstt+V~q-~q (600,360,60)~q-~q (425,305,185)

60
40

4
20

2

0
Ratio

Ratio

0

2
1
0

200

300

400

500

600

35

2
1
0

700
mT [GeV]200∫ Ldt=20.3fb , s=8TeV
-1

300

400

500

600
mT [GeV]Datatt
W+jets30

Z+jetsQCD

Events/25GeV

25

Single Top
Dibosons

20

tt+V
~
g-~
g (665,625,585)

15
10
5

Ratio

0

2
1
0 100

120

140

160

180

200

220 240mT [GeV]Figure 75: mT distributions in Tight (left), Loose (right) and Soft (bottom) Signal Regions. Signals
taken from around the exclusion limits are piled up on top of the background distributions. For
Tight SR, gluino pair productions with (mg̃ ,mχ̃±1 ,mχ̃0 )=(1200 GeV, 660 GeV, 60 GeV) (magenta) and1(mg̃ ,mχ̃±1 ,mχ̃0 )=(985 GeV, 705 GeV, 425 GeV) (cyan) are shown. For Loose SR, squark pair produc1
tions with (mq̃ ,mχ̃±1 ,mχ̃0 )=(600 GeV, 360 GeV, 60 GeV) (magenta) and (mq̃ ,mχ̃±1 ,mχ̃0 )=(425 GeV, 305 GeV,
1
1
185 GeV) (cyan) are shown. For Soft SR, gluino pair production with (mg̃ ,mχ̃±1 ,mχ̃0 )=(665 GeV, 625 GeV,
1
585 GeV) is shown in magenta. The last bin includes the overflow events.

134

G Fit results for the Signal Regions
Tables 38-40 show the decomposition of the errors. Negligible backgrounds are omitted from the tables.
The percentages show the size of the uncertainty relative to the total expected background. Normalization
errors for tt¯ and W+jets are dominated by the statistical uncertainties determined in the Control Regions,which are strongly anti-correlated to the JES uncertainties, therefore the total uncertainties are evaluatedto be much smaller than the simple square-sum of these components. Normalization errors for the otherminor backgrounds are uncertainties assigned to their cross-sections and the acceptances as discussed in
Section 7.2. Theory uncertainties are discussed in Section 7.2. For more details and interpretations, see
the text in Section 8.1.

135

Tight SR (El)Tight SR (Mu)Total background√expectation
Total statistical ( Nexp )

6.52
±2.55

5.31
±2.30

Total background systematic±1.17 [17.99%]±1.03 [19.40%]

Normalization (tt¯)
Normalization (W+jets)
JES
JER
Theory (tt¯)
Theory (W+jets)
Normalization (Z+jets)
Normalization (Dibosons)Normalization (Single Top)b-Tag
QCD (ele)
QCD (muo)±1.83 [28.0%]±0.71 [10.9%]±1.84 [28.3%]±0.13 [2.1%]±0.27 [4.2%]±0.07 [1.1%]±0.00 [0.00%]±0.39 [6.0%]±0.34 [5.2%]±0.15 [2.3%]±0.21 [3.2%]±0.00 [0.00%]±1.64 [31.0%]±0.53 [10.0%]±1.71 [32.2%]±0.02 [0.44%]±0.24 [4.6%]±0.05 [1.0%]±0.02 [0.31%]±0.09 [1.7%]±0.45 [8.5%]±0.03 [0.65%]±0.00 [0.00%]±0.02 [0.38%]

channelTable 38: Breakdown of the dominant systematic uncertainties on background estimates in the Tight
Signal Regions. Note that the individual uncertainties can be correlated, and do not necessarily add
up quadratically to the total background uncertainty. The percentages show the size of the uncertainty
relative to the total expected background.
Loose SR (El)

Loose SR (Mu)Total background√expectation
Total statistical ( Nexp )166.60±12.91161.12±12.69Total background systematic±20.35 [12.22%]±18.56 [11.52%]

Normalization (tt¯)
Normalization (W+jets)
JES
JER
Theory (tt¯)
Theory (W+jets)
Normalization (Z+jets)
Normalization (Dibosons)Normalization (Single Top)b-Tag
QCD (ele)
QCD (muo)±21.88 [13.1%]±8.47 [5.1%]±15.88 [9.5%]±0.07 [0.04%]±6.03 [3.6%]±0.58 [0.35%]±0.26 [0.15%]±5.65 [3.4%]±8.24 [4.9%]±0.92 [0.55%]±1.92 [1.2%]±0.00 [0.00%]±20.23 [12.6%]±8.35 [5.2%]±14.72 [9.1%]±0.06 [0.04%]±5.58 [3.5%]±0.57 [0.35%]±1.12 [0.70%]±6.07 [3.8%]±6.59 [4.1%]±0.34 [0.21%]±0.00 [0.00%]±2.10 [1.3%]

channelTable 39: Breakdown of the dominant systematic uncertainties on background estimates in the Loose
Signal Regions. Note that the individual uncertainties can be correlated, and do not necessarily add
up quadratically to the total background uncertainty. The percentages show the size of the uncertainty
relative to the total expected background.
136

Soft SR (El+Mu)

channelTotal background√expectation
Total statistical ( Nexp )

35.37
±5.95

Total background systematic±4.57 [12.91%]

Normalization (tt¯)
Normalization (W+jets)
JES
JER
Theory (tt¯)
Theory (W+jets)
Normalization (Z+jets)
Normalization (Dibosons)Normalization (Single Top)b-Tag
QCD (ele+muo)±3.54 [10.0%]±2.95 [8.4%]±5.22 [14.7%]±0.00 [0.01%]±2.48 [7.0%]±0.49 [1.4%]±0.05 [0.14%]±0.71 [2.0%]±2.05 [5.8%]±0.12 [0.35%]±1.55 [4.4%]

Table 40: Breakdown of the dominant systematic uncertainties on background estimates in the Signal
Regions. Note that the individual uncertainties can be correlated, and do not necessarily add up quadratically to the total background uncertainty. The percentages show the size of the uncertainty relative tothe total expected background.

137

H Profile-likelihood and CL s
We use a complicated likelihood function in the limit calculation, containing a lot of parameters. Amongthem, Parameter Of Interest (POI) is namely the one we are interested in, and the others are called nuisance parameters. Profile-Likelihood method eliminates the nuisance parameters and defines a simple
likelihood as a function of POI to be used in the limit calculation.
The analyses in proton-proton collider in general suﬀer from large backgrounds, which leads to a big
statistical fluctuation in the observed number of events. As a result, there frequently happen the cases
in which an under-fluctuation mistakenly excludes a given signal model. To avoid this, a quantity called
CL s is used to set the limit, which includes a punishment term for such problems and gives a conservative
limit.

H.1 Likelihood
We begins with a simple experiment, in which only one background and one signal compose all observed
events. They are provided as histograms with multiple bins for the signal region and a 1-binned histogram
for the control region where the background is normalized. Then likelihood function L is defined as
L(µ, θ) =N∏

Pois(µs j (θ) + b j (θ); n j ) · Pois(u(θ); m) · Lconstrain (θ),

(118)

j=1

where θ is the vector of all nuisance parameters, j = 1..N is the index of bins in the signal region
histogram, s j (θ) and b j (θ) are the expected number of signal and background in the signal region, n j
is the number of observed events in j-th bin in the signal region, and u(θ) and m are the expected andobserved number of events in the control region. POI of this likelihood function is µ, called Signal
Strength, which is defined as the fraction of a given signal yield with respect to the nominal one. The
scale factor for the background is not explicitly shown but included in θ. Pois(λ; n) is Poisson probability
function with n observed and λ expected events. The explicit form of Pois(λ, n) is the following.
Pois(λ; n) =

λn −λ
e .
n!

(119)

Lconstrain (θ) is a term to constrain θ. In practice, Gaussian function is mostly used. For example, assuming
θi are constrained around ci with the errors of σi , then Lconstrain (θ) is written as, (θi − ci )2  ,Lconstrain (θ) =exp −
√
2
2σ
2πσ
i
i
i=1
K
∏

1

(120)

where K is the number of nuisance parameters included in θ

H.2 Profile-likelihood
Profile likelihood ratio is then defined as
λ(µ) =L(µ, θmax (µ)),
L(µmax , θmax )(121)

where θmax (µ) is a set of nuisance parameters which maximizes the likelihood function L for a givenµ. µmax and θmax in the denominator are the values which maximize the likelihood function L. In otherwords, the denominator is the maximum-likelihood. It is also convenient to use a statistictµ = −2 ln λ(µ)
138

(122)

f(tµ|µ)tµ,obsp−valuetµFigure 76: Illustration of the relation between pµ and f (tµ |µ). This plot is cited from Ref. [81].

as an estimator. Note that λ(µ) runs from 0 to 1, thus tµ can take all real value.
Then, we can think of a Probability Density Function (PDF) of tµ for a given µ. Let’s put it as f (tµ |µ).
For example, the probability of disagreement pµ for a given µ can be shown as below using f (tµ |µ),∫ ∞pµ =
f (tµ |µ)dtµ ,(123)
tµ,obswhere tµ,obs is the value of the statistic tµ calculated from the observed data. Figure 76 illustrates therelation of these variables.
H.2.1 Constraints and approximations
An important constraint on the signal strength µ is the prohibition of unphysical negative value. So, if
one finds the data such that µmax < 0, then the best physical agreement occurs at µmax = 0. We defineλ̃(µ) as follow:
 L(µ,θ (µ))
max L(µmax ,θmax ) (µmax ≥ 0),(124)
λ̃(µ) =  L(µ,θmax (µ)) (µmax < 0)L(0,θmax (0))
where θmax (0) is a set of nuisance parameters which maximize the likelihood function L under a constraintof µ = 0. Then, tµ is also modified as,t˜µ = −2 ln λ̃(µ).
(125)
We then think of an approximation of the complicated function, which is used in the optimization
procedure in Appendix B. First, we introduce a function which converts p-values into an equivalentsignificance, Z, defined such that a Gaussian distributed variable found Z standard deviations above its
mean has an upper-tail probability equal to p. That is,
Z = Φ−1 (1 − p),(126)

where Φ−1 is the quantile (inverse of the cumulative distribution) of the standard Gaussian. The significance of finding no signal under the assumption of the nominal signal strength, med[Z0 |1], is approximated as,√√med[Z0 |1] = q0 ∼ 2((s + b) ln(1 + s/b) − s).
(127)

139

Expanding the logarithm, one finds,s
med[Z0 |1] ∼ √ .
bThis is a well-known formula widely used for the cases where s + b is large enough.

(128)

H.3 CL s method
The p-value for the upper limit is defined as the upper-tail probability for the observed events under theassumption of a signal existence. As this p-value assumes both signal and backgrounds, it is denoted as
p s+b . On the other hand, the p-value assuming only background is denoted as pb . If the observed events
is completely consistent with the expected background events, pb becomes 1.
We define CL s+b as follow,
CL s+b = 1 − p s+b .
(129)

f(q)

A given signal model is excluded at 95% Confidence Level (CL) if CL s+b < 0.95 for this model.
0.5

f(q|b)
0.4

f(q|s+b)

qobs

0.3

p

0.2

b

0.1

p

s+b

0
-10

-8

-6

-4

-2

0
q

Figure 77: Illustration of the problem of CL s method. f (q|s + b) and f (q|b) show the probability density
functions for signal+background and background-only hypotheses. qobs is q calculated from observed
number of events. p s+b and p s are the p-values for signal+background and background-only hypotheses.
This plot is cited from Ref. [81].
The problem of CL s+b method is illustrated in Fig. 77. f (q|s + b) and f (q|b) show the probability
density functions for signal+background and background-only hypotheses. qobs is q calculated fromobserved number of events. p s+b and p s are the p-values for signal+background and background-only
hypotheses. In the illustration, the number of background events b is so large compared with the numberof signal events s that the probability density function of signal+background hypothesis f (q|s + b) does
not diﬀer much from the one of the background-only hypothesis, rather almost overlapping each other.
In such a case, CL s+b often (once in twenty times at the limit of b  s) excludes a given signal model
mistakenly due to an under-fluctuation of observed events.
Naturally, a model with small number of signal events with respect to the number of backgrounds,
should loose the sensitivity. CL s is defined with a penalty term, considering this requirement, as
CL s =

CL s+b
.
CL b

140

(130)

If the two distributions f (q|b) and f (q|s + b) are widely separated, then CL b = 1 − pb is only slightly lessthan 1, and thus exclusion based on CL s is similar to that obtained from CL s . If, however, one has little
sensitivity to the signal model, i.e. the two distributions are close together, 1− pb becomes small, thus thep-value of s + b is penalized. In this way, one is prevented from excluding signal models mistakenly incases of low sensitivity. As can be read from the equation, CL s always gives more conservative exclusion
sensitivity than CL s+b does.

141

I Tile Calorimeter calibration using scrapping muon
I.1 Introduction
In March 2010, the ATLAS detector was exposed to muons produced by a 450 GeV proton beam partiallyhitting (scrapping) one of the LHC collimators placed at a distance of about 180 m from the center ofthe detector. The data are used to validate the inter-calibration of the hadronic calorimeter (TileCal).
Inter-calibration, or uniformity, of Tile calorimeter is important because it tells us if all components areworking as expected. The uniformity is compared with Monte Carlo simulation, therefore is is also agood validation that the geometry and response are well described in the Monte Carlo.
I.1.1 Tile calorimeter
TileCal is a sampling plastic-scintillator/steel detector. It is divided into four cylindrical sections, referred
to as long barrels (LBA and LBC) and extended barrels (EBA and EBC). Each cylinder is composed of
64 azimuthal segments, referred to as modules. The modules are segmented in z-axis and in radial-depth
by routing optical fibers to diﬀerent Photo Multiplier Tubes (PMT) forming cells. The resulting typicalcell dimensions are approximately ∆η × ∆φ = 0.1 × 0.1 (0.2 × 0.1 in the last radial layer). The layout of
the LBA and EBA cells is shown in Fig. 78.

Figure 78: Long Barrel (LBA) (left) and Extended Barrel (EBA) (right) sections of the calorimeter. Horizontal lines deliminate the 11 rows of scintillating tiles. Full horizontal lines define the radial layers.
Full vertical lines show the cell boundaries formed by grouping optical fibers from the scintillating tiles
for read-out by separate photo-multipliers. Also shown are lines of pseudo-rapidity η. The maximum
longitudinal distance between the sections is 72 cm. The LBA and EBA sections cover the regions of0≤ η ≤1.0 and 0.8≤ η ≤1.7 respectively. The LBC and EBC sections cover symmetrically the negative
pseudo-rapidity region.

I.1.2 Muon spectrometer system
Muon Spectrometer (MS) is immersed in a magnetic field provided by three toroids, one in the barrel (|η| ≤1.1) and one for each end-cap (1.1< |η| ≤2.7), with an integral field strength of 2-8 T·m. For
most of the acceptance, Monitored Drift Tube (MDT) chambers are deployed [82]. In the end-cap of theinner region, Cathode Strip Chambers (CSC) [82] are used because of their capability to cope with highbackground rates. MDT chambers are composed of two Multi Layers (ML) made of three or four layersof tubes. The spatial resolution attainable with a single tube is about 80 µm. Information from MDT was142

used in this analysis to determine the momentum of the muons from scraping beam in C-side (z<0) after
crossing TileCal.
I.1.3 Trigger system
The direction of the muons forms a small angle with respect to the beam axis (see Fig. 79 and Section I.2),
therefore, the downstream wheels of TGC [82] were used as trigger. Due to the large distance between
the End-Caps, only the TGC placed downstream were in time with the beam. They also allowed ameasurement of the coordinate of the muons in the radial direction parallel to MDT wires. The toroid
magnetic field [83] was turned on during the run.

Figure 79: Display of one measured muon event. The muon arrives from the A-side (z>0), which isshown as the horizontal yellow line. The green panels are muon spectrometers with hits recorded, andthe yellow and magenta cells show the calorimeter activities.

I.1.4 Scraping beam
The muons from the scraping proton beam were produced by moving the jaws of TCTH (horizontal
tertiary collimators) towards the beam in 100 µm steps. Data were taken when an ATLAS trigger rate
ranged between 100-500 Hz.

I.2 Data analysis
The analysis is based on about 410 k recorded events. The tracks are reconstructed using the informationof Muon Spectrometer. In C-side, the measurement of three coordinates of each data point allows determination of the track momentum, polar and azimuth angles. In A-side, TGCs were out of time, thus only
raw track information could be obtained.
I.2.1 Muon track selection criteria
The following selection criteria are applied:
1. Exactly one reconstructed track in C-side of MS detector.
143

2. The reconstruction quality of the tracks is enhanced by requiring a number of MDT hits larger than20.
The distribution of the reconstructed momentum is shown in Fig. 80.
3. A event is retained when the momentum p reconstructed using MS chambers of C-side is larger
than pmin =4 GeV.

Mean = 9.32 ± 0.02 GeV
RMS = 8.66 ± 0.01 GeVMean = 9.39 ± 0.03 GeV
RMS = 9.61 ± 0.02 GeV

25000

Data

Mean = 2.97 ± 0.00 rad
RMS = 0.10 ± 0.00 rad

Mean = 2.97 ± 0.00 rad
RMS = 0.10 ± 0.00 rad

Data

25000

MC

MC

20000

20000
15000
15000
10000
10000

5000

5000

0
0

5

10

15

20

25

0
0

30
35
40
Track momentum [GeV]

0.5

1

1.5

2

2.5

3
3.5
4
Polar angel of the track [rad]Figure 80: Distributions of the reconstructed track momentum (left) and its polar angle (right) at z=6150 mm (C-side). The black (red) histogram is obtained using experimental (simulated) events selected
applying the cut 1 and cut 2 discussed in the text. The same colors indicate the Mean and the RMS of thetwo distributions respectively.

I.2.2 Monte Carlo simulation
Monte Carlo (MC) that simulates the interaction of muons from scraping beam within the ATLAS detector is based on GEANT4 [33, 84] and Athena that provide the physics models, the geometry description
and the tracking tools. The track momentum, x and y positions measured in C-side is extrapolated backto the A-side using the method described in Ref. [85]. Numerical propagation of the track parametersand covariance matrix that takes into account the materials and magnetic field is employed here. The
extrapolated kinematic quantities in A-side are used to generate simulation events. Consequently, thesesimulated muons are propagated to C-side, reconstructed there, and extrapolated back to A-side, where
their spectra are compared to the original ones. Diﬀerences between the experimental and simulated
spectra are taken into account in the determination of systematic uncertainties. The digitization step ofcalorimeter simulation, which emulates the behavior of electronics, allows applying the same energy
reconstruction procedure to experimental and simulated events.
I.2.3 Calorimeter response and further selection criteria
The estimator of the muon response for each TileCal cell is defined using the ratio of the energy dE
deposited by the track in crossed cells. The track extrapolation, discussed in Section I.2.2, provides
crossing points of the muon track in each layer. Additional linear interpolations are performed using
detailed cell geometry to define the entry and exit points in the crossed cells. The track path length dl isthen evaluated as the distance between these points for every cell crossed by the muon.
Identified tracks can be accompanied by other tracks that are not reconstructed because they do notreach the MS at C-side. They can aﬀect the measurement of the energy deposit in a cell. To reduce such
eﬀects, an isolation criterion is applied:144

4. The number of adjacent cells (the definition is illustrated in Fig. 81) with an energy larger than
60 MeV, Nne , to the one crossed by the reconstructed track is required to be smaller or equal toNne,low =2.
To improve the quality of measurements, additional cuts are applied:
5. Only cell signals produced by tracks with dl >100 mm are retained.
6. To reduce extrapolation errors due to multiple scattering and to remove residual noise contribution,
a cut dE > dEcut =60 MeV is applied to the measured cell energy dE.
7. The cells with more than 10% of tracks producing a signal that is compatible with pedestal (dE <60 MeV),
are not considered in the analysis.
8. Malfunctioning cells are identified when the absolute diﬀerence of the mean values of dE/dl between data and MC exceeds 5 times of the uncertainty. These cells are removed from both data
and MC.

Figure 81: Illustration of how adjacent cells are defined. The figures show the cells viewed from the beamaxis. The blue cell is the one crossed by the reconstructed track. The 5 (8) green cells in A, D (BC(B))
layers are considered as adjacent cells.
Truncated mean, hdE/dlit , is used to define the response to muons for the layers with pseudo-rapidity
ηc . The mean is computed by truncating a fraction (F=1%) of entries in the upper side of the dE/dl
distributions. It is preferred to a normal mean because it is less aﬀected by rare energy-loss processes,
such as bremsstrahlung or energetic γ-rays, which can cause large fluctuations on the full mean. The
results show some non-linearity and other residual non-uniformities such as diﬀerences in momentum
and path spectra along η and layers. To compensate for these eﬀects, the ratio of truncated means between
experimental and simulated data
hdE/dlitR=.
(131)
hdE/dlitMC
is defined.

145

220
100

Cell : A+3 (A-side)

200
180

Cell : D+2 (A-side)

Data : Mean = 1.32 ± 0.01 MeV/mm

Data : Mean = 1.35 ± 0.02 MeV/mm

MC : Mean = 1.32 ± 0.01 MeV/mm

MC : Mean = 1.38 ± 0.02 MeV/mm

80

160
140

60

120
100

40

80
60

20

40
20
0
-1

0

1

2

3

4

0
-1

5
6
dE/dl [MeV/mm]

0

1

2

3

4

5
6
dE/dl [MeV/mm]

Figure 82: Distribution of dE/dl for the cells LB-A3 (left) and LB-D2 (right) (See Fig. 78) obtained fromexperimental (black) and simulated data (red).

I.3 Results
The experimental results: a) uniformity of the response of the cells and b) layer inter-calibration, arediscussed in this section.
I.3.1 Uniformity of calorimeter cell response
Here, the determinations of the ratios Eq. (131) of a given pseudo-rapidity ηc and layer are discussed. To
make the ratios statistically meaningful, the following condition is introduced:
9. Only cells with more than 50 entries in data and MC are considered.
Figure. 83 shows the results as a function of ηc for the cells belonging to the diﬀerent radial layers. The
response of the cells of a given radial layer is found to be uniform inside the errors. The horizontal lines
in Fig. 83 correspond to the determination means.
I.3.2 Inter-calibration of radial layers
The systematic uncertainties on the inter-calibration of the radial layers are discussed in this section.
To take correlations into account, the ratios of µφ for each pair of layers
Il,l0 =

µφ (l)µφ (l0 )(132)

is defined. In Eq. 132 l and l0 indicate the layers LB-A, LB-BC, LB-D, EB-A, EB-B and EB-D.
Systematic eﬀects on determination of Il,l0 are evaluated considering the following sources:
1. The minimum momentum of tracks (cut 3) in Section I.2.1. In the systematic error study pmin =0 GeV
and pmin =8 GeV are used.
2. The maximum number of adjacent cells, Nne , with dE > dEne =60 MeV (cut 4) in Section I.2.3.
Two cases, Nne,low =0 and Nne,low =4, are considered.
3. The cut value of dEcut (cut 6) in Section I.2.3. Two values of dEcut =30 MeV and 90 MeV are used.
4. The fraction F used in truncated mean (see Section I.2.3). The fractions F equal to 0% and 2%
instead of F=1% are used to obtain the systematic errors.
146

EB

EB

LB

LB

A

B

D

A

BC

D

A

-

+0.0130.990−0.014

0.995+0.017−0.0131.003+0.013−0.0151.012+0.011−0.0111.000+0.019−0.019B

1.010+0.013−0.013-1.005+0.011−0.0131.012+0.011−0.0101.021+0.008−0.0101.009+0.016−0.016D

1.005+0.013−0.013+0.0100.995−0.013-

1.008+0.012−0.0171.017+0.010−0.0101.005+0.017−0.018A

0.997+0.013−0.015+0.0120.988−0.010

0.993+0.015−0.016-1.009+0.010−0.011

0.997+0.018−0.017

BC

0.988+0.014−0.010+0.0110.979−0.009

0.984+0.015−0.0100.991+0.013−0.010-0.988+0.017−0.016D

1.000+0.028−0.019+0.0230.991−0.016

0.995+0.025−0.0181.003+0.025−0.0171.012+0.020−0.017-

Table 41: Results of the layer responses Il,l0 . Total errors, including statistical and systematic eﬀects, arereported.
5. The eﬀect of the cell removing (cuts 7, 8 discussed in Section I.2.3) is estimated by removing thesecriteria in the analysis. The estimated largest systematic eﬀect is smaller than 0.5%.
Other considered systematic errors are:
6. As shown in Fig. 80, the diﬀerences between data and MC track momentum varies with layers.
Diﬀerences up to ±20% are observed. The eﬀects on the relative responses are uncorrelated andare estimated to be 0.4% by Bethe-Bloch formula.
7. The uncertainty on the radial correction measured in beam test using 90◦ muons [86] were also
considered. The eﬀects of this systematic source are uncorrelated and are estimated to be 0.3%
corresponding to the statistical errors of the measurements at beam tests.
The determinations of Il,l0 are reported in Table 41. The total errors include statistical and systematic errors (sources 1 to 7). They are obtained by adding positive and negative deviations separately inquadrature. In the case where the diﬀerences between the obtained values of Il,l0 and the one corresponding to the nominal value of the parameter have the same sign, the larger variation in absolute value isretained in the determination of the total systematic error.
I.3.3 Conclusion
Muon events produced by scraping 450 GeV protons in one collimator of the LHC machine have beenused to test the calibration of hadronic barrel calorimeter, TileCal, of the ATLAS detector. The analysis
is based on the comparison between experimental and simulated data. For each layer, the response of
the diﬀerent cells is quite flat without any structure. The responses of all the layer pairs are found to beconsistent within 1-2 % uncertainties including systematics. They are consistent with the scale value ofthe jet energy measurement set at beam tests using electrons [86].

147<dE/dl>data/<dE/dl>mc<dE/dl>data/<dE/dl>mc<dE/dl>data/<dE/dl>mc

1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
-2

1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
-2

1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
-2

A-layer:All

-1.5

-1

-0.5

0

0.5

1

1.5

-1

-0.5

0

0.5

1

1.5

-1

-0.5

0

0.5

1

1.5

ηc

2

BC-layer:All

-1.5

ηc

2

D-layer:All

-1.5

ηc

2

Figure 83: Ratios of the truncated means of the experimental and simulated distributions of the energy
deposited in the cells by muons from the scraping beam per unit of path length as a function of the cell’s
pseudo-rapidity ηc . Results and statistical errors obtained for the cell belonging to layers A (top), BC
and B (middle) and D (bottom) are reported. The horizontal lines correspond to the means of the EBA,
LBA, LBC and EBC measurements.

148