学位論文
Search for Supersymmetric Partners of Gluons√
in Proton-Proton Collisions at s = 13 TeV（重心系 13 TeV の陽子-陽子衝突を用いた
グルーオンの超対称性粒子の探索）

平成 28 年 2 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
南 雄人

Search for Supersymmetric Partners√ of Gluons
in Proton-Proton Collisions at s = 13 TeV
Yuto Minami

1

Abstract
Supersymmetry (SUSY) is one of the most promising theories which
could explain physics beyond the Standard Model (SM). The Large Hadron Collider (LHC) provides proton-proton collisions at the world’s highest
energies, where production of coloured SUSY particles is highly expected. The R−parity conserved Minimal Supersymmetric Standard Model(MSSM) is phenomenologically motivated. Under R−parity conservation,SUSY particles are pair produced from the collision of SM particles andthe lightest SUSY particle (LSP) is stable. According to phenomenologicalexpectations, SUSY partners of quarks (squarks) are likely to have large
masses (∼O(10) TeV) which provide large radiative corrections to make the
Higgs boson as heavy as 125 GeV. On the other hand, it is expected that SUSY
partneres of gluons (gluinos) are possibly light enough to be pair-produced in
the proton-proton collisions at the LHC. Each gluino decays into two quarks
and a SUSY partner of electroweak gauge boson (electroweakino) via virtual
squark. The electroweakino decays to lighter SUSY particles until the LSP
is finally produced. Since light gluinos with masses up to ∼ 1.3 TeV werealready excluded by the previous SUSY searches at the LHC, a focus is now
on heavier gluinos whose production may be characterized by non-planar
multi-jet with large missing transverse energy (ETmiss ).
In this thesis, gluino pair-production is searched for using events withlarge ETmiss , jets, and no lepton in the final states of the proton-proton col√lisions recorded by the ATLAS detector at s= 13 TeV in 2015. The total
amount of data used correspond to an integrated luminosity of 3.2 fb−1 .
To optimize the event selection for non-planar multi-jet events, a variable"aplanarity" is newly introduced, which results in better signal selection
efficiencies over the previous searches. Four different event selections areprepared to cover a large region of gluino mass and event kinematics.
To estimate the number of SM background (BG) events after the event
selection, a new method has been developed which does not rely on Monte
Carlo (MC) simulations as much as possible. This method is carefully
validated with data outside the signal regions.
No significant excess is observed after the event selections. This result
is interpreted using simplified models of gluino decays, where gluinos arepair-produced and decay in a way to preserve R−parity. For massless LSPs,
gluinos with masses up to ∼ 1530 GeV are excluded with 95% confidence
level. This represents the most stringent constraint on SUSY models to date.

2

Contents
1

Introduction: Standard Model and Supersymmetry
1.1 The standard model
1.1.1 Problems of standard model
1.2 Supersymmetry
1.3 MSSM
1.3.1 R-parity
1.3.2 SUSY breaking term
1.3.3 Target SUSY particles
1.4 Objectives of this thesis

6
6
6
11
12
14
15
16
17

2

LHC and ATLAS detector
2.1 Large Hadron Collider
2.2 ATLAS detector
2.2.1 Overview of the ATLAS detector
2.2.2 The coordinate system and nomenclature
2.2.3 Magnet system
2.2.4 Inner Detector
2.2.5 Calorimeter
2.2.6 Muon spectrometer
2.2.7 Luminosity detector

20
20
21
21
21
22
22
25
27
27

3

Data set and Monte Carlo samples
3.1 Data samples
3.2 Monte Carlo samples
3.2.1 Standard Model MC samples
3.2.2 Signal samples

29
29
29
30
31

4

Object definition and acquisition from data
4.1 Jets
4.1.1 B-jets
4.1.2 Jet cleaning
4.2 Electrons
4.3 Photons
4.3.1 Photon conversion
4.3.2 Photon identification
4.3.3 Photon isolation
4.3.4 Efficiency and purity of photons
4.4 Muons
4.5 Overlap removal

34
34
35
35
36
37
38
38
41
41
43
43

3

4.6
4.7
4.8
5

6

Missing transverse momentum
Triggers
4.7.1 Triggers used in this analysis
Event cleaning

44
44
45
45

Event selection and optimization
5.1 Discriminating variables
5.2 Study of aplanarity
5.2.1 Definition of aplanarity, sphericity, and transverse sphericity[60]5.2.2 Thrust
5.2.3 Comparison of event shape variables
5.2.4 Jets Systematic effects for aplanarity
5.3 Optimization procedure
5.3.1 Definition of significane
5.3.2 Optimization with TMVA
5.3.3 Results of optimization with TMVA
5.3.4 Distribution check with TMVA results
5.3.5 The optimized SRs

49
50
50
55
61
61
62
63
63
65

Background estimation
6.1 Top BGs and W BGs
6.2 Multi-jet BGs
6.3 Diboson BGs
6.4 Z(→ νν)+jets BG estimation with γ replacement
6.5 Data-driven γ replacement
6.6 ABCD method for γ+jets CR
6.6.1 Selection
6.6.2 Monte Carlo sample
6.6.3 Evaluation of the 2D correlation
6.6.4 Systematic Uncertainty in γ ABCD method
6.7 WXYZ method
6.7.1 Small Corrections for WXYZ method
6.7.2 WXYZ method with ABCD method
6.7.3 WXYZ method without ABCD method
6.7.4 Fitting implementation of ABCD and WXYZ method
6.7.5 Removing contaminating events in CRs
6.8 γ/Z and W/Z check
6.9 Expectation from MCs
6.10 Purity estimation in γ CR
6.10.1 Data/MC comparison

75
75
76
76
77
80
80
80
82
83
83
84
87
87
88
88
91
92
95
98
98

4

47
47
48

6.10.2 Purity estimation with isolation template fitting
6.11 Summary of CRs
6.12 Strategy of validation regions
6.13 Fit results for control regions and validation regions

99
106
109
109

7

Statistical treatment
7.1 Log likelihood
7.2 Profile log likelihood
7.2.1 Approximation for discovery limit
7.3 CLS technique
7.4 Systematic uncertainties
7.4.1 Experimental uncertainties
7.4.2 Theoretical uncertainties

127
127
128
129
130
130
130
131

8

Results
8.1 Fit results for signal region
8.2 Interpretations and discussions

133
133
141

9

Conclusion

145

Appendix

148

A Photon
A.1 Jet-Photon overlap removal validation
A.2 Photon purity estimation with ABCD method
A.2.1 The difference of overlap-removal and ID order
A.2.2 Correlation study for ABCD method

148
148
150
150
153

B TMVA
B.1 Genetic algorithm
B.1.1 Determination of opimized cut combination

154
154
155

C ABCD method
C.1 ABCD method with correction

156
157

5

1

Introduction: Standard Model and Supersymmetry

The standard model (SM) of particle physics is very successful model. It consists ofquarks, leptons, gauge bosons, and Higgs particle, and all the predicted particles
were discovered. In Sec.1.1, the SM and its problems are described. These
problems are called physics beyond SM. Supersymmetry (SUSY) is one of thepromising theory which can explain the physics beyond SM. The details of SUSY
and target signal of this thesis are described in Sec.1.2. The objectives of thisthesis are described in Sec.1.4.

1.1

The standard model

Thanks to the discovery of Higgs particle [1, 2], the content of elementary particles
in the Standard Model (SM) is completed (Figure 1).

Figure 1: Standard model particles[3].

1.1.1

Problems of standard model

Hierarchy problem
The order of Planck scale is ∼ 1019 GeV. This is the scale where quantum effects
of gravity is not negligible. In contrast, the mass scale of all the SM particles,
6

including Higgs particle, are at most ∼ 102 GeV. This is called the electroweak(EW) scale. Because huge difference between the EW scale and the Planck scale,there arises one problem in quantum corrections to Higgs mass. The Higgs fieldhas Yukawa couplings with a SM fermion, like:
L = −λ f ψ̄Hψ(1)This term allows the first diagram of Figure 2 and the quantum correction yields
quadratic divergence∆m2H (ψ) ∼ −Λ2,(2)where Λ is the ultraviolet cutoff scale in the calculation. If we consider Λ as the
Planck scale, this term becomes the quadrature of the Planck scale. This is also
the case for heavy neutrino scale and the GUT scale (described afterwards). To fix
the Higgs mass divergence within the EW scale, fine tuning is needed to cancel theeffects of the large radiative correction. This problem is called hierarchy problem.
One solution for this problem is to introduce scalar partners of fermions, like
L = −λ 2f |H ||φ|.

(3)This term make the second diagram of Figure 2 and the quantum correction yields∆m2H (φ) ∼ +Λ2 + m2φ log(Λ).

(4)

Then the quadratic divergences of Eq.(2) and (4) are cancelled (Figure 2). In
supersymmetry, all the fermions have scalar partners. Therefore, this problem is
automatically solved with supersymmetry.
t̃t∆m2H =−Λ2+Λ2

Figure 2: Cancellation of quadratic divergence between contributions from top
quark, and scalar top quark.

Dark matter
There are many evidences for the existence of Dark Matter (DM). The DM is ahypothetical matter which is introduced to explain some astronomical phenomena.

7

If the DM is made up with massive particles, they do not interact with the electromagnetic force and are stable. The oldest and direct evidence is from "Galaxy
rotation curves". Indirect but most accurate determination of ΩDM is from "Cosmic
microwave background (CMB) " measurement.
Galaxy rotation curves If a galaxy obeys Newton dynamics, the rotational
velocity of stars is expected from the equations:
GM (r)mmrv(r) 2=: Balance of gravitaion and centrifugal force, (5)2r2rr
GM (r)
hence, v(r) =,(6)rwhere, r is the radial length fromRthe centre of the galaxy, ρ(r) is the mass densityof visible matters, and M (r) = 4πr 2 ρ(r)dr. If there are no matter at the outof galaxy disk, v(r) ∝ r −1/2 . However, the observed rotation curve of a galaxy is
almost constant at large distances as shown in Figure 3. This means some matter
exist at the end of galaxy disk in addition to visible matters.
CMB With the anisotropy of CMB, the density of matters in space is determined indirectly. From the results of Planck satellite [5], the baryonic matter
density isΩb h2 = 0.02207 ± 0.00033,(7)
where h is the Hubble constant (100 km/(s·Mpc)). The non-baryonic cold dark
matter density isΩc h2 = 0.1196 ± 0.0031,(8)
and this indicate the existence of DM. Candidates for DM particles are sterile
neutrino, axion, and supersymmetric particles. In supersymmetry , the Lightest
Supersymmetric Particles (LSP) is neutral and stable, and can be a candidate forthe DM, as far as R-parity (1.3.1) is conserved. The DM is one of the strong
motivation for supersymmetry.
Grand unification
The coupling unification including electromagnetic, weak, and strong interaction
is expected. If they are unified at some energy scale, the coupling constants ofthese theories (α g 0, α g, α gs ) become the same value. These coupling constants
are related to gauge couplings:
αg 0 =g2
g2
g02, αg =, α gs = s .
4π
4π
4π
8

(9)

Figure 3: The rotation curve of NGC 6503 from Ref. [4]. The dashed and dottedlines are expected contributions from visible matters, disk and gasses. The dashdotted line is the expected contributions from dark matter. The observed line isflat and can be explained by existence of dark matter.
In renormalization group, the coupling constants (actually they are not constants)vary with energy scale. This is called "running" couplings. The coupling constantas a function of energy is represented as follows:
1
β
E
1
=
+
ln( ),
α(E) α(E0 ) 2π
E0

(10)

where E0 is the energy scale we measure the initial coupling constants α(E0 ) andis usually Z-mass scale, and β is the beta function which depends on the theory (itdepends on the degree of group, and number of fermions and scalars).
The unification scale cannot be obtained simply with the Eq. (10) and (9).
The SM representation is arbitrarily chosen and not suitable for unification. For

9example, in the SM the covariant derivative can be modified as follows
τi
Y
λa a
A µ + ig W µi + ig0 B µ,
2!
2
2
!


a
g s cs λ ag cτi ig0 c0Y= ∂µ + i
Aµ + i
W +i 0
B µ,
cs
2
c 2 µ
c
2

D µ = ∂µ + igs

(11)

Dµ

(12)

where c, c0, cs are arbitrary constants. If the three groups are unified in somescale, the three groups must be the subgroup of one large group. This condition
imposes the equations:
!2
!2
!2
c0Y
cs λ a
cτi
= Tr
Tr
= Tr
(13)
2
2
2
From this equation, the gauge couplings becomer
5 0
gs, g,g.
3(14)

Therefore, if we define α0 = 53 α g 0 and use the coupling constants in Z mass scale
and beta function in SM from 1-loop, Eq.(10) become:17E
α s (E) = 8.47 + 2π ln( MZ ),19/6
1E
α g (E) = 29.6 + 2π ln( MZ ),(15)−41/101E
α 0 (E) = 59.0 + 2π ln( MZ ).

These three functions can be written in linear function,yi = ai x + bi,


(16)



where x=ln MEZ /2π and y = 1/α(E). If these three lines meet at one point E, thecondition is!
!
a1 − a2 b3 − b2
= 1.
(17)
a3 − a2 b1 − b2
In the SM case, from Eq. (15), Eq. (17) become 1.36 and is not equal to 1 (leftfigure of Fig 4). If we introduce MSSM(Sec.1.3), Eq. (10) become:13E
α s (E) = 8.47 + 2π ln( MZ ),1−1E
α g (E) = 29.6 + 2π ln( MZ ),
−33/5
1
E
α 0 (E) = 59.0 + 2π ln( MZ ).

10

(18)

In this case, the Eq. (17) is 1.006 and MSSM shows possibility to be GUT (rightfigure of Fig 4). If we expect GUT, supersymmetry becomes promising beyond

Figure 4: Running of gauge coupling in SM and MSSM [6]. The left figure is thecase for SM and there is no meeting point. The right figure is the case for MSSM.
SM theory.

1.2

Supersymmetry

The notation and logical layout of this section mainly follows "SuperSymmetry
Demistified"[7] and "Supersymmetry primer"[8].
Supersymmetry (SUSY) introduces the transformation between a fermion anda boson[8]Q |fermioni = |bosoni , Q |bosoni = |fermioni(19), where Q is the SUSY generator. With the transformation, each SM particle has
its "superpartner". The naming schemes for the superpatner is• To add prefix "s-" for fermions, e.g. superpartner of electron is selectron.
• To add suffix "-ino" for bosons, e.g. superpartner of gluon is gluino.
The formalization both including SUSY and Poincaré algebras is constrainedby Haag-Lopuszanski-Sohnius[9]. As a result, the SUSY algebra is introduced as:()
Qα, Q̄ β̇ = 2(σ µ )α β̇ Pµ,(20)()
Qα, Q β = 0,(21)()
Q̄α̇, Q̄ β̇ = 0,(22)fg
Qα, Pµ = 0,(23)fgQ̄α̇, Pµ = 0,(24)
11where Pµ is the translation generator of Poicaré group, dotted character meansright-chiral spinor, no dotted character means left-chiral spinor, and α = 1,2 andβ̇ =1,2 are the two types of spinor indices. Including the commutation rules ofLorentz generators (Mµν ) in Poincaré group,ff

Qα, MµνgQ̄ α̇, Mµν

g

=



=



σ µν

β

σ̄ µν

 α̇

α

Qβ

(25)

β

Qb .

(26)

Next, Grassmann number (θ) is introduced to make "superfield" which is transformed with both SUSY and Poincaré transformations. In this section, only
left-chiral superfields are used:1
V = φ(y) + θ · χ(y) + θ · θF (y),2(27)

where y µ = x µ − 2i θσ µ θ̄ (Wess-Zumino gauge), θ is Grassmann number, φ is ascalar field, χ is a fermion field, F is an auxiliary field, and a dot product meansχ · χ ≡ χT (−iσ 2 ) χ and hence χ · χ = χ2 χ1 − χ1 χ2 , and 1,2 means two typesof spinor indices. Only left-chiral fields are enough to describe fundamentals of
the SUSY. These fields are transformed as,
δφ
=ζ·χ
µ
δ χ = −i χσ (iσ 2 ζ ∗ )∂φ + FζδF= −iζ † σ¯µ ∂µ χ

(boson to fermion),(28)(fermion to boson, and fermion to F),(29)(F to fermion),(30)

where ζ is a fermion. Using these superfields, a minimal extension of the SM withSUSY is made.

1.3

MSSM

The minimal extension of the SM with SUSY is called Minimal SupersymmetricStandard Model (MSSM). Since this is an extension of the SM, the Lagrangian of
this model should include• fermion kinetic terms,• gauge bosons kinetic terms,• Higgs bosons kinetic terms,• Higgs bosons potential terms,• Higgs-fermion Yukawa coupling terms.
12The superfield of each particle can be written using Eq. 27. The summary ofsuperfileds are in Table 1. For example, the SU (2) L left-chiral quarks of first
generation are written as,
!
!
!
1
Fu
φ̃u
χu
,
(31)
Q1st =
+θ·
+ θ·θ
Fd
φ̃d
χd
2
where χ means quark, and φ̃u means superpartner of quark (squark). The corresponding anti-up and anti-down quarks are written as,
U = φ̃ū + θ · χū + 12 θ · θFū,(32)

D = φ̃d¯ + θ · χ d¯ + 12 θ · θFd¯.
Similarly, the other fermions can be written in superfiled.
Higgs fields (H ) are also written in superfield style. Though complex conjugate
Higgs field is introduced in SM, H † cannot be used. This is because superpotential
must be holomorphic to make SUSY-invariant Lagrangian. Thus, two Higgs fields
are introduced for MSSM.
About gauge vector superfields, V = V † is imposed. From this, for example,
SU (3)C superfield is written as1
1
1
1
G a = θσ µ G aµ + √ θ · θ θ̄ · λ̄ Ca + + √ θ̄ · θ̄θ · λ Ca − θ · θ θ̄ · θ̄ DCa
2
8
2 2
2 2

(33)

Kinetic terms of fermions and Higgs are composed of fermion or Higgs superfields
and gauge superfields. For the Qi , that becomes
Lkinetic = Qi† exp Y g0 B + gs G a λ a + gW i τi Qi ,
(34)
D

R
where V † V means d 2 θd 2 θ̄V † V. From this the interactions like gluinoD
quark-squark are derived.
Kinetic terms of gauge vector fields are written as
1
1
1
B · B| F + Tr(W · W )| F + Tr(G · G)| F ,
(35)
4
2
2
R
where Vi Vj means d 2 θVi Vj .
F
For now, the kinetic term of fermions, Higgs, and gauge bosons are implemented. The rest is implemented by the "superpotential". General gauge invariant
MSSM superpotentials are written as
Lgauge =

ij

ij

ij

W = yu Ui (Q j ◦ Hu ) − yd Di (Q j ◦ Hd ) − ye Ei (L j ◦ Hd ) + µHu ◦ Hd, (36)13Superfield

SU (3)CSU (2) L

U (1)Y

Description

fermions and Higgs bosons
Qi

3

2

1/3

quarks and squarks

Ui

3̄

1

-4/3

anti-up type quarks andsquarks

Di

3̄

1

2/3

anti-down quarks and squarks

Li

1

2

-1

leptons and sleptons

Ei

1

2

2

anti-leptons and sleptons

Hu

1

2

1

Higgs and Higgsinos

Hd

1

2

-1

Higgs and Higgsinos

gauge bosons
B

1

1

0

B and bino

W

1

1

0

W and winos

G

1

1

0

gluons and gluinos

Table 1: Summary of superfields. sleptons are the superpartner of leptons, Higgsinos are superpartners of Higgs. Bino, wino, gluino are superpartners of B, W, andg for each.
where A◦A means AT iτ2 A, ys are Yukawa couplings, from first to third terms means(s)fermion-(s)fermion-Higgs(ino) interactions and include Yukawa couplings, andforth term is called µ term.
Finally, all the terms needed for SM are implemented. In addition to theseterms, actually, there are some possible terms can be implemented. However theseterms are not desired, since they violate the lepton/baryon quantum numbers. The
terms areij

ij

W = a1 Di (Q j ◦ L) + a2 H ◦ L + a3 Li (L j ◦ E) + f cabc U a (D b ◦ D c ), (37)where as and f are coupling constants. For example, the first term and last term
lead to rapid proton decay. To avoid this R-parity conservation is introduced. The
details are described in Section 1.3.1.
1.3.1

R-parity

The first term and last term of Eq.37 leads to the rapid proton decay(Figure 5).
However, the life time of proton is limited by the search with the Super-Kamiokande
14experiment[10]. To avoid the lepton and baryon quantum number violation, "Rparity" is introduced. This is defined as
R = (−1) 3(B−L)+2s,(38)

where B and L are baryon and lepton number, and s is the spin. For SM particles
R = 1 and for SUSY paticles R = −1. If R−parity conservation is imposed, all theinteractions in Eq.37 are rejected.
R−parity is also motivated from the theoretical point of view. In SO(10) grandunified theories, the R−parity conservation automatically occurs[11].
If R-parity is conserved, two SUSY particles should simultaneously be generated with the collision of SM particles. Once SUSY particles are generated, they
can only decay into another SUSY particle with a SM particle or SM particles.
Therefore, the lightest SUSY particle (LSP) cannot decays into any other particles
and becomes a possible candidate for the dark matter.

Figure 5: Diagram of proton decays to e+ π 0 [8].

1.3.2

SUSY breaking term

If supersymmetry is not broken, the supersymmetric partners of the SM particles
have the same mass. However, such SUSY particles are not observed. Therefore,
a SUSY breaking is needed to explain the experimental fact. If vacuum state |0>
is not invariant under SUSY transformation, the SUSY breaks spontaneously. Itmeans Qα |0 >, 0 and Qα† |0 >, 0. The hamiltonian H is the operator P0 . Thiscan be derived from Eq.20,
2H = {Q1, Q1† } + {Q2, Q2† }(39)

Therefore the vacuum expectation value (vev) is
2 h0| H |0i = h0| Q1 Q1† |0i + h0| Q1† Q1 |0i + h0| Q2 Q2† |0i + h0| Q2† Q2 |0i(40)

Since the vacuum is assumed not to be SUSY invariant,h0| H |0i > 0,
15

(41)

is derived. However, there is no theoretical mechanism to break SUSY spontaneously within MSSM. With any term which can break SUSY spontaneously, oneof superpartner particles with mass lighter than the SM particles is predicted after
the SUSY breaking, and such particles are not observed. Therefore, SUSY breaking term should be added explicitly. Such terms are added as "hidden sector". It
is assumed that the SUSY breaks in this hidden sector. The interaction between
particles of MSSM and hidden sector is mediated only by "messenger interaction".
There are some models of mechanisms with different "messenger interactions",
and each model predicts different mass spectrum of SUSY particles.
mSUGRA mSUGRA stands for minimal SUper GRAvity model. In this model
gravity is the messenger interaction[12]. From this model, the ratios of the massesof three gauginos are predicted[8] to be
Mgluino : Mwino : Mbino ≈ 6 : 2 : 1.

(42)

Since R−parity is assumed to be conserved, this bino become the LSP. Therefore
Mgluino : MLSP ≈ 6 : 1.
GMSB GMSB stands for Gauge Mediated Symmetry Breaking. In this model,
a messenger interaction is gauge interaction[13]. From this model, the ratios ofthe masses of three gauginos are predicted[8] to be the same as mSUGRA case
(Eq.42).
AMSB AMSB stands for Anomaly Mediated Symmetry Breaking[14]. In thismodel, the messenger interaction is via anomaly. In typical models, the ratios ofthe masses of three gauginos are predicted[15] to be
Mgluino : Mbino : Mwino ≈ 7 : 3 : 1.

(43)

Since R−parity is assumed to be conserved, this wino become the LSP. Therefore
Mgluino : MLSP ≈ 7 : 1.
1.3.3

Target SUSY particles

Since the LHC is a hadron collider (Sec.2.1), the coloured SUSY particle production cross section is high (Figure 6). Therefore gluino or squark productions arehighly expected. Moreover, these particles are produced in pair, since the R−parity
conservation is highly motivated as described in Sec.1.3.1.
Squark mass has relation to the observed light Higgs mass of 125 GeV calculated with radiative corrections. With some reasonable parameter settings, a
16√Figure 6: Cross section for SUSY particles in s =8 TeV and 13,14 TeV [16].
squark (q̃) mass is expected to be greater than ∼ 10 TeV (Figure7). In contrast,
there is no such constraint on gluino (g̃) mass and hence gluino would possibly
be discovered in the LHC-ATLAS experiment. Therefore, the target particle isgluino. Since squarks are heavy, the each of pair-produced gluinos decays directly
into "electroweakino" and quark-antiquark pair via a virtual squark. This typicaldecay model is interpreted with "simplified model" (Sec.3.2.2). In Run1 (previous run of the LHC described in Sec.2.1), the LHC-ATLAS experiment excluded
gluino masses up to 1330 GeV [18] as shown in Figure 8. Therefore, pair-produced
gluinos whose masses & 1.3 TeV are the target of this analysis.

1.4

Objectives of this thesis

A search for supersymmetric partner of gluon (gluino) which decays hadronicallyis presented in this thesis.√ The new data recorded by the ATLAS detector inthat inproton-proton collision at s= 13 TeV is used. This energy
R is about twice−1
the previous LHC run. The analysed data correspond to Ldt = 3.2 fb .
The structure of this thesis is as follows. In the Chapter 2, overview of
the LHC and the ATLAS detector are described. In the Chapter 3, the useddata and Monte Carlo samples are described. The signal samples used for the
event selection optimization and interpretation are described in this section. In
Chapter 4, the used objects in this analysis and the triggers to select the objects aredescribed. Since this analysis uses hadronic events, the reconstruction of jets aredescribed in precise. Some performances of photons are also described, since thestudies about photons are also important in this analysis. In Chapter 5, a variable"aplanarity" is introduced in addition to the conventional discriminant variables.
Including aplanarity, the event selection is optimized for gluino signals as the17Figure 7: Mh contour in the tan β vs, MS (sparticle mass) plane. Solid line is central
value, dashed lines are 1σ contour, and dotted lines are 2σ contour. Xt /MS = 0,
µ = MS [17] .
target. In Chapter 6, the estimation method of background events after the event
selection is described. A new dedicated method to estimate number of events inthe signal region mainly using data is applied to this analysis. Also, validationof the estimated number of background events is described. For the backgroundestimation of Z (→ νν)+jets events, the events with hard photons are used. The
purity estimation of photon events is also described in this section. In Chapter 7,
the fitting method used in this analysis and statistical treatment for exclusion of
signals are described. In Chapter 8, the observed number of events after the event
selection are described with the estimated number of events. Using the results, theinterpretation with some signal models are presented. Finally in the Chapter 9, theconclusion of this analysis is given.

18

Figure 8: Exclusion contours (95%CL) in the mass plane of LSP and gluino fromprevious ATLAS analysis[18]. The model is the case pair-produced gluino decaysg̃ → qq χ̃01 . The solid and dotted red line show the observed limit and its ±1σ
excursion with signal theoretical uncertainties. The dashed blue line shows the
expected limit.

19

2

LHC and ATLAS detector

2.1

Large Hadron Collider

The Large Hadron Collider (LHC)[19] at CERN (the European Organization for
Nuclear Research) is a collider with two-ring superconducting accelerator and isinstalled in the 26.7 km tunnel underground near Geneva (Figure√ 9). It is designed
to collide proton beams with a center-of-mass energy (CME, s) of 14 TeV andwith a peak luminosity of 1034 cm−2 s−1 . The LHC is designed to accelerate 2,808
bunches for each proton beam and the bunch spacing is 25 ns. It is also designed tocollide heavy ions (Pb) with an energy of 2.8 TeV/nucleon and a peak luminosityof 5.1 × 1027 cm−2 s−1 .
√During 2011 and 2012 (Run1 period), the LHC ran at s =7 and 8 TeV, andpeak luminosity reached 7.7 × 1033 cm−2 s−1 with bunch spacing 50 ns.
The period
energy is√ from 2015 is referred to as Run2. the center-of-mass
33−2
increased to s =13 TeV and peak luminosity reached 5.0 × 10 cm s−1 withbunch spacing 25 ns. The recorded data with the ATLAS detector (Sec.2.2) is
described in Chapter.3.

Figure 9: The conceptual figure of LHC[20].

20

2.2

ATLAS detector

The ATLAS (A Troidal LHC ApparatuS) detector [21] is a general purpose detector
built for probing proton-proton and heavy ion collision.
2.2.1

Overview of the ATLAS detector

The detector layout is in Figure 10. The ATLAS detector has the cylindrical shape.
In the transverse plane, from inner to outer, the ATLAS detector is composed of
the Inner Detector (ID), superconducting solenoid magnet, Liquid-Argon (LAr)electromagnetic (EM) calorimeter, scintillator-tile hadronic calorimeter and themuon chambers which is surrounded by toroid magnets. The both end-caps of thecylinder are covered with LAr hadronic calorimeters, toroid magnets and muonchambers.

Figure 10: The overall layout of the ATLAS detector.[20]2.2.2

The coordinate system and nomenclature

For a three-dimensional coordination system, right-handed coordinate system isused. The definition is as follows:• x-axis: Direction from collision point to the center of the LHC ring.
21

• y-axis: Upwards direction perpendicular to the plane of the LHC ring.
• z-axis: One of the beam directions.
Azimuthal angle φ and polar angle θ are defined as usual polar coordinates.
To describe the 4 momentum of the particle, E, pT, η, φ are used.
E is the energy of the particle.
pT is a transverse momentumqpT = p2x + p2y .
(44)
η is a pseudo-rapidity and defined as!
θη = −ln tan
,
2

(45)

where θ is the polar angle. This η is the massless approximation of rapidity!
1
E + pzy = ln.
(46)
2
E − pzThe distance in the pseudo-rapidity and azimuthal angle space is defined asq(47)∆R = ∆η 2 + ∆φ2 .
2.2.3

Magnet system

The ATLAS magnet system consists of four superconducting magnets:• A solenoid magnet: The solenoid magnet is installed in barrel regions. It
covers ID ( Sec.2.2.4) and provides 2 T axial magnetic field for tracking.
• A barrel troid: The barrel troid provides approximately 0.5 T magnetic field
for central muon detectors.
• Two end-cap troids: Each end-cap troid provides approximately 1 T magnetic
field for end-cap detectors.
The overview of magnet system is shown in Figure 11.
2.2.4

Inner Detector

The Inner Detector (ID) is used for tracking charged particles. The ID is in themagnetic field of 2 T and the full tracking coverage is in |η| ≤ 2.5. From inner toouter in radial, the ID is composed of pixel detector, semiconductor tracker (SCT),
and the transition radiation tracker (TRT) as shown in Figure 12. The radiation
length (X0 ) as a function of η is in Figure 13.
22

Figure 11: Overview of magnet system in the ATLAS detector[22].
Pixel detector The pixel detector([24]) is the nearest detector to the beam-pipe.
It is designed to perform with high granularity and precision measurement. Precise
measurement with pixel detector determines the impact parameter and can finddecay vertices of particle with measurable decay length. The detector consists of
4 barrel layers and 6 disk layers (3 for each end-cap). The innermost barrel layer
is called Insertable B Layer (IBL)[23]. The pixel size of detectors except for IBL
is 50 × 400 µm and of IBL is 50 × 250 µm. The total 4 barrel layers are at mean
radius of ∼ 33.25, ∼ 50.5, ∼ 88.5, and ∼ 122.5 mm. The intrinsic accuracy inbarrel is 10 µm (R-φ) and 115 µm (z), and in end-cap is 10 µm (R-φ) and 115 µm(R).
Semiconductor tracker The SCT consists of layers of silicon microstrip detectors. The SCT system is designed to determine the track, impact parameter and vertex position. The SCT in barrel have eight layers which covers 255 < R < 549 mm
and |z| < 805 mm, and the SCT in each end-cap has nine wheel disks which cover
251 < R < 610 mm and 810 < |z| < 2797 mm.
Transition radiation tracker The TRT consists of 4 mm diameter straw tube
detectors. The TRT provides large number of hits for the track and provides
intrinsic accuracy of 130 µm. In barrel region, the straw tubes are aligned along
beam axis, and covers 554 < R < 1082 mm and |z| < 780 mm. In end-cap
region, the straw tubes are arranged radially and covers 617 < R < 1106 mm and827 < |z| < 2744 mm. In total, the TRT provides tracking in the range |η| < 2.0.

23

Figure 12: The sectional view of Inner Detector (ID) [20].

Figure 13: Radiation length versus η for each ID component. [23].

242.2.5

Calorimeter

The overview of the ATLAS calorimeter is presented in Figure 14. The calorimeterconsists of 4 types of calorimeter:• Electromagnetic (EM) calorimeter which covers |η| < 3.2.
• Hadronic barrel calorimeter which covers |η| < 1.7.
• Hadronic end-cap calorimeter which covers 1.5 < |η| < 3.2.
• Forward calorimeter which covers 3.1 < |η| < 4.9.
In total, the calorimeter covers the range |η| < 4.9. The granularity of the
EM calorimeter is very fine and provides precise measurements of energies andpositions for electrons and photons. The other calorimeter is for jet reconstruction
and measurement of ETmiss .

Figure 14: The overview of the ATLAS calorimeters[22].

25layerPresampler
Calorimeter

layer
Presampler
1st layer
2nd layer
3rd layer

EM calorimeter
BarrelEnd-cap|η| coverage
Number of layers|η| coverage
Number of layers|η| < 1.52
1
1.5 < |η| < 1.8
1|η| < 1.35
31.375 < |η| < 1.5
2
1.35 < |η| < 1.475
2
1.5 < |η| < 2.5
3
2.5 < |η| < 3.2
2|η| coverage
Granularity∆η × ∆φ|η| coverage
Granularity∆η × ∆φ|η| < 1.52
0.025 × 0.1|η| < 1.52
0.025 × 0.1|η| < 1.52
0.025/8 × 0.1|η| < 1.52
0.025/8 × 0.1
1.40 < |η| < 1.475
0.025 × 0.025
1.40 < |η| < 1.475
0.025 × 0.025|η| < 1.4
0.075 × 0.025|η| < 1.4
0.075 × 0.025
1.40 < |η| < 1.475
0.025 × 0.1
1.40 < |η| < 1.475
0.025 × 0.1|η| < 1.375
0.050 × 0.025|η| < 1.375
0.050 × 0.025

Table 2: Pseudo rapidity coverage, granularity and number of layers of the calorimeter system[21].

Electromagnetic calorimeter The EM calorimeter consists of LAr detectors
with electrodes and lead absorbers. The electrode has accordion geometry which
provides complete φ symmetry without azimuthal cracks. The summary of parameters is in Table 2. In the barrel region, the EM calorimeter has thickness >22X0 . In the end-cap region, the EM calorimeter have thickness >24X0 . The
barrel region which ID covers (|η| < 2.5) is required for precision measurement.
The EM calorimeter is segmented into three layers in radial and shower shape isused in the reconstruction. The first layer (also called "strip section") is equippedwith narrow strips in the η direction, and it realises precise η position measurement. This layer is used to measure the energy before the showering and provides
improved particle identification (e/π, γ/π 0 , and so on). The second layer is used
to measure the electromagnetic showers. The third layer is mainly used for the
separation from hadrons. In the end-cap, the calorimeter has two layers. In theregion of |η| < 1.8, presampler detector is installed inside of the EM calorimeter,
and it is used to correct the energy loss in the inner detectors or materials preceding
the EM calorimeter.
Tile calorimeter The tile calorimeter[21] consists of scintillating tiles and ironabsorber. The signals are read out via wave length shifting fibres to photomultipliers (PMTs). The tile calorimeter is composed of one barrel which covers range
of |η| < 1.0 and of two extended barrels which cover range of 0.8 < |η| < 1.7. In
radius, they covers range of 2.28 < R < 4.25 m. Each barrel is segmented in threelayers. The barrel layers have 1.5, 4.1 and 1.8 interaction length (λ) from inner toouter. Extended barrel layers have 1.5, 2.6 , and 3.3 λ.
26LAr Hadronic end-cap calorimeter The LAr Hadronic End-cap Calorimeter(HEC)[21] consists of two wheels at the behind of EM end-cap calorimeter andthey share the same LAr cryostats. The covering region is 0.475 < R < 2.03 m
and 1.5 < |η| < 3.2 and it has overlap with the tile calorimeter, and the forward
calorimeter.
LAr forward calorimeter The Forward Calorimeter (FCal)[21] consists of threemodules. One is made of copper and the other are made of tungsten. The FCal
covers the range of 3.1 < |η| < 4.9 and has ∼ 10λ. For the minimization of neutron
albedo in the ID cavity, the FCal is spaced from EM calorimeter by 1.2 m.
2.2.6

Muon spectrometer

The overview of the muon spectrometer[21] is Figure 15. The muon system is composed of Monitored Drift Tubes (MDT), Cathode Strip Chambers (CSC), Resistive
Plate Chambers (RPC), and Thin Gap Chambers (TGC). The main parameters are
in Table 3.
• MDTs cover large |η| region and provide precision measurement of track
bended by magnetic fields.
• CSCs are multiwire proportional chambers with cathodes segmented into
strips. They have high granularity and withstand the background conditions.
• RPCs are gas detector and the unit is a gas gap formed by two parallel
resistive bakelite plates.
• TGCs are multiwire proportional chambers.
RPCs and TGCs are used for triggering with pT of muons, for bunch-crossing
identification (ID), and for measuring muon direction with orthogonal coordinate
to MDTs.
2.2.7

Luminosity detector

The ID (2.2.4) is also used in luminosity measurement. The ID provides primaryvertices in proton-proton collision. The actual luminosity measurements are performed by LUCID[25, 26].
LUCID is a Cherenkov detector and is installed around beampipe at |z| = ± 17
m from interaction point (IP). It covers range 5.6 < |η| < 6.0. The inelastic
proton-proton collision scattering is detected by the Cherenkov photons created by
the charged particles. The Cherenkov photons are transferred to photomultipliertubes(PMTs). The hit pattern data of PMTs of LUCID is processed with Field
27

Figure 15: Overview of the ATLAS muon spectrometer components[20].
Components
MDT
CSC
RPC

Coverage in |η||η| < 2.7 (2.0 for inner most layer)
2.0< |η| < 2.7|η| < 1.05

TGC

1.05 < |η| < 2.7 (2.4 for trigger)

Function or target
Precision-tracking
Precision-tracking
pT threshold for triggering, bunchcrossing ID, and orthogonal measurementpT threshold for triggering, bunchcrossing ID, orthogonal measurement

Table 3: Main parameters of muon spectrometer[21].
Programmable Gate Arrays (FPGAs) and provides luminosity for given bunch
spacing.

28

3Data set and Monte Carlo samples

In this chapter the recorded data with the ATLAS detector is described in Sec.3.1.
The used Monte Carlo simulated samples are described in Sec.3.2.

3.1

Data samples

Total Integrated Luminosity [fb-1]√
The cumulative luminosity as a function of date in s = 13 TeV run is in Figure 16. The total recorded luminosity measured with ATLAS luminosity detector(Sec.2.2.7) is 3.9 fb−1 . Since not all detector status are good during a period, theperiods when all theR detector worked well are vetoed. Then the actually usable
data correspond to Ldt = 3.2 fb−1 .

ATLAS Online Luminosity5

s = 13 TeV

LHC Delivered
ATLAS Recorded

4

Total Delivered: 4.2 fb-1
Total Recorded: 3.9 fb-1

3
2
1
0
23/05

20/06

18/07

15/08

12/09

10/10 07/11
Day in 2015√
Figure 16: Total accumulated luminosity as a function of day at
proton-proton collision in 2015[27].

3.2

s = 13 TeVMonte Carlo samples

In this section, Monte Carlo (MC) simulated samples used in this analysis aredescribed. MC samples are needed to simulate the produced SM processes inproton-proton collision. In this analysis, MC simulated samples are widely usedin these studies:29• Event selection optimization to define signal region (SR) where a numberof events is counted.
• Background (BG) event estimation in SR.
• Contaminating event estimation in control region (CR).
• Study about the behaviour of SM process event (like, ABCD method study
in Sec.6.6).
The generation of MC simulated samples is as follows:
1. Generate partons for hard-process from Parton Distribution Function (PDF).
CT10[28], CT10f4[29], and NNPDF[30] are used as the PDF sets.
2. Matrix Element (ME) hard-process is generated with incoming two partonsin some order of α s . The α s used in ME calculation varies depending on
the interaction energy. The reference energy scale is fixed as "renormalization scale" and the α s of given energy is calculated with the approximatedfunction.
3. Parton shower (PS) is combined with the ME processes, since it is difficult togenerate high multiplicity parton processes with ME level calculation. The
parton shower from incoming partons is called initial state radiation (ISR)
and from outgoing partons is called final state radiation (FSR). To avoid
the overlap process in ME+PS combination, various merging processes ofpartons from ME and PS, such as a MLM merging[31] and a CKKW-L
merging[32], are applied.
4. The decay of heavy flavour partons (c, b) are simulated. This is by EvtGen[33] except for Sherpa samples.
5. The final state objects without detector simulation are called "Truth" objects.
These objects are processed with one of the following three detector simulations. One is the full simulation of ATLAS detector with Geant4[34].
Second one is the fast simulation with parametrized performance of the ATLAS detector. Third one is the smearing method which smears the jets pT
and ETmiss with Run1 ATLAS detector resolution [35].
3.2.1Standard Model MC samples

The used processes of the standard model MC processes, generators, and PDFs arelisted in Table 4. All of these samples are processed with Geant4 full-simulation.
The details of each process are described in the following paragraphs.
30

W, Z +jets: Both ME and PS are calculated with Sherpa2.1[36] using CT10
PDF set. The ME up to two partons are calculated at next-to-leading order (NLO)
and up to two additional partons are calculated at leading order (LO). The crosssection is normalized to next-to-next-to-leading order (NNLO). The alternative
MC samples are generated with Madgraph5 for ME and Pythia8[37] for PS.
γ+jets: Both ME and PS are calculated with Sherpa2.1 using CT10 PDF set.
γ
The ME up to three or four partons are calculated at LO with the filter, pT >35 GeV.
t t¯ and single top: The ME of t t¯, single top (s-channel and Wt-channel) processes
are generated with Powheg-Box v2 with CT10 PDF set at NLO. The ME of single
top (t-channel) is generated with Powheg-Box v1 with CT10f4 PDF set at NLO.
The PS is calculated with Pythia6[38]. The t t¯ process cross section is normalized
to NNLO+next-to-next-to-leading logarithm (NNLL). The alternative t t¯ sample isgenerated with "aMC@NLO"[39] for ME and Herwig++[40] for PS.
t t¯ + W /Z/WW : The samples are generated with Madgraph5 at LO for ME andwith Pythia8 for PS. NNPDF is used for PDF set. The cross section is normalized
to NLO.
Diboson process(Z Z, W Z, WW ): The samples are generated with Sherpa2.1
with CT10 PDF set. The main diboson processes in which the both bosons decay
leptonically are generated at NLO and additional up to three partons are generated
at LO. Z Z sample in which one of the bosons decays hadronically is generated at
NLO up to one parton and additional partons are generated at LO. W Z and WW
samples in which one of the bosons decays hadronically are generated at NLO only
for main processes and all additional partons are generated at LO.
Multi-jet: The multi-jet process is generated with Pythia8 at LO using NNPDF
as PDF set.
3.2.2

Signal samples

As described in Sec.1.3.3, the target signal is pair-produced gluinos each of which
decays into two quarks and one electroweakino. These typical decay models areinterpreted with "simplified model".
• Direct-decay model: For the case electroweakino is the LSP, the simplified
model g̃ → q q̄ χ̃01 is assumed (Figure 17(a)). In this model, gluinos arepair-produced and each gluino decays, g̃ → q q̄ χ̃01 , with branching ratio(BR)=100%.
31

Process

PDF

Generator

Z (→ νν) + jets
¯ + jets
Z/γ? (→ ` `)CT10

Sherpa2.1

CT10

Sherpa2.1

W (→ `ν) + jets

CT10

Sherpa2.1

γ + jetst t¯ and single top(s− and Wt− channel)

CT10

Sherpa2.1

CT10

Powheg-Boxv2 + Pythia6

Single top
t t¯ + W /Z/WW

CT10f4

Powheg-Boxv1 + Pythia6

NNPDF

Madgraph5+Pythia8

Diboson (Z Z, W Z, WW )CT10

Sherpa2.1

Multi-jet

NNPDF

Pythia8

Alternative MC samples
Z (→ νν) + jets
¯ + jets
Z/γ? (→ ` `)NNPDF

Madgraph5+Pythia8

NNPDF

Madgraph5+Pythia8

W (→ `ν) + jets
t t¯

NNPDF

Madgraph5+Pythia8

CT10

aMC@NLO + Herwig++

Table 4: Summary of the used MC samples for the SM processes with usedgenerator and PDF information.

• Onestep-decay model: For the case electroweakino is the second lightest
particle and have charge, the simplified model , g̃ → q q̄ χ̃±1 → q q̄W ± χ̃01
is assumed (Figure 17(b)). The BR of g̃ → q q̄ χ̃±1 and of χ̃±1 → W ± χ̃01±are
 simplified to be 100%. The masses of particles are set as m( χ̃1 ) =m(g̃) + m( χ̃01 ) /2.
These signal samples are produced with Madgraph5+Pythia8 using NNPDF for
the PDF set. The cross section of gluino pair-production is normalized to the crosssection calculated with NLL-fast[41–46]. The detector simulation for these signal
samples are processed with fast simulation.

32

q

q

W

p

q

p

g̃

g̃
g̃
p

q

χ̃01

χ̃±
1

χ̃01

χ̃∓
1

p

q

g̃

χ̃01
W

q

q
(a)

χ̃01

q

(b)

Figure 17: The Feynman diagrams of pair-produced gluinos. (a) shows directdecay of gluinos. (b) shows onestep-decay of gluinos. Though partons in protons
actually interact and produce gluinos, all such processes are represented by one
grey circle for simplicity.

33

4

Object definition and acquisition from data

In this chapter, definitions of physics objects used in this analysis are described.
Reconstruction and clustering methods of jets are described in Sec.4.1. Definitionsof electrons and muons are described in Sec.4.2 and Sec.4.4. Definition of a photon,variables used for photon identification, and performance of some isolation cuts forphotons are described in detail (Sec.4.3) since photons are used for the estimationof the major background of Z (→ νν)+jets events as described in Chapter 6. Afterthe description of objects definitions, triggers and cleaning selection to extract theobjects from data are described in Sec.4.7 and Sec.4.8.

4.1

Jets

Final state hadronic particles leave showers in the EM-calorimeter and the hadronic
calorimeter. This shower deposits their energy in multiple calorimeter cells. The
cell energies are summed up to form clusters. Jets are composed of the clusters. For
the jets used in this analysis, clustering method follows topological clustering[47]which is described in the following paragraphs.
In this analysis, jets are reconstructed using the anti-kT algorithm[48] withcone of size 0.4. Acceptance of jets are required to be pT > 20 GeV and |η| < 2.8 .
Moreover, jet cleaning (quality) cuts (Sec.4.1.2) are also applied. The baseline
jets are required to pass BadLoose quality cut. These jets are called Loose jets.
To calculate some variables used in this analysis, signal jets with pT > 50 GeV areused. To prepare top and W control regions, the information of jets with or withoutb-hadrons is used. The jet identification definitions are summarized in Table 5.
Topological clustering First, seed cells are put into a seed list with the descending order of S/N, where S is the energy and N is the RMS value of noise, and cells
which pass a threshold, S/N > 6, are identified as seed cells. Second, the neighbouring cells around the seed cells are added to seed cells if the neighbouring cells
pass a threshold, S/N > 3, where neighbouring cells mean the eight surrounding
cells in the same calorimeter layer. These two processes are iterated until the seed
list is empty. With the clustered cells, jets are reconstructed with anti-kt clustering
algorithm as described in following paragraph.
Jet clustering algorithm
In jet clustering algorithm, the distance between clusters (di j ), and between a34

cluster and beam (diB ) are used. In general, these are defined:di j =2p 2pmin(kti , kti )diB = kti ,
2p

∆i2j
R2

,

(48)
(49)

where kt is the transverse momentum (pT ), R is cone size, and ∆i j = (η i − η j ) 2 +(φi2 − φ2j ).
These variables are computed to find the minimum di j and diB .
• If di j < diB : The 4-vector of ith and jth clusters are summed. Thencalculate next minimum distances.
• If diB < di j : The ith cluster is determined as a "jet", and ith cluster isremoved from the list of clusters.
These processes are iterated until all clusters are clustered to jets.
In the anti-kt algorithm, p = −1. This means that objects with large kt
tend to compose minimum d and tend to include soft objects. Then, the soft
objects don’t define the boundary of jet cone and the jet become infra-red collinear
safe. Therefore, the jets are robust against the uncertainty of hadronization andunderlying event contamination, and are easy to be calibrated. In this analysis
R = 0.4 is used. After the jet clustering, the energy of jets with calorimeter in the
EM scale is corrected to energy of hadron with response of hadron estimated with
MC simulation[49].
4.1.1

B-jetsThe jets from b-hadrons (b-jets) are tagged using information from ID. The taggingof b-jets are called b-tagging and boosted-decision-tree (BDT) based algorithm
MV2c20 is used[50, 51] in the ATLAS. If a jet is associated with a track whichis reconstructed with ID hits, the jet is evalulated with MV2c20 value thresholdoperating point. The operating point corresponds to the efficiency of 77% for truthb-jets. In this operating point, the rejection power (inverse of efficiency) for charm
quark, light flavour quark, and τ-jet are expected to be approximately 5, 10 and
140 for each[51]. Since the tagging uses information from ID, b-tagging is applied
for jets in the range |η| < 2.5.
4.1.2

Jet cleaning

For the rejection of non-collision jets and detector noise background, BadLooseand BadTight jet cleaning selections are applied[52]. In the BadLoose cleaning,35

requirements for variables such as an energy fraction in the HEC is not large, anenergy fraction in the EM calorimeter is not small, and an energy fraction in one
layer is not large are applied. BadLoose selection is applied for all jets in theevents. If at least one jet does not pass the selection, the event is vetoed. In the
BadTight cleaning, a requirement for a variable such as an energy fraction of
tracks from a primary vertex is not small is applied. BadTight selection is applied
for the events with two leading jets which have pT > 100 GeV. If the jets in an event
don’t pass the cleaning cut, the event is vetoed.
Selection

Description
Baseline jet

AcceptancepT > 20 GeV & |η| < 2.8

ID

Loose
Signal jet

AcceptancepT > 50 GeV
B-jet

AcceptanceB-taggingpT > 50 GeV & |η| < 2.5
MV2c20 working pointwith 77% efficiency

Table 5: The definitions for baseline jet, signal jet, and B-jet identification.

4.2

Electrons

The electron clusters are reconstructed with the information from EM calorimeter[53]. The seed clusters with energy > 2.5 GeV from 2nd layer cell unit
(3 × 5 in η × φ) are formed by sliding window algorithm. If there are neighbouring
clusters, the duplicated clusters are removed. This algorithm is also used in photon
reconstruction (Sec.4.3). A cluster is identified as an electron, if there are at least
one associating track which is reconstructed with the information from the ID(|η| < 2.5). A track is determined as best track, if the track is nearest to the cluster
barycentre in the 2nd layer of the EM calorimeter.
For the identification of electron, likelihood based identification (ID) criteria[54] is applied. The variables, such as shower shape, measured in the EM
calorimeter are used for the calculation of likelihood. Three levels of working
point(Loose ID, Medium ID, and Tight ID ) are prepared depending on theselection tightness.
36

For a baseline electron, pT > 10 GeV and |η| < 2.47 acceptance cut, andloose ID selection is applied.
For a signal electron, significance of impact parameter requirement, |d 0 |/σ <5, longitudinal impact parameter requirement, |z0 · sin(θ)| < 0.5 mm, Tight
likelihood based identification criteria, and an isolation requirement from theother particles are applied. This isolation selection uses the information about thepT sum of tracks around the electron and/or transverse energy of clusters around anelectron. In this analysis GradientLoose isolation working point (WP) is used.
This isolation WP is likelihood based, and GradientLoose is defined to realize
electron efficiency of
ε = (0.057 · pT [GeV] + 95.57)% for (25 GeV < pT < 60 GeV),(50)

where ε = 95% at pT of 25 GeV and ε = 99% at pT of 60 GeV.
The definitions of electron are summarized in Table 6.
Selection

Description
Baseline electron

AcceptancepT > 10 GeV & |η| < 2.47

ID

Loose
Signal electron

ID

Tight

Isolation

GradientLoose|d 0 |/σ < 5|z0 · sin(θ)| < 0.5 mm

Impact parameter

Table 6: The definitions for baseline and signal electron identification.

4.3

Photons

The clustering method is the same as electrons (Sec.4.2). A photon is identified with using conversion information, identification (Sec.4.3.2), and isolation(Sec.4.3.3).
For a reconstructed photon, pT > 25 GeV and acceptance,|η| < 1.37||1.52 <|η| < 2.37, are required. The range 1.37 < |η| < 1.52 is removed, since the region
has a crack region between barrel and end-cap calorimeters. The identificationand isolation selection of photons are described in the following paragraphs.
The summary of photon definition is in Table 7.
37

Selection

Description
Baseline photon

AcceptancepT > 25 GeV & |η| < 1.37||1.52 < |η| < 2.37

ID

Tight
Signal photon

AcceptancepT > 130 GeVIsolation

Cone40

Table 7: The definitions for baseline and signal photon identification.
4.3.1

Photon conversion

If a vertex from one or two track matches to a photon cluster, the photon isreconstructed as converted photon, else the photon is reconstructed as unconverted
photon.
4.3.2

Photon identification

The variables used for photon identification is described in Table 8. With thesevariables, two types of IDs, Tight and Loose, are determined. The definition of
Loose and Tight photon ID are in Table 9 and Table 10 for each. The Tight ID
selection includes the Loose ID selection.

38

Name

Description

Variables using the information in the first layer of the EM calorimter (strip section)
DeltaE:= E2nd max − Emin , where E2nd max is the the energy of the
2nd maximum strip, and Emin is the energy in the strip whichhave minimum value between 1st and 2nd maximum strip.

Eratio:= (E1 − E2 )/(E1 + E2 ), where E1 is the energy of a strip
with maximum energy and E2 is the energy of a strip with
2nd maximum energy.

f1:= Eall−strips /EE M , where Eall−strips is the energy in all strips
in the cluster, and EE M is the energy reconstructed in the
EM calorimeter.

fracm

E(±3)−E(±1), where E(±i) is the energy in ±i strips aroundE(±1)

the strip with maximum energy
weta1

Shower width in ±1 strips around a strip with maximum
energy.

wtot

Total lateral shower width in strips.
Variables using the information of the hadronic calorimeter

Rhad1:= EThad,1st /ET , where EThad,1st is ET in the first layer of thehadronic calorimeter. This variable is only used in the range|η| < 0.8|||η| > 1.37 .

Rhad:= EThad,all /ET , where EThad,all is ET of all the hadronic calorimeter. This variable is only used in the range 0.8 < |η| <1.37 .

Variables using the information of energy in the second layer of the EM calorimeter
e277

Energies in 7 × 7 (η × φ) cell window.

Reta:=e237/e277, where e237 is the energies in 3 × 7 (η × φ) cell
window. Reta is ratio of energies in η.

Rphi:= e233/e237 (in φ), where e233 is the energies in 3 × 3(η × φ) cell window. Rphi is ratio of energies in φ.

weta2

Width of shower (in η direction)
Table 8: Variables definitions used for photon identification cuts.

39Name \ η range
Rhad (for |η | < 0.8or |η | > 1.5) >Rhad1 (for 0.8 < |η | < 1.5)
e277 >
Reta >
weta2 <

0.0 ∼ 0.6

∼ 0.8

∼ 1.15∼ 1.37

1.52 ∼ 1.81

∼ 2.01∼ 2.370.0606

0.052370.06482

0.04788

0.06506

0.06201

0.91750.01290.90000.01420.91090.01360.04908
0.1
0.89120.01390.89220.01520.92210.01280.89030.0125

Table 9: Loose ID configuration. The cut values are given in the table for each|η| range. These cuts are applied both converted and non-converted photons.
Definitions of the variables are given in Table 8.

Name \ η range
Rhad (for |η | < 0.8or |η | > 1.5)
Rhad1 (for 0.8 < |η | < 1.5) <e277 >
Reta >
Rphi >
weta2 <
f1 >DeltaE [MeV]<
Eratio >wtot <
fracm <
weta1 <

conversion

0.0 ∼ 0.6

∼ 0.8

∼ 1.15∼ 1.37

1.52 ∼ 1.81

∼ 2.01∼ 2.37

converted
non converted
bothconverted
non-converted
converted
non-converted
converted
non-converted
bothconverted
non-converted
converted
non-converted
converted
non-converted
converted
non-converted
converted
non-converted

0.014530.030.013230.030

0.029540.035

0.03132
0.03073

0.029930.05

0.04377
0.038940.9206
0.93120.51200.9
0.01180.011890.91050.90080.37600.85
0.01420.013370.91180.92590.51070.84
0.01270.011120.89380.9131
0.51130.91680.01510.01300

0.0.9222
0.92380.53970.9
0.01270.01208

0.89300.90700.470834
0.9
0.01250.01251

187.5
200
0.827
0.830
3.481
3.12
0.35390.600
0.7606
0.6671

175
111.5
0.857
0.854
3.513
3.20
0.42030.500
0.72560.7129

150
140
0.835
0.839
3.303
3.10
0.52120.600
0.77820.72070.03433
0.027250.1
0.91830.9206
0.53650.90200.01340.01276
0.005
150
140
0.790
0.783
3.214
2.92
0.59580.511
0.78230.7452176.455
250
0.842
0.896
3.909
3.00
0.58060.508
0.79310.7489

400
400
0.850
0.820
3.354
3.68
0.38220.238
0.77070.6867

493.3
400
0.80
0.840
2.232
2.15
0.27150.230
0.69280.6339

Table 10: Tight ID configuration. The cut values are given in the table. The
cut values are varied depending on conversion information and |η| range. All theselections require Loose ID intrinsically. Definitions of the variables are given in
Table 8.

40

4.3.3

Photon isolation

For the isolation, two types of variables are used, ptconeX and etconeX.
• ptconeX: The pT sum of tracks in the defined cone around the photon. The
tracks of the photon is excluded for the calculation,• topoetconeX: The transverse energy sum of the topological clusters in thedefined cone excluding the objective photon energy,
where X is 100 times value of the cone size (e.g. X=40 means conesize (∆R)=0.4).
From these variables, three types of isolation Working Points (WP) are preparedin the ATLAS experiment as in Table 11.
Working point nameCone40Cone20Cone40CaloOnly

topoetconeX based
topoetocone40 < 0.022 pT + 2.45 (GeV)
topoetocone20 < 0.065 pT (GeV)
topoetocone40 < 0.022 pT + 2.45 (GeV)

ptconeX based
ptcone20/pT < 0.05
ptcone20/pT < 0.05-

Table 11: Isolation working points used in ATLAS experiments.

4.3.4

Efficiency and purity of photons

The efficiency and purity of photons for each WP are checked using MC samples.
For the true(or signal) photon samples, γ+jets (Sherpa) is used. For the jet-tophoton fake (or background, BG) samples, Pythia multi-jets samples are used.
The definition of efficiency and purity are as follows:
Eff =

Sig

Niso

Niso + Nnon−isoSig

Purity =

Sig

,

(51)

.

(52)

Sig

Niso

Niso + NBG
isoSig

For this study, all the Tight ID passed photons are used. The results of theperformance is Figure 18. Since purity is important, Cone40 WP is used.

41

puritypurity1
Cone200.95

Cone401
Cone200.95

Cone40Cone40CaloOnly

Cone40CaloOnly

0.9

0.9

0.85

0.85

0.8

0.8

0.75

0.75

0.7

0.86

0.88

0.9

0.92

0.94

0.96

0.98

0.7

1
eff

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1
eff

(a) Purity vs efficiency for photon pT >130 GeV.

(b) Purity vs efficiency for photon pT >500 GeV.

Figure 18: Purity vs efficiency performance for each WP. After the selection: one
Tight ID photon and Njet (pT > 50 GeV) ≥ 2. The errors are MC statistical errors.

42

4.4

Muons

Muons are reconstructed with combining the information from inner detector andmuon spectrometer[55]. A muon candidate is required to be pT > 10 GeV and|η| < 2.4.
A baseline muon is required to pass Medium identification requirements[56].
This selection uses "stand-alone" muons, which the muon track is reconstructed
only in muon spectrometer, and use "combined" muons, which the muon track isreconstructed both in muon spectrometer and inner detector. This selection uses
the information of hits in each detector and momentum of muons. This selection istargeted to minimize the systematic uncertainties in calibration and reconstruction.
For a signal muon, significance of impact parameter requirement, |d 0 |/σ < 3,longitudinal impact parameter requirement, |z0 ·sin(θ)| < 0.5 mm, and isolation requirement from the other particles are applied. The isolation cut GradientLooseis the same definition as that of electrons which realize the efficiency of Eq 50.
The summary of muon definition is in Table 12.
Selection

Description
Baseline muon

AcceptancepT >10 GeV & |η| < 2.5

IDMediumSignal Muon

AcceptancepT >25 GeV & |η| < 2.4

Isolation

GradientLoose|d 0 |/σ < 3|z0 · sin(θ)| < 0.5 mm

Impact parameter

Table 12: The definitions for baseline and signal muon identification.

4.5

Overlap removal

A cluster or track is assigned to be different objects. To remove these duplicatedobjects, overlap removal (OR) of objects is applied for baseline objects. In theregions where photons are not used, the procedure of OR is,
1. e − µ OR: If e and µ are reconstructed using same track, the electron isremoved.
2. e−jet OR: If ∆R(e,jet) < 0.2, the jet is removed.
43

3. jet-e OR: If 0.4 > ∆R(e,jet)≥ 0.2, the electron is removed.
4. µ−jet OR: If ∆R(µ,jet) < 0.4 for the jet with Ntrack ≤ 2, the jet is removed.
5. jet-µ OR: If ∆R(µ,jet) < 0.4 for the jet with Ntrack > 2, the muon is removed.
In the regions where photons are used, additionally,
6. e-γ OR: If ∆R(γ, e) < 0.4, the γ is removed.
7. µ-γ OR: If ∆R(γ, µ) < 0.4, the γ is removed.
8. γ-jet OR: If ∆R(γ, jet) < 0.4, the jet is removed.
The validation study of γ-jet OR is described in Appendix A.1.

4.6

Missing transverse momentum

All the reconstructed and calibrated objects are used for ETmiss reconstruction[57].
The ETmiss is calculated from the vector sum of each component:
X
X
X
X
X
jets
µ
γ
e
~ miss = − *.
~~~~p~TSoftTerm +/ .
p
+
p
+
p
+
p
+
E
T
T
T
T
T
µ
jets
γ
SoftTerm, e(53)

The negative sum of p~T for the calibrated electrons (e), photons (γ), muons (µ),
and jets after overlap removal are used. The p~T not associated to these objects but
deposited in the detector is summed as "SoftTerm". In this analysis, Track Soft
Term (TST) is used. The TST is calculated from tracks which are reconstructedwith ID but are not associated with electrons, photons, muons or jets.

4.7

Triggers

The designed bunch crossing rate of the LHC is 40 MHz. The ATLAS trigger
system is designed to record a few hundreds Hz events from the 40 MHz bunch
crossing rate[58]. This is limited by the data processing or data storage capacity.
For the reduction of rates, the trigger system selects the events with selected physics
objects, e.g. electrons, muons, photons, jets(including b−jets, τ−jets) and ETmiss .
The ATLAS trigger system consists with three levels of processing. The firstlevel (L1) is the trigger with hardware which uses the information from calorimeterand muon detectors (RPCs and TGCs). The second level (L2) and the third (Event
Filter, EF) are the triggers with software which use all the information fromdetectors. The L2 and EF are together called the High Level Trigger (HLT). With
L1 trigger, approximately ∼ 100 kHz rate events are selected and with HLT .
1 kHz rate events are selected.
44

4.7.1

Triggers used in this analysis

To select data events which is interesting for this analysis, the events which passtriggers are used. In this analysis "No lepton", "One lepton", "Two leptons", and"One photon" events are used as described in Chapter 5 and Chapter 6. The triggers
dedicated for each event are used.
Electron trigger Two types of one-electron triggers are ORed, and used for "One
lepton" and "Two leptons" events selection. The first trigger require electrons with
Loose ID , isolated and pTe > 24 GeV. The latter trigger requires electrons with
Medium ID and pTe > 60 GeV.
Muon trigger Two types of one-muon triggers are ORed, and used for "One
lepton" and "Two leptons" events selection. The first trigger requires muons withµµ
Loose ID and pT > 20 GeV. The latter trigger requires muons with pT > 50 GeV.
Photon trigger One-photon trigger is used for "One photon" event selection.
γ
The trigger requires photons with Loose ID and pT > 120 GeV.
ETmiss trigger ETmiss trigger is used for "No lepton" event selection. The trigger
requires an event with ETmiss > 70 GeV. In order to get ETmiss events whose efficiency
for the ETmiss trigger becomes '1, ETmiss > 200 GeV is applied as off-line cut.

4.8

Event cleaning

For the rejection of detector noise background or events with mis-reconstructed,
event cleaning cuts summarized in Table 13 are applied. Details are described infollowing paragraphs.
Jet cleaning: As described in Sec 4.1, BadLoose and BadTight jet cleaning isapplied for all events.
Cosmic or fake muon veto: Fake muons are reconstructed when not-muon
object hits the muon spectrometer or when tracks are mis-matched. Cosmic
muons also make background events. Such events should be vetoed since themuons make large fake ETmiss . Such muons are not from hard collision of protons
and have large impact parameter. Therefore, the event is vetoed if muons after
overlap removal have |z0 |> 1 mm & |d 0 |>0.2 mm remains.

45

The other cleaning related to muons is applied to reject the badly reconstructedmuon events whose ETmiss have large muon fraction. The veto condition is
ETmiss Muons
ETmisswhere ETmiss Muons = −Number1
2

Cleaning
Jet cleaning
Cosmic muon3

Bad muonP· cos(φ(ETmiss Muons ) − φ(ETmiss )) > 0.5 ,(54)µ~T in Sec.4.6.
µp

Description of event veto condition
LooseBad jets with pT > 20 GeV. TightBad leading two jets with pT > 100 GeV.
Muons with |z0 |> 1 mm && |d 0 |>0.2 mm after overlap removal.
Events with

ETmiss M u o ns
· cos(φ(ETmiss Muons ) − φ(ETmiss )) > 0.5
ETmissTable 13: The summary table of cleaning.

46

5

Event selection and optimization

This chapter describes the event selection optimization. The selected region forsearching signal events is called "signal region (SR)". In Sec.5.1, the discriminating variables which are also used in the previous analysis [59] are described. In
addition to these variables, the "aplanarity" is introduced in this analysis and thestudies related to aplanarity are described in Sec.5.2. With these variables, thefinal SR optimization is described in Sec.5.3.

5.1

Discriminating variables
jet• "Njet " is number of jets with pT > 50 GeV. Compared to the SM backgrounds, Njet tend to be large for signal events since gluinos are pair-produced
and each gluino decays into Nparton ≥ 2.
• "ETmiss " is the missing transverse momentum and defined in Sec.4.6. Since
LSPs make large ETmiss events, requiring high ETmiss reduce the SM backgrounds. In some control regions for the background estimation describedin Sec.6, a lepton (e, µ) or γ is added to ETmiss to reproduce the ETmiss behaviour of a Z boson which decays into two neutrinos. Such ETmiss is written
as ETmiss0.
• "Effective mass (meff ) " is defined asmeff =N jet
X

pT jet,i + ETmiss,

(55)

i=1

where scalar sum of jets with pT > 50 GeV is used. This variable has strong
correlation with the energy of produced objects and helps to select SUSY
signal events.
miss• "min ∆φ(jet, E missT )" is the minimum azimuthal angle between jets and E T .
The jets with pT > 50 GeV are used for calculation of this variable. Thisvariable has strong discriminating power to reduce fake ETmiss events fromjet energy mismeasurements. This variable also reduces the events whichhave neutrinos from semi-leptonic decay of heavy flavour hadrons.

• "ETmiss /meff (N jet )" is the ETmiss to meff ratio. In this meff calculation, numberof jets up to N jet is considered. Since LSP does not exist in most of the SMprocesses, requiring large value of this variable reduces the SM backgrounds.
This also reduces fake ETmiss events from jets mismeasurements. This variable also reduces the events which have neutrinos from semi-leptonic decayof heavy flavour hadrons.
47

√
PN
• "ETmiss / HT " is the ETmiss to HT ratio, where HT = i=1jet pT jet,i . Since LSP
does not exist in most of the SM processes, requiring large value of thisvariable also reduces the SM backgrounds. This also reduces fake ETmiss
events from jets mismeasurements since ETmiss resolution is proportional to√
HT . This variable also reduces the events which have neutrinos fromsemi-leptonic decay of heavy flavour hadrons.

5.2

Study of aplanarity

Aplanarity[60] is introduced for g̃− g̃ production search in addition to the variables
used in previous search [59]. Aplanarity is the variable which have the informationthat the jets event is whether 3D shape (neither planar nor linear) or not. The
dominant BG processes of g̃ − g̃ search is Z(→ νν)+jets and the second dominantis W(→ `ν)+jets. In these BG events, hadron jets are mainly produced in the
opposite direction of the vector boson. Therefore, the shape of jets become linear
or planar as shown in Figure 19(b). In contrast, for the g̃ − g̃ production, the event
shape become not-planar shape as shown in Figure 19(a). This is because• The gluinos are produced in pair.
• The gluinos which we are searching for are heavy and are not boosted.
• Each gluino decays into three bodies (g̃ → χ̃01 qq).
Aplanarity is the variable which is sensitive to the differences.

Figure 19: Conceptual figures of (a) signal and (b) background(Z (→ νν)+jets)
events.
In this section, some study of aplanarity is described. The definitions of event
shape variables are in Sec.5.2.1 and Sec.5.2.2. The comparison of aplanarity withthe other event shape variables are in Sec.5.2.3. The evaluation of jets systematics
to aplanarity is described in Sec.5.2.4.
48

5.2.1

Definition of aplanarity, sphericity, and transverse sphericity[60]Aplanarity was generally used to evaluate not-planar event shape. In this paper,
aplanarity is derived from the momentum tensor of jets,
P2
Pix Piy Pix Piz
+
*. ix
2
Piy
Piy Piz //. Piy Pix
i=1
Piz2 , Piz Pix Piz Piy

NX
jets

(56)

The momentum tensor is diagonalized to,
λ1 0 0*. 0 λ0 +/2, 0 0 λ3-(57)

P3The λs are normalized to be i=1
λ i = 1, and named to be λ 1 > λ 2 > λ 3 . In caseλ 1  λ 2, λ 3 , the event shape is linear. In case λ 1 > λ 2  λ 3 , the event shapeis planar. In case λ 3 is large, the event shape is neither linear nor planar. The
definition and meaning of aplanarity, sphericity and transverse sphericity (ST ) arein Table 14.
nameAplanarity

definition
3
2 λ3

Sphericity
ST

3
2 (λ 2 + λ 3 )2
2 λ 1λ+λ2

meaning
Range is [0,0.5]. Aplanarity → 0.5 means the event is notplanar.
Range is [0,1]. Sphericity → 1 means the event is not linear.
Range is [0,1]. ST → 1 means the event is planar.

Table 14: Definition and meaning of variables

Safe aplanarity The definition of safe-aplanarity is similar to the aplanarity.
The only difference is to divide the momentum tensor by the momentum of eachjet:
P2
Pix Piy Pix Piz
NX
jets
*. ix
+
2
Piy
Piy Piz // /|Pi |(58). Piy Pix2
i=1
Piz , Piz Pix Piz Piy
Though the first motivation to introduce this variable is for infra-red collinear
safety of jet events, the jets clustered with the anti-kt algorithm is already collinear
safe. Therefore this variable is considered only for the sensitivity comparison.

49

5.2.2ThrustThrust and Transverse Thrust(Tt ) [61] is the event shape variable to evaluate thenon-linearity of events. The definition of thrust in this analysis is:P~i |i jet |T̂ · p
Thrust = 1 − P
,
(59)
~i |
i |p
where T̂ is the direction which make the sum of projected jet momentum maximum.
This variable is used to evaluate the event is linear or not. The event is linear in
the limit of Thrust → 0, and the difference from 0 means the event is not linear.
The definition of Transverse thrust in this analysis isP~t · p~ti |i jet | n
Tt = 1 − max P,(60)
i | p~ti |where n~t is the direction in transverse plane which makes the sum of projected jet
pT maximum. The event in the transverse plane is linear in the limit of Tt → 0,
and the difference from 0 means the event is not linear.
5.2.3

Comparison of event shape variables

In this section, six variables, including aplanarity, are studied in point of sensitivity.
MC samples• Signal sample: gluino direct-decay simplified model, m(g̃) = 1.6 TeV andm( χ̃01 ) = 250 GeV, is used as a bench mark• BG samples:Z(→ νν)+jets, W(→ lν)+jets, and t t¯ samples are used
Pre-selection To compare the shape variables, 4 jets pre-selections (Table 15)
are applied for the samples. This is because more than 3 quarks or gluons areproduced from the signal.
Simple Optimization The simple common cut combination of some promisingvariables used in the previous search [59](Table 16) are used in addition to theshape variables. And the scanned cut values for each event shape variables are in
Table 17. The optimization is executed by changing all the cut combinations tomaximize the significance,
Significance = q

NSignal
2 + (N σ2
NBG + σ stat
BG syst )

50

,

(61)

variable

cuts

ETmiss [GeV] >250

pT ( j1 ) [GeV] >130

pT ( j4 ) [GeV] >60∆φ(jet1,2,(3), E missT )min >0.4∆φ(jeti>3, E missT )min >0.2

Table 15: 4jets Pre-selection for the comparison of shape variables
where NSignal and NBG are number of signal and background events, σ stat is MC
statistical uncertainty, and σ syst is overall systematic uncertainty on estimatedbackground events. This significance is maximized under these conditions:• σsyst /NBG = 20%• NSignal >= 1 and NBG >= 1
• Target integrated luminosity:

R

Ldt = 3.0 fb−1

The first condition is from the typical error from previous analysis [59]. The
second condition is to avoid the over-training with very tight cut and small numberof events in CRs.
variablescanned values

ETmiss [GeV] >[250,600] with 50 intervals

jetmeff Nj >= 4, pT > 60GeV [TeV]>
ETmiss /meff (4j ) >

[1.8, 2.8] with 0.2 intervals
0.00, 0.02, 0.05, 0.07, 0.10, 0.12, 0.15

Table 16: Common cut combination
The optimization results and the distributions of shape variables for signal and
BGs, after pre-selections and all the other cuts, are in Table 18-23, and Figure 2025. "After all the other cuts" means the all cuts are applied except for the cut ofthe plotted variable. Because of a ETmiss cut, ETmiss /meff (4j ) is of no use.
Results The summary of significance for each shape variable is in Table 24.
Among the variables aplanarity shows the best performance. Therefore, aplanarity
is added to final optimization.
51

variable

scanned values

Aplanarity >[0.02,0.10] with 0.02 intervals

Safe Aplanarity >[0.01,0.10] with 0.01 intervals

Sphericity >[0.02,0.30] with 0.02 intervals

ST >[0.02,0.30] with 0.02 intervals

Thrust >[0.02,0.30] with 0.02 intervals

TT >[0.02,0.2] with 0.02 intervals

events/0.02

Table 17: Cut values for event shape variables

Z+jetsW+jetstt~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

variable

cutvalue

Aplanarity >0.04

ETmiss [GeV] >600

meff (Nj,pT >60GeV >= 4)[TeV]>

2.6

ETmiss /meff (4j ) >0.0

Signal/BG

1

4Aplanarity

200
00.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

0.2

0.22 0.24

Aplanarity

Figure 20: Aplanarity distribution
after all the other cuts (including pre-selections).
The (dark
Table 18: Optimized cuts with using
blue/blue/green) histogram shows
aplanarity.
Z (→ νν) + jets/W (→ `ν) + jets/t t¯
BG processes. The (red/magenta)line shows the (SM total/signal)
histogram. The lower pad shows
the signal to BG ratio of number of
events per bin.

52

events/0.02

cutvalue

W+jetstt~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

1

Safe aplanarity >0.09

ETmiss [GeV] >450

meff (Nj,pT >60GeV >= 4)[TeV]>

2.4

ETmiss /meff (4j ) >0.0

Signal/BG

variable

Z+jets400
0

cutvalue

Sphericity >0.2

ETmiss [GeV] >500

meff (Nj,pT >60GeV >= 4)[TeV]>

2.4

ETmiss /meff (4j ) >0.0

cutvalueST >missET [GeV] >0.18

meff (Nj,pT >60GeV >= 4)[TeV]>

2.6

ETmiss /meff (4j ) >0.0

0.12 0.14 0.16 0.18

0.2

0.22 0.24

Z+jetsW+jetstt~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

1

4Sphericity

2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Sphericity

Figure 22: Sphericity distribution
after all the other cuts.

events/0.1

variable

0.1

Figure 21: Safe aplanarity distribution after all the other cuts.

00
0Table 20: Optimized cuts with using
sphericity.

0.02 0.04 0.06 0.08

events/0.07

variable

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
SafeAplanarity

Signal/BG

Table 19: Optimized cuts with using
safe aplanarity.

SafeAplanarity

2

Z+jetsW+jets1tt~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

Signal/BG

600
4

00
0

Table 21: Optimized cuts with using
ST .

ST

2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
1

ST

Figure 23: ST distribution after all
the other cuts.

53

Thrust >0.22

ETmiss [GeV] >550

meff (Nj,pT >60GeV >= 4)[TeV]>

2.6

ETmiss /meff (4j ) >0.0

events/0.1

cutvalue

W+jetstt

4

cutvalueTT >missET [GeV] >0.14

meff (Nj,pT >60GeV >= 4)[TeV]>

2.6

ETmiss /meff (4j ) >

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ThrustFigure 24: Thrust distribution after
all the other cuts.

events/0.07

variableThrust200
0Table 22: Optimized cuts with using
thrust.

~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

1Signal/BG

variable

Z+jetsZ+jetsW+jets1tt~∼0m(g)=1.6 TeV, m( χ 1) = 0.25 TeV

Signal/BG

600
4

00
0

Table 23: Optimized cuts with using
TT .

TT

2

0.1

0.2

0.3

0.4

0.5

0.6

0.1

0.2

0.3

0.4

0.5

0.6

0.7
0.7

TT

Figure 25: TT distribution after all
the other cuts.

variable

cut value

significance

NSignalNBG

Aplanarity> 0.04

3.0+0.18−0.15

3.42 ± 0.04

1.22 ± 0.13

2.66+0.12
−0.11
+0.09
2.43−0.08
2.37+0.10
−0.09
+0.08
2.16−0.07
2.14+0.08−0.07

5.02 ± 0.04

3.09 ± 0.24

6.16 ± 0.05

5.2 ± 0.3

4.47 ± 0.04

3.12 ± 0.23

4.59 ± 0.04

3.83 ± 0.25

4.98 ± 0.04

4.51 ± 0.28

Safe aplanarity> 0.09Sphericity

> 0.2

ST

> 0.18TT> 0.14Thrust> 0.22

Table 24: Significance of shape variables. The variables are sorted in descendingorder of significance. The errors show the statistical error on the MC samples.

54

5.2.4

Jets Systematic effects for aplanarity

In this section, the jets systematic effects for aplanarity are studied in comparison
with number of jets selection(6-jets) which shows the best performance for largem(g̃) and small m( χ̃01 ) region in Run1 search. It can be suspected that aplanarity
is strongly affected by jets systematics, since aplanarity reflects the arrangementof jets. In such case, the sensitivity for signal events become worse, even thoughaplanarity have the discriminant power. Therefore, this study is very important.
jet

Selections for the study 6jet region (N jet >= 6, pT > 60 GeV) is prepared tocompare the systematic effects, since 6jet region showed the best sensitivity forthe target signal in previous search [59]. The optimization method is the sameas in the Sec. 5.2.3. For the 6 jets selection, ETmiss /meff (6j ) cut is used instead ofETmiss for following the previous search. And the optimized selections are shownin Table 25.
varriable

4jet+aplanarity

6jet

Njet (pT > 60 GeV) >=4

6

ETmiss [GeV] >

600

-

jet
meff (pT > 60 GeV)[TeV]>

2.6

2.4

Aplanarity >

0.04

-

-

0.15

ETmiss /meff (6j ) >Table 25: Selections of 4jet+aplanarity region and 6jet region for the study.

Uncertainties used for the study The used MC sample are the same as the study
in Sec.5.2.3. To evaluate the jet related systematic effects, these 5 components ofjet systematics are considered.
• Theory uncertainty– ISR : Initial state radiation (ISR) uncertaintiy. The nominal scale forthe first emission in MLM matching in Madgraph is multiplied byfactors of 0.5 and 2.0.
– FSR : Final state radiation (FSR) uncertainty. The nominal Λ value
used in running αs is multiplied by factors of 0.5 and 2.0.
– Scale: The nominal values used for the variation of the factorization
and renormalization scales are multiplied by factors of 0.5 and 2.0.
55

– ME-PS matching: The nominal jet matching scale to separate theparton generation in Matrix-Element (ME) and Parton Shower (PS) is
multiplied by factors of 0.5 and 2.0.
• experimental uncertainty– JES : The Jet Energy Scale (JES) uncertainty. This arises from thecomparison of jets from data and MC. In run1, the uncertainty is about
1.5% (This value is justified as in Figure 58) for jet pT about 60 GeV.
Jet pT is scaled by 100 ± 1.5% to evaluate this uncertainty simply.

events/1

events/0.05

The distributions of aplanarity and Njet after all the other cuts for each region
are in figure 27-30.

NONE
DOWN
UP

1

NONE
DOWN
UP

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

Aplanarity

2

4

6

8

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after all the othercuts of 4jet region.

(b) Njet distributions after all the other cutsof 6jet region.

Figure 26: Aplanarity and Njet distributions for ISR systematic variations.
(Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

56

events/1

events/0.05

NONE
DOWN
UP

1

NONE
DOWN
UP

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

2

4

6

8

Aplanarity

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after all the othercuts of 4jet region.

(b) Njet distributions after all the other cutsof 6jet region.

events/1

events/0.05

Figure 27: Aplanarity and Njet distributions for FSR systematic variations.
(Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

NONE
DOWN
UP

1

NONE
DOWN
UP

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

Aplanarity

2

4

6

8

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after all the othercuts of 4jet region.

(b) Njet distributions after all the other cutsof 6jet region.

Figure 28: Aplanarity and Njet distributions for Scale systematic variations.
(Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

57

events/1

events/0.05

NONE
DOWN
UP

1

NONE
DOWN
UP

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

2

4

6

8

Aplanarity

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after all the othercuts of 4jet region.

(b) Njet distributions after all the other cutsof 6jet region.

events/1

events/0.05

Figure 29: Aplanarity and Njet distributions for ME-PS matching systematic variations. (Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

NONE
DOWN
UP

1

NONE
DOWN
UP

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

Aplanarity

2

4

6

8

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after all the othercuts of 4jet region.

(b) Njet distributions after all the other cutsof 6jet region.

Figure 30: Aplanarity and Njet distributions for JES systematic variations.
(Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

58

Results The systematic effects for aplanarity and Njet are summarized in Table 26.
Except for a JES systematic, all the systematic effects for aplanarity are small compared to Njet ≥ 6 selection. In total, the systematic uncertainty effects withaplanarity cut is comparable to Njet selection.
The large JES systematic effect for 4jet region is strangely large. From thedefinition as written in 5.2.1, the scale of eigenvalue is normalized to calculate
aplanarity. In fact, this JES effects are from ETmiss . The Figure 31(a) shows the
JES systematic effects only after the Njet ≥ 4. The systematic uncertainty effect issummarized in Table 27. Then, the systematic uncertainty from JES for aplanarity
cut is very small compared to Njet selection.
component

4jets+aplanarity

6jets

+2.9
−1.7 %+2.9−0.0 %+0.0 %−1.0+0.4 %−0.0+7.0 %
−6.8
8.1 %
−7.1

+4.7 %−5.9+2.5 %−2.5+0.0 %−1.6+0.05 %
−0.8
+4.9
%
−4.6
7.2 %
−8.1

ISR
FSR
Scale
ME-PS matching
JES
Total uncertainty

events/1

events/0.05

Table 26: Summary of the systematic effects for 4jets region and 6jet region.

10
NONE
DOWN
UP

NONE
DOWN
UP

1

1

1.5

1.5

Aplanarity

Njet(pt>60 GeV))

1
0.5
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5
0

0.5

Aplanarity

2

4

6

8

10

12

Njet(pt>60 GeV))(a) Aplanarity distributions after Njet ≥ 4.

(b) Njet distributions after Njet ≥ 4.

Figure 31: Aplanarity and Njet distributions for JES systematic variations.
(Black/Blue/Red) solid lines show (nominal/scale-down/scale-up) variation.

59

component
JES

4jets+aplanarity

6jets+0.25 %
−0.25

+1.5 %−1.8

Table 27: JES variation effects for 4jet region and 6jet region only after the Njet ≥ 4
cut.

60

5.3

Optimization procedure

The overview of the procedure is
1. Optimize with TMVA for all the signal points (TMVA is described in AppendixB)
2. Select some signal points to determine signal regions
3. Determine cuts with distribution after all the other cutsThis optimization is dedicated for the 3σ reach of g̃− g̃ signal. For the optimization,
all the SM Monte Carlo samples described in Sec.3.2 are used. The definition of
the significance used in the optimization is described in Sec.5.3.1.
5.3.1

Definition of significane

If the number of events is not small the very simple significance (Z) can be used,
as
nsig
Z=q
,
(62)
2
nBG + (σBG )where nsig and nBG are number of signal and background events, and σ BG is theuncertainty of the background estimation. However, this significance is derived
with approximation that nBG and nsig are not small. In my analysis, the SRs are
determined to make the BG events small. In such case, the alternative evaluation
method is needed.
Therefore in this analysis, the other simple way to evaluate Z which is introduced in [62] is used. This is a solution for frequentist to the problem that ameasurement of the number of events in SR and a measurement of the number of
events in the control region (CR) to estimate the number of events in SR. In SR,
the measurement x distributed as Poisson around nsig + n BG . The estimated eventsfrom CR y distributed as Poisson around τ · n BG , where τ = σnBG
2 , and uncertainty
BG

in BG estimation is taken into account with τ. In summary, the probability density
function (p.d.f) become,P(x, y|nsig + n BG, τ) = Pois(x|nsig + n BG ) · Pois(y|τn BG )From this, the p−value is calculated as
B 1/(1 + τ), nsig + nBG, 1 + n BG · τ,p=
B nsig + nBG, 1 + n BG · τ

61

(63)

(64)

where B of numerator is a incomplete beta function and of denominator is beta
function. Then the significance (Z) is evaluated with the a one-tailed test ofGaussian distribution,√
Z = 2erf −1 (1 − 2p),(65)
where erf is the error function. Thanks to the appropriate treatment of estimated n BG with Poisson p.d.f, the evaluation of Z become much realistic for themeasurement of small number of events compared to Eq.62.
Conditions in calculating significanceance is as follows,

The conditions for calculating signific-• σBG /NBG = 30%• NSignal >= 1 and NBG >= 1
• Target integrated luminosity:

R

Ldt = 3.0 fb−1

The first condition is from the typical error from previous analysis [59]. The
second condition is to avoid the over-training with very tight cut and small numberof events in CRs.
5.3.2

Optimization with TMVA

The details of the Genetic Algorithm (GA) in TMVA[63] is described in Appendix. B. Pre-selections for input samples of BGs and signals are in Table 28.
For the five Njet cuts regions (N=[2,6]), the optimization method is applied after
the pre-selection. The variables used in optimization are in Table 29.
variablecondition

number of lepton ==~ miss [GeV] >
E

0

T
jet
pT 1st [GeV] >min ∆φ(jet1,2,(3), E missT ) >min ∆φ(jeti>3, E missT ) >number of jet (pT > 50 GeV) [GeV]≥

200
200
0.4
0.2
N

Table 28: Pre-selection for the Njet region.

62

variable~ missETjet

pT 1stjet

pT 2ndjet

pT 3r djet

pT 4thjetmeff (pT > 50GeV)
Aplanarity√
ETmiss /meff (Nj ) or ETmiss / HT
Only in 2jet region∆φ(jet1,2,(3), E missT )min∆φ(jeti>3, E missT )minTable 29: Scanned variables for optimization.
5.3.3

Results of optimization with TMVA

The 3σ sensitivity reaches with the best optimized cuts for each signal point are
in Figure 32. From the gluino direct-decay models(Figure 32(a)), three typicalpoints are selected for final signal region. From the gluino onestep-decay models(Figure 32(b)), one typical point is selected for final signal region.
For the different signal models, four points near the 3σ-reach line are selected(Table 30). The resultant cuts from the raw outputs of TMVA are summarized inTable 31.
5.3.4

Distribution check with TMVA results

The distribution after all the other cuts are checked to avoid :1. the local minimum of TMVA optimization
2. the meaningless cut which is already applied intrinsically after the other cuts.
If this cut remains, it would become difficult to get enough events in loosened
control regions which are used in background estimation (Chapter 6)
As an example, the distributions for SR4jL after all the other cuts are shown in
Figure 33, and 34. For each variable, dedicated check is done in point of S/Benhancement, as follows.
63SR name
SR4jL

signal points(m(g̃), m( χ̃01 )) =(1400, 200) (GeV)

SR4jM(m(g̃), m( χ̃01 )) =(1200, 600) (GeV)SR2jC(m(g̃), m( χ̃01 )) =(812, 787) (GeV)SR6jL(m(g̃), m( χ̃±1 ), m( χ̃01 ))=(1385, 705, 25) (GeV)

description
Gluino direct-decay model. This point is selected as a
typical point of large mass gap sample. This mass relation
is similar to the typical SUSY-model like mSUGRA andAMSB.
Gluino direct-decay model. This point is selected as a
typical point of middle mass gap sample.
Gluino direct-decay model. This point is selected as a
typical point of compressed mass sample. Since the mass
gap is small, the Njet cannot be high. Therefore, 2jetregion shows highest sensitivity.
Gluino one-step-decay model. This point is selected as a
typical point of large mass gap sample. Since the decaychain is long, Njet become high. Therefore, 6jet region
shows highest sensitivity.

Table 30: The selected mass points on the 3σ reach. Descriptions for each signal
mass points are described.
1. Aplanarity : aplanarity > 0.03 cut is chosen.
2. ETmiss : ETmiss > 470 GeV cut is chosen.
3. meff : meff > 2000. GeV is chosen.
jet

jet

jet

jet

4. pT 1st : No pT 1st cut is applied, since the cut is already applied intrinsicallyby the other cuts.
5. pT 2nd : No pT 2nd cut is applied, since the cut is already applied intrinsicallyby the other cuts.
jet

jet

jet

jet

6. pT 3r d : No pT 3r d cut is applied, since the cut doesn’t have significant
effects.
7. pT 4th : No pT 4th cut is applied, since the cut doesn’t have significant
effects.
8. ETmiss /meff (N j = 4) : No ETmiss /meff (N j = 4) cut is applied, since the cut isalready applied intrinsically by the other cuts.

64variable

cut values
Region

SR2jC

SR4jL

SR4JM

SR6jL

800

470.5

485.7

269.1

750.0

273.8

200.

218.4

50.0

84.5

138.5

210.7

-

56.4

55.9

106.3

-

83.9

90.3

142.1

meff (incl.) [GeV] >1900.

1948.51363.71776.4

Aplanarity

0.

0.020

0.039

0.066

ETmiss /meff (Nj )

0.25

0.

0.

0.07

ETmiss [GeV] >jet
pT 1st [GeV] >jet
pT 2nd [GeV] >jet
pT 3r d [GeV] >jet
pT 4th [GeV] >Only optimized in 2jet regionmin ∆φ(jet1,2,(3), E miss
T )

0.4

min ∆φ(jeti>3, E miss
T )

0.2

Table 31: The raw result of TMVA cut optimization.
miss
9. ∆φ(jet1,2,(3), E missT ) : ∆φ(jet1,2,(3), E T ) > 0.4 is applied to reduce multi-jets
backgrounds.
miss
10. min ∆φ(jeti>3, E missT ) : min ∆φ(jeti>3, E T ) > 0.2 is applied to reduce
multi-jets backgrounds.

5.3.5

The optimized SRs

In real event selection with data, some selections related to data acquisition isapplied (e.g. trigger and cleaning). A baseline selection including such selection
is summarized in Table 32. The final SRs definitions after the baseline selection
are determined as in Table 33. The MC expected distributions of variables in all
SRs after all the other cuts are in Figure 35-38, and it can be seen that the final
cuts effectively select signal events.

65

selection

description

cleaning

cleaning cuts described in Section 4.8

trigger

ETmiss trigger

ETmiss >200 GeVjet
pT 1st >jet
pT 2nd >200 GeV50 GeV

Table 32: Baseline selection for SR event selection.

66∼m(χ0) (GeV)

1400
pt_50_Njet_2
pt_50_Njet_3
1200

pt_50_Njet_4
pt_50_Njet_5

1000

pt_50_Njet_6∫ L dt=3.0 fb

800

-1

600

400

200

0
200

400

600

800

1000

1200

1400

1600

1800

m(~
g) (GeV)∼m(χ0) (GeV)(a) g̃g̃ → q q̄q q̄ χ̃01 χ̃01 samples.
1400
pt_50_Njet_2
pt_50_Njet_3
1200

pt_50_Njet_4
pt_50_Njet_5

1000

pt_50_Njet_6∫ L dt=3.0 fb

800

-1

600

400

200

0
200

400

600

800

1000

1200

1400

1600

1800

m(~
g) (GeV)(b) g̃g̃ → q q̄q q̄ χ̃±1 χ̃±1 → q q̄q q̄W ± W ± χ̃01 χ̃01 ( m( χ̃±1 ) = (m(g̃) + m( χ̃01 ))/2 )samples.

R
Figure 32: Expected 3σ sensitivity reach with Ldt = 3.0fb−1 . The cuts are
optimized for each signal point. (Black/Red/Blue/Green/Orange) solid lines show
the reach for (2/3/4/5/6)jet region.

67

events/50 GeV

events/0.01

Z+jetsW+jets∫top
dibosonL dt =3.0 fb

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV

10

1

1
1

10-1
2
1.5
1
0.5
00
0

10-1
2
1.5
1
0.5
00
0

Aplanarity

0.02 0.04

0.06

0.08

0.1

0.12 0.14

0.16

0.02

0.06

0.08

0.1

0.12

0.16

0.04

0.14

0.18

0.2

0.18

0.2

miss

ET
200

400

600

800 1000 1200 1400 1600 1800 2000

200

400

600

800

1000

1200

1400

1600

Aplanarity

events/50 GeV

events/100 GeV

1800

2000

Emiss
(GeV)
T

(b) ETmiss(a) Aplanarity
10

(GeV)

Z+jetsW+jets∫top
dibosonL dt =3.0 fb

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

1

1

10-1

10-1
2
1.5
1
0.5
00
0

2
1.5
1
0.5
00
0

meff (incl.)(GeV)
500

1000

1500

2000

2500

3000

500

1000

1500

2000

2500

3000

3500

4000

3500

4000

jet01 pt (GeV)

200

400

600

800

1000

1200

200

400

600

800

1000

1200

meff (incl.)(GeV)

1600(d) pT 1st
events/50 GeV

events/50 GeV

1600

1400

jet

(c) me f f (incl.)
Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

1

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

1

10-1
2
1.5
1
0.5
00
0

1400

jet01 pt (GeV)

10-1
2
1.5
1
0.5
00
0

jet02 pt (GeV)

200

400

600

800

1000

200

400

600

800

1000

1200

1400

1200

1400

jet03 pt (GeV)

100

200

300

400

500

100

200

300

400

500

jet02 pt (GeV)

600

700

600

700

jet03 pt (GeV)

jet

jet

(e) pT 2nd(f) pT 3r dR
Figure 33: Distributions of variables after all the other cuts.
Ldt = 3.0 fb−1 .
The lower pad shows the ratio of signal events to background events.

68events/0.05

events/50 GeV

10

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

1

W+jets∫ L dt =3.0 fb

topdiboson

1

10-1
2
1.5
1
0.5
00
0

jet04 pt (GeV)

100

200

300

400

500

100

200

300

400

500

600

700

600

700

miss

ET /meff(Nj=4)
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.9

1

0.8

0.9

1

(b) ETmiss /meff (N j = 4)

jetevents/100 GeV(a) pT 4th
Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV

10

0.8

Emiss
T /meff(Nj=4)

jet04 pt (GeV)

events/100 GeV

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV

1

10-1
2
1.5
1
0.5
00
0

Z+jets101

10Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

1
1

10-1

10-1
2
1.5
1
0.5
00
0

min∆ φ (jet

miss

,E

T

1,2,(3)

0.5

1

1.5

2

0.5

1

1.5

2

2.5
2.5

2
1.5
1
0.5
00
0

)

3

min∆ φ (jet3

,Emiss)T

1,2,(3)min∆ φ (jet

miss

,E

N>=4

0.5

1

1.5

2

0.5

1

1.5

2

2.5

)

3

2.5

min∆ φ (jetN>=4(c) ∆φ(jet1,2, (3), E miss
T )

T

3

,Emiss)T(d) min ∆φ(jeti>3, E missT )R
Figure 34: Distributions of variables after all the other cuts.
Ldt = 3.0 fb−1 .
The lower pad shows the ratio of signal events to background events.

69

N jet (pT > 50 GeV) ≥
Emiss
[GeV]
T

>

Aplanarity >meff (incl.) [GeV] >

SR2jC

SR4jL

SR4jM

SR6jL

2

4

4

6

800.

470.

450.

400

-

0.03

0.07

0.07

1900

2000

1600

1850

min ∆φ(jet1,2,(3), E missT ) >min ∆φ(jeti>3, E missT ) >Target signal

0.4(m(g̃), m( χ̃01 )) =(812, 787) [GeV]

0.2(m(g̃), m( χ̃01 )) =(1400, 200) [GeV](m(g̃), m( χ̃01 )) =(1200, 600) [GeV]70

Table 33: The selection criteria for each singal region.

(m(g̃), m( χ̃±1 ), m( χ̃01 )) =(1385, 705, 25) [GeV]events/50 GeV

events/100 GeV

Z+jetsW+jets∫ L dt =3.0 fb

top

10

diboson

-1

dijet
~
∼0
m(g)=812 GeV, m( χ )=787 GeV
1

102

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=812 GeV, m( χ )=787 GeV
1

10

1

10-1
2
1.5
1
0.5
00
0

Signal/BG

Signal/BG

1meff (incl.)(GeV)
500
500

1000
1000

1500
1500

2000
2000

2500
2500

3000
3000

3500 4000
3500 4000
meff (incl.)(GeV)

10-1
2
1.5
1
0.5
00
0

miss

ET
200
200

600
600

(GeV)

800 1000 1200 1400 1600 1800 2000
800 1000 1200 1400 1600 1800 2000
miss
ET (GeV)(b) ETmiss distribution.

(a) meff distribution.
events/100 GeV

400
400

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=812 GeV, m( χ )=787 GeV

101

Signal/BG

1

10-1
2
1.5
1
0.5
00
0

min∆ φ (jet

,E

2.5
2.5
min∆ φ (jet

,E

miss

1,2,(3)

0.5
0.5

1
1

1.5
1.5

2
2

T

)

3

1,2,(3)

3
miss
T

)

~ miss )(c) min ∆φ(jet, ET

Figure 35: Distributions of each variable used in SR2jC after all the other cuts. Signal sample is the gluino direct-decay model :(m(g̃), m( χ̃01 )) = (812, 787) [GeV].
The lower pad shows ratio of signal events to background events.

71

events/0.01

W+jets∫ L dt =3.0 fb

topdiboson

10

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV

Z+jetsW+jets

1

10-1
2
1.5
1
0.5
00
0

10-1
2
1.5
1
0.5
00
0

meff (incl.)(GeV)
1000
1000

1500
1500

2000
2000

2500
2500

3000
3000

3500 4000
3500 4000
meff (incl.)(GeV)

events/100 GeV

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV

10

1

0.06
0.06

0.08
0.08

0.1
0.1

0.12 0.14
0.12 0.14

0.16
0.16

0.18 0.2
0.18 0.2
Aplanarity

W+jetsdiboson

miss

(GeV)

800 1000 1200 1400 1600 1800 2000
800 1000 1200 1400 1600 1800 2000
miss
ET (GeV)

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV
1

10-1
2
1.5
1
0.5
00
0

ET

∫ L dt =3.0 fb

top

10-1
2
1.5
1
0.5
00
0

600
600

0.02 0.04
0.02 0.04

10

1

400
400

Aplanarity

Z+jets

1

200
200

-1

dijet
~
∼0
m(g)=1.4 TeV, m(χ )=0.2 TeV(b) Aplanarity distribution.

Signal/BG

events/50 GeV(a) meff distribution.

Signal/BG

diboson

1

1

500
500

∫ L dt =3.0 fb

top

10

1

Signal/BG

events/100 GeV
Signal/BG

Z+jetsmin∆ φ (jet

,E

2.5
2.5
min∆ φ (jet

,E

miss

1,2,(3)

0.5
0.5

1
1

1.5
1.5

2
2

T

)

3

1,2,(3)

3
miss
T

)

~ miss )(d) min ∆φ(jet, E
T(c) ETmiss distribution.

Figure 36: Distributions of each variable used in SR4jL after all the other cuts. Signal sample is the gluino direct-decay model :(m(g̃), m( χ̃01 )) = (1400, 200) [GeV].
The lower pad shows ratio of signal events to background events.

72

events/0.01

events/100 GeV

10

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.2 TeV, m(χ )=0.6 TeV

102

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.2 TeV, m(χ )=0.6 TeV

1

1

10
1
1

2
1.5
1
0.5
00
0

Signal/BG

Signal/BG

10-1
meff (incl.)(GeV)
500
500

1000
1000

1500
1500

2000
2000

2500
2500

3000
3000

3500 4000
3500 4000
meff (incl.)(GeV)

10-1
2
1.5
1
0.5
00
0

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.2 TeV, m(χ )=0.6 TeV

100.02 0.04
0.02 0.04

0.06
0.06

0.08
0.08

0.1
0.1

0.12 0.14
0.12 0.14

0.16
0.16

0.18 0.2
0.18 0.2
Aplanarity(b) Aplanarity distribution.
events/100 GeV

events/50 GeV(a) meff distribution.

Aplanarity

1

Z+jetsW+jets10∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼0
m(g)=1.2 TeV, m(χ )=0.6 TeV
1

1

10-1
2
1.5
1
0.5
00
0

miss

ET
200
200

400
400

600
600

Signal/BG

Signal/BG

1

(GeV)

800 1000 1200 1400 1600 1800 2000
800 1000 1200 1400 1600 1800 2000
miss
ET (GeV)

10-1
2
1.5
1
0.5
00
0

min∆ φ (jet

,E

2.5
2.5
min∆ φ (jet

,E

miss

1,2,(3)

0.5
0.5

1
1

1.5
1.5

2
2

T

)

3

1,2,(3)

3
miss
T

)

~ miss )(d) min ∆φ(jet, E
T(c) ETmiss distribution.

Figure 37: Distributions of each variable used in SR4jM after all the othercuts. Signal sample is the gluino direct-decay model :(m(g̃), m( χ̃01 )) =(1200, 600) [GeV]. The lower pad shows ratio of signal events to background
events.

73

events/0.01

events/100 GeV

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

10

-1

dijet
~
∼±
∼0
m(g)=1385 GeV, m(χ )=705 GeV, m( χ )=25 GeV
1

1

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

-1

dijet
~
∼±
∼0
m(g)=1385 GeV, m(χ )=705 GeV, m( χ )=25 GeV

10

1

1

1

10-1
2
1.5
1
0.5
00
0

Signal/BG

Signal/BG

1meff (incl.)(GeV)
500
500

1000
1000

1500
1500

2000
2000

2500
2500

3000
3000

3500 4000
3500 4000
meff (incl.)(GeV)

10-1
2
1.5
1
0.5
00
0

Z+jetsW+jets∫ L dt =3.0 fb

top

10

diboson

-1

dijet
~
∼±
∼0
m(g)=1385 GeV, m(χ )=705 GeV, m( χ )=25 GeV
1

1

0.06
0.06

0.08
0.08

0.1
0.1

0.12 0.14
0.12 0.14

0.16
0.16

0.18 0.2
0.18 0.2
Aplanarity

Z+jetsW+jets∫ L dt =3.0 fb

topdiboson

10

-1

dijet
~
∼±
∼0
m(g)=1385 GeV, m(χ )=705 GeV, m( χ )=25 GeV
1

1

1

Signal/BG

Signal/BG

1

10-1
2
1.5
1
0.5
00
0

0.02 0.04
0.02 0.04(b) Aplanarity distribution.
events/100 GeV

events/50 GeV(a) meff distribution.

Aplanarity

miss
ET (GeV)

200
200

400
400

600
600

800 1000 1200 1400 1600 1800 2000
800 1000 1200 1400 1600 1800 2000
miss
ET (GeV)

10-1
2
1.5
1
0.5
00
0

min∆ φ (jet

,E

2.5
2.5
min∆ φ (jet

,E

miss

1,2,(3)

0.5
0.5

1
1

1.5
1.5

2
2

T

)

3

1,2,(3)

3
miss
T

)

~ miss )(d) min ∆φ(jet, E
T(c) ETmiss distribution.

Figure 38: Distributions of each variable used in SR6jL after all the other cuts.
Signal sample is the gluino onestep-decay model :(m(g̃), m( χ̃±1 ), m( χ̃01 )) =(1385, 705, 25) [GeV]. The lower pad shows ratio of signal events to background
events.

74

6

Background estimation

SM processes in signal region (SR) become the background (BG) events. The
precise estimation of BG events is needed for higher signal sensitivity. In thischapter, the BG estimation methods used in this analysis are explained. For the
BG estimation, many control regions (CRs) are prepared. In each CR, contributed
SM processes are selected, and the events are used for SM BG estimation in SRs.
These CRs are summarized in Sec. 6.11.
One way to estimate the SM backgrounds in SR is to use MC simulated samples.
To remove the difference of acceptance between data and MC samples, some CRs
are prepared. For example, as described in 6.1, a CR where SM W +jets events areenhanced is prepared to normalize the number of events, and the normalization
factor is also used for W +jets SM process in a SR.
Another way to estimate the SM backgrounds is to use theoretical assumption.
To estimate the hard Z (→ νν)+jets BGs, γ+jets events are used as described inSec.6.4. For this estimation, various CRs are prepared.

6.1

Top BGs and W BGs

Top and W+jets BGs in a SR are estimated with MC samples. To correct thedifference in acceptance between data and MC, these MC samples are normalizedin 1-lepton (e or µ ) and 30 GeV < mT (`, E missT )1 <100 GeV region. This selection
enhances the event with W boson which decays to `ν. In the region, b-tagged(NBjet ≥) event is used for normalization of top MC samples (µT op ) and b-veto(NBjet = 0) event is used for normalization of W+jets samples (µW ). The btagged region is named top control region (CRT) and the SM process, t t¯ →bb̄W (qq)W (`ν), is enriched. The b-vetoed region is named W control region(CRW) and the SM process, W (→ `ν)+jets, is enriched. The µT op and µW are
fit simultaneously in both CRT and CRW, since b-tag or b-veto migration exists
because of the b-tag efficiency. In SR, the process W decays to hadronic decaying
tau is dominant. To select the similar kinematic phase space, leptons in CRT and
CRW are dealt as jets to reproduce the hadronic tau decay. The meff distributionsin CRT and CRW for SR4jL signal region are shown in Figure 39, and the nominal
number of events estimated with MC samples is normalized to the number ofobserved events in high meff region. The summary of top and W CRs is in
Table 34.
1mT (`, E miss
T ) =

q

2ETmiss pT` (1 − cos φ), where φ = ∆φ(p`T, E missT )75

Events/200.0∫ L dt = 3.2 fb s=13 TeV-1

CRT_no_meffcut for SR4jL
Data 2015 ( s = 13 TeV)
SM Total
Z+jetsDibosonW+jetst t (+X) & single top

2

10

103

1

500

1000

1500

2000

2500

3000

3500

4000

meff(incl.) (GeV)

CRW_no_meffcut for SR4jL
SM Total
Z+jetsDibosont t (+X) & single top
W+jets101
500 1000 1500 2000 2500 3000 3500 4000

-1

2

10

30
2.5
2
1.5
1
0.5
0
0

∫ L dt = 3.2 fb s=13 TeV

Data 2015 ( s = 13 TeV)

10DATA / MCEvents/200.0
DATA / MC

103

30
2.5
2
1.5
1
0.5
0
0

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

meff(incl.) (GeV)(a) meff distribution in CRT for SR4jL.

(b) meff distribution in CRW for SR4jL.

Figure 39: meff distribution in top CR and W CR. The normalizations of the MC
samples are before the fit. In the high meff region (larger than the point indicatedby red arrow), the number of events estimated with MC samples is normalized tothat of observed data. The red shaded band in SM total and yellow band in ratio
plot show MC statistical error plus systematic errors. The systematic errors arefrom generator uncertainties and JES uncertainty described in Sec.7.4.

6.2

Multi-jet BGs

The multi-jet background in high ETmiss region is mainly from mis-measurementof jet momentum. The imbalance from jets momentum causes ETmiss . The heavy
flavour hadrons which decay semi-leptonically also make ETmiss due to missing
miss is small. Therefore, theneutrinos. In such events, the min ∆φ(jet, E missT ) and ET
miss cuts.
number of multi-jets events is very small after min ∆φ(jet, E missT ) and ET
For the estimation of this BG events, multi-jets MC samples are used. To correct
the discrepancies of acceptance and cross section for data and MC, multi-jet MC
is normalized in the QCD multi-jets CR (CRQ) where inverted min ∆φ(jet, E missT )cut is imposed. The fit parameter for normalization is µ Multi jets .

6.3

Diboson BGs

The BG events from WW, WZ, and ZZ processes are estimated with MC samples.
The CRs for these processes are not prepared, since these processes have small
production cross sections. Though pure CRs for these processes can be preparedby requiring two or three leptons, branching ratios for two or three leptons are verysmall and enough events cannot be prepared in small integrated luminosity case.

76

sample nametop

region for
constraint
fit value
process forconstraint
Lepton is dealt
asused regions

CRW,CRT

description
compared to
SR-like cutsW

top loose

W loosetop very loose

CRTL

-

CRTVL

µTop
µW
µTopL
t t̄ →W(`ν)+jets
t t̄ →
b b̄W (qq)W (`ν)
b b̄W (qq)W (`ν)
jet
SR, CRY,SR,
CRYMA,CRY,
CRYMa,CRYMA,
VRZMa,
CRYMa,VRWMA,
VRZll,
VRWMa,
VRZllMa
VRZll,
VRZllMa
ETmiss , aplanarity,min ∆φ cuts areloosened.

CRWL,
CRZllL,CRYmA,
CRYma,
VRWmA,
VRZllmA

W veryloose-µTopVLt t̄ →
b b̄W (qq)W (`ν)
0
E miss= E miss+ p~T `T
T-

CRZllL,CRYmA,
CRYma,
VRZllmA

meff cut and aplanarity
cuts are inverted.

CRWVL,
CRZllVL-CRTVL,
CRZllVL

ETmiss 0 and meff cuts areinverted. No min ∆φ andaplanarity cuts.

Table 34: Summary of implementation of top and W CRs. (top or W) loose andvery loose samples are used in data-driven γ replacement described in Sec.6.5.

6.4

Z(→ νν)+jets BG estimation with γ replacement

Z(→ νν)+jets background is the dominant BG in SR. The simple way to estimate
this BG is using Z(→ ``)+jets events in 2 lepton region where the events are very=
pure. However, the ratio of Branching Ratio (BR) is small, BR(Z→ee)+BR(Z→µµ)BR(Z→νν)
6/20. Therefore, small number of events can be obtained in tight CR with similar
selection to SR. In such case, it is difficult to estimate Z(→ νν)+jets events in
SR. To avoid this problem, γ replace method[64, 65] is used in this analysis. Thismethod uses the theoretical basis that the γ+jets and Z+jets are produced with thesame diagram (Figure 40).
ν
γ

ū

ū

Z
ν̄
g

g
u

u
g

g

g

g

(a) Feynman diagram of uū → γ + 4ggg(b) Feynman diagram of uū → Z (→ νν)+4g

Figure 40: Feynman diagrams of uū → V + 4g.
There are some differences between Z+jets and γ+jets events which should be77

taken into account:• Difference in reconstruction efficiency and cross section between Z and γ• Difference in couplings of partons with bosons (Z or γ)• Difference in mass of Z and γ
The reconstruction efficiency and cross section of γ+jets event have to be normalized to Z (→ νν)+jets events and the correction is described in Sec.6.5.
The difference in coupling make difference in number of jets in the production.
If the same number of jets cut is imposed for γ+jets selection as for SR selection,
this difference is negligible.
The difference in mass is solved by selecting high boson pT region. Since
the mass difference become negligible in high boson pT region, the difference inboson pT distribution of Z and γ is negligible. From the previous research [64],the pT ratio of V+jets (V=Z and γ) follows empirical rule,np2
R = R0 * 2 T 2 + ,, pT + MZ -(66)

where R0 is the constant value, MZ is the mass of Z-boson, and n is constantdetermined empirically. At the limit MZ is negligible compared to boson pT , theR become constant R0 . n ≈ 1.2 is determined empirically in Ref.[64] from the
distributions as in the Figure 41. With this rule, The |R-R0 | is at most 5% whenpTV > 400 GeV(Figure 42).
Thus, if the region where pTV is high enough can be prepared, behaviour of
Z+jets events is similar to that of γ+jets events and can be estimated with γ+jets
events except for cross section and acceptance differences. This is solved by thedata-driven γ replacement method described in Sec.6.5. In the CR of γ (CRY)γ~ miss | is used for event selection, andof this estimation method, ETmiss0 = | p~T + E
Tthe same selection criteria as SR are imposed to reproduce the ETmiss cut to the
Z (→ νν) events in SRs.
The other subject to be accounted is the purity in CRs of γ. For the control ofγ+jets events, the high purity of γ is important. This estimation is described inSec.6.10.

78

Figure 41: The boson pT ratio for the process pp → V + 1parton from Pythia8[64].

Figure 42: The |R-R0 | distribution of Eq. 66.

79

6.5

Data-driven γ replacement

In the case that pT of the vector boson is high enough, the difference in distributions
between Z and γ are small. And the difference is only for the cross section andacceptance. In the case that ETmiss cut in SR and ETmiss0 cut in γ+jets selection aretight (ETmiss or ETmiss0 >∼ 400 GeV), the WXYZ method described Sec.6.7 is used inthis analysis. Moreover, to enhance the γ+jets events, ABCD method using γ+jets
events described in Sec.6.6 is used. Though this BG estimation method is no one
tried before, the validity of this method is well studied. In previous analysis [59],the γ to Z correction is derived with MC samples, hence the estimated numberof Z (→ νν)+jets events has large systematic uncertainty due to the generator. To
avoid such uncertainty and experimental one (e.g JES uncertainty), this data-driven
BG estimation is adopted in this analysis.

6.6

ABCD method for γ+jets CR

In most of the Signal Regions (SRs), the dominant Background (BG) process is
Z (→ νν)+jets events. This number of events can be estimated with using γ+jets
events in γ+jets CR (CRY) which is determined by the similar kinematic selection
criteria as SR.
Since tight selection criteria are needed for higher sensitivity of signals, numberof events in CRY inevitably becomes small after the tight selection. Therefore,
enhancement of number of events in CRY is needed.
In SR4jL, SR4jM, and SR6jL, effective mass (meff ) and aplanarity cuts areused. Effective mass reflects the mass scale of the center of production system,
and aplanarity reflects the non-planarity of the jet events. Therefore, these twovariables are quite independent.
In this section, ABCD method with meff and aplanarity are studied. The generaldescription of ABCD method is described in Appendix C.
6.6.1

Selection

For this study, a simple selection is applied(Table 35). Nj(pT > 60 GeV) ≥ 4
cut is applied since aplanarity cut is mainly used in 4-jet region. ETmiss0 means~ miss , i.e. E miss0 =absolute value of the vector sum of γ transverse momentum and E
TT~ miss |.
| p~T γ + E
TFor the ABCD method with meff and aplanarity, the four regions in Table 36
are prepared. The four regions are also shown in Figure 43.

80Variable
Number of Leptons
Nj(pT > 60 GeV)min∆φ( jet 1,2,3, ETmiss )min∆φ( jet N j>=4, ETmiss )pT ( j1 )ETmiss ’

Cut Value
== 0
≥4
> 0.4
> 0.2
> 130 GeV
> 600 GeV

Table 35: Selections used in the study of ABCD method in γ CR.
Region namecut conditionA
meff > 2600 GeV& aplanarity> 0.04
B
meff > 2600 GeV& aplanarity≤ 0.04
C2600 GeV > meff > 1600 GeV& aplanarity> 0.04
D2600 GeV > meff > 1600 GeV& aplanarity≤ 0.04
Table 36: Regions for ABCD method. The number of events in A region need tobe estimated from the number of events in the other regions.

Figure43: 2D distribution of meff vs aplanarity, and definitions of four regions.
R
L dt =3.0 fb−1 . Aplanarity is divided into 20 bins and the range is [0.0, 0.2]
. meff is divided into 19 bins and the range is [1600, 2000] (GeV). The nominal
γ+jets MC sample described in Sec.6.6.2 is used.
81

6.6.2Monte Carlo sample

For the study of systematic errors due to the γ+jets event generators, one nominal
Monte Carlo (MC) truth sample and four systematic MC truth samples are generated (Table 37). All the MC are generated with Sherpa. The distributions ofmeff and aplanarity for each sample are shown in Fig 44. Cross sections used forsystematic samples are the same as nominal MC.
Varied parameters
NominalFactorization scale 0.25
Factorization scale 4.0
Renormalization scale 0.25
Renormalization scale 4.0

Generator
Sherpa 1.8
Sherpa 2.1
Sherpa 2.1
Sherpa 2.1
Sherpa 2.1

Number of Events
4500000
4500000
4500000
4500000
4500000

events/200 GeV

Table 37: γ+jets MC samples used in this analysis.

102

nominalfac025
fac4
reno025
reno4

10

1

2
1.5
1
0.5
0

meff(pT>60 GeV)(GeV)

1600

1800

2000

2200

2400

2600

events/0.04

meff(pT>60 GeV)(GeV)

nominalfac025
fac4
reno025
reno4

102

10

1

2
1.5
1
0.5
0
0

Aplanarity

0.02

0.04

0.06

0.08

0.1

Aplanarity

Figure 44: Distributions ofR meff and aplanarity for the γ+jets MC samples withvarying QCD parameters. Ldt =3.0 fb−1

82

6.6.3

Evaluation of the 2D correlation

The correlation of meff and aplanarity was evaluated after the selection shownin Table 35. 2D histogram of the variables is plotted in Figure 43. With thishistogram, the correlation factor is calculated to be 0.0124 . Thus the ABCD
method can be applicable for meff and aplanarity, since correlation factor is small
compared to 1.0 .
6.6.4

Systematic Uncertainty in γ ABCD method

The actual uncertainty for ABCD is evaluated in this section. Because of weakcorrelation, this equation can be assumed,A(C RY ) ' B ×

C
,
D

(67)

where A, B, C, and D show the number of events in each corresponding region.
Therefore, the value to evaluate difference can be written as,
R−1=

A D
× − 1,B C(68),where R = BA × CD .
R − 1 value is calculated for each systematic sample (Table 38).
Varied parameters
NominalFactorization scale 0.25
Factorization scale 4.0
Renormalization scale 0.25
Renormalization scale 4.0

R−1
0.01622-0.04401-0.02619
0.00071-0.02653

R − 1 error (MC stat.)0.000270.000750.000450.00001
0.00047

Table 38: R − 1 values for each systematic sample
As a result, the R − 1 value and uncertainties for R − 1 are,(R − 1) = 0.01622 ± 0.00027(MCstat.) ± 0.043(syst.),(69)

where uncertainty of each systematic sample is half of the difference from thenominal sample. An expected number of events in region A is 2.98 ± 0.04 (MCstat. error) and in region B is 11.6 ± 0.08 (MC stat. error). Therefore, 3.89 timesof events can be gained, and statistical error of observed number of events can be
decreased from ∼58% to ∼29% only with increasing systematic uncertainty by atmost ∼4%.
83

6.7

WXYZ method

Philosophy of this method is the following:(1) Since the major background in SR is Z (→ νν)+jets events, this number
should be reliably estimated by using number of events in various CRs, notrelying on the MC simulation as much as possible.
(2) The ratios between numbers of events in one CR to the other CR (scale
factors) should be evaluated in two CRs where reasonably large number of
events are expected.
The definitions of each CRs are summarized in Table 48 in Sec.6.11 and it would
help to understand the method.
This is the method to estimate X (Z → νν) events in SR using W(W → `ν),Y(γ), and Z(Z→ ``) events in each CR. In high vector boson pT region, the ratioof pTV distributions for γ and Z, as well as that for γ and W are flat, since the massdifferences are negligible. Using this fact, the Z(→ νν)+jets in SR are estimatedwith γ+jets in CR of γ (CRY) where similar selections are applied to SR. At
this point, the key issue is to normalize the number of γ+jets events to that ofZ(→ νν)+jets events. This is represented in equation,!
Z(νν) + jets
γ+jets,dataZ(νν),expected
,
(70)
· SF
NSR
= NCRYγ + jets
where SF means Scale Factor. One of the simple ideas is to prepare SF in loose
CR and normalize γ+jets events to Z(→ ``)+jets events. However, the numberof Z(→ ``)+jets events become too small with tight pTZ cut. In order to avoid
this problem, W(→ `ν)+jets evens are used intermediately for the normalization.
Similar to the relation between Z+jets and γ+jets, W+jets and γ+jets behave
similarly with high pTV cut. Therefore, at first, number of γ+jets events are once
normalized to number of W(→ `ν)+jets events in loose CR as in the Figure 45.
This CR is defined with the same ETmiss0 2 cut but with inverted aplanarity and meffcuts.

2 ETmiss 0= |E miss+ pT (γ)| for γ, and ETmiss 0= |E miss+ pT (lepton)| for W(→ `ν). For the caseTT~ miss . Therefore E miss 0 is missing p~T of W
of W(→ `ν), the neutrino p~T is already included in E
TTγ
Wboson. For large pW
T , where W boson mass is negligible, pT and pT are expected to have similar
distributions.

84

Figure 45: Conceptual figure of the WXYZ method. There are three types of CRs.
First is the tight CR which has similar kinematic cut as SR. Second is the loose(L)CR where meff cut and aplanarity cut are inverted to the selection imposed in SR.
Third is the very loose (VL) CR where pTV cut and meff cut are inverted to theselection imposed in SR. In tight CR, a γCR is named as CRY. In Loose CR, theγCR is named as CRYL, and a CR for W (→ `ν)+jets is named as CRWL, whichmeans loose CR of W. In very loose CR, a CR for W (→ `ν)+jets is named as
CRWVL, which means very loose CR of W, and a CR for Z (→ ``)+jets is namedjets
as CRZllVL, which means very loose CR of Z (→ ``). The SF Z (→νν)+
γ+ jets  is the W (→`ν)+jetsratio of number of events in SR (Z (→ νν)) to CRY. The SF
is theγ+jets Z (→``)+ jets 
ratio of number of events in CRWL to CRYL. The SF W (→`ν)+ jets is the ratio of
jets
number of events in CRZllVL to CRWVL. The SF ZZ (→νν)+(→``)+ jets is the correction
factorand branching
The WXYZ
methodacceptance W (→`ν)+ratio.
 Z (→νν)+assume
 that of lepton
jets
Z (→``)+ jets
jets
jets
SF Z (→νν)+
=
SF
·
SF
·
SF
γ+ jets
γ+ jets
W (→`ν)+ jets
Z (→``)+ jets . Such
SF is evaluated in the CR where reasonably large number of events is expected forthe corresponding data sample.

85

These are represented with equation,!
!
!
Z(νν) + jets
W(`ν) + jets
Z(νν) + jets
SF
= SF
· SF
γ + jets
γ + jetsW(`ν) + jets!
W(`ν)+jets,data
NCRWL
Z(νν) + jets=,
· SF
γ+jets,dataW(`ν) + jets
NCRYL

(71)

where CRUL (U=W or γ ) is loose CR with the same ETmiss0 cut in CRY and withinverted meff and Aplanarity cut.
Secondly, the W(→ `ν)+jets events are normalized to Z(→ ``) events in veryloose CR, where inverted ETmiss0 cut is applied as shown in Figure 45. The massdifference between W and Z is negligible compared to the minimum ETmiss0 cut> 200 GeV which is applied for very loose CRs. These are represented withequation,!
!
Z(``)+jets,data
NCRZllVL
Z(νν) + jets
Z(νν) + jets
SF
= W(`ν)+jets,data · SF,W(`ν) + jetsZ(``) + jets
NCRWVL

(72)

miss 0where CRUVL (first U= Zll or W ) is the very loose CR with inverted ET cut ofZ (νν)+ jets
CRYL or CRWL. The SF Z (``)+ jets includes the lepton acceptance correction
and BR correction. In this analysis, this SF is calculated from MC,!
Z(νν)+jets,MC
NVRZVLZ(νν) + jets
= Z(``)+jets,MC ,SFZ(``) + jets
NCRZllVL(73)

Summarizing Eq. (70, 71, 72, and 73):
Z(``)+jets,dataZ(νν)+jets,MCW(`ν)+jets,data
NCRZllVL
NVRZVLγ+jets,data NCRWL
Z(νν),expected· W(`ν)+jets,data · Z(``)+jets,MC
NSR= NCRY·γ+jets,dataNCRYL
NCRWVL
NCRZllVL

This is the basic of the WXYZ method.

86

(74)

6.7.1

Small Corrections for WXYZ method

There are some assumption in WXYZ method and they are put aside in Sec.6.7.
At first, in Eq. (71), it is assumed that
γ+jetsRZ/Y :=

NZ(νν)· NCRYLSR
γ+jetsNCRY · NZ(νν)
VRZL

' 1,

(75)

where VRZL is the 0-lepton loose cut region whose cut is similar to CRYL. IfRZ/Y − 1 evaluated by MC is not zero, the value RZ/Y should be multiplied toγ+jetsNCRYL and the difference from 1 should be considered as uncertainty.
Secondly, in Eq. (72), it is assumed that
Z(``)+jets

RZ/W :=

NCRZllL

W(`ν)+jets· NCRWVL

W(`ν)+jets

NCRWL

Z(``)+jets· NCRZllVL

' 1,

(76)


If RZ/W − 1 evaluated by MC is not zero, the value RZ/W should be multipliedZ(``)+jets
to NCRZllVL and the difference from 1 should be considered as uncertainty.
6.7.2

WXYZ method with ABCD method

For the estimation of Z → νν BG in SR with meff and aplanarity cut, ABCD
method with meff and aplanarity (Sec.6.6) is also used. For the ABCD method, theCRY in Sec.6.7 is renamed as CRYMA, which means the CR of γ where both meff
cut and aplanarity cut are imposed. In the naming scheme for CRs, the followings
are used,• M : meff cut is imposed.
• A : aplanarity cut is imposed.
• m : Inverted meff cut is imposed.
• a : Inverted aplanarity cut is imposed.
For ABCD method, 3 additional CR for γ+jets is needed,• CRYMa: A CR of γ where meff cut and inverted aplanarity cut are imposed.
• CRYmA: A CR of γ where inverted meff cut, and aplanarity cut are imposed.
• CRYma: A CR of γ where inverted meff cut, and inverted aplanarity cut are
imposed.

87

Using these regions, ABCD method can be written:
γ+jets,data
γ+jets,data
NCRYMa · NCRYmA
γ+jets,data
NCRYMA =.
γ+jets,data
NCRYma(77)

If the correction factor is needed for ABCD method, Eq. (77) is corrected,
γ+jets,data
γ+jets,data
NCRYMa ·RYABCD ·NCRYmA
γ+jets,data


N
=

γ+jets,data
NCRYma CRYMAγ+jets,MC γ+jets,MC
NCRYMA ·NCRYma RYABCD := Nγ+jets,MC ·Nγ+jets,MC
CRYmA

CRYMa





(78)

Including all Eq. (74, 76, 75, 78),Z(νν),expected

NSR=

γ+jets,data

NCRYMaγ+jets,dataW(`ν)+jets,data· RYABCD · NCRYmA
NCRWL· RZ/Y·γ+jets,data
γ+jets,data
NCRYmaNCRYmaZ(``)+jets,data·Z(νν)+jets,MC· RZ/W NVRZVL· Z(``)+jets,MC ,W(`ν)+jets,data
NCRWVL
NCRZllVL

NCRZllVL(79)

where CRYma is also used as CRYL.
6.7.3

WXYZ method without ABCD method

As in the Table 33, aplanarity cut is not imposed for SR2jC. For the backgroundestimation in SR2jC, WXYZ method without ABCD method is used. This is thesame as Eq.74 with correction factors Eq.75 and Eq.76. To use the same naming
scheme as WXYZ method with ABCD method, WXYZ method without ABCD
method is written as,W(`ν)+jets,data· RZ/Yγ+jets,data NCRWL
Z(νν),expected
NSR= NCRYMA ·γ+jets,data
NCRYmaZ(``)+jets,dataZ(νν)+jets,MC
NCRZllVL· RZ/W NVRZVL·· Z(``)+jets,MC ,W(`ν)+jets,data
NCRWVL
NCRZllVL(80)

where CRYMA is the CRY,and CRYma is the region meff cut is inverted. Because
aplanarity cut is not applied, the "A" and "a" in the names of CRs are meaningless.
6.7.4

Fitting implementation of ABCD and WXYZ method

The implementation of simultaneous fit is very complex for solving the correlation
among many CRs. For this, the same variable (ε in this section) should be used in88different CRs to transfer the correlation effects. The definition of fit parameter is in
Table 39. These parameters are simultaneously fitted in the all control regions. To
avoid the local minimum, initial value is obtained from MC estimation. However,the parameters can freely change ± 100% from the nominal value. The same
number of CRs are prepared as these fit parameters. Therefore, all the parameters
are determined, unless other nuisance parameters.
In addition to these fit parameters, there are correction factors Rs as in Eq.(75,76, and 78), andZ(``)+jets,MC
NCRZllVL(81)
SF``/νν = Z(νν)+jets,MC ,NVRZVL
where the numerator and denominator of SF are inverted for technical requirement.
R correction factors are evaluated with using MC. For the conservative estimation,
the fit range (error) of Rs are set to include 1.0. SF``/νν values are derived fromfull simulated MC.
Now all the materials are prepared. The actual fitting implementations aredescribed in following paragraphs.
Practical implementation of WXYZ with ABCD method
Summarizing all Eq. (79, 81) and Table 39, the practical implementation with fit
parameters are,µZ · ε YMA · ε YMa · RYABCD CRYMa · µZ · ε YMA · ε YmA CRYmAµZ SR =
µZ · ε YMA · ε YMa · ε YmA CRYma
µZ · ε YMA · ε YMa · ε YmA · ε WL · RZ/Y CRWL·(82)
µZ · ε YMA · ε YMa · ε YmA CRYma
µZ · ε CRZllVL · RZ/W · SF``/νν CRZllVL·.
µZ · ε YMA · ε WL · ε CRZllVL CRWVL
As you can calculate, all the parameters (ε) in right hand side are cancelled in
total.
Practical implementation of WXYZ without ABCD method
Summarizing all Eq. (80, 81) and Table 39, the practical implementation with fit
parameters are,
µZ · ε YMA · ε Yma · ε WL · RZ/Y CRWLµZ SR = µZ · ε YMA CRYMA ·µZ · ε YMA · ε Yma CRYma(83)µZ · ε CRZllVL · RZ/W · SF``/νν CRZllVL·.
µZ · ε YMA · ε WL · ε CRZllVL CRWVL

89

variable definition descriptionµZ

NZ(νν)SRε YMA

NCRYMA

ε YmA

Number of Z+jets events in SR.

γ+jetsNZ(νν)SR

Ratio of number of events in CRYMA (γ+jets) to
SR(Z+jets).

γ+jetsNCRYmAγ+jetsNCRYMA

Ratio of number of events in CRYmA (γ+jets) to
CRYMA (γ+jets). This is not used in WXYZ
method without ABCD method.

ε YMaγ+jetsNCRYMaγ+jetsNCRYMA

Ratio of number of events in CRYMa (γ+jets) to
CRYMA (γ+jets). This is not used in WXYZ
method without ABCD method.

ε Ymaγ+jetsNCRYmaγ+jetsNCRYMA

Ratio of number of events in CRYma (γ+jets)
to CRYMA (γ+jets).
This is not used in
WXYZ method with ABCD method, sinceε Yma = ε YmA · ε YMa .

ε WLε CRZllVL

W(`ν)+jets

NCRWL

γ+jetsNCRYmaRatio of number of events in CRWL (W(`ν) + jets)
to CRYma (γ+jets).

Z(νν)+jets

NVRZVLZ(νν)+jets

NSR

Ratio of number of events in VRZVL(Z+jets) to
SR(Z+jets).

Table 39: Definitions of fit parameters in simultaneous fit. The fitted values andscan ranges are listed in Table 43-46 for different SRs.

90

Validation region (VR) with WXYZ method
Using all the information in previous sections, some validation regions can be
implemented as described in Table 40. The "One photon", "One lepton", "Two
lepton", and "No lepton" definitions and pre-selections are described afterwards
in Table 47. The details of the selections are summarized afterwards in Sec.6.12.
Region Name

implementation in
WXYZ+ABCD

implementation in
WXYZ w/o ABCD

Description

CRYMAµZ · εYMA-"One photon" VR when WXYZ w/o
ABCD is used.

VRZllµZ · SF` ` /νν"Two lepton", Z(``) VR with similar
kinematic selection criteria as SR.

VRZllmAµZ · εmA · SF` ` /νν-"Two lepton", Z(``) VR.

VRZllMaµZ · εMa · SF` ` /νν · RYABCD-"Two lepton", Z(``) VR.

VRZMaµZ · εMa · RYABCD-"No lepton" VR.

VRZmaµZ · εMa · εmAµZ · εma"No lepton" VR.

VRWMAµZ · εYMA · εWL"One lepton", W (→ `ν) VR.

VRWmAµZ · εYMA · εmA · εWL-"One lepton", W (→ `ν) VR.

VRWMaµZ · εYMA · εMa · εWL · RYABCD-"One lepton", W (→ `ν) VR.

Table 40: All the possible implementation of VRs with εs and Rs in(ABCD+)WXYZ method. The naming scheme, e.g. MA, is the same as describedin Sec.6.7.2 and Sec.6.7.3. The "One photon", "One lepton", "Two lepton", and"No lepton" definitions and pre-selections are in Table 47.

6.7.5

Removing contaminating events in CRs

The contaminating events in CRs have to be removed. The MC samples are used
to remove the contamination as follows• CRWL: Diboson, Z+jets and top MCs are used to remove the contamination.
The nominal diboson MC sample is used. The normalization factor of Z+jets
MCs (µ Z L ) is fitted in CRZllL. The normalization factor of Top MCs (µT opL )is fitted in CRTL.
• CRWVL : Diboson, Z+jets and top MCs are used to remove the contamination. The nominal diboson and Z+jets MC samples are used. The
normalization factor of Top MCs (µT opV L ) is fitted in CRTVL.
91

• CRZllVL: Diboson, W+jets and top MCs are used to remove the contamination. The nominal diboson and W+jets MC samples are used. The
normalization factor of Top MCs (µT opV L ) is fitted in CRTVL.
• CRZLllL: Diboson, W+jets and top MCs are used to remove the contamination. The nominal diboson and W+jets MC samples are used. The
normalization factor of Top MCs (µT opL ) is fitted in CRTL.
• CRTL : Diboson, W+jets and Z+jets MCs are used to remove the contamination. The nominal diboson and W+jets MC samples are used. The
normalization factor of Z+jets MCs (µ Z L ) is fitted in CRZllL.
• CRTVL: Diboson, W+jets and Z+jets MCs are used to remove the contamination. The nominal MC samples are used.
The details of top and W MC usage are summarized in Table 34.

6.8

γ/Z and W/Z check

Before the usage of WXYZ method described in Sec6.7, some points given below
should be checked:
1. The number of event ratio (γ/Z ) of meff and aplanarity distribution after thetight pTV cut. Because Z/γ ratio is extrapolated from high meff and aplanarity
regions to low meff and aplanarity region, the flatness of the ratio distribution
is needed.
2. The number of event ratio (W/Z) of ETmiss distribution after the inverted meffcut. Because W/Z ratio is Z/W ratio is extrapolated from low ETmiss to highETmiss region, the flatness of the ratio distribution is needed.
For the study of γ/Z ratio or W/Z ratio, the baseline selection (Table 41) is prepared.
These studies are done with truth Sherpa samples calculated at leading order, andjet and ETmiss smearing described in Sec.3.2 are applied.
For the study of γ/Z ratio, the distributions are checked as in Figure 46. Since
the ratio plot is flat, it is acceptable to extrapolate γ/Z ratio along aplanarity andmeff .
For the study of W/Z ratio, the distributions are checked as in Figure 47. Since
the ratio plot is flat, it is acceptable to extrapolate W/Z ratio along ETmiss .

~ miss + p~T (γ)| for γ sample.
3ETmiss for Z sample, and | ETmiss~ miss + p~T (lepton)| for W(`ν) sample.
4ET for Z sample, and | ET92

variable namecut value

Nlep =

0

Njet (pT > 60GeV) ≥4

pT ( j1st ) >130 GeV0min ∆φ(jet1,2,(3), E miss
) >
T

0.4

0
min ∆φ(jeti>3, E miss
)>
T

0.2

events/125 GeV

events/0.01

Table 41: Baseline selection for the study of γ/Z ratio and W/Z ratio. In Z(νν)
00sample, E missis vector sum of p~T of neutrinos. In W(`ν) sample, E missis vector
T
T
0
miss
sum of pT of neutrinos and a lepton. In γ sample, E T
is vector sum of p~T ofneutrinos and γ.

Zjets
Yjets

102

10

γ /Z

γ /Z

1.5
0

Aplanarity

0.02

0.04

0.06

0.08

1.5
1

0.1

1600

0.5
0

10

1

1

1

Zjets
Yjets

102

meff(pT>60 GeV)(GeV)
1800

2000

2200

1800

2000

2200

2400

2600

2800

2400

2600

2800

0.5
0.02

0.04

0.06

0.08

0.1

1600

Aplanarity

meff(pT>60 GeV)(GeV)(a) Aplanarity distribution after the meff >1600 GeV cut in addition.

(b) meff distribution.

Figure 46: In addition to the baseline cut (Table 41), ETmiss0 > 600 GeV cut 3isapplied for MC event samples. Overflow bin is merged into the highest bin. In
each figure, the lower plot shows the ratio of distributions for γ+jets and Z(νν)+jets
events after the normalization.

93

events/400 GeV

events/0.01

Zjets
Wjets

3

10

102

10

10

1

1

1.5
1

0

W/Z

W/Z

102

Aplanarity

0.01

0.02

0.03

0.04

1.5

meff(pT>60 GeV)(GeV)

1

0.05

0.5
0

Zjets
Wjets

3

10

1000

1500

2000

2500

3000

1000

1500

2000

2500

3000

0.5
0.01

0.02

0.03

0.04

0.05

Aplanarity

meff(pT>60 GeV)(GeV)(b) meff distribution.

events/110 GeV(a) Aplanarity distribution.
Zjets
Wjets

3

10

102

10

W/Z

1

1.5
1

MET'(GeV)
200

300

400

500

600

700

200

300

400

500

600

700

0.5

MET'(GeV)(c) ETmiss or ETmiss 0 distribution.

Figure 47: In addition to the baseline cut (Table 41), ETmiss0 > 200 GeV cut4isapplied for MC event samples. Overflow bin is merged into the highest bin. In
each figure, the lower plot shows the ratio of distributions for W(`ν)+jets andZ(νν)+jets events after the normalization.

94

6.9

Expectation from MCs

Expected number of events in each CR is summarized in Table 42. In SR2jC,
CRYMa and CRYmA don’t exist since no aplanarity cut is applied. The expected
number of events in each region is not small, hence it is good for backgroundestimation.
SR2jC

SR4jL

SR4jM

SR6jL

SR

24.8 ± 0.2

5.02 ± 0.07

6.0 ± 0.1

1.41 ± 0.05

CRYMA

58.6 ± 0.7

10.4 ± 0.3

12.8 ± 0.4

2.7 ± 0.2

CRYMa

-

21.4 ± 0.5

86 ± 18.1 ± 0.3

CRYmA

-

90 ± 129.3 ± 0.7

6.2 ± 0.3

CRYma

55.0 ± 0.8

186 ± 1228 ± 2

21.6 ± 0.7

CRWL19.9 ± 0.2

62.7 ± 0.7

75.4 ± 0.9

7.2 ± 0.3

CRWVL

3074 ± 27

493 ± 11439 ± 1034.6 ± 2.2

CRZllVL

567 ± 595 ± 284 ± 28.1 ± 0.8

Table 42: Expected number of events in each CRs. The error is MC statisticalerrors.
The evaluated parameters for data-driven BG estimation with MCs are in
Table (43, 44, 45, 46). The estimated value with MC is set as initial value in fitting
to avoid local minimum. The fit range (or error) for the main parameters like ε ∗is set to be ±100% of the initial value. The SF``/νν value and errors are fromexpected ratio and statistical error estimated with MC for each.
About the correction factors (Rs), they ideally expected to be ' 1. Therefore,
the maximum between MC statistical error and the difference from 1 is set as
uncertainties for fit. Since the values of all fit parameters (ε ∗ ) are determined withall the CRs unless correction factor Rs, errors from R result in uncertainties of thismethod.

95

Parameter

Value

Error from MC

Error for fit

µZ

24.8

±0.2

±100%

ε YMA

2.35

±0.03

±100%

ε Yma

0.94

±0.01

±100%

ε WL

0.363

±0.007±100%

ε CRZllVL

136

±1

±100%

Correction factors and uncertainties.
SF``/νν

0.168±0.001±0.001

RZ/Y

1.29

±0.04

±0.29

RZ/W

0.893

±0.04

±0.11

Table 43: SR2jC: The estimated parameters with MC and errors for fit. The MCstatistical error is calculated from first-order approximation of error propagation.

Parameter

Value

Error from MC

Error for fit

µZ

5.02

±0.02

±100%

ε YMA

2.09

±0.08

±100%

ε YMa

2.04

±0.09

±100%

ε YmA

8.6

±0.3

±100%

ε WL

0.338

±0.005±100%

ε CRZllVL

135

±3

±100%

Correction factors and uncertainties.
SF``/νν

0.140±0.004±0.004

RABCD

1.01

±0.04

±0.04

RZ/Y

1.39

±0.05

±0.39

RZ/W

1.01

±0.04

±0.04

Table 44: SR4jL: The estimated parameters with MC and errors for fit. The MCstatistical error is calculated from first-order approximation of error propagation.

96

Parameter

Value

Error from MC

Error for fit

µZ

6.0

±0.1

±100%

ε YMA

2.12

±0.08

±100%

ε YMa

6.7

±0.2

±100%

ε YmA

2.3

±0.1

±100%

ε WL

0.330

±0.005±100%

ε CRZllVL

99

±2

±100%

Correction factors and uncertainties.
SF``/νν

0.141±0.005±0.005

RABCD

1.16

±0.05

±0.16

RZ/Y

1.39

±0.05

±0.39

RZ/W

1.04

±0.04

±0.04

Table 45: SR4jM: The estimated parameters with MC and errors for fit. The MCstatistical error is calculated from first-order approximation of error propagation.

Parameter

Value

Error from MC

Error for fit

µZ

1.41

±0.05

±100%

ε YMA

1.8

±0.1

±100%

ε YMa

3.0

±0.2

±100%

ε YmA

2.3

±0.3

±100%

ε WL

0.33

±0.01

±100%

ε CRZllVL

41

±2

±100%

Correction factors and uncertainties.
SF``/νν

0.143

±0.01

±0.01

RABCD

1.13

±0.13

±0.13

RZ/Y

1.32

±0.13

±0.32

RZ/W

0.95

±0.10

±0.10

Table 46: SR6jL: The estimated parameters with MC and errors for fit. The MCstatistical error is calculated from first-order approximation of error propagation.

97

6.10

Purity estimation in γ CR

For the γ replace, the purity of γ+jets events in γ CR is very important. In γ CR,
the main component is true γ+jets events and the rest is multi-jet events with afaking photon (fake-photon). The data-driven purity estimation is needed since
the fake-photon behaviour of MCs is not reliable, because hard π 0 production in
the hadronic fragmentation may not be described by the hadronization models.
The first candidate method to estimate fake-photon is ABCD method as described in Appendix C using photon ID and isolation. However, this method does
not work since photon ID and isolation cut have strong correlation as described inAppendix A.2.2. The other way to estimate fake photon events is ABCD methodwith correction Appendix C.1. For this method, data and MC distributions arecompared.
6.10.1

Data/MC comparison

For the ABCD method wtih correction, the good estimation of ε ( NNBA or NNCA in
Appendix C.1 ) for true photon events is needed. In this section, the MC and data
are compared for the variables used in isolation cut and Tight ID cut after the
Loose ID selection.
The Loose ID selections are:• After the photon trigger• No electron or muon
• Exact one Loose ID photon (pT > 130 GeV )• Njet (pT > 50 GeV) ≥ 2
R
Used data correspond to Ldt = 1.46 fb−1 .
so
The distributions of isolation variables are in Figure 48. The ε of NNNon−I
can
I so
be used since the MC to data ratio distributions are flat.
The distributions of ID related variables are shown in Figure 49 and 50. In
most of variables, the MC to data ratio distributions are not flat. Especially, theMC cannot estimate the data events in the regions which are not-Tight but Looseas shown in Fig. 49. The actual boolean plots of each cut used in Tight ID areN
ight
shown in Figure 51. It is clear that ε of NNon−T
cannot be used. Therefore, theT ight
ABCD method cannot be used for the purity estimation even with correction withR (Appendix C.1).

98

∫ L dt = 1.459 fb

events/0.01

events/0.01

Data

103

-1

QCD
γ +jets

102

Data

103

SM total

γ +jets

10

1

1

0.1

0.2

0

0.1

0.2

2
1.5
−10.1
0.5
0
−0.1

Data/MC

Data/MC0

topoetcone20/pT
0.3
0.4
0.3

0.4

-1

QCD

102

10

2
1.5
−10.1
0.5
0
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∫ L dt = 1.459 fb

SM total

0

0.1

0.2

0

0.1

0.2

topoetcone20/pT

topoetcone40/pT
0.3
0.4
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0.4

topoetcone40/pT(b) topoetcone40/pT

events/0.025(a) topoetcone20/pT
104

Data

∫ L dt = 1.459 fb-1

SM total
310QCD
γ +jets

2

10

10
1

Data/MC

2
1.5
−10.1
0.5
0
−0.1

0

0.1

0.2

ptcone20/pT
0.3
0.4

0

0.1

0.2

0.3

0.4

ptcone20/pT(c) ptcone20/pT

Figure 48: Distributions of isolation variables after Loose photon selection. The
yellow histogram is estimated true photon MC samples, the orange histogram isestimated fake photon from QCD multi-jet MC samples, and dots are observed
date events.
6.10.2

Purity estimation with isolation template fitting

From the study in previous section, we got that the MC can be used only after
Tight ID cut. Therefore, the one way to estimate the purity of photons is to fit the
template of isolation variables from MCs after the Tight ID cut. In the isolation
cuts, two variables are used:topoetoconeX and ptconeX as described in Sec.4.3.3.
In such case, the 2D distributions should be used as template. However, in low
data stat. case, we cannot prepare enough number of events for fitting. To fulfil
these requirements, 2-bin template of isolation cut (iso & non-iso) is used.
To select the clean γ events, one photon and one jet events are selected:• After the one-photon trigger• No electron or muon99

• Exact one Tight ID photon (pT > 130 GeV )• Exact one jet(pT > 130 GeV) & veto 2nd jet(pT > 50 GeV)0
• ∆φ(jet1, E miss)min > 1.0
T

After the fit, the purity as a function of photon pT is estimated as shown in Figure 52.
As expected, the purity becomes higher as photon pT becomes higher. In highphoton pT region, the purity is about 96±2%. This is pure enough to neglect
the fake photon contamination compared to the other systematic uncertainties.
However, this is not the realistic case. It is expected that the purity becomes worse
if the jets are close to a photon. Therefore, γ+2jet events are selected:• After the one-photon trigger• No electron or muon
• Exact one Tight ID photon (pT > 130 GeV )• leading jet(pT > 130 GeV) & 2nd jet(pT > 50 GeV) & veto 3rd jet(pT > 50 GeV)0
• ∆φ(jet1,2, E miss)min regions : Low[0.4,2.0], High[2.0,3.14], and All[0.4,3.14]
T0)min variations, the effect of jets near the photon is taken
With these ∆φ(jet1,2, E missTinto account. The results of purity vs. photon pT is shown in Figure 53. Even in
the case jets are near a photon, the purity is about 96±2% and the contaminationof fake photon is negligible.

100

Data

∫ L dt = 1.459 fb

events/0.05

events/0.1 GeV

104

104

-1

SM total

103

QCD

γ +jets

γ +jets

102

102

10

10

1

1

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

DeltaE
1.8
2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2
1.5
10
0.5
0
0

Data/MC

Data/MC

2
1.5
10
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0

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103

QCD∫ L dt = 1.459 fb

Data

2

0.1

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Eratio
0.9
1

0.1

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DeltaE

Data

103∫ L dt = 1.459 fb

events/0.1(b) Eratio

events/0.01(a) DeltaE
104-1

SM total

QCD
γ +jets

102
10

1

1

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

f1
0.5

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

2
1.5
10
0.5
0
0

Data/MC

0.05

0.2

0.4

0.6

0.8

1

1.2

0.2

0.4

0.6

0.8

1

1.2

fracm
1.4
1.4

f1

fracm

∫ L dt = 1.459 fb

Data(d) fracm
events/0.5

events/0.01(c) f1
104

104

-1

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103

QCD

QCD
γ +jets

102

10

10

1

1

0.82 0.84

0.86

0.88

0.9

0.92 0.94

0.96

Rphi
0.98
1

0.82

0.86

0.88

0.9

0.92

0.96

0.98

0.94

2
1.5
10
0.5
0
0

Data/MC

Data/MC-1

SM total

γ +jets

0.84∫ L dt = 1.459 fb

Data

103

102

2
1.5
1
0.8
0.5
0
0.8

-1

SM total

γ +jets

10

Data/MC∫ L dt = 1.459 fb

Data

103

QCD

102

2
1.5
10
0.5
0
0

1

Eratio

1

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

Rphi

wtot
10
10

wtot

(e) Rphi(f) wtot

Figure 49: Distributions of ID related variables after Loose photon selection. The
yellow histogram is estimated true photon MC samples, the orange histogram isestimated fake photon from QCD multi-jet MC samples, and dots are observed
date events.

101

events/0.04

104∫ L dt = 1.459 fb

Data

-1

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103

QCD
γ +jets

102
10
1

Data/MC

2
1.5
10
0.5
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1

0.2

0.3

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weta1
0.8
0.8

weta1

Data

104

∫ L dt = 1.459 fb

events/0.001

events/0.002(a) weta1

104-1

SM total

103

Data

103

QCD

γ +jets

2

10

102

10

10

1

1

0.01

0.015

0.02

0.025

0.03

Rhad
0.035

0.005

0.01

0.015

0.02

0.025

0.03

0.035

2
1.5
1 0
0.5
0
0

Data/MC

Data/MC

0.005

0.005

0.01

0.015

0.02

Rhad1
0.025

0.005

0.01

0.015

0.02

0.025

Rhad

Rhad1

Data

∫ L dt = 1.459 fb(c) Rhad1 (loose cut is applied in Loose ID)
events/0.01

events/0.001(b) Rhad (loose cut is applied in Loose ID)

104

104

-1

SM total
310QCD
γ +jets

10

10

1

1

Data/MC

Data/MC

2
1.5
1
0.8
0.5
0
0.8

weta
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0.01

-1

SM total
QCD
γ +jets102

0.002 0.004 0.006 0.008∫ L dt = 1.459 fb

Data

103

102

2
1.5
10
0.5
0
0

-1

QCD

γ +jets

2
1.5
1 0
0.5
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0

∫ L dt = 1.459 fb

SM total

0.012 0.014 0.016 0.018

0.02

0.82 0.84

0.86

0.88

0.9

0.92 0.94

phton_Reta0.96 0.98
1

0.82

0.86

0.88

0.9

0.92

0.96

0.84

0.94

0.98

1

phton_Reta

weta(d) weta2 (loose cut is applied in Loose ID)(e) Reta (loose cut is applied in Loose ID)

Figure 50: Distributions of ID related variables after Loose photon selection.
Except for weta1, all these variables are also used in Loose ID selection. The
yellow histogram is estimated true photon MC samples, the orange histogram isestimated fake photon from QCD multi-jet MC samples, and dots are observed
date events.

102

-1

104

SM total103∫ L dt = 1.459 fb

Data

-1

104

SM total

103

QCD

events/1∫ L dt = 1.459 fb

Data

events/1

events/1

104

γ +jets

QCD
γ +jets

102

102

10

10

10

1

1

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Is_Eratio
1.8
2

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γ +jets∫ L dt = 1.459 fb

Data

104

QCD

-1

QCD

103

γ +jets

102

102

10

10

10

1

1

0.6

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1.2

1.4

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10

2
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10
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0

2

∫ L dt = 1.459 fb

Data

104

QCD

3

10

γ +jets-1

104

SM total
QCD103

γ +jets

10

10

10

1

1

1

2
1.5
10
0.5
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0

2
1.5
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Is_Rphi
1.8
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Is_weta2
1.8
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1.4

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Is_Rphi(g) Is Rphi cut

2

Data/MC102

Data/MC102

Data/MC

102

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1.4

1.6

1.2

1.4

1.6

Is_fracm
1.8
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2

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SM total
QCD
γ +jets

0.2

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1.8
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events/1-1

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Is_weta1(e) Is Reta cut
events/1

events/1∫ L dt = 1.459 fb

Data

3

1

0.8

Is_Reta(d) Is HadLeak cut
104

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1

Is_Reta
1.8
2Data/MC

0.4

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10
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Data/MC

Data/MC

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Is_HadLeak
1.6
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Data

104

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(c) Is fracm cut
events/1

events/1

events/1∫ L dt = 1.459 fb

Data

0.2

Is_fracm(b) Is Eratio cut

SM total

1032

Is_Eratio(a) Is DeltaE cut
104

2
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10
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0
0

Data/MC

0.4

0.2

2
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Data/MC

Data/MC

0.2

Is_DeltaE
1.6
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QCD
γ +jets

102

2
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10
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∫ L dt = 1.459 fb

Data
SM total103∫ L dt = 1.459 fb

Data

-1

SM total
QCD
γ +jets

0.2

0.4

0.6

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1

1.2

1.4

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Is_wtot
1.8
2

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0.6

0.8

1

1.2

1.4

1.6

1.8

Is_weta2(h) Is weta2 cut

2Is_wtot(i) Is wtot cut

Figure 51: Distributions of boolean used in Tight ID after Loose photon selection.
The yellow histogram is estimated true photon MC samples, the orange histogramis estimated fake photon from QCD multi-jet MC samples, and dots are observed
date events.

103

Purity

1.1
1
0.9
0.8
0.7
1j_Cone20
1j_Cone40

0.6

1j_Cone40CaloOnly

0.5
0100 200 300 400 500 600 700 800 900 1000pT (GeV)Figure 52: Purity vs. photon pT distribution with γ+1 jet events. (Black/Red/Blue)histograms show the purity for (Cone20/Cone40/Cone40CaloOnly) isolation cut.

104

Purity

1.1
1
0.9
0.8
0.7
exact2j_Cone40
exact2j_LowdPhi_Cone40

0.6

exact2j_HighdPhi_Cone40

0.5
0100 200 300 400 500 600 700 800 900 1000pT (GeV)Figure 53: Purity vs. photon pT distribution with γ+2 jet events. Isolation cut
is Cone40. (Black/Red/Blue) histograms show the purity for (All/Low/High) ∆φregion.

105

6.11

Summary of CRs

In previous sections, many CRs are introduced. In this section, all the CRs usedin this analysis are summarized.
The classification and pre-selection of one or two leptons, one photon, and no
lepton regions are summarized in Table 47. With the classification, the detailed
cuts applied for each CRs are summarized in Table 48.

106

CR type

One photon

Target process

γ+jetsTrigger

one-photon

One leptont t¯ → bb̄W (qq)W (`ν)

No lepton

Z(→ ``)+jets

multi-jets
ETmiss trigger

one-electron or one-muon

Cleaning
Objectselection

W (`ν)+jets

Two lepton

The same as SRs
1 signal photon,

1 signal e/µ, pT ` > 25GeV

no e/µno e/µ--107

B-jet selection-

NB jet >= 1

Mass related
selection-

30 < mT (E missT , p~T ` ) < 100 GeV

66 < m`` < 116 GeV

-

Extra
description

ETmiss0 =+ p~T γ | is dealt|E missT
as ETmiss1. ` is dealt as jet

ETmiss0 =P2|E miss+ i=1
p~T `,i | isT
missdealt as ET

use normal
ETmissETmiss (’) >jet

NB jet == 0

2 oposit sign signale/µ (2nd pT ` > 10
GeV)

+ p~T ` | is dealt as ETmiss
2 . ETmiss0 = |E missT
200 GeVpT 1st >200 GeVpT 2nd >50 GeV

jet

Table 47: Control region (CR) type classification with object. These are pre-selections for the CRs and validation regions.
The used triggers are described in Sec.4.7.1.

CR name∆φ cuttight ETmiss (’) cut

meff cutaplanarity cut

usage of the CR

CR type : one photon region
CRYMA

+

+

+

+

fitting data-driven parameters.

CRYMa

+

+

+

-

fitting data-driven parameters.

CRYmA

+

+

-

+

fitting data-driven parameters.

CRYma

+

+

-

-

fitting data-driven parameters.

CR type : one lepton region, lepton is dealt as jet
CRT

non

non

+

non

fitting µT op and µW .

CRW

non

non

+

non

fitting µT op and µW .

108

CR type : one lepton region, ETmiss 0 = |E miss
+ p~T ` | is dealt as ETmiss
T
CRWL

+

+

-

-

fitting data-driven parameters.

CRTL

+

+

-

-

fitting µT opL .

CRWVL

non

-

-

non

fitting data-driven parameters.

CRTVL

non

-

-

non

fitting µT opV L .

CR type : two lepton region
CRZllL++--

fitting µ Z L .

CRZllVL

non

-

-

non

fitting data-driven parameters.

CR type : No lepton region
CRQ

-

+

+

non

fitting µ Z L .

Table 48: The summary table of all CRs. "+" means the cut is applied, "-" means the inverted cut is applied, and "non"means the cut is not applied to the CR.

6.12

Strategy of validation regions

To validate the background estimation method, validation regions (VRs) areneeded. Before SRs are opened, the agreement between observed and estimated events in VRs are checked. The previous analyses depend more on MC
simulated samples. In this analysis, numbers of events in various CRs are used,
hence to justify the method, checks using validation regions are very important.
Using VRs, the BG estimation method is validated quantitatively.
In (ABCD+)WXYZ method, various regions can be assigned as validation
region candidates as described in Table 40. The validation regions are chosen withreasonable selection as summarized in Table 49.

6.13

Fit results for control regions and validation regions

The background only fit except for SRs is executed with maximum log likelihood
method which is described afterwards in Sec.7.1. The estimated and observed
events in validation regions (VRs) are checked before the unblinding of the SRs.
Fit results of CRs are in Table 50-67.
The numbers of estimated events and observed events in validation regions(VRs) are in Table 58-66. The comparisons of observed estimated number of
events in VRs are plotted in Figure 54-55.
The estimated events show good agreement with observed data in VRs. Therefore SRs are unblinded. The (ABCD+)WXYZ method is very complex and themethod which was not used in previous analyses. The agreement in VRs shows
the new possibility for the BG estimation method more reliable than the previous
BG estimation methods which depend mainly on MC samples.

109

regiondescription"No lepton" validation regions

VRZMa

Inverted aplanarity cut is applied. Since top and W samples are normalized in tight meff CRs, this region is one of the best VRs for SR
estimation. This region cannot be prepared for SR2jC, since aplanarity
cut is not applied.

VRZma

Inverted meff and inverted aplanarity cut are applied. Since top andW samples are normalized only in tight meff CRs, this region is notnecessarily validate the BG estimation. Therefore, this region is onlyused for SR2jC where VRZMa cannot be used.

+ p~T ` | is dealt as ETmiss"One lepton" validation regions. ETmiss0 = |E missT
VRWMA

SR-like cuts are applied. This region have possibility of disagreement,
since the W+jets to γ+jets ratio is determined in the region with inverted
meff and inverted aplanarity cuts. However, this region is one of the best
VRs since the kinematic selection is similar to SR.

VRWMa

Inverted aplanarity cut is applied. This region have possibility of disagreement, since ABCD method εs are determined in γ+jets region.

Inverted meff cut is applied. This region have possibility of disagreement,
since ABCD method εs are determined in γ+jets region.
P2
Two lepton validation regions. ETmiss0 = |E miss
+ i=1
p~T `,i | is dealt as ETmiss
T

VRWmA

VRZll

SR-like cuts are applied. This region is one of the best VRs except forthe small number of events, since the kinematic selection is similar to SR
selection. The possibility of disagreement is from the lepton acceptance.

VRZllMa

Inverted aplanarity cut is applied. This region have possibility of disagreement, since ABCD method εs are determined in γ+jets region.

VRZllmA

Inverted meff cut is applied. This region have possibility of disagreement,
since ABCD method εs are determined in γ+jets region.

One photon validation regions. ETmiss0 = |E miss
+ p~T γ | is dealt as ETmiss
T
CRYMA

SR-like cuts are applied. This region is the validation region for ABCD
method in γ+jets region.

Table 49: The summary of validation regions (VRs). The features of each VR isdescribed. The implementation of each VR is described in Table 40. In each VR,
discrepancies between expected and observed number of events are investigated.

110SR2jC channel

CRT

CRW

CRQ

CRYMA

CRYma

CRWL

Observed events

37

73

21

100

82

31

Fitted bkg events

37.00 ± 6.08

72.98 ± 8.54

21.00 ± 4.58

99.98 ± 9.68

81.96 ± 8.72

31.11 ± 5.00

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
6.62 ± 1.44
0.09 ± 0.03
0.00 ± 0.00
26.34 ± 6.55
3.95 ± 0.39
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
46.43 ± 9.37
1.43 ± 0.09
0.00 ± 0.00
8.10 ± 2.29
17.02 ± 1.73
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

16.37 ± 4.61
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.62 ± 0.54
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
1.29 ± 0.36
0.00 ± 0.00
0.00 ± 0.00
0.33 ± 0.19
0.53 ± 0.04
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
97.83 ± 9.69
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.41 ± 0.16
0.44+0.66−0.44
0.00 ± 0.00
1.52 ± 0.31
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
79.58 ± 8.80
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.71 ± 0.72
3.12 ± 2.82
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.59 ± 0.32
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
22.69 ± 5.48
0.00 ± 0.00
0.00 ± 0.00

Table 50: SR2jC : Background fit results for the contorol regionsRCRT, CRW, CRQ,
CRYMA, CRYma and CRWL, for an integrated luminosity of L dt = 3.2 fb−1 .
The errors are the statistical plus systematic uncertainties.

SR2jC channel

CRTL

CRZllL

CRWVL

CRZllVL

Observed events

9

8

4020

721

2603

Fitted bkg events

8.98 ± 2.97

8.00 ± 2.83

4018.11 ± 69.36

720.93 ± 26.35

2603.21 ± 79.46

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.67 ± 0.28
5.89 ± 3.10
0.00 ± 0.00
2.38 ± 0.81
0.00 ± 0.00
0.04 ± 0.02
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.43 ± 0.29
0.05+0.65−0.05
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
7.53 ± 2.91
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
324.55 ± 16.74
0.00 ± 0.00
449.64 ± 138.98
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
60.01 ± 7.60
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
3183.92 ± 152.07
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
73.43 ± 4.37
0.00 ± 0.00
59.80 ± 17.86
0.00 ± 0.00
0.12+0.16−0.12
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
587.58 ± 31.78

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
73.97 ± 5.34
0.00 ± 0.00
2105.64 ± 617.60
0.00 ± 0.00
414.28+554.24−414.280.00 ± 0.00
9.33 ± 2.75
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

CRTVL

Table 51: SR2jC : Background fit results for the contorol regions
R CRTL, CRZllL,CRWVL, CRZllVL, and CRTVL, for an integrated luminosity of L dt = 3.2 fb−1 .
The errors are the statistical plus systematic uncertainties.

111

SR4jL channel

CRT

CRW

CRQ

CRYMa

CRYma

CRYmA

Observed events

24

40

104

31

243

133

Fitted bkg events

24.01 ± 4.90

39.99 ± 6.33

104.01 ± 10.20

30.97 ± 6.38

243.13 ± 32.98

132.93 ± 18.22

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
4.05 ± 1.34
0.07 ± 0.02
0.00 ± 0.00
17.08 ± 5.33
2.80 ± 0.36
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
23.15 ± 7.18
1.10 ± 0.40
0.00 ± 0.00
4.87 ± 2.02
10.87 ± 1.37
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

95.39 ± 10.23
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
8.62 ± 0.83
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.53 ± 0.21
0.00 ± 0.00
0.00 ± 0.00
0.30 ± 0.15
0.20 ± 0.04
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
29.95 ± 6.37
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.49 ± 0.21
4.20 ± 1.79
0.00 ± 0.00
5.15 ± 3.64
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
232.28 ± 33.30
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.17 ± 0.18
0.98 ± 0.54
0.00 ± 0.00
2.78 ± 0.42
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
127.99 ± 18.14
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

Table 52: SR4jL : Background fit results for the contorol regions RCRT, CRW, CRQ,
CRYMa, CRYma and CRYmA, for an integrated luminosity of L dt = 3.2 fb−1 .
The errors are the statistical plus systematic uncertainties.

SR4jL channel

CRWL

CRTL

CRZllL

CRWVL

CRZllVL

Observed events

97

78

15

680

116

1034

Fitted bkg events

97.00 ± 9.63

77.96 ± 9.35

15.01 ± 3.87

680.03 ± 57.05

116.02 ± 10.56

1033.90 ± 32.62

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
16.45 ± 2.38
12.53 ± 4.65
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.59 ± 0.24
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
67.44 ± 10.16
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.84 ± 0.41
59.14 ± 18.60
0.00 ± 0.00
13.87 ± 13.26
0.00 ± 0.00
0.11 ± 0.05
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.04 ± 0.55
1.16 ± 0.60
0.00 ± 0.00
0.01 ± 0.01
0.00 ± 0.00
9.79 ± 3.96
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
89.17 ± 7.56
0.00 ± 0.00
137.89 ± 28.85
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
11.99 ± 1.82
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
440.98 ± 60.77
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
20.20 ± 1.69
0.00 ± 0.00
20.48 ± 4.73
0.00 ± 0.00
0.03 ± 0.02
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
75.31 ± 11.68

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
27.69 ± 2.82
0.00 ± 0.00
895.76 ± 166.95
0.00 ± 0.00
106.81+158.04−106.810.00 ± 0.00
3.63 ± 0.66
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

CRTVL

Table 53: SR4jL : Background fit results for the contorol regions CRWL,R CRTL,
CRZllL, CRWVL, CRZllVL and CRTVL, for an integrated luminosity of L dt =3.2 fb−1 . The errors are the statistical plus systematic uncertainties.

112SR4jM channel

CRT

CRW

CRQ

CRYMa

CRYma

CRYmA

Observed events

91

126

183

140

284

52

Fitted bkg events

90.99 ± 9.54

125.99 ± 11.23

182.97 ± 13.53

139.97 ± 24.39

283.88 ± 47.73

51.98 ± 10.72

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
16.22 ± 3.49
0.20 ± 0.02
0.00 ± 0.00
67.56 ± 10.60
7.01 ± 0.41
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
83.86 ± 12.42
1.82 ± 0.15
0.00 ± 0.00
15.32 ± 3.36
25.00 ± 2.58
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

167.47 ± 13.61
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
15.49 ± 1.45
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
2.34 ± 0.48
0.00 ± 0.00
0.00 ± 0.00
0.98 ± 0.40
1.05 ± 0.10
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
135.61 ± 24.38
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.84 ± 0.14
4.92 ± 2.13
0.00 ± 0.00
6.29 ± 4.51
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
270.84 ± 48.10
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.33 ± 0.09
0.22 ± 0.19
0.00 ± 0.00
0.79 ± 0.18
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
50.64 ± 10.72
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

Table 54: SR4jM : Background fit results for the contorol regions CRT,R CRW,
CRQ, CRYMa, CRYma and CRYmA, for an integrated luminosity of L dt =3.2 fb−1 . The errors are the statistical plus systematic uncertainties.

SR4jM channel

CRWL

CRTL

CRZllL

CRWVL

CRZllVL

Observed events

115

95

14

600

100

947

Fitted bkg events

115.12 ± 13.94

94.96 ± 10.47

14.00 ± 3.74

599.62 ± 67.87

100.12 ± 9.47

946.97 ± 30.83

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
19.02 ± 2.26
14.25 ± 5.49
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.45 ± 0.22
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
81.40 ± 14.40
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
5.23 ± 0.97
72.49 ± 23.16
0.00 ± 0.00
17.13 ± 17.11
0.00 ± 0.00
0.11 ± 0.05
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.80 ± 0.72
1.32 ± 0.79
0.00 ± 0.00
0.01+0.01−0.01
0.00 ± 0.00
7.87 ± 3.91
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
75.83 ± 6.03
0.00 ± 0.00
124.92 ± 25.16
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
10.59 ± 1.70
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
388.27 ± 70.10
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
16.93 ± 1.11
0.00 ± 0.00
19.00 ± 3.92
0.00 ± 0.00
0.03 ± 0.01
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
64.16 ± 10.18

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
23.67 ± 2.55
0.00 ± 0.00
827.31 ± 142.10
0.00 ± 0.00
92.72+136.60−92.720.00 ± 0.00
3.27 ± 0.65
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL eventsCRTVL

Table 55: SR4jM : Background fit results for the contorol regions CRWL,R CRTL,
CRZllL, CRWVL, CRZllVL and CRTVL, for an integrated luminosity of L dt =3.2 fb−1 . The errors are the statistical plus systematic uncertainties.

113

SR6jL channel

CRT

CRW

CRQ

CRYMa

CRYma

Observed events

20

25

49

6

23

11

Fitted bkg events

20.00 ± 4.47

25.00 ± 5.00

48.99 ± 7.04

6.00 ± 2.64

22.96 ± 7.92

10.99 ± 4.34

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
5.24 ± 1.75
0.05 ± 0.01
0.00 ± 0.00
12.93 ± 5.01
1.78 ± 0.20
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
18.47 ± 5.36
0.17 ± 0.07
0.00 ± 0.00
2.10 ± 0.95
4.26 ± 0.62
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

46.19 ± 7.12
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
2.80 ± 0.76
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.46 ± 0.24
0.00 ± 0.00
0.00 ± 0.00
0.14 ± 0.10
0.11 ± 0.06
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
5.29 ± 2.65
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.31 ± 0.12
1.23 ± 0.47
0.00 ± 0.00
0.64 ± 0.21
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
20.78 ± 7.97
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.12 ± 0.06
0.28 ± 0.18
0.00 ± 0.00
0.20 ± 0.12
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
10.39 ± 4.37
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

CRYmA

Table 56: SR6jL : Background fit results for the contorol regions RCRT, CRW, CRQ,
CRYMa, CRYma and CRYmA, for an integrated luminosity of L dt = 3.2 fb−1 .
The errors are the statistical plus systematic uncertainties.

SR6jL channel

CRWL

CRTL

CRZllL

CRWVL

CRZllVLCRTVL

Observed events

14

24

1

51

8

168

50.93 ± 8.38

8.04 ± 2.24

168.00 ± 13.29

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
10.89 ± 1.60
0.00 ± 0.00
16.92 ± 4.65
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.96 ± 0.18
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
22.16 ± 9.77
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
2.76 ± 0.59
0.00 ± 0.00
2.35 ± 0.84
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
2.93 ± 2.36

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
3.99 ± 0.80
0.00 ± 0.00
147.81 ± 25.83
0.00 ± 0.00
15.79+19.46−15.790.00 ± 0.00
0.40+0.45−0.40
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

Fitted bkg events

14.01 ± 4.94

23.95 ± 4.88

1.10+2.70−1.10

Fitted Multijets events
Fitted Wjets events
Fitted Zjets events
Fitted GAMMAjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted TopVL events
Fitted WjetsL events
Fitted WjetsVL events
Fitted ZjetsL events
Fitted ZjetsVL events
Fitted CRYMA events
Fitted CRYMa events
Fitted CRYmA events
Fitted CRYma events
Fitted CRYL events
Fitted CRWL events
Fitted CRWVL events
Fitted CRZllVL events

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
2.44 ± 0.59
3.16 ± 1.04
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.10
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
8.42 ± 5.15
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.95 ± 0.28
20.58 ± 5.47
0.00 ± 0.00
2.42 ± 2.12
0.00 ± 0.00
0.00 ± 0.05
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.67 ± 0.13
0.43 ± 0.28
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 2.68
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

Table 57: SR6jL : Background fit results for the contorol regions CRWL,R CRTL,
CRZllL, CRWVL, CRZllVL and CRTVL, for an integrated luminosity of L dt =3.2 fb−1 . The errors are the statistical plus systematic uncertainties.

114

SR2jC channel

VRZma

VRZll

VRWMA

Observed events

35

5

32

Fitted bkg events

39.91 ± 7.65

6.34 ± 1.61

30.45 ± 6.98

Fitted Multijets events
Fitted Zjets events
Fitted Wjets events
Fitted Top events
Fitted Diboson events
Fitted ZjetsL events
Fitted TopL events
Fitted WjetsL events
Fitted VRZma events
Fitted VRZll events
Fitted VRWMA events

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
5.13 ± 2.73
0.00 ± 0.00
1.42 ± 1.09
5.25 ± 0.58
28.10 ± 7.18
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.15 ± 0.07
1.69 ± 1.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.51 ± 1.27
0.00 ± 0.00

0.00 ± 0.00
0.22 ± 0.13
0.00 ± 0.00
2.04 ± 1.00
6.47 ± 3.35
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
21.71 ± 6.13

MC exp. SM events

41.29

6.11

31.53

MC exp. Multijets events
MC exp. Zjets events
MC exp. Wjets events
MC exp. Top events
MC exp. Diboson events
MC exp. ZjetsL events
MC exp. TopL events
MC exp. WjetsL events
MC exp. VRZma events
MC exp. VRZll events
MC exp. VRWMA events

0.00
0.00
0.00
0.00
5.13
0.00
0.92
5.25
29.98
0.00
0.00

0.00
0.00
0.00
0.26
1.69
0.00
0.00
0.00
0.00
4.16
0.00

0.00
0.22
0.00
3.69
6.47
0.00
0.00
0.00
0.00
0.00
21.16

Table 58: SR2jC : Background fit results for the validation
regions VRZma,
R
VRZll, and VRWMA, for an integrated luminosity of L dt = 3.2 fb−1 . Nominal
MC expectations (normalised to MC cross-sections) are given for comparison.
The errors are the statistical plus systematic uncertainties.

115

SR4jL channel

VRZMa

VRZll

VRZllmA

VRZllMa

Observed events

18

1

6

3

Fitted bkg events

17.15 ± 4.35

1.29 ± 0.50

7.01 ± 2.07

1.65 ± 0.61

Fitted Multijets events
Fitted Wjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted WjetsL events
Fitted VRZma events
Fitted VRZMa events
Fitted VRZmA events
Fitted VRZll events
Fitted VRZllMa events
Fitted VRZllmA events

0.09 ± 0.02
2.74 ± 0.92
1.40 ± 0.58
5.43 ± 2.78
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
7.49 ± 3.15
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00+0.01−0.00
0.72 ± 0.43
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.57 ± 0.26
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.44 ± 0.28
2.09 ± 1.09
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.48 ± 1.74

0.00 ± 0.00
0.00 ± 0.00
0.02+0.18−0.02
0.58 ± 0.36
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.05 ± 0.44
0.00 ± 0.00

MC exp. SM events

22.90

1.43

8.97

2.05

MC exp. Multijets events
MC exp. Wjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. WjetsL events
MC exp. VRZma events
MC exp. VRZMa events
MC exp. VRZmA events
MC exp. VRZll events
MC exp. VRZllMa events
MC exp. VRZllmA events

0.07
4.47
2.69
5.43
0.00
0.00
0.00
10.24
0.00
0.00
0.00
0.00

0.00
0.00
0.01
0.72
0.00
0.00
0.00
0.00
0.00
0.70
0.00
0.00

0.00
0.00
0.84
2.09
0.00
0.00
0.00
0.00
0.00
0.00
0.00
6.03

0.00
0.00
0.04
0.58
0.00
0.00
0.00
0.00
0.00
0.00
1.43
0.00

Table 59: SR4jL : Background fit results for the validationRregions VRZMa, VRZll,
VRZllmA, and VRZllMa, for an integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised to MC cross-sections) are given for comparison.
The errors are the statistical plus systematic uncertainties.

116

SR4jL channel

CRYMA

Observed events

12

Fitted bkg events

16.99 ± 3.87

Fitted Wjets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted CRYMA events

0.23 ± 0.09
0.00 ± 0.00
0.18 ± 0.12
0.24 ± 0.17
16.34 ± 3.86

MC exp. SM events

11.41

MC exp. Wjets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. CRYMA events

0.38
0.00
0.35
0.24
10.44

Table 60: SR4jL : Backgroundfit results for the validation region CRYMA, for anR
integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised
to MC cross-sections) are given for comparison. The errors are the statistical plus
systematic uncertainties.

117SR4jL channel

VRWMA

VRWMa

VRWmA

Observed events

5

16

50

Fitted bkg events

5.54 ± 1.50

11.50 ± 3.50

42.35 ± 12.97

Fitted Multijets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted ZjetsL events
Fitted VRWMA events
Fitted VRWMa events
Fitted VRWmA events

0.00 ± 0.00
0.05 ± 0.02
0.36 ± 0.19
1.73 ± 0.91
0.00 ± 0.00
0.00 ± 0.00
3.41 ± 1.16
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.10 ± 0.03
1.04 ± 0.51
2.88 ± 1.56
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
7.49 ± 3.15
0.00 ± 0.00

0.00 ± 0.00
0.36 ± 0.09
2.59 ± 0.96
7.40 ± 3.93
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
32.00 ± 12.44

MC exp. SM events

5.98

15.20

55.83

MC exp. Multijets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. ZjetsL events
MC exp. VRWMA events
MC exp. VRWMa events
MC exp. VRWmA events

0.00
0.05
0.69
1.73
0.00
0.00
3.52
0.00
0.00

0.00
0.10
1.99
2.88
0.00
0.00
0.00
10.24
0.00

0.00
0.36
4.97
7.41
0.00
0.00
0.00
0.00
43.10

Table 61: SR4jL : Background fit results for the validation
regions VRWMA,R
VRWMa, and VRWmA, for an integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised to MC cross-sections) are given for comparison.
The errors are the statistical plus systematic uncertainties.

118SR4jM channel

VRZMa

VRZll

VRZllmA

VRZllMa

Observed events

68

1

4

12

Fitted bkg events

74.50 ± 13.44

1.38 ± 0.43

2.40 ± 0.64

7.48 ± 1.85

Fitted Multijets events
Fitted Wjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted WjetsL events
Fitted VRZma events
Fitted VRZMa events
Fitted VRZmA events
Fitted VRZll events
Fitted VRZllMa events
Fitted VRZllmA events

0.91 ± 0.14
14.73 ± 2.83
7.88 ± 1.90
17.69 ± 9.01
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
33.29 ± 9.65
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.05 ± 0.04
0.57 ± 0.33
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.76 ± 0.27
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.11 ± 0.07
0.53 ± 0.33
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.75 ± 0.54

0.00 ± 0.00
0.01 ± 0.00
0.42 ± 0.15
2.36 ± 1.23
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
4.69 ± 1.36
0.00 ± 0.00

MC exp. SM events

90.52

1.51

2.97

8.75

MC exp. Multijets events
MC exp. Wjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. WjetsL events
MC exp. VRZma events
MC exp. VRZMa events
MC exp. VRZmA events
MC exp. VRZll events
MC exp. VRZllMa events
MC exp. VRZllmA events

0.70
18.66
13.13
17.69
0.00
0.00
0.00
40.33
0.00
0.00
0.00
0.00

0.00
0.00
0.09
0.57
0.00
0.00
0.00
0.00
0.00
0.85
0.00
0.00

0.00
0.00
0.19
0.53
0.00
0.00
0.00
0.00
0.00
0.00
0.00
2.25

0.00
0.01
0.70
2.36
0.00
0.00
0.00
0.00
0.00
0.00
5.68
0.00

Table 62: SR4jM : Background fit results for the validation Rregions VRZMa,
VRZll, VRZllmA, and VRZllMa, for an integrated luminosity of L dt = 3.2 fb−1 .
Nominal MC expectations (normalised to MC cross-sections) are given for comparison. The errors are the statistical plus systematic uncertainties.

119SR4jM channel

VRWMA

VRWMa

VRWmA

Observed events

9

55

13

Fitted bkg events

6.38 ± 1.53

47.68 ± 11.02

15.35 ± 4.02

Fitted Multijets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted ZjetsL events
Fitted VRWMA events
Fitted VRWMa events
Fitted VRWmA events

0.00 ± 0.00
0.08 ± 0.02
0.42 ± 0.25
1.13 ± 0.62
0.00 ± 0.00
0.00 ± 0.00
4.76 ± 1.34
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.40 ± 0.11
3.97 ± 1.00
10.02 ± 5.27
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
33.29 ± 9.65
0.00 ± 0.00

0.00 ± 0.00
0.10 ± 0.04
0.71 ± 0.23
2.11 ± 1.22
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
12.43 ± 3.84

MC exp. SM events

6.10

57.38

19.39

MC exp. Multijets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. ZjetsL events
MC exp. VRWMA events
MC exp. VRWMa events
MC exp. VRWmA events

0.00
0.08
0.70
1.13
0.00
0.00
4.19
0.00
0.00

0.00
0.40
6.62
10.02
0.00
0.00
0.00
40.33
0.00

0.00
0.10
1.19
2.11
0.00
0.00
0.00
0.00
15.99

Table 63: SR4jM : Background fit results for the validation
regions VRWMA,R
VRWMa, and VRWmA, for an integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised to MC cross-sections) are given for comparison.
The errors shown are the statistical plus systematic uncertainties. The errors shownfor the signal region are systematic uncertainties only.

120

SR4jM channel

CRYMA

Observed events

19

Fitted bkg events

22.88 ± 5.87

Fitted Wjets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted CRYMA events

0.51 ± 0.20
0.00 ± 0.00
0.27 ± 0.20
0.25 ± 0.18
21.85 ± 5.85

MC exp. SM events

14.05

MC exp. Wjets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. CRYMA events

0.65
0.00
0.45
0.25
12.70

Table 64: SR4jM : Backgroundfit results for the validation region CRYMA, for anR
integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised
to MC cross-sections) are given for comparison. The errors are the statistical plus
systematic uncertainties.

121

SR6jL channel

VRZMa

VRZll

VRZllmA

VRZllMa

Observed events

10

0

1

2

Fitted bkg events

8.79 ± 2.33

0.25 ± 0.19

0.67 ± 0.42

0.59 ± 0.33

Fitted Multijets events
Fitted Wjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted WjetsL events
Fitted VRZma events
Fitted VRZMa events
Fitted VRZmA events
Fitted VRZll events
Fitted VRZllMa events
Fitted VRZllmA events

0.03 ± 0.02
3.47 ± 1.32
1.26 ± 0.69
2.44 ± 1.29
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.59 ± 1.52
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.00+0.00−0.00
0.15+0.15−0.15
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.10+0.10−0.10
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.00 ± 0.00
0.04+0.04−0.04
0.18 ± 0.13
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.44 ± 0.41

0.00 ± 0.00
0.00 ± 0.00
0.01+0.02−0.01
0.35 ± 0.25
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.23 ± 0.22
0.00 ± 0.00

MC exp. SM events

12.34

0.35

0.80

0.97

MC exp. Multijets events
MC exp. Wjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. WjetsL events
MC exp. VRZma events
MC exp. VRZMa events
MC exp. VRZmA events
MC exp. VRZll events
MC exp. VRZllMa events
MC exp. VRZllmA events

0.02
2.58
3.06
2.45
0.00
0.00
0.00
4.23
0.00
0.00
0.00
0.00

0.00
0.00
0.01
0.15
0.00
0.00
0.00
0.00
0.00
0.20
0.00
0.00

0.00
0.00
0.10
0.18
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.52

0.00
0.00
0.02
0.36
0.00
0.00
0.00
0.00
0.00
0.00
0.60
0.00

Table 65: SR6jL : Background fit results for the validation regions VRZMa,R
VRZll, VRZllmA, and VRZllMa regions, for an integrated luminosity of L dt =3.2 fb−1 . Nominal MC expectations (normalised to MC cross-sections) are given
for comparison. The errors are the statistical plus systematic uncertainties.

122SR6jL channel

VRWMA

VRWMa

VRWmA

Observed events

1

3

5

Fitted bkg events

1.12 ± 0.72

3.15 ± 1.66

3.89 ± 2.90

Fitted Multijets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted TopL events
Fitted ZjetsL events
Fitted VRWMA events
Fitted VRWMa events
Fitted VRWmA events

0.00 ± 0.00
0.01 ± 0.01
0.06 ± 0.06
0.33 ± 0.27
0.00 ± 0.00
0.00 ± 0.00
0.72 ± 0.67
0.00 ± 0.00
0.00 ± 0.00

0.00 ± 0.00
0.03 ± 0.01
0.38 ± 0.21
1.15 ± 0.62
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
1.59 ± 1.52
0.00 ± 0.00

0.00 ± 0.00
0.03 ± 0.01
0.25 ± 0.22
0.47 ± 0.42
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
3.13 ± 2.86

MC exp. SM events

1.37

6.33

4.78

MC exp. Multijets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. TopL events
MC exp. ZjetsL events
MC exp. VRWMA events
MC exp. VRWMa events
MC exp. VRWmA events

0.00
0.01
0.15
0.33
0.00
0.00
0.88
0.00
0.00

0.00
0.03
0.92
1.15
0.00
0.00
0.00
4.23
0.00

0.00
0.03
0.61
0.47
0.00
0.00
0.00
0.00
3.66

Table 66: SR6jL : Background fit results for the validation regions
VRWMA,R
VRWMa, and VRWmA regions, for an integrated luminosity of L dt = 3.2 fb−1 .
Nominal MC expectations (normalised to MC cross-sections) are given for comparison. The errors are the statistical plus systematic uncertainties.

123SR6jL channel

CRYMA

Observed events

2

Fitted bkg events

2.55 ± 1.48

Fitted Wjets events
Fitted Zjets events
Fitted Top events
Fitted Diboson events
Fitted CRYMA events

0.14 ± 0.07
0.00 ± 0.00
0.06 ± 0.05
0.00 ± 0.00
2.34 ± 1.48

MC exp. SM events

2.92

MC exp. Wjets events
MC exp. Zjets events
MC exp. Top events
MC exp. Diboson events
MC exp. CRYMA events

0.11
0.00
0.15
0.00
2.66

Table 67: SR6jL : Backgroundfit results for the validation region CRYMA, for anR
integrated luminosity of L dt = 3.2 fb−1 . Nominal MC expectations (normalised
to MC cross-sections) are given for comparison. The errors are the statistical plus
systematic uncertainties.

124

Number of events

SR2jC

10

3

Multi-jet
W+jetsZ+jetstt(+X)&single top
Diboson

102

10

(n

obs

- npred) / σtot

1

CRT

CRW

CRQ

CRYMA CRYma

CRWL

CRTL

CRZllL CRWVL CRZllVL CRTVL

VRZll

VRZma VRWMA

CRT

CRW

CRQ

CRYMA CRYma CRWL

CRTL

CRZllL CRWVL CRZllVL CRTVL

VRZll

VRZma VRWMA

20−2

Number of events

SR4jL
10

3

Multi-jet
W+jetsZ+jetstt(+X)&single top
Diboson

102

10

(n

obs

- npred) / σtot

1

CRT

2

CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VR
V
V
C
V
V
V
Ma Zll RZllm RZllMaRWMARWMa RWmA RYMAL
llL
llVL VL
Ma
ma
mA
L
VL
A

0
−2
CRT CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VRZ VRZ VRZ VRW VRW VRW CRY
Ma
llllmA llMa MA Ma mA MA
L
llL
Ma ma mAL
VL llVL VL

Figure 54: The comparison of expected and observed number of events in thecontrol regions (CRs) and validation regions (VRs) for SR2jC and SR4jL. The
validation regions are listed in Table 40. In upper pad, the histograms show thepredicted SM number of events and the black dots show the observed number of
events. The blue shaded error bands are statistical error plus systematic uncertainties. The lower pad shows
the pull plots for the CRs and the VRs. The plotted
value is nobs − n pred /σtot , where nobs and n pred are the observed and predicted
number of events, and σtot is the total combination of statistical and systematic
uncertainties. The error bands are plotted only for validation regions.
125

Number of events

SR4jM
10

3

Multi-jet
W+jetsZ+jetstt(+X)&single top
Diboson

102

10

(n

obs

- npred) / σtot

1

CRT

2

CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VR
V
V
C
V
V
V
Ma Zll RZllm RZllMaRWMARWMa RWmA RYMAL
llL
llVL VL
Ma
ma
mA
L
VL
A

0
−2
CRT CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VRZ VRZ VRZ VRW VRW VRW CRY
Ma
llllmA llMa MA Ma mA MA
L
llL
Ma ma mAL
VL llVL VL

Number of events

SR6jL
102

Multi-jet
W+jetsZ+jetstt(+X)&single top
Diboson

10

(n

obs

- npred) / σtot

1

CRT

2

CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VR
V
V
C
V
V
V
Ma Zll RZllm RZllMaRWMARWMa RWmA RYMAL
llL
llVL VL
Ma
ma
mA
L
VL
A

0
−2
CRT CRW CRQ CRY CRY CRY CRW CRT CRZ CRW CRZ CRT VRZ VRZ VRZ VRZ VRW VRW VRW CRY
Ma
llllmA llMa MA Ma mA MA
L
llL
Ma ma mAL
VL llVL VL

Figure 55: The comparison of expected and observed number of events in thecontrol regions (CRs) and validation regions (VRs) for SR4jM and SR6jL. The
validation regions are listed in Table 40.In upper pad, the histograms show thepredicted SM number of events and the black dots show the observed number of
events. The blue shaded error bands are statistical error plus systematic uncertainties. The lower pad shows
the pull plots for the CRs and the VRs. The plotted
value is nobs − n pred /σtot , where nobs and n pred are the observed and predicted
number of events, and σtot is the total combination of statistical and systematic
uncertainties. The error bands are plotted only for validation regions.
126

7

Statistical treatment

In this analysis, the SM process backgrounds (BGs) in signal region (SR) are
estimated with both MC-based and data-driven method. For the BG estimation
using the MC simulated SM samples, control regions (CRs) where the events of the
SM processes fully dominate are prepared to normalize the difference of acceptance
between data and MC. For the BG estimation using data-driven method, sufficientnumber of CRs are needed to estimate one SM process in SRs. The details aredescribed in Chapter 6. To estimate the SM process BGs with CRs, a simultaneous
fit in all the CRs is needed. For the evaluation of signal exclusion limit, proper
statistical treatment is needed. These are processed using profile log likelihood
which is described in Sec.7.1 and Sec.7.2. For the exclusion, CL s method is used
and is described in Sec.7.3. In the fit, systematic uncertainties are taken into
account and are described in Sec.7.4.

7.1

Log likelihood

For simplification, at first, the case of one-bin measurement is considered. In suchcase, the probability density function (PDF) is
P (n| µ sig, S, B) = Pois(n| µ sig S + B),(84)

where n is observed number of events, µ sig is signal strength, B is expected numberof background events, S is expected number of signal events, and Pois is Poisson
function. µ sig = 0 correspond to background-only hypothesis and µ sig = 1
correspond to signal and background hypothesis. The likelihood function L is P,
and the fit is executed to maximize log L.
In actual measurement, there are systematic uncertainties in the expected number of events for signal and background, B(θ) and S(θ) . These θs are the parameterof systematic uncertainties and the PDF isY
P (θ |θ 0, σθ 0 ) =Gaus(θ 0j − θ j , σθ 0 ),
(85)
j

j∈Sys

where Gaus(θ 0j − θ j , σθ 0 ) is the Gaussian distribution function of θ j around θ 0jjwith standard deviation, σθ j . Since multiple CRs are prepared in this analysis, thetotal likelihood function become,L(n| µ sig, S, B, θ) = Pois(nSR |λ(µ sig, S, B, θ))SR
·

NC R
Y

Pois(ni |λ(µ sig, Si, Bi, θ)) ·

i∈C R

Y

j

j∈Sys

127

Gaus(θ 0j − θ j , σθ 0 ),(86)where λ is expected value for Poisson distribution, and λ is a function of µ sig , S,
B, and θ.
As described in Chapter. 6, multiple parameters are fitted in multiple CRs.
Therefore, more precisely, λ(µ sig, Si, Bi, θ) becomesλ(µ sig, Si, µ MCs, B0 MCs, Bi, µ Z , ε, θ),(87)

where B0 MCs and µ MCs are the nominal expected numbers of events estimatedfrom the SM process with MC samples and their normalization factors fitted in
CRs, µ Z is the expected number of events for Z (→ νν)+jets in SR, and ε are thefit parameters used for the estimation of µ Z as described in Table 39. For example
in CRWL with ABCD+WXYZ method, using the Eq.(82), the expected value ofPoisson isdibosonλ(µ sig, Si, µ MCs, B0 MCs, Bi, µ Z , ε, θ) = µ sig · SCRWL + µT opL · BCRWL + BCRWL
Z+jets+ BCRWL + µ Z · εY M A · εY Ma · εY m A · εW L · RZ/Y ,
(88)
Top

where RZ/Y is included in θ.

7.2

Profile log likelihood

To evaluate p-value of this analysis, profile log likelihood method is used. For theevaluation of one hypothesized µ sig 5, the profile likelihood ratio is given byqµ =ˆ
L(µ| θ̂)L( µ̂| θ̂)(89)

where θ is a set of the parameters including nuisance ones, θ̂ˆ is the θ which
maximize L for one given µ, and µ̂ and θ̂ are the determined values which
maximize L. If q µ is near 1, it means good agreement between hypothesized µ
value and observed data. It is much convenient to define statistict µ = −2 ln q µ,

(90)

since q µ moves in the range of [0,1] and t µ moves in the range of [0,∞]. With
this transformation, q µ exclusion can be interpreted with significance defined in
one-sided test of Gaussian distribution.
Now, the discrepancy between data and µ is in proportion to t µ . The degree of
disagreement is then represented by p-value,Z ∞pµ =f (t µ | µ)dt µ,(91)
t µobs5From this section, µsig is represented with µ128where f (t µ | µ) is the distribution of the t µ as in Figure 56(a). The interpretation of
p−value in significance (Z) is assuming the Gaussian distribution. The p−value
from t µ is converted to Z assuming the relation of Z and p−value in Gaussian
distribution as shown in Figure 56(b).

Figure 56: Distributions of statistics[66]. (a) Distribution of t µ and the relation to p−value
 the observed data. (b) Distribution of Gauss function√  from
φ(x) = 1/ 2π exp −x 2 /2 , and relation between p−value and Z (significance)
is shown.

7.2.1

Approximation for discovery limit

For the discovery limit, background only hypothesis (µ=0) is tested. For the simple
test of discovery limit, we assume the likelihood function,
L(µ) = Poiss(n| µS + B).

(92)

Then, the discovery q0 become,L(0)µ̂ ≥ 0, −2 ln L(µ̂)
q0 = 
0µ̂ < 0.

If n is approximated to be µS + B and µ = 1, significance become
s
!
!
S+B
Z0 ' 2 (S + B) ln
−S
B

(93)

(94)

For the case B  S, this can be expanded to beS
Z0 ' √ .
B
This is widely used to evaluate significance simply.
129

(95)

7.3

CLS techniqueIn this analysis CLS [67] is used for the upper limit calculation.
In past, for the signal exclusion fit, p-value with µ = 1 hypothesis is calculated.
With such p−value (pS+B ), CLS+B = pS+B is defined and used for confidence
level (CL) of exclusion. This is the case for measurement with large number of
events. However, this is not appropriate for number-counting measurement likethis analysis. The sensitivity is evaluated with CL B = 1 − pB , where pB is thep−value with µ = 0 hypothesis. If the expected number of events in a SR is small,the f (t µ | µ) for µ = 1 and µ = 0 are similar as in Figure 57. In this case, thesignal is excluded because the CL S+B is small, even though the measurement has
low sensitivity because the CL B is small. To avoid this problem, CLS technique isused. This assumes the probability of S + B ≤ Nobs under the condition, B ≤ Nobs ,i.e.
P ((S + B) ≤ Nobs )P ((S + B) ≤ Nobs |B ≤ Nobs ) =.
(96)
P(B ≤ Nobs )If these are interpreted to CL, CLS is defined:
CLS+B
,
(97)
CLB
where CLB is the CL for background only hypothesis. This CLS is widely used inparticle physics to evaluate the exclusion confidence level.
CLS =

7.4

Systematic uncertainties

The origin of systematic uncertainties are classified into experimental uncertainties
and theoretical uncertainties. These uncertainties are taken into account in the final
fit as nuisance parameters.
7.4.1

Experimental uncertainties

The primary candidates of experimental uncertainties are luminosity uncertainty,
jet energy scale (JES) uncertainty, jet energy resolution (JER), and ETmiss resolution(MER) and these uncertainties are taken into account in the fit. The lepton
reconstruction uncertainties and b−tag uncertainties are not considered since theeffect for the SRs are expected to be negligible.
Luminosity uncertainty: The uncertainties on the integrated luminosity is ±5%.
This uncertainty is considered only in the exclusion fit.
JES uncertainty: The measurement of JES is described in Refs.[69–71]. The
uncertainties are measured as a function of pT and η of jet (Figure 58).
130

Figure 57: The distribution of the t µ under the hypothesis of µ = 0 and µ = 1 [68].
CLB = 1 − pB and CLS+B = pS+B .
JER: The measurement of JER is described in Ref.[72]. The uncertainty of JER
is added in the fit.
MET SoftTerm: As described in Sec.4.6, ETmiss consists of objects and "SoftTerm". The systematic uncertainties from each object are separated from "MET"
uncertainty. Thus, the resolution and scale uncertainties from ETmiss, SoftTerm aretaken into account.
7.4.2

Theoretical uncertainties

The considered theoretical uncertainties are the uncertainties from theoreticalmodelling of SM backgrounds with MC, the uncertainties from data-driven BG
estimation (Sec. 6.5), and theoretical uncertainty of signal cross section.
MC uncertainties The theoretical uncertainties of SM MCs are evaluated withcomparing the different generators. For W /Z+jets MCs, the difference of Sherpa2.1
and Madgraph5+Pythia8 is used. For t t¯ MCs, the difference between PowhegBox+Pythia6 and "aMC@NLO+Herwig++", the parton showering difference
between Pythia8 and Herwig++, and the difference in tuning of underlying events131√Figure 58: JES uncertainties estimated with s = 13 TeV data√with 25 ns bunch
spacing[71]. The green band shows the total uncertainty
for s = 13 TeV data.
√
The purple band shows the total uncertainty for s = 8 TeV data (Run1). (a)jetshows the uncertainty as a function of pT in η = 0. (b) shows the uncertainty as
jeta function of η with pT = 40 GeV.
between A14[73] and Perugia2012[74] are taken into account. For the MCs including diboson processes, a flat 50% scale uncertainty is applied conservatively
to cover all the uncertainties including PDF uncertainty and this uncertainty isapplied only in SRs and validation regions (VRs) where the background estimation method is validated. In addition to these theoretical uncertainties, statisticaluncertainties of MC samples are also taken into account.
Uncertainties from data-driven BG estimation This is the uncertainty fromthe BG estimation method. The details of this uncertainties are described inSec.6.5.
Signal cross section uncertainty This uncertainty consists of these three components.
• Scale uncertainty : Uncertainties from factorization and renormalization
scale. Both scales are varied with factors of 0.5 and 2, and the difference
from nominal is evaluated as scale uncertainties.
• PDF uncertainty : PDF are extrapolated from experimental measurement,such as HERA[75] and Tevatron. The propagation of uncertainties areevaluated with CTEQ[76] and MSTW[77] PDF sets.
• Strong coupling (α s ) uncertainty: The cross section uncertainties from α Svariation with CTEQ is considered.
132

8Results

The estimated and observed events after the fits are described in 8.1. The interpretation of the results using simplified model of gluino pair-production is describedin 8.2.

8.1

Fit results for signal region

The observed events and expected events of SR2jC, SR4jL, SR4jM, SR6jL aresummarized in Table 68. The breakdown of dominant systematic errors in each
Signal regions

SR2jL

SR4jL

SR4jM

SR6jL

Observed events

45

12

14

4

Fitted bkg events

44.51 ± 9.37

9.21 ± 2.39

11.45 ± 2.40

2.79 ± 0.96

Fitted Multijets events
Fitted Wjets events
Fitted Top events
Fitted Diboson events
Fitted Z_SR events

0.06 ± 0.02
5.51 ± 1.20
1.34 ± 0.68
10.70 ± 5.40
26.89 ± 7.57

0.01+0.02−0.01
1.66 ± 0.74
0.78 ± 0.41
2.67 ± 1.37
4.08 ± 1.84

0.01+0.01−0.01
2.58 ± 0.99
1.19 ± 0.30
2.31 ± 1.19
5.36 ± 1.92

0.11 ± 0.04
1.20 ± 0.53
0.28 ± 0.21
0.49 ± 0.26
0.70+0.74−0.70

MC exp. SM events

46.69

11.91

13.60

3.56

MC exp. Multijets events
MC exp. Wjets events
MC exp. Top events
MC exp. Diboson events
MC exp. Z_SR events

0.04
8.72
2.43
10.70
24.80

0.01
2.71
1.50
2.67
5.02

0.01
3.28
1.99
2.31
6.02

0.10
0.89
0.66
0.49
1.41

Table
R 68: Background fit results for the Signal regions for an integrated luminosityof L dt = 3.2 fb−1 . Nominal MC expectations (normalised to MC cross-sections)
are given for comparison.
SR is summarized in Table 69 -72.
The distributions of meff and aplanarity in each signal region are shown in
Figure 59-60. The distribution of Z+jets events in SR is evaluated from the distribution of γ+jets events in CRYMA region with normalization factor (1/εY M A).
These are not the actual estimated number of events for SR4jL, SR4jM, and SR6jL,
because the number of events in CRYMA is estimated with ABCD method.
Since significant excess is not observed, model independent upper limits arecalculated conservatively. The summary of limits are in Table 73. It shows 95%
133Uncertainty of channel

SR_cuts

Total background expectationp
Total statistical error ( Nexp )Total background systematic error

44.51
±6.67
±9.37 [21.05%]µZ
Systematics Dibosons
JESµW jets
MC statistics
Generator Top
Generator WµT op
Top radiation
Top tuning
MET SoftTermJERµ Multi jets
Top flagmentation±7.57 [17.0%]±5.35 [12.0%]±1.35 [3.04%]±1.15 [2.6%]±0.74 [1.7%]±0.58 [1.3%]±0.35 [0.79%]±0.34 [0.77%]±0.13 [0.30%]±0.13 [0.30%]±0.12 [0.27%]±0.11 [0.26%]±0.02 [0.04%]±0.01 [0.02%]

Table 69: Breakdown of the dominant systematic uncertainties in the estimated number of background events in SR2jC. Note that the uncertainties can becorrelated, and do not necessarily add up quadratically to the total backgrounduncertainty. The percentages show the size of the uncertainty relative to the total
expected background.

134

Uncertainty of channel

SR_cuts

Total background expectationp
Total statistical error ( Nexp )Total background systematic error

9.21
±3.03
±2.39 [25.98%]µZ
Systematics DibosonsµW jets
Generator W
MC statistics
JES
Generator TopµT op
Top flagmentation
MET SoftTerm
Top tuning
Top radiation
JERµ Multi jets

±1.84 [20.0%]±1.33 [14.5%]±0.54 [5.9%]±0.48 [5.3%]±0.38 [4.1%]±0.37 [4.0%]±0.31 [3.3%]±0.25 [2.7%]±0.14 [1.5%]±0.12 [1.31%]±0.08 [0.85%]±0.08 [0.85%]±0.06 [0.66%]±0.00 [0.03%]

Table 70: Breakdown of the dominant systematic uncertainties in the estimated number of background events in SR4jL. Note that the uncertainties can becorrelated, and do not necessarily add up quadratically to the total backgrounduncertainty. The percentages show the size of the uncertainty relative to the total
expected background.

135

Uncertainty of channel

SR_cuts

Total background expectationp
Total statistical error ( Nexp )Total background systematic error

11.45
±3.38
±2.40 [21.01%]µZ
Systematics Dibosons
Generator W
MC statisticsµW jets
JES
JER
µT op
Top radiation
Top tuning
Generator Top
MET SoftTerm
Top flagmentationµ Multi jets

±1.92 [16.7%]±1.15 [10.1%]±0.81 [7.0%]±0.42 [3.6%]±0.40 [3.5%]±0.39 [3.4%]±0.24 [2.1%]±0.19 [1.7%]±0.12 [1.0%]±0.12 [1.0%]±0.11 [0.92%]±0.03 [0.27%]±0.02 [0.17%]±0.00 [0.01%]

Table 71: Breakdown of the dominant systematic uncertainties in the estimated number of background events in SR4jM. Note that the uncertainties can becorrelated, and do not necessarily add up quadratically to the total backgrounduncertainty. The percentages show the size of the uncertainty relative to the total
expected background.

136

Uncertainty of channel

SR_cuts

Total background expectationp
Total statistical error ( Nexp )Total background systematic error

2.79
±1.67
±0.96 [34.54%]µZµW jets
Generator W
MC statistics
Systematics Dibosons
Generator Top
µT op
JES
MET SoftTerm
Top flagmentationµ Multi jets
Top radiation
Top tuning
JER±0.74 [26.4%]±0.36 [12.8%]±0.32 [11.3%]±0.28 [9.9%]±0.25 [8.8%]±0.17 [6.0%]±0.11 [3.9%]±0.09 [3.4%]±0.05 [1.7%]±0.04 [1.5%]±0.04 [1.4%]±0.03 [1.0%]±0.03 [1.0%]±0.03 [0.97%]

Table 72: Breakdown of the dominant systematic uncertainties in the estimated number of background events in SR6jL. Note that the uncertainties can becorrelated, and do not necessarily add up quadratically to the total backgrounduncertainty. The percentages show the size of the uncertainty relative to the total
expected background.

137

Signal channel
SR2jC
SR4jL
SR4jM
SR6jL

h σi95
[fb]
obs

95
Sobs

95
Sexp

CL B

p(s = 0)

7.45
3.47
3.67
1.98

23.9
11.1
11.8
6.4

23.5+7.5−5.4
9.1+3.9−2.8
10.0+4.3−2.9
5.7+2.6
−1.7

0.52
0.71
0.68
0.66

0.47
0.25
0.29
0.30

Table 73: Left to right: 95% CL upper limits on the visible cross section (h σi95
)
obs
95
95
and on the number of signal events (Sobs ). The third column (Sexp ) shows the 95%
CL upper limit on the number of signal events, given the expected number (and±1σ excursions on the expectation) of background events. The last two columns
indicate the CL B value, i.e. the confidence level observed for the background-only
hypothesis, and the discovery p-value (p(s = 0)).
CL upper limits to visible cross section ( h σi95), observed number of signal
obs
95
95
events ( Sobs ), expected number of signal events (Sexp ) , and the p0 value.

138

Events/200.0

Events/200.0∫ L dt = 3.2 fb s=13 TeV-1

SR2jC, m (incl.)>1900 (GeV)
eff

Data 2015 ( s = 13 TeV)
SM Total~~~ ∼gg direct, m(g, χ 01 )=(812, 787)
Multijett t (+X) & single top
W+jetsDibosonZ+jets from γ +jets

10

SR4jL, m (incl.)>2000 (GeV)
eff

Data 2015 ( s = 13 TeV)
SM Total~~~ ∼gg direct, m(g, χ 01 )=(1400, 200)
Multijett t (+X) & single top
W+jetsDibosonZ+jets from γ +jets

1

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

DATA / MCDATA / MC

-1

10

1

30
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2
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0

∫ L dt = 3.2 fb s=13 TeV

30
2.5
2
1.5
1
0.5
0
0

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

meff(incl.) (GeV)-1

SR4jM, m (incl.)>1600 (GeV)
eff

Data 2015 ( s = 13 TeV)
SM Total~~~ ∼gg direct, m(g, χ 01 )=(1200, 600)
Multijett t (+X) & single top
DibosonW+jetsZ+jets from γ +jets

10

4000

(b) meff distribution in SR4jL.
Events/200.0

Events/200.0(a) meff distribution in SR2jC.
∫ L dt = 3.2 fb s=13 TeV

3500

meff(incl.) (GeV)10∫ L dt = 3.2 fb s=13 TeV-1

SR6jL, m (incl.)>1850 (GeV)
eff

Data 2015 ( s = 13 TeV)
SM Total~~~ ∼ ∼gg onestep, m(g, χ ±1 , χ 01 )=(1385, 705, 25)
Multijett t (+X) & single top
DibosonZ+jets from γ +jets
W+jets

1

30
2.5
2
1.5
1
0.5
0
0

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

meff(incl.) (GeV)(c) meff distribution in SR4jM.

DATA / MCDATA / MC

1

30
2.5
2
1.5
1
0.5
0
0

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

meff(incl.) (GeV)(d) meff distribution in SR6jL.

Figure 59: meff distributions in each SR before the meff cut (shown with red
arrow). The black dots show the observed data events. The red histogram show
the total SM backgrounds. The dashed lines show the expected signal histogramsfrom MC simulation. The normalization of top, W, and multi-jet samples arefrom the fit results. The meff distributions of Z+jets samples are evaluated from
γ+jets events in CRYMA region, and the normalization factor is the inverse of
ε YMA . The red shaded band in SM Total and yellow band in ratio plot show thetotal combined error of the MC statistical error, systematic errors, fitting error innormalization factor, and data statistical error in γ+jets events. Systematic errors
are generator uncertainties and JES uncertainty as described in Sec.7.4. Errors in
the normalization factors and systematic uncertainties are applied independently,
though they have correlation. Therefore the errors become larger than the actual
ones. In SR4jL, SR4jM, SR6jL, the number of events in CRYMA is estimatedwith ABCD method, and hence the errors from data statistics in Z+jets (γ+jets)
become larger than actual ones.
139Events/0.01∫ L dt = 3.2 fb s=13 TeV-1

SR4jL, Aplanarity>0.03
Data 2015 ( s = 13 TeV)
SM Total~~~ ∼gg direct, m(g, χ 01 )=(1400, 200)
Multijett t (+X) & single top
W+jetsDibosonZ+jets from γ +jets

10

DATA / MC

1

30
2.5
2
1.5
1
0.5
0
0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Aplanarity

102∫ L dt = 3.2 fb s=13 TeV

Events/0.01

Events/0.01(a) aplanarity distribution in SR4jL.
-1

SR4jM, Aplanarity>0.07
Data 2015 ( s = 13 TeV)
SM Total~~~ ∼gg direct, m(g, χ 01 )=(1200, 600)
Multijett t (+X) & single top
W+jetsDibosonZ+jets from γ +jets

1010∫ L dt = 3.2 fb s=13 TeV-1

SR6jL, Aplanarity>0.07
Data 2015 ( s = 13 TeV)
SM Total~~~ ∼ ∼gg onestep, m(g, χ ±1 , χ 01 )=(1385, 705, 25)
Multijett t (+X) & single top
Z+jets from γ +jets
DibosonW+jets

1

30
2.5
2
1.5
1
0.5
0
0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Aplanarity(b) aplanarity distribution in SR4jM.

DATA / MCDATA / MC

1

30
2.5
2
1.5
1
0.5
0
0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Aplanarity(c) aplanarity distribution in SR6jL.

Figure 60: Aplanarity distributions in each SR before the aplanarity cut (shownwith red arrow). The black dots show the observed data events. The red histogramshow the total SM backgrounds. The dashed lines show the expected signal
histograms from MC simulation. The normalization of top, W, and multi-jet
samples are from the fit results. The aplanarity distributions of Z+jets samples areevaluated from γ+jets events in CRYMA region, and the normalization factor is
the inverse of ε YMA . The red shaded band in SM Total and yellow band in ratio
plot show the total combined error of the MC statistical error, systematic errors,
fitting error in normalization factor, and data statistical error in γ+jets events.
Systematic errors are generator uncertainties and JES uncertainty as describedin Sec.7.4. Errors in the normalization factors and systematic uncertainties areapplied independently, though they have correlation. Therefore the errors becomelarger than the actual ones. In SR4jL, SR4jM, SR6jL, the number of events in
CRYMA is estimated with ABCD method, and hence the errors from data statistics
in Z+jets (γ+jets) become larger than actual ones.
140

8.2

Interpretations and discussions

The Figure 61 shows the limit for the gluino direct-decay simiplified model. For
the case m( χ̃01 ) = 0, the gluino mass is excluded up to 1530 GeV. The comparison
with the CMS Run1 analysis with MT2 variable[78] is shown in Figure 62.
The Figure 63 shows the limit for the gluino onestep-decay simplified model.
For the case m( χ̃01 ) = 0, the gluino mass is excluded up to 1510 GeV. There is
no results from the Run1 CMS experiment with the same signal samples. As areference, the results of the Run1 CMS experiment using different gluino onestepdecay simplified model is shown in Figure 64. The model include neutral Next
to Lightest SUSY Particle(NLSP) which decays into Z in addition to the onestepdecay simplified model of this thesis.
0~~~
gg production, B (g → qq ∼χ )=100%

Observed limit

1200

1

mχ∼0 [GeV]

1

1400

1000

∫ Ldt = 3.2 fb , s = 13 TeV

Exp. limits (± 1 σexp )-1

ATLAS Observed limit (20.3 fb -1, 8 TeV)

0-leptons, 2,4,6 jets
(Fit to SR,CRs)

4jL

2jC
4jM
4jM
4jM
4jL
4jL
4jM
4jM
4jM
4jM
4jL
2jC
2jC
2jC
4jM
4jM
4jM
4jL
4jL
2jC
4jM
4jM
4jM
4jL
4jL
2jC
2jC
2jC
4jL
4jM
4jM
4jL
4jL
4jL
4jM
4jM
4jM
4jL
4jL
2jC
2jC
2jC
2jC
4jM
4jM
4jM
4jL
4jL
4jL
2jC
4jM
4jM
4jM
4jL
4jL
4jL
4jM
4jL
4jL
4jL
4jL
4jM
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jM
4jL
4jL
4jL
2jC
4jM
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jM
4jM
4jM
4jL
4jL
4jL
4jL

400

600

All limits at 95% CL.

800

1

m

400

g~ <

m

χ∼ 0

600

200

0
200

800

1000

1200

1400

1600

1800

2000

m~g [GeV]

Figure 61: Exclustion contour with 95% CL for gluino pair-production with gluino
decaying directly into LSP and quarks. The blue dashed contour and yellow bandshow the expected limit with 1σ excursion with systematic uncertainties. The redsolid and dotted contours show the observed limit with 1σ excursion with signal
theoretical uncertainties. The pale purple region shows the observed
 limit fromthe ATLAS Run1 analyses[79]. The stars are from optimized point m(g̃), m( χ̃01 )of SR4jL, SR2jL, SR4jM .

141

0
~~
~
gg production, B (g → qq ∼χ )=100%

Observed limit

1200∫ Ldt = 3.2 fb , s = 13 TeV

1000

0-leptons, 2,4,6 jets1mχ∼0 [GeV]1

1400
Exp. limits (± 1 σexp )-1

CMS Observed limit (19.5 fb-1, 8 TeV)

(Fit to SR,CRs)

4jL

2jC
4jM
4jM
4jM
4jL
4jL
4jM
4jM
4jM
4jM
4jL
2jC
2jC
2jC
4jM
4jM
4jM
4jL
4jL
2jC
4jM
4jM
4jM
4jL
4jL
2jC
2jC
2jC
4jL
4jM
4jM
4jL
4jL
4jL
4jM
4jM
4jM
4jL
4jL
2jC
2jC
2jC
2jC
4jM
4jM
4jM
4jL
4jL
4jL
2jC
4jM
4jM
4jM
4jL
4jL
4jL
4jM
4jL
4jL
4jL
4jL
4jM
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jM
4jL
4jL
4jL
2jC
4jM
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jL
4jM
4jM
4jM
4jL
4jL
4jL
4jL

400

600

All limits at 95% CL.

800

1

m

400

g~ <

m

χ∼ 0

600

200

0
200

800

1000

1200

1400

1600

1800

2000

m~g [GeV]

Figure 62: Exclustion contour with 95% CL for gluino pair-production with gluino
decaying directly into LSP and quarks. The blue dashed contour and yellow bandshow the expected limit with 1σ excursion with systematic uncertainties. The redsolid and dotted contours show the observed limit with 1σ excursion with signal
theoretical uncertainties. The pale purple region shows the observed limit fromthe
 CMS Run1 analysis[78] with MT2 variable. The stars are from optimized pointm(g̃), m( χ̃01 ) of SR4jL, SR2jL, SR4jM .
As described in introduction, the typical mass spectrum of m(g̃) : m( χ̃01 ) ∼6 : 1 or 7 : 1. In order to target the m(g̃) ∼1.4 TeV, dedicated SRs are prepared.
SR4jL is prepared for gluino direct-decay model and SR6jL is prepared for gluino
onestep-decay model. No significant excess is observed in these SRs and signal
models are excluded up to m(g̃) ∼ 1.5 TeV in both models. The excluded points
correspond to the typical mass spectrum are excluded by SR4jL for gluino directdecay case and SR6jL for onestep-decay case. The prepared SRs dedicated fortarget signal worked effectively.
In the gluino direct-decay model, light m(g̃) and m( χ̃01 ) region are not excluded
with Run2 data whereas the region is already excluded in Run1. Since heavy gluino
is targeted in this analysis, large meff selection is prepared in any SRs. Therefore,
light m(g̃) regions cannot be excluded with this analysis.

142

0
0
~~
~
±
±
~
gg production, B (g → qq ∼
χ → qq W± ∼χ )=100%, m(∼
χ )=(m(g) + m(∼χ ))/21

1

1

Observed limit

1200∫ Ldt = 3.2 fb , s = 13 TeV

1000

0-leptons, 2,4,6 jets1mχ∼0 [GeV]1

1400
Exp. limits (± 1 σexp )-1

ATLAS Observed limit (20.3 fb -1, 8 TeV)

(Fit to SR,CRs)

800

2jC
2jC
2jC
2jC
2jC
2jC
2jC

g~ <

m

400

2jC
2jC
1

m

χ∼ 0

600

2jC

2jC
2jC

All limits at 95% CL.

4jM

6jL

2jC

4jL

4jM
6jL

6jL

2jC
4jL

6jL

4jM

6jL

6jL

6jL

0
200

400

600

800

1000

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

6jL

4jM

2jC
2jC

6jL

6jL

4jM

2jC
2jC

200

4jM

6jL

6jL
6jL

6jL

6jL

6jL

1200

1400

1600

6jL

6jL

6jL
6jL

6jL
6jL

1800

2000

m~g [GeV]

Figure 63: Exclustion contour with 95% CL for gluino pair-production in onestepdecay model. Each gluino decays into q q̄ χ̃±1 and χ̃±1 decays into W χ̃01 . The
assumed mass relation is m( χ̃±1 ) = m(g̃) + m( χ̃01 ) /2. The red solid and dotted
contours show the observed limit with 1σ excursion with signal theoretical uncertainties. The blue dashed contour and yellow band show the expected limit with
1σ excursion with systematic uncertainties. The pale purple region shows theobserved
 limit fromthe ATLAS Run1 analyses[18]. The stars are from optimized
point m(g̃), m( χ̃01 ) of SR6jLSR2jL, SR4jM, SR2jL.
In the gluino onestep-decay model, the mass points around m(g̃) : m( χ̃±1 ) : m( χ̃01 )∼900 : 700 : 500 are not excluded whereas the region is excluded in Run1 analysis.
These regions are not typical mass regions and dedicated SRs are not prepared. Insuch region, large ETmiss is not efficient since mass gaps of gauginos are very small.
Therefore, a SR with much smaller ETmiss cut will be needed. In the case, the other
BG estimation will be needed since data-driven γ replacement is effective only forhigh ETmiss region SM background estimation. Therefore, in future analysis withlarge integrated luminosity, the low ETmiss region dedicated for the small mass gap
regions will be needed.

143

1000
900

0
~~ ~
pp → g g, g → q q V ∼χ1 NLO+NLL exclusion

Observed ± 1 σtheory
Expected ± 1 σexperiment

800
700
600

1

m∼χ±/ ∼χ0 = 0.5(m∼0 + m~g)
1

2

χ

1

10-1

(d)

500
400

10-2

300
200
100
0
400 500 600 700 800 900 1000 1100 1200 1300 1400

95% C.L. upper limit on cross section (pb)m∼χ0 [GeV]

CMS , L = 19.5 fb-1, s = 8 TeV

m~g [GeV]
Figure 64: Exclustion contour with 95% CL for gluino pair-production in onestepdecay model from the CMS experiment Run1 analysis[80]. Each gluino decays
into q q̄ + χ̃±1 / χ̃02 and χ̃±1 / χ̃02 decays into W /Z + χ̃01 . The assumed mass relationis m( χ̃±1 / χ̃02 ) = m(g̃) + m( χ̃01 ) /2. The black solid and dotted contours show
the observed limit with 1σ excursion with signal theoretical uncertainties. The
red solid and dotted contours show the expected limit with 1σ excursion withsystematic uncertainties.

144

9

ConclusionThis√ thesis reports a search for gluino pair-production−1in proton-proton collision
at s = 13 TeV with an integrated luminosity of 3.2 fb recorded by the ATLAS
detector at CERN. Gluino pair-production is searched for using events with large
ETmiss , jets, and no lepton in the final states of the proton-proton collisions.
To optimize the event selection for non-planar multi-jet events, a variable"aplanarity" is newly introduced, which results in better signal sensitivity overthe previous searches. Four signal regions (SRs) are prepared for gluino pair
production search. SR2jC is the SR for the case m( χ̃01 ) is close to m(g̃). SR4jL
is the SR for the case difference between m(g̃) and m( χ̃01 ) is large. SR4jM is the
SR for the case m(g̃) ∼ 2m( χ̃01 ). SR6jL is the SR for the case difference betweenm(g̃) and m( χ̃01 ) is large in the simplified model of gluino onestep-decay.
A new method to evaluate number of background (BG) events using the real
data is applied in this analysis. For the claim of discovery of SUSY signal, datadriven BG estimation method is important. Therefore, a BG estimation method
which does not rely on the MC simulation as much as possible is devised andapplied. The number of events estimated with the method and that of observed datashows good agreement. This means the new BG estimation method is evaluatedto be effective.
No significant excess is observed in SRs. The exclusion of SUSY signals isinterpreted using simplified models in which gluinos are pair-produced and eachgluino decays into two quarks and an electroweakino. In gluino direct-decay
model in which the electroweakino is LSP, gluinos with masses up to 1530 GeV
are excluded for the massless LSP at 95% CL. This result is also interpreted withgluino onestep-decay simplified model in which the electroweakino is χ̃±1 and χ̃±1
decays into W and LSP. For the massless LSP, gluinos with masses up to 1510 GeV
is excluded at 95% CL.
In some typical mass spectrum described in the introduction (Sec.1.3.2) likem(g̃) : m( χ̃01 )= 6:1 or 7:1, the gluinos with masses up to ∼1510 GeV are excluded
in both model.
These results give a new constraint in SUSY models or parameter space which
is not excluded by Run1 SUSY search.
In future, the LHC-ATLAS
experiment plans to accumulate data which cor√−1
respond to ∼ 100 fb at s=13 (or 14) TeV until 2018. From my simple study,
it is expected to reach gluinos with masses up to 2100 GeV in direct-decay modelfor the massless LSP at 3σ sensitivity reach with the data. Therefore, it might bepossible that a gluino with mass which is not excluded by this thesis is discoveredin near future.

145

Acknowledgements
I would like to show my greatest appreciation to my supervisor, Prof. Sachio
Komamiya, for his generosity to accept me as a Ph.D. students. Without his
support, I could not continue my research.
I would like to express my gratitude to Dr. Naoko Kanaya, for her help toimplement new variables to the group analysis and encourage to the development of background estimation method. Her support is also helpful to search an
comfortable apartment in France, and this lead to increase work efficiency.
I appreciate the feedback offered by Prof. Shoji Asai. His epoch making
idea and deep knowledge always helped my analysis. I had many support fromDr. Shimpei Yamamoto about maintenance of computing resource and knowledge
about statistical treatment. I would like to thank Prof. Junich Tanaka and Prof.
Yuji Enari for the help for upgrade study about the LAr calorimeter and manysuggestions for my analysis. I had discussion with Dr. Tatsuya Masubuchi about
the background estimation method and it gave me a deep understanding. I superultra hyper miracle thank Dr. Takashi Yamanaka for his generous support not only
for the analysis but also the private life in France. I would like to express mygratitude to Dr. Takuya Nobe for his suggestion for my thesis.
I am deeply grateful to all the staffs and students of ICEPP, the University ofTokyo, and KEK for many supports for research and staying at CERN. I would liketo thank Prof. Tatsuo Kawamoto, Prof. Tomio Kobayashi, Prof. Koji Terashi, Dr.
Koji Nakamura, Dr. Keita Hanawa, Dr. Tomoyuki Saito, Dr. Yuichi Sasaki, Dr.
Shingo Kazama, Dr. Yohei Yamaguchi, Dr. Keisuke Yoshihara, Mr. Masahiro
Morinaga, Ms. Aine Kobayashi, Mr. Shion Chen, Mr. Chikuma Kato, Ms.
Chihiro Kozakai, Mr. Tatsuya Mori, and Mr. Shunsuke Adachi.
I would like to appreciate the members of analysis group at CERN: Dr.Jamie
Boyd, Dr. Tommaso Lari, Dr. Nikola Makovec, Dr. Chris Young, Dr. MarijaVranjes Milosavljevic, and Dr. Laurent Duflot for them enormous support as aconvener of the groups. Dr. Judita Mamuzic for help of usage of TMVA. Dr. Yu
Nakahama for help of the fit implementation. Dr. Geraldine Conti and Mr. Baptiste
Akio Jean abeloos for cooperation of photon studies. Dr. Monica D’Onofrio forher help to study the generator of γ+jets. Dr. Jeanette Miriam Lorenz, Dr. Sophio
Pataraia, and Dr. Sarah Louise Williams for help and cooperation to implement
simultaneous fit for data-driven background estimation.
I would like to thank all the members of the ATLAS experiments and the LHC
staffs.
For comfortable staying at CERN , I would like to show my appreciation to
Mr. Vladimir Troubetzkoi and Ms. Masako Hayashi.
I would like to express my gratitude to my colleagues of the company I was
employed for accepting my retirement and wishing my success.
146

Finally, I want to thank my family.

147

Appendix
A

PhotonIn this section, some studies related to photons are described.

A.1

Jet-Photon overlap removal validation

According to the definition of jets in Sec.4.1, photons are also reconstructed asjets. Therefore, the same objects must be removed. In this removal, these threepoints should be considered:
1. ∆R of photon and jet which are from the same truth photons. This is for theremoval of overlap objects.
2. ∆R of photon (from truth photons) and jet (not from truth photons). This is
for the check of miss-removal of jets.
3. ∆R of photon (not from truth photons) and jet (not from truth photons). Thisis for the check of removal of fake photons.
For the 1 and 2, γ+jets MC samples are used. For the 3, QCD multi-jet MC sample
are used. The photons are baseline photons (Tight ID) after the overlap removalwith electrons and muons are selected. Matching of reconstructed photons withtruth photons are with the condition, ∆R < 0.05. The jets are baseline jets after theoverlap removal with electrons and muons. Matching of reconstructed jets withtruth photons are with the condition, ∆R < 0.4.
The 2D distribution in ∆R and pT plane of 1 is shown in Figure 65(a). The
candidate ∆R size for overlap removal is 0.4, since the isolation cone size of photon
is at most 0.4 and cone size of jet is 0.4. From the figure, it can be seen the ∆<0.4
is enough to remove the overlap.
γ control region is used to estimate the events of Z (→ νν)+jets events in signal
region. If the OR with ∆R <0.4 removes truth jets around a photon, the number ofjets behaviour in γ become different and not suitable for the estimation of Z+jets
events. Therefore, the ∆R of truth photons and jets are checked with Figure 65(b).
In the region, ∆R<0.4, around truth photons, the jets events are very small andnegligible. Thus the excess removal of jets are not worth consideration.
If the ∆R of jet→ γ photon and jets have difference with the truth one, the OR
can be used to remove fake events. Therefore, the ∆R of not truth photons and jets
are checked with Figure 65(c). If the fake evens is dominant in the region awayfrom ∆R∼ 0.0 (e.g. 0.2 < ∆R < 0.4), much tight OR can be used to reduce fake148

events. However, the fake dominant region is also around ∆R ∼ 0.0. Thus the OR
cannot help for fake events reduction.
In summary, the overlap removal between photon and jets is only with removalof jets in ∆R<0.4 of photons.
pT_vs_dRTruthPhNonPhJet
106

dR

dR

pT_vs_dRTruthPhTruthPhJet
1
0.9
105

0.8
0.7

0.6
0.5

102

0.4

0.4
2

10

0.3
0.2

0.3

100 200 300 400 500 600 700 800

10

0.2

10

0.1

0.1
0

103

0.7

103

0.5

104

0.9
0.8

104

0.6

1

0

1

100 200 300 400 500 600 700 800

1pT (GeV)pT (GeV)(a) ∆R between photon and jet which arefrom the same truth photons.

(b) ∆R between photon (from truth photon)and jet (not from truth photon).

dR

pT_vs_dRNonPhNonPhJet
1
0.9

108

0.8

107

0.7

106

0.6

105

0.5

104

0.4

103

0.3
0.2

102

0.1

10

0

100 200 300 400 500 600 700 800

1pT (GeV)(c) ∆R between photon (not from truth
photon) and jet (not from truth photon).

Figure 65: 2D distribution of ∆RvspT . Number of events are for the case,
1.0fb−1 .

149

R

Ldt =

A.2

Photon purity estimation with ABCD method

For the estimation of photon purity, ABCD method using phton ID selection andisolation selection is considered.
A.2.1

The difference of overlap-removal and ID order

For the ABCD method, photon ID and isolation cuts are considered. For the ID
based cuts, baseline photon is Loose ID and the two regions are with Tight ID
cut. In final γ CR, we use photons which pass Overlap Removal (OR) with theexact one Tight ID photon selection. Therefore the difference between two typesof selections need to be studied.
• Photons pass OR with exact one Tight ID photon.
• Photons pass Tight ID after OR with exact one Loose ID photon.
With true γ+jets samples and fake-photon (multi-jet) samples, some variables
distributions used in γ CR are checked. In both cases, Cone40 isolation is applied.
And no jet related cuts are applied. The comparison for true γ+jets samples are
Figure 66 and for fake-photon samples are Figure 67. In any distributions, there
are no difference within MC stat. error. Thus, the OR removal with exact one
Loose ID photon can be used for the study of Tight ID photon.

150

105

events/1

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106
Tight Id

4

10

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3

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104

102

102

10

10

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1

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10-2

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2
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00
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00
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800 1000 1200 1400 1600 1800 2000

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400

600

800

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1400

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1600

1800

2000

Njet(pT>40 GeV))

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4

6

8

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4

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8

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Photon pT(GeV)

events/40 GeV

events/0.01

105
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103

Loose Id

104

Tight Id

103

Loose Id

102

10

10

1

1

10-1

10-1

10-2

10-2
2
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1
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00
0

Aplanarity

0.02 0.04

0.06

0.08

0.1

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0.16

0.02

0.06

0.08

0.1

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meff(pT>60 GeV)(GeV)

500

1000

1500

2000

2500

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2500

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events/20 GeV

events/0.31

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4

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4000

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106

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3000

meff(pT>60 GeV)(GeV)(c) Aplanarity

105

14

105

102

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1
0.5
00
0

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12

(b) Njet (pT > 40 GeV)(a) Photon pT

104

12

Njet(pT>40 GeV))min∆φ(jet

0.5

1

1.5

2

0.5

1

1.5

2

T

2.5
2.5

min∆ φ(jet

2
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1
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00
0

,Emiss')

1,2,3

3
3

,Emiss')Tjet01 pT (GeV)

200

400

600

800

1000

1200

1400

200

400

600

800

1000

1200

1400

jet01 pT (GeV)1,2,3(e) min∆φ( ji, ETmiss )(f) Jet 01 pT

Figure 66: Distributions of each variable with two selection criteria for true photon
samples. Black solid line shows the OR with exact one Tight ID photon. Red
dotted line shows the Tight ID after the OR with exact one Loose ID photon.
The below pad is the ratio plot.

151events/1

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105
4Tight Id

103

Loose Id

10

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103

Loose Id

102

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Photon pT(GeV)

200

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events/40 GeV

events/0.01

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104

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0.5

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1400

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600

800

1000

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jet01 pT (GeV)1,2,3(e) min∆φ( ji, ETmiss )(f) Jet01pT

Figure 67: Distributions of each variable with two selection criteria for fakephoton samples. Black solid line shows the OR with exact one Tight ID photon.
Red dotted line shows the Tight ID after the OR with exact one Loose ID photon.
The below pad is the ratio plot.

152

A.2.2

Correlation study for ABCD method

The target of ABCD method is to estimate multi-jet BGs with data-driven way.
Therefore, the correlation between Tight ID related selections with isolation cut
after Loose photon ID selection are studied.
The value to evaluate the correlation is R Eq.(107). I selected one loose ID
photon (pT > 500 GeV) with multi-jet MC samples to evaluate the R-value. The
summary table of the R for each cuts used in Tight ID is Table 74. Even thesmallest |R| value, the difference from 1 is 29%. Therefore, the simple ABCD
method cannot be applied.
cutname
DeltaE
Eratio
fracm
wtot
weta1
weta2
Rphi
HadLeak
Reta
f1

|R-1|
0.29
0.80
2.63
3.89
96.9
242.4
336.0
1040.4
1622.02362.5correlation factor
0.065
0.082
0.085
0.079
0.048
0.083
0.032
0.056
0.043
0.032

Table 74: R value and correlation factor of each cut used in Tight ID and Cone40
Isolation cut. The cuts are sorted ascending order with |R| value.

153

B

TMVA

The Toolkit for MultiVariate Analysis (TMVA)[63] is the software for evaluationof multivariate classification. It includes many packages depend on the purpose ofanalysis. For the cut optimization, " Rectangular cut optimization " is used. This
optimize the rectangular cuts on discriminating variables. In this package, some
types of algorithm are implemented. Among them, Genetic Algorithm (GA) is
used in this study.

B.1

Genetic algorithm

Each candidate cut combination is called individual and the group of individual iscalled population. The cut values of discriminating variables for each individualis called genomes. The GA is used to make a cut combination which shows
smallest efficiency of BG samples for each efficiency of signal samples. The
signal efficiency is scanned from 0% to maximum%, and the best optimized cut
combinations which minimize the BG efficiency are determined for each signal
efficiency. The procedure of the algorithm is as follows:
1. Initialization: The population is generated randomly at first. In this analysis
300 individuals are generated.
2. Selection: The performance of cut combinations of individuals are evaluated. Evaluation is based on the smallness of the efficiency of BG samples
against a given signal efficiency. The worst fraction of the population is
discarded.
3. Reproduction: The selected individuals are copied. Some of them are
mutated randomly following the Gaussian p.d.f. This means the cut valuesof individuals are changed randomly.
4. Termination: The steps of selection and reproduction is iterated up to 40
times. The best 10 individuals are saved.
This cycle is executed independently 3 times. The best individual is selectedamong the top 30 selections. Then, the best cut combination which minimize BG
efficiency for a given signal efficiency is determined.
This algorithm provide higher speed and detailed optimization compared tobrute force optimization which scan all the cut combinations of discriminantvariables with discrete scan intervals. With some signal points, the optimized cut
combinations by GA and brute force method are compared. Since the optimized
results are similar, GA method is adopted.

154

B.1.1

Determination of opimized cut combination

From the processes of GA in TMVA, combinations of a signal efficiency, a BG
efficiency, and a cut combination are determined. From the combinations, a cut
combination which maximize the significance is determined using the corresponding signal efficiency and the BG efficiency.

155

C

ABCD method

The ABCD method is one of the data-driven estimation method. The idea of the
ABCD method is very simple.
The region which you want to estimate a component (signal) is defined as "A".
And for the ABCD method, two cuts which have small correlation for the signal
events are needed. If such cuts (cut1 and cut2) exists, the rest regions (B, C, D) isdefined as in Table 75.

pass cut2veto cut2veto cut1
BD

pass cut1
A
C

Table 75: Definition of ABCD regions. "A" is the region where the events need
to be estimated.
In these conditions, this equation holds:
NA NC
=
,
NB ND

(98)

since two selections with cut1 and cut2 have small correlation. At this point, thesmall correlation between two cuts is not necessary as far as the Eq.(98) holds.
Thanks to Eq.(98), the signal events in A can be estimated with these equations:
Nobs
B = NA × ε B,

(99)

Nobs
C = NA × ε C,

(100)

Sig
Nobs
D = NA × ε B × ε C,

(101)

Sig

Sig

Sig

obs
obs
where Nobs
B , NC , ND is the observed events in each region, N A is the estimatedsignal events in region A, and the εs are,
Sig

εB =

NB

Sig

(102)

NA

Sig

εC =

NC

Sig

.

(103)

NA

In actual cases, the events in regions for the ABCD method is not pure withsignal. In such case, the BG components should be subtracted for the method. In
156total, the equation is :BG
Nobs
B = NA × ε B + NB ,

(104)

BG
Nobs
C = NA × ε C + NC ,

(105)

BG
Nobs
D = NA × ε B × ε C + ND ,

(106)

Sig

Sig

Sig

C.1

ABCD method with correction

If the condition Eq.(98) does not hold and there are two components which shouldbe estimated from observed data, the ABCD method in Appendix C cannot be
used. In such case, semi data-driven estimation method is needed. In this section,
the ABCD method with using some variables from MC is explained. For thisestimation, some conditions are needed:• In each region for ABCD method, one signal and one BG components are
dominant.
• For signal events, only the normalization of MC samples should be decided
from data. This means ε B , ε C , and ε D from signal MC can be used.
• For BG events, only the double-ratio from MC estimation can be used. The
double-ratio is defined as
RBG,MC :=BG
NBG
A · ND
BG
NBG
B · NC.

(107)

The assumed situation of this method is that signal component is γ+jets event
and BG component is jet→ γ fake event, and selections are ID cut and isolation
cut. True photon events is comparatively reproduced with MC compared to fakephoton events. Therefore, the ratio (ε) from signal MC is used and only the Rfrom BG MC is used. Under this condition, this one equation holds:
obs − ε Sig,MC NSig
obs − ε Sig,MC NSig
N
N
C
A
C
A
B
B
Sig
BG,MC
NA = Nobs
.
(108)


A −R
Sig,MC Sig
obs
ND − ε DNA
Sig

From this equation, the N A is determined uniquely and the uncertainty for thisestimation is from MC stat. error of ε and R, and the stat. error of observed data.

157

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