Doctoral Dissertation
ZÎ÷á

Search for right-handed ] gauge boson decaying
into charged lepton andboosted right-handedpneutrino in 139 fb 1 of s = 13 TeV proton-proton
collisions with the ATLAS detector(ATLAS⌧˙hkJQã139 fb 1 n}P}P]Å«¸øí(D_Õ√˚®ÕÎÆ¸13 TeVkJQãw˚Ï◊»ÛhÛ˚MnÕDÀÂ¸»ÍŒk) YãÛ˚M]‹ΩÛ¢")A dissertation Submitted for the Degree of Doctor of Philosophy
December 2022
‰å4t12

ZÎ ⌃f

3À

Department of Physics, Graduate School of Science,
The University of Tokyoq¨'f'fb⌃f˚v—i⌃f⇥;
Reiyo Oishi'Û ≤â

Doctoral Dissertation
Search for right-handed ] gauge boson decaying
into charged lepton andboosted right-handedpneutrino in 139 fb 1 of s = 13 TeV proton-proton
collisions with the ATLAS detector

Reiyo Oishi
The University of Tokyo

Abstract

The standard model (SM) gives a successful description for almost the all phenomena of particle physics.
However, there are some problems such as the observation of tiny masses of left-handed neutrinos andbaryon dominance in the universe. One possible model which solve these inconsistencies is the left-rightsymmetric model (LRSM) accompanying right-handed neutrinos #R and right-handed , boson ,R . A
search for ,R decaying into #R , ? ? ! ,R± ! ✓ ± #R ! ✓ ± ✓ ± @@ 0, in the framework of LRSM is presented
in this thesis.
The analysis is based on a proton-proton collisions data at a center-of-mass energy of 13 TeV collectedby the ATLAS detector at the Large Hadron Collider in 2015 - 2018, corresponding to an integrated
luminosity of 139 fb 1 . The search is performed in both electron and muon final states, using a large-radius
jet to reconstruct the decay products from the #R ! ✓@@ 0, targeting on the phase space with large mass
splitting between ,R and #R , " = <(,R ) <(#R ). Depending on the ", two analysis strategies are
considered in the electron channel; one is to identify the electron from the #R decay as isolated from thelarge-radius jet; the other is to reconstruct the #R ! 4@@ 0 as a single large-radius jet. In the muon channel,
two muons are always required, since the higher efficiency can be kept even for large " signals. Event
selection, strategies of the dominant background estimations are developed.
No excess is observed in all lepton flavour final states and ,R mass is excluded up to 6.4 TeV for the #R
mass of 1.0 TeV at 95% confidence level. Compared to the previous LHC analyses, it corresponds to the
expansion of exclusion limits by 1.5 TeV and 1.4 TeV for electron and muon final states, respectively.

3

Contents
1 Introduction
1.1 Standard model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 U(1) gauge transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 SU(2) gauge transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Inconsistency between weak interactions and the SU(2) gauge transformation . .
1.1.4 Glashow-Weinberg-Salam theory . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.4.1 SU(2) ⇥ U(1) gauge transformation . . . . . . . . . . . . . . . . . . .
1.1.4.2 Spontaneous symmetry breaking . . . . . . . . . . . . . . . . . . . .
1.1.4.3 Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.4.4 Interactions with leptons . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.5 SU(3) gauge transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Remaining problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Finite masses of the left-handed neutrinos . . . . . . . . . . . . . . . . . . . . .
1.2.2 Baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Right-handed neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Target #R and ,R particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Previous and future experimental constrains . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Results of the ATLAS and CMS analysis . . . . . . . . . . . . . . . . . . . . .
1.5.2 Constraints from the other experiments . . . . . . . . . . . . . . . . . . . . . .
1.6 Strategy of LRSM search in boosted topology . . . . . . . . . . . . . . . . . . . . . . .

7
7
8
8
9
9
10
11
12
12
14
15
15
16
18
19
21
21
22
24

2 LHC-ATLAS experiment
2.1 Large Hadron Collider (LHC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 LUCID-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4.1 Electromagnetic calorimeter . . . . . . . . . . . . . . . . . . . . . . .
2.2.4.2 Hadron calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Trigger and data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.0.1 L1 trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.0.2 HLT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26
26
27
29
29
29
30
31
31
32
32
33
33

3 Dataset and Monte-Calro samples
3.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34
34
34

4

3.3

Monte-Calro samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 General description of inclusive cross-section . . . . . . . . . . . . . . . . . . .
3.3.2 Simulated signal samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Simulated background samples . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
36
36
37

4 Object reconstruction and identification
4.1 Charged track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Primary vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Topological Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 B-tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Overlap removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Missing Transverse Energy (⇢ Tmiss ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 Large radius jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39
39
39
40
40
42
43
44
45
46
47
47

5 Event selection
5.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Definition of one electron signal region (SR1e) . . . . . . . . . . . . . . . . . . . . . .
5.3 Definition of two electron signal region (SR2e) . . . . . . . . . . . . . . . . . . . . . .
5.4 Definition of two muon signal region (SR2mu) . . . . . . . . . . . . . . . . . . . . . .
5.5 Binning in signal regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48
48
50
51
51
60

6 Background estimation
6.1 Background estimation method for SR1e . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Validation of ,+jets estimation with extra VRs . . . . . . . . . . . . . . . . . .
6.1.2 Validation of QCD multi-jet estimation with extra VRs . . . . . . . . . . . . . .
6.1.3 Validation of W+jets estimation with extra VRs . . . . . . . . . . . . . . . . . .
6.1.3.1 Data to MC agreement in high-,R mass . . . . . . . . . . . . . . . .
6.1.3.2 Photon to electron fake factor . . . . . . . . . . . . . . . . . . . . . .
6.2 Background estimation method for SR2e . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Background estimation method for SR2mu . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Summary of background estimation method . . . . . . . . . . . . . . . . . . . . . . . .

62
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66
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66
68
69
69

7 Statistical analysis
7.1 Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Hypothesis test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 Experimental uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Theoretical uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.3 Ad-hoc uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.4 Summary of systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . .

73
73
75
76
76
77
78
79

8 Extra VRs fit result
8.1 ,+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80
80

5

8.2
8.3

QCD multi-jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
W+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 Data to MC agreement in high-,R mass . . . . . . . . . . . . . . . . . . . . . .
8.3.2 Photon to electron fake factor . . . . . . . . . . . . . . . . . . . . . . . . . . .
/+jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 <(,R ) modeling of / (! 44) sample . . . . . . . . . . . . . . . . . . . . . . .
8.4.2 <(,R ) mass modeling of / (! ``) sample . . . . . . . . . . . . . . . . . . . .

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9 Results
9.1 Search for the signal with background only fits . . . . . . . . . . . . . . . . . . . . . . .
9.1.1 Electron final states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1.2 Muon final states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Upper limits on BSM events with model independent fits . . . . . . . . . . . . . . . . .
9.3 Exclusion limits on signal events with model dependent fits . . . . . . . . . . . . . . . .
9.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.1 Comparison to the other LHC results . . . . . . . . . . . . . . . . . . . . . . .
9.4.2 Comparison to the non-LHC experiments . . . . . . . . . . . . . . . . . . . . .
9.4.3 Cross section and coupling constant upper limits . . . . . . . . . . . . . . . . .

90
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94
96
96
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97
98
98

10 Conclusion

103

8.4

6

1 Introduction
The Standard Model (SM) consists of 12 fermions and four gauge bosons which mediate interactions
between elementary particles, as well as a Higgs boson which generates the Higgs field and gives someparticles mass via the Higgs mechanism. Figure 1.1 shows all elementary particles in the SM [1]. The SMis the most successful theory to describe many experimental results. However, it can not explain someobservations and appropriate modifications are required. In this section, first two major problems will be
discussed: tiny masses of left-handed neutrinos and baryon asymmetry. Then, right-handed , bosons andright-handed neutrinos as a solution of these problems are introduced.
1st

standard matter

1

1.777 GeV1

1/2

` neutrino

80.4 GeVag

1/2

photon

1/2< 18.2 MeV

a`

a4

tau

g neutrino

12 fermions(+12 anti-fermions)increasing mass !

±1

,±
1/2

1

W

g
1/2

< 190 keV

< 2 eV6gluon

1

91.2 GeV/
10

weak nuclear force (weak isospin)

1/2

Higgs

electromagnetic force (charge)

bottomstrong nuclear force (color)

muon

1

1/2

r

1/2

spin

1/3

lo

6 leptons(+6 anti-leptons)

`

4

1/2

4.7 GeV

125.1 GeV

co105.7 MeVC

topchargecolors
mass

/B

1

2/3

R/G

511 keV/B

B
strangeforce carriers

/B

1/3

R/G

95 MeV173.2 GeV

Goldstonebosonsgeneration

R/G

/B

1/3

1/2

4 neutrino

R/G

1/2

down

electron

2/3

charm

/B

3

1.28 GeV

1/2

R/G

4.8 MeV

3rd

unstable matter

2/B

6 quarks(+6 anti-quarks)

D

up

2/3

R/G

2.3 MeV

2nd

1

5 bosons(+1 opposite charge ,)Figure 1.1: Elementary particles in the standard model [2]. The quarks (D, 3, 2, B, C and 1) and leptons(4 , a4 , ` , a ` , g and a g ) constitute substance and have spin 1/2. There are antiparticles of each particle with an
opposite charge. The gauge bosons (6, W, /, , ± ) are spin 1 particles and mediate interactions between fermions.
The Higgs boson ( ) is a spin-less particle and generates masses of elementary particles.

1.1 Standard model
SM is a gauge theory that has symmetry with respect to the group (* (3) 2 ⇥ (* (2) ! ⇥ * (1). . One of
the simplest example of a gauge theory is the countless combinations of electromagnetic potential A andelectrostatic potential q that achieve an electric field and a magnetic field satisfying Maxwell’s equations
with respect to ⇤ can be prepared as follows:
A ! A0 = A + r · ⇤,7

q ! q0 = q

m⇤
.
mC

A gauge symmetry in the SM is a symmetry not changing the Lagrangian when the fields representing theparticles are modified by certain rules like an unitary transformation.

1.1.1 U(1) gauge transformation
Considering a local gauge transformation for a fermion field k(G):k(G) ! k(G) 0 = exp( 8@U(G))k(G),(1.1)

where U(G) is a function of time and space and can take on different values at different points in space-time.
This is a phase transformation x and classified as a one dimensional unitary transformation, U(1). For thetransformation of equation 1.1, the derivative is also replaced to satisfy the Dirac equation as follows:m` ! ⇡ ` = m` + 8@
where

` (G)

(1.2)

` (G) is a gauge field which interacts with the fermion field k(G) as follows:⇥

8W ` m` + 8@

` (G)

⇤
< k(G) = 0.

For the transformation of the fermion field shown in the equation 1.1, the gauge fieldtransformed to restore the Dirac equation as follows:` (G) !

0
` (G) =

` needs to be` (G) + m` U(G).

One significant feature of the gauge field ` introduced when assuming U(1) symmetry is that the kinetic
term of ` is gauge invariant, but the mass term of ` is not the case. This predicts that the mass of theparticle mediating the interactions related to the U(1) symmetry is exactly zero.

1.1.2 SU(2) gauge transformation
The U(1) gauge transformation is a phase transformation of a field indicating the particle without any
change in its flavor. In the weak interaction, two types of fermions are always involved, e.g. the lepton
number in beta decay is conserved by a neutrino turning into an electron. The SU(2) transformation isused to describe the reaction of such paired particles. The SU(2) transformation is expressed using threeparameters " and a set of Pauli matrices 2 as follows:
✓
◆
✓
◆
✓
◆
0 1
0
8
1 0
+ U2
+ U3
.
" · 2 = U1
1 0
8 0
0
1
If this matrix is applied to the electron and electron neutrino doublet, this causes mixing:
✓
◆ ✓
◆
k a4
(U1 8U2 )k4 + U3 k a4
"·2
=
.
k4
(U1 + 8U2 )k a4 + U3 k4Then, the gauge transformation in SU(2) is defined as follows:
✓
◆
✓ 0 ◆
✓
◆✓
◆
8
k a4
k a4
k a4
!
= exp
"(G) · 2
,
k4
k40
k4
2
8

(1.3)

where "(x) is a function of time and space x and can take on different values at different points inspace-time. Assuming that U(G) is small, equation 1.3 is expanded to the first order of U, and the gaugetransformation can be written as follows:✓◆✓ 0 ◆ ✓
◆✓
◆
8
k a4
k a4
k a4
!
= 1
"(G) · 2
.
k4
k40
k4
2
The Dirac equation without interaction is not invariant under this gauge transformation, and it is necessary
to introduce a covariant derivation ⇡ ` as equation 1.2.
m` ! ⇡ ` = m` +86
] ` (G) · 2
2

where 6 is a coupling constant and W ` = (,1 , ,2 , ,3 ) is a set of the gauge field. The gauge transformationof W ` is defined as follows:1, `8 (G) ! , `80 = , `8 + m` U8 (G)
6

’
9:

9

n8 9 : , ` (G)U : (G),

where n 8 9 : is the structure constants of SU(2). The interaction of the fermion doublet with the gauge field, ` is invariant. Like the U(1) gauge field, the SU(2) gauge field also requires that the masses of W ` isexactly zero to keep Lagrangian invariant in any SU(2) transformation.

1.1.3 Inconsistency between weak interactions and the SU(2) gauge transformation
The interaction between fermion doubles and gauge fields can be described through the SU(2) gaugetransformation. However, the following conditions required by a SU(2) gauge transformation clearly differ
from the experimental facts in some aspects.
• Since the SU(2) gauge transformation for the fermion doublet can mix different particles, paired
fermions need to have same features, like their masses, to maintain the gauge invariance. This isclearly different from the experimental facts.
• SU(2) gauge invariance requires massless gauge bosons. This means that the interactions can bepropagated to infinity distance, but the reach of the weak interaction is short and the masses of themediating particles need to be heavy.
• The interactions described by the SU(2) with fermion doublets are vector type and conserve parity.
However, the weak interaction in reality is a V-A type and the parity is non-conservative.

1.1.4 Glashow-Weinberg-Salam theory
The Glashow-Weinberg-Salam theory [3–5] was proposed as a theory that considers electromagnetic andweak interactions as one gauge theory and is consistent with most of experimental results. This theory isbased on a gauge transformation of the direct product of SU(2) and U(1).

91.1.4.1 SU(2) ⇥ U(1) gauge transformation
In the SM scope, weak interaction couples to only left-handed doublets and right-handed neutrinos do notexist. Therefore, different gauge transformations are adapted for the left- and right-handed particles. In thefollowing a doublet of the left-handed electron and the electron neutrino and a singlet of the right-handed
electron are considered:✓ ◆ ✓1
◆
✓
◆
✓
◆
8
8
a!
(1 W5 )k a4
0
2
!=
= 1
! ! = exp
V(G). exp"(G) · 2 !,4!
2
2
2 (1 W5 )k 4
✓
◆
8
8
' 1
V(G).
"(G) · 2 !
2
2
✓
◆
1
8
4 ' = (1 + W5 )k4 ! 4 0' = exp
V(G). 4 '
2
2
✓
◆
8
' 1
V(G). 4 ' ,2where . is called the weak hypercharge and is a generator of U(1) group and 2 is a set of generator of SU(2)group. The weak hypercharge has the following relationship with charge & and weak isospin ) 3 ⌘ 12 f 3 :.
,2
The weak hypercharge of ! and 4 ' can be obtained by operating on the charge operator & and weak isospin) 3 as follows:
✓ ◆ ✓
◆
a
0
& ! =
4!
4!
✓ ◆
✓
◆✓ ◆
✓
◆
1 1 0 a!
1 a!
3 a!
)
=
=
4!
1 4!
2 0
2 4!
& = )3 +Therefore, the weak hypercharge of the left-handed doublet ! can be obtained as follows:
✓ ◆
✓
◆ ✓
◆
✓ ◆
a!
0
a!
a!
=2
=
.
4!
4!
4!
4!

The left-handed doublet is an eigenstate of . with an eigenvalue of 1. On the other hand, for theright-handed singlet, the eigenvalue of . is 2 as follows:&4 ' = 4 ' ,) 3 4 ' = 0,2(&) 3 )4 ' = 24 ' .

The gauge fields ⌫ ` and W ` corresponding to the U(1) and SU(2) transformations are introduced. The
covariant derivatives are as follows:86 086! : m` ! ⇡ ` = m` +⌫ `. + W ` · 2,
22
86 0
4 ' : m` ! ⇡ ` = m` +⌫ `. ,
2
where 6 and 6 0 are coupling constants for U(1) and SU(2), respectively. The gauge fields are accordingly
transformed as follows:1⌫ ` ! ⌫ 0` = ⌫ ` + 0 m` V,
6
1
W ` ! W0` = W ` + m` " W ` ⇥ U.
6

10

The SU(2)⇥U(1) gauge transformation can be performed without changing the following Lagrangian.
✓
◆
86 0
86
`
L = 8!W m` +⌫ `. + W ` · 2 !
2
2
✓
◆
0
86
1
1
+84 ' W ` m` +⌫ `. 4 '⌫ `a ⌫ `a
W `a · W `a
(1.4)
2
4
4
⌫ `a = m` ⌫ a ma ⌫ `
’
9
8
, `a
= m` ,a8 ma , `8n 8 9 : , ` ,a:9:

1.1.4.2 Spontaneous symmetry breaking
The gauge invariances corresponding to the electromagnetic and weak interactions require that the mass ofthe particles representing the gauge fields (gauge particles) are exactly zero. To make the theory more
realistic, “Spontaneous symmetry breaking” is introduced. This concept is based on the idea that theLagrangian, which represents the physical system, is gauge invariant, but the vacuum is not gauge invariant
and has a finite expectation value. The Higgs field embodies this idea, and the equations of motion for thegauge particles are modified by the interaction of the vacuum with the Higgs field, as if the gauge particles
had finite masses. In the following, the mechanism that gives masses to the gauge particles through the
Higgs mechanism is explained.
In the Glashow-Weinberg-Salam theory, a doublet of complex scalar fields q with q+ and q0 are introduced.
The Lagrangian density becomes as follows:✓ +◆q
q= 0 ,q1
1⌫ `a ⌫ `a
W `a W `a + (⇡ ` q) † (⇡ ` q) + (q).
(1.5)
4
4
The third term is the kinetic energy term of the complex scalar field and the fourth term is the potential
term. The mass dimension of a scalar field is 1, and in terms of building a renormalizable theory, + (q) is
generally expressed as follows:+ (q) = `2 q† q + _(q† q) 2 .
L=

The complex scalar field is decomposed into scalar fields as follows:✓ +◆✓◆1 q+' + 8q+
q
q= 0 = p00 .
q
2 q ' + 8q

Three of the four scalar fields are used to give finite masses to the three gauge particles mediating the weakinteraction, and the remaining one constitutes the Higgs field with finite vacuum expectation value. Thus,
this complex scalar field doublet is the minimum requirement to give masses to the gauge particles.
The potential + (q) can be expanded using the four scalar fields as follows:+ (q) =

1 2
`
2



q+'

2

+ q+

2


⇣ ⌘2 ⇣ ⌘2⇣ ⌘2 ⇣ ⌘2 2
1
2
2
+ q0' + q0
+ _ q+' + q+ + q0' + q0.
4

11

The second term is always positive since every scalar field is real. So the _ > 0 is required to have aminimum value. When `2 0, this is the case when all four scalar fields have a vacuum expectation valueof 0, and the gauge particles can not be given masses. On the other hand, when `2 < 0, the potential
minima are the case shown below:
q+'

2

+ q+

2

⇣ ⌘2 ⇣ ⌘2+ q0' + q0 =`2.
_

At this stage, the four scalar fields are equivalent and there is a degree of freedom for scalar fieldtransformation. However,p if the vacuum state is the gauge transformed so that one scalar field has a vacuum
expectation value E =`2 /_, the symmetry that existed between scalar fields is broken. This is called
spontaneous symmetry breaking.
1.1.4.3 Higgs mechanism
Gauge particles gain masses by interacting with the Higgs field, so mass terms appear in the kinetic energy
term in equation 1.5:
✓ 0
◆✓ ◆
1
6
6
0
` †
(⇡ q) (⇡ ` q) =(0, a)⌫ ` + W` · 2
a
2
2
2
⇣
⌘
⇣
⌘ a2 ⇣
⌘⇣
⌘
2
2
6 a
=
, 1` 8, 2` , `1 + 8, `2 +6, 3` 6 0 ⌫ ` 6, `3 6 0 ⌫ `
8
8
⇣
⌘ 1
1
+`
` +
2 `
=
", 2 , , ` + , , ` + "/ / / ` .
2
2

The quantities corresponding to the gauge fields , `± , / ` and a mass-less gauge field for a photon ` which
is defined as the orthogonality field with respect to / ` and masses ", , "/ are defined as follows:⌘
1 ⇣, `± = p , `1 ⌥ 8, `2 ,2

6, `3 6 0 ⌫ `6 0, `3 + 6⌫ `/` = p,=,p`
6 2 + 6 02
6 2 + 6 02p
6 2 + 6 02 a
6a", =, "/ =.
2
2
The gauge invariance requires that the mass of the gauge particles should be zero. The gauge particles arevector bosons with spin 1 and have two degree of freedom. However, in the interaction with the Higgs field,
having masses restores one degree of freedom. This can be interpreted as the absorption of three of four
degrees of freedom possessed by the complex scalar field. The other one degree makes non-zero vacuum
expectation value. Such a mechanism is called Higgs mechanism.
1.1.4.4 Interactions with leptons
The interactions between leptons and gauge fields can be found in equation 1.4. Rewriting ⌫ ` and , `3 interms of the ` which is formed by a photon and / ` which is formed by a neutral weak gauge particle, the12result is as follows:

◆
86 0
86
86 0
⌫ `. + ] ` · 2 ! + 8 4̄ ' W ` ⌫ `. 4 '
2
2
2
!
0
1
6 02. 6 2
` 66 (. + 1)=
ā ! W/ ` a!
pp`
2
6 2 + 6 02
6 2 + 6 02!
01
1)
6 02. + 6 2` 66 (.
4̄ ! W
/` 4!
p
p
`
2
6 2 + 6 02
6 2 + 6 02
!
1
66 0.
6 02.
`
4̄ ' W p
/` 4'
p
`
2
6 2 + 6 02
6 2 + 6 02
⌘
6 ⇣
` +
`
ā
W
,
4
+
4̄
W
,
a
(1.6)
p
!
!
` !
` ! .
2
Substituting the value of the weak hypercharge and defining the coupling constant between an electron anda photon as 4, the relation between 4 and 6, 6 0 is as follows:¯ `L = 8 !W

✓

4=p

66 0
6 2 + 6 02

= 6 sin \ , ,where \ , is known as the Weinberg angle and represents the mixing of the U(1) and SU(2) gaugetransformations. The Lagrangian density of equation 1.6 is summarized for each gauge field as follows:
L =[ 4 ( 4̄W ` 4)] `✓
6` 1 W5`āW
a + 4̄W 2 sin2 \ ,2 cos \ ,
2
✓
◆
6
1 W5
1 W5
4, `+ + 4̄W `a, ` .
p āW `
2
2
2

1
2

W5

◆

4 /`

The first term represents the interaction between the electron current and photon ` (electromagnetic
interaction). Photons couple with the same strength regardless of whether they are left-handed or righthanded. Neutrinos have no charge and do not couple to photons. The second term is the coupling between
leptons and the neutral weak boson /. It represents the weak interaction involving the current, which
does not change its charge. The third term represents a weak interaction that changes charge and couples
to the charged weak boson , ± . It can be seen that the charged weak interaction is not present only inthe left-handed component, whereas the neutral weak interaction also contributes to the right-handed
component.
Similar to gauge particles, fermion masses can be produced by interactions with the Higgs field. The
following Lagrangian density is assumed for the interaction of electrons with the Higgs field [5]:⇣⌘L = 64 !q4 ' + 4q† ! ,(1.7)

where 64 indicates the coupling constant between an electron and the Higgs field, which is called the
Yukawa coupling. Using the vacuum expectation value of the complex scalar field that constitutes theSU(2) doublet, equation 1.7 is expanded as follows:

✓ ◆
✓ ◆
64
0
a
L =
4 ' + 4 ' (0, a) !
p (a ! , 4 ! )
a
4
!
2
64 a
64 a
=
p (4 ! 4 ' + 4 ' 4 ! ) = p 44.
2
2

13

The parameter 64 is related to the electron mass < 4 by the following equation:
64 a<4 = p .
2(1.8)

From equation 1.8, the coupling constant between fermions and the Higgs field has a liner relation with
their masses.

1.1.5 SU(3) gauge transformation
The SU(2) gauge transformation is that of a field describing the particles mediating the weak interactions.
In the strong interaction, three states of a certain fermion are involved. The SU(3) transformation is used todescribe the reaction among such states. The SU(3) transformation is expressed using eight parameters "and a set of Gell-Mann matrices , as follows:1"· , =
2
+

0
U1 ©
≠1
2
´0
0
U5 ©
≠0
2
´8

1 0
0
8
™ U2 ©
0 0Æ̈ +
≠8 0
2
0 0
´0 0
0
8
0 0
™ U6 ©
0 0 Æ̈ +
≠0 0
2
0 0
´0 1

0
1
™ U3 ©
0Æ̈ +
≠0
2
0
´0

0 0
0 0 1
™ U4 ©
™
1 0Æ̈ +
≠0 0 0Æ̈2
0 0´1 0 0
0
0 0 0
1 0 0
™ U7 ©
™ U8 ©
™
1Æ̈ +8 Æ̈ + p ≠0 1 0 Æ̈ .
≠0 0
2
2 3 0 002
´0 8 0´

The gauge transformation in SU(3) is defined as follows:

✓
◆ k
k'
k0
8
1 © '™
© ™
© 0' ™
"(G) · , ≠k⌧ Æ̈≠k⌧ Æ̈ ! ≠k⌧ Æ̈ = exp
2
2
0
k
k
⌫
´
´ ⌫
´k ⌫

(1.9)

where " is a function of time and space x and can take on different values at different points in space-timeand ', ⌧, ⌫ are a quantity exchanged by the strong interaction and are called color charge. Assuming that
U(G) is small, equation 1.9 is expanded to the first order of U, and the gauge transformation can be written
as follows:
✓
◆ k
k'
k0
8
1 © '™
© ™
© 0' ™
"(G) · , ≠k⌧ Æ̈ .
≠k⌧ Æ̈ ! ≠k⌧ Æ̈ = 1
2
2
0
k
k
´ ⌫
´ ⌫
´k ⌫
It is necessary to introduce a following covariant derivative to restore the Dirac equation:m` ! ⇡ ` = m`

86 0
G (G) · , 0 ,2 `where 6 is a strong coupling constant and G ` = (⌧ 1 , ⌧ 2 , ⌧ 3 , ⌧ 4 , ⌧ 5 , ⌧ 6 , ⌧ 7 , ⌧ 8 ) is a set of the gauge
field. They are called gluons. The gauge transformation of M - is defined as follows:188⌧ 8` (G) ! ⌧ 80
` (G) = ⌧ ` (G) + m` n
6

’
9:

9

58 9 : ⌧ ` (G)n : (G),

where 58 9 : is the structure constants of SU(3). The interaction of the fermion triplet with the gauge field M is invariant. The masses of M - is exactly zero to keep Lagrangian invariant in any SU(3) transformation.

14

1.2 Remaining problems
1.2.1 Finite masses of the left-handed neutrinos
One of the most important properties of neutrinos is neutrino oscillation to change the neutrino flavors
associated with the passage of time. Neutrinos were thought to be mass-less particles in the SM. However,observation of neutrino oscillations unveiled their finite masses [6, 7]. In the following, the necessity ofneutrino masses is discussed with the Schr•odinger picture if the neutrino oscillation exist.
The flavor eigenstates of neutrinos |a U i (U = 4, `, g) can be expressed as linear functions of mass eigenstates|a8 i (8 = 1, 2, 3) with a 3 ⇥ 3 unitary matrix * which is called Pontecorvo-Maki-Nakagawa-Sakata (PMNSor simply MNS) matrix [8, 9] as follows:|a U i =3’8=1(1.10)* U8 |a8 i.

Since the PMNS matrix is unitary, there are nine independent parameters in total. Three of them arerotation angle parameters (\ 12 , \ 13 , \ 23 ). Others are phase parameters, but if neutrinos are Dirac particles,
five out of six parameters can be absorbed by the phase of left-handed leptons because they do not havemass terms in the Lagrangian. The remaining phase parameter X is known as the Dirac CP phase. Whereas,in the case of Majorana neutrinos, due to the loss of a degree of freedom for left-handed neutrinos, two
additional phase parameters, _ 1 and _2 which are known as Majorana CP phases, remain. With theseparameters, the PMNS matrix can be written as follow.
2 13 B12
4 8 X B13 4 8_1™©
8X
2 12 2 23 4 B12 B13 B23
2 12 B23 Æ̈ ≠ 0
4 8 X 2 23 B12 B13 2 12 B23 2 13 2 23 ´ 0

2 12 2 13©
[ = ≠ 2 23 B12 4 8 X 2 12 B13 B23
8X´ B12 B23 4 2 12 2 23 B13

where 2 8 9 = cos \ 8 9 and B8 9 = sin \ 8 9 .

0
4 8_2
0

0
™
0Æ̈ ,
1

The time evolution of a mass eigenstate can be written as:83|a8 (C)i = H |a8 (C)i = ⇢ 8 |a8 (C)i3C
|a8 (C)i = 4G ?( 8⇢ 8 C)|a8 (0)i,where H and ⇢ 8 are the Hamiltonian and expected energy of mass eigenstate |a8 i. Hence, from equation 1.10,
the flavor eigenstate |a U i at a time C can be written as:’|a U (C)i =* U8 exp( 8⇢ 8 C)|a8 (0)i
(1.11)
8

In the case of the ultra-relativistic limit, ⇢ 8 can be expressed as:⇢8 =hence, equation 1.11 becomes as follows:|a U (C)i =’q? 28 + < 82 ⇠ ? 8 +* U8 exp( 8 ? 8 C) exp

8

15

< 82
,
2⇢ 8
!
8< 82 C|a8 (0)i.
2⇢ 8

As the same analogy, the flavor eigenstate ha V (C 0)| at a time C 0 becomes as follows:!
’8< 29 C 0†00ha V (C )| =*V 9 exp(8 ? 9 C ) exp
ha 9 (0)|2⇢ 9
9The transition amplitude ha V (C 0)|a U (C)i can be decomposed to be:
ha V (C 0)|a U (C)i =’8†* U8 *V8
exp [ 8 ? 8 (CC 0)] exp"

8< 82 (C C 0)2⇢ 8#

The a U (0) ! a V (C) transition probability %(a U (0) ! a V (C)) is calculated below:%(a U (0) ! a V (C)) = |ha V (C)|a U (0)i| 2=’†* U8 *V8
exp(8 ? 8 C) exp

8

=

’’
8

=

8

†
* U8 *V8* †U 9 *V 9 exp[8( ? 89’’8< 82 C2⇢ 8†
* U8 *V8* †U 9 *V 9 exp

9

✓

!2

"

< 82
? 9 )C] exp 82⇢ 8◆
8 8 9C
,
2⇢

< 29
2⇢ 9

! #
C

where 8 9 ⌘ < 82 < 29 is a mass squared difference. In the above calculation, it is assumed that the
momentum and energy of all mass eigenstates are the same. According to this equation, neutrino oscillation
can occur only when there is a non-zero mixing angle (\ 8 9 < 0) and at least two neutrino masses are notdegenerated (< 8 < < 9 ).
Since there are no right-handed neutrinos in the SM, the Dirac mass term can not be formed. If the neutrino
masses are derived from unknown physics at the Planck scale, it is too small compared to the observationsof neutrino oscillations. Physics at a scale smaller than the Planck scale is needed. In section 1.3, heavy
right-handed neutrinos are introduced at a moderate energy scale and they leads to the derivation of massesof the left-handed neutrinos.

1.2.2 Baryon asymmetry
The constituents of the current universe are made up of matter with little anti-matter and observations ofcosmic background radiations have led to a detailed investigation of the baryon dominance in the university.
As conditions for generating non-zero baryon numbers, the following three conditions, known as the
Sakharov conditions [10], are required to produce the matter and anti-matter imbalance.
1. Baryon number violation
The initial condition of the baryon number is 0. The baryon number violation is needed to produce
the baryon asymmetry.
2. C-symmetry and CP-symmetry violation
If the C- or CP-symmetry is preserved, the amount of a certain matter is the same as one of its
anti-matter.

16

3. Interactions out of thermal equilibrium
Under conditions of a perfect thermal equilibrium, since the particles and anti-particles have thesame mass due to CPT-invariance, the counter-reaction of the condition 1 above also occurs in thesame amount, so the matter and anti-matter are present in the same amount and can not make thebaryon asymmetry.
A model called an electroweak baryogenesis [11, 12] is an attempt to explain the baryon number dominancewithin the framework of the SM. The baryon number is broken by the effect of quantum anomalies, and theC- and CP-symmetry are broken by the weak interactions. However, the third condition of interactions outof thermal equilibrium, can not be explained. The CP violation is also too small to explain the productionof sufficient baryon number. Therefore, a theory beyond the SM must be required to enhance CP violationand explain the deviation from thermal equilibrium.
In the following, the relation between the baryon number and the lepton number and the lepton number
violation which indirectly induces the baryon number violation are explained. Furthermore, the necessity
for left-handed and right-handed particles to interact with different fields is also explained.
Baryon and lepton currents are defined as follows:

`

9!

1’
` *
⇡ ` ⇡
(& ! W ` & ! + @*' W @' + @' W @' )
3 8=1
3

`

9⌫ =
=

3
’
8=1

(! ! W ` ! ! + ; ' W ` ; ' )⇡where & ! and ! ! is a quark and lepton doublet, respectively. @*' , @ ' and ; ' is a singlet of a quark andlepton as follows:
✓ ◆
✓ ◆
D!
4
*
⇡
&! =
, @' = D', @' = 3', ! ! = ! , ;' = 4' .
3!
a4!

By using the Dirac and adjoint Dirac equations, the preservation of a current of a spinor k can be proven:m` (kW ` k) = (m` k)W ` k + km` W ` k= k m/ k + k m/k= 8<kk8<kk = 0.

Hence, the baryon and lepton currents are also preserved and the baryon number ⌫ and lepton numbers !
given by equation 1.12 are also preserved in classical fields,
π
π
3 0
⌫⌘
3 G 9⌫ , ! ⌘3 3 G 9 !0 .
(1.12)

However, due to a quantum anomaly [13], such a conservation law is broken and the baryon and lepton
currents are not preserved in quantized fields as follows:``m` 9 ⌫ = m` 9 ! =

#6 2
6
32c 2

`a (!) ˜`a(!)`a (') ˜

`a

(') ,

where #6 is three which corresponds to the number of fermion families, 6 indicates a coupling constantwhich is assumed to be common for both left- and right-handed interactions and `a (!) and `a (') are17the field strength coupling to left-handed and right-handed particles, respectively. From the above equation,
it is clear that ⌫ ! is preserved. In case both left and right-handed particles are connected to the samegauge field, like QED and QCD, this quantum anomaly vanished. Therefore, the minimum extension toachieve baryon and lepton number violation to the SM is to introduce the weak interaction to right-handed
particles and couple them with different fields from the left-handed one.
Above a phase transition temperature where the separation of the electromagnetic and weak interactions
occurs, the cross-section of the process that exchanges lepton and baryon numbers, known as the sphaleronprocess [14], increases rapidly. Therefore, the baryon-dominated universe is also explained by creating
lepton numbers and converting them to baryon numbers.

1.3 Right-handed neutrinos
While preserving the gauge symmetry of the SM, right handed neutrinos a ' are introduced as follows:
L = LSM + L a' ,kinematics + L a' ,mass
L a,kinematics = a ' 8 m/a '"' 2
L a,mass =H U ! ! U a' U
a a ' + ⌘.2.
2 'The first term of L a,mass is the Dirac mass term coming from the vacuum expectation value (VEV) of the
Higgs field . The second term is the Majorana mass term and "' is a mass scale independent of the
VEV. The Majorana mass term is not necessarily required to explain neutrino masses but is essential toexplain the baryon-dominated universe from the lepton number breaking.
The Seesaw mechanism [15–17] naturally accounts for tiny masses of left-handed neutrinos. Here, let us
assume the case of a single neutrino generation. The neutrino mass term can be written as follows:✓◆✓ ◆1
0 < ! a 2!
2
a! a'L a,mass =+ ⌘.2.
< ! "' a '2
Eigenvalues of the above mass matrix are:

✓
q
1
_=
"' ± "'2
2

4< 2!

◆

.

(1.13)

Assuming that "' has a very high energy scale compared to < ! , equation 1.13 becomes as follows:< 2!
(1 + O (\ 2 ))"'= "' (1 + O (\ 2 ))

<a =
"#

where \ is < ! /"' . The < a and " # correspond to the mass of a left-handed and a right-handed neutrino,
respectively. The larger the " # the smaller the < a is, hence this mechanism is called the Seesaw
mechanism. In the above explanation, right-handed neutrinos are assumed to be gauge singlets. This
scenario is called the Type-I seesaw mechanism. However, right-handed neutrinos do not have to begauge singlets. For example, some models introduce SU(2) triplet scalars or fermions, which are called
Type-II [18, 19] and Type-III [20] seesaw mechanisms, respectively.

18

As shown in Section 1.2.2, baryon asymmetry can be explained in terms of the lepton number breaking. In
particular, the lepton number breaking scenario due to the decay of heavy right-handed neutrinos is called
the leptogenesis [21]. Since right-handed neutrinos are Majorana particles and antiparticles of them are
identical to themselves, they can produce lepton numbers. A part of these lepton numbers is converted tobaryon numbers via the sphaleron process.
There is no limit on the number of generations of the right-handed neutrinos, but when considering
theoretical models that follow a larger group than the SM, the number of generations for right-handed
neutrinos is probable to be also three, as for left-handed neutrinos.

1.4 Target TR and ]R particles
The Left-Right Symmetric Model [15, 17, 22–28] (LRSM) is based on the following gauge group:⌧ LRSM = (* (2) ! ⇥ (* (2) ' ⇥ * (1).̃ ,(1.14)

plus a symmetry between the left and right sectors. Quarks and leptons are completely left-rightsymmetric
✓ ◆
✓ ◆
D
a
& !,' =
, ! !,' =
,
3 !,'
4 !,'

where a ' represents a right-handed neutrino. The U(1) gauge group has a charge .̃ different to the standard
model hypercharge. Relation between the charge and the weak hypercharge expressed in equation 1.1.4.1
in SM is modified by adding (* (2) ' group as follows:& = )!3 + )'3 +.̃,2where )!3 and )'3 is the third generator of (* (2) ! and (* (2) ' , respectively. Similar to the equation 1.1.4.1,
the weak hypercharge .̃ is obtained for ! ! and & ! as follows:
✓ ◆
✓
◆ ✓
◆
✓ ◆
a!
0
a!
a!
.̃ ! ! = .̃
=2
=
,
4!
4!
4!
4!
✓ ◆
✓ 2
◆ ✓
◆ ✓ ◆
✓ ◆
1 D!
D!
D!
D!
0
3
=
.
.̃& ! = .̃
=2 1
3!
3!
0
3 3!
3 3!
These equations imply that .̃ = ⌫! and LRSM adapts it as the charge of * (1) group.

The SM introduces a symmetric complex scalar field doublet which is spontaneously broken and gives a
non-zero vacuum expectation value. Consequently weak bosons get finite masses. The LRSM, on the other
hand, introduces two complex fields scalar triplets ! 2 (1 ! , 3' , 2), ' 2 (1 ! , 3' , 2) and a bi-doublet
2 (2 ! , 2' , 0) [29], according to the gauge group of equation 1.14:
 0
 + p
++
q1 q+2
/ 2
p
=
,
,
!,' =
0
0
+
q1 q2
/ 2 !,'
One of the complex triplets gives masses to the right-handed weak bosons and the other one for left-handed
weak bosons. The vacuum expectation value of the right-handed triplet is large than the left-handed one,
resulting right-handed weak bosons having much larger masses than the SM weak bosons.

19The spontaneously symmetry breaking in LRSM is done with two steps. At the first stage of the breaking,according to [29], the ⌧ LRSM downs to the (* (2) ! ⇥ * (1) group:0 0
h ! i = 0, h ' i =.
a' 0
At the next stage, the neutral components
down to * (1)EM group:develop a vacuum expectation value and break the (* (2) ! ⇥* (1)
h i=



a1 0
,
0 a2

2 = 6 2 a 2 ⌘ 6 2 (a 2 + a 2 ) and 6 ⌘ 6 = 6 denotes the SU(2) gauge
where a1,2 are real and positive, ",!
'12coupling constants. In turn, ! develops a tiny vacuum expectation value h ! i / a 2 /a ' .

The right-handed gauge boson masses are expressed as follows [30]:
2
",
R

"/2 '

' 6 2 a 2' ,2
' 2(6 2 + 6 2⌫ ! )a 2' ' 3",.
R(1.15)As shown in equation 1.15, the mass of the right-handed / boson is heavier than the right-handed , boson("/' ' 1.7",R ), and the ,R mass limit is more important for LRSM. In the above, the mixing of the leftand right-handed gauge bosons, which is expressed as a product of vacuum expectation values of a1 and a2 ,is not taken into account.
The target of this thesis searches for the production of the heavy right-handed bosons with the subsequent
decay to the final state containing two charged SM leptons and two quarks: ,R ! #R ✓ ! ,R⇤ ✓✓ ! ✓✓ 9 9(i.e. Keung-Senjanovi∆ process [31] in Figure 1.2). The left-right mixing is not considered and #R isproduced as an intermediate state in the decay of ,R . When <(,R ) > <(#R ), the on-shell ,R masscan be reconstructed from the invariant mass of the ✓✓ 9 9 system. Alternatively, when <(,R ) < <(#R ),the second ,R in the decay chain is on-shell and can be reconstructed from the invariant mass of the 9 9system.
If the #R are Majorana particles, #R can account for the masses of the known neutrinos via the Type-I
Seesaw mechanism. In the Type-I Seesaw mechanism within LRSM, masses of the #R are coupled to thea ! masses through a mixing matrix. In minimum Seesaw mechanisms, the right-handed bosons typicallyhave a mass around the Grand Unification Scale, but particular parameter values can be found where #R
and ,R can have masses in the GeV-TeV range, i.e. within the energy reach of the LHC. The Type-I
Seesaw mechanism requires both the known a ! and hypothetical #R to be Majorana particles, allowing
lepton number violating processes.
The decay chain considered in this analysis is below:? ? ! ,R ! ✓#R ! ✓✓@@ 0 .
In the following, a lepton produced from ,R decay is named leading lepton and one produced from #R
decay is named sub-leading lepton. In this analysis, the case where the ,R has a large mass and a small
momentum is considered, so the leading lepton has a larger momentum. The lepton flavors considered inthis thesis are electron and muon, and no flavor mixing is assumed.
In case the #R is a Majorana particle, 50 % of events have the same-sign lepton pair. On the other hand,assuming a Dirac particle, the opposite-sign lepton pair is ideally expected in all events. The actual

20

@¯

,R⇤

@¯
#R

✓

,R
@

@

✓

Figure 1.2: Feynman diagram for the Keung-Senjanovi∆ process [31], shown for the <(,R ) > <(#R ) case. For the
inverted mass hierarchy, first ,R in the decay chain is off-shell (as shown by a ⇤ in the second ,R above), rather than
the second one.

analysis is performed assuming that the #R is a Majorana particle, and the case of a Dirac particle is alsointerpreted.
The characteristic signature at the detector depends on the balance between the mass of the ,R and #R ;if ,R and #R have similar masses, all final state particles are reconstructed separately, which is called“resolved” analysis. On the other hand, if ,R > #R case, the two quarks from off-shell ,R are recognized
as a single jet by boosting #R , resulting in an event with two leptons and one large-R jet, which is called“boosted” analysis. In the boosted analysis, hadrons from #R decay are reconstructed as a single large-radius(large-') jet. This thesis focuses on boosted analyses.

1.5 Previous and future experimental constrains
1.5.1 Results of the ATLAS and CMS analysis
Searches in the boosted channels have been performed by ATLAS [32–34] and CMS [35–38]. The
latest exclusion limits for electron and muon final states by ATLAS (80 fb 1 ) are shown in Figure 1.3,
and CMS (138 fb 1 ) in Figure 1.4. In both ATLAS and CMS analyses, the sensitivity in the electron
channel was lower than the muon channel in the large " = <(,R ) <(#R ) region for example the masspoint (<(,R ), <(#R )) = (5 TeV, 100 GeV) was not covered in electron channel. This was because thereconstruction efficiency of the electron from the #R decay is dropped in this mass region due to hadron
activities closeby the sub-leading electron.

21

In both the ATLAS and CMS analyses, the number of observed data in the electron channels exceeded thenumber of backgrounds estimated using MC. The global significance for ATLAS and CMS was 2.4f and
2.8f, respectively.

(a) Electron final state(b) Muon final state

Figure 1.3: Observed (black solid line) and expected (red dashed line) at 95 % confidence level in the <(,R ) and<(#R ) 2-D plane by ATLAS in electron (a) and muon (b) final state for boosted topology. The exclusion limits withresolved topology are overlaid by the blue line [34].

(a) Electron final state(b) Muon final state

Figure 1.4: Observed (black solid line) and expected (black dashed line) at 95 % confidence level in the <(,R ) and<(#R ) 2-D plane by CMS in electron (a) and muon (b) final state. Constraints from boosted topology only, resolved
only and combined are shown as solid blue, solid green and dashed black line [38], respectively.

1.5.2 Constraints from the other experiments
Some of the other experiments, for example, neutrino-less double beta decay and lepton-flavor violation
searches, can give constraints on the target signal of this analysis. Each experiment has its own uniquephase space in the two-dimensional planes of <(,R ) and <(#R ) masses. Furthermore, future lepton
collider can be used to search for the model as well.
Meson Mixing22¯ andThe LRSM can enhance the flavor changing neutral current (FCNC) processes, such as⌫ 3,B ⌫¯ 3,B oscillations, by the contribution of the ,R in the box diagram. The lower limit on the massof the ,R from the current results [39] is about 3 TeV, assuming equal mixing matrices for left- andright-handed quarks, as shown by the pale red exclusion line in Figure 1.5. This is a strong motivation to
search for sub-TeV ,R in this analysis.
Neutrinoless Double Beta Decay
The Majorana right-handed neutrino with the electron flavor and ,R boson can contribute to the neutrinolessdouble beta decay (0aVV) diagram. Assuming purely right-handed contribution to the 0aVV decay, thenon-observation of this lepton number violating process can be used to set limits on the masses of the ,R
and #R in the LRSM. The decay amplitude of that process is:4⌧ 2 <,
!

’

2
+48
,
< #'8 < , 4
8 2flavor'

where < ,! , < ,' and < #'8 are masses of ,L , ,R and 8-th #R , and +48 is the mixing of left-handed
electron neutrino and 8-th right-handed neutrino #R [40]. This equation shows that the half-life time of the
40aVV is proportional to the multiplication of < ,and < #'8 . the current limits on the half-life time of'
4 ). The
0aVV corresponds to the small value of the upper boundary on the #R mass (< #'8 < const./< ,'excluded region by the GERDA experiment using 76 Ge target [41] is shown by the violet exclusion line in
Figure 1.5. The region of < ,' > 3 TeV and #R mass around 100 GeV is not covered until the future
ton-scale 0aVV experiments reach 1027 yr sensitivity. This region is one of the the main targets of thisthesis.
Table 1.1: Isotopes of interest and observed limits of half-life time for various neutrinoless double beta decay
experiments.

Collaboration
CUPID [42]CUORE [43]
GERDA [41]KamLAND-Zen [44]EXO-200 [45]Isotope of interest

Limit at 90% C.L. [years]

82 Se

4.6 ⇥ 1024
3.2 ⇥ 1025
1.8 ⇥ 1026
1.07 ⇥ 1026
3.5 ⇥ 1025

130 Te76 Ge

136 Xe136 XeExpected sensitivity of the ILC
Future lepton colliders, e.g. International Linear Collider (ILC), can also search for ,R and #R in the
LRSM. In the large " = <(,R ) <(#R ) region, the dominant right-handed neutrino production process
is the following decay mode:
4 + 4 ! #R #R ! 4 ± 4 ⌥ + 4 9 .

The cross section of the above decay process strongly depends on the initial beam polarization. The
expected sensitivities in two polarization scenarios; one is no polarization (0,0) and the other is (80%,30%) polarization for electron and positron, are shown in Figure 1.5. The ,R masses up to 6.5 TeV withpa 500 fb 1 integrated luminosity at B = 500 GeV can be excluded at the #R mass around 100 GeV [46] asshown the black exclusion line in Figure 1.5. The exclusion reach with the 250 GeV option is expected to
be lower.
This analysis can cover the region which will be covered by future ton-scale 0aVV experiments and ILC, byusing the LHC Run 2 data.

23

ATLAS Resolved 36 fb -1 (95% CL)

900

ATLAS Boosted 80 fb-1 (95% CL)

Rm(N ) [GeV]1000

CMS Combined 138 fb -1 (95% CL)0ν0ν β β (T 1/2 = 1.8 × 10

800

26

years, 90% CL)

FCNC (95% CL)
ILC (Unpolarized, 95% CL)

700

ILC (Polarized, 95% CL)

600
500
400
300
200
100
0

3000

4000

5000

6000

7000
8000
m(W ) [GeV]R

Figure 1.5: Expected and observed 95% CLs in ,R mass and #R massp plane. Black and gray exclusion lines represent
the CL from ILC with and without the initial beam polarization at B = 500 GeV [46], respectively. 90% CLs fromthe neutrino less double beta decay [41] and 95% CLs from the meson mixing [39] are shown as purple and pale red
exclusion lines, respectively. 95% CLs with ATLAS resolved analysis with 36 fb 1 [33], ATLAS boosted analysis
with 80 fb 1 [34] and CMS analysis with 138 fb 1 [38] introduced in Section 1.5.1 are shown as green, blue and dark
yellow exclusion lines, respectively.

1.6 Strategy of LRSM search in boosted topology
In this thesis, different approaches are used to increase sensitivity in the electron and muon final states.
For the electron channel, a new signal region that requires only one electron in an event is introduced
to explore ,R#R phase spaces. This is an orthogonal region with the one that was used in theprevious analysis [34] by the required electrons numbers. The final sensitivities are derived by a statisticallycombination of these two regions. For the muon channel, the sensitivities are improved by re-optimizing
the signal region that requires two muons. Schematic views of above regions are shown in Figure 1.6. In
addition to the above updates, every signal regions are changed to use the reconstructed ,R mass shape
more while taking into account the robustness of the background estimation.
This thesis is organized as follows. Chapter 2 explains an overview of the LHC experiment and ATLAS
detectors. Chapter 3 provides an overview of the dataset and Monte Carlo simulation samples. Chapter 4
describes details of reconstructed objects with the ATLAS detector. Chapter 5 shows details of analysis

24

@¯
,R⇤

@¯
#R
4

(a) Two electron channel

,R⇤

@¯
#R

4

,R
@

@

@¯

4
(b) One electron channel

,R⇤

@¯
#R

4

,R
@

@

@¯

`

,R
@

@

`
(c) Two muon channel

Figure 1.6: Definition of three different channels. Regions are classified by the flavor and the number of leptons
required in an event. The colored particles are the final state particles; red is reconstructed as electrons, blue asmuons, green as jets.

strategies to maximize sensitivity. Chapter 7 describes the background of statistical treatments of thedetector and theoretical effects. Chapter 9 provides the results for searching right-handed particles followedby Chapter 10 discussing interpretations of the results and giving the conclusion of this thesis.

25

2 LHC-ATLAS experiment
2.1 Large Hadron Collider (LHC)The Large Hadron Collider (LHC) [47] shown in Figure 2.1 is the world’s most powerful facility forparticle physics research hosted by the European Organization for Nuclear Research (CERN). It is asuperconducting collider located about 100 m underground in Geneva, Switzerland, that is capable ofpaccelerating proton beams to a center-of-mass energy of B = 13 TeV1 .

The CERN accelerator complex
Complexe des accélérateurs du CERNCMSNorth Area

LHC

GIF++

2008 (27 km)

CENF

ALICE

2015

LHCb

2016

TT20

TT40

TT41

SPS
1976 (7 km)

TI2

TT10

TI8

AWAKE

ATLAS

HiRadMat
2011

2016

TT66

TT2

AD

ELENA

1999 (182 m)

2016 (31 m)

ISOLDEBOOSTER

1992

1972 (157 m)
RIBs
p

p

2001

IRRAD/CHARM

1959 (628 m)

p

CLEAR

LINAC 2e-

LEIR

LINAC 3Ions

ions

East AreaPSnp (protons)

REX/HIE
2001/2015

n-ToF

2017

2005 (78 m)

RIBs (Radioactive Ion Beams)n (neutrons)– (antiprotons)pe- (electrons)

LHC - Large Hadron Collider // SPS - Super Proton Synchrotron // PS - Proton Synchrotron // AD - Antiproton Decelerator // CLEAR - CERN Linear
Electron Accelerator for Research // AWAKE - Advanced WAKefield Experiment // ISOLDE - Isotope Separator OnLine // REX/HIE - Radioactive
EXperiment/High Intensity and Energy ISOLDE // LEIR - Low Energy Ion Ring // LINAC - LINear ACcelerator // n-ToF - Neutrons Time Of Flight //HiRadMat - High-Radiation to Materials // CHARM - Cern High energy AcceleRator Mixed field facility // IRRAD - proton IRRADiation facility //GIF++ - Gamma Irradiation Facility // CENF - CErn Neutrino platForm

Figure 2.1: The schematic view of the CERN accelerator complex [48]. The LHC is the dark blue line in a complex
chain of particle accelerators. The smaller machines are used in a chain to help boost the particles to their final
energies and provide beams to a whole set of smaller experiments.
1 It was designed to achieve to a center-of-mass energy of 14 TeV.

26

Protons are produced by a duoplasmatron source at 100 keV and accelerated by a linear accelerator(LINAC2) to 50 MeV. This is followed by a circular boosted (BOOSTER) where the protons attain energies
of 1.4 GeV. Finally, the Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS) accelerate theprotons to 26 GeV and 450 GeV, respectively. After that protons are injected to the LHC and accelerated byfollowing circular trajectories due to the magnetic fields produced from superconducting dipole magnets.
These magnets are cooled to temperatures below 2 K using superfluid Helium.
ATLAS (A Toroidal LHC Apparatus) [49], CMS (Compact Muon Solenoid) [50], ALICE (A Large Ion
Collider Experiment) [51] and LHCb (Large Hadron Collider beauty) [52] detectors are installed at the
LHC. ATLAS and CMS are used for a comprehensive search for new physics and precise measurements of
the SM processes. ALICE is used for the investigation of the phenomenon known as quark-gluon plasmathat occurs in the early universe. LHCb aims for studies of phenomena relating to bottom quarks like CP
symmetry violation.
The instantaneous luminosity is defined as:!=

5rev =1 # 12,
4cn V G,H

where 5rev is the number of times a proton rotates through the LHC ring per second, =1 is the numberof bunches carrying a proton bundle, # 1 is the number of protons per bundle, n is the initial geometricemittance, [ G,H is the beam size in G-H plane and is the geometric luminosity reduction factor. The
typical values of these parameters for each year are shown in Table 2.1.
p
Table 2.1: Selected LHC parameters of ? ? collisions at B = 13 TeV in 2015-2018 [53]. The values are representativeof the best accelerator performance during normal physics operation. In 2017 run, two different conditions wereapplied. “8b4e“ denotes a pattern of eight bunches separated by 25 ns followed by a four bunch-slot gap.

Parameter

2015

2016

2017

2018

Frequency ( 5rev [Hz])Bunch spacing [ns]Maximum number of colliding bunch pairs (=1 )Typical proton bunch population (# 1 /1011 protons)
Emittance ([ [m])Beam size in G-H plane (V G,H [`m])
Geometric luminosity reduction factor ( )

11253
25
2232
1.1
0.3
0.8
0.94

11253
25
2208
1.1
0.3
0.4
0.94

11253
25/8b4e2544/1909
1.1/1.2
0.3
0.3
0.94

11253
25
2554
1.1
0.3
0.3-0.25
0.94

2.2 ATLAS detector
The ATLAS detector, shown in Figure 2.2, is a 44 m long and 25 m height and 7000 t weight multi purpose
detector. The total number of readout channel from the detector is about 160 million, and the cable lengthis approximately 3000 km. It consists of sub detectors with different particle detector techniques and has acomplex magnet system.
The ATLAS adopts a right-handed coordinate system, defining the I-axis as the direction of the beam axis,
the G-axis as the axis from the center of the detector to the center of the LHC ring, and the H-axis as the axis
perpendicular to them. At the same time, the pesudorapidity [, which indicates the position with respect to27

Figure 2.2: The schematic view of the ATLAS detector [49].

the beam axis, and the azimuth angle q, indicates the rotation with respect to the beam axis, are used todenote the locations of particles.
The rapidity H is a variable related to the Lorentz transformation of the particle with respect to the beamaxis direction, and is defined as follow:✓◆© ⇢ + %z ™
1
⇢ + %zÆ
H = ln= ln ≠≠ q
Æ̈
2
⇢ %z
2
2
?T + <´(2.1)

where ⇢, ? z , ? T , < represent energy, momentum respect to the beam axis, momentum in the direction
orthogonal to the beam axis and the invariant mass, respectively. In considering a Lorentz transformationof the particle with respect to the beam axis, the rapidity, shown in equation 2.1, varies by using variables
V = a/2 = tanh and W which correspond to the difference between the reference system and thetransformed systems as follows:
!
✓
◆
0
0
⇢ + %I
0
1
1W⇢ + VW% I + W%I + VW⇢
H!H =
ln 0
= ln
0
2
2
W⇢ + VW% I W%I VW⇢
⇢ %I
✓
◆
1
1+V
= H + ln
=H+
(2.2)
2
1 V
As shown in equation 2.2, the rapidity between different particles does not depend on the choice of a frame.
Since the maximum rapidity of a particle depends on its energy and maximum energy of a particle is halfof the center of energy in the center of mass system, the maximum value of the rapidity can be calculated28

as follows:

✓p

q

q

◆

©
™
p
<2 ™ 1 ≠ÆÆ = ln ≠Æ ' ln BÆ̈ 2 ≠
Æ
<
<2
≠
Æ̈
<2
´
The maximum value of the rapidity depends on the mass of a particle. The pesudorapidity is a massless
approximation of the the rapidity and expressed using the polar angle \ from the center point of the detector
as follows:
✓
◆
✓
◆
1
⇢ + ⇢ cos \\[ = ln= ln tan(2.3)
2⇢ ⇢ cos \
2
p

B
2 +

B
B2
1 ©≠ 2 + 4⇠"
H <0G = ln ≠ p
q
2
B
B2
4
´ 2

B2
4

<2

As the definition of equation 2.3, [ can take ±1 and represents the position in the beam axis direction.

2.2.1 LUCID-2
The LUCID-2 (LUminosity Cherenkov Integrating Detector) [53] is a dedicated luminosity monitor. Thiswas updated during the long shutdown between Run 1 and Run 2 experiment to cope with the higher
luminosity. LUCID-2 consists of two modules (A and C) placed around the beam-pipe and symmetricalwith respect to the interaction points, at 17 m from it. Each module consists of 16 PMTs, grouped by
4⇥4 groups with 207 ⌫8 radioactive sources deposited on the windows for calibration purpose. In addition,
there are also 4 bundles of quartz fibers read out by PMTs located 1.5 m away from the detector in a lower
radiation area.

2.2.2 Magnet system
The magnet system [54] used in the ATLAS experiment is divided into three components, Central Solenoid,
Barrel Toroid and Endcap Toroid, all of which are superconducting magnets, as shown in Figure 2.3. The
magnetic field of the Central Solenoid is 2 T, provided for the accurate charged particle track reconstruction
inside the inner tracker, and consists of a 5.3 m long and 2.4 m diameter single-phase coil. Since it isinstalled inside the calorimeter, a low molecular weight substance is used. Each of the Barrel Toroid andEndcap Toroid are divided into eight sub-magnets and installed along the beam axis. They are used for the
purpose of bending the muon trajectories. The strength of the magnetic field is varied depending on thearea of the detector.

2.2.3 Inner detector
The inner detector [55] illustrated in Figure 2.4 is located closest to the interaction point. The inner detector
is 6.2 m long and 2.1 m in diameter, and is divided into a barrel region and an end cap region, covering up to|[|  2.5. The barrel region is a cylinder-shaped detector, while in the end cap region, the detector structure
is perpendicular to the beam axis. The 2 T magnetic field from the central solenoid bends the trajectoriesof the charged particles, and momenta can be measured from their curvature. The inner detector consists of
Pixel Detector (Pixel), Semi-Conductor Tracker (SCT), and Transition Radiation Tracker (TRT).

29

Figure 2.3: The magnet system [54] in the ATLAS experiment.

2.2.4 Calorimeter
Calorimeters illustrated in Figure 2.5 are divided into the electromagnetic calorimeter [56] used for
detecting electrons and photons and the hadron calorimeter [57] used for detecting hadron activities.
Whole-area electromagnetic calorimeter and end-cap and forward area hadron calorimeter use liquid argon
as a detector layer due to its high radiation resistance, and different materials as an absorber (lead, copper ortungsten), depending on the area of the detector. Input particles cause a cascade shower, whereby electrons
ionized from the liquid argon atoms are read out as a signal. The energy of the input particles has a very
good linearity with the number of ionized electrons. Hadron calorimeter in the barrel-region is called tile
calorimeter and have iron as the absorber and plastic scintillator as the detector.
All the calorimeters are sampling calorimeter, and the energy resolution is generally expressed by thefollowing [58]:
f(⇢)
0
1
=
2.
p
⇢
⇢
⇢
The first term is called the noise term and represents the contributions of noise and pileup effects and is
predominant at low energy region. The second term is called the sampling term, which depends on theconditions of the active and absorber layers, and it dominant in the energy range of 10 to 100 GeV. The
third term is called the constant term and has the largest contribution in the high energy region. Typicalvalues of them are listed in Table 2.2.

30

Figure 2.4: The inner detector [55] in the ATLAS detector.
Table 2.2: The typical value of noise term, sampling term and constant term for the electromagnetic calorimeter.
Electron energy measurements with a module of the EM barrel LAr calorimeter had been studies in the range from10 to 245 GeV impinging at [ = 0.687 during test beam [58].

Parameter
Noise term 0
Sampling term 1
Constant term 2

Typical value
0.25 % · GeVp
10.1 ± 0.1 % · GeV
0.17 ± 0.04 % · GeV

2.2.4.1 Electromagnetic calorimeter
The electromagnetic calorimeter covers |[| < 4.9 and is a three-layer detector. It is a very finely divided
detector in the [ direction, fine enough to identify the two photons from c 0 decay. It has as characteristic
accordion structure, which can eliminate the insensitive region in the q direction.
2.2.4.2 Hadron calorimeter
The hadron calorimeter is installed outside the electromagnetic calorimeter because hadrons only drop partof their energy into the electromagnetic calorimeter. The hadron calorimeter relies on the strong interaction
to measure the energy of the hadrons and stops them not to reach to the muon spectrometer.
The gap between hadronic calorimeter barrel and extended barrel and electromagnetic calorimeter barrel
and end-cap sections which has 1.37 < |[| < 1.52 is known as “crack-region“. Special cells made by31

Figure 2.5: The calorimeters [57] in the ATLAS detector.

scintillators are installed.

2.2.5 Muon spectrometer
The muon spectrometer [59] shown in Figure 2.6 is located at the outermost layer of the detector because
muon, which has a small cross-section of bremsstrahlung thanks to its large mass compared to the electron,
are not absorbed by the calorimeter except for neutrinos. For the accurate momentum measurement, themagnetic field from the toroid magnet is used to bend the muon orbit with respect ti the A-I plane. The
muon spectrometer consists of Monitored Drift Tubes (MDT), Thin-Gap Chambers (TGC), Resistive-Plate
Chambers (RPC) and Cathode Strip Chambers (CSC). TGC and RPC are used for trigger issuances.

2.3 Trigger and data acquisition system
One of the biggest challenges in the ATLAS detector is to select and acquire events of interest from thelarge amount of proton collision data. The ATLAS detector is exposed to proton collision data at 25 ns
intervals during Run 2, reducing the event acquisition rate from 40 MHz of nominal bunch crossing to
1 kHz. ATLAS has a two-stage triggering system, with first-stage triggering performed by a hardware-based
Level One (L1) trigger, followed by a software-based High-Level Trigger (HLT). For events passing theconditions of L1 trigger, all detector information is stored in the Readout Driver (ROD) and sent to the
Data Acquisition (DAQ) system. Subsequently, events fulfilling the conditions of HLT are stores in a large
storage for physics analysis.

32

MDT chambers

12 m
Resistive plate chambers
10
Barrel toroid coil
8

Thin gapchambers

64End-cap
toroid2
Radiation shield

Cathode strip
chambers
0

20

18

16

14

12

10

8

6

4

2m

Figure 2.6: The schematic of A-I cross section view of the muon spectrometer [59].

2.3.0.1 L1 trigger
The L1 trigger [60] roughly surveys high momentum muons, electrons, photons, jets and tau particles
and ⇢ Tmiss described in section 4.10 within 2.5 `s using limited detector information. This can reduce thecollection frequency from 40 MHz to 100 kHz. L1 trigger further defines the ‘Region of interest (RoI)‘,
which is information about the rough energy distribution, and sends them to the High level trigger.
2.3.0.2 HLTThe high level trigger [61–64] performs a more detailed investigation of the detector information andtrigger recipes that depend on the particle of interest, with an event storing time of about 550 ms. Finally,
the collection frequency is reduced to about 1 kHz.

33

3 Dataset and Monte-Calro samples
3.1 Datasetp
The data used in this analysis were collected during 2015, 2016, 2017 and 2018 at B = 13 TeV. The
combined 2015-2018 integrated luminosity is 139 fb 1 with the uncertainty of 1.7 % [65], obtained using
the LUCID-2 detector for the primary luminosity measurements. Table 3.1 shows the integrated luminosity
for each year.
Table 3.1: Summary of integrated luminosity for each year.

Year

Integrated luminosity in fb 1

2015
2016
2017
2018

3.22
33.0
44.3
58.5

Total

139

Another important parameter related to the instantaneous luminosity is the average number of inelastic
interactions per bunch crossing, known as the pile-up. The average number of pile-up per bunch crossing in
the dataset is 33.7. The pile-up degrades the performance of the reconstructed physics objects and makes
the identification of vertices and the reconstruction of tracks more difficult. The detector response canbe longer than the duration time of 25 ns between two different bunches and be affected by not only thepresent bunch (in-time pile-up) but also pile-up from previous and following bunches (out-time pile-up).
The cumulative luminosity, delivered by the LHC, recorded by ATLAS, saved for physics analysis, and theluminosity as a function of pile-up are shown in Figure 3.1.

3.2 Trigger
Since the signal event in this analysis has an isolated lepton with a large momentum in clean environment,such a lepton is used as the trigger condition. Several unprescaled1 HLT (single lepton trigger) following
the L1, as listed in Table 3.2, are used to maximize the data statistics.
"L1EM20" means that the L1 trigger imposes an transverse energy threshold of 20 GeV or higher on EM
objects reconstructed in the electromagnetic calorimeter. “V” and “H” indicate that the ⇢ T correction ismade for the [ direction and the hadron calorimeter information is not used in the construction of the EM
1 For example, if the momentum of the lepton required by the trigger is low and the trigger rate is high, more trigger accepts may

be issued than allowed. In such a case, the event rate to be obtained may be intentionally reduced, which is called prescale.

34

Recorded Luminosity [pb-1/0.1]

ATLAS
140 Preliminary120

s = 13 TeV

LHC Delivered
ATLAS Recorded

100

Delivered: 156 fb-1
Recorded: 147 fb-1
Physics: 139 fb-1

Good for Physics

8060
2/19 calibration

40
20

600
ATLAS Online, 13 TeV
500∫Ldt=146.9 fb-1
2015: <µ> = 13.4
2016: <µ> = 25.1
2017: <µ> = 37.8
2018: <µ> = 36.1
Total: <µ> = 33.7

400
300
200

2/19 calibration

Total Integrated Luminosity fb-1

160

100
0
0

0

'15 ul '15 an '16 ul '16 an '17 ul '17 an '18 ul '18
J
J
J
J
Jan
J
J
J

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing

Month in Year(a) Integrated luminosity(b) Interactions per bunch

Figure 3.1: (a) The integrated luminosity delivered to LHC (green) and ATLAS (yellow) in Run 2 period [66]. The
blue histogram shows the one recorded for physics analysis after requiring the data quality. (b) The luminosity
recorded by ATLAS as a function of mean number of proton interactions per bunch crossing in Run 2 period [66].

objects, respectively. On the other hand, "L1MU15" means that muon ? T above 15 GeV is required in theL1 trigger.
The numbers following "HLT_e" or "HLT_mu" indicate the ⇢ T or ? T threshold in HLT. The "lhmedium"and "lhloose" denote the requirement of an electron identification using the likelihood discriminant of themultivariate techniques. The "nod0" means no information on the impact parameter is used. "ivarmedium"and "iloose" represent the additional requirements of an isolation.
Table 3.2: A summary of trigger requirements. A logical OR is performed for a given year.

Channel2015

2016, 2017 and 2018

Electron

HLT_e24_lhmedium_L1EM20VH
HLT_e60_lhmedium
HLT_e120_lhloose

HLT_e26_lhtight_nod0_ivarloose
HLT_e60_lhmedium_nod0
HLT_e140_lhloose_nod0

Muon

HLT_mu20_iloose_L1MU15
HLT_mu26_ivarmedium
HLT_mu50

3.3 Monte-Calro samples
Monte Carlo (MC) simulated samples are used to model both the background and signal processes. The
full set of simulated samples is summarized in Table 3.3. The generated events are processed througha simulation of the ATLAS detector geometry and response using G
4 [67], and through the samereconstruction software as the one used in the collected data.
The effect of pile-up is also included in the simulation [68]: simulated events are re-weighted to reproduce
the actual pile-up distribution as shown in Figure 3.1(b). The simulated event is then multiplied by (1/0.99)
and (1/1.07) to realize the mean of observed pile-up and vertex, respectively. The middle value of them35

(1/1.03) is used as nominal and (1/0.99) and (1/1.07) are applied as up and down type pile-up re-weighting
scale factor. respectively.

3.3.1 General description of inclusive cross-section
An inclusive cross section f for ? ? ! - calculated at n-th order in perturbation theory is factorized into a”hard part” f̂8 9 and ”normalization parts” 58, 9 as follows:
π
’π
2
f=
3G1 58 (G 1 , ` )3G 2 5 9 (G 2 , `2 ) f̂8 9 (G 1 , G2 , `2' ),8, 9

where G 1 and G 2 represent longitudinal momentum fractions of struck partons in two different protons and58, 9 are known as parton density functions (PDF) which are probability density functions for finding aparton with a certain scale G.
PDF is obtained by fitting many data from various experiments with a certain function.
` and ` ' are known as a factorization scale and a renormalisation scale, respectively. ` is introduced
to cure the ultraviolet divergences which appear because of large momentum in the loops of the Feynman
diagrams. On the other hand, ` ' is introduced to cure the infrared divergences which appear because eithera virtual or a real particle can reach a zero momentum, or a massless particle radiates another masslessparticles.
The “hard part” f̂ is expanded with the series of a strong coupling constant UB as follows:f̂ = = UB f̂ 1 + UB2 f̂ 2 + · · · + UB= f̂ = + O (UB=+1 )In this analysis, MC samples with up to next-to-next leading order (NNLO) corresponding to second
order expansion are used. The strong coupling constant UB is also determined experimentally. The
renormalisation group equation is then used in the MC generator to predict the value of UB at different
energy scales that appear in the generated process.
The PDFs are obtained by fitting many data from various experiments with a certain function for theparton content of the proton at a given scale. The Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution
equations [69–71] are then used to estimate the PDFs at different scales.
The cross section above is at parton level. Most MC samples are then converted to a cross section at
hadron level by interfacing to showering and hadronization generators. In that process, (I) events with #partons and (II) events with N-1 partons plus one hard radiation from the shower indicate the same physicalphenomenon, and only one of them needs to be selected. This is called parton-jet matching, which uses acertain cutoff scale to determine whether to retrieve (I) or (II).

3.3.2 Simulated signal samples
The signal events described by the LRSM is implemented in the M_ MC@NLO [72] generator
at leading-order (LO) using FeynRules [73]. For the simulated signal produced M
MC@NLO isinterfaced to P
8.230 [74] for parton showering. The A14 parameter set [75] is used for tuning theshower. The NNPDF3.1[76] parton distribution function set enters in the matrix element calculationand the NNPDF2.3 [77] is used in the parton shower.

36

96

55

.09

3000 0

08

0.9

88

3

2.1
.34

2.2

01

6

9.7

91

7
8.3
5.6

500

86

6

1.2

3

6

8.5

3.5

1

38

0.0

5

48

0.0

1

6

2
0.3
07

65

2

0.7

0.3

0.4

8

1
0.9
7
0.9

4

7

70

0.0

0.1

3.5

7
5..021
5.3
5

31

0.1

58

0.5

9

1.8

32
.3
3434.26
23

49

0.2
0.2

7
1.3

4.3

10

71

5

5

1000 2

0.4
1.1

2.9

1500 1

0.0

2
0.2

5

6

8

31

0.1
8

2
0.9

6.5

11

0.4

2.3

2000 1

2

27

0.0

0.1

8

2
4.4

0.0
89

0.6
1.6

2500 4

5

93

0.3

fb

Black numbers represent X-section [fb]NR [GeV]The simulation includes a Majorana #R with a 50 % mixture of same-sign and opposite-sign lepton pairs.
This enables studies in both the opposite-signal and same-sign channels. The generated signal mass points
and their cross section are shown in Figure 3.2. In the case of a Dirac #R , only opposite-sign leptons can
produced so that the measured cross-section can be double that simulated samples. The signal samples do
not include lepton flavour-mixing, although this is a free parameter of the model and could be studied in
the future.

4
1..229
1.33
1

8

1.6

4.5

5

77

35
0.5 4
8
5
.
0 4
4
0.6
51
0..7522
0

5.5

01

0.2

65

0.2

5

68

0.0

53

0.1

7

16

0.3

92
0.3 1
4
0..44675
0.48
0

6

15

0.1

7
0.1

28

1

2
0.2

87
0.2 4
1
0.2

0.1

10−1

68
0.1 4
9
0..12098
0.21
0

6.5
7
WR [TeV]Figure 3.2: Generated MC signal points in the 2D plane of ,R mass and #R mass. Black numbers represent thecross-section.

3.3.3 Simulated background samples
The production of ,// boson in association with jets is simulated with the NNPDF3.0
PDF set andthe ATLAS configuration of S
2.2.11 [78], which includes matrix elements for up to five partons at
LO and up to two partons at NLO. They are calculated with the C[79] and O
L[80] libraries
and matched with the S
parton shower [81] using the M @NLO prescription with a set of tuned
parameters developed by the S
authors.
For the background contributions originating from the QCD multÚet is generated using P
8.230 [82]with LO matrix elements for dÚet production which are matched to the parton shower. The renormalisationand factorisation scales are set to the geometricmean of the squared transverse masses of the two outgoingq

particles in the matrix element, ?ˆT = ( ? 2T,1 + < 12 ) ( ? 2T,2 + < 22 ). The NNPDF2.3 PDF set [83] is usedin the matrix element generation, the parton shower, and the simulation of the multi-parton interactions.
The A14 set of tuned parameters is used.

37

The production of W in association with jets is simulated with the ATLAS configuration of S
2.2.2 [78] as well as ,// boson production. Matrix elements are calculated for up to two partons at NLO
and four partons at LO. The NNPDF3.0
set of parton distribution functions is used in the S
parton shower.
For the background contributions originating from the top-quark related processes were modelled using theP
v2 [84–87] generator at NLO with the NNPDF3.0
PDF set. The events were interfacedwith P
8.230 [82] for the parton shower and hadronization modelling with the A14 tune and the
NNPDF3.0
set of PDFs. Top quark decay is modeled using M S[84, 88] to preserve spincorrelations. The decays of bottom and charm hadrons are performed by E G 1.6.0 [89] program in all
top-quark processes.
The diboson (,,, , /, / /) processes decaying into four leptons and at least one quark are simulated with
the ATLAS configuration of S
2.2.2 and S
2.2.1 [78] generator with NNPDF3.0
set [76],
which includes matrix elements for no or one parton at NLO and up to three partons at LO.
The MC samples generated at NLO prediction are normalized to the cross section at NNLO prediction.
Table 3.3: Simulated signal and background samples. The corresponding event generator, parton shower, cross-section
normalization, PDF set used for the matrix element and set of tuned parameters are shown for each sample. The
generator cross-section of the generator used to generate the sample is used where not specifically stated otherwise.
Physics process
Signal, (! ✓a) + jets
¯ + jets/ (! ✓✓)
W+jetsQCD multi-jet
C C¯
single-top
di-boson

Generator
M

S
S
S
P
P
P
S

_ MC@NLO
2.2.112.2.11
2.2.2
8.230
v2
v2
2.2.1

PDF set
NNPDF3.1
NNPDF3.0
NNPDF3.0
NNPDF3.0
NNPDF2.3
NNPDF3.0
NNPDF3.0
NNPDF3.0

38

Cross-section
normalization
LO
NNLO
NNLO
NNLO
LO
NNLO
NNLO
NNLO

Parton shower
P

P
P
P

S
S
S

S

8.230

8.230
8.230
8.230

Tune
S
S
S

S

A14

A14
A14
A14

4 Object reconstruction and identification
In this section, details of the object selection are described. The physics objects to reconstruct the final
discriminant (<(,R )) are electrons, muons and large-' jets. Small-' jets and missing transverse energy isalso used to select the signal candidate events.

4.1 Charged track
When a charged particle passes through the inner detector, it leaves signals at each layer of them. By
combining them in the following three steps [90], the trajectory of a charged particle is reconstructed as a“track”.
1. Charged particle reconstruction begins by clustering the signals in each later of the inner detector.
The three-dimensional clusters are called “space-points”.
2. Seed-tracks are created based on these space-points. Then, preliminary tracks are formed by using a
combinatorial Kalman filter [91]. There are still different tracks having the same space-points andare needed to solve these ambiguities.
3. A “track score” is introduced to assign a quality to each track. Track score depends on the position of
space-points, expected trajectory which is not observed and the j2 of the track fit. Tracks with bad
quality are eventually discarded, and the remaining tracks are required to pass minimum conditions
shown in Table 4.1. 30BL and I BL
0 are the transverse and longitudinal impact parameter with respect
to the beam line.
Table 4.1: Charged track criteria.

Feature

Value

?T
|[|
|30BL ||I BL
0 sin \|

500 MeV< 2.5< 2.0 mm
< 3.0 mm

4.2 Primary vertex
The points where at least two tracks intersect are called vertexes, and multiple vertexes are generated due tothe pile-up at a single bunch crossing. A primary vertex is defined as the most energetic vertex, which isÕdefined as the largest ? 2T , where ? T is the transverse momentum of the associated tracks.
394.3 Topological Cluster
The energy deposited by particles in each cell of the calorimeter is combined to form a topological cluster(topo-cluster) [92]. The three-dimensional information of the calorimeter cells is used to reconstruct the
topo-cluster, and the sum of the energies of the grouped cells is assigned as the energy that the topo-cluster
has. At the same time, the direction of the incident particles is also observed. The condition to include acalorimeter cell as a component of a topo-cluster is given below:EMe cell=EM⇢ cellEM
fnoise,cell

EM is a cell signal significance which represents a significance of energy deposit relative to thewhere e cell
EM is the energy measured in the calorimeter cell. Both quantities are measured by thenoise fcellEM and ⇢ cell
EM energy scale. The energy deposit by electron and photons is correctly handled with the EM energy
scale, and any corrections for hadrons are not taken into account.

The following steps are used to reconstruct topo-clusters.
⇢ " > 4.
1. A proto-cluster, a candidate of topo-cluster, reconstruction starts from a seed cell having e 24;;
⇢ " | > 2, the cell is merged into the proto-cluster. As long as the
2. If a neighboring cell fulfil |e 24;;
conditions are met, the step 2 is repeated.

3. If a neighboring cell fulfil 2
broken.

⇢ " | > 0, the cell is merged into the proto-cluster and the loop is|e 24;;

In case two different proto-clusters are adjacent to each other, and they are close to each other separated by⇢ " | > 2, they are merged.
a cell satisfying |e 24;;

4.4 JetQuarks and gluons are observed in the detector as a set of particles, which looks like a spray, due to thehadronization process. Hadrons interact with the detector materials and leave a signal with a wider radiusthan that of the EM object. Jet energy measurements can be improved by making complete use of theinformation from both the tracking and topo-cluster, which is known as a particle-flow object [93] behaving
as a single particle. The energy deposit of particle-flow object is formed by replacing the topo-cluster’s
energy with the momenta of tracks that are matched to the topo-cluster. Jet reconstruction is performedby combining the particle-flow objects with the anti-: C algorithm [93]. The anti-: C algorithm uses the
distance 38 9 between different particle-flow objects as an indicator below:
!
'829
1
1
38 9 = <8= 2 , 2,? T,8 ? T, 9 ' 2
where ? T,8 and ? T, 9 are the ? T of the 8-th and 9-th particle-flow objects and '8 9 is the angular distance
between them given by the following:q'8 9 = ([8 [ 9 ) 2 + (q8 q 9 ) 2 .
40

' is a parameter and corresponds to the cone size. ' = 0.4 is used to form small-' jet.
The algorithm calculates the smallest 38 9 and 38⌫ = 1/? 2T,8 . If the 38 9 is smaller than 38⌫ , two particle-flow
objects, labeled 8-th and 9-th, are merged into a new object which is re-labeled as 8-th. This procedure
is repeated until the 38⌫ becomes the smallest. This 8-th object is recognized as a jet and the all usedparticle-flow objects in the jet are removed from the list of particle-flow objects, and then the anti-: C
algorithm is applied to the remaining particle-flow objects.
Energy of topo-clusters are scaled at EM scale, so jets handling hadron objects need to be calibrated withfollowing methods. This is done with several steps by comparing MC and data [94].
Origin correction
The origin correction corrects the direction of jet to point to the hard-scattering vertex from the centerof the detector while keeping the jet energy constant. This correction improves the [ resolution.
Pile-up correction
Pile-up produces soft backgrounds and can obscure the energy of the jets. In-time and out-time
pile-up are canceled out with area-based and residual pile-up correction as follows:reco? corr
T = ?Td⇥U([) ⇥ (#vertex

1)V([) ⇥ `,where ? reco
and ? corrT
T represent jet ? T at the EM scale and corrected scale, respectively. The second
term corresponds to the area-based pile-up correction. d is an average ? T density measured in theevents. The third and fourth terms correspond to the residual correction based on the number ofreconstructed vertex #vertex and the mean number of inelastic interactions per bunch crossing `. U
and V are coefficients which are functions of [.
Absolute MC-based calibration
To calibrate the energy of the reconstructed jet at the EM scale topo-clusters, MC samples are used.
The comparison of the reconstructed energy with the truth jet’s energy, where the truth jet is formedby performing anti-: C algorithm against stable and visible truth particles, by using the MC truth
information is performed. The correction is performed depending on the [ and ⇢ T of a target jet.
The calibration factors are derived by fitting ⇢)reco /⇢)truth with a gaussian function.
Global sequential calibration
Since the number of color charges is different between quark- or gluon-origin jets, the calorimeter
responses are different as well. A quark-origin jet tends to have hadrons with higher ? T and fewer
accompanied particles than a gluon-origin jet. Not only calorimeter and tracking information but
also muon spectrometer is used to correct jet energies. This correction improves the agreements
between data and MC to within 2-4%.
Residual in situ calibration
As the final step, the differences between MC and data are corrected using the response 'in situ whichis ? T ratio of a jet against other well-measured reference object like Z boson and photon. The ratioof the 'in situ between data and MC is used to correct the jet ? T as a function of ? T and [.
The above procedures correct only jet energy scale responses, but the resolution of energy response are stillneeded to be calibrated.

41

The jet energy resolution is parameterized as a function of three terms [95],
f?T
#
=
?T
?T

(
p
?T

⇠,

where # indicates the effect of noise derived from electronic noise and pile-up effects, ( indicates the
sampling term, and ⇠ is a ? T independent constant term. The jet energy resolution is measured withobserved data in 2017 corresponding to an integrated luminosity of 44 fb 1 . For the central pesudorapidity
region, W+jets and /+jets events are used to measure with good precision. On the other hand, in the forward
pesudorapidity region, dÚet events give the most precise determination of the resolution. Typical values forjets with a radius parameter ' = 0.4 shown in Table 4.2.
Table 4.2: Three constants for jet energy resolution measured for jets with radius parameter ' = 0.4 [93].

|[| range(0.0, 0.8)
(0.8, 1.2)
(1.2, 2.1)
(2.1, 2.8)

N [GeV ]p
S [ GeV]C

4.12 ± 0.74
3.66 ± 0.75
4.27 ± 0.75
3.38 ± 0.65

0.74 ± 0.10
0.64 ± 0.13
0.58 ± 0.15
0.26 ± 0.36

0.023 ± 0.003
0.039 ± 0.009
0.034 ± 0.007
0.050 ± 0.010

The baseline criteria for reconstructed jet are summarized in Table 4.3.
Table 4.3: Small-' jet selection criteria.

FeatureValue

Radius parameter '
?T
|[|
Mass

0.4
> 20 GeV< 4.0> 0 GeV

4.5 B-tagging
Jets derived from b-quarks, 1-jets, have some characteristics such as a longer life time than other quarks
and a secondary vertex that is displaced from the primary vertex. Based on these features, a b-tagging
algorithm, to determine whether each jet is b-quark induced or not, is applied. In this analysis, DL1r [96]b-tagging algorithm is used.
DL1r performs identification using a deep learning neural network, and the input includes discriminantvariables constructed by a recurrent neural network, which can take advantages of spatial and kinematic
correlations between different tracks generated from the same b-quark. This approach has been found to
improve performance primarily for jet with high ? T [97].
The working points are defined by a single cut value on the discriminant output distribution. 77% working
point, which is expected to provide the best signal sensitivity, is employed in this analysis. In a sample ofsimulated SM C C¯ events, the rejection factors of 600 and 11 are achieved for light-flavour and charm jets,
respectively. The performance of the b-tag strongly depends on the ? T of a jet; the efficiency decreases

42from 65% when the 1-jet ? T is about 500 GeV to 10% when the ? T is about 2 TeV. To compensate for themis-modelling of the MC with respect to the data, a scale factor is adapted according to the jet ? T .

4.6 Electron
Electrons sometimes emit photons by bremsstrahlung, which in turn produce a electron-positron pair. By
repeating these processes, a cascade shower is formed in the calorimeter. In addition, since the electrons
are charged particles, they leave trajectories in the inner detector. Electrons are reconstructed with these
two information.
There are several basic definitions of electrons in different working points and they are generally common
to all ATLAS analysis. These basic definitions are based on three categories: electron reconstruction,
identification and isolation. Most analyses then choose one of the basic working points and complement itwith additional specific analysis cuts.
The electron reconstruction efficiency measured with 2015 and 2016 data is greater than 98% in almost all
the phase space [98]. In order to account for differences in simulation and data, scale factors are applied toreconstructed electrons in MC. The scale factors are expressed in bins of electron ? T and [. They differ
from unity up to 0.5% in all of the bins at most. In addition, transverse (30 ) and longitudinal (I 0 ) trackparameters with respect to a primary vertex are used to ensure that an electron originates from a primaryvertex.
There is no guarantee that objects reconstructed as electrons, are truly electrons. The main sources of fakeelectrons are jets and electron from photon conversions. In this analysis, two general working points areused to discriminate between prompt and fake electrons by using a multivariate likelihood fit of the tracking
and calorimeter information. The identification working points used are Medium for baseline electron andTight for signal like events. The efficiencies for identifying a prompt electron with ⇢ T = 40 GeV are 93%
and 80% for the Medium and Tight operating points, respectively [99]. The electrons tagged by the Tight
working point are a subset of electrons tagged by the Medium working point. Dedicated scale factors areneeded to use these electron identification working points as well as the electron reconstruction.
There are several working points for the isolation category. They depend on the degree of separation of theelectron from other objects and how widely the energy is distributed. They are determined based on how
topoetcone20
much of the energy deposit is centered in the range of ' < 0.2, labelled as ? T, with respect tothe electron:
topoetcone20?T/? T4 < max(3.5 GeV/? T4 , 0.015)

topoetcone20?T/? T4 < 0.2

for FCHighPtCaloOnly
for FCLoose.

Scale factors for the isolation are also needed to be applied to ensure the data-to-MC agreement.
The definition of electrons used in analyses is summarized in Table 4.4. The “Baseline” electron definition
is used to count up the number of leptons in an event. The “Leading” electron is defined base on thecharacteristic of electrons in the signal-like events, and is required at the event selection stage.
The electron used in this analysis has a flag called Ambiguity. This is a variable that indicates whether
the reconstructed electron is a prompt electron or it is recognized as an electron from a photon conversion.
Electrons from photon conversions often have a track with the opposite sign to the track associated to the43Table 4.4: Electron selection criteria.

FeatureBaseline electron|[|?T
Track to vertex association
Identification
Isolation

Leading electron(0.0, 1.37] or [1.52, 2.47]> 25 GeV> 200 GeV
|30 /f(30 )| < 5.0| I 0 sin \| < 0.5 mm
MediumTight
FCLoose
FCHighPtCaloOnly

electron in the vicinity. In that case, Ambiguity > 1 is assigned, otherwise 1. The Ambiguity flag is a
non-calibrated variable as a common ATLAS analysis one, so that possible shape variations are taken into
account as discussed in Section 7.3.

4.7 Muon
Since muons have small energy loss due to bremsstrahlung, they pass through the calorimeter andleave information in muon spectrometers. In addition, they leave signals in the inner trackers as well.
Reconstruction of muon, muon candidates are reconstructed in the inner tracker and muon spectrometer,
and then they are combined by a matching algorithm [100].
There are several working points in the muon identification: Loose, Medium, Tight and High-? T [101].
Muon identification depends on the number of hits in the detectors. Medium and Tight are used in thisanalysis. They requires two precision stations which have at least three hist in the MDT and CSC detectors.
Muons passing Tight are a subset of those passing Medium and fulfil further requirements on compatibilityof the charge to the momentum and absolute difference between the ? T observed in the inner tracker andmuon spectrometer.
There are several working points in the muon isolation: FCVeryLoose, FCLoose, FCMedium and
FCTight [101]. FCTight is used in this analysis. They depends on the energy spreadness in the innertracker and calorimeter. Track-based isolation is defined as the scalar sum of the ? T of the tracks associated`with the primary vertex in a given ' = min(10 GeV/? T , 0.3) around the muon, excluding the track
associated to the muon, labelled as ? varcone30. Calorimeter-based isolation is defined as the sum of theTtransverse energy of calorimeter cell clusters in a cone size of ' < 0.2 around the muon subtracting the
topoetcone20
energy deposit of the muon itself, labelled as ⇢ T. FCTight requires the following conditions:
topoetcone20?T`/? T < 0.15,⇢ Tvarcone30 /? T < 0.04.
`

The reconstruction efficiency is measured by / ! `` events, and except for the region of |[| < 0.1, theefficiency is more than 98 %.
Two set of muon selection requirements are defined for this analysis. Muon satisfying these criteria arereferred to as Baseline and Leading muons, as defined in Table 4.5. Leading muons are used in the signal
region, while Baseline muons are used to count up the number of leptons in an event.

44

Table 4.5: Muon selection criteria.

FeatureBaseline muon

Leading muon

(0.0, 2.5]
> 28 GeV> 200 GeV
|30 /f(30 )| < 3.0| I 0 sin \| < 0.5 mm
MediumTight
N/A
FCTight|[|?T
Track to vertex association
Identification
Isolation

The baseline muon does not require any isolation requirement in order to reconstruct the sub-leading muonwithout the influence of hadron activities from #R decay. This can improves signal sensitivity especially inthe low #R mass region by a factor of 10.

4.8 Photon
Photons do not play an important role in this analysis, but they are used for the validation of the W+jets
estimation in the SR. The reconstruction of the photon depends on the measurement of the electromagnetic
shower formed in the electromagnetic calorimeter. Rectangular clusters formed in the calorimeter cells areseeded to form the photons. It is also required that the energy deposit in the hadronic calorimeter be small
or absent. Photons with no tracks associated with the cluster are called as ”unconverted photons”, while
photons with a pair of oppositely-charged tracks are called as a ”converted photon” [102].
There are several working points in the photon identification: Loose and Tight [103]. The Loose
selection depends on shower shapes in the second layer of the electromagnetic calorimeter and on theenergy deposited in the hadronic calorimeter. The Tight selection requires additional information fromthe most inner layer of the calorimeter, and are separately optimised for unconverted and converted photons,
to account for the generally broader lateral shower profile of the latter.
There are several working points in the photon isolation as well: FCLoose, FCTight and FCTightCaloOnly.
They depend on the transverse energy flow in the calorimeter and inner tracker. The calorimeter isolation⇢ T,iso is obtained by summing the ⇢ T in the calorimeter in cones around the direction of the photon
topoetcone40
topoetcone20
candidate, ⇢ T,isofor ' < 0.4 and ⇢ T,isofor ' < 0.2. The track isolation ? T,iso is obtainedby summing the ? T of all the tracks with ? T above 1 GeV excluding the tracks relating to photon conversions
in a cone around the direction of the photon candidate with a fixed cone size of ' < 0.2, labelled as? etcone20. FCLoose and FCTightCaloOnly are used in this analysis and they are defined as follows:
T,iso
topoetcone40⇢ T,iso

topoetcone20⇢ T,isoW

W

W/⇢ T < 0.022 + 2.45 GeV/⇢ T/⇢ T < 0.065,? etcone20/⇢ T < 0.05
T,isoW

for FCTightCaloOnly
for FCLoose.

The reconstruction efficiency is measured depending on the photon energy [104]. The photon efficiency
increases with increasing ⇢ T , from about 60 % (50 %) for unconverted (converted) photon at ⇢ T = 10 GeV
to over 90 % at ⇢ T = 100 GeV.

45

Two set of photon selection requirements are defined for this analysis. Photon satisfying these criteria arereferred to as Baseline and Leading photons, as defined in Table 4.6. Baseline photons are used to count up
the number of photons, while Leading photons are prepared to recognize signal like events.
Table 4.6: Photon selection criteria.

FeatureBaseline photon|[|?T
Identification
Isolation

Leading photon(0.0, 1.37] or [1.52, 2.47]> 25 GeV> 200 GeV
Loose
Tight
FCLoose
FCTightCaloOnly

4.9 Overlap removal
The above objects are reconstructed in parallel by combining the detector information. There are manycases where a single particle is reconstructed as different objects. For example, since electrons and jets
leave similar signals in the calorimeter, they are often reconstructed as both objects. To avoid double
counting of a single particle, a procedure called “overlap removal“ is applied by following proceduresshown in Table 4.7.
Table 4.7: The order of overlap removal. Baseline leptons shown in Table
q 4.4 and 4.5 and photon shown in Table 4.6

are used in below overlap removal prescription.
where H denotes the rapidity.

' is calculated by(qReference

qTarget ) 2 + (H Reference

H Target ) 2

StepReference

TargetCriterion

1.
2.
3.
4.

Electron
Muon
Electron
Jet

ElectronElectron
Muon
Electron5.
6.

Electron
Muon

Jet
Jet

If there is a shared track, softer electron is discarded.
If there is a shared track, any electrons are discarded.
If there is a shared track, any muons are discarded.
If ' < 0.2 and jet is not 1-tagged and electron ? T is greater than
100 GeV, any electrons are discarded.
If ' < 0.4, any jets are discarded.
If ' < 0.4, any muons are discarded.

In many typical ATLAS analyses, the jet-muon overlap removal (jets and muons are used as reference
and target object, respectively) is performed. However, in this analysis, this overlap removal is not used to
improve the reconstruction efficiency of the sub-leading muons.
For an event with electrons in the final state, as described in Section 5, one electron and two electrons
channels are defined. With the same analogy, one muon channel can be defined. However there is asignificant disadvantage in one muon channel. Due to the lack of sub-leading muon, its energy deposit can
not be handled and ,R and #R mass reconstructions become inaccurate. It is mainly noticeable when the
sub-leading muon is generated close to the large-' jet, resulting in a significant loss of sensitivity in phasespace where #R / ,R is small.

46

4.10 Missing Transverse Energy (K Tmiss )Since the LHC is a proton-proton collision experiment, only transverse energy is conserved to be zero.
Longitudinal energy is not conserved because the energies of the quarks and gluons in the protons are
not determined. Therefore, if there is a bias in the reconstructed energy distribution in the G-H plane, it isinterpreted as an invisible particle, like a neutrino, flying in the opposite direction of the bias, which can’t
be observed by detector. Hence, by using the vector sum of the reconstructed object’s energy, the missing
transverse energy (⇢ Tmiss ) is defined as follows.
’
’
’
’
’
jet
`
W
⇢ Tmiss =
⇢T
⇢ Te
⇢T
⇢T
⇢ Tsoft termÕ jet ÕÕ `
Õ W
where ⇢ T , ⇢ Te , ⇢ T and ⇢ T are the transverse energy obtained from the vector sum of reconstructedÕ
jets, electrons, muons, and photons, respectively. The soft term, ⇢ Tsoft term , is defined as the vector sum of
tracks derived from the primary vertex, but not used for other object reconstructions [105].

Among the components of the ⇢ Tmiss , hard terms have their own dedicated energy calibration system, so it is
only necessary to estimate the uncertainties derived from the soft term. These uncertainties are estimatedby decomposing the soft term into two components, one perpendicular to the hard term and the otherparallel to the hard term, and comparing the data and MC.

4.11 Large radius jet
The reconstruction of hadronically-decaying heavy particles often form a large radius jet (large-' jet). It
means that it is possible to reconstruct most of the decay particles derived from a heavy particle as a single
jet, which is often used in new particle searches.
The large-' jets are reconstructed by combining calibrated small-' jets by using the anti-: C algorithm witha radius parameter of 1.0 [106]. These large-' jets are trimmed by discarding any constituent small-' jets
which have less than 5% of a large-' jet’s ? T .
The largest advantage of combining small-' jets to form large-' jets is that large-' jets with small masses
can be used for analysis. Since large-' jets are used for the purpose of reconstructing decay products from
#R , this helps in the search for signals with small #R masses. Also, by using calibrated small-R jets, there
is no need to consider additional systematic uncertainty for the large-' jets.

47

5 Event selection
In this sectionpevent level criteria to define signal regions are discussed. These criteria are optimized tomaximize (/ ⌫, where ( and ⌫ indicate the number of signal and background events, for a benchmark
signal mass point for each signal region. The benchmark mass point is selected from the mass points not
excluded in the previous analysis. It is confirmed that the optimization does not depend significantly on thesignal mass point used as a benchmark.
In the signal events, very high-? T lepton and right-handed neutrino #R from ,R decay are produced
back-to-back in the G-H plane. In this topology, the angular distance between two quarks from #R decay isgetting small depending on ", and they form a single large-' jet in the detector level reconstruction. In
this analysis, at least two quarks of #R origin can not be separated and are components of the large-' jet.
For higher " signals, the large-' jet geometrically overlaps with the lepton from the #R decay.
In the muon channel, this second muon can be identified even for very high " signals, since muon-jet
overlap removal and any isolation requirements for sub-leading muon are deactivated. Signal region isdefined by requiring two muons in an event (SR2mu).
On the other hand, electrons are reconstructed using calorimeter in the similar way as jets, so the electronfrom #R decay is indistinguishable from jets depending on the mass difference between ,R and #R .
Therefore, signal regions are defined according to the number of electrons in an event (SR1e and SR2e has
exactly one and two reconstructed electron, respectively).
The final discriminant is the ,R mass reconstructed with the large-R jet and the leading lepton (< ✓ ) for
SR1e, and the large-R jet and two leptons (< ✓✓ ) for SR2e and SR2mu. Every signal regions are required
to have ,R mass greater than 3 TeV and regions with ,R mass less than 3 TeV are used as control orvalidation regions. More details of region definitions for control and validation regions can be found in
Section 6.
In this analysis, following seven background processes are considered: ,+jets, QCD multi-jet, W+jets,/+jets, C C¯, single-top and di-boson. Other minor processes account for less than 1 % and they are negligibly
small.

5.1 Preselection
Number of large-X jets
Exactly one large-' jet in an event is required. As shown in Figure 5.1(a), 5.2(a) and 5.3(a), about
90 % of the signal events have only one large-' jet. Especially in one electron channel, limiting thenumber of objects in an event has the advantage to ensure that the kinematics of the QCD multi-jet
can be well modeled by using the leading order MC samples except for its normalization.

48

Table 5.1: Definition of the signal regions.

Variable

SR1e

SR2e

Number of large-' jets

SR2mu

1

Number of electrons

1

2

0

Number of muons

0

0

2

Number of additional leptons

0

Number of 1-tagged jets

0

Leading lepton ? T> 200 GeV

Leading lepton identification

LHTight

Tight

Leading lepton isolation

FCHighPtCaloOnly

FCTight

Sub-leading lepton ? T

N/A> 28 GeV⇢ Tmiss> 26 GeV< 200 GeV

N/A

cos\

> 0.7

N/A

[ between large-' jet and electron

< 2.0

N/A

q between large-' jet and leading lepton> 2.0

Di-lepton ? T

N/ADi-lepton mass

N/A

,R mass> 200 GeV
> 200 GeV
> 3 TeV

Leading lepton selection
The lepton from ,R decay, which is called the leading lepton, is highly boosted and well isolated.
Since the target ,R mass is TeV scale, similar ? T with a large-' jet can be expected for the leading
lepton. Thus, same ? T threshold with large-' jet of 200 GeV is used. The ? T distribution for each
SR is shown in Figure 5.1(b), 5.2(b) and 5.3(b). In addition, since the leading lepton is found in aclean environment, the tighter identification and isolation shown in Section 4.6 and 4.7 are imposed.
5 between the leading lepton and large-X jet
Since the mass of ,R is assumed to be heavy, the momentum of the ,R is small and the leading
electron and the large-' jet from a ,R decay is produced back-to-back in the G-H plane. To enhancesuch topology, q > 2.0 is applied as shown in Figure 5.1(c), 5.2(c) and 5.3(c).
Number of b-tagged jets
Most of the C C¯ and single top background events have at least one 1-tagged jet as shown in Figure 5.1(d),5.2(d) and 5.3(d). To suppress them, zero 1-tagged jet in an event is required. Especially in two
lepton channels, the number of C C¯ can be reduced by a factor of 10, allowing it to be treated as aminor background.

49

5.2 Definition of one electron signal region (SR1e)
SR1e is introduced to improve the sensitivity in the largest " phase space. It requires exactly one
reconstructed electron from ,R decay and one large-' jet reconstructed from the entire decay products
0of the #R (#R ! 4@@ ! ). The large-' jet mass is expected to peak around the #R mass. The signal
region is optimized for the signal events at the benchmark mass point (<(,R ), <(#R )) = (5 TeV, 50 GeV)
against the SM background events.
( between the electron and the large-X jet
In terms of the suppression of QCD multi-jet and W+jets events, [ = |[4 [ | < 2.0 is applied.
The background events produced in a C-channel diagram with a large ,R mass tend to have a large[. On the other hand, the most of the on-shell ,R signals are generated in B-channel process andthey have smaller [ as shown Figure 5.5(a). With this criterion, QCD multi-jet and W+jets events
can be reduced by a factor of 4.
Missing transverse energy (K Tmiss )While signal events ideally have zero ⇢ Tmiss , some background processes, in particular ,+jets, C C¯ andsingle top, have real ⇢ Tmiss from neutrinos. The ⇢ Tmiss upper cut can reduce a part of them as shownin Figure 5.5(b); the ⇢ Tmiss is required to be smaller than 200 GeV. Furthermore, ⇢ Tmiss is used todefine the control and validation regions for background estimation described in Section 6.1.
Decay angle by assuming ] ! e. decay (cos ))Due to the upper cut on the ⇢ Tmiss and leading lepton ? T , the ,+jets events are strongly biased tohave a large cos \ where \ is the decay angle of the electron from , ! boson decay in the rest frameof the , ! boson. The , ! boson rest frame is computed from ⇢ Tmiss and the leading electron by
assuming that the , ! boson mass is 80.4 GeV and ⇢ Tmiss is derived only from a neutrino by solving
the following equations for ? a,z .
q⇢ Tmiss =? 2a,G + ? 2a,H
2
",

⇢a

= (⇢ 4 + ⇢ a ) 2 ( ?Æ4 + ?Æa ) 2q=? 2a,G + ? 2a,H + ? 2a,I

The ? a,z can have an imaginary value. In that case, the imaginary part is discarded and the only
real part is used for the cos\ calculation. When two real different solutions are available, the lowest
solution is selected. To enhance the signal events, as shown in Figure 5.5(c), cos\ > 0.7 is applied.
The definition of SR1e is summarized in Table 5.1. The mass distribution is shown in Figure 5.5(d). After
applying all of the selections above, the number of background in thepsignal region is found to be 12.7±3.2,
while the signal is 25.8±5.1 at the pre-fit level, corresponding to (/ ⌫ = 7.1 for 139 fb 1 .
The most dominant background processes in the signal region are , (! 4a)+jets, QCD multi-jet andW+jets events shown in Figure 5.4.

50

@¯

6

4

@

,

(a) , (! 4a)+jets

@

@

a¯4

@

6

6

W

@

@
(b) QCD multi-jet

6@(c) W+jets

Figure 5.4: Feynman diagrams of dominant backgrounds in SR1e. The red and green colored particles arereconstructed as electrons and large-' jets, respectively.

5.3 Definition of two electron signal region (SR2e)
At the intermediate " phase space, a second electron can be identified close to the large-' jet as shown in
Figure 5.9(b). Sub-leading electron ? T distribution can be found in Figure 5.9(a). By requiring it, smaller
background events are expected than SR1e. SR2e is optimized to maximize the sensitivity for the signal
events at the benchmark mass point (<(,R ), <(#R )) = (5 TeV, 500 GeV) against the SM background
events. Events with exactly two electrons and one large-' jet in an event are selected.
Di-electron mass
The two electrons’ invariant mass peaks around / boson mass as shown in Figure 5.6(a). Di-electronmass greater than 200 GeV is required. This cut decreases the /+jets yields by a factor of 100.
K Tmiss
For further reduction of ,+jets and C C¯ events, ⇢ Tmiss < 200 GeV is applied as shown in Figure 5.6(b).
The definition of SR2e is summarized in Table 5.1. The mass distribution is shown in Figure 5.6(c). After
applying all of the selections above, the number of background in the signal
p region is found to be 13.3 ± 3.6,
while the signal is 25.8 ± 5.1 at the pre-fit level, corresponding to (/ ⌫ = 7.1 for 139 fb 1 .

The most dominant background process in the signal region is the / (! 44)+jets shown in Figure 5.7(a).
The contributions from QCD multi-jet and W+jets processes are negligibly small.

5.4 Definition of two muon signal region (SR2mu)
SR2mu is optimized to maximize the sensitivity for the signal events at the benchmark mass point (<(,R ),<(#R )) = (5 TeV, 500 GeV) against the SM background events. Events with exactly two muons and one
large-' jet in an event are selected. Sub-leading muon ? T and ' between the large-' jet distributions areshown in Figure 5.9(c) and 5.9(d), respectively. Sub-leading muon can be identified close to the large-'
jet.

51

Di-muon mass
The two muons’ invariant mass peaks around / boson mass as shown in Figure 5.8(a). Thus, di-muon
mass greater than 200 GeV is required as well as SR2e. This cut decreases the /+jets yields by afactor of 100.
Di-muon p T
To suppress the contribution from top-quark related background as shown in Figure 5.8(b). di-muon? T greater than 200 GeV cut is also applied. Due to the high ? T muon from ,R decay, its resolution
getting worse. To keep the signal efficiency, any ⇢ Tmiss cut is not employed.
The definition of SR2mu is summarized in Table 5.1. The mass distribution is shown in Figure 5.8(c).
After applying all of the selections above, the number of background in the psignal region is found to be
5.3±2.5, while the signal is 22.6±4.3 at the pre-fit level, corresponding to (/ ⌫ = 9.2 for 139 fb 1 .
The most dominant process in the signal region is the / (! ``)+jets shown in Figure 5.7(b).
@¯

6

@¯

4

`

/

/

@

6

`+

@

4+
(a) / (! 44)+jets(b) / (! ``)+jets

Figure 5.7: Feynman diagrams of dominant backgrounds in SR2e and SR2mu. The red, blue and green coloredparticles are reconstructed as electrons, muons and large-' jets, respectively.

52

9Single-toptt

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Figure 5.1: Distributions of variables used in the preselection in one electron channel. The red histograms represent
the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 50 GeV). Overflowed and underflowed eventsare merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show the value and directionof a certain cut to define SR1e, respectively. All the cuts enumerated in Table 5.1 except a variable shown in each
sub-label are applied. (a) shows the large-' jet multiplicity distribution. (b) shows the electron ? T distribution. (c)shows the q between large-' jet and electron distribution. (d) shows the 1-tagged jet multiplicity distribution. The
number of ,+jets, QCD multi-jet, W+jets and /+jets yields are normalized with normalization factors shown in thelegend which are obtained by dedicated CRs. The ratios of data over MC and statistical uncertainties are displayed as
black points and red hashed histograms in the bottom panels, respectively.

53

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Figure 5.2: Distributions of variables used in the preselection in two electron channel. The red histograms represent
the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 500 GeV). Overflowed and underflowed
events are merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show the value anddirection of a certain cut to define SR2e, respectively. Every cuts enumerated in Table 5.1 except a variable shown ineach sub-label are applied. (a) shows the large-' jet multiplicity distribution. (b) shows the leading electron ? T
distribution. (c) shows the q between large-' jet and leading electron distribution. (d) shows the 1-tagged jet
multiplicity distribution. The number of /+jets yield is normalized with a normalization factor shown in the legend
which is obtained by a dedicated CR. The ratios of data over MC and statistical uncertainties are displayed as black
points and red hashed histograms in the bottom panels, respectively.

54

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Figure 5.3: Distributions of variables used in the preselection in two muon channel. The red histograms represent
the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 500 GeV). Overflowed and underflowed
events are merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show the value
and direction of a certain cut to define SR2mu, respectively. Every cuts enumerated in Table 5.1 except a variableshown in each sub-label are applied. (a) shows the large-' jet multiplicity distribution. (b) shows the leading muon
? T distribution. (c) shows the q between large-' jet and leading muon distribution. (d) shows the 1-tagged jet
multiplicity distribution. The number of /+jets yield is normalized with a normalization factor shown in the legend
which is obtained by a dedicated CR. The ratios of data over MC and statistical uncertainties are displayed as black
points and red hashed histograms in the bottom panels, respectively.

55

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6

10

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107

5data / Model1010(d) < 4

Figure 5.5: Distributions of variables used in the additional selection in one electron channel. The red histograms
represent the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 50 GeV). Overflowed and underflowed
events are merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show the value anddirection of a certain cut to define SR1e, respectively. All cuts enumerated in Table 5.1 except a variable shownin each sub-label are applied. (a) shows the [ between large-' jet and electron distribution. (b) shows the ⇢ Tmiss
distribution. (c) shows the distribution of the electron helicity angle computed by assuming the standard model W
boson decay. Due to the relatively balanced electron ? T and ⇢ Tmiss , ,+jets, C C¯, diboson and single top backgroundhave a wide distribution. On the other hand, QCD multi-jet and /+jets backgrounds which have no ⇢ Tmiss in truthlevel mainly are biased in the large value side. (d) shows the distribution of invariant mass of a large-' jet andan electron which corresponds to ,R mass. The number of ,+jets, QCD multi-jet, W+jets and /+jets yields arenormalized with normalization factors shown in the legend which are obtained by dedicated CRs. The ratios of dataover MC and statistical uncertainties are displayed as black points and red hashed histograms in the bottom panels,
respectively.

56

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(c) < 44

Figure 5.6: Distributions of variables used in thee additional selection in two electron channel. The red histograms
represent the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 500 GeV). Overflowed andunderflowed events are merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show thevalue and direction of a certain cut to define SR2e, respectively. All cuts enumerated in Table 5.1 except a variableshown in each sub-label are applied. (a) shows the di-electron mass distribution. (b) shows the ⇢ Tmiss distribution.
(c) shows the distribution of invariant mass of a large-' jet and two electrons which corresponds to ,R mass. The
number /+jets yield is normalized with a normalization factor shown in the legend which is obtained by a dedicated
CR. The ratios of data over MC and statistical uncertainties are displayed as black points and red hashed histogramsin the bottom panels, respectively.

57

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Figure 5.8: Distributions of variables used in the additional selection in two muon channel. The red histograms
represent the shape of the reference signal events of (<(,R ), <(#R )) = (5 TeV, 500 GeV). Overflowed andunderflowed events are merged in the closest bin in each distribution. Blue vertical line and horizontal arrow show
the value and direction of a certain cut to define SR2mu, respectively. All cuts enumerated in Table 5.1 except avariable shown in each sub-label are applied. (a) shows the di-muon mass distribution. (b) shows the di-muon ? T
distribution. (c) shows the distribution of invariant mass of a large-' jet and two muons which corresponds to ,R
mass. The number of /+jets yield is normalized with a normalization factor which is obtained by a dedicated CR.
The ratios of data over MC and statistical uncertainties are displayed as black points and red histograms in the bottom
panels, respectively.

58

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Figure 5.9: Distributions of variables related to the sub-leading leptons. The red histograms represent the shapeof the reference signal events of (<(,R ), <(#R )) = (5 TeV, 500 GeV). Overflowed and underflowed events are
merged in the closest bin in each distribution. (a) shows the sub-leading electron ? T distribution. (b) shows the 'between large-' jet and sub-leading electron distribution. (c) shows the sub-leading muon ? T distribution. (d) shows
the ' between large-' jet and sub-leading muon distribution. The number of /+jets yield is normalized with anormalization factor which is obtained by a dedicated CR. The ratios of data over MC and statistical uncertainties are
displayed as black points and red histograms in the bottom panels, respectively.

59

5.5 Binning in signal regions
The signal sensitivities are improved by modifying the binning of the final discriminant observable of<(,R ) taking into account the ,R mass resolution of the signal events and the stability of the backgroundestimation. For both electron and muon final states, the expected exclusion limits are evaluated for thefollowing three different configurations.
A: 1-bin signal regions.
B: 2-bin signal regions with a fixed bin width of 1 TeV: [3,4] TeV and > 4 TeV.
C: 3-bin signal regions with a fixed bin width of 1 TeV: [3,4] TeV, (4,5] TeV and > 5 TeV.

105

Background104

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Events / 500 GeV

These configurations are visualized in Figure 5.10.

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7000
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Figure 5.10: The schematic views of configuration A, B and C are visualized in (a), (b) and (c), respectively. The
black dashed lines and arrows indicate the thresholds and widths of bins. Blue and red histograms show the ,R mass
distributions of background and signal, respectively. The signal with the mass point of (<(,R ), <(#R )) = (5 TeV,
50 GeV) is used as a benchmark mass point. The all background distributions are given by one electron channel.

The expected limits with each configuration are visualized in Figure 5.11. The differences between
configurations A to B are large, about 700 GeV and 500 GeV gain in <(,R ) is expected for electron andmuon channel, respectively. On the other hand, the difference between configurations B to C is relatively
small, about a few hundreds GeV. Especially in the muon channel, the maximum gain is only about
100 GeV. The improvement in the region with the smallest #R in the electron channel is the largest. Thisis due to the large reduction in the number of background events in the heaviest ,R mass region in the one
electron channel.
Seemingly, configuration C appears to be the best, but as the number of bins is increased, the number ofbackground events becomes too small in the bin with the heaviest <(,R ), making it difficult to performbackground estimation. Especially in one electron channel, the number of ,+jets MC sample in above
5 TeV is expected to be exactly zero and that requires smoothing or other processing of the <(,R )distribution. To avoid such a processing in this analysis, the 2-bin signal region with a fixed bin width of
1 TeV (Configuration B) is chosen for all signal regions.

60s = 13 TeV, 139 fb-1, All limits at 95% CL

Muon channelm(N ) [GeV]Expected Limit (A)Majorana scenario

Expected Limit (B)4000m(W R) = m(NR)

Expected Limit (A)4500
Majorana scenario

Expected Limit (B)4000m(W R) = m(NR)

Expected Limit (C)3500

s = 13 TeV, 139 fb-1, All limits at 95% CL

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3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000m(W ) [GeV]RR(a) Electron(b) Muon

Figure 5.11: (a) The expected 95 % CL upper limits for electron channel. (b) The expected 95 % CL upper limits formuon channel. Only statistical uncertainties are considered in every plots. The expected exclusions with configuration(A), (B) and (C) are shown as red, green and blue lines, respectively.

61

6 Background estimation
In this section, the methods of background estimation are described. The number of events for the major
background processes in SRs are estimated by applying correction factors to the simulated events. These
correction factors are obtained by adjusting the number of background events in the simulation to those in
the observed data in specific control regions (CRs). The correction factor is called a normalization factor(NF) and this method is called the “semi-data driven method”:
post-fit#SR, MC =#CR, data
pre-fit#CR, MC

pre-fit⇥ #SR, MC = #pre-fit⇥ #SR, MC .

Estimating background is assumed that the ratio of CR to SR is well modeled by the simulation. Each major
background has unique CRs and its NF is calculated individually while taking into account the impact
of systematic uncertainties, which are discussed in more details in Section 7.3. For minor backgroundprocesses, the number of events is estimated based only on MC.
In the following discussion, “pre-fit” and “post-fit” are defined as the state before and after the NFs are
multiplied by the major background events, respectively.
Validation regions (VRs) are also used for the purpose to test background event estimations. There arefollowing two types of VRs.
Extra VRs
For each major background, the assumption that the ratio of CR to SR is well modeled by the MC
must be checked. This is a so-called shape modeling check and the extra VRs are defined for thispurpose. NFs in extra VRs can be different from those obtained the CRs. Since extra VRs are set tohave completely orthogonal phase spaces with the SRs, the signal contamination is negligibly small.
Standard VRs
They are defined in regions between SRs and CRs and used for the purpose of confirming that the
NFs obtained in CRs work properly. The same NFs are applied in the standard VRs as SRs.
As introduced in Section 5, the names of the SRs are defined based on the number of leptons, i.e. SR1e,SR2e, and SR2mu. The names of CRs and standard VRs are also based on the number of leptons, lepton
flavor and the name of background process estimated in that region. The definitions of extra VRs follow
those of actual CRs/SRs. Therefore, their names depend on the target background process and which
region is mimicked.
The detail of background estimation method for SR1e, SR2e and SR2mu is explained in the following
sections. The schematic pictures of the all SRs, CRs and standard VRs are shown in Figure 6.1.

62

VR1e

CRW1e

VRW1e
[bin 1]SR1e[bin 2]SR1e[bin 1]0.7
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mee [GeV]mμμ [GeV](a) Regions relating ,+jets process

CRLow2eSR2e[bin 2]SR2e[bin 1]VR2e

200

CRLow2mu

VR2mu

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120
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m(WR) [TeV]234m(WR) [TeV](c) Regions relating / (! 44)+jets process(d) Regions relating / (! ``)+jets process

Figure 6.1: Schematic views of region definitions. (a) shows the regions relating for ,+jets estimation. (b) shows theregions relating QCD multi-jet estimation. (c) shows the regions relating / (! 44)+jets estimation. (d) shows theregions relating / (! ``)+jets estimation.

6.1 Background estimation method for SR1e
The dominant SM background processes in SR1e are ,+jets (40%), QCD multi-jet with a misidentified
electron (20%) and W+jets with an electron from photon conversion (20%). To estimate these backgroundcontributions, CRLow1e, CRW1e, CRFake1e and CRW1e are defined as shown in Figure 6.1(a), 6.1(b) andTable 6.1.
The QCD multi-jet and W+jets events in SR1e contain a high-? T fake electron and high-? T large-' jetproduced back-to-back in G-H plane, and there is no additional jet in the event. For this event topology,
the leading order di-jet and W+jets MC samples are relatively reliable except for the prediction of theircross-sections. So, not only for ,+jets but also for QCD multi-jet and W+jets, their contributions in SR1e
are estimated by the semi-data driven method using MC samples to predict their normalization factors.
The ,+jets normalization factor is mainly determined in CRW1e which has low-cos \ region [0.0, 0.7].
As shown in Figure 5.5(c), ,+jets occupancy is quite high in that region. Given the lower cos \, themomentum of the electron and neutrino from ,-boson decay is relatively balanced.

63

Table 6.1: Definitions of signal and control regions for one electron channel. The selection cuts to define CRs areshown with the underlines with respect to SR1e. The other cuts are the same as SR1e. The last column shows avariable for binning and the number of bins.
Variable

SR1e

CRLow1e

CRW1e

CRFake1eElectron isolation

FCHighPtCaloOnly

FCHighPtCaloOnly

FCHighPtCaloOnly

cos \Ambiguity,R mass in TeV

> 0.7
N/A
> 3.0

> 0.7
== 1
[1.0, 2.0]

[0.0, 0.7]
N/A
[1.0, 2.0]

FCLoose and not
FCHighPtCaloOnly
> 0.7
N/A
[1.0, 2.0]

Number of bins

2 in ,R mass

1

1

1

CRW1e
FCHighPtCaloOnly
> 0.7
> 1
[1.0, 2.0]
1

The QCD multi-jet contribution is mainly estimated in CRFake1e which requires the inverted electron
isolation criteria. A prompt electron from the ,// decay is well isolated. However a fake electron in the
QCD multi-jet events deposits its energy in wider calorimeter regions as shown in Figure 6.2(a). Thus,
the QCD multi-jet occupancy in CRFake1e is pretty high. On the other hand, most of the fake electrons
in W+jets events are electrons from the photon conversion. Thus, they satisfy the FCHighPtCaloOnly
isolation condition.
There are different properties in the associated tracks between a electron derived from the photon conversion
and a prompt electron. Utilizing them, CRW1e is introduced to estimate W+jets events. As shown in
Figure 6.2(b), the purity of W+jets is high in the bin with Ambiguity = 2. On the other hand, almost no
W+jets remain in the bin with Ambiguity = -1. CRW1e is defined to have Ambiguity != -1.
CRLow1e is introduced to give an additional constraint to the normalization factors and to reflect thefeatures of the most proximate regions with SR1e. CRLow1e is the exactly same phase space with CRW1e
except the requirement of electron Ambiguity == -1. This helps to disentangle W+jets from ,+jets andmakes it easy to estimate them independently.
Finally the obtained normalization factors are transferred to the high-<(,R ) regions assuming the MC
simulation of <(,R ) distribution is well modeled. To confirm it, a standard VR, VR1e, with intermediate
mass interval between SR1e and CRLow1e is defined. Also, VRW1e and VRFake1e are defined forverification of transfers of ,+jets and QCD multi-jet normalization factor to low- to high-mass regionswith high purity regions, respectively. The definitions of them are summarized in Table 6.2.
Table 6.2: Definitions of standard validation regions for one electron channel. The selection cuts to define VRs areshown with the underlines with respect to SR1e. The other cuts are the same as SR1e. The last column shows avariable for binning and the number of bins.
Variable

VR1e

VRW1e

VRFake1eElectron isolationcos \,R mass in TeV

FCHighPtCaloOnly> 0.7(2.0, 3.0]

FCHighPtCaloOnly[0.0, 0.7]
> 2.0

FCLoose and not FCHighPtCaloOnly
> 0.7
> 2.0

Number of bins

1

2 in ,R mass

2 in ,R mass

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Figure 6.2: Pre-fit distributions of variables to define CRFake1e and CRW1e. (a) shows the distribution of the
spreadness of energy deposition from the electron. (b) shows the Ambiguity of the electron. Blue vertical lines
and horizontal arrows in (a) and (b) indicate the value and direction of CRFake1e and CRW1e, respectively. The
number of ,+jets, QCD multi-jet, W+jets and /+jets yields are normalized with normalization factors which are
obtained by dedicated CRs. The ratio of data over MC and statistical uncertainties are displayed as black points andred histograms in the bottom panels, respectively.

6.1.1 Validation of ]+jets estimation with extra VRs
To check the ,+jets estimation along the cos \ and ,R mass distributions, extra VRs (VRWSR1e ,VRWCRLow1e and VRWCRW1e ) are defined as summarized in Table 6.3. They require the electron? T < 200 GeV and ⇢ Tmiss > 200 GeV (c.f. ? T > 200 GeV and ⇢ Tmiss < 200 GeV in SR1e). Since thecos \ calculation assumes the , ! 4a process and ⇢ Tmiss derived only from the neutrino, cos \ is biased
towards negative values in these regions as shown in Figure 6.3(a). The ? T requirement for electrons
in the object selection (? T > 25 GeV) reduces events with cos \ ' 1. For VRWSR1e and VRWCRLow1e ,1  cos \ < 0.7 is required, while 0.7  cos \ < 0.0 for VRWCRW1e . The invariant mass of a neutrino
and a large-' jet, < a, , is used for low- to high-mass extrapolation instead of the mass of an electron and alarge-' jet system. To increase the data statistics, the mass threshold between VRWCRLow1e and VRWSR1e
is set at 2 TeV. The contributions of QCD multi-jet and W+jets are negligible in these regions due to thelarge-⇢ Tmiss requirement. The purity of ,+jets in VRWSR1e is greater than 90%. The fit to these extra VRs
are performed just to confirm the ,+jets estimation strategy works well, and they are not involved in theactual CRs + SRs fits.

6.1.2 Validation of QCD multi-jet estimation with extra VRs
To check the QCD multi-jet estimation strategy assuming the simulated lepton isolation efficiency for the fakeelectrons agrees with the data, extra VRs are defined: VRFakeSR1e , VRFakeCRLow1e and VRFakeCRFake1e ,as summarized in Table 6.4. The electron is required to satisfy the LHMedium identification but failingthe LHTight to ensure an orthogonality with SR1e. To increase the data statistics, the mass threshold
between VRFakeCRFake1e and VRFakeSR1e is set at 2 TeV. As shown in Figure 6.3(b), the contributions of65

Table 6.3: Definitions of extra validation regions for the ,+jets estimation. The other cuts are the same as SR1e.
The last column indicates the number bins and variable for binning.
Variable

VRWSR1e

VRWCRLow1e

VRWCRW1eSR1eElectron ? T in GeV⇢ Tmiss in GeV
cos \,R mass in TeV

< 200
> 200
< 0.7
> 2.0

< 200
> 200
< 0.7
[1.0, 2.0]

< 200
> 200
[ 0.7, 0.0)
[1.0, 2.0]

> 200
< 200
> 0.7
> 3.0

2 in < a, mass1

1

2 in ,R mass

Number of bins,+jets and W+jets are negligible in these regions due to the inverted electron identification. The purity of
QCD multi-jet is about 92 % in VRFakeSR1e . The fit to these extra VRs are performed just to confirm theestimation strategy works well, and they are not involved in the actual CRs + SRs fits.
Table 6.4: Definitions of extra validation regions for QCD multi-jet estimation. The other cuts are the same as SR1e.
The last column indicates the number of bins and variable for binning.
Variable

VRFakeSR1eVRFakeCRLow1e

VRFakeCRFake1e

Electron identification

Medium andnot Tight

Medium andnot Tight

Electron isolation

FCHighPtCaloOnly

FCHighPtCaloOnly,R mass in TeV> 2.0[1.0, 2.0]

Medium andnot Tight
FCLoose and not
FCHighPtCaloOnly[1.0, 2.0]

Number of bins

2 in ,R mass

1

1

SR1e
Tight
FCHighPtCaloOnly> 3.0
2 in ,R mass

6.1.3 Validation of $+jets estimation with extra VRs
While the W+jets normalization factor is well determined in CRW1e, the distribution of ,R mass relays on
MC simulation, thus the following points need to be verified. The fits to following extra VRs are performed
just to confirm the W+jets estimation strategy works fine, and they are not involved in the actual CRs + SRs
fits.
6.1.3.1 Data to MC agreement in high-]R mass
To validate the reliability of the W+jets MC event shapes, following extra VRs with a photon instead of anelectron are defined: SR1ph, VR1ph, CRLow1ph and CRFake1ph as summarized in Table 6.5. ,+jets
occupancy is negligibly small in every regions because it requires the number of electron exactly zero.
Therefore any regions to control ,+jets are not needed. The W+jets accounts for about 54 % in SR1ph.
The sub-dominant background process is QCD multi-jet which is normalized in CRFake1ph.
6.1.3.2 Photon to electron fake factor
In case the photon-to-electron fake factor depending on a photon ? T and [ in simulation does not agreewith data, it gives mis-modeling of ,R mass distribution in SR1e, even if the < W, modeling of the W+jets

66

7

10

6

s = 13 TeV, 139 fb-1

10

γ +jets × 1.00

dijet × 1.00

Single-top

Z+jets × 1.00

Di-bosontt

W+jets × 1.00

SignalEvents / 0.01

Events / 0.05

8

10

107
6

10

104

104

tt

Di-bosonZ+jets × 1.00

W+jets × 1.00

γ +jets × 0.12

dijet × 0.81

Signal

3

10

3

10

102

102

10

10

1

1

10−1

10−1

10−2

10−2

−3

−3

10

10
−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1
cos( θ)data / Model

−0.8

1.5

20

1

1
0.5

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

0
0

1
cos(θ)

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16
0.18
0.2
topoetcone20 / pt

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16
0.18
0.2
topoetcone20 / pt

1.5

0.5
0
−1

Single-top

Data

5

10

2− 1

s = 13 TeV, 139 fb-1

10

Data

5

data / Model810(a) cos \(b) Energy spreadness of the electron

Figure 6.3: Pre-fit distributions of variables to define VRWCRLow1e and VRFakeCRLow1e . (a) shows the distribution of
the electron decay angle computed by assuming the standard model , boson decay. As show in Table 4.4, since theelectron requires ? T greater than 25 GeV, the number of events with cos \ ' 1 is small. (b) shows the distributionof the spreadness of energy deposition from the electron. Blue vertical lines and horizontal arrows in (a) and (b)indicate the value and direction of VRWCRLow1e and VRFakeCRLow1e , respectively. The number of ,+jets and QCD
multi-jet yields are normalized. These normalization factors are obtained by dedicated CRs. Red hashed histograms
shown in the bottom panels correspond only statistical uncertainties.
Table 6.5: Definitions of extra validating regions for W+jets estimation. Other cuts are the same as SR1e. The lastcolumn indicates the number of bins and variable for binning.
Variable

SR1ph

VR1ph

CRLow1ph

CRFake1phSR1eFCHighPtCaloOnly
2 in ,R mass

Number of (e, W)(0, 1)(0, 1)(0, 1)

Photon isolation

FCTightCaloOnly

FCTightCaloOnly

FCTightCaloOnly,R mass in TeV> 3.0(2.0, 3.0]

[1.0, 2.0](0, 1)FCLoose and not
FCTightCaloOnly[1.0, 2.0]

Number of bins

2 in <W, mass

1

1

1

(1, N/A)> 3.0

MC is good. To confirm the photon-to-electron fake factor is well modeled and does not affect the ,Rreconstruction, following two set of extra VRs are employed.
• Check the MC to data agreement in regions with optimized cos \ and isolation cuts to enhance W+jets
events with [ to be from 2.0 to 3.0 for ensuring an orthogonality with actual SR/CR. VRWSR1e ,VRWCRLow1e , VRWCRW1e and VRWCRFake1e are defined as summarized in Table 6.6. The occupancy
of W+jets in VRWSR1e is about 42 % and it is the dominant background process.
• Check the MC to data agreement in the exactly same regions with above optimized phase spaces
except a requirement of a photon instead of an electron. VRWSR1ph , VRWCRFake1ph and VRWCRFake1phare defined as summarized in Table 6.7. ,+jets occupancy is negligibly small in every regions
because it require the number of electron exactly zero. Therefore there is no region to control ,+jets
yields. The occupancy of W+jets in VRWSR1ph is about 63 % and it is enough to check the estimation
strategy.
In case of similar MC to data agreements even in high-,R mass regions are observed, it can be concluded

67

that photon to electron fake factor is well modeled by MC.
Table 6.6: Definitions of extra validation regions for the W+jets estimation. Other cuts are the same as SR1e. The lastcolumn indicates the number of bins and variable for binning.
Variable

VRWSR1e

VRWCRLow1e

VRWCRW1eVRWCRFake1e

SR1e[2.0, 3.0]

[2.0, 3.0]

[2.0, 3.0]

Electron isolation

FCHighPtCaloOnly

FCHighPtCaloOnly

FCHighPtCaloOnly

cos \,R mass in TeV

> 0.7
> 2.0

> 0.7
[1.0, 2.0]

[0.0, 0.7]
[1.0, 2.0]

[2.0, 3.0]
FCLoose and not
FCHighPtCaloOnly> 0.7[1.0, 2.0]

Number of bins

2 in <W, mass

1

1

1

[4;,

< 2.0
FCHighPtCaloOnly
> 0.7
> 3.0
2 in ,R mass

Table 6.7: Definitions of extra validation regions for the W+jets estimation. Other cuts are the same as SR1e. The lastcolumn indicates the number of bins and variable for binning.
Variable

VRWSR1ph

VRWCRLow1ph

VRWCRFake1ph

SR1e

Number of (e, W)(0, 1)(0, 1)(1, N/A)

Photon isolation

FCTightCaloOnnly

FCTightCaloOnly

FCHighPtCaloOnly,R mass in TeV> 2.0[1.0, 2.0](0, 1)FCLoose and not
FCTightCaloOnly[1.0, 2.0]

Number of bins

2 in ,R mass1

1

2 in ,R mass

> 3.0

6.2 Background estimation method for SR2e
The dominant SM background in SR2e is / (! 44)+jets (85%). The normalization factor for /+jets
is treated as a free parameter and obtained from the data in CRLow2e. The other backgrounds are
estimated by the MC simulation. To check the extrapolation from low- to high-,R mass region, a standard
VR named VR2e between CRLow2e and SR2e, is prepared. The estimated normalization factor for/+jets in CRLow2e is also used in SR1e and VR1e, since ? T regimes of truth / boson for them are
similar. The extra VRs, namely VRZSR2e and VRZCRLow2e , are prepared by requiring di-electron mass
120 GeV < < 41,42 < 200 GeV to verify the extrapolation from low- to high-,R mass with little signal
contamination. The purity of /+jets in VRZSR2e is about 98 % as shown in Figure 5.6(a). The studies inthese extra VRs are found in Section 8.4. The definitions of all regions related to two electron channels are
summarized in Table 6.8.
Table 6.8: Definitions of regions for the two electron channel. The selection cuts to define CR/VRs are shown withthe underlines with respect to SR2e. The last column indicates the number of bins and variable for binning.
Variable

SR2e

VR2e

CRLow2eVRZSR2e

VRZCRLow2e

Di-electron mass in GeV,R mass in TeV

> 200
> 3.0

> 200
(2.0, 3.0]

> 200
[1.0, 2.0][120, 200]
> 2.0[120, 200]
[1.0, 2.0]

2 in ,R mass1

1

2 in ,R mass

1

Number of bins

68

6.3 Background estimation method for SR2mu
The dominant SM background in SR2mu is / (! ``)+jets (80%). The normalization factor for /+jets
is treated as a free parameter and obtained from the data in CRLow2mu. The other backgrounds are
estimated by the MC simulation. To check the extrapolation from low- to high-,R mass region, a standard
VR named VR2mu between CRLow2mu and SR2mu, is prepared. The extra VRs, namely VRZSR2mu
and VRZCRLow2mu , are prepared to verify the extrapolation from low- to high-,R mass with little signal
contamination as shown in Figure 5.8(a). The studies in these extra VRs are found in Section 8.4. The
definitions of all regions related to two muon channels are summarized in Table 6.9.
Table 6.9: Definitions of regions for two muon channel. The selection cuts to define CR/VRs are shown with theunderlines with respect to SR2mu. The last column indicates the number of bins variable for binning.
Variable

SR2mu

VR2mu

CRLow2mu

VRZSR2mu

VRZCRLow2mu

Di-muon mass in GeV,R mass in TeV

> 200
> 3.0

> 200
(2.0, 3.0]

> 200
[1.0, 2.0][120, 200]
>2.0[120, 200]
[1.0, 2.0]

2 in ,R mass1

1

2 in ,R mass

1

Number of bins

6.4 Summary of background estimation method
The fractions of the background components in CRs and standard VRs and SRs are visualized in Figure 6.4
and 6.5.
In this section, various fit configurations described above are summarized. Two different “main” fits are
performed to search for signals in electron channel and muon channel. In addition, seven independent fitswith extra VRs are performed to verify estimation strategies. They are put together in Table 6.10.
In the SR+CR fit for the electron channel, the floating normalization factors for ,+jets, QCD multi-jet andW+jets are applied to only regions with the suffix ”1e”. The /+jets normalization is floated in both regionswith the suffix “1e” and “2e”, and treated as fully correlated between them. In the muon channel, only the/+jets normalization is treated as free. The separate fits to electron and muon channels are performed, andthey are not combined for the final result. For most extra VR studies, thanks to high purity, it is enough tofloat the target background process and give a fixed cross-section uncertainty, i.e. only ,+jets is floated in,+jets extra VRs.
The normalization factors to be considered in each fit are put together in Table 6.11.

69

Table 6.10: Summary of the background estimation strategies. There are 9 different fit configurations. Two of themare performed to derive final results. The other fits are performed independently to validate the strategies.
Fit configuration

Normalization factors obtained inNormalization factors applied to

Fit result inElectron SR+CR fit

CRLow1e, CRW1e, CRFake1e and CRLow2e

SR1e, VR1e, SR2e and VR2e

Section 9.1.1

Extra VRs for , +jets

VRWCRLow1e and VRWCRW1e

VRWSR1eSection 8.1

VRFakeCRLow1e and VRFakeCRFake1e

VRFakeSR1eSection 8.2

CRLow1ph and CRFake1ph
VRWCRLow1e , VRWCRW1e and VRWCRFake1e
VRWCRLow1ph and VRWCRFake1ph

SR1ph and VR1ph
VRWSR1e
VRWSR1phSection 8.3.1
Section 8.3.2
Section 8.3.2

Extra VRs for / (! 44)+jets

VRZCRLow2e

VRZSR2eSection 8.4.1

Muon SR+CR fit

CRLow2mu

SR2mu and VR2mu

Section 9.1.2

Extra VRs for / (! ``)+jets

VRZCRLow2mu

VRZSR2mu

Section 8.4.2

Extra VRs for QCD multi-jet
Extra VRs for W+jets

Table 6.11: The normalization factors considered in each fit, and the regions for which the given normalization factor
is applied.
Fit configuration

Normalization factor

To be applied toElectron SR+CR fit,+jetsQCD multi-jet
W+jets/+jetsCRLow1e, CRW1e, VRW1e, CRFake1e, VR1e and SR1eCRLow1e, CRW1e, CRFake1e, VRFake1e, VR1e and SR1eCRLow1e, CRW1e, CRFake1e, VR1e and SR1eCRLow1e, CRW1e, CRFake1e, VR1e, SR1e, CRLow2e and SR2eExtra VRs for ,+jets,+jetsVRWCRLow1e , VRWCRW1e and VRWSR1e

QCD multi-jet

VRFakeCRLow1e , VRFakeCRFake1e and VRFakeSR1eW+jetsQCD multi-jet

CRLow1ph, CRFake1ph and SR1ph

W+jetsQCD multi-jet,+jetsVRWCRLow1e , VRWCRW1e , VRWCRFake1e and VRWSR1e

W+jetsQCD multi-jet

VRWCRFake1ph , VRWCRFake1ph and VRWSR1ph/+jetsVRZCRLow2e and VRZSR2e

Muon SR+CR fit/+jetsCRLow2mu, VR2mu and SR2mu

Extra VRs for / (! ``)+jets/+jetsVRZCRLow2mu and VRZSR2mu

Extra VRs for QCD multi-jet

Extra VRs for W+jets

Extra VRs for / (! 44)+jets

70Fraction [ % ]s = 13 TeV, 139 fb-1
Di-bosonSingle-top
W+jetsγ +jets

140
120

QCD multi-jet
tt
Z+jets

100
80
60
40
20
0

CRLow1e

CRγ 1e

VR1e

SR1e (1st bin)

SR1e (2nd bin)(a) CRLow1e, CRW1e, VR1e, SR1e

Fraction [ % ]s = 13 TeV, 139 fb-1
Di-bosonSingle-top
W+jetsγ +jets

140
120

QCD multi-jet
tt
Z+jets

100
80
60
40
20
0

CRW1e

VRW1e (1st bin)

VRW1e (2nd bin)(b) CRW1e, VRW1e

Fraction [ % ]s = 13 TeV, 139 fb-1
Di-bosonSingle-top
W+jetsγ +jets

140
120

QCD multi-jet
tt
Z+jets

100
80
60
40
20
0

CRFake1e

VRFake1e (1st bin)

VRFake1e (2nd bin)(c) CRFake1e, VRFake1e

Figure 6.4: Breakdown of the pre-fit SM components in each region for one electron channel.

71

Fraction [ % ]s = 13 TeV, 139 fb-1
Di-bosonSingle-top
W+jetsγ +jets

140
120

QCD multi-jet
tt
Z+jets

100
80
60
40
20
0

CRLow2eVR2eSR2e (1st bin)SR2e (2nd bin)(a) CRLow2e, VR2e, SR2e

Fraction [ % ]s = 13 TeV, 139 fb-1
Di-bosonSingle-top
W+jetsγ +jets

140
120

QCD multi-jet
tt
Z+jets

100
80
60
40
20
0

CRLow2mu

VR2mu

SR2mu (1st bin)

SR2mu (2nd bin)(b) CRLow2mu, VR2mu, SR2mu

Figure 6.5: Breakdown of the pre-fit SM components in each region for two lepton channels.

72

7 Statistical analysis
The profile Log Likelihood Ratio (LLR) approach is used to estimate the number of background in SRs(background only fit), determine an upper bound on BSM events (model-independent fit) and exclude
a certain signal hypothesis (model-dependent fit) [107]. In the fitting procedure, the maximization of a
LLR is executed taking into account the effects of systematic uncertainties. The purpose of each fitting
configuration is described below.
Background only fit
The purpose is to estimate the backgrounds in SRs and VRs without any signal assumptions.
Only CRs are used to constrain the normalization and nuisance parameters. Any potential signal
contamination is assumed to be neglected in all regions. Results can be found in Section 9.1.
Model-independent fit
The purpose is to set model-independent limits on the number of BSM events in a certain SR. BothCRs and a SR are used in the fit. The signal contribution is considered only in the SR. Results canbe found in Section 9.2.
Model-dependent fit
The purpose is to set limits on a specific model of BSM physics. Both CRs and SRs are used in thefit. The potential signal contribution is also taken into account in all regions. Results can be found in
Section 9.3.

7.1 Likelihood function
A likelihood function is defined by Poisson terms which describe the statistical fluctuations of data
convoluted with Gaussian terms which describe systematic uncertainties:÷÷!(n| -, s, b, )) =%8 ⇥⌧ (\ 9 ),8 2 {Regions}

9 2 {Systematic sources}%8 = %(=8 |_8 ) =_8=8 _8
4 ,=8 !

where %8 is a poisson probability distribution for a certain region 8. ⌧ (\ 9 ) is a gaussian probability
distribution of a certain systematic uncertainty 9. Each systematic uncertainty \ 9 is usually given in unitsof the standard deviation. Each poisson probability density distribution %8 can be decomposed with thenumber of observed events =8 and the expected number of events _ 8 :where _8 is given by:_8 ( -, B8 , b, )) = B8 ()) · ` B +’: 2 {Background with NF}

and each parameter is defined below.

73

1 8,: ()) · ` : +’; 2 {Background without NF}

1 8,; ()),

• 8 corresponds to a region (SR1e, CRW1e, CRFake1e etc.) and bin number (first and second bin in
SR1e etc.).
• : corresponds to a background component with a normalization factor ` : (,+jets, QCD multi-jet,
W+jets, /+jets for electron CRs/SRs fit).
• ; corresponds to a background component without a normalization factor (C C¯, diboson, single top).
• B8 corresponds to the number of signal in region 8.
• 1 8,: and 1 8,; correspond to the number of background : and ; in region 8, respectively.
• ` B corresponds to a normalization factor for signal, which is called a signal strength.
• ` : corresponds to a normalization factor for background :.
• ) corresponds to a set of the nuisance parameters which describe the systematic uncertainties.
The mean of standard deviation of all probability density distribution is set to 0 and \ = ±1 corresponds to±1f variation. Since s and b depend only on a set of systematic uncertainty ), the likelihood function canbe denoted as ! (`, )).

In actual fitting procedure, for easy calculation, the logarithm of the likelihood is used. ` and ) aretreated as parameters of LLR, and a set of parameters that maximizes LLR is considered as post-fit
values. If the numbers of background and signal do not depend strongly on a certain systematic source(_8 | \= =0 ⇠ _8 | \= =±1 ), 1f variation of each systematic uncertainty can be interpreted as 1/2 variation of thelog likelihood function.
!!' =
=
=

! (`, ))| \= =0!(`, ))| \= =±1
log !(`, ))| \= =0 log !(`, ))| \= =±1’’
log %8 | \= =0log %8 | \= =±1
log !(`, )) = log’

8 2 {Regions}

+

=
=
=
⇠
⇠

9 2 {Systematic sources}’✓

8 2 {Regions}log ⌧ 9 \= =0’

9 2 {Systematic sources}◆_8 | \= =01=8 log_8 | \8 =0 + _8 | \8 =±1_|
2
8 \= =±1
8
⇢
✓
◆
’
=8
1
=8 + =8 ± < 8=8 log
=
±
<
2
8
8
8
( 1
)
’
’ ( 1) :+1 ✓ ⌥< 8 ◆ :
1
=8
± <8
:
=
±
<
2
8
8
8
:=1
⇢
✓
◆
’
<8
1
⌥=8
± <8
=
±
<
2
8
8
8

log ⌧ 9 \= =±1

12

where < 8 represents the variation of yield with respect to the systematic source \ 8 . Maclaurin expansion
was used to remove a logarithmic function.
The post-fit error of each nuisance parameter is implemented by varying the log likelihood by 1/2.

74

7.2 Hypothesis test
The profile likelihood ratio [108] is defined as:!!'(` B ) =ˆˆ!(n|` B , ))ˆ!(n| `ˆB , ))

ˆ is the maximum likelihood obtained by varying both ` B and ) (unconditional fit), \ˆ andwhere !(n| `ˆB , ))ˆˆ is the maximum likelihood obtained by floating ) with`ˆB return the maximum likelihood, and !(=|` B , ))a fixed ` B (conditional fit), )ˆˆ corresponds to ) returns the maximum likelihood for a given ` B . In thelatter case, the value of ) depends on the value of ` B . !!'(` B ) is less than or equal to 1. A test statistics@ `B [108] is defined as:@ `B = 2 log !!'(` B )Signal-like data has more likely to exhibit a low test-statistic (@ `B close to 0) and background-like data has alarge @ `B for ` B = 1. On the other hand, for ` B = 0, signal-like data has a large @ `B and the background-likedata has a small @ `B .

The ?-value ? `B for a given ` B is calculated as the cumulative probability of @ `B above the observed test
statistics @ obs`B as follows:0? `B = %(@ `B > @ obs`B |` B ) =

π 1
@`obs
B

5 (@ `B |` B0 )3@ `B

where 5 (@ `B |` B0 ) is a probability density function (PDF) of ` B under the assumption of the signal strength` B0 . In this analysis, the approximation method defined in Ref. [108] is used instead of the toy Monte Carloto obtain the PDF. The ?-value with the signal plus background hypothesis is called ? B+1 and the ?-value
with the background only hypothesis is quoted as 1 ? 1 as follows:
π 1? B+1 = %(@ `B > @ obs
|`
=
1)
=
5 (@ `B |` B = 1)3@ `B ,
(7.1)
B
`B
@`obs

1

? 1 = %(@ `B > @ obs`B |` B = 0) =

π 1B
@`obs
B

5 (@ `B |` B = 0)3@ `B .

(7.2)

where both parameters depends on the value of ` B for the test statistics. ⇠ ! B+1 is defined as the case of@ `B = @ 1 in equation 7.1 and ⇠ ! 1 and ? 0 are defined as the case of @ `B = @ 0 in equation 7.2. In case of
the ? 0 > 0.5, 0.5 is assigned to ? 0 instead. ⇠ ! B is defined as⇠ !B =⇠ ! B+1.
⇠ !1

The exclusion of a signal hypothesis at the 95% confidence level is defined to be ⇠ ! B less than 0.05 [109].
By dividing ⇠ ! B+1 by ⇠ ! 1 , the integrity of background estimations can also be taken into account in thesignal hypothesis tests.

75

7.3 Systematic uncertainties
There are three types of systematic uncertainties for event yields expectations: ”experimental uncertainty”,”theoretical uncertainty” and ”ad-hoc uncertainty”. The details of all the uncertainties are explained in thefollowing. Correlations between the different regions and bins are taken into account, and they can vary
the shape of the variables used to define the regions, such as ,R mass and cos \.

7.3.1 Experimental uncertainty
The experimental uncertainties associated with the reconstruction and calibration of each object are
discussed in this section. The variations of the event yields in all regions are included and correlated. They
are treated as nuisance parameters as described in Section 7.1.
Jets

As discussed in Section 4.4, the jets used in this analysis are calibrated for energy scale, energy
resolution and mass scale. More than 100 independent systematic sources are considered [94].
However, they are grouped up to skim the size of uncertainties. Compared to other experimental
uncertainties, the high ? T jets have large variation and can have a significant impact on the evaluationof signal sensitivities.

Leptons
The uncertainties for the electron and muon calibrations are included. Not only the variations ofscale and resolution of the lepton momentum but also variations of the identification and isolation
efficiencies are taken into account [99, 100]. The size of these uncertainties are generally smaller
than the jet uncertainties.
Flavour tagging
As discussed in Section 4.5, the flavor tagging depends on many variables and is calibrated. The
uncertainties on the calibration of the efficiencies for 1 , 2 and light-flavor are included [110].
In particular, these uncertainties are large for signal samples with heavy #R since one-third of theevents have a top quark and a bottom quark in the final states originated from #R ! ✓ ±,R⇤ ! ✓ ± @@ 0decay process.
Luminosity
The size of uncertainty on luminosity is obtained by using the LUCID-2 introduced in Section 2.2.1.
The uncertainty of the combined 2015 – 2018 integrated luminosity is 1.7% [53].
Pile-up reweighting
As discussed in Section 3.3, the uncertainty on the pile-up re-weighting is included. Up- anddown-type variations are given by applying (1/0.99) and (1/1.07) as a scale factor, respectively [68].
This uncertainty does not give a big impact on signal sensitivities.
K Tmiss soft term
As discussed in Section 4.10, the calibration to scale and resolution is performed for the soft term thatis one of the components of ⇢ Tmiss . The uncertainty sources derived from them are included [105].

76

Monte Carlo sample statistics
Since MC is used to estimate background events, the statistical uncertainties of the simulated events
also affect the signal sensitivity. Especially in regions where tight cuts are applied, such as signal
regions, they can have significant impacts.

7.3.2 Theoretical uncertainty
For major background components, theoretical uncertainties are assigned for the shape variations of <(,R ),cos \ distributions as well as the electron isolation efficiency and electron ambiguity type, which are used
to categorize events into SRs, VRs and CRs. Two different methods are employed to evaluate them.
• As as event-by-event weight
Theoretical uncertainties which can vary the ,R mass shape are evaluated by fitting the variationto-nominal ratio with a liner function. Although all <(,R ) distribution is binned in 4 different
mass intervals, the liner function is fitted to more finer binned shape. Since the linear function is afunction of ,R mass, a variation is given as weight for each event.
• As an uncertainty of the transfer factor
Theory uncertainties can also be estimated as variations of a transfer factor (TF) from Region 1 (R1)to Region 2 (R2):(#R2 /#R1 )variation.
variation =(#R2 /#R1 )nominal
variation is estimated for each major MC sample, region and systematic source separately. For thesimplicity, only one background component is assumed to exists in R1 and R2. In that case, theexpected number of data events in R1 can be expressed by:#R1,data ==#R2,data⇥ #R1,MC = # ⇥ #R1,MC#R2,MC#R1,MC⇥ #R2,data = ) ⇥ #R2,data .
#R2,MC

Here, # (a normalization factor) is the parameter estimated by the fit denoted as ` : in equation 7.1.
The systematic variation is applied to ) i.e.
)!

variation ⇥ ).

The uncertainty sources that vary the MC expectations in R1 and R2 to the same direction arecanceled by taking the ratio () ) in advance. That is why the theoretical uncertainties are not applied
to the R1, where the variation sample is normalized to the nominal sample. R1 can be selected
arbitrarily, and for each background, a region of high purity is used.
The types of theoretical uncertainties vary depending on the background processes, but most of them comefrom the same sources. As shown in Section 3.3.1, the inclusive cross-section can differ depending on the
choice of PDF, factorization scale (` ), renormalisation scale (` ' ) and strong coupling constant (UB ).
There are more than 100 variations available for selecting PDFs, depending on the form of the function
form. Envelops of them are taken and the size of PDF variations are evaluated with the largest and smallest
variations with respect to the nominal as the up- and down-type, respectively. The uncertainties of therenormalization and factorization scale variation are evaluated by multiplying 2 and 1/2 to the nominal77` and ` ' . Uncertainties on the UB are given at different value (UB = 0.118 for nominal, UB = 0.119 for
up-type, UB = 0.117 for down-type).
\ (], `, $)+jets
The matching of jets by matrix elements and parton showering (CKKW) is accounted for in the event
produced by the S
event generator. The nominal value is 20 GeV, but 15 GeV and 30 GeV are
used as variation. The error for soft gluon emission (QSF) is also taken into account by varying to 2
and 1/2 with respect to the nominal value. These theoretical uncertainties for ++jets are the largest
systematic uncertainties.
QCD multi-jet
Parameters of P
8 are tuned for high ? T events depending on the multi-parton interaction
parameters and initial and final state radiation parameters with P
MC tune system [111].
By using variations along the principle directions of the covariance matrix of the parameters at the
tuned minimum, systematic uncertainties are evaluated. These uncertainties provide good coverageof the experimental and modelling uncertainties.
Other backgrounds (t t¯, di-boson, single-top)
Minor backgrounds have a fixed flat 50 % cross-section uncertainty to cover possible yield variations
in all regions. These uncertainties are conservative and it is confirmed that they do not affect thesignal sensitivities so much.
SignalThe cross section uncertainties are derived by varying scale variations and PDF sets. The size offraction of them are about 10 % and 20 % depending on the ,R mass, respectively. In both variations,a large amount of change is expected as the ,R mass increases.
In addition to the above stuffs, a possible uncertainty due to the choice of generator is accounted to themajor background processes. The nominal and alternative generators are given in Table 3.3 and Table 7.1,
respectively. The size of uncertainty is obtained by comparing them and symmetrization with respect tothe nominal is performed to make it both-side uncertainty.
Table 7.1: Simulated background samples with an alternative generator. The corresponding event generator, parton
shower, cross-section normalization, PDF set used for the matrix element and set of tuned parameters are shown foreach sample.
Physics process, (! ✓a) + jets
/ (! ✓✓) + jets
W+jetsQCD multi-jet

Generator
M
M

P

S

_ MC@NLO_ MC@NLO
8.230

PDF setCross-section
normalization

NNPDF3.0
NNPDF3.0
NNPDF2.3
CT14

NLO
NLO
LO
NNLO

Parton shower

Tune

P
P
P

A14
A14
A14

S

8.230
8.230
8.230

S

7.3.3 Ad-hoc uncertainty
The experimental and theoretical uncertainties are generally large enough to account for variations of MC
shapes. However, there are some additional uncertainties to cover mis-modeling found in extra VRs or
possible shape variations for the non-calibrated variable of the electron Ambiguity.

78

Mis-modeling of QCD multi-jet MC in extra VR
A data-to-MC disagreement is observed in QCD multi-jet extra VRs with high-,R mass and thismight exist in SR1e. To cover them, the slope of the data-to-MC ratio against the ,R mass distribution
is included only for QCD multi-jet. More details are discussed in Section 8.2.
Possible shape variation for electron Ambiguity
Even the electron Ambiguity is used to define the CRW1e and CRLow1e to disentangle W+jets from,+jets, it is a non-calibrated variable. The possible shape variations of ,+jets, QCD multi-jet andW+jets are included by comparing MC with data.
Possible shape variation for high- p T muon
As described in Section 4.7, higher muon ? T leads larger uncertainty. However, MC does not include
perfect detector simulation, so possible shape variation is considered as a systematic uncertainty.
This becomes larger as ,R mass increases. Since minor backgrounds have flat 50% cross section
uncertainties, this systematic uncertainty is assigned only to /+jets.

7.3.4 Summary of systematic uncertainties

Relative Uncertainty [%]Figure 7.1 shows the relative size of individual systematic uncertainties and total uncertainties by taking into
account the correlations on the background prediction in SR1e, SR2e and SR2mu. The dominant systematic
uncertainty in SRs is the theoretical uncertainty. Because the total uncertainties takes correlations between
various systematic uncertainties into account, there are some regions in which the total uncertainty issmaller than the individual systematic uncertainties. Since SR1e and SR2e are fitted simultaneously,systematic uncertainties are correlated. On the other hand, SR2mu is a single SR in muon channel.

120
100

s = 13 TeV, 139 fb-1

Uncorrelated:
MC Stat. uncertainty
Data Stat. uncertainty
Experimental
TheoryAd-hocTotal uncertainty(correlated)

80
60
40
20
0

SR1e (2nd bin) SR1e (1st bin) SR2e (2nd bin) SR2e (1st bin) SR2mu (2nd bin)SR2mu (1st bin)

Figure 7.1: Breakdown of the systematic uncertainties on the background prediction and total uncertainties by taking
into account the correlations.

79

8 Extra VRs fit result
This chapter shows the results of the background only fit to the extra VRs introduced in Chapter 6. Summaryof purposes for each extra VRs fit can be found in Table 8.1. To get straight to the point, reasonabledata-to-MC agreements are observed in all the extra VRs fits. This means that good background estimationin every SRs can be anticipated.
Table 8.1: Summary of purposes of extra VRs fits. Details and region definitions can be found and fit results can befound in corresponding section.
Process

Purpose

Details in

Results in,+jetsTo confirm that ,+jets estimation with the cos \ and <(,R )distributions reproduces data well in the regions with theinverted electron ? T and ⇢ Tmiss .

Section 6.1.1

Section 8.1

QCD multi-jet

To confirm that QCD multi-jet estimation with the electron
isolation and <(,R ) distributions reproduces data well in theregions with the inverted electron identification.

Section 6.1.2

Section 8.2

W+jetsTo confirm that the <(,R ) distribution of W+jets MC reproduces data well in high purity phase spaces, which require aphoton instead of an electron.

Section 6.1.3.1

Section 8.3.1

To confirm that the <(,R ) distribution of W+jets MC reproduces the data well regardless of the photon-to-electron fakefactor.

Section 6.1.3.2

Section 8.3.2/ (! 44)+jets

To confirm that / (! 44)+jets estimation with the <(,R )distribution reproduces data well in the regions with thedifferent di-electron mass interval.

Section 6.2

Section 8.4.1/ (! ``)+jets

To confirm that / (! ``)+jets estimation with the <(,R )distribution reproduces data well in the regions with thedifferent di-muon mass interval.

Section 6.3

Section 8.4.2

8.1 ]+jets
As discussed in Section 6.1.1, a background only fit to VRWCRLow1e and VRWCRW1e with a full set ofsystematic uncertainties is performed to obtain the normalization factor for ,+jets. This normalization
factor is then applied to the ,+jets samples in VRWSR1e . The impacts of fitted systematic uncertainties
are transferred into VRWSR1e as well.
The post-fit background yield in each region is shown in Table 8.2 with the number of observed data. The
fitted normalization factor for ,+jets is 1.00 ± 0.05. The observed number of data in the first and second

80bin of VRWSR1e are 253 and 20, respectively. While the total post-fit MC event in them are 250.3 ± 26.5 and13.1 ± 1.6 which correspond to agreements within 2f as shown in Figure 8.1. Since ,+jets normalization
factor has large anti-correlations with the cross section uncertainties of C C¯ and di-boson as shown in
Figure 8.2, the error of total post-fit yield becomes smaller than the error of individual process.
Table 8.2: Results of background-only fit to VRWCRW1e for integrated luminosity of 139 fb 1 . The errors are
statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction, where thenegative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected. The mostbottom row shows the total pre-fit MC events.
channelVRWCRW1eVRWCRLow1e

VRWSR1e (1st bin)

VRWSR1e (2nd bin)

Observed events

7774

9247

253

20

Fitted bkg events

7783.3 ± 86.4

9237.6 ± 99.9

250.3 ± 26.5

13.1 ± 1.6

Fitted ,+jets events
Fitted C C¯ events
Fitted di-boson events
Fitted /+jets events
Fitted single-top events
Fitted QCD multi-jet events
Fitted W+jets events

6668.4 ± 378.9
481.6 ± 277.8
400.2 ± 202.1
115.5 ± 57.8
107.4 ± 60.9
10.3+24.1
10.3

8127.7 ± 387.9
403.0 ± 236.3
465.4 ± 235.4
143.4 ± 72.3
95.5 ± 53.4
2.6 ± 1.6

7921.09283.9EventsPre-fit background events

data
Wjets
dibosonSingleTop
Gammajets

107
10

6

10

5

s=13 TeV, 139 fb-1

215.5 ± 27.7
8.2 ± 5.1
21.8 ± 11.0
2.3 ± 1.2
2.6 ± 1.6
0.0+0.0
0.0
252.4

12.4 ± 1.4
0.4 ± 0.4
0.1 ± 0.1
0.2 ± 0.2
0.0+0.0
0.0
13.2

total background
ttbar
Zjets
dijet

104
10

3

102
10
1

(n

obs

- npred) / σtot

10− 1
10− 2
2

VRWCRW1eVRWCRLow1e

VRWSR1e (1st bin)

VRWSR1e (2nd bin)

VRWCRW1eVRWCRLow1e

VRWSR1e (1st bin)

VRWSR1e (2nd bin)0
−2

Figure 8.1: Data vs post-fit MC expectation of ,+jets extra VRs. The bottom panel shows the ratio of difference
between observed data and post-fit MC expectation divided by the total uncertainty ftot .

The main sources of the uncertainties are theoretical uncertainties and MC statistics in the highest-,R massbins. Since the upper cut for lepton ? T is applied, the impact of jet energy scale is relatively significant.

81s = 13 TeV, 139 fb-1
Correlation matrix for different MC yields

1

Normalization factor of W+jets

-0.12

-0.18

-0.60

-0.00

-0.57

1.00

Cross section of t t

-0.01

0.00

-0.01

-0.00

1.00

-0.57

0.8
0.6
0.4

Cross section of QCD multi-jet

-0.00

0.00

-0.00

1.00

-0.00

-0.00

Cross section of Di-boson

-0.00

-0.00

1.00

-0.00

-0.01

-0.60

Cross section of Z+jets

0.00

1.00

-0.00

0.00

0.00

-0.18

0.2
0
−0.2
−0.4
−0.6

-0.12
Normalization factor of W+jets-0.01
Cross section of t t-0.00
Cross section of QCD multi-jet-0.00
Cross section of Di-boson

0.00
Cross section of Z+jets

1.00

Cross section of Single-top

Cross section of Single-top

−0.8
−1

Figure 8.2: Post-fit correlation matrix of the ,+jets normalization factor and cross section uncertainties for minor
backgrounds obtained by the extra ,+jets VRs fit. Since the W+jets yields are exactly zero in all regions, crosssection uncertainty for that is not shown.

8.2 QCD multi-jet
As discussed in Section 6.1.2, a background only fit to VRFakeCRLow1e and VRFakeCRFake1e with a fullset of systematic uncertainties is performed to obtain the normalization factor for QCD multi-jet. This
normalization factor is then applied to the QCD multi-jet sample in VRFakeSR1e . The impacts of fitted
systematic uncertainties are transferred into VRFakeSR1e as well.
The post-fit background yield in each region is shown in Table 8.3 with the number of observed events indata. The fitted normalization factor for QCD multi-jet is 0.82 ± 0.02. The observed number of data in thefirst and second bin of VRFakeSR1e are 58 and 6, respectively. While the total fitted MC event in them are
928.6 ± 161.8 and 126.7 ± 44.5 which correspond to agreements within 1f as shown in Figure 8.3.

In the region of ,R mass up to 3 TeV, MC agrees data within 1f, however there is a positive slope in thedata to MC ratio as shown in the bottom panel of Figure 8.3, which may lead to underestimation of thenumber of MC events in the region above 3 TeV. To avoid this, data to MC ratio is fitted with a linear
function to obtain possible shape variation only to QCD multi-jet events.

The main sources of the uncertainties are theoretical uncertainties and MC statistics in the highest-,Rmass bins. Electron energy scales and jet energy resolution uncertainties are also significant.

82

Table 8.3: Results of VRFakeCRFake1e for integrated luminosity of 139 fb 1 . The errors are statistical plus systematic
uncertainties. Uncertainties on the fitted yields are symmetric by construction, where the negative error is truncatedwhen reaching to zero event yield. “ ” indicates exactly zero event is expected.
channelVRFakeCRFake1e

VRFakeCRLow1e

VRFakeSR1e (1st bin)

VRFakeSR1e (2nd bin)

Observed events

1538

11945

995

168

Fitted bkg events

1538.2 ± 39.5

11945.4 ± 109.3

928.6 ± 161.8

126.7 ± 44.5

2811.815216.7

1179.8

157.5

Fitted QCD multi-jet events
Fitted W+jets events
Fitted ,+jets events
Fitted /+jets events
Fitted di-boson events
Fitted C C¯ events
Fitted single-top events

EventsPre-fit background events

101263.0 ± 69.3
29.7 ± 17.3
179.1 ± 90.0
47.1 ± 23.7
12.4 ± 6.4
5.3 ± 3.3
1.7 ± 1.1

11887.8 ± 134.4
17.4 ± 9.4
29.3 ± 14.7
6.7 ± 3.4
1.7 ± 0.9
2.4 ± 1.5
0.1+0.2
0.1

922.4 ± 162.0
1.3 ± 0.8
3.4 ± 2.0
0.4 ± 0.2
0.1 ± 0.1
1.0 ± 0.8

126.1 ± 44.5
0.1 ± 0.1
0.4 ± 0.3
0.1 ± 0.1
0.0+0.0
0.0

8

data
dijet
Wjets
dibosonSingleTop

107
10

6

10

5

s=13 TeV, 139 fb-1

total backgroundGammajets
Zjets
ttbar

104
10

3

102
10
1

10− 2
2

VRFakeCRFake1e

VRFakeCRLow1e

VRFakeSR1e (1st bin)

VRFakeSR1e (2nd bin)

VRFakeCRFake1e

VRFakeCRLow1e

VRFakeSR1e (1st bin)

VRFakeSR1e (2nd bin)

0
−2

(n

obs

- npred) / σtot

10− 1Figure 8.3: Data vs post-fit MC expectation of QCD multi-jet extra VRs. Bottom panel shows the ratio of difference
between observed data and post-fit MC expectation divided by the total uncertainty ftot . A positive slope is observed
from VRFakeCRLow1e to VRFakeSR1e .

8.3 $+jets
Validations of the W+jets estimation method are made in two steps. First, the modeling of W+jets MC ischecked in the regions with the exactly same phase spaces to actual CRs and SR except requiring a photon
instead of an electron. Then a possible mis-modeling of the photon to electron fake factor is studied withtwo different sets of extra VRs.

83

8.3.1 Data to MC agreement in high-]R mass
As discussed in Section 6.1.3.1, a background only fit to CRLow1ph and CRFake1ph with a full set ofsystematic uncertainties are performed to obtain the normalization factors for QCD multi-jet and W+jets.
These normalization factors are then applied to the QCD multi-jet and W+jets events in SR1ph, respectively.
The impacts of fitted systematic uncertainties are transferred into SR1ph as well.
The post-fit background yields in each region is shown in Table 8.4 with the number of event in data. The
fitted normalization factors for QCD multi-jet and W+jets are 0.56 ± 0.02 and 0.19 ± 0.06, respectively.
The number of observed data in the first and second bins of SR1ph are 33 and 5, respectively. While thetotal MC events in them are 27.5 ± 4.6 and 3.4 ± 0.9 which correspond to agreements within 1f as shownin Figure 8.4.
Table 8.4: Results of background-only fit to CRLow1ph and CRFake1ph for integrated luminosity of 139 fb 1 . The
errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction,
where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected.
The most bottom row shows the total pre-fit MC events.
channelCRFake1ph

CRLow1ph

VR1ph

SR1ph (1st bin)

SR1ph (2nd bin)

Observed events

6904

11500

327

33

5

Fitted bkg events

6903.9 ± 83.1

11500.2 ± 107.2

365.2 ± 34.5

27.5 ± 4.6

3.4 ± 0.9

0.1 ± 0.0
0.0 ± 0.0

0.0 ± 0.0

105.4

12.3

Fitted W+jets events
Fitted QCD multi-jet events
Fitted C C̄ events
Fitted , +jets events
Fitted / +jets events
Fitted single-top events
Fitted di-boson events
Pre-fit background events

1729.9 ± 86.2
5125.9 ± 130.4
16.6 ± 11.4
19.5 ± 9.7
8.9 ± 4.5
2.5 ± 1.8
0.7 ± 0.4
18136.2

7839.7 ± 201.2
3586.1 ± 154.6
7.5 ± 6.3
42.9 ± 21.5
18.8 ± 9.4
2.9 ± 2.0
2.4 ± 1.3
47230.8

243.7 ± 25.3
119.9 ± 21.8
0.1 ± 0.1
1.0 ± 0.6
0.3 ± 0.1
0.3 ± 0.2
1482.716.5 ± 2.9
11.0 ± 3.6

1.8 ± 0.5
1.5 ± 0.8

The shape modeling of the W+jets MC is reliable in the phase space requiring only one large-' jet anda photon, except for its normalization. The normalization can be determined properly from data in theCRs.

8.3.2 Photon to electron fake factor
As discussed in Section 6.1.3.2, two sets of extra VRs are prepared, one is the regions with [ from 2.0 to
3.0 to ensure an orthogonality with the actual CRs and SR and the other one is further requesting a photon
instead of an electron, to ensure that the photon to electron fake factor is well modeled in MC and does
not affect the ,R mass reconstruction. In the following, data-to-MC agreements obtained by those two
independent fits are depicted.
• A background only fit to VRWCRLow1e , VRWCRW1e and VRWCRFake1e with a full set of systematic
uncertainties is performed to obtain the normalization factors for ,+jets, QCD multi-jet and W+jets.
These normalization factors are then applied to the corresponding background processes. The
impacts of fitted systematic uncertainties are transferred into VRWSR1e as well.
The post-fit background yield in each region is shown in Table 8.5 with the number of events in data.
The fitted normalization factors for ,+jets, QCD multi-jet and W+jets are 0.97 ± 0.11, 0.43 ± 0.02

84

Events

10

8

data
Gammajets
ttbar
Zjets
diboson

107
10

6

10

5

s=13 TeV, 139 fb-1

total background
dijet
Wjets
SingleTop

104
10

3

102
10
1

10− 2
2

(n

obs

- npred) / σtot

10− 1
CRFake1ph_cuts

CRLow1ph

VR1ph

SR1ph (1st bin)

SR1ph (2nd bin)

CRFake1ph_cuts

CRLow1ph

VR1ph

SR1ph (1st bin)

SR1ph (2nd bin)0
−2

Figure 8.4: Data vs post-fit MC expectation of W+jets extra VRs with the exactly same phase space with SR1e except
requiring a photon instead of an electron. Bottom panel shows the ratio of difference between observed data andpost-fit MC expectation divided by the total uncertainty ftot .

and 0.24 ± 0.01, respectively. The number of observed data in the first and second bin of VRWSR1eare 26 and 3, respectively. While the total MC events in them are 27.7 ± 7.7 and 1.7 ± 0.6 whichcorrespond to agreements within 1f as shown in Figure 8.5.
Table 8.5: Results of background-only fit to VRWCRLow1e and VRWCRFake1e for integrated luminosity of 139 fb 1 . The
errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction,
where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected.
The most bottom row shows the total pre-fit MC events.
channelVRWCRW1eVRWCRFake1e

VRWCRLow1e

VRWSR1e (1st bin)

VRWSR1e (2nd bin)

Observed events

4709

3811

796

26

3

Fitted bkg events

4708.8 ± 68.8

3810.9 ± 61.8

796.0 ± 28.1

27.7 ± 7.7

1.7 ± 0.6

0.7 ± 0.4

0.0 ± 0.0

73.5

4.5

Fitted W+jets events
Fitted , +jets events
Fitted QCD multi-jet events
Fitted / +jets events
Fitted C C̄ events
Fitted di-boson events
Fitted single-top events
Pre-fit background events

630.4 ± 413.5
2943.1 ± 500.1
285.0 ± 64.5
495.4 ± 67.4
153.5 ± 90.1
168.0 ± 84.5
33.4 ± 19.0
8201.1537.0 ± 265.9
268.4 ± 93.8
2747.6 ± 195.1
228.7 ± 37.4
9.9 ± 6.3
17.4 ± 9.8
2.0 ± 1.5
9379.7242.7 ± 118.9
234.6 ± 82.2
104.9 ± 18.4
187.9 ± 33.4
5.4 ± 3.7
17.8 ± 9.7
2.7 ± 1.7
1788.2

12.6 ± 8.1
6.2 ± 3.5
3.1 ± 1.0
5.2 ± 1.9

0.7 ± 0.4
0.3 ± 0.3
0.4 ± 0.2
0.3 ± 0.2

• A background only fit to VRWCRLow1ph and VRWCRFake1ph with a full set of systematic uncertainties
is performed to obtain the normalization factors for QCD multi-jet and W+jets. These normalization
factors are than applied to the corresponding background processes. The impacts of fitted systematic
uncertainties are transferred into VRWSR1ph as well.
The post-fit background yield in each region is shown in Table 8.6 with the number of events indata. The fitted normalization factors for QCD multi-jet and W+jets are 0.49 ± 0.03 and 0.12 ± 0.01,
respectively. The number of observed data in the first and second bin of VRWSR1ph are 48 and 4,85

Events

107
10

6

10

5

data
Wjets
Gammajets
ttbar
SingleTops=13 TeV, 139 fb-1

total background
dijet
Zjets
diboson

104
10

3

102
10
1

10− 2
2

VRGammaCRW1e

VRGammaCRFake1e

VRGammaCRLow1e

VRGammaSR1e (1st bin)

VRGammaSR1e (2nd bin)

VRGammaCRW1e

VRGammaCRFake1e

VRGammaCRLow1e

VRGammaSR1e (1st bin) VRGammaSR1e (2nd bin)

0
−2

(n

obs

- npred) / σtot

10− 1Figure 8.5: Data vs post-fit expectation of W+jets extra VRs with different [ interval compared to SR1e. Bottom
panel shows the ratio of difference between observed data and post-fit MC expectation divided by the total uncertainty
ftot .

respectively. While the total MC events in them are 59.2 ± 7.3 and 4.6 ± 1.0 which correspond toagreements within 1f as shown in Figure 8.6.
Table 8.6: Results of background-only fit to VRWCRLow1ph and VRWCRFake1ph for integrated luminosity of 139 fb 1 .
The errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction,
where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected.
The most bottom row shows the total pre-fit MC events.
channelVRWCRFake1ph

VRWCRLow1ph

VRWSR1ph (1st bin)

VRWSR1ph (2nd bin)

Observed events

7281

1312

48

4

Fitted bkg events

7281.0 ± 85.4

1312.0 ± 36.3

59.2 ± 7.3

4.6 ± 1.0

Fitted W+jets events
Fitted QCD multi-jet events
Fitted ,+jets events
Fitted /+jets events
Fitted C C¯ events
Fitted di-boson events
Fitted single-top events
Pre-fit background events

1516.9 ± 225.5
5723.6 ± 246.7
23.6 ± 11.9
5.9 ± 3.0
9.4 ± 5.8
0.7 ± 0.3
1.0 ± 0.524102.9860.1 ± 92.4
444.1 ± 82.8
2.9 ± 1.9
2.9 ± 1.5
1.5 ± 1.5
0.3 ± 0.2
0.2 ± 0.1
7960.439.4 ± 6.5
19.7 ± 4.2

2.9 ± 0.8
1.7 ± 0.7

0.1 ± 0.1

363.0

27.5

Consequently, it is confirmed that the photon to electron fake factor is well modeled by MC and the ,Rmass can be correctly reconstructed using MC even when a fake electron is requested.

86Events

107
10

6

10

5

data
Gammajets
Wjets
ttbar
SingleTops=13 TeV, 139 fb-1

total background
dijet
Zjets
diboson

104
10

3

102
10
1

10− 2
2

VRGammaCRFake1ph

VRGammaCRLow1ph

VRGammaSR1ph (1st bin)

VRGammaSR1ph (2st bin)

VRGammaCRFake1ph

VRGammaCRLow1ph

VRGammaSR1ph (1st bin)

VRGammaSR1ph (2st bin)

0
−2

(n

obs

- npred) / σtot

10− 1Figure 8.6: Data vs post-fit MC expectation of W+jets extra VRs defined in Table 6.7. Bottom panel shows the ratio ofdifference between observed data and post-fit MC divided by the total uncertainty. ftot .

8.4 `+jets
8.4.1 m(]R ) modeling of `(! ee) sample
A background only fit to VRZCRLow2e with a full set of systematic uncertainties is performed to obtain thenormalization factor for / (! 44)+jets. This normalization factor is then applied to the /+jets events in
VRZSR2e . The impacts of fitted systematic uncertainties are transferred into VRZSR2e as well.
The post-fit background yield in each region is shown in Table 8.7 with the number of events in data. The
fitted normalization factor for / (! 44)+jets is 1.27 ± 0.09. The number of observed data in the first andsecond bin of VRZSR2e are 17 and 1, respectively. While the total fitted MC event in them are 14.7 ± 3.9
and 1.2 ± 0.7 which correspond to agreements within 1f as shown in Figure 8.7.

8.4.2 m(]R ) mass modeling of `(! --) sample
A background only fit to VRZCRLow2mu with a full set of systematic uncertainties is performed to obtainthe normalization factor for / (! ``)+jets. This normalization factor is then applied to the /+jets eventsin VRZSR2mu . The impacts of fitted systematic uncertainties are transferred into VRZSR2mu as well.
The post-fit background yield in each region is shown in Table 8.8 with the number of events in data. The
fitted normalization factor for / (! ``)+jets is 1.17 ± 0.04. The number of observed data in the first andsecond bin of VRZSR2mu are 23 and 2, respectively. While the total fitted MC event in them are 22.3 ± 5.7
and 3.7 ± 2.2 which correspond to agreements within 1f as shown in Figure 8.8.

87

Table 8.7: Results of background-only fit to VRZCRLow2e for integrated luminosity of 139 fb 1 . The errors are
statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction, where thenegative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected. The mostbottom row shows the total pre-fit MC events.
channel

VRZCRLow2e

VRZSR2e (1st bin)

VRZSR2e (2nd bin)

Observed events

358

17

1

Fitted bkg events

358.0 ± 18.9

14.7 ± 3.9

1.2 ± 0.7

Fitted /+jets events
Fitted di-boson events
Fitted C C¯ events
Fitted ,+jets events
Fitted single-top events
Fitted QCD multi-jet events
Fitted W+jets events

EventsPre-fit background events

10

6

10

5

321.1 ± 22.6
21.2 ± 10.6
8.8 ± 4.9
2.0 ± 1.0
1.5 ± 1.0

13.3 ± 3.9
0.8 ± 0.4
0.2 ± 0.1
0.4 ± 0.2

0.0 ± 0.0

0.0 ± 0.0

3.4 ± 1.9
289.1

11.8

data
Zjets
ttbar
SingleTop
Gammajets

s=13 TeV, 139 fb-1

104
10

1.2 ± 0.7
0.1 ± 0.0

1.0

total backgrounddiboson
Wjets
dijet

3

102
10
1

(n

obs

- npred) / σtot

10

−1

10− 2
2

VRZCRLow2e

VRZSR2e (1st bin)

VRZSR2e (2nd bin)

VRZCRLow2e

VRZSR2e (1st bin)

VRZSR2e (2nd bin)0
−2

Figure 8.7: Data vs post-fit MC expectation of / (! 44)+jets extra VRs. Bottom panel shows the ratio of difference
between observed data and post-fit MC expectation divided by the total uncertainty ftot .

88

Table 8.8: Results of background-only fit to VRZCRLow2mu for integrated luminosity of 139 fb 1 . The errors are
statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction, where thenegative error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected. The mostbottom row shows the total pre-fit MC events.
channel

VRZCRLow2mu

VRZSR2mu (1st bin)

VRZSR2mu (2nd bin)

Observed events

399

23

2

Fitted bkg events

399.1 ± 20.0

337.6 ± 29.1
33.3 ± 16.7
18.2 ± 10.7
6.8 ± 3.6
3.1 ± 2.0
0.1 ± 0.1

22.3 ± 5.7

19.1 ± 5.8
1.8 ± 0.9
0.8 ± 0.5
0.3 ± 0.3
0.3 ± 0.2
0.1 ± 0.1

3.7 ± 2.2

412.9

23.1

3.8

Fitted /+jets events
Fitted di-boson events
Fitted C C¯ events
Fitted ,+jets events
Fitted single-top events
Fitted QCD multi-jet events
Fitted W+jets events

EventsPre-fit background events

10

6

10

5

data
Zjets
ttbar
SingleTop
Gammajets

s=13 TeV, 139 fb-1

104
10

3.2 ± 2.2
0.3 ± 0.2
0.2 ± 0.1
0.0 ± 0.0

total backgrounddiboson
Wjets
dijet

3

102
10
1

(n

obs

- npred) / σtot

10

−1

10− 2
2

VRZCRLow2mu

VRZSR2mu (1st bin)

VRZSR2mu (2nd bin)

VRZCRLow2mu

VRZSR2mu (1st bin)

VRZSR2mu (2nd bin)0
−2

Figure 8.8: Data vs post-fit MC expectation of / (! ``)+jets extra VRs. Bottom panel shows the ratio of difference
between observed data and post-fit MC expectation divided by the total uncertainty. ftot represents the total
uncertainty.

89

9 Results
The background estimation methods explained in Section 6 have been performed in extra VRs in Section 8.
Generally good MC to data consistencies are observed in the post-fit level.
Results of simultaneous fit with three different fitting configurations are presented in this section. Section 9.1
shows the results of background only fits to electron and muon final state separately. The results of model
independent fit are reported in Section 9.2 followed by model dependent fit results in Section 9.3.

9.1 Search for the signal with background only fits
9.1.1 Electron final states
As discussed in Section 6.1 and 6.2, a background only fit to CRW1e, CRFake1e, CRW1e, CRLow1e and
CRLow2e with a full set of systematic uncertainties is performed to estimate normalization factors for,+jets, QCD multi-jet, W+jets and /+jets. These normalization factors are then applied in heavier mass
regions. As summarized in Table 6.11, ,+jets, QCD multi-jet and W+jets normalization factors are applied
to one electron regions only, while /+jets normalization factor is transferred into both one and two electron
channels.
The post-fit yield in each region is shown in Table 9.1-9.4 with the number of events in data. The fitted
normalization factors for ,+jets, QCD multi-jet, W+jets and /+jets are 1.05 ± 0.03, 0.56 ± 0.01, 0.38 ± 0.06
and 1.23 ± 0.10, respectively. The number of observed data in the first and second bin of SR1e are 10 and
0, respectively, while the total fitted MC in them are 11.9 ± 2.9 and 0.8 ± 0.3, respectively. The number ofobserved data in the first and second bin of SR2e are 3 and 0, while the total fitted MC in them are 3.5 ± 1.2
and 0.3 ± 0.2, respectively. As shown in Figure 9.1, the MC reproduces the data very well in all regions.
These results indicate no signal is found in the all SRs.

90

Table 9.1: Results of background-only fit to CRLow1e, CRW1e, CRFake1e and CRLow2e for integrated luminosityof 139 fb 1 . The errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetricby construction, where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero
event is expected. The most bottom row shows the total pre-fit MC events.
channel

CRW1e

VRW1e (1st bin)

VRW1e (2nd bin)

Observed events

5631

37

0

Fitted bkg events

5634.9 ± 74.7

34.5 ± 7.1

0.4 ± 0.2

Fitted ,+jets events
Fitted C C¯ events
Fitted di-boson events
Fitted W+jets events
Fitted /+jets events
Fitted single-top events
Fitted QCD multi-jet events
Pre-fit background events

4856.1 ± 173.8
172.3 ± 108.1
251.2 ± 125.7
95.1 ± 38.3
111.8 ± 31.8
60.5 ± 35.3
87.6 ± 16.2

28.8 ± 6.8
1.2 ± 0.8
2.49 ± 1.72
0.6+0.9
0.6
0.6 ± 0.3
0.3+0.6
0.3
0.5 ± 0.23

5827.436.4

0.4 ± 0.2

0.0+0.0
0.0
0.0+0.0
0.0
0.4

Table 9.2: Results of background-only fit to CRLow1e, CRW1e, CRFake1e and CRLow2e for integrated luminosityof 139 fb 1 . The errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetricby construction, where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero
event is expected. The most bottom row shows the total pre-fit MC events.
channelCRFake1e

VRFake1e (1st bin)

VRFake1e (2nd bin)

Observed events

14988

809

101

Fitted bkg events

14987.9 ± 122.6

716.4 ± 109.7

101.2 ± 46.7

26883.4

1291.5

206.5

Fitted QCD multi-jet events
Fitted ,+jets events
Fitted W+jets events
Fitted /+jets events
Fitted C C¯ events
Fitted di-boson events
Fitted single-top events
Pre-fit background events

13834.6 ± 151.5
348.4 ± 16.3
626.9 ± 86.2
121.7 ± 10.4
27.6 ± 16.7
23.8 ± 12.1
5.1 ± 2.7

673.4 ± 109.6
8.3 ± 2.2
28.2 ± 5.1
3.8 ± 0.9
1.2 ± 0.8
1.1 ± 0.8
0.3 ± 0.2

91

66.5 ± 34.7
0.6 ± 0.4
32.9 ± 15.5
0.7 ± 0.4
0.3 ± 0.2
0.2 ± 0.1

Table 9.3: Results of background only fit to CRLow1e, CRW1e, CRFake1e, CRW1e and CRLow2e for integrated
luminosity of 139 fb 1 . The errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are
symmetric by construction, where the negative error is truncated when reaching to zero event yield. “ ” indicatesexactly zero event is expected. The most bottom row shows the total pre-fit MC events.
channelObserved events
Fitted bkg events
Fitted , +jets events
Fitted W+jets events
Fitted QCD multi-jet events
Fitted / +jets events
Fitted di-boson events
Fitted C C̄ events
Fitted single-top events
Pre-fit background events

CRLow1e

CRW1e

VR1e

SR1e (1st bin)

SR1e (2nd bin)

7988

4611

239

10

0

4611.3 ± 68.1

249.4 ± 34.7

11.9 ± 2.9

0.8 ± 0.3

7509.1

309.4

16.5

1.3

7983.1 ± 89.6

5849.6 ± 159.7
278.8 ± 51.5
89.1 ± 53.7
1350.9 ± 108.4
309.9 ± 156.7
58.8 ± 38.0
46.0 ± 28.6
7886.91502.9 ± 120.2
1365.5 ± 155.2
1101.6 ± 38.8
482.6 ± 39.1
87.8 ± 44.4
52.9 ± 32.9
18.1 ± 10.5

140.7 ± 33.3
31.6 ± 5.4
29.1 ± 4.8
29.4 ± 6.0
13.5 ± 6.9
3.0 ± 1.8
2.0 ± 2.0

5.6 ± 2.7
2.0 ± 0.5
2.2 ± 0.8
1.1 ± 0.5
0.7 ± 0.4
0.2 ± 0.1
0.1+0.2
0.1

0.3 ± 0.2
0.2 ± 0.1
0.2 ± 0.1
0.0+0.00.0
0.1 ± 0.1

Table 9.4: Results of background-only fit to CRLow1e, CRW1e, CRFake1e and CRLow2e for integrated luminosityof 139 fb 1 . The errors are statistical plus systematic uncertainties. Uncertainties on the fitted yields are symmetricby construction, where the negative error is truncated when reaching to zero event yield. “ ” indicates exactly zero
event is expected. The most bottom row shows the total pre-fit MC events.
channelCRLow2eVR2eSR2e (1st bin)SR2e (2nd bin)

Observed events

751

39

3

0

Fitted bkg events

751.8 ± 27.5

43.4 ± 7.4

3.5 ± 1.2

0.3 ± 0.2

Fitted /+jets events
Fitted C C¯ events
Fitted ,+jets events
Fitted single-top events
Fitted W+jets events
Fitted di-boson events
Fitted QCD multi-jet events
Pre-fit background events

622.5 ± 50.8
28.8 ± 17.8
17.8 ± 8.9
8.4 ± 4.9
3.1 ± 1.5
71.3 ± 35.2
638.3

34.8 ± 7.6
1.0 ± 0.5
2.1 ± 1.1
0.2+0.3
0.2
0.8 ± 0.4
4.3 ± 2.1
0.2 ± 0.136.9

922.7 ± 1.2
0.2 ± 0.2
0.2 ± 0.1
0.0 ± 0.0
0.0+0.00.0
0.3 ± 0.2
3.0

0.3 ± 0.2
0.0+0.0
0.0

0.3

Events

10

8

data
Wjets
dijet
dibosonSingleTop

107
10

6

10

5

-1

s=13 TeV, 139 fb

total backgroundGammajets
Zjets
ttbar

104
10

3

102
10
1

(n

obs

- npred) / σtot

10

−1

10− 2
2

CRW

1e

0

VRW

VRW
VRF
V
CRγ
C
C
1e
ake RFake RLow
1e ( RFake
1
1e (
1e (
1e
1st
2nd
1st
2nd e
bin)
bin)
bin)
bin)

VR1

SR1

VRW
VR
VRF
V
CRγ
VR1
C
C
1e
ake RFake RLowe1e ( W1e ( RFake
1e (
1
1
1
1st
2
1st e (2nd ebin) nd bin e
bin)
bin)
)

SR1

1e (

e

SR1
C
VR2
e (2 RLow
e
2e
st b
nd b
in)
in)

SR2

S
V
C
e (1 R1e (2 RLow R2e
2
st b
nd b
in)
in) e

SR2

e (1

SR2
e (2
st b
nd b
in)
in)

e (1

−2
CRW

1e

S
e (1 R2e (2
st b
nd b
in)
in)

Figure 9.1: Data vs post-fit MC expectation of CR/VR/SR for electron channel. Bottom panel shows the difference
between observed data and post-fit MC expectation divided by the total uncertainty ftot .

93

9.1.2 Muon final states
As discussed in Section 6.3, a background only fit to CRLow2mu with a full set of systematic uncertainties
is performed to estimate a normalization factor for /+jets. This normalization factor is then applied inheavier mass regions.
The post-fit yields in each region is shown in Table 9.5 with the number of events in data. The fitted
normalization factor is 1.12 ± 0.18. The number of observed data in the first and second bin of SR2mu are
2 and 0, respectively. While the total fitted MC in them are 4.5 ± 1.9 and 0.8 ± 0.6, respectively. As shownin Figure 9.2, the MC reproduces the data very well in all regions. This result indicates no signal is foundin the SR2mu.
Table 9.5: Results of background-only fit to CRLow2mu for integral luminosity of 139 fb 1 . The errors are statisticalplus systematic uncertainties. Uncertainties on the fitted yields are symmetric by construction, where the negative
error is truncated when reaching to zero event yield. “ ” indicates exactly zero event is expected. The most bottom
row shows the total pre-fit MC events.
channelCRLow2mu

VR2mu

SR2mu (1st bin)

SR2mu (2nd bin)

Observed events

950

46

2

0

Fitted bkg events

950.2 ± 31.1

54.4 ± 10.9

4.5 ± 1.9

0.8 ± 0.6

Fitted /+jets events
Fitted di-boson events
Fitted ,+jets events
Fitted C C¯ events
Fitted single-top events
Fitted QCD multi-jet events
Fitted W+jets events
Pre-fit background events

644.5 ± 102.9
108.2 ± 54.3
98.1 ± 52.3
78.0 ± 46.3
20.4 ± 12.0
0.9 ± 0.5

38.1 ± 12.1
6.7 ± 3.4
4.7 ± 2.9
3.8 ± 2.2
0.9 ± 0.6
0.2 ± 0.2

882.3

50.4

94

3.2 ± 1.9
0.8 ± 0.4
0.2+0.2
0.2

0.6 ± 0.6
0.1 ± 0.1
0.1 ± 0.1

0.3+0.3
0.3

4.1

0.8

Events

10

6

10

5

10

4

10

3

data
Zjets
Wjets
SingleTop
Gammajets-1

s=13 TeV, 139 fb

total backgrounddiboson
ttbar
dijet

102
10
1

(n

obs

- npred) / σtot

10− 1
10− 2
2

CRLow2mu

VR2mu

SR2mu (1st bin)

SR2mu (2nd bin)

CRLow2mu

VR2mu

SR2mu (1st bin)

SR2mu (2nd bin)0
−2

Figure 9.2: Data vs post-fit MC expectation of CR/VR/SR for muon channel. Bottom panel shows the ratio ofdifference between observed data and post-fit MC expectation divided by the total uncertainty ftot .

95

9.2 Upper limits on BSM events with model independent fits
In the background only fits described in the previous section, any SR is not convoluted in the likelihood
function given in equation 7.1. Instead of such an approach, a single bin SR where the ,R mass isgreater than 3 TeV is introduced to evaluate the number of possible BSM events using the ? 0 -value, called
model-independent fit. The ? 0 -value is obtained with the background only hypothesis as explained in
Section 7.2. Model-independent fits are performed to all three SRs and ? 0 -values for them are obtained tobe 0.5. These results mean that the observed events are consistent with the background only hypothesis or
the existence of the deficits. In this analysis, the deficits are observed as shown in Table 9.3, 9.4 and 9.5.
No BSM events are found.
Then, the hypothesis tests for various ` B are performed and Figure 9.3 shows ⇠ ! B , ⇠ ! 1 and ⇠ ! B+1
described in Section 7.2. The upper limit of expected (observed) BSM events at ?-value (⇠ ! B ) of 0.05
for expected (observed) events, where the expected (observed) line and horizontal line at 0.05 intersect
95 (( 95 ) in Table 9.6, respectively. The visible cross section, which isin Figure 9.3, are expressed as (expobsdefined as the number of observed events divided by luminosity, are also shown in Table 9.6.
s = 13 TeV, 139 fb-1

0.8

1.2
Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs
Observed CLs+b
Observed CLb

1

0.8

1.2

0.8

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

2

4

6

8

10

12

14

16

18

20
µ

0
0

2

4

6

8

10

12

14

16

18

s

Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs
Observed CLs+b
Observed CLb

1

0.6

0
0

s = 13 TeV, 139 fb-1

SR2mu

p-value

Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs
Observed CLs+b
Observed CLb

1

s = 13 TeV, 139 fb-1

SR2e

p-valuep-value

SR1e

1.2

20
µ

0
0

2

4

6

8

10

12

14

16

18

s

(a) One electron SRs(b) Two electron SR(c) Two muon SR

Figure 9.3: Expected and observed ⇠ ! B (red), observed ⇠ ! B+1 (blue), and observed ⇠ ! 1 (black) as a function of thesignal strength ` B for (a) one electron, (b) two electron and (c) two muon channel. The expected ⇠ ! B value with
±1f (green band) and ±2f (yellow band) are overlaid. The red horizontal lines indicate the p-value at 0.05.
95 ) with ±1f excursions, observed
Table 9.6: ? 0 -value, expected 95% CL upper limit on the number of BSM events ((exp9595% CL upper limit on the number of BSM events ((obs) and visible cross section for SR1e, SR2e and SR2mu.

Signal region
SR1e
SR2e
SR2mu

? 0 (` B = 0)
0.5
0.5
0.5

95
(exp

95
(obs

9.3+4.1
2.7
5.5+2.8
1.8
5.8+2.9
1.8

7.6
4.9
3.9

95
hn fiobs
[fb]

0.06
0.04
0.03

9.3 Exclusion limits on signal events with model dependent fits
In order to determine whether a particular signal model is rejected at 95% confidence level, model dependent
fits are performed. As explained in Section 1.3, the right-handed neutrinos are Majorana particles and

96

20
µ

50% of signal events have same-sign lepton pairs, called Majorana scenario. The CR/SR definitions andthe handling of the normalization factors are exactly the same as those for background-only fits discussed
in Section 9.1, except that the multi-bins SRs are convoluted into the likelihood and a signal sample
is included. The compatibility of the observed data with background-only or signal-plus-backgroundhypothesis is checked using the CLs prescription as explained in Secion 7.2. The upper limit on the given
cross section for various ,R and #R hypothesis are obtained.
The excluded phase space in the two-dimensional plane of ,R and #R masses obtained from the upper
limits are shown in Figure 9.4. ,R mass is excluded up to 6.4 TeV for #R mass at 1.0 TeV at the 95%
confidence level for both electron and muon channels.

9.4 Discussion
9.4.1 Comparison to the other LHC results
Figures 9.5(a) and 9.5(b) show the comparisons between the results already published with the datadelivered by LHC and the result of this analysis for the Majorana scenario. The exclusion limits are
improved by 1.5 TeV and 1.4 TeV in heavier ,R mass for #R mass at around 200 GeV compared to theprevious publication with 80 fb 1 by ATLAS [34] for electron and muon channels, respectively.
There are some reasons of these improvement except for the data increasement. The optimization of
binning in SRs discussed in Section 5.5 improves the ratio of the number of signal events to the number ofbackground in the highest ,R mass region. This enables to search for high-mass ,R signals which havesmall cross sections. Re-optimizations of two lepton channels improve the ratio of the number of signal
events to the number of background. In addition, by adding SR1e for electron channel and deactivating themuon-jet overlap removal and any isolation requirement for the sub-leading muon for muon channel, thesensitivity is improved in the region of #R mass below 100 GeV. This region is investigated for the firsttime in the ATLAS. This is a benefit of using large-' jets formed by combining small-' jets as explainedin Section 4.11.
Since the LRSM model assumes that the neutrinos are Majorana particles, 50% of the signal events are
generated to have same-sign lepton pairs and the other 50% to have opposite-sign lepton pairs. On the other
hand, in case Dirac particles are considered, called Dirac scenario, all lepton pairs in the final state areopposite-sign. The exclusion limits for the Dirac scenario by using the exactly same analytical methods as
the Majorana scenario are evaluated by selecting only events with a lepton pair of opposite-sign in the truthlevel for signal samples and doubling the cross section as shown in Figures 9.5(c) and 9.5(d). ,R mass is
excluded up to 6.4 TeV for #R mass at 1.0 TeV at the 95 % confidence level for both electron and muonchannel. The exclusion limits are improved by 1.7 TeV and 1.6 TeV at #R mass of 500 GeV comparing
to the previous publication with 36 fb 1 by ATLAS [34] for electron and muon channel, respectively.
Interpretations of Dirac scenario were not done in the previous ATLAS boosted [34] and latest CMS
analyses [38]. These comparisons clearly show that the exclusion limits set by this analysis gives the best
sensitivities in most of the phase space.

97

9.4.2 Comparison to the non-LHC experiments
Figure 9.6 shows the observed upper limits in the region with <(#R ) < 1000 GeV. In that region, theexclusion limit of this analysis is almost independent of <(,R ) and up to roughly <(,R ) = 6.2 TeV is
excluded. Compared to the results obtained in the non-LHC experiments, the most stringent limits are
obtained with respect to the <(,R ) except in the region of <(#R ) < 50 GeV where #R is less likely todecay to the off-shell ,R . Even in comparison with the expected results that would be obtained with ILC,
more restrict limit is obtained in the most phase space.

9.4.3 Cross section and coupling constant upper limits
The upper limits on the product of the cross section for ,R production from proton collision, f( ? ? ! ,R ),and the branching fractions, B(,R ! ✓✓@ @¯0), for given <(#R ) hypothesis are scanned with respect to the<(,R ). The upper limits are visualized in Figure 9.7 for <(#R ) = 50 GeV and 1 TeV with the resultsby ATLAS dÚet resonance search with 139 fb 1 [113]. The cross section upper limit in dÚet resonanceis scaled by multiplying B(,R ! ✓✓@ @¯0) over B(,R ! @ @¯0) by taking into account the unitarity of themixing matrix for right-handed particles. The <(,R ) where the observed limit and theoretical crosssection intersect corresponds to the maximum exclusion limit for a given <(#R ) at 95% CL. Comparing
to the dÚet resonance results, restrictions with heavier ,R mass of about 1.0 to 1.5 TeV are observed
depending on the #R mass.

98s = 13 TeV, 139 fb-1, All limits at 95% CL
Boosted Expected (± 1 σexp )R

4500
Majorana scenario

SR1e only

4000

SR2e onlym(W R) = m(NR)

3500

1

Boosted Observed
06

3000 0.92500 0.0

-05

-13

6e
-28

-23

-17

2e

-41

3e

3

00

0.0

-166
6e-18
19ee-1

-09

5e

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00

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5000

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3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000m(W ) [GeV]R(a) Electron channels = 13 TeV, 139 fb-1, All limits at 95% CL

4500

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Boosted Expected (± 1 σexp )Majorana scenario

4000m(W R) = m(NR)1

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3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000m(W ) [GeV]R(b) Muon channel

Figure 9.4: The expected and observed 95 % CL upper limits: (a) electron channel. (b) muon channel. Black,blue and pink dashed lines represent the expected CL upper limits for combined expected, SR1e only and SR2e
only, respectively. Dark red solid line represents the observed CL upper limit. Yellow band represents the one
standard-deviation of the expected limit. Each gray number shows the CLs value for each signal mass point.

99s = 13 TeV, 139 fb-1, All limits at 95% CL

4500

SR1e only

4000

SR2e only
Boosted Observed (This analysis)
Resolved Observedm(W R) = m(NR)

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(a) Majorana electron neutrino
Electron channel(b) Majorana muon neutrinos = 13 TeV, 139 fb-1, All limits at 95% CL
Boosted Expected ( ±1 σ exp )4000

SR2e only
Boosted Observed (This analysis)m(W R) = m(NR)

Boosted Expected ( ±1 σ exp )4500
Dirac scenario

4000m(W R) = m(NR)

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Observed Limit (CMS Combined 138 fb-1)

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m(N ) [GeV]

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-1

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1000m(W R) = 10 × m(NR)

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3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000m(W ) [GeV]

3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000m(W ) [GeV]RR(c) Dirac electron neutrino(d) Dirac muon neutrino

Figure 9.5: The expected and observed 95 % CL upper limits: (a) Majorana electron neutrino scenario. (c) Dirac
electron scenario. (b) Majorana muon neutrino scenario. (d) for Dirac muon neutrino scenario. Black, blue and pinkdashed lines represent the expected CL upper limits for combined expected, SR1e only and SR2e only, respectively.
Yellow band represents the one standard-deviation of the expected limit. Red, black, yellow, green and blue solidlines represent the observed CL upper limits for this analysis, ATLAS resolved analysis with 139 fb 1 [112], CMS
analysis [38] with 138 fb 1 , ATLAS resolved analysis [33] with 36 fb 1 and the ATLAS boosted analysis [34] with
80 fb 1 , respectively.

100

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Rm(N ) [GeV]

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0ν ββ (T

0ν
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= 1.8 × 10 years, 90% CL)

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700

ILC (Polarized, 95% CL)

600
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Figure 9.6: Observed and expected exclusion region in ,R mass and #R mass plane. Sold dark red line represents
the observed 95% CL limit of this analysis. Black andp gray exclusion lines represent the expected results from
ILC with and without the initial beam polarization at B = 500 GeV [46], respectively. 90% exclusion from theneutrino less double beta decay [41] and 95% exclusion from the meson mixing [39] are shown as purple and pale
red lines, respectively. 95% exclusion with ATLAS resolved analysis with 36 fb 1 [33], ATLAS boosted analysis
with 80 fb 1 [34] and CMS analysis with 138 fb 1 [38] are shown as green, blue and dark yellow lines, respectively.

101

102

Electron channel, m(NR) = 1000 GeV

s = 13 TeV, 139 fb-1, All limits at 95% CL

Expected Limit (±2 σexp)
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Expected Limit
Theory (g = g )R
L
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ATLAS di-jet resonance 139 fb-1

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R

R

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σ(pp → W )B (W → eeqq') [fb]s = 13 TeV, 139 fb-1, All limits at 95% CL

Electron channel, m(NR) = 50 GeV

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ATLAS di-jet resonance 139 fb-1

s = 13 TeV, 139 fb-1, All limits at 95% CL

Muon channel, m(NR) = 1000 GeV

Expected Limit (±2 σexp)
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Theory (g = g )R
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ATLAS di-jet resonance 139 fb-1

102

R

R

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102(b) Electron channel, <(#R ) = 1000 GeV
σ(pp → W )B (W → µµqq') [fb]3R

σ(pp → W )B (W → µµqq') [fb](a) Electron channel, <(#R ) = 50 GeV
106500 7000m(W ) [GeV]

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Figure 9.7: Upper limits for the cross section of ? ? ! ,R ! ✓✓@@ 0 for (a) shows the limit for <(#R ) = 50 GeV in
the electron final state, (b) shows the limit for <(#R ) = 1000 GeV in the electron final state, (c) shows the limit for<(#R ) = 50 GeV in the muon final state, and (d) shows the limit for <(#R ) = 1000 GeV in the muon final state.
Red bold, black bold and black dashed lines denote theoretical cross section, observed cross section upper limit andexpected cross section upper limit, respectively. Observed cross section limits of ATLAS dÚet resonance search with
139fb 1 [113] are also displayed as blue sold lines. Yellow and green bands indicate the 1 f and 2 f coverage of the
expected upper limits.

102

10 Conclusion
This thesis has been presented a search for right-handed neutrino #R and right-handed , boson ,R inpfinal states with two same flavour leptons and a large-' jet using proton-proton collisions at B = 13 TeV
with the ATLAS detector. The data is collected in 2015-2018 corresponding to the integrated luminosityof 139 fb 1 .
To extend the searchable region, event selections are re-optimized from the previous analysis. Furthermore,for electron channel, a new signal region requiring exactly one electron is introduced to cover lower #R
mass region. Two different SRs are orthogonal between each other and they are statistically combined
to evaluate final sensitivities. For muon channel, the object selection and overlap removal are optimized
as well. The sub-leading muon from #R decay is not required to pass any isolation criteria and overlap
removal with jets is deactivated.
The background estimation methods have been developed to estimate dominant backgrounds by preparing
dedicated control regions. Extrapolations from CRs to SRs are validated by using regions with similarphase spaces, called extra VRs, for each background. The post-fit results reasonably agree with observed
data in all extra VRs showing the methods work well. Finally, the search for the signal has been performed
and the observed data is consistent with the post-fit background yield within one standard deviation. No
excess is observed in the all signal regions.
No excess is observed in every signal regions. Hence, the exclusion limits are set. In the scenario where
the neutrinos are Majorana particles, ,R mass is excluded up to 6.4 TeV at the #R mass of 1.0 TeV for
both electron and muon channels. Compared to the previous results, it corresponds to the expansion of
exclusion limits by 1.5 TeV and 1.4 TeV for electron and muon channels, respectively. The exclusion limits
for Dirac particle scenario are also evaluated and it is observed that the exclusion power is comparable
to that of the Majorana particles. In addition, the search sensitivity is successfully extended to #R mass
below 100 GeV for the first time in the ATLAS experiment.

103

Acknowledgements
I have received a lot of advice and help from many people during the course of this research. First, I amvery grateful to my advisor, Prof. Junichi Tanaka, for not only supporting my research but also helping
me to continue my life at CERN. I am also very grateful to Dr. Takuya Nobe for not only giving me
many attentive supports at every step of research processes but also providing me with a lot of supports
to make living at CREN a pleasant experience. I want to express my gratitude to Dr. Yuji Enari, Dr.
Yasukuki Okumura, Dr. Koji Terashi, Dr. Tatuya Mashbuchi, Dr. Ryu Sawada, Dr. Tomoyuki Saito, Prof.
Masaya Ishino, Dr. Saito Masahiko, Dr. Morinaga Masahiro, and Dr. Ryu Sawada not only provided
important comments and suggestions at the analysis meetings, but also helped me by correcting my slides
and practicing my presentation for the conference, which enabled me to proceed with the analysis in theright direction.
Dr. Matthias Saimpert, Dr. Merve Nazlim Agaras, Dr. Flavia de Almeida Dias, and Dr. Tamara Vazquez
Schroeder led the analysis in ATLAS and provided many comments at group and sub-group meetings.
I would also like to thank the members of the analysis group, Dr. Neofytos Themistokleous, Dr. BenjaminMichael Wynne, Dr. Christos Lepnodopoulos, and Dr. Edson Carquin Leopez, who were very helpful in
our weekly discussions. I would like to thank them all.
I am grateful to Dr. Shion Chen, Dr. Tomoya Iizawa, Dr. Tomohiro Inada, Dr. Maeda Junpei, and many
students who spent their research lift with me for their help during my stay at CERN, which has been avery comfortable experience.
I would also like to thank the ICEPP secretaries for all the administrative work they did for me, including
travel arrangements to CERN, which allowed me to concentrate on my research. Finally, I would like tothank my family for their constant support even though I was far away from my hometown, and for theircontinuous support in everything I did. Thanks to many people, I was able to make the most of my three
years in the doctoral program.

104

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