Evidence for a Higgs Boson in Tau Decays with
mR0
the CMS Detector
MASSACHUSETTS 1NE
OF TECHNOLOGY
by
Valentina Dutta,
LIBRARIES
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Physics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2014
@ Massachusetts Institute of Technology 2014. All rights reserved.
Signature redacted
A uth or ...................................
.......
Department of Physics
May 28, 2014
Signature redacted
Certified by.............................................
Markus Klute
Assistant Professor
Thesis Supervisor
Signature redacted
A ccepted by .........................
............
ProTe sssor Krishna Rajagopal
Associate Department Head for Education
2
Evidence for a Higgs Boson in Tau Decays with the CMS
Detector
by
Valentina Dutta
Submitted to the Department of Physics
on May 28, 2014, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Physics
Abstract
In this thesis, I describe the search for a Higgs boson through its decay to a pair of tan
leptons with the tau-pair subsequently decaying to ail electron, a muon, and neutrinos.
The search is performed using data collected from proton-proton collisions by the
Compact Muon Solenoid experiment at the Large Hadron Collider, corresponding to
5.0 fby of integrated luminosity recorded at a center-of-mass energy of 7 TeV and
19.7 fb-' at 8 TeV. The expected significance for a Standard Model Higgs boson signal
with a mass of 125 GeV is at the level of 1.2 standard deviations for the electronmuon tau-pair decay mode. A mild excess of events is seen above the SM background
expectation in this decay mode, consistent with a SM Higgs boson of mass 125 GeV.
In combination with results using other tau-pair decay modes, an excess of events
above the background expectation is seen at the level of 3.4 standard deviations.
This constitutes the first evidence for a Higgs boson to decay to leptons. This thesis
also describes an analysis of the data in the context of physics beyond the Standard
Model, particularly in the framework of its Minimal Supersymnnetric extension.
Thesis Supervisor: Markus Klute
Title: Assistant Professor
3
4
Acknowledgments
I would like to express my deep gratitude to my research supervisor, Professor Markus
Klute, for his guidance and support over the past few years, for helping me to find
encouragement and motivation when I needed them, and for impelling me to try to
do better. I cannot imagine the course of my PhD without his help and counsel.
Thanks also to Steve Nahn for his excellent advice and for always being a source of
good cheer, and to Professor Christoph Paus for many enlightening and entertaining
discussions. I have learned a lot while working with members of the MIT PPC group,
during meetings, informal discussions, and even during conversations completely unrelated to physics. The group is characterized by intellectual excellence, a passion for
physics, as well as a spirit of fellowship and good humor which have all made being
a part of it a special experience.
I would particularly like to thank the people I have worked with closely on the
H
-
rT analysis: Roger Wolf, Phil Harris, Matthew Chan, and Aram Apyan. Even
at stressful times (of which we experienced quite a few), working with them has always
been enjoyable. Thanks to other past and present members of the MIT group, including Pieter Everaerts, Si Xie, Josh Bendavid, Kevin Sung, Guillelmo Gomez-Ceballos,
Marco Zanetti, Fabian St6ckli, Duncan Ralph, Mingining Yang, Andrew Levin, Erik
Butz, Gerry Bauer, Sham Sumorok, Leonardo Di Matteo, Max Goncharov, Stephanie
Brandt, Xinmei Niu, and Jay Lawhorn, for their help and advice at various times and
for providing an agreeable and inspiring environment to work in, both at CERN and
at MIT. Special thanks go to Pieter and Josh for being excellent friends during my
time at CERN.
Thanks, in fact, to all of my friends in the Geneva area and in the US; without
them, getting through my PhD with my humor and sanity relatively intact would
probably have been impossible.
Finally, I must express my gratitude to my family, for their love, support, and
encouragement over the years: especially to my parents, Nirmalendu and Indrani,
and to my brother Joydeep, and my sister-in-law Purbali.
5
6
Contents
1
2
Introduction
13
1.1
Theoretical Overview of the Standard Model . . . . . . . . . . . . . .
14
1.1.1
Electroweak Theory . . . . . . . . . . . . . . . . . . . . . . . .
15
1.1.2
The Higgs Mechanism
17
1.2
Higgs Boson Production at the LHC
1.3
The H
-
1.3.1
. . . . . . . . . . . . . . . . . .
19
Decay Mode . . . . . . . . . . . . . . . . . . . . . . .
21
The T-Lepton . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
1.4
The Minimal Supersyinietric Standard Model . . . . . . . . . . . . .
23
1.5
Analysis Overview
26
T+--
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The CMS Detector at the LHC
28
2.1
The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . .
28
2.2
The Compact Muon Solenoid Detector
. . . . . . . . . . . . . . . . .
30
2.2.1
The Tracking System . . . . . . . . . . . . . . . . . . . . . . .
31
2.2.2
The Electromagnetic Calorimeter
33
2.2.3
The Hadron Calorimeter . . . . . . . . . . . . . . . . . . . . ..
35
2.2.4
The Muon System
. . . . . . . . . . . . . . . . . . . . . . . .
37
2.2.5
Triggering and Data Acquisition . . . . . . . . . . . . . . . . .
39
Luminosity Measurement . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.3
3
. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
Datasets and Event Simulation
43
3.1
D atasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.2
Event Sim ulation
45
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4
3.2.1
Event Generation . . . . . . . . .
45
3.2.2
Parton Showering, Hadronization, and Underlying Event
46
3.2.3
Pileup Simulation . . . . . . . . . . . .
46
3.2.4
Detector Simulation
. . . . . . . . . .
47
3.3
Signal Processes . . . . . . . . . . . . . . . . .
47
3.4
SM Backgrounds
. . . . . . . . . . . . . . . .
50
Event Reconstruction and Object Selection
4.1
Primary Vertex . . . . . . . . . . . . . . . . .
55
4.2
Particle Flow . . . . . . . . . . . . . . . . . .
56
4.3
Jet Reconstruction
. . . . . . . . . . . . . . .
57
4.3.1
Jet Energy Corrections . . . . . . . . .
58
4.3.2
Pileup Jet Identification . . . . . . . .
58
4.3.3
b-Jet Tagging . . . . . . . . . . . . . .
59
. . . . . . . .
59
. . .
60
. . . . . . . . . . .
61
Muon Reconstruction . . . . . . . . . . . . . .
62
Muon Identification . . . . . . . . . . .
63
. . . . . . . . . . . .
63
. . . . . . . . .
64
4.7
Lepton Isolation . . . . . . . . . . . . . . . . .
67
4.8
Di-T Mass Reconstruction
. . . . . . . . . . .
68
4.4
4.5
Missing Energy Reconstruction
4.4.1
MVA Missing Transverse Energy
4.4.2
Recoil Corrections
4.5.1
4.6
Electron Reconstruction
4.6.1
5
54
Electron Identification
72
Event Selection
5.1
Trigger Selection
. . . . . . . . .... .... .. .
72
5.2
Lepton Selection
. . . . . . . . ... .... ... .
74
5.3
Lepton Selection Efficiency . . . . . . . . . . . . . .
76
5.3.1
Tag-and-Probe Method . . . . . . . . . . . .
77
5.3.2
Lepton Identification and Isolation Efficiency
77
5.3.3
Trigger Efficiency . . . . . . . . . . . . . . .
80
8
5.4
b-Tagging Efficiency and Mis-Tag Rate . . . . . . . . . .
81
5.5
Topological Selection . . . . . . . . . . . . . . . . . . . .
82
5.5.1
Standard Model Higgs Analysis Selection . . . . .
83
5.5.2
MSSM Higgs Analysis Selection . . . . . . . . . .
84
Event Classification . . . . . . . . . . . . . . . . . . . . .
89
5.6.1
Standard Model Higgs Analysis Event Categories
89
5.6.2
MSSM Higgs Analysis Event Categories
94
5.6
6
Signal and Background Modeling
95
6.1
Signal M odeling . . . . . . . . . . . . . . . . . . . .
. . . . .
95
6.2
Background Estimation . . . . . . . . . . . . . . . .
. . . . .
96
6.2.1
Drell-Yan T-Pair Production (Z
. .
. . . . .
96
6.2.2
Top-Quark Pair Production (t)
. . . . . . .
. . . . .
98
6.2.3
Jet-Induced Backgrounds: W+jets and QCD Multijet Production 99
6.2.4
Other Backgrounds: Di-Boson, Single-Top
. . . . .
103
6.2.5
H
. . . . . . . . . . . . . .
. . . . .
103
Control Distributions . . . . . . . . . . . . . . . . .
. . . . .
104
6.3
7
. . . . .
->
WW -+ 212v
-> TT)
.
Systematic Uncertainties
114
7.1
Luminosity
115
7.2
Lepton Selection
. . . . . . . . . . . . . . . . . . .
116
7.3
Lepton Energy Scale . . . . . . . . . . . . . . . . .
116
7.4
Jet Energy Scale
. . . . . . . . . . . . . . . . . . .
117
7.5
$T Scale . . . . . . . . . . . . . . . . . . . . . . . .
118
7.6
b-Tagging and Mis-Tag Rate . . . . . . . . . . . . .
119
7.7
Other Normalization Uncertainties
. . . . . . . . .
119
Normalization . . . . . . . . . . . .
119
7.8
. . . . . . . . . . . . . . . . . . . . . .
7.7.1
Z
7.7.2
tt Normalization
. . . . . . . . . . . . . . .
120
7.7.3
Fakes . . . . . . . . . . . . . . . . . . . . . .
120
7.7.4
Di-Boson Normalization
121
-
TT
. . . . . . . . . . .
Theoretical Uncertainties on SM Signal Processes
9
.
121
7.9
7.8.1
PDF Uncertainty . . . . . . . . . . . . . . . .
. . . . . . 122
7.8.2
Scale Uncertainty . . . . . . . . . . . . . . . .
. . . . . .
122
7.8.3
Parton Shower Modeling Uncertainty.....
. . . . . .
123
7.8.4
Higgs
. . . . . .
123
PT
Spectrum Uncertainty . . . . . . . .
Theoretical Uncertainties on MSSM Signal Processes
7.10 Summary of Systematic Uncertainties . . . . . . . . .
8
. . . . . .
124
Statistical Analysis and Results
127
Statistical Procedure . . . . .
128
8.1
8.2
9
. . . . . . 124
8.1.1
Likelihood Construction . . . . . . .
. . . . . . . . . . . . 128
8.1.2
Limit Calculation . . . . . . . . . . .
. . . . . . . . . . . . 129
8.1.3
Significance Calculation
. . . . . . .
. . . . . . . . . . . .
130
8.1.4
Coupling Fits . . . . . . . . . . . . .
. . . . . . . . . . . .
131
Standard Model Higgs Analysis Results . . .
. . . . . . . . . . . .
132
8.2.1
Di-T Mass Distributions
. . . . . . .
. . . . . . . . . . . . 132
8.2.2
Event Yields . . . . . . . . . . . . . .
135
8.2.3
Upper Limits on Signal Strength
. .
136
8.2.4
Significance . . . . . . . . . . . . . .
137
8.2.5
Combination with Other T-Pair Final States
138
8.2.6
Combined results of SM Higgs boson searches in fermionic decay
m odes . . . . . . . . . . . . . . . . . . . . .
142
8.3
Results from ATLAS H
Search . . . . . . . .
143
8.4
MSSM Higgs Analysis Results . . . . . . . . . . . .
144
-
TT
8.4.1
Di-T Mass Distributions
. . . . . . . . . . .
145
8.4.2
Event Yields . . . . . . . . . . . . . . . . . .
145
8.4.3
Model-Independent Single Resonance Search
145
8.4.4
MSSM Higgs Boson Search . . . . . . . . . .
150
8.4.5
Combination with Other T-Pair Final States
151
8.4.6
Intepretation of MSSM Higgs Boson Search Results
153
158
Perspective
10
10 Conclusion
162
A Lepton Efficiencies
165
B Tables of Exclusion Limits
172
11
12
Chapter 1
Introduction
The search for the Higgs boson has been one of the great scientific quests of the last
half-century. In July 2012, physicists at the Large Hadron Collider announced the
discovery of a new particle with properties consistent with those of a Higgs boson [1,2];
the very next year, the Nobel Prize in Physics would be awarded to Peter Higgs and
Francois Englert for their contributions to the theory of the Higgs mechanism [3-8].
The discovery marked the start of a new era for particle physics. An immediate
concern was verifying whether the observed state was compatible with the properties
of the Higgs boson predicted by the Standard Model (SM) [9,10]. The discovery was
driven by significant excesses observed in searches for the SM Higgs boson decaying to
pairs of Z bosons, pairs of photons, and pairs of W bosons. Thus far, measurements
of the couplings of the new boson to W and Z bosons agree with the expectations
for the SM Higgs boson [11,12], and its spin-parity properties appear consistent with
those of the SM Higgs boson [12-14].
A key ingredient in determining whether the observed boson is the SM Higgs boson
is the measurement of its couplings to fermions. The 7-pair decay mode is particularly
interesting since it allows the study of the Higgs boson couplings to leptons.
13
1.1
Theoretical Overview of the Standard Model
The Standard Model of particle physics describes the observed elementary particles
and their interactions. It includes 12 spin-1/2 fermions, 6 leptons and 6 quarks. The
known leptons come in two categories: the electron (e), the muon (p), and the tau
(T),
each with one unit of electric charge, and three corresponding neutrinos (Ve, V,
V'),
which are electrically neutral. Leptons do not interact via the strong interaction.
They are classified in three generations:
(1.1)
The 6 known flavors of quarks are either "up-type" quarks - the up (u), charm (c),
and top (t) quarks - carrying an electric charge of +2/3, or "down-type" quarks - the
down (d), strange (s), and bottom (b) quarks - carrying an electric charge of -1/3.
Quarks also carry "color charge", a property related to the strong interaction. Like
the leptons, they are grouped in three generations:
C
U
d )
(S)
t
b
(1.2)
Each of the 12 fermions has a corresponding anti-particle carrying the opposite charge.
In the SM, gauge bosons with spin 1 mediate the electromagnetic, weak, and
strong interactions. The photon, which is massless and electrically neutral, mediates
the electromagnetic interaction between electrically charged particles. The massive
W+, W-, and Z bosons are the mediators of the weak interaction; the W+ and Walso carry electric charge of +1
and -1
respectively. Eight massless gluons mediate
the strong interaction between quarks which carry a color charge; gluons themselves
also carry color charge and participate in the strong interaction.
Mathematically, the SM is formulated as a quantum field theory with the gauge
symmetry group SU(3)c ® SU(2)L ® U(1)Y [15].
14
The color sector, i.e., the strong
interactions between quarks and gluons, is governed by the SU(3)c subgroup. The
electroweak interactions are described by the SU(2)L
(
U(1)y subgroup [9, 10, 16].
SU(2)L is the symmetry of weak isospin which couples only to"left-handed" chiral
states and U(1)y the symmetry of weak hypercharge.
1.1.1
Electroweak Theory
The SU(2)L transformations of weak isospin operate only on left-handed fermion
doublets, which can be represented as
VC
1
(1.3)
for the leptons or as
U
c
t
d'
S'
b'
(1.4)
for the quarks; the subscript L denotes left-handed spinors. The left-handed doublets
have weak isospin T =,
while right-handed fermions form isospin singlets with
T = 0 and do not couple to the SU(2)L gauge field. They are denoted as eR, PL,
(leptons) and uR, d' , CR,
S' , tR,
TR
b' (quarks). The prime notation used for the quarks
indicates their weak eigenstates, a mixing of the mass eigenstates represented by
d'
d
')
=VCK
b'
A
s
,
(1.5)
b
with VCKAI being the Cabibbo-Kobayashi-Maskawa (CKM) matrix [17,18].
The U(1)y symmetry is generated by the weak hypercharge operator, defined by
Q
where
Q
=
T3 +
y
,(1.6)
2
is the electric charge and T3 the third component of weak isospin. Unlike
15
weak isospin, the weak hypercharge couples to both left-handed and right-handed
components of fermions.
The gauge fields associated with the SU(2)L 0 U(1)y symmetry group are repre-
sented as W, W, W for weak isospin and B, for weak hypercharge. The observable
electroweak bosons - the charged W+, the neutral Z, and the photon - are obtained
from the gauge fields by
(W 1 T W)
W
AP
(1.7)
cos OwW3 - sin OwB
(1.8)
sin OwW + cos w B,
(1.9)
where Ow is known as the weak mixing angle. It can be expressed in terms of the
coupling constants of SU(2)L (g) and of U(1)y (g') by the relations
sin 0w =
g2
(1.11)
w=
cos
(1.10)
,
± g'2
g
2
+ g'
2
Ow is a free parameter of the SM and is experimentally measured to be ~ 30'.
The gauge field part of the Lagrangian of electroweak interactions is given by
1
L
a
1
-
(1.12)
-BBl
and the fermionic part by
+ i-
L=Xi
Here XL,
V>R
i TaW," XL +
-
_Ri ll
+ iP YB,) 'OR.
(1.13)
denote a left-handed doublet and right-handed singlet of weak isospin
respectively, -" the Dirac matrices,
T'
the Pauli spin matrices, and Y the hypercharge
operator.
The SU(2)L 0 U(1)y gauge symmetry of the electroweak Lagrangian prohibits
16
mass terms for the gauge bosons of the form MI2 WTW"
since they would break local
gauge invariance and render the theory unrenormalizable. An explicit mass term for
the fermions of the form
=rn (OL=R
+
(1.14)
45R4L)
violates SU(2)L gauge symmetry since the SU(2)L transformations operate differently
on left-handed and right-handed states.
However, the W and Z bosons and the
fermions are experimentally known to be massive.
This mass problem is solved by
introducing spontaneous symmetry breaking via the Higgs mechanism.
1.1.2
The Higgs Mechanism
In the SM, the Higgs mechanism introduces a Higgs field, a complex SU(2) doublet
of scalar fields
(+0
heh
with weak isospin T =
Iand weak hypercharge
1.
+
g
)
(1.15)
Y = 1. The Lagrangian describing
the Higgs sector can be written as
2
L
(&II-+i5BP
+
raW7"
~f_4P2 5 4 ~
A(0,0)2
(1.16)
with pt2 < 0, A > 0. The potential
V(O) = P 250 t
-A
(t0)
2
(1.17)
has its minima at
11 2
$t "A .
17
(1.18)
The vacuum or ground state is chosen to be
This choice guarantees that Qqo = 0, and therefore the electromagnetic U(1) gauge
symmetry generated by
Q is
unbroken by the Higgs mechanism and the photon re-
mains massless.
Recasting the Higgs field as deviations from the vacuum, in the form
(1.20)
1
=
(X)
vf-
v + h(x))
and inserting it in the Lagrangian for the Higgs and gauge fields gives rise to explicit
The gauge boson masses can be identified by
mass terms for the gauge bosons.
substituting the vacuum state
#o in the
Lagrangian, with the mass of the W being
given by
1
Mw =v-g,
(1.21)
2
and the mass of the Z by
Mz =v
1
2
g 2 + g' 2 ,
(1.22)
while the photon remains massless. Comparing Equations 1.21 and 1.22 with Equation 1.11 shows that Mw = Mz cosOw.
The terms of the potential in Equation 1.17 become
EV
=
- Avh 3
-22
_
=
2
- h2
-
h
(1.23)
-Ah4
4
3mhh
-
V2
4
Ah4
(1.24)
allowing the identification of a scalar particle, the Higgs boson, with mass
mh =
2P
2 =
18
2Av,
(1.25)
as the quantum of the field h(x). The Higgs boson mass is not predicted by the SM
and needs to be determined experimentally.
The source of fermion masses in the SM is the introduction of a Yukawa coupling
between the fermion fields and the Higgs field:
2
-m
ICY = -
V
(YLO'OR +
(1.26)
ROXL).
Using the expansion from Equation 1.20 results in
Y
m('LOR
+
VOROL)
-
_~(
V
7
L<)R + 4'RVL)h
(1.27)
(1.28)
for each fermion. We obtain a mass term, n4'<, for the fermions, and a coupling
between the fermion and the Higgs scalar given by
4'Ooh.
The strength of the
coupling is proportional to the mass of the fermion.
The Higgs boson has been the subject of a decades-long experimental search in
order to confirm the theory of the Higgs mechanism. One of the principal goals in
mind when building the Large Hadron Collider (LHC) at CERN was to either find
the Higgs boson or to disprove its existence.
1.2
Higgs Boson Production at the LHC
The Higgs boson can be produced in proton-proton collisions at the LHC through
one of several mechanisms, involving interactions between the underlying quarks
and gluons (partons).
Calculating the cross section of different processes arising
out of proton-proton collisions requires knowledge of the parton distribution functions (PDFs) within the proton. The Higgs boson production mechanism with the
highest cross section is the process of gluon fusion, in which two initial state gluons
produce a Higgs boson through an intermediate heavy fermion loop. The dominant
contribution to this process is via a top quark loop, since the coupling of the Higgs
boson to fermions is proportional to their mass. The process with the second-highest
19
q
q'
H
W/Z
H
qqq
(b) vector boson fusion
(a) gluon fusion
g
-
W/ Z
H
W/Z
H
hh
g
q
(c) W/Z-associated production
t
(d) tt-associated production
Figure 1-1: Feynman diagrams showing the mechanisms of Higgs boson production
at the LHC.
production rate, roughly an order of magnitude lower than that of gluon fusion, is
that of vector boson fusion (VBF), in which the Higgs boson is produced by a pair
of W or Z bosons radiated by initial state quarks. The VBF Higgs boson production
signature is characterized by two energetic quarks largely separated in rapidity. Next,
the Higgs boson can be produced in association with a W or Z boson through the
process of Higgs-strahlung, with the Higgs boson being radiated by a vector boson.
Finally, Higgs boson production associated with a top-antitop quark pair has an even
lower cross section. Leading order Feynman diagrams for these four principal modes
of Higgs boson production at the LHC are displayed in Fig. 1-1, while the production
cross sections for each mode as a function of the Higgs boson mass at a center-of-mass
20
102
-
I
'
I
25
-I
I
-\s=8TeV
-
I)
102
+
10
IV4
f
\sMH8[eV]
M
10-1
1
00
200
80 100
300
400
1000
MH [GeV]
Figure 1-2: Higgs boson production cross sections at V/s = 8 TeV.
energy of 8 TeV are shown in Fig. 1-2 [19].
The Higgs boson can decay directly to pairs of fermions or vector bosons or,
through loops, to gluon pairs, photon pairs, or to a photon and Z boson. For Higgs
boson masses below about twice the W boson mass, the predominant decay modes
are to pairs of bottom quarks, tau leptons, or charm quarks, or through top loops
to gluon pairs. Although at these masses the phase space for decays to a pair of W
bosons is reduced due to the requirement that one of the W bosons must be off-shell,
the strength of the coupling of the Higgs boson to the W boson ensures a respectable
branching ratio for W boson pairs. The branching ratios for different decay modes
for a Higgs boson mass of less than 200 GeV are shown in Fig. 1-3 [20].
1.3
The H -+
-r+r-
Decay Mode
With the discovery of a new boson by the ATLAS and CMS collaborations at the
LHC [1,2], studying the properties of the newly-discovered state and determining its
compatibility with the SM Higgs boson became the immediate goal. Measurement of
its couplings to fermions is particularly important in order to establish the nature of
21
(11
- U))
bb
WW
-)
0-
CCC
10~
100
120
140
160
180
200
MH [GeV]
Figure 1-3: Higgs boson branching ratios at low mass.
this particle. While there are indirect constraints on the coupling of the Higgs boson
to the top quark from the measurements in the bosonic final states, determination of
the coupling to down-type fermions requires a direct measurement of the Higgs boson
decay to the corresponding fermionic final states. Studying the decays of the Higgs
boson to pairs of T-leptons and bottom quarks is crucial in this regard.
For masses below
-
130 GeV, the decay of the Higgs boson to a pair of T-leptons
has a significant branching ratio. Although the bb decay mode has a higher branching
ratio at these masses, the extremely large backgrounds from QCD multijet production
make this mode very challenging experimentally, and it is only feasible to study
it through the lens of the associated production or VBF production mechanisms,
which have lower cross section
[21].
The H -+
large backgrounds, notably from the Z -+
TT
TT
decay mode does suffer from
process; exploiting the VBF production
topology or the topology for gluon fusion production with an additional jet improves
22
the sensitivity for studying this process. This decay mode is particularly important
because it allows the measurement of the coupling of the Higgs boson to leptons.
1.3.1
The -r-Lepton
The T is the heaviest lepton with a mass of 1.777 GeV; due to its massive nature
it can decay to lighter particles. Taus decay through the weak interaction to a tau
neutrino and a virtual W boson which subsequently produces an electron or a muon
and the corresponding neutrino, or decays hadronically. Figure 1-4 shows a Feynman
digram representing tau decays.
Table 1.1 summarizes the branching ratios for the most prevalent tau decay modes.
Hadronic decays of the tau are the most prevalent, occurring about 65% of the time.
The leptonic decays, to an electron and two neutrinos or to a muon and two neutrinos,
account for 17.8% and 17.4% of tau decays each [22]. Neutrinos in the final state make
the reconstruction of the tau challenging since they do not interact in the detector
and can only be detected by measuring an imbalance in the visible energy in the
detector.
VT
IT~
e~, p-, ~d,s
w
Figure 1-4: Feynman diagram representing the decay of the T-lepton.
1.4
The Minimal Supersymmetric Standard
Model
The SM has been remarkably successful from the experimental point of view. Nevertheless, there are aspects of the theory that are unsatisfactory; one such problem is
that the Higgs boson mass is subject to quadratically divergent radiative corrections
23
Decay mode
Branching fraction (%)
eve, 7
17.83 ± 0.04
1vtvI- 1r
7± V77±70V~r25.52
17.41 ± 0.04
10.83 10.06
7T0
9.30
8.99
±0.09
l0VT
7r_7rr±_V_
0.11
+_0.06
Table 1.1: The most prevalent T-lepton decay modes and their branching fractions,
as a percentage of the total tau decay width.
at high energy. A popular solution to this problem is the introduction of supersymmetry (SUSY) [23,24], a symmetry relating fermions to bosons, which would protect
the Higgs mass from divergent radiative corrections. An additional attraction is that
SUSY could provide a candidate for the dark matter in our universe.
The Minimal Supersymmetric Standard Model (MSSM) is a minimal extension
of the SM incorporating supersymmetry [25,26]. Each particle of the SM is assigned
a superpartner; there are scalar partners for the fermions (known as sleptons and
squarks), and fermionic partners for the gauge bosons (gauginos) and the Higgs boson
(Higgsino). Unlike in the SM, the Higgs sector in the MSSM requires two scalar doublets, with vacuum expectation values
vI, v 2 ,
and five physical Higgs bosons. Three
of these are neutral: the h, the H (both CP-even), and the A (CP-odd), and two are
charged: the H+ and H-. At tree level, the MSSM Higgs sector can be parametrized
in terms of
mA,
the mass of the CP-odd neutral Higgs boson, and tan 3, the ratio of
the vacuum expectation values of the two doublets.
The major production mechanisms for the neutral MSSM Higgs bosons in protonproton collisions are through gluon fusion via a b-quark loop, and associated production with b-quarks. These are illustrated in Fig. 1-5. The couplings of the neutral
MSSM Higgs bosons to down-type fermions like b-quarks and T-leptons are enhanced
at large values of tan 0, resulting in significantly higher branching ratios for the
T-
pair neutral Higgs boson decay mode than in the SM. The enhanced coupling to the
bottom quark also boosts the b-associated production mechanism; the presence of bquarks in the final state can therefore be used to improve the sensitivity of an MSSM
24
Higgs boson search.
g
g
b
A/H/h
b
>-
-
-
-
-
-
A/H/h
-
--
(a) gluon fusion
(b) b-associated production
Figure 1-5: Diagrams showing the mechanisms of neutral MSSM Higgs boson production at the LHC.
At tree level, the masses of the three neutral MSSM Higgs bosons are related by
2
mh,H
1(M2 +-mn2
2
2
/V(M2+m 2
Zi
2
-4mm
AZ
co
COS2
2\.
With the inclusion of higher order radiative corrections, an upper bound of
(29
(1.9)
-
135
GeV [27] is placed on mh, the mass of the light scalar Higgs boson, with an uncertainty
of up to 3 GeV on mh depending on the region of parameter space under consideration.
At the same time, for mA
>
mz, the heavy scalar H and the pseudo-scalar A become
almost degenerate in mass, with mH ~ mA.
Searches for neutral MSSM Higgs bosons are usually presented in the context
of benchmark scenarios, in which the values of SUSY parameters which, through
radiative corrections, affect the Higgs boson masses, cross sections, and branching
ratios, are fixed to certain values. Results are interpreted in the parameter space of
mA and tan,3. The m"x scenario [28, 29] has been used for previous searches and
allows the light scalar h to reach its maximal value of
-
135 GeV, for mA > mz
(known as the "decoupling region"). This is the scenario used in this analysis for the
presentation of the search results.
The discovery of the Higgs-like boson near 125 GeV brings new interest to searches
in the context of the MSSM, since the 125 GeV boson could be compatible with the
Higgs sector expected in the MSSM within the existing experimental uncertainties. In
25
particular, this state can be interpreted as the light MSSM scalar h while searching for
the additional Higgs bosons predicted by the MSSM, and could have a behavior similar
to the expected behavior of the SM Higgs boson. Such a constraint on mh affects
the permitted regions of parameter space; large regions of parameter space would be
ruled out in the mm"x scenario which favors a slightly heavier h in the decoupling
region. However, the interpretation of MSSM Higgs boson search results in the
m"ax
scenario is still relevant since it places conservative lower bounds on allowed regions of
parameter space. Moreover, slight modifications of the mm"x scenario brought about
by adjusting the value of the stop mixing parameter (Xt), would remove much of the
restriction on allowed parameter space [30, 31] by permitting a lighter h.
1.5
Analysis Overview
The search for a Higgs boson decaying to pairs of T-leptons with the CMS detector [32] relies on selecting the T-pair decay products. All possible T-pair final
states are studied at CMS. They are denoted by the visible T-pair decay products:
ThTh,
p'rh, ETh, ep, ee, pp; there are also between 2 and 4 neutrinos produced in each
case. The primary focus of this thesis is on the study of the ey final state with 4
neutrinos from the two leptonic tau decays.
The analysis strategy starts with the selection of proton-proton collision events
passing a trigger based on the presence of an electron and a muon candidate. A
variety of offline selection requirements are imposed, consisting of a combination of
simple cuts requiring measured quantities to be above or below a given threshold,
and multivariate techniques which also make use of the correlations between observables. The goal is to improve the ratio of signal-to-background and achieve the best
possible sensitivity for identifying a signal. Finally, the classification of the selected
events in categories improves the sensitivity of the analysis, and a statistical analysis
is performed to obtain the results. The results are combined with those from the
analyses of other T-pair final states to obtain the combined significance of the search
for a Higgs boson decaying to T-pairs.
26
The same trigger requirements and lepton candidate selection criteria are applied
in the context of both the SM Higgs boson search (henceforward also referred to as the
SM analysis) and the search for neutral MSSM Higgs bosons (henceforward referred
to as the MSSM analysis). However, the two analyses rely on different approaches to
background rejection based on event topology, and different categorizations of events
which target the relevant Higgs boson production mechanisms in each case.
27
Chapter 2
The CMS Detector at the LHC
2.1
The Large Hadron Collider
The largest and highest-energy particle collider built to date, the Large Hadron Collider (LHC) [33] is a remarkable feat of engineering. Located at the European Organization for Nuclear Research (CERN) facilities on the border of Switzerland and
France, the LHC occupies a tunnel, 27 km in circumference, at depths of upto 175
m beneath the French and Swiss countryside near the Swiss town of Geneva. The
high energies of the circulating proton beams in the LHC are achieved by a series
of accelerators which boost the protons to successively higher energies before finally
injecting them into the LHC, the last in the chain of accelerators. Figure 2-1 shows
a schematic representation of the accelerator complex at CERN.
The protons in the LHC are obtained by ionizing hydrogen gas by applying an
electric field.
They are first accelerated to an energy of 50 MeV by the Linac 2
linear accelerator, then injected into the Proton Synchrotron Booster (PSB), which
accelerates them to 1.4 GeV. This is followed by the Proton Synchrotron (PS), where
they are arranged into bunches and accelerated to 25 GeV, and then the Super Proton
Synchrotron (SPS), which accelerates them to 450 GeV. They are then finally injected
into the two LHC beam pipes, with one beam of protons circulating clockwise and the
other beam counterclockwise, and accelerated up to their maximum energy. A large
28
number of superconducting electromagnets are responsible for the transport of the
beams along their desired trajectory in the LHC. 1232 dipole magnets, each 15 m in
length, bend the beams, while 392 quadrupole magnets, 5 - 7 m in length, focus them.
The two beams collide at the four detectors located around the LHC ring: ALICE,
ATLAS, CMS, and LHCb. Prior to entering the detectors, the beams are squeezed
or made narrower in order to increase the probability of collisions. Collisions in 2010
and 2011 took place with each beam reaching an energy of 3.5 TeV for a total collision
energy of 7 TeV, and in 2012 with an energy per beam of 4 TeV for a total collision
energy of 8 TeV. The LHC delivered instantaneous luminosities of up to 3.5 x 1033
cm-2 s-1 in 2011 and up to 7.7 x 1033 cm- 2 S-1 in 2012.
The design parameters
of the LHC correspond to a bunch spacing of 25 ns, with beams consisting of 2808
bunches and 1011 protons per bunch, achieving the design instantaneous luminosity
of 104 cm- 2 s- 1 with an average of 20 proton-proton interactions per bunch crossing.
Figure 2-2 displays graphs of the total integrated luminosity delivered by the LHC
and recorded by the CMS experiment in 2011 and 2012.
CMS
LHC
No th Area
ALICE
LHCb
TT41
TT40
SPS
T12
n of
Tin
HiadatATL
T8
C NG S
AS
Hi~dT6
Gran Sasso
AD
TT2
O
SE
am
E st Area
Figure 2-1: A schematic representation of the accelerator complex at CERN.
29
CMS Integrated Luminosity, pp. 2011,
CMS Integrated Luminosity, pp, 2012, /a= 8 TeV
W= 7 TeV
Data included from 2011-03-13 17:00 to 2011-10-30 16:09 UTC
7
6
Data included from 2012-04-04 22:37 to 2012-12-16 20:49 UTC
7
LHC
Delivered: 6.13
CMS Recorded; 5.55
25
lb
lb
6
I
LHC Delivered: 23.30 lb
CMS Recorded: 21.79 fb
20
20
0
C
C
15
415
4
0
3
2 -
10
2
1
1
0
25
Y
S0
01
Date (UTC)
0
Date (UTC)
(a) Total integrated luminosity in 2011
(b) Total integrated luminosity in 2012
Figure 2-2: Cumulative luminosity per day delivered by the LHC (in blue) and
recorded by CMS (in orange) during proton-proton collisions at Fs = 7 TeV in
2011 (left) and at \s = 8 TeV in 2012 (right).
2.2
The Compact Muon Solenoid Detector
One of the two large general-purpose detectors located around the LHC ring, the
Compact Muon Solenoid (CMS) detector [32] is located deep underground at interaction point 5 on the ring, near the French village of Cessy. The cylindrical detector
is 15 m in diameter and 22 m long, weighing a total of 12500 tons. The design of the
detector is built around the superconducting solenoid magnet which gives the detector its name; 12.5 m long and 6 m in diameter, it produces a 3.8 T magnetic field and
is the largest magnet of its type ever built. The magnet is key for the precise momentum measurement for high-energy charged particles. Located inside the solenoid
are a silicon-based tracking system, an electromagnetic calorimeter and a hadronic
calorimeter. Outside the solenoid is the iron return yoke of the magnet, interspersed
with layers of a muon detector. A cutaway diagram showing the different sections of
the CMS detector is shown in Fig. 2-3.
The coordinate system used by CMS is right-handed and has its designated origin
at the collision point. The x-axis points towards the center of the LHC ring, the
y-axis points vertically upward towards the surface, and the z-axis in the direction of
the beam. The azimuthal angle q represents the angle measured counter-clockwise in
the xy plane from the x-axis, while the polar angle 0 is measured counter-clockwise
30
Siperconducting Solenoid
e
Slicon Tracker
Pbel Debctor
Very-forward
Calorimeter
Preshower
Hadronic
Calorimeter
Bectromagnetic
Calorimeter
Muon
Compact Muon Solenoid
Figure 2-3: A cutaway diagram showing the different components of the CMS detector.
in the rz plane from the z-axis, r being the radial coordinate in the xy plane. The
pseudorapidity coordinate, q, is commonly used to describe the angle with respect to
the beam axis and is defined as
0
2
=- ln[tan(-)]
(2.1)
A brief description of the different components of the CMS detector follows.
2.2.1
The Tracking System
At the high luminosities delivered by the LHC, there are multiple proton-proton
interactions occurring during each bunch crossing, each producing large numbers of
particles. In order to identify the trajectories of charged particles with high precision
and assign them to the correct interaction, high granularity and a quick response time
are required. The CMS inner tracking system is based entirely on silicon detector
technology and is the largest silicon tracker ever built, containing about 200 m 2 of
active silicon area. The tracker consists of an inner pixel detector and an outer silicon
31
-1.5
-1.3
-0.9
-1.1
-0.7
-0.5
-0.3
0
-0.1
1
0.3
0.5
0.7
0.9
1.3
1.1
1.5
-1.7
1200
1
-1.9
1000
1.9
-2.1
---.
800~
_
2.1__
_
-2.5
2.5
lii2I.3
-23_ 6001
400
III
i
r(mm)1
II
_200
TEC-
PIXEL
e
TEC+
-200I
I
-400
-600
IIIII
i
IIl
______
..800j
-1000
-1200
-2600
-2200
-1800
-1400
-1000
-600
-200
200
600
1000
1400
1800
2200
2600
Figure 2-4: A view of the CMS tracker in the rz plane showing its different sections.
strip detector. Figure 2-4 shows the layout of the tracker in the rz plane.
Pixel Detector
The detector closest to the interaction point is the silicon pixel detector, consisting
of 66 million pixels, each a cell 100 x 150 pm 2 in size. There are three barrel layers,
53 cm long, located at radii of 4.4 cm, 7.3 cm, and 10.2 cm with respect to the beam
line, and two endcap disks on each side located at z = ±34.5 cm and z
t46.5
±
cm, extending from a radius of about 6 cm to 15 cm. The pixel detector has a
pseudorapidity coverage of -2.5 < r < 2.5 and is able to achieve a spatial resolution
of 15 - 20 pm for a single hit. It is essential for the reconstruction of secondary
vertices and for high-level triggering.
Silicon Strip Detector
Surrounding the pixel detector is the silicon strip detector, consisting of 9.3 million
strips arranged in 15148 modules distributed in four subsystems: the Tracker Inner
Barrel (TIB), the Tracker Inner Disks (TID), the Tracker Outer Barrel (TOB), and
the Tracker Endcaps (TEC). The TIB and TID, using silicon micro-strip sensors 320
pm in thickness, occupy the radial region from 20 cm to 55 cm; the TIB consists of
four layers and the TID of three disks on each side. The TIB has a strip pitch varying
32
from 80 pin to 120 pim with a single point resolution of 23 - 35 pim. The strip pitch
in the TID varies from 100 - 141 pnm. The TOB extends to a radius of 116 cm and to
a distance of 118 cm in the z direction with six layers of micro-strip sensors 500 pim
thick, varying in pitch from 183 pm for the first four layers to 122 pim for the outer
two layers, and in resolution from 53 pm to 35 pm. The TEC occupies the region
124 cm < jzj < 282 cm and 22.5 cm < Jrj < 113.5 cm. There are 9 disks on each side
with up to seven rings of silicon micro-strip sensors either 320 jim or 500 pm thick;
the radial strips range in pitch from 97 pm to 184 pim. The modules in the first two
layers of the TIB and TOB, the first two rings of the TID and TEC, and the fifth ring
of the TEC have a second module mounted at a stereo angle of 100 mrad, providing
a measurement in the z direction in the TIB and TOB and in the radial direction in
the TID and TEC. This provides a single point resolution of 230 pim in the TIB and
530 pm in the TOB in the z direction.
2.2.2
The Electromagnetic Calorimeter
The electromagnetic calorimeter (ECAL) is situated inside the CMS magnetic coil and
is designed to measure the the energy of electrons and photons with precision. The
ECAL is composed of 75848 scintillating lead tungstate (PbWO 4 ) crystals arranged
in a cylindrical barrel and two endcap sections. The crystals have a high density of
8.28 g/cm 3 , a short radiation length (Xo) of 0.89 cm and a small Moliere radius of
2.2 cm. These characteristics ensure a high granularity and a compact detector. The
crystals produce 80% of their scintillation light within 25 ns allowing for a fast detector
response. The light produced is in the blue-green range with a broad maximum in
wavelength at 420 - 430 uni. However, the amount of light emitted is fairly low and
is sensitive to temperature. To address this issue, a cooling system was designed to
maintain the temperature of the crystals to within 0.1'C. Photodetectors are used to
collect the light produced when electrons or photons enter the ECAL. In the barrel
region silicon avalanche photodiodes (APDs) are used while in the endcaps vacuum
phototriodes (VPTs) are used.
The ECAL barrel region (EB) occupies the pseudorapidity range of 1rj| < 1.479.
33
r~-0, 0.3Xr
Preshower (E
rip,24.7Xe
Figure 2-5: A schematic diagram of a cross section of the CMS electromagnetic
calorimeter, showing the arrangement of the barrel (EB), endcap (EE), and preshower
(ES) sections.
The crystals in the barrel are tapered with a cross section of 22 x 22 mm 2 for the
front face and 26 x 26 mm 2 for the rear face. They are 230 mm long, corresponding to
25.8 radiation lengths. The endcaps (EE) occupy the pseudorapidity range 1.479 <
Ir4 < 3.0. The crystals in the endcap are 220 mm long (24.7 Xo); they have a front
face cross section of 28.6 x 28.6 mm 2 and a rear face cross section of 30 x 30 mm 2 . A
preshower sub-detector (ES) is placed in front of the endcaps with the primary goal of
identifying neutral pions in the range 1.653 < Ir/| < 2.6. This detector is a sampling
calorimeter consisting of alternating lead layers, to initiate electromagnetic showers,
and planes of silicon strip sensors, one located at a thickness of 2 X 0 and another at
3 Xo, to measure the energy deposited and the shower shape. A schematic diagram
representing a cross section of the ECAL is shown in Fig. 2-5.
The energy resolution of the ECAL can be parametrized as
)2 = (S)2
E/
E
(2.2)
()
E
an
with S representing a stochastic term, N a noise term, and C a constant.
34
.T
The
stochastic term has contributions from fluctuations in the lateral shower containment
(1.5 - 2 %), and from photostatistics (2.1 %).
The contributions to the noise term
come from electronics noise, digitization noise, and noise from pileup. The constant
term comes from a variety of sources, including the longitudinal non-uniformity of the
light collection, calibration errors, and energy leakage from the rear of the crystals.
Test beam measurements conducted in 2004 found a typical energy resolution of
(2.8%
2
2-
E
=
o2)2
)2
E
+ (12%
E
+ (0.30%)2
(2.3)
with E being measured in GeV.
Although the ECAL crystals were designed to be resistant to radiation damage,
they do suffer from a reduction in transparency as color centers form in the crystal
and absorb some of the transmitted light [34]. These changes in transparency need
to be monitored and corrected for. A laser monitoring system is used for the purpose of tracking changes in crystal transparency over time and deriving appropriate
corrections.
2.2.3
The Hadron Calorimeter
Surrounding the ECAL is the CMS hadron calorimeter (HCAL). The HCAL is important for measuring neutral and charged hadrons and also for the measurement
of missing transverse energy coming from neutrinos or from exotic particles. The
HCAL uses sampling calorimeter technology, with alternating layers of absorber and
scintillator. A barrel section (HB) covers the pseudorapidity range up to 1,q < 1.3
and endcaps occupy the region 1.3 < Iql < 3.0. The amount of material in the HB is
restricted since it is contained between the ECAL and the solenoid coil; in order to
absorb any remaining part of the hadronic shower, an outer calorimeter (HO) or tail
catcher is placed outside the magnet.
Finally, radiation-hard forward calorimeters
(HF) extend the pseudorapidity coverage in the range 3.0 < 1r| < 5.2. Figure 2-6
shows the layout of the different HCAL sections.
The HCAL barrel is constructed from brass absorber plates alternating with plas35
rill
Figure 2-6: Longitudinal view of CMS showing the barrel (HB), endcap (HE) outer
(HE), and forward (HF) sections of the HCAL.
tic scintillator tiles; the innermost and outermost absorber plates are made of stainless
steel in order to provide structural strength. The total absorber thickness ranges from
5.82 interaction lengths at ir77 = 0 to 10.6 interaction lengths at 1r/j = 1.3, with the
crystal ECAL providing an additional 1.1 interaction lengths. Hadronic particles interact with the absorber to produce secondary particles, resulting in hadronic showers
as they pass through the successive layers of absorber. As the showers develop, they
cause the active scintillator layers to emit light in the blue-violet range. Wavelength
shifting fibres absorb the scintillation and shift it to the green range of the spectrum;
the light signals are digitized and read out using hybrid photodiodes (HPDs) which
can operate in a high magnetic field. An HPD consists of a photocathode and a pixelated silicon photodiode and produces a gain of roughly 2000. The HB is segmented
into sectors, or towers, occupying an area of 0.087 x 0.087 each in rT# space.
Since the size of the HB is restricted by its placement within the solenoid, the
HO is designed to provide additional stopping power to catch the tails of hadronic
showers. The HO utilizes the iron return yoke of the magnet as an absorber with layers
36
of scintillator interspersed with the iron. The granularity of the HO, like that of the
HB, is 0.087 x 0.087 in rpb. In combination with the solenoid, the HO increases the
total amount of material to at least 11.8 interaction lengths, except at the boundary
between barrel and endcap regions.
The HE, like the HB, is made from alternating layers of brass absorber (steel is
used for the inner and outer layers) and scintillator. In combination with the ECAL,
the absorber corresponds to about 10 interaction lengths of material. The granularity
of the HE is 0.087 x 0.087 for Ir/1 < 1.6 and about 0.17 x 0.17 for Irj1 > 1.6. The HE
also uses HPDs as photodetectors.
The HF, located in the forward region of the detector, needs to be able to withstand extremely high particle fluxes. This requires the active material to be radiation
hard. Quartz fibers were chosen for this purpose to provide the active medium, and
steel is used as an absorber. Charged particles traveling through the fibers cause
Cherenkov light to be emitted; the light is guided to photomultiplier tubes to be read
out.
Test beam studies conducted in 2002 measured the energy resolution of the HCAL
for single pions to be
o-2
()-
E
(
11
-/E
)
22
2
(5.5%)2
(2.4)
with E being measured in GeV.
2.2.4
The Muon System
Muons are able to pass through the calorimeters with minimal loss of energy and reach
the outermost layers of CMS, the muon detectors. Placed outside the solenoid, the
muon system has a cylindrical barrel section and two endcaps. It relies on three types
of gaseous particle detectors: drift tube chambers in the barrel region, cathode strip
chambers in the endcaps, and resistive plate chambers in both barrel and endcap
regions. Figure 2-7 shows a longitudinal view of the muon system illustrating the
layout of the stations containing each of these three types of detectors.
37
'U'
800
eta= 0.8'/
a.
RPC
'
1.04
1.2
700
MB3
6 M 3
-1
500
1.6
400
2.1
300
2.4
CSC
200
100
0e
0
200
400
60 )
800
1o000
1200
Z (cm)
Figure 2-7: Longitudinal quarter view of CMS showing the layout of the drift tube
(DT) stations, the cathode strip chamber (CSC) stations, and the resistive plate
chamber (RPC) stations in the muon system.
Drift Tubes
Drift tube (DT) chambers are used in the barrel region, in the pseudorapidity range
1rqj < 1.2. The 250 DT chambers are arranged in 4 stations - concentric cylinders
centered on the beam line - interspersed with the layers of the magnet return yoke.
The four stations each have eight chambers providing a measurement in the r# plane;
additionally, the inner three stations have four chambers providing a measurement in
the z direction. Chambers are composed of 2 or 3 superlayers, each with 4 layers of
drift cells. Drift cells in neighboring layers are offset by a half-cell width with respect
to each other in order to avoid dead spots. The gas used in the drift cells is a mixture
of argon and carbon dioxide. The drift cells have a cross section of 13 x 42 mm 2 . The
maximum drift length within a single cell is 21 mm, which corresponds to a drift time
of 380 ns in the Ar-CO 2 mixture.
38
Cathode Strip Chambers
Cathode strip chambers (CSCs), 468 in total, are used in the endcaps of the muon
system in the pseudorapidity range 0.9 <
'rj < 2.4. Each endcap has 4 stations
of CSCs alternating with the iron return yoke layers.
The CSCs are trapezoidal
multiwire proportional chambers containing cathode strips running radially outward,
perpendicular to anode wires running in the azimuthal direction. Both strips and
wires are read out, allowing measurements of both radial and azimuthal coordinates.
Resistive Plate Chambers
Layers of resistive plate chambers (RPCs) are embedded in both the barrel and the
endcaps of the muon system, providing coverage for
|r|
< 1.6. There are 480 RPCs,
arranged in 6 layers, embedded in the barrel: there is at least one layer in each of
the stations, with the first two stations having 2 layers. The endcaps each have 216
RPCs arranged in 3 layers.
RPCs are based on a double-gap design, with a gap
width of 2 mm, operating in avalanche mode. The fast response and excellent timing
resolution provided by the RPCs allow the muon triggering system to identify the
bunch crossing from which a muon originated.
2.2.5
Triggering and Data Acquisition
During its run in 2011 and 2012, the LHC delivered proton-proton collisions with a
bunch spacing of 50 ns, corresponding to a crossing rate of 20 MHz. However, multiple
proton-proton interactions can take place at each bunch crossing (an average of 20
per second for the design luminosity), resulting in interaction rates several orders of
magnitude beyond current data processing and storage capacities. A trigger system is
therefore essential in order to reduce the rate of events to be recorded to a manageable
level, with the goal of only retaining events which show signs of interesting physics.
This reduction in rate is achieved in CMS using a two-stage process:
the Level-
1 (LI) trigger and the High-Level trigger (HLT). The LI trigger relies on custom
programmable electronics and has a nominal output rate of 100 kHz. The HLT uses
39
software and can implement sophisticated algorithms in order to further reduce the
rate down to a few hundred Hz.
The Li trigger makes use of coarse information from the calorimeters and the
muon system, while the full readout from each detector component is held in buffers
in the front-end electronics. Information from the tracker is not used by the Li trigger.
Every bunch crossing is analyzed; the latency allowed before the transmission of the
Li decision to the front-end electronics is 3.2 ps. Transverse energies measured in
groups of ECAL crystals or HCAL towers are used to determine electron/photon
candidates, hadronic tau candidate vetoes, and transverse energy sums in calorimeter
regions. A global calorimeter trigger uses this information to find jets, compute
the total transverse energy and missing transverse energy, and determine the best
electron/photon candidates. From the muon systems, track segments and hit patterns
are combined to find tracks and determine muon candidates; information from the
calorimeters is also used by a global muon trigger to find the best muon candidates.
The final Li trigger decision of whether to accept or reject the event is then based
on the candidate trigger objects delivered by the calorimeters and muon systems electrons/photons, muons, jets, hadronic taus - and global information such as the
total and missing transverse energies.
The arrival of a Li accept initiates the extraction of the data stored in the frontend buffers and transmission to the CMS data acquisition (DAQ) system by Front-End
Drivers (FEDs). An event builder assembles the fragments from all the FEDs into
a single event. The data is then transferred to a computing farm where the HLT,
essentially a software filter system, comes into play.
The HLT reduces the rate of events to be stored by a further factor of about a
1000. The HLT uses faster versions of the offline event reconstruction software and
uses sophisticated algorithms in applying selection criteria to determine which events
should be stored. The full detector information can be incorporated, including information from the tracker. Improved position and momentum resolution are available
with respect to the Li. Muon trigger rates can be reduced with respect to Li through
the use of the improved resolution, and the presence of a track can be used to distin40
guish between electron and photon candidates which are triggered by the presence of
energy clusters in the ECAL. The position of the interaction points corresponding to
proton-proton collisions can be reconstructed using tracks from the pixel detector. In
order to reduce computing, the HLT employs various trigger levels and attempts to
reject an event as soon as possible. Physics objects are reconstructed using candidates
identified by the Li trigger as a starting point. To minimize the amount of processing,
a strategy of partial reconstruction is adopted: only the quantities necessary for applying a set of selection criteria are reconstructed. Thus track reconstruction, which
is expensive in terms of CPU usage, is only performed when necessary after other
selection requirements have been applied.
2.3
Luminosity Measurement
The luminosity delivered to CMS is measured by a method which counts the number
of clusters reconstructed in the pixel detector, which is expected to be proportional
to the instantaneous luminosity [35-37].
The instantaneous luminosity for proton-proton collisions is given by
C =
forbit
27ru a,
.
(2.5)
Here N1 and N2 are the numbers of protons per bunch in the two colliding proton
beams, determined by measuring the electric current of the beam, and nb is the
number of colliding proton bunches per beam, which is determined beforehand. The
orbit frequency of the bunches in the LHC,
forbit,
is fixed at 11246 Hz. The effective
area of overlap between the colliding beams is given by 27Fr ory, with or, and o, being
the effective beam widths in the x and y directions respectively. These are measured
using a procedure known as a Van der Meer scan [38], which profiles the beam shapes
in the x and y directions by varying the beam positions relative to each other and
measuring the pixel activity. The beam profiles are found to be described by the sum
of two Gaussian distributions with a common mean value. The ratio of the absolute
41
luminosity to the pixel activity measured during a Van der Meer scan determines the
calibration of the pixel luminosity measurement; the instantaneous luminosity is then
monitored during the course of data-taking by measuring the pixel activity.
42
Chapter 3
Datasets and Event Simulation
The analysis procedure relies on the implementation of an event selection applied
to collision data and to the simulated event samples which are used to model the
signal and background processes of interest.
The datasets derived from recorded
proton-proton collisions which are used for this analysis, and the simulated datasets
used to model various processes are discussed in the following sections, followed by a
brief description of the signal and background processes which are of interest for this
analysis.
3.1
Datasets
Events passing the HLT (Section 2.2.5) are grouped, based on the trigger requirements they fulfill, into collections known as primary datasets to ease processing and
to address the requirements of different physics analyses. For instance, events passing triggers which require the presence of an electron trigger object are grouped into
a "SingleElectron" dataset.
Trigger paths are defined by a sequence of trigger re-
quirements, starting with an LI trigger seed, followed by a series of filters imposing
different requirements on selected objects. The primary dataset of interest for the
T-pair final state with an electron and a muon is the "MuEG" primary dataset, referring to trigger paths requiring both a muon candidate and an electron or photon
43
candidate (triggers based on electrons start at LI with the identification of isolated
electromagnetic objects which could be electron or photon candidates). Muon candidates are based on matching a tracker track with compatible track segments in
the muon system. Electron candidates are found by matching energy clusters in the
ECAL with a track.
Table 3.1 contains a list of the data samples used to select events for the analysis. The entries correspond to events collected in different data-taking periods; the
"PromptReco" label refers to events which have undergone the prompt reconstruction
process, while the remaining data samples have undergone a further re-reconstruction
with improved calibration. The integrated luminosity quoted corresponds only to the
data considered suitable for physics analyses. The data analyzed corresponds to an integrated luminosity of 5.0 fb- 1 collected at
x/=
7 TeV in 2011, and 19.7 fb--collected
at F = 8 TeV in 2012.
Integrated Luminosity (fb')
Data Samples for 2011
0.2
/MuEG/Run201lA-lOMayReReco-vl/AOD
1.0
/MuEG/Run2011A-PromptReco-v4/AOD
0.4
/MuEG/Run201 1A-05Aug2Ol 1-vl/AOD
0.7
/MuEG/Run201 1A-030ct201 1-vI/AOD
2.7
/MuEG/Run201 1B-PromptReco-vl/AOD
5.0
Total integrated luminosity
Data Samples for 2012
0.9
/MuEG/Run2012A-22Jan2013-vI/AOD
4.4
/MuEG/Run2012B-22Jan2013-vI/AOD
7.0
/MuEG/Run2012C-22Jan2013-v1/AOD
7.4
/MuEG/Run2012D-22Jan2013-vI/AOD
19.7
Total integrated luminosity
Dataset Name
Table 3.1: List of data samples used for different data-taking periods in 2011 and
2012 and the corresponding integrated luminosity collected in each. The AOD label
refers to the data format used for storing events.
44
3.2
Event Simulation
Monte Carlo (MC) simulations are a very important element of particle physics data
analyses, and are used to model the signal and background processes being studied.
The production of a sample of Monte Carlo simulated events starts with the
generation of the particles produced in the hard scattering process using an event
generator, followed by parton showering and hadronization processes, simulation of
the underlying event, and of the passage of the particles produced through the CMS
detector.
3.2.1
Event Generation
Event generators make use of parton distribution functions (PDFs), which provide
the probability density for a parton to carry a given momentum fraction, to describe the distribution of parton momenta within the incoming protons. PDFs are
determined from fits to experimental data, including deep inelastic scattering data
from lepton-nucleon scattering experiments, data from proton-nucleon scattering experiments, electroweak W and Z boson production studies, and studies of jet production.
The event generators sample events based on the kinematics of particles
produced in the hard scattering process. The sampling makes use of PDFs for the
incoming protons and matrix element calculations of the underlying physics process.
The matrix element calculations may be leading order (LO) or next-to-leading order
(NLO), depending on the event generator.
The POWHEG [39-42], MADGRAPH [43],
and PYTHIA [44] event generators are used for this analysis.
matrix element calculations, while
MADGRAPH
POWHEG uses NLO
and PYTHIA use LO matrix element
calculations for event generation. The decays of T-leptons are handled separately by
interfacing the event generator to the TAUOLA [45] package.
45
3.2.2
Parton Showering, Hadronization, and Underlying
Event
Higher order QCD corrections are taken into account by introducing additional partons to the event, while the effects of initial or final state photon radiation are taken
into account with the addition of radiated photons. The outgoing partons are then
hadronized and unstable hadrons allowed to decay. These processes are handled by
PYTHIA
for this analysis; events generated by POWHEG or MADGRAPH are passed to
PYTHIA
for parton showering and hadronization. Simulation of the underlying event,
due to the "spectator interactions" of partons not involved in the hard scatter, is
also added. The collections of parameter settings used in
PYTHIA
to model the un-
derlying event are known as "tunes". The default tunes used by CMS for samples
simulated at \
= 7 TeV and V = 8 TeV are known as the "Z2" and the "Z2*"
tunes respectively [46].
In order to avoid double counting, emitted partons generated by
MADGRAPH
POWHEG
or
are matched to the clusters of hadrons produced from the showering and
hadronization steps by
PYTHIA.
The
MADGRAPH
generator includes parton emission
diagrams for up to four partons and provides a better description of jet multiplicity
and kinematics.
3.2.3
Pileup Simulation
The effects of pileup interactions are modeled by incorporating additional inelastic
proton-proton collisions simulated using
PYTHIA.
The distribution of the number of
simulated pileup interactions is based on a prediction of the pileup distribution expected in observed events. In order to achieve a better description of observed events,
simulated events are re-weighted in order to match the expected pileup distribution
for each data-taking period, which is computed based on the instantaneous luminosity
profile for the period in question.
46
3.2.4
Detector Simulation
The passage of the final state particles produced through the CMS detector and the
detector response is simulated with the help of the
GEANT4
[47] program. The de-
tector simulation includes an implementation of the detector geometry, the effect of
the passage of particles through the detector material and energy losses.
Particle
trajectories are determined, including the effects of the magnetic field. The electronic
readouts from the different components are emulated for each event, including simulations of the effects of detector noise. The simulated event output produced is in
the same format as data from actual collisions and undergoes event reconstruction
(as described in Chapter 4) and further processing in the same manner as real data.
The simulated events thus obtained can be analyzed using the same procedures as
for observed collision events. In order to model the observed data as closely as possible, several corrections are applied to simulation. These include the pileup reweighing
procedure described above, various corrections to account for differences in efficiencies
for selecting objects between data and simulation (Sections 5.3 and 5.4), and energy
scale corrections applied to simulated objects like jets based on measurements from
observed data (Section 4.3.1). Events selected in data may then be compared to the
predictions for signal and background processes with the help of the simulated event
samples.
3.3
Signal Processes
The SM Higgs boson analysis searches for a Higgs boson produced through one of the
following processes:
Gluon fusion (gg -± H): this is the dominant SM Higgs boson production process.
Two initial state gluons produce a Higgs boson through an intermediate fermion
loop (primarily a top quark loop).
Vector boson fusion (VBF): this is second most prevalent SM Higgs boson production process. Initial state quarks radiate a pair of W or Z bosons which
47
produce a Higgs boson.
Associated production with a vector boson (VH): this process does not contribute significantly to the expected signal yield in this analysis. The Higgs
boson is produced in association with a W or Z boson which radiates the Higgs
boson.
Simulated Higgs boson signal samples are produced for a range of Higgs boson masses;
the analysis makes use of samples generated for Higgs boson masses between mH
90
GeV and mH =145 GeV in 5 GeV steps. The Higgs boson production cross sections
used are provided by the LHC Higgs Cross Section Working Group [20]. The cross
sections calculated for gluon fusion has terms up to NNLO and next-to-next-to-leading
log (NNLL) terms, while the cross sections calculated for VBF and VH production
include NNLO QCD and NLO electroweak terms. The branching ratios to T-pairs
is determined using the
HDECAY
program [48-50], with NLO QCD and electroweak
corrections. The production cross sections and branching ratios to T-lepton pairs used
for SM Higgs bosons are listed in Tables 3.2 and 3.3 [19,20,51].
The MSSM Higgs boson analysis searches for neutral Higgs bosons produced
through the following mechanisms:
Gluon fusion: this is the dominant production mechanism for low and intermediate
values of the tan 3 parameter (the ratio of the vacuum expectation values of
the two Higgs doublets in the MSSM).
Because of the enhancement of the
coupling to down-type fermions in the MSSM, the gluon fusion process through
an intermediate b-quark loop has an enhanced contribution in the MSSM.
Associated production with b-quarks: this mechanism becomes more dominant
at higher values of tan 3 due to an enhanced coupling to b-quarks. This process
is also initiated by initial state gluons.
Simulated samples are produced for hypothetical MSSM Higgs boson masses ranging
from 90 GeV to 1 TeV. The MSSM neutral Higgs boson production cross sections
and their uncertainties which are used in this analysis are provided by the LHC Higgs
48
mH
[GeV]
90
95
100
105
110
115
Cross section [pb]
Gluon fusion V BF
WH
ZH
___ = 7 TeV
29.03
1.723
1.654
0.8959
26.10
1.639
1.404
0.7678
23.64
1.557
1.195
0.6616
21.45
1.478
1.029
0.5724
19.56
1.404 0.8847 0.4978
17.89
1.344 0.7626 0.4345
tt H
0.2162
0.1880
0.1637
0.1432
0.1257
0.1105
120
16.43
1.279
0.6617
0.3808
125
15.13
1.222
0.5785
0.3351
0.08632
130
13.98
1.168
0.5059
0.2957
0.07660
135
12.95
1.117
0.4431
0.2616
0.06816
140
12.02
1.069
0.3846
0.2322
0.06079
145
11.45
1.023
0.3437
0.2068
0.05429
90
95
100
105
110
115
120
125
130
135
140
145
36.23
32.69
29.68
27.01
24.70
22.66
20.86
19.27
17.85
16.57
15.42
14.46
s=8TeV
2.191
1.990
2.084 1.695
1.988 1.447
1.897 1.242
1.809 1.071
1.729 0.9266
1.649 0.8052
1.578 0.7046
1.511 0.6169
1.448 0.5416
1.389 0.4768
1.333 0.4216
1.092
0.9383
0.8102
0.7022
0.6125
0.5358
0.4710
0.4153
0.3671
0.3259
0.2898
0.2583
0.3202
0.2786
0.2433
0.2133
0.1871
0.1651
0.1459
0.1293
0.1149
0.1024
0.09150
0.08199
0.09758
Table 3.2: SM Higgs boson cross sections for different production processes at 7 and
8 TeV.
Cross Section Working Group for the
mja"
benchmark scenario. For small and mod-
erate values of the tan / parameter, the gluon fusion process, mediated largely by top
and bottom quark loops, dominates for the production of MSSM neutral Higgs bosons.
The cross sections are calculated at NLO in QCD by HIGLU [52,53]. Corrections to
the top quark loop contribution at NNLO are provided by the GGHONNLO [54-58]
program. For larger values of tan 0, associated production with b-quarks becomes
more prevalent. The cross sections for this process are calculated at NLO in what is
known as the four-flavor (4FS) scheme, and at NNLO in what is known as the five49
mH
[GeV]
90
95
H
-±
100
105
110
115
120
125
130
135
140
145
TT branching ratio
8.33 x 10-2
8.32 x 10-2
8.28 x 10-2
8.17 x 10-2
7.95 x 10-2
7.58 x 10-2
7.04 x 10-2
6.32 x 10-2
5.45 x 10-2
4.49 x 10-2
3.52 x 10-2
2.61 x 10-2
Table 3.3: Branching ratios for the Higgs boson decay to T-lepton pairs.
flavor scheme (5FS) using the BBHQNNLO program [59]. The 4FS and 5FS calcula-
tions are combined using a procedure known as "Santander matching" [60]. The Higgs
Yukawa couplings used for the cross section calculations and branching ratios for neutral MSSM Higgs boson decays to T-pairs are obtained from FEYNHIGGS [27,61-63].
Figure 3-1 shows the branching ratios to 7-pairs computed for different values of tan j
as a function of mA, while Fig. 3-2 shows the product of the production cross sections
for the two main MSSM Higgs boson production modes with the 7-pair branching
ratios for two different values of tan 3. The enhancement with respect to the expectation for the SM Higgs boson at higher values of
mA
and tan 0 is illustrated in these
plots.
SM Backgrounds
3.4
One of the principal challenges of this analysis is the discrimination of a Higgs signal
from the large sources of background. The primary background processes are listed
below:
Drell-Yan T-pair production (Z
-±
TT):
this is the dominant source of background
after the selection of two well-identified leptons of opposite charge and has the
50
1
10-1
MSSM
-E
------! IIM I N - gg- aI
........
---
0
2
>mv
- ----
tan b=
--------
tan p~=5
0
.....
...
10-
10
..
--.
BR(t), SM
10-
100
200
300
500
mA/H [GeV]
400
Figure 3-1: Branching ratios for the MSSM pseudo-scalar Higgs boson A for decays to
r-lepton pairs for different values of tan 3 computed in the mj"' scenario, compared
to the T-pair branching ratio for a SM Higgs boson.
same final state as the signal, making it challenging to discriminate against.
Top-pair production (tt): both top-quarks decay, through a W boson, producing
leptons. b-quark jets will also be present from the top-pair decay.
Di-boson production (WW, WZ, ZZ): di-boson production, with the W or Z bosons
decaying into leptons, constitutes another possible source of background.
W boson production with additional jets (W+jets): this constitutes a background in the case that the W boson decays to a lepton while a jet fakes a good
quality lepton.
QCD multijet production: a jet or non-isolated lepton can fake a good quality
lepton. Despite the high cross section, the contribution from this background
is reduced by the requirement that both selected leptons must be fakes.
Associated single top production (tW): single top production is much rarer than
tf production, but constitutes a small source of background when leptons are
51
-,
-L
1005
9
.
.
.
.1
10 4
10
--- ----------
X
1
.1
.1
.
.1
1 1
.1
1 1 1 1
gg-+ bb$ (tan P=5... 30)
gg-+ ( (tan P=5...30)
gg-+ H (SM)
qq-* qqH (SM)
10
10
10"2
I
10 -3
tan p3-s
10 -4
1010-
100
200
300
500
400
m[ [GeV]
Figure 3-2: Product of the production cross section with the branching ratios for
decays to r-lepton pairs as a function the mass of the MSSM pseudo-scalar Higgs
boson A for different values of tan /3 computed in the mm" scenario for gluon fusion
(gg
--
q) production and associated production with b-quarks (gg -+ bbq). The rates
for SM gluon fusion and VBF Higgs boson production are shown for comparison.
produced from the top-quark and associated W boson decay.
Z
-4
pp: this is a very small source of background in the event that one of the muons
radiates a photon which converts to electrons; one of these electrons may be
identified as a signal electron while the other muon from the Z boson decay is
identified as a signal muon.
Z
±
ll+jets: Z -+ 11 events in which one of the leptons (an electron or a muon)
escapes detection while a jet fakes a muon or electron are another small source
of background.
H
-
WW: the decay of the Higgs to a pair of W bosons which decay leptonically
also constitutes a source of background due to the combination of leptons and
neutrinos in the final state, particularly in event categories which exploit VBF
production. Although this is a Higgs boson induced process, it is treated as a
52
Process
Generator
___
Z -+ iiTT
tt - X
tt- 2l21v/2b (*)
Cross section [pb]
-- 7 TeV
=
s = 8 TeV
MADGRAPH
3048
3504
MADGRAPH
164
POWHEG
-
X(tW)
WW - 212v
WZ -+ 313v
POWHEG
15.7
225
26.2
109
22.2
WZ -4 212q
MADGRAPH
4.78
0.857
1.79
5.82
1.06
2.21
ZZ
MADGRAPH
0.064
0.181
MADGRAPH
0.250
0.776
0.716
2.50
ti
t
lIv2q2b (*)
-
41
ZZ -+ 212v
ZZ -+ 212q
-
POWHEG
MADGRAPH
MADGRAPH
MADGRAPH
Table 3.4: Cross sections and event generators corresponding to simulated event
samples used for modeling background processes at V=
7 and 8 TeV. The inclusive
Z - i,
Irr
cross sections are computed at NNLO using FEWZ [64], the inclusive
di-boson cross sections at NLO using MCFM [65], and W/Z boson branching ratios
are taken from [22]. The single-top cross sections are obtained using approximate
NNLO calculations [66,67]. The CMS measured cross sections are used for tt [68,69].
The simulated samples labeled (*) are only used in the analysis of 8 TeV data.
background for the H -+
TT
search which targets the T-pair decay mode.
The methods used for estimating each background contribution are discussed in
Chapter 6. The cross sections used to estimate the normalizations for various background processes are obtained from CMS experimental measurements in some cases
and from theoretical NLO calculations in others. A list of the cross sections corresponding to the different simulated event samples used to model SM background
processes in the analysis of 7 and 8 TeV data may be found in Table 3.4; the table
also lists the event generator used for producing each simulated sample.
53
Chapter 4
Event Reconstruction and Object
Selection
The search for a Higgs boson decaying to T-lepton pairs relies on the reconstruction
of the T-pair decay products. For the final state with an electron, a muon, and four
neutrinos, the reconstruction of leptons (electrons and muons) and missing energy,
which indicates the presence of neutrinos, is very important. The reconstruction of
jets is also critical since the analysis makes use of jets to categorize events in order to target different Higgs boson production mechanisms. Vertex reconstruction
plays a role in verifying that the objects selected for the analysis originated from
the hard-scattering process. Events which have been accepted by the trigger system
(Section 2.2.5) are processed using sophisticated software algorithms in order to reconstruct different physics objects. The specific triggers used to collect data for this
analysis are described further in Section 5.1. The large amount of hadronic activity
inherent to proton-proton collisions and the increased activity due to pileup present
challenges to successful event reconstruction.
In order to model the expected behavior of various processes in the detector, Monte
Carlo simulations are used, in which particles originating from a given physics process
are generated and their stable decay products are propagated through a simulation
of the detector. Simulated events also undergo the event reconstruction process in a
54
manner analogous to observed data in order to allow for a direct comparison between
data and simulation.
4.1
Primary Vertex
Successful reconstruction of proton-proton interaction vertices is a significant challenge in the high-luminosity environment of the LHC. Vertex reconstruction is performed using the tracks produced by charged particles originating from the collisions.
Tracks which are consistent with having their origin at the same interaction point are
clustered using the Deterministic Annealing (DA) clustering algorithm [70]. A fit is
then performed to obtain the vertex position, or common point of origin, corresponding to each cluster of tracks. The tracking system provides a resolution of ~ 50 Pm in
separating vertices. When multiple vertices are reconstructed in an event, the vertex
with the largest sum of the p2 of tracks associated with that vertex is taken to belong
to the hard-scattering process and is referred to as the primary vertex. Any other
reconstructed vertices in the event are assumed to be due to additional proton-proton
collisions in the same bunch-crossing, referred to as in-time pileup. Pileup originating from collisions in the preceding or succeeding bunch-crossings is referred to as
out-of-time pileup.
Some additional requirements are imposed on the selected primary vertex in the
analysis:
" The distance in z from the primary vertex to the nominal interaction point
(located at the origin of the CMS coordinate system) must not exceed 24 cm.
" The transverse distance from the vertex to the nominal interaction point must
not exceed 2 cm.
" The number of degrees of freedom for the vertex fit should be at least 4.
Figure 4-1 shows the expected and observed distribution of the number of reconstructed vertices for 2011 and 2012 for events selected by this analysis using the
criteria described in Section 5.2.
55
CMS Preliminary,
(1)
4-
is = 7 TeV, L = 5.0 fb
J....
2500
eja----- 4--
1
CMS Preliminary, is = 8 TeV, L = 19.7 fb
5xH(12 5Ge5xH(125 GeV)-oWW
observed
U,
electroweak
2000
5xH(1 25 GeV) -
9-
WN
OCD
bkg. uncertainty
bkg. uncertainty
[Z
Tobserved
electroweak
5000
SQCD
-
6000
1
4000
1500
3000
1000
2000
500
0
1000
0
10
20
0
30
20
30
Figure 4-1: Distribution of the number of reconstructed vertices for the 2011 (left)
and 2012 (right) data-taking periods for events selected by this analysis (Section 5.2).
The points represent the observed distribution while the stacked histograms represent
the expected distributions for each contributing SM process. The shaded black area
represents the uncertainty on the total expected background contribution.
4.2
Particle Flow
CMS makes use of a particle flow (PF) algorithm [71-73] which utilizes information from all the sub-detectors in an attempt to identify and reconstruct all of the
particles produced in the proton-proton collisions. The particles reconstructed by
the algorithm, known as particle flow candidates, are classified as muons, electrons,
photons, charged hadrons, or neutral hadrons.
The PF algorithm starts with tracks from the silicon tracker, muon segments
from the muon system, and energy clusters from the ECAL and HCAL. The latter
are seeded by crystals or towers in which the energy deposits exceed a certain threshold; adjacent crystals or towers are iteratively added to the cluster if they contain
sufficient energy. Tracks are then extrapolated into the calorimeters and associated
with clusters if they are found to pass within the cluster boundaries, ECAL and
HCAL clusters are linked together if their positions are compatible, and muon segments are linked to compatible tracks. These combinations form the building blocks
used to assign PF candidates. As each PF candidate is identified, the associated
56
blocks and elements are iteratively removed from the list in order to avoid double
counting. Isolated PF muons are identified by imposing a restriction on the energy
sum of tracks and calorimeter deposits around a reconstructed muon. PF electrons
are formed from blocks containing a track and an energy cluster with the help of
a multivariate discriminator used to reject pions; clusters which appear to originate
from bremsstrahlung photons are associated with the electrons. Any remaining blocks
containing both tracks and clusters are used to reconstruct charged hadrons. Finally,
any remaining ECAL clusters not linked to a track form PF photons, while HCAL
clusters not linked to a track form neutral hadrons.
Particle flow candidates are used for the reconstruction of jets, hadronic taus, and
missing transverse energy ($T), computation of isolation quantities as a measure of
additional activity around lepton candidates, and mitigation of the effect of pileup
on the analysis.
4.3
Jet Reconstruction
Jets are collimated bundles of particles produced by the hadronization of a quark or
gluon (parton), through QCD interactions. They are reconstructed based on the list of
PF candidates using the anti-kT clustering algorithm [74] with a distance parameter of
0.5. The algorithm computes a "distance" between each pair of particles and between
each particle and the beam line:
dij
=
min (kT, k)
diB
=
k 2,
R2
(4.1)
(4.2)
with kTi, yi, and /i being the transverse momentum, rapidity, and azimuthal angle
of particle i respectively. R is a distance parameter which is chosen to be 0.5 for
this analysis.
The parameter p, determining the relative power of the energy and
geometrical scales, is chosen to be -1
for the anti-kT algorithm. Pairs of particles
are successively combined based on which of these distances is smallest. If dij < diB,
57
particles i and
j
are combined, adding their momenta; otherwise particle i is removed
from the collection and promoted to a jet. The process is iteratively repeated on all
remaining particles until there are none left.
Jet Energy Corrections
4.3.1
In order to achieve a more accurate estimate of the original parton energy, corrections
are applied to the jet energy to account for pileup and non-uniformities in detector
response. The contribution of particles coming from pileup and the underlying event is
estimated to be the product of the jet area and an event-by-event density p computed
using the FastJet technique [75-77] and is subtracted from the jet energy. Corrections
are then applied as a function of the
PT
and q of the jet in order to calibrate the jet
energy scale and to match the jet energy response in simulation to the observed
response in data. The correction factors are derived using di-jet, 7+jets, and Z+jets
events [78]. Jets selected for the analysis are required to have mg1
< 4.7 and to have
a corrected transverse momentum greater than 30 GeV unless they are identified as
b-jets (Section 4.3.3), in which case they are required to have a corrected
PT
> 20
GeV. They are also required to be a distance AR > 0.5 away in 71q space (AR =
2
4.3.2
+ -(Am)
(AO) 2 ) from the leptons selected in the analysis.
Pileup Jet Identification
Particles originating from pileup interactions may be clustered by the jet reconstruction process into pileup jets. Pileup jets tend to have lower momentum than jets
originating from the hard scattering process; however, multiple softer pileup jets may
overlap and be reconstructed as a high-pT jet. Such jets tend to be more diffuse
in shape than jets originating from the hard interaction (non-pileup jets). In order
to distinguish between pileup jets and non-pileup jets, a multivariate discriminator
based on a Boosted Decision Tree (BDT) implemented in TMVA [79] is used [80].
Information used in the discriminator includes the compatibility of the tracks belonging to the jet constituents with the selected primary vertex, variables describing the
58
jet shape, and the numbers of charged and neutral components in the jet. The BDT
is trained using a simulated sample of Z -+ pp + jets events in which reconstructed
jets matched to those coming from generated partons are treated as non-pileup jets
and all others as pileup jets.
Jets selected in the analysis are required to exceed a threshold on the discriminator
value known as the Loose working point. This working point is ~ 95% efficient for
jets with
PT
> 25 GeV. For jets with
PT
> 30 GeV, the working point corresponds to
an efficiency of > 99% for jets within the tracker volume (,r1 1 < 2.4) and ~ 95% for
jets outside the tracker volume.
4.3.3
b-Jet Tagging
The identification of jets originating from b-quarks is important to the analysis both
in order to reject the tt background and, in the context of the search for MSSM
neutral Higgs bosons, to target Higgs boson production in association with b-quarks.
Algorithms used for identifying or "tagging" b-jets exploit properties such as the
relatively long lifetime of b hadrons which results in displaced secondary vertices.
The Combined Secondary Vertex (CSV) algorithm is used in this analysis for btagging [81]. It is implemented in the form of a likelihood discriminant, combining
information about track impact parameters and reconstructed secondary vertices. In
this analysis, jets are considered to be b-tagged if they have a CSV discriminator
value greater than 0.679 (known as the CSV Medium working point), PT > 20 GeV,
and lql < 2.4 (i.e., they lie within the tracker volume).
4.4
Missing Energy Reconstruction
The detection of neutrinos, which do not interact in the detector, relies on the conservation of the total transverse momentum in an event, which should be zero. Any
imbalance in the total transverse momentum indicates the presence of undetectable
particles like neutrinos.
Making use of the list of particles generated by the PF
59
algorithm, the PF missing transverse energy (MET or
$T)
vector is computed as
(4.3)
$P -Ti,
i
with
Pri
4.4.1
{all PF candidates}
being the transverse momentum vector of the ith PF candidate.
MVA Missing Transverse Energy
Reconstruction of the missing transverse energy ($T) is especially important for this
analysis due to the presence of neutrinos from the decay of the T-lepton. The
$
plays
an important role in the rejection of non-di-T backgrounds and in the reconstruction
of the T-pair invariant mass. However, effects such as mis-measurement of particle
momenta can result in a corresponding mis-measurement of the
$T.
The presence of
particles due to pileup also introduces a random component to the
$T.
Increasing
levels of pileup, with the corresponding increase in the number of particles in the
detector, result in a significant degradation of the
$k
resolution. In order to reduce
these adverse effects, the analysis makes use of a multivariate BDT regression technique, referred to as the MVA missing transverse energy (MVA
$vregression
makes use of 5 alternative methods of computing the
" The negative vector
"
$T)
PT
sum of all PF candidates (PF
[82]. The MVA
$T
in the event:
$k).
The negative vector PT sum of all tracks associated to the selected primary
vertex.
* The negative vector PT sum of all tracks associated to the selected primary vertex and all neutral PF candidates within jets passing the pileup jet identification
described in Section 4.3.2.
" The negative vector PT sum of all tracks associated to the selected primary vertex and all neutral PF candidates within jets failing the pileup jet identification.
* The negative vector PT sum of all tracks associated to the selected primary
vertex and all neutral PF candidates plus the positive vector sum of all neutral
60
PF candidates within jets failing the pileup jet identification.
The two selected leptons in the event are excluded from the
each of these measures of
$T,
PT
sum in each case. For
a hadronic recoil vector is computed as
_
-Z
ijrp
(4.4)
with j"P corresponding the PT vectors of the visible leptons originating from the hard
interaction. The magnitude and azimuthal angle 0 of the recoil, the scalar E ET of
each of the
$T
variables, the momentum vectors of the two highest momentum jets
in the event, and the number of vertices reconstructed in the event form the inputs
for the BDT regression.
The regression computes a correction to the magnitude
and angle of the PF recoil in an attempt to match the true hadronic recoil. The
regression is trained based on the recoil in a simulated sample of Z -> PP events,
which are expected to have no inherent
Z -+
1up
$T,
and validated on a data sample selecting
events. The corrected recoil, added to the vector sum of the
leptons according to Eq. 4.4, produces a corrected measure of the
The improvement achieved by the MVA
PT
of the visible
gT.
T is illustrated in Fig. 4-2, which shows
the resolution and response of the components of the recoil parallel and perpendicular
to the Z boson direction as a function of the number of reconstructed vertices for
simulated and observed Z -± pup event samples. At 21 reconstructed vertices, the
average for 2012, the MVA
to the raw PF
4.4.2
$T improves
the resolution by a factor of two with respect
$T.
Recoil Corrections
Differences between data and simulation in the gT response and resolution are accounted for using corrections derived based on the hadronic recoil in Z -* PP events.
The response and resolution of the components of the recoil parallel (u1l) and perpendicular (ua)
to the Z boson are parametrized as a function of the Z boson
PT
and the number of reconstructed jets. The parametrization of the recoil determined
61
CMS Preliminary 2012
30
CMS Preliminary 2012
, , ,
,130
U'
Data Particle Flow 9
0
25
0
Data Particle Flow
-25-MC Particle Flow
20
.
I
MC Particle Flow
20
* +
Data Particle Flow MVA
U)
0
y
y
15
MC Particle Flow MVA
10
.
t
Data Particle Flow MVA
*U,
0
-
0
15
MC Particle Flow MVA
10
*
5-
5
0
10
20
30
0
Number of Primary Vertices
10
20
30
Number of Primary Vertices
Figure 4-2: Resolution of the components of the reconstructed recoil in the directions
parallel (left) and perpendicular (right) to the Z boson direction versus the number
of reconstructed primary vertices for simulated and observed Z -± ppi events.
from data is compared to simulation for a sample of Z -* pH events and corrections
for the response and resolution of the recoil are derived. These recoil corrections are
then applied to simulated events as a function of the PT of the generated Higgs or Z
boson and the number of jets. The
of the
4.5
PT
$Tis
then recomputed as the negative vector sum
of the leptons and the corrected hadronic recoil.
Muon Reconstruction
Muon reconstruction relies on information from the silicon tracker and the muon
system. One approach starts by combining hits in the muon stations to form segments
which are then used to reconstruct tracks. Muons based only on tracks in the muon
system are known as Standalone muons. Global muons are reconstructed by matching
standalone muons to tracks in the tracker. A global x 2 fit to the tracker track and
the muon system hits determines the parameters of the global muon. Hits used for
constructing the standalone muon may be removed from the global fit if they are
incompatible with the trajectory. The combined information from the tracker and
the muon chambers provides an improved measurement of the muon trajectory. An
62
alternative approach attempts to match a tracker track with a segment in a muon
station. Muons reconstructed in this manner are known as Tracker muons.
4.5.1
Muon Identification
Muons selected in the analysis are required to be either Global or Tracker muons.
They are also required to have been identified as muons by the PF algorithm. Some
additional quality requirements are imposed:
o The normalized
X2 of the
global track fit is required to be be smaller than 10.
o At least one segment in the muon stations is required to be included in the
global track fit.
o The muon are required to have track segments in at least two muon stations.
o The muon is required to have at least one hit in the silicon pixel detector and
hits in more than 5 layers of the inner track detector.
These selection criteria are referred to as the Tight muon identification criteria.
In order to reduce background from non-prompt muons, which could be produced
in semi-leptonic decays of heavy flavor hadrons, and from pileup, constraints are
also applied on the impact parameter of the muon track with respect to the primary
vertex in the longitudinal direction (d,) and in the transverse plane (do). The impact
parameters are required to satisfy Id2l < 0.1 cm and
4.6
|dol
< 0.02 cm.
Electron Reconstruction
Electrons are reconstructed based on the presence of a track in the tracker and energy
deposits in the ECAL. The reconstruction is complicated by the fact that they tend
to lose a substantial portion of their energy through bremsstrahlung.
The energy
loss is described well by the Bethe-Heitler model [83], however, its distribution is
non-Gaussian which introduces challenges for the electron track reconstruction.
63
The electron reconstruction
[84]
begins with a supercluster, a group of ECAL
crystal clusters combined in order to capture the energy of the electromagnetic shower.
A supercluster in the barrel region is seeded by a 5 x 1 cluster centered on a crystal
with an energy deposit exceeding the seed threshold; adjacent 5 x 1 clusters in the /
direction are added to the supercluster if they contain some of the shower energy. In
the endcap, a supercluster is seeded by a 5 x 5 cluster centered on the seed crystal; an
iterative process adds overlapping 5 x 5 arrays centered on crystals on the supercluster
border to the supercluster if those crystals contain sufficient energy.
A reconstructed supercluster is matched with compatible track segments in the
pixel detector, accounting for the effect of the magnetic field. Compatible hits in
successive tracker layers are then added in order to reconstruct the electron track.
One method used for the track fitting uses the Kalman Filter (KF) technique [85].
However, this technique is not optimal unless the energy loss distribution is Gaussian.
Therefore, a Gaussian Sum Filter (GSF) technique [86], based on a sum of Gaussian
distributions, is used in order to model the energy loss through bremsstrahlung in a
manner closely approximating the Bethe-Heitler description. The combination of a
GSF track and compatible supercluster is known as a GSF electron. The momentum assigned to the electron is derived using a weighted mean of the supercluster
energy and the track momentum measurements, with the weights depending on the
uncertainties of each measurement.
4.6.1
Electron Identification
GSF electrons are selected for the analysis based on a BDT discriminator which uses
variables relating to the track quality, cluster shape, and kinematics. The following
variables are used as inputs to the BDT:
" Normalized x 2 of the KF track fit.
* Number of valid hits in the KF track fit.
" Normalized X2 of the GSF track fit.
64
* jArjjnj, rj distance between the supercluster and the track evaluated at the primary vertex.
*
distance between the supercluster and the track evaluated at the pri-
IAbinl,
mary vertex.
*
jAcaiol q
distance between the supercluster seed and the track evaluated at the
calorimeter surface.
* o-is, cluster covariance matrix characterizing shower width in the r direction.
" uoo, cluster covariance matrix characterizing shower width in the
#
direction.
" H/E, the ratio of hadronic to electromagnetic energy.
" Supercluster width in the rj direction.
" Supercluster width in the
"
#
direction.
fbrem, the estimated fraction of bremsstrahlung energy in the electron energy.
" Ratio of energy in 1 x 5 array of cells to energy in 5 x 5 array around the seed
cluster.
" R 9 , the ratio of energy in 3 x 3 array around the supercluster seed to the
supercluster energy.
" Ratio between the electron cluster energy and the track momentum evaluated
at the ECAL surface.
" Ratio between the seed cluster energy and the track momentum evaluated at
the ECAL surface.
01
E
1
,
where E is the electron energy and p the track momentum.
o Ratio of energy in pre-shower detector to supercluster energy.
65
/rjI
PTbJ
< 20 GeV
PT > 20 GeV
PT
< 0.8
0.925
0.905
0.8 < rjl < 1.479
0.915
0.955
IT|
> 1.479
0.965
0.975
Table 4.1: Thresholds applied on the electron identification BDT discriminator output
in different PT and T1 ranges. Selected electrons are required to have a discriminator
output exceeding the appropriate threshold value.
The sample of electrons treated as signal electrons in the BDT training is derived
from a selection of Z -± ec events in data, while the sample of background electrons
is derived from a selection of multijet events in which a jet is misidentified as an
electron candidate.
The detector response differs according to the electron 71.
separately for three different
T1
The BDT is trained
regions, corresponding to the ECAL endcap (I'q
>
1.479), the forward barrel region (0.8 < 171 < 1.479), and the central barrel region
(IT1
< 0.8). It is also trained separately for low-PT electrons (PT < 20 GeV) and high-
PT
electrons (PT > 20 GeV). An electron is considered to pass the BDT selection if the
discriminator exceeds the thresholds listed in Table 4.1. In addition, electrons selected
by the analysis are required to satisfy the impact parameter constraints Id, < 0.1 cm
and Idol < 0.02 cm with respect to the primary vertex.
The conversion of a photon into an electron-positron pair in the detector can be a
source of background, particularly in the case that one of the conversion legs carries
most of the initial photon momentum. In order to minimize the probability that a
selected electron comes from a photon conversion, electron candidates with tracks
missing hits expected in the inner tracker layers are rejected. Vertex fits are also
performed for pairs of compatible tracks; if the vertex fit probability is larger than
10-6,
neither of the tracks have hits in the tracker layers between the interaction point
and the fitted vertex, and the transverse distance between the fitted vertex and the
selected primary vertex exceeds 2 cm, the pair is identified as a conversion and any
electron candidate with a track corresponding to one of the tracks in the conversion
is rejected.
66
4.7
Lepton Isolation
Lepton candidates originating from jets tend to be surrounded by additional hadronic
activity and are generally less isolated from other particles than the signal leptons
which should be selected for the analysis. Lepton isolation is a further criterion used
for rejecting backgrounds.
Lepton isolation is computed by summing the PT of PF candidates in the neighborhood of the selected lepton, within a cone of size AR = 0.4. The lepton itself is
excluded from the isolation sum by applying an inner veto cone for particles to be
included, as detailed in Table 4.2. In the case of charged PF candidates, the candidate
is excluded if the lepton track matches the track of the PF candidate. In computing
the muon isolation, photon and neutral hadron candidates are considered only if their
transverse energy exceeds 0.5 GeV.
Additional particles originating from pileup can result in increased values of the
isolation quantity, making a restriction on the isolation variable less efficient. To assist discrimination against pileup, charged PF candidates can be further classified as
coning from the hard interaction, or as coming from pileup, based on whether or not
the track of the charged particle can be associated with the selected primary vertex,
determined by the z distance between the track and the primary vertex. Charged
particles for which this distance is greater than 0.1 cm are designated as originating
from pileup and are not used to compute isolation. However, the identification of
particles coming from the selected primary vertex based on the association of their
tracks with the vertex is only feasible for charged particles. A further correction is
applied for the contribution of neutral particles used to compute the isolation which
may be due to pileup and is known as the A/ correction. The pileup contribution of
charged hadrons is first computed by taking the PT sum of all charged hadron candidates within the isolation cone which fail the primary vertex association; in the case
of the muon isolation they are required to have PT > 0.5 GeV and be outside a cone
of size AR = 0.01 around the selected lepton. The neutral contribution from pileup is
then estimated to be one-half of the charged contribution, based on the approximate
67
e isolation veto cone size
0.01 (barrel), 0.015 (endcap)
0.0
0.08
0.0
p isolation veto cone size
0.0001
0.01
0.01
0.01
PF candidate type
Charged
Neutral hadron
Photon
Charged, PU
Table 4.2: Minimum AR (with respect to lepton candidate) of PF candidates used
to compute contributions to lepton isolation for different candidate types.
relative frequency of charged hadron and neutral hadron production. This estimate
is subtracted from the neutral contribution to the isolation sum; the maximum correction allowed is the full value of the original neutral isolation contribution. The
corrected combined isolation is defined as
PT +max
I :
where Echarged PT,
neutral PT,
0,
PT +
and
Z
PT
(4.5)
PT)
PT
ycharged,PU
neutral
charged
are the contributions of charged particles,
neutral hadrons, and photons to the isolation sum and
Zcharged,PU
the estimated
contribution of charged hadrons originating from pileup.
Selected leptons are required to be isolated by applying a maximum threshold on
their relative isolation,
II
(4.6)
PT
with pl being the lepton transverse momentum.
Ire, < 0.15 and Irel < 0.10 in the barrel (1gj
The restriction for electrons is
< 1.479) and endcap (171
regions respectively. Muons in the region IT,} < 1.5
( rj
> 1.479)
> 1.5) are required to have
Irel < 0.15 (Irei < 0.10).
4.8
Di--r Mass Reconstruction
Reconstruction of the T-pair invariant mass is an important element of the analysis
since it is the variable used to extract the presence of a H -+
TT
signal. However,
the reconstruction of the di-tau system is complicated by the presence of neutrinos
68
CMS Simulation, Is
=
8 TeV
(1 0.16 -
0.14
CMS Simulation,
ep
Z-m
------
H--TT, m
0.10
= 125 GeV
E> 0.12
------
H-mTt, m = 125 GeV
.
10.10 -
-
0.08
0.0
0.06 --
0.04
0.040.02-
0.020.00
ep
8 TeV
~Z-)*TT
0 -z-
CD
is =
0
50
100
''
''''
150
200
'
O
250
.
0
..
50
100
150
200
250
MT [GeV]
mvis [GeV]
Figure 4-3: Distributions of the invariant mass of the visible T-pair decay products,
mvis (left) and the SVFit mass (right) compared for samples of simulated Z -+ TT
events and H -- TT events for an SM Higgs boson of mass mH = 125 GeV. The
histograms are normalized to have unit area.
from the T-lepton decay which carry a significant portion of the energy. An algorithm
known as SVFit is used to estimate the r-pair invariant mass, mm-, based on the
momenta of the visible products from the T-lepton decay and the $g. The SVFit
mass provides a better separation of signal from the Z
-+
Tr
background than just
the mass of the visible decay products (mvis) as can be seen in Fig. 4-3, and achieves
a resolution of 15 - 20 % on
A fully-leptonic
T
mIT.
decay is characterized by 3 unconstrained parameters, chosen
to be:
" The fraction of energy carried by the visible lepton from the tau decay, x.
" The azimuthal angle
#
of the tau direction.
" The mass of the two-neutrino system, m,,.
Constraints are provided by the four-momentum of the visible lepton from the
and
$x
and
$,,
T
decay,
the x- and y-components of the $T. A maximum-likelihood method
is used to estimate the most probable value of m,, based on the known parameters.
69
The m,, reconstruction relies on constructing a likelihood function
f
V|p
is VIS, a1
,(4.7)
62)
for measuring the observed gT with components
$X and $y,
given that the four-
momenta of the visible tau decay products have the values piis and piis, and that
the unknown parameters characterizing the two tau decays have the values d
(x,
#1 , mn,mi)
and a2 = (X 2 , #2 , m,,,2). The likelihood is a product of three likelihood
functions, modeling the kinematics of the two tau decays and the compatibility of a
T-pair decay hypothesis with the measured
$Trespectively.
Matrix elements [87] are
used to model the leptonic tau decays:
, =
d
dx dmn,, do
c 4m2" [(m2
+ 2m!,)(mi
'
(T
within the constraints 0 < x < 1 and 0 < mv, < mV1
-
-
m!,)]
V'
,
(4.8)
x. The likelihood function
quantifying the compatibility of a tau decay hypothesis with the measured
$T
is
defined to be
T
L, (gT) =exp
1
: P"
x-
--
1
V-.
Here, V is a covariance matrix representing the expected
using a
$--significance
$X - Z P/
$T
(4.9)
resolution estimated
algorithm [88],
V
(
f
,
(4.10)
and IV is the determinant of the matrix. E p", Z p" represent the sum of the neutrino
momenta in the x and y directions respectively.
The probability of measuring a mass mI
70
is computed from the combined likeli-
hood as
P(mT)
J S (mrn
- ms (p1
,
f& 'T
PVis
s
,
d
-d ,
(4.11)
and the best estimate for m,, is taken to be the value of m'T which maximizes
this probability. The VEGAS integration program [89] is used to compute the integral, scanning mTT in steps of a few GeV. The best estimate of
performing a quadratic fit to the value of
mTT
mTT
is obtained by
found by the scan to maximize the
likelihood and the two neighboring points and taking the most probable value found
by the fit.
71
Chapter 5
Event Selection
As described in Section 1.5, the H
-
TT
analysis relies on the selection of the T-pair
decay products. For the final state with an electron, a muon, and 4 neutrinos, referred
to in this thesis as the ep, final state, this implies the selection of a well-identified and
isolated electron and muon of opposite charge. A sequence of selection requirements
is imposed in order to reject sources of background while preserving a high efficiency
for signal events. The selected events are then classified in categories in order to
improve the analysis sensitivity by exploiting Higgs boson production kinematics or
by benefiting from improved mass resolution in the designated categories.
5.1
Trigger Selection
The eu selection relies on events passing either a "Mul7Ele8" trigger at HLT, requiring a muon candidate of
PT >
17 GeV and electron candidate of
or a "Mu8_Ele17" trigger at HLT, requiring a muon candidate of
electron candidate of
PT >
PT
PT
> 8 GeV,
> 8 GeV and
17 GeV. In order to cope with increasing instantaneous
luminosities and maintain reasonable trigger rates, the quality requirements on the
electron leg of the trigger became more stringent with the progress of data-taking in
2011 and 2012, as did the
PT
thresholds applied on the trigger objects at the Li trig-
ger level. At the beginning of the 2011 data-taking period, both triggers were seeded
72
by an Li trigger requiring a muon candidate with PT > 3 GeV and a Li electron
or photon (e/-y) candidate with PT > 5 GeV. The version of the Mul7_Ele8 trigger
used at the end of the data-taking period in 2011 had an Li requirement of a muon
candidate of PT > 12 GeV and an e/-y candidate of PT > 5 GeV, while the version of
the Mu8Ele17 trigger used at that time required an e/
candidate of PT > 12 GeV
and no threshold on the muon leg at L1. In 2012, the Mui7_Ele8 trigger was seeded
by an Li trigger requiring a muon candidate of PT > 12 GeV and an e/-y candidate
of PT > 7 GeV.
Table 5.1 lists all of the HLT paths used in the analysis and the integrated luminosity corresponding to the data collected with each trigger. Only one version of
each of the Mui7_Ele8 and the Mu8_Ele17 triggers was used at any given time. The
successive versions of each trigger imposed slightly more stringent identification and
isolation criteria on the trigger objects. The selection criteria imposed on the electron
trigger object are indicated in the names of the trigger paths listed in Table. 5.1 and
further described in Table 5.2. Events selected for the analysis were required to pass
at least one of these triggers.
Integrated Luminosity (fb 1 )
Trigger Path
2011
Mu17_Ele8_CaloIdL
Mu17_Ele8_CaloIdT_CaloIsoVL
Mu8_Ele17_CaloIdL
Mu8_Ele17_CaloIdT_CaloIsoVL
2.0
3.0
1.2
3.8
2012
Mul7_Ele8_CaloIdT-CaloIsoVL-TrkIdVL-TrkIsoVL
Mu8_Ele17_CaloIdTCaloIsoVLTrkIdVL-TrkIsoVL
19.7
19.7
Table 5.1: List of trigger paths used to select events and the integrated luminosity of
the data collected with each of the triggers.
73
Trigger name label
Calo~dL
Calo~dT
TrkIdVL
CalolsoVL
Trk~soVL
Selection criteria for barrel (endcap) electrons
H/E < 0.15 (0.10)
C< 0.014 (0.035)
H/E < 0.10 (0.075)
CldUicx
< 0.011 (0.031)
<0.01 (0.01)
TAVin < 0.15 (0.10)
ECALIso/ET < 0.2 (0.2)
HCALIso/ET < 0.2 (0.2)
Trklso/ET < 0.2 (0.2)
Table 5.2: Requirements on electron trigger objects corresponding to different labels
used in HLT trigger path names. The H/E, -inin, IATin , and JA5inl variables are described in Section 4.6.1. ECALIso, HCALIso, and TrkIso refer to isolation quantities
computed based on energy deposits in the ECAL, HCAL, and tracker respectively
within a cone of size AR = 0.3 around the object.
5.2
Lepton Selection
After applying the trigger requirements, further offline selection criteria are imposed.
The selection requires one muon in the pseudorapidity range 1r1 < 2.1 and one electron
with IrA < 2.3. Asymmetric PT thresholds are applied on the leptons; the leading and
trailing leptons are required to have PT > 20 GeV and PT > 10 GeV respectively.
Selected events with a low-PT muon between 10 and 20 GeV are required to have
passed the Mu8_Ele17 trigger, while those with an electron between 10 and 20 GeV are
required to have passed the Mu17_Ele8 trigger. Events in which the PT of both leptons
exceeds 20 GeV can be selected by either trigger. In order to ensure that the leptons
selected offline are the same as the objects which fired the trigger, the selected electron
and muon are required to be within AR < 0.5 of the corresponding trigger objects,
where AR represents the distance in ?1k space. The muon and electron are required
to fulfill the identification and isolation requirements described in Sections 4.5-4.7.
The asymmetric choice of pseuodorapidity thresholds on the lepton candidates
are driven by slightly different analysis considerations. The restriction on the muon
T1
was originally dictated by triggering limitations and coherence with analyses in
other final states involving muons; and although the current eu triggers used in the
74
analysis would permit the offline selection of muons up to 2.4 in rl,, no advantage in
sensitivity has been found from such an expansion of the muon 'q acceptance. Thus
the offline restriction on muons to be selected in the range rj| < 2.1 is maintained.
Conversely, the triggers used for the analysis would permit the offline selection of
electrons up to 2.5 in Ilq. However, the restriction of electrons to IqI < 2.3 is driven by
considerations related to the estimation of the Z
TT background. This background
-
is modeled using an embedding technique described in Section 6.2.1, which relies on
the selection of two reconstructed muons in collision data which are then replaced
with simulated tau decays. The restrictions on the kinematic acceptance for muons
result in poor statistics for events with visible
T
decay products reconstructed at
higher values of 17j in the embedded event sample, motivating a threshold of 2.3 on
the electron pseudorapidity. Again, this choice is found to have no adverse effect on
the sensitivity of the analysis.
A dedicated analysis targeting the associated VH production node considers final
states with 3 or 4 leptons (electrons, muons, or hadronic taus) coming from the T-pair
decay and from the decay of the associated W or Z boson
[901.
In order to remove
any overlap of events, events selected in the ey final state are removed if they are
found to have an additional electron or muon with PT
>
10 GeV fulfilling the selection
criteria used in the VH analysis. These selection criteria are listed in Table 5.3.
Electron selection criteria for additional lepton veto
Kinematics
PT > 10 GeV, IrI < 2.5
Impact parameter Id2| < 0.2 cm, Idol < 0.045 cm
Identification
Electron identification BDT (Section 4.6.1)
Isolation
Irel < 0.3
Muon selection criteria for additional lepton veto
Kinematics
PT > 10 GeV, lql < 2.4
Impact parameter Id2l < 0.2 cm, Idol < 0.045 cm
Identification
Tight muon identification (Section 4.5.1)
Isolation
Irel < 0.3
Table 5.3: Selection criteria used for additional lepton veto. Events containing an
additional electron or muon satisfying the corresponding requirements are rejected
from the analysis.
75
A possible, albeit small, source of background to this analysis comes from Z
-+
pp events in which one of the muons from the Z boson decay radiates a photon
which could convert to electrons, one of which may satisfy the electron selection
requirements. In order to suppress this background to negligible levels, the selected
electron is required to have no additional reconstructed muon with PT > 3 GeV within
AR < 0.3 to reduce the likelihood that the electron comes from a photon radiated
by a muon.
5.3
Lepton Selection Efficiency
While Monte Carlo simulation provides an excellent modeling of physics processes
and description of detector response for the most part, there may still be differences
with respect to collision data in describing the detector due to inaccurate detector
simulation or changing conditions with the progress of data-taking. Such discrepancies can lead to differences in the efficiencies for selecting physics objects between
collision data and simulation. These discrepancies can be corrected for by measuring
the efficiencies for selecting the relevant physics objects in observed data and simulation, and applying the appropriate corrections to the simulation in order to provide
a better description of the data. The correction takes the form of a scale factor,
Edata/EMC,
applied to simulation as a weight on an event-by-event basis, where
Edata
and EMC are the efficiencies measured in data and simulation respectively. The efficiency measurements most relevant for this analysis are those of the lepton selection
efficiencies.
The absolute efficiency for selecting a lepton cannot, in general, be measured
in data. Instead, the procedure followed measures the conditional probability of a
reconstructed object (a GSF electron or a Global muon), to fulfill the additional
stricter requirements implemented in the analysis selection.
Measuring the same
probability in simulation and applying the corresponding scale factor, Edata/EMC to
simulation provides a good reproduction of the data selection efficiency in simulation.
The method used to determine lepton selection efficiencies relies on Z boson decays
76
to pairs of leptons and is known as the tag-and-probe method [91].
5.3.1
Tag-and-Probe Method
The tag-and-probe technique relies on the selection of Z
-+
cc or Z
-
pp events. The
procedure begins with the selection of di-lepton events. Stringent selection criteria
are imposed on one of the two lepton candidates in order to reduce backgrounds; this
lepton is known as the "tag". The other lepton is known as the "probe"; the efficiency
for the selection requirements under study is given by
=
N pass
Npass + Nfail
(5.1)
where Npass and Nfai1 are the numbers of probes passing or failing the requirements
respectively.
In order to select Z boson events with high purity, the di-lepton mass is required to
be in a window around the Z boson mass, chosen to be between 76 GeV and 106 GeV
for this analysis. In the cases where the remaining backgrounds are deemed to be nonnegligible, the numbers of passing and failing probes and the corresponding efficiencies
are determined after background subtraction by performing a simultaneous likelihood
fit to the di-lepton mass distributions from the event samples in which the probes pass
or fail the selection requirements, known as the "passing" and "failing" samples. Since
the detector response differs in different kinematic regions, the selection efficiencies
and the corresponding data-to-simulation scale factors are measured in bins of PT and
r for this analysis.
5.3.2
Lepton Identification and Isolation Efficiency
The efficiencies for identification and isolation requirements are measured in one step
for electrons and muons using an implementation of the tag-and-probe technique.
For the purpose of this analysis, the tag electron (or muon) is required to be a GSF
electron (or Global muon) which satisfies the corresponding lepton identification and
isolation requirements. The probe lepton is a GSF electron or Global muon within
77
the
PT
and y range for which the efficiency is being measured. In order to prevent
any bias in the probe selection from trigger requirements, the events used for the
measurement are collected using single lepton triggers which are fired by the tag
leptons. The selected events are divided into passing and failing samples based on
whether or not the probe passes the identification and isolation requirements.
A
simultaneous likelihood fit to the di-lepton mass distributions for the passing and
failing samples is performed to measure the efficiency in data.
The signal model used for the likelihood fit is obtained from a convolution of
the mass shape template derived from simulation with a Gaussian distribution. The
simulation is thus used to model effects like final state radiation and detector effects
which influence the shape of the mass distribution, while the Gaussian accounts for
differences in modeling the energy scale and resolution between data and simulation.
For the electron efficiency measurement, an exponential function is used to model
the background shape in the passing sample, and a double exponential for the background in the failing sample. In the case of the muon efficiency measurement, the
background levels are small in both the passing and failing samples; consequently,
an exponential model is used for the background shape in both samples. Figure 5-1
shows representative examples of the fit results used to determine the efficiencies for
electrons and muons.
The measurement of the lepton identification and isolation efficiency in simulation
does not suffer from the added complication of background contamination because of
the availability of the MC generator information. The measurement can be directly
performed on objects matched to leptons at generator level. Both tag and probe
leptons are required to be matched to generator-level leptons originating from the
Z boson decay within AR < 0.5. The efficiency in each bin of
PT
and
ij
is then
simply calculated by counting the number of passing and failing probes in that bin
and computing the passing fraction using Eq. 5.1. The efficiencies and scale factors
measured for the electron and muon identification and isolation efficiencies in different
PT
and
Tj
regions are listed in Appendix A. The derived scale factors are applied as
event weights to simulation as a function of the
78
PT
and T of the selected electron and
Failing probes
Passing probes
C/)
: 1.5 <
900
JI~
1711< 2.3
15 GeV
< p < 20 GeV
-T
800
11978 Events
=0.2
I'
-0,0021
CD
:
1.5 < ITl < 2.3
> 5000
N=~g1'40.±
l
±91
=1
0490.8
=32685.0 ±242.4"
N
72616 Events
02.7 ±18.1
N 00
N.-= 1
700
=00021
E= 0.2430
15 GeV < p < 20 GeV
13545.6 t 255.5'
4000
600
500
3000
400
2000
300
200
-
1000
100
.
0
80
100
80
12
12
100
Mee [GeV]
mee [GeV]
Failing probes
Passing probes
+00007
50000
0.0 < 1r1< 0.8
1
25 GeV < pT < 30 GeV
364057 Events
40000
0.8
<
<
_0.0
D18000
25 GeV< p < 30 GeV
0=0.8141-0.
N =3189235 605.
LJ 6000
N00 =2805.3t156.3-
14000
95704 Events
E=0. 31410
N = 7 2834.6
N
=2
297.2
888.1± 93.9
12000
30000-
10000
8000
20000-
6000
............I .........
4000
10000:
2000
80
100
0
120
m,, [GeV]
80
100
120
m,, [GeV]
Figure 5-1: Examples of results of the simultaneous fit to the di-lepton mass distributions from the passing and failing samples used for electron (top) and muon (bottom)
identification and isolation efficiency measurements. The examples shown are the fits
used the measure the efficiency of electrons in the range 15 GeV < PT < 20 GeV
and 1.5 < IrI < 2.3 (endcap region) and of muons in the range 25 GeV < PT < 30
GeV and 0.0 < 17| < 0.8 (barrel region). The dashed red curve represents the fitted
background while the solid blue curve represents the sum of the fitted signal and
background in each sample.
muon. Figure 5-2 shows the efficiencies for 8 TeV data and simulation measured in
bins of PT and TI.
79
w
1. 0-
1.0
0.
0.8
0.
0.6
0. 4 -
0.4
-
0--0
-t
-uData
-0-M
+MC
0.
0. 0 .
50
100
-
-
-UData
0.2
0.0
15 0
e pT [GeV]
w
+sMC
-2
0
2
e il
U.)
1.
1.0
0. 8
0.8
0. 6
0.6
0
0.
0.4
-w Data
0. 2 -0.
-
Data
0.2
+MC
+MC
50
100
0.0
150
-2
0
2
pl
PT [GeV]
p
Figure 5-2: Lepton identification and isolation efficiencies measured in 8 TeV data
and simulation for electrons (top) and muons (bottom), as a function of lepton PT
and r.
5.3.3
Trigger Efficiency
The efficiency an event to pass the trigger is derived from the efficiencies of an electron and muon passing the full selection requirements to pass the corresponding leg of
the electron-muon trigger, which is described in Section 5.1. The trigger efficiency is
measured using Z --+ Tr events in the eu channel which satisfy the offline ep selection
requirements. For the measurement of the electron trigger efficiency, electron-muon
events are collected using a single muon trigger fired by the selected muon. The muon
is treated like a tag lepton and is required to pass the full muon selection require80
ments.
The selected electron, which is required to pass the full electron selection
requirements, is treated as the probe. The electron trigger efficiency is derived from
the fraction of probe electrons which pass the electron leg of the trigger. Similarly,
for measuring the muon trigger efficiency, events are collected using a single electron
trigger fired by the selected electron and both leptons are required to pass the full
selection. The muon trigger efficiency is then measured from the fraction of probe
muons which pass the muon leg of the trigger. Since the background contamination
from non-cp events after applying the full lepton selection is quite low, the efficiencies
are obtained by simply counting the number of passing and failing probes in each case
and calculating the fraction of passing probes in the sample. As for the identification
and isolation efficiencies, the trigger efficiencies are also calculated in bins of PT and
Rather than applying the trigger efficiencies measured in data to the simulation
directly, simulated events selected in the analysis are required to pass the cy trigger
implemented in simulation, and the scale factors between the trigger efficiencies measured for data and simulation are applied to bring the simulated efficiencies closer to
the observed efficiencies. The scale factors are applied in the form of event-by-event
weights to the simulation. The efficiencies and scale factors measured for the electron and muon trigger legs in different
PT
and q regions are listed in Appendix A.
Figure 5-3 shows the efficiencies for 8 TeV data and simulation measured in bins of
PT
and I.
5.4
b-Tagging Efficiency and Mis-Tag Rate
The use of b-tagging to identify events which contain a b-jet is relevant for the categorization of events in both the MSSM and SM analyses (Section 5.6). Differences
between simulation and data in the efficiency for tagging b-jets and the rate for mistagging jets from light quarks or gluons are corrected for by using measurements of the
efficiencies and scale factors in data and simulation [92, 93]. The procedure followed
attempts to correct the simulation to have the same b-tagging efficiency and mis-tag
81
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
-uData
0.2
-5Data
0.2
+ MC
0.c
MC
50
100
e
0.0
150
pT[GeV]
-2
0
2
en
w
1.C
1.0
O.8
0.8
O.6
0.6
0.4
0.4
-uData
SData
0.2Il
O.0
-- U
0.2
+WMC
50
100
0.U
150
[pT
+MC
-
0
2
L1
[GeV]
Figure 5-3: Trigger efficiencies measured in 8 TeV data and simulation for the electron
leg (top) and muon leg (bottom) of the epu trigger, as a function of lepton PT and q.
rate as data by re-classifying randomly chosen subsets of b-tagged and untagged jets
as un-tagged or b-tagged respectively as required. The efficiencies and scale factors
are applied based on the
PT,
q, and flavor of the jet in simulation.
Topological Selection
5.5
The principal source of background after the lepton selection is from the electroweak
Z
-4
TT
process with the same T-pair final state, with a cross section several orders of
magnitude larger than that expected for the signal. In order to improve discrimination
82
against the Z
-
TT
background, selected events are classified in categories designed
to enhance Higgs boson production by exploiting the production kinematics. The
selection criteria used for the categories also result in improved T-pair reconstructed
mass resolution which allows for better separation of a signal, at higher mass, from the
Z
-+
TT
background, which peaks at the Z boson mass. Prior to this categorization of
events, a selection is applied based on event topology in order to reduce other sources
of background such as tt, W+jets, and QCD multijet production.
5.5.1
Standard Model Higgs Analysis Selection
The topological selection applied makes use of a multivariate analysis based on a
Boosted Decision Tree (BDT), relying not only on discriminating variables but also
on their correlations.
The goal of this selection is to discriminate between signal
events and events originating from non-di-T sources, primarily tt, by relying on the
expected kinematics of events with genuine T-pairs. The variables used target distinguishing information about the event such as the correlation between the directions
of the visible leptons and the
$Twhich
are strongly related for di-tau events, impact
parameter information which could indicate the relatively long lifetime of the tau,
and b-tagging information which could identify a tt event. The following variables are
used in the BDT:
*
pls,
the transverse momentum of the combined four vector of the two selected
leptons projected onto their bisector in the transverse plane.
* p(,
the projection of the missing transverse energy vector on the same bisector.
* The A0 between the electron and muon.
* The missing transverse energy,
e
The transverse mass mT(ll,
$T)
9T.
between the dilepton system and the
mT(ll, 9T) =I2pfTg$(1 - cos(A#(ll,
83
VT))),
$T.
Here
(5.2)
where pj is the PT of the dilepton system and AO(1l,
between the dilepton system and the
$T)
the azimuthal angle
$.
" The transverse impact parameter do of the electron with respect to the selected
primary vertex.
* The CSV b-tag discriminator value of the leading (highest-pT) jet with PT > 20
GeV in the event, providing it exceeds the CSV Loose threshold of 0.244. This
cut-off is used because the CSV distribution is not well-modeled in simulation
at very low values below the Loose threshold.
Figure 5-4 shows the distributions of these variables for simulated gluon fusion and
VBF signal samples for a Higgs boson of mass 125 GeV, and for the tt and fakeinduced (W+jets/multijet) backgrounds. Each of the variables provides discriminating power between the signal and background. The BDT is trained using a combination of simulated gluon fusion and VBF signal events against the tt and fake-induced
backgrounds. The output of the topological BDT is shown for the relevant samples in
Fig. 5-5, demonstrating the power of the discriminator to separate signal from background. Events are selected if they have a BDT output exceeding -0.5; this threshold
is chosen to maximize the signal significance. This working point corresponds to an
efficiency of > 96% and > 91% for simulated samples of gluon fusion and VBF signal
events respectively.
Figures 5-6 and 5-7 show the distributions of the BDT input variables for the
observed data and for the expected background contributions for the 2011 and 2012
data-taking periods respectively. The BDT output distributions are shown in Fig. 58. The techniques used to model the various signal and background processes are
described in Chapter 6. These distributions are obtained after applying the lepton
selection.
5.5.2
MSSM Higgs Analysis Selection
In the case of the search for neutral MSSM Higgs bosons decaying to tau pairs, an
alternative topological selection is applied which relies on the correlation between
84
m.0.18
ggH(125)-r
-
qqH(125)-4TT
0.18
0.14
-
fakes
0.16
-
DI
40.20
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ggH(125)-+t
qqH(125)-+TT
t
-
-
-
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0107
7
-
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-
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-
<0.20
fakes
-
0.14
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ggH(125)-+T' qqH(125)-mT
t
fakes
0.14
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0.12
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0.10
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0.02
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00
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00
10
20
30
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40
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50
60
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P. [GeV]
-
ggH(25)-TT
qqH(125)-+tt
-
fakes
-
0
-50
O 0J
100
50
0.0....
0.07 -
-
0.06
-
.
L~V
0.18-''''
..........
ggH(125)--TT
qqH(125)-T
--
fakes
0.5
1.0
1.5
2.0
-
0.16
-
0.14
-
~-
2.5
3.0
ggH(125)-nT
qqH(125)-m
fakes
0.12-
0.05
0.08-
0.100.04
0.06
0.08
-
0.03.
0.06:
0.04
-0.02-
0.02
0..0 20
40
60
80
100
0.04
0.0.04
J1--00
0.022
120
0
140
F [GeV]
20
10
30
40
60
50
70
80
90 100
m1(Il1 )
.020-0.015-0.010-0.005 0.000 0.005 0.010 0.015 0.020
e dO
.................
-ggH(125)--oTc
qqH(125)-+-T
0-14-ft
-
0.12
fakes
0.10
0.08
0.06
0.04
0.02
OO A
.1
. . . 1.1
, - I...
0.2
0.3
0.4
1... 11. . . . .
0.5
0.6
07
08
0
1.0
b-tag discriminator
Figure 5-4: Distributions of discriminating variables used as inputs for the topological
BDT; the distributions are shown for simulated gluon fusion (ggH) and VBF (qqH)
events, for simulated tt events, and for a sample of QCD multijet and W+jets events
(labeled as "fakes"). Each histogram is normalized to have an area of 1. From upper
row (left) to bottom row: projected visible transverse momentum p"iS, projected
transverse missing energy p(, A0 between the electron and muon, transverse missing
energy $T, transverse mass mT between the dilepton system and the $T, do of the
electron with respect to the selected primary vertex, CSV discriminator value of the
highest-PT jet with PT > 20 GeV passing the CSV Loose working point in the event.
the pC and pvis projections. This simpler selection is used because some of the BDT
variables and their correlations may be affected by the choice of model for the signal.
85
'i'''
~50.24
0.22
'''i'
ggH(125)-*tt
-
qqH(125)-m
0.20
-
-t
f
--
0.18
111111'''1'
--
fakes
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02-
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
BDT output
Figure 5-5: Output of the topological BDT for simulated gluon fusion (ggH) and
VBF (qqH) events, for simulated tt events, and for a sample of QCD multijet and
W+jets events (labeled as "fakes"). Each histogram is normalized to have an area of
1. The analysis selects events which exceed a threshold of -0.5 on the BDT output.
The analysis strives to be model-independent as far as possible.
Genuine di-T events are expected to have the visible leptons close to each other in
r/c space and genuine missing energy from the neutrinos in the same direction as the
leptons. In events with one or more fake leptons, the separation between the lepton
candidates is more evenly distributed and the missing energy need not be correlated
with the lepton candidates. The selection applied requires the quantity
D( with a = 0.85, to be larger than -20.
-(5.3) =
The cut is also useful in rejecting tf events,
86
CMS Preliminary, is =7 TeV, L=
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2500
2000
1500
1000
500
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b-Tag Discriminator
Figure 5-6: Discriminating variables used as input for the topological BDT for the
data collected in 2011. From upper row (left) to bottom row: projected visible
transverse momentum pvS, projected transverse missing energy 0(, A# between the
electron and muon, transverse missing energy $T, transverse mass mT between the
dilepton system and the transverse missing energy, do of the electron with respect to
the selected primary vertex, CSV discriminator value of the leading jet with PT > 20
GeV passing the CSVL working point in the event.
despite the presence of two real leptons, since the more complicated top-quark decays
result in more diluted projections. The values of both ce and the threshold applied on
D( are chosen in order to maximize the significance for observing a signal. Figure 5-9
shows the distribution of the D( variable for the data and the expected backgrounds
87
CMS Preliminary, Is = 8 TeV, L = 19.7
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-------
ep
-0-
5xH(125 GeV)-+WW
observed
eltoweak
16000
14000
a QCD
bk9 uncertainty-
-
12000
8000
10000
8000|
Preliminary, %=
300 0.-05
0-010H
G
0.5
0.010
0.015
0.020
6000
6000
600
4000--
4
000
2000
2000
00
400
L
2001
DOO
150
ET
mT
[GeV]
CMS Preliminary, is =8 TeV, L = 19.7
(11)
[GeV]
0.005
0.020
e do(PV)
fb'
42
C
16000
e
-0-
W 14000
observed
lectroweak
-
12000
bguncertainty
10000
8000
6000
4000
2000
0.4
0.6
0.8
1.0
b-Tag Discriminator
Figure 5-7: Discriminating variables used as input for the topological BDT for the
data collected in 2012. From upper row (left) to bottom row: projected visible
transverse momentum pvlS, projected transverse missing energy 0(, AO between the
electron and muon, transverse missing energy $T, transverse mass mT between the
dilepton system and the transverse missing energy, do of the electron with respect to
the selected primary vertex, CSV discriminator value of the leading jet with PT > 20
GeV passing the CSVL working point in the event.
in 2011 and 2012 for events passing the lepton selection.
88
CMS Preliminary, is = 7 TeV, L = 5.0 fb"
CMS Preliminary, is = 7 TeV, L = 5.0 fb'
U)
C
5xH(125 GeV)->rT
--
5 10000
------- 5xH(125 GeV)-)WW
observed
-g
U)
5xH(1'25
---Ge )-+TT
------- 5xH(1 25 GeV)->WW
--0
106 le L
observed
electroweak
electroweak
8000
10 5
Cbkg
uncertainty
b kg. uncertainty
~
6000
1
104
4000
101
2000
102
-1.0
-0.5
0.0
0.5
1.
10kj
-1.0
0
-0.5
0.5
0.0
BDT output
CMS Preliminary, %s 8 TeV, L = 19.7
-----------
a) 50000
BDT output
CMS Preliminary, is =8 TeV, L = 19.7
fb7'
U)
5xH(125 GeV).-+n
5xH(125
10 7
5xH(125 GeV)-rWW
observed
fb"
---i-5xH(1 25 GAV-'TT*
4-
Z-mnnT
-----GeV)
-e-observed
WW
W
electroweak
Zeectroweak
aCD
40000
1.0
10
C]bkg. uncertainty
QCD
5
[~~~)bkg.
uncertainty
104
30000
103
20000
102
10000
0
-1.0
10
-0.5
0.0
0.5
1.0
-1.0
BDT output
Figure 5-8:
(upper left)
(lower left)
value larger
5.6
5.6.1
-0.5
0.0
0.5
1.0
BDT output
Output of the topological BDT for the data collected in 2011 in linear
and log scale (upper right) and for the data collected in 2012 in linear
and log scale (lower right). Selected events are required to have a BDT
than -0.5.
Event Classification
Standard Model Higgs Analysis Event Categories
Selected events are classified in the following 6 mutually exclusive event categories in
order to exploit the topology of Higgs production mechanisms through gluon fusion
or VBF and in order to further discriminate against background processes. The VBF
process in particular provides a distinct experimental signature of two energetic jets
89
CMS Preliminary, IS = 7 TeV, L =
-
800080
7000
CMS Preliminary, is = 8 TeV, L -= 19.7 W1
5.0 fb
__I
)-sak
(1ew
-- 5xH( 25 GeV) WW
observed
ern
30000
ek
_.,
e
5xH( 25 GeV)-4WW
observed
eectroweak
electroweak
250002
6000
Lulbkg. uncertainty
li]bkg. uncertainty
5000
20000
4000
15000
3000
10000
2000
1000
00
-150
-100
-50
0
50
D,
-150
100
[GeV]
-100
-50
0
50
100
D, [GeV]
Figure 5-9: Distribution of the D( variable for the data collected in 2011 (left) and
2012 (right).
largely separated in rapidity, due to the two quarks produced in association with the
Higgs boson. Due to an absence of color exchange, no additional jet is expected in
the rapidity gap between these two jets, referred to as the "tagging" jets. Two of the
event categories are optimized to provide sensitivity to VBF Higgs boson production,
while the others are sensitive to gluon fusion Higgs boson production. Distributions
of variables which are relevant for the event categorization are shown for the different
signal processes in Fig. 5-10. The fractional composition of the signal contribution in
each event category, as well as for the inclusive selection, is illustrated in Fig. 5-11.
9 VBF tight: This event category exploits the topology of Higgs boson production through the VBF process and has an improved purity for selecting VBF
signal events. At least 2 jets with PT > 30 GeV fulfilling the jet selection criteria described in Section 4.3 are required. The difference in 7 between these
two jets ( A5jj) is required to be greater than 4.0 and the mass of the di-jet
system (mjj) is required to be greater than 700 GeV. A central jet veto requires
no additional jet with PT > 30 GeV between the two selected jets. The PT of
the Higgs boson candidate system, constructed from the leptons and the
$T, is
required to be greater than 100 GeV. These requirements enhance VBF Higgs
boson production and reduce the background from Drell-Yan T-pair produc-
90
-ggH(125)-mT
qqH(125)-mtr
VH(125)-+tt
0.
0.
0.
5
0.
0.
2 -0.
0.0 0.5 1.0
1.5
2.0 2.5 3.0 3.5 4.0 4.5 5.0
Number of jets
0.40
-
0.30
-
0.35
ggH(125)-:TT
qqH(125)-*tVH(1 25)-m
0.35
-
0.30
-
ggH(125)-+'rT
qqH(125)-mr' VH(125)-+-T
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
100
50
150
200
251
0
50
I I AI I I
100
'"
150
Leading jet pT [GeV]
0.40
-
0.35
PT (t)
:5
ggH(125)- T
qqH(125)-+TVH(125)-+-T
-
0.45
0.45
0.35
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
-
300
[GeV]
-ggH(1 25)-+-n -qq H(1 25)--mr
- VH(1 25)--TT
-
0.40
0.30
0.00
250
200
-..
.
..
0.05
0
" "
"
'
"
.
100 200 300 400 500 600 700 800 9001000
0.00
0
1
2
3
4
5
6
7
8
AT(jj)
M(jj) [GeV]
Figure 5-10: Comparison of distributions for the different SM Higgs boson signal
125 GeV at N/s =
processes, shown for simulated event samples produced for mH
8 TeV. Top row: number of reconstructed jets with PT > 30 GeV. Middle row:
leading jet PT for events with at least one reconstructed jet, Higgs candidate system
PT. Bottom row: invariant mass of two leading jets and distance in pseudorapidity
between them for events with at least two reconstructed jets with PT > 30 GeV. All
distributions are normalized to have unit area.
91
*ggH
*VBF
*VH
Inclusive
0-Jet low p
0-Jet high p
1-Jet low p
1-Jet high p
VBF loose
VBF tight
0
10 20 30 40 50 60 70 80 90100
Signal composition (%)
Figure 5-11: Estimated SM Higgs boson signal composition (as percentage of the total
signal yield) for mH = 125 GeV in each event category and the inclusive selection for
the 8 TeV analysis.
tion. In order to suppress background from tt events, an additional veto on any
b-tagged jet with PT > 20 GeV is applied.
* VBF loose: This category is intended to select VBF signal events which fail
to satisfy the more stringent criteria described for the VBF tight category. The
events in this category are required to not be selected in the VBF tight category,
to have at least 2 selected jets with
PT >
30 GeV satisfying I r/?j
> 3.5 and
mjj > 500 GeV, no jet with PT > 30 GeV between the selected jets, and no
b-tagged jet with PT > 20 GeV.
e 1-Jet: This category is mainly intended to exploit the process of gluon fusion
Higgs boson production with an additional jet. The Higgs boson system tends
92
to be boosted due to its recoil against a high-pT jet in such events. The higher
PT
of the Higgs boson leads to a selection of events with higher
scattering process; the corresponding better precision in the
$Tin
$T
the hard
measurement
improves the reconstruction of the invariant di-T mass. Additionally, it allows
better separation of the Higgs boson signal from the Drell-Yan di-T production,
which is expected to have a softer PT spectrum. Events assigned to this category
are required to have at least one jet with PT > 30 GeV and to not be selected
in either the VBF tight or VBF loose event categories.
Events with one or
more b-tagged jets with PT > 20 GeV are vetoed in order to suppress the tt
background.
This category is further split into two sub-categories based on whether or not
the PT of the muon is greater than 35 GeV. The high lepton PT sub-category is
introduced for better discrimination against the Drell-Yan 7-pair background.
Events in which the muon PT is smaller than or equal to 35 GeV are added to
the low lepton PT sub-category.
e 0-Jet: All selected events which do not fall into any of the above event categories are collected in this category. An event in this category is required to
have no jet with PT > 30 GeV and no b-tagged jet with PT > 20 GeV. The 0Jet category contains the large majority of the events selected by this analysis.
Its main purpose is to provide constraints on experimentally measured quantities. Measurements of the electron energy scale, efficiencies, and background
normalizations are constrained in this category and propagated to other categories allowing for a precise measurement of the signal sensitivity in the other
categories.
As for the 1-Jet category, this category is also split into two sub-categories
based on the muon PT.
93
5.6.2
MSSM Higgs Analysis Event Categories
In order to enhance the sensitivity of the MSSM Higgs boson search, the sample of
selected events is split into the following two mutually exclusive event categories.
e B-Tag: This event category is intended to exploit the production of Higgs
bosons in association with b-quarks, a process which is enhanced in the MSSM.
At least one b-tagged jet with
PT
> 20 GeV is required in this category. Events
in this category are required to not have more than one jet with
PT
> 30 GeV
in order to suppress the large tt background.
e No B-Tag: This event category is mainly sensitive to the gluon fusion production mechanism. Events in this category are required to have no b-tagged jets
with
PT
> 20 GeV.
94
Chapter 6
Signal and Background Modeling
Despite the efforts to suppress Standard Model background processes with respect
to the Higgs boson signal, the expected contribution from a signal in the collision
events selected by the analysis is still much smaller than the expected background
contribution.
Before evaluating the existence of a possible signal in the data by
identifying an excess of events over the background expectation, one must have an
excellent description of the SM background processes which could enter into the
selection, and of the expected behavior of the signal processes under study. The
techniques used to describe the relevant physics processes rely both on simulation
and on observed data. In the cases where Monte Carlo simulation is used, corrections
are applied to the simulation in order to account for differences between simulation
and observed data.
6.1
Signal Modeling
The expected behavior of the signal processes under study is modeled based on theoretical calculations by way of simulation. The gluon fusion and VBF processes are
simulated using POWHEG [94,95] interfaced with PYTHIA for parton showering and
hadronization.
For the gluon fusion simulation, the
PT
distribution of the Higgs
boson obtained from POWHEG at NLO is re-weighted using next-to-next-to-leading
95
order (NNLO) k-factors calculated using the HRES program [96].
the effect of the re-weighting.
Figure 6-1 shows
The effects of the finite mass of the top-quark are
taken into account in these calculations. The simulated event samples used to model
the associated production of a Higgs boson with a W or Z boson is produced using
PYTHIA.
C,,
)efault
35
30
Re-weighted
-
25
20
15
10
5
1.2
0
1.0
0.8 -
0
100
200
300
Higgs pT [GeV]
Figure 6-1: Effects of the re-weighting of the NLO Higgs PT spectrum obtained from
POWHEG (labeled "Default") using NNLO k-factors obtained using HRES.
The MSSM signal processes are modeled using simulated samples produced with
PYTHIA.
The cross sections and branching ratios used to obtain the normalizations
for each signal contribution are discussed in Section 3.3.
6.2
6.2.1
Background Estimation
Drell-Yan ir-Pair Production (Z -+ r-r)
This is the largest source of background for the analysis. The Drell-Yan process
involves the annihilation of a quark and anti-quark producing a Z boson (or a virtual
96
photon), subsequently decaying to pairs of oppositely-charged leptons. The presence
of the decay products of a real T-lepton pair makes the final state for the Drell-Yan
7-pair background indistinguishable from the signal. The correct modeling of this
background is crucial for the analysis and is done with the help of a sample of events
produced using a technique known as "embedding".
This "embedded sample" is
derived from a sample of observed events obtained using criteria designed to select
Z -± pp events.
The reconstructed muons in this sample are replaced by simulated T-leptons which
are decayed by TAUOLA. The kinematics of the simulated taus are determined based
on the kinematics of the original reconstructed muons. The list of reconstructed PF
candidates for each event is updated by replacing the PF muons with the reconstructed tau decay products.
PF-based reconstruction algorithms, such as
$T
and
jet reconstruction, are then run using the updated list. Events for which the visible tau decay products satisfy
PT
and
TI
requirements determined by the kinematic
thresholds used in the analysis event selection are allowed to enter into the embedded
sample.
Events which fail these requirements have their T-lepton decays repeated,
until the kinematic requirements on the visible decay products are satisfied. For the
final sample of embedded events, an event-by-event weight is applied based on the
probability of obtaining the corresponding tau kinematics. The embedded sample has
the advantage of providing a better description of jets, gT, and pileup effects than
a purely simulated sample. The embedded technique also improves the background
modeling by providing a sample with large statistics thanks to the large number of
Z
-+
pp events produced in collision data. Since the visible leptons are modeled
using simulation however, data-to-simulation scale factors are applied to account for
discrepancies in lepton selection efficiencies.
The background contamination in the embedded sample due to the selection of dimuon events not originating from the Drell-Yan process is evaluated by applying the
embedding procedure to simulated event samples describing other processes, such as
tt or di-boson events which could potentially enter the selection. The contamination
due to these processes has been found to be negligible in the analysis event categories,
97
with the slight exception of the tt contamination in the B-tag event category which has
a small effect. Accordingly, the estimated tt yield in this category is adjusted down
by 2% percent in order to compensate for the slight over-estimation of tt. Systematic
uncertainties related to this effect are assessed and incorporated into the analysis
(Section 7.7.2).
A simulation-based estimate of the inclusive yield (prior to event categorization)
for this process is obtained from a sample produced with MADGRAPH interfaced with
PYTHIA as described in Section 3.2.2.
The yield is then corrected based on the
observed Drell-Yan yield by measuring a scale factor between the yields observed in
data and predicted by simulation for a selection of Z -± ppu events and rescaling the
inclusive Z
Z
-
TT
-
TT
yield in simulation accordingly. This prediction of the inclusive
yield based on Z -
The efficiencies for Z
-
TT
pp events is used to normalize the embedded sample.
events to enter the selection for the individual event
categories are determined using the embedded sample which has been normalized to
the inclusive prediction.
6.2.2
Top-Quark Pair Production (tt)
The leptonic decays of top-quark pairs can also produce final states in which an
electron, a muon, and
$7
are present. The tE background is modeled with the help of
simulation produced using MADGRAPH interfaced with PYTHIA for the analysis of 7
TeV data and using POWHEG interfaced with PYTHIA for the analysis of 8 TeV data
(due to a lack of sufficient statistics, the MADGRAPH sample generated at 8 TeV does
not adequately describe the phase space under consideration).
The inclusive tt yield obtained from simulation is corrected to account for residual
differences between observed data and simulation by applying a scale factor measured
between the yields observed in data and predicted by simulation in a tt-enriched
selection of events. The tt-enriched selection requires events with an electron and
muon which satisfy the lepton selection requirements described in Section 5.2 to
have at least 2 jets with PT > 30 GeV, at least one b-tagged jet with PT > 20
GeV, and large
$
(greater than 80 GeV). This selection has an expected purity of
98
about 92% for selecting tf events. A scale factor between the yields obtained in data
and predicted by simulation is obtained after subtracting the remaining estimated
background contributions. Scale factors of 0.95 t 0.10 and 0.96 ± 0.10 are measured
for the analysis of the 7 TeV data and 8 TeV data respectively. These scale factors
are then used to adjust the inclusive tt yield predicted by simulation to the observed
yield.
6.2.3
Jet-Induced Backgrounds: W + jets and QCD
Multijet Production
Background sources for which one or both of the selected lepton candidates are "fakes"
or mis-identified leptons are referred to as fake backgrounds.
The main sources of
fake backgrounds are W+jet events, in which the W boson decays leptonically and
a jet is mis-identified as a lepton, and QCD multijet events, in which both selected
lepton candidates are mis-identified jets or leptons from heavy flavor decays. Z+jet
events, in which the Z boson decays leptonically but one lepton escapes identification
and a jet is mis-identified as a lepton of the other flavor, are another small source.
These fake backgrounds are estimated from data using a procedure known as the
"fake-rate" method. This method relies on the determination of the efficiency
Efake
of
a "fakeable" object, defined by a relaxed set of selection requirements, to fulfill the
additional stricter lepton selection requirements for the analysis. The efficiency Efake
is referred to as the fake-rate.
A fakeable electron is defined by the following requirements:
" The candidate is required to be reconstructed as a GSF electron (Section 4.6).
" It has
PT >
10 GeV and lr/ < 2.3.
" It satisfies the impact parameter constraints Idol < 0.2 cm for the transverse
impact parameter and Id, < 0.1 cm for the longitudinal impact parameter with
respect to the selected primary vertex.
" It satisfies the conversion rejection requirements described in Section 4.6.1.
99
* It satisfies oi,
< 0.01(0.03), Aoi5,l < 0.15(0.10), Ainl < 0.007(0.009) if it is
in the barrel (endcap) region.
(These variables are described further in Sec-
tion 4.6.1.)
" It has relative track isolation, relative ECAL isolation, and relative HCAL
isolation all less than 0.2.
These isolation quantities are computed from the
energy sum of the tracks or energy deposits measured in the corresponding
sub-detectors in the vicinity of the candidate, normalized to the candidate PT.
A fakeable muon is defined by the following requirements:
" The candidate is required to be reconstructed as a Global muon (Section 4.5).
" It has pT > 10 GeV and Irl < 2.1.
* It has Idol < 0.2 cm with respect to the selected primary vertex.
" It has relative track isolation, relative ECAL isolation, and relative HCAL isolation all less than 0.4 if it has PT > 20 GeV, otherwise it should have absolute
track isolation, absolute ECAL isolation, and absolute HCAL isolation all less
than 8 GeV.
The fake-rates are measured in data from a background-enriched sample of events
collected by single lepton triggers. The rates for background events with objects which
fire these single lepton triggers are too high for all events to be stored; therefore, a
"prescale" procedure is implemented for such triggers. Only one out of every N events
which fire the trigger is accepted and stored for analysis; N is known as the trigger
prescale factor, and is adjusted to maintain a manageable trigger rate while allowing
for the collection of a reasonable control sample.
Events in the calibration sample used for measuring the fake-rates are required
to have passed one of a set of single lepton triggers, to have one fakeable object as
defined by the criteria listed above, and one reconstructed jet, separated from the
fakeable object by AR > 1.0.
The reconstructed jet is required to have PT > 25
GeV for the muon fake-rate calibration sample and PT > 35 GeV for the electron
100
fake-rate calibration sample; these thresholds are chosen so that the kinematics of
the system recoiling against the jet approximate the expected phase space for the
background being estimated. In order to prevent the fakeable objects used for the
fake-rate computation from being real leptons from W boson decays, the PF
$T is
required to be less than 20 GeV for the sample collected at 7 TeV and less than 25
GeV for the sample collected at 8 TeV. Real leptons from Z boson decays are rejected
by requiring that the event not have a second reconstructed lepton. The measured
efficiency for fakeable objects to pass the full lepton selection requirements, Efake,
is
parametrized in bins of the fakeable object PT and T. Figure 6-2 shows the fake-rates
measured in 8 TeV data for electron and muon fakeable objects.
. 2.0
1.5
0
1.0
0.12
0.10
5-5
0.5
.- 2.0
0.26
0
2?1.5
.0
0.24
0.22
-1.00
0.5
14
0.20
0.0
0.08
0.0
0.18
-0.5
0.06
-0.5
0.16
-1.5
0.04
-1.
0.12
0.10
-2.
0
-2.0.02
10
15
20
25
30
35
fakeable object pT [GeV]
10
15
20
25
30
35
fakeable object pT [GeV]
0.08
Figure 6-2: Fake-rates measured for electron (left) and muon (right) fakeable objects,
as defined in Section 6.2.3, to pass the full lepton selection requirements in 8 TeV
data, parametrized in bins of PT and ij.
The fake-rates computed from the calibration samples are then applied to a sample of observed events which pass the full analysis selection requirements, with the
exception that one of the lepton candidates is required to pass the fakeable object
selection but fail the full lepton selection criteria. This lepton is referred to as the
"failing" lepton. Each event in this sample is then given an event weight based on
the fake-rate measured for the PT
-
I
bin occupied by the fakeable object; the weight
101
is computed as
(Pf , rfail)
Efakei(Pil, rfail)
_fake
1-
(6.1)
where pfai and r7fail are the PT and rI of the failing lepton in the event and Efake(P fil,
the fake-rate value measured for the corresponding
PT
fail)
and rq bin. The sum of the
event weights computed for all events in the sample provides a prediction of the fake
background yield.
The procedure described above double counts the contribution from multijet
events for which both leptons are fakes. The extent of the double counting is estimated by requiring both leptons in the selection to be failing leptons, i.e., fakeable
objects which fail the full lepton selection. The event weights for this sample are then
computed as
6
fake
ll
1
1 - Efake(r
fal
with pj,
rfail
and pfail
Efake(Pll, rfail), Efake
fail
fail)
ail) X
representing the
ail)
PT
Efake (p
,
1-ilEfake(PT2,
(fail
ail)
'a2)
1 fail
(6.2)
and q of the two failing leptons and
the corresponding fake-rates. The contribution of the
double-counted background is estimated by summing all the event weights computed
in this sample; this contribution is then subtracted from the overall fake-rate prediction.
Since the lepton selection used in the analysis is not fully efficient for selecting
events with two real leptons, the fake background estimate obtained from the application of the fake-rate method has some contamination from processes with real leptons
which fail the full lepton selection. The extent of this contamination is estimated by
applying the fake-rate extrapolation procedure to di-boson, tt, and Drell-Yan simulation, requiring the failing leptons to be matched to real leptons (based on the
true generator information). This contamination is found to be 17% of the inclusive
yield obtained from the fake-rate prediction; the overall fake prediction is scaled down
accordingly to account for this inefficiency.
While the fake-rate method provides the predicted rate of the fake-induced backgrounds, the shapes of the distributions for the relevant observables and m,, for the
fake backgrounds are estimated from a sample of observed events in which the elec102
tron and muon candidates fulfill the lepton selection requirements but have the same
charge, instead of the opposite charge as required in the full event selection for the
analysis. The same-charge selection provides a description of processes for which a jet
is mis-identified as a lepton, including QCD multijet events and W/Z + jets events
in which one of the selected leptons is a mis-identified jet. The same-charge sample is normalized inclusively to the yield predicted by the fake-rate procedure. The
number of events in the same-charge sample is not sufficient to provide an adequate
description of the fake background for all event categories; in order to obtain sufficient statistics in the 0-Jet high muon PT category, the electron isolation requirement
is inverted, while for the 0-Jet low muon PT and 1-Jet low muon PT categories, the
electron isolation requirement is removed. In the 1-Jet high muon pT and VBF event
categories, the same-charge sample does not contain sufficient events to provide a
reasonable description of the fake background even after relaxing isolation requirements; the shape of the fake background in these categories is predicted using the
event sample obtained from the application of the fake-rate procedure.
6.2.4
Other Backgrounds: Di-Boson, Single-Top
Backgrounds from di-boson production (WW, WZ, ZZ) with the W or Z bosons decaying leptonically constitute a relatively small contribution to the total background
and are modeled using simulation, which is produced using
with
PYTHIA.
MADGRAPH
interfaced
Another relatively small source of background is the production of
a single top quark in association with a W boson. This process is simulated using
POWHEG
interfaced with
PYTHIA.
The normalizations for these backgrounds are esti-
mated from simulation based on the cross sections listed in Table 3.4, after the relevant
data-to-simulation correction factors discussed in Chapter 5 have been applied.
6.2.5
H -+ WW -+ 212v
SM Higgs boson events decaying to pairs of W bosons which further decay leptonically
are found to have an expected contribution at almost the same level as the H
103
-+
r
signal for the VBF event categories, and a somewhat reduced contribution for the
other SM analysis event categories. For the purpose of this analysis, which targets
the T-pair decay mode, the SM Higgs boson with mass mH = 125 GeV is treated
as a background process. The H
in the same way as the H
-
TT
-
WW background is modeled using simulation,
signal (Section 6.1). For the purpose of estimating
the normalization of this background, the Higgs boson production cross sections and
branching ratio to W boson pairs are obtained as described in Section 6.1.
The
relevant data-to-simulation correction factors are applied as for other simulationbased background estimations.
6.3
Control Distributions
Figures 6-3 - 6-17 demonstrate that the data is well-modeled by the background
predictions for both 2011 and 2012 for distributions of relevant observables. These
include the lepton kinematics, the Higgs candidate
PT,
the visible mass and the SVFit
mass, the number of jets and number of b-tagged jets, jet kinematics, and the m1 1
and IA7gjj distributions. All of these are produced after applying the topological
BDT selection (Section 5.5.1).
The leading jet
PT
and q distributions (Fig. 6-10,
Fig. 6-11) are produced with the additional requirement of a jet with
PT
> 30 GeV
in the selected events, while the sub-leading jet kinematic distributions and the mjj
and IA733 distributions (Fig. 6-12 - 6-15) are produced requiring at least 2 jets in the
selected events. The leading b-jet distributions (Fig. 6-16 and Fig. 6-17) are produced
requiring at least one b-tagged jet with
PT
> 20 GeV in the event. The processes
labelled as "electroweak" include the expected di-boson and single-top contributions.
In all cases, good agreement is seen between the observed and expected distributions
within the estimated uncertainties on the background estimations, providing confidence that the event kinematics are described correctly by the techniques discussed
in the preceding sections.
104
1
CMS Preliminary, is = 7 TeV, L = 5.0 fb
CMS Preliminary, is = 7 TeV, L = 5.0 fb'1
CD,
2500
-
-------------
---
ci
5xH(125 GeV)-nr
5xH(125 GeV)-WW
observed
-
U)
4,
w:
electroweak
ti
QCD
bkg. uncertainty
2000
1.............5xH(125 Ge
------- 5xH(125 Ge V)-+WW
-9observed
250 0
20(
0
1500
15(
0
1000
10(
0
electroweak
-if
QCD
bkg. uncerta inty
5( 0
500
0
-2
-1
0
0
20
0
2
1
60
40
80
100
PT [GeV]
= 7 TeV, L = 5.0 fb~
CMS Preliminary, %8
CMS Preliminary, is = 7 TeV, L = 5.0 fbW,
(D
a)
2500
----
-e
5xH(1 25
U)
C
e)t
------- 5xH(125 GeV)-)WW
-e-- observed
-if
2000
LU
electroweak
200 0
uCD
e
[
------ 5x1(125 GeV)-*tr
-------0-
250
]bkg. uncertainty
electroweak
ti
-
1500
150 0
1000
100 0
5xH(125 GeV)-*WW
observe
QCD
[ ]bkg. unc ertainty
0500
0
50
0
-2
-1
0
0
2
20
40
60
80
100
e p [GeV]
e ii
Figure 6-3: Pseudorapidity r; (left) and transverse momentum PT (right) for the
selected muons (upper row) and the selected electrons (bottom row) for the data
collected in 2011.
105
CMS Preliminary,
+-
9000
is = 8 TeV,
!! i
L = 19.7 fb
C
CMS
Preliminary,
. . . . . .
. . . .
I
U,
-5xH(1
CD
25 GeV)-TCt
----- 5xH(1 25 GeV)->WW
-@observed
-mr
8000
is = 8 TeV, L = 19.7 fb71
5xH(125 GeV)-+t
------ 5xH(125 GeV)-4WW
observed
Z-4Ttr
ep.
>10000
electroweak
electroweak
t-t
- i
QCD
7000
QCD
8000
bkg. uncertainty
bkg. uncertainty
6000
6000
5000
4000
4000
3000
2000
2000
1000
0
-2
-1
0
0
2
0
U
20
40
60
80
100
I PT [GeV]
CMS Preliminary, is = 8 TeV, L = 19.7 fb
10000
1
CMS Preliminary, is = 8 TeV, L = 19.7 b'
U)
4-
--- xH(125 Ge'V)->tc'
-e
----
5xH(125 GeV)-4WW
observed
a,
- electroweak
-T
-i
8000
------ 5xH(125 GeV 1 '
----. 5xH(125 GeV )-WW
-@observed
10000
8000
QCD
6000
6000
4000
4000
2000
2000
0
-2
-1
0
1
-1C
electroweak
t!
QCD
[--Jbkg. uncertain
bkg. uncertainty
0
2
0
20
40
' '
60
ty
80
100
e pT [GeV]
Figure 6-4: Pseudorapidity rq (left) and transverse momentum PT (right) for the
selected muons (upper row) and the selected electrons (bottom row) for the data
collected in 2012.
106
CMS Preliminary, is = 7 TeV, L = 5.0
CMS Preliminary, is = 8 TeV, L = 19.7
4U) 22000
(D) 20000
W 18000
------- 5xH(1 25 GeV)-rWW
observed
4500
w
fb
*ee"uuZ-uw
4000
ejectroweak
ti
] QCD
3500
2
i----
---
7
electroweak
-
ti
QCD
16000
e
bkg. uncertainty
fb
5x1(1 25 GeV)5xH(1 25 GeV)-+WW
observed
7
bkg. uncertainty
14000
3000
12000
-7
2500
-
10000
2000
8000
1500
6000
1000
4000
500
2000
0
0
50
100
150
200
pT(rt)
0
250
0
50
100
150
200
[GeV]
PT(Tt)
250
[GeV]
Figure 6-5: Higgs candidate system PT for the data collected in 2011 (left) and 2012
(right).
1
1
CMS Preliminary, is = 7 TeV, L = 5.0 fb '
0
CMS Preliminary, is = 8 TeV, L = 19.7 fb
------- 5xH(125 GeV)-+WW
-0observed
600
-xH(125GeV)-+KT
z
---- xH(125 GeV)-+rr
------ 5xH(125 GeV)->WW
observed
Z-+TT
electroweak
i
QCD
bkg. uncertainty
.eg
2200
200(
electroweak
500
2400
180(
QCD
bkg. uncertainty
1 60(
z0
400
0
300 -
-
140(
-
120(
100(
800
200 -
600
W-
400
8 e-
200
100-
0
100
200
0
300
mv,, [GeV]
100
200
300
mvis [GeV]
Figure 6-6: Visible mass, myi,, of the T-pair decay products for the data collected in
2011 (left) and 2012 (right).
107
-
CMS Preliminary, is = 7 TeV, L = 5.0 fb-'
CMS Preliminary, is = 8 TeV, L = 19.7 fb'
1600
(D~
400
0
350
------- 5xH(1 25 GeV)-+MW
5xH(125 GeV)-*WW
---0
observed
:-ep
--
--. 1400 eg
-----0-
electroweak
17
300
electroweak
ti
QCD
7
xH(125 GeV)-+tr
5xH(125 GeV)-4WW
observed
1200
-t-
bkg. uncertainty
QCD
bkg. uncertainty
-
z
250
1000
a
800
200
600
150
100
400
50
200
0
0
100
200
0
300
3
200
100
300
m, [GeV]
M, [GeV]
Figure 6-7: SVFit mass, m,,, for the data collected in 2011 (left) and 2012 (right).
CMS Preliminary, is = 7 TeV, L = 5.0 fb
U)
W
C
5xH(125 GeV)-4t
101 eg
177777
5xH(125 GeV)-+WW
observed
electroweak
ti
QCD e
10 5
U)
CMS Preliminary, is =
ci 7 1 '
1097
L = 19.7 fb
1
5xH(125 GeV)-Jtr
eo
uJ
8 TeV,
----
-
10
5xH(125 GeV)-+WW
observed
electroweak
if
QCD
bkg. uncertainty
bkg. uncertainty
105
104
10
4
3
10
10
10 r
10
0
2
4
0
6
Number of Jets
2
1
6
Number of Jets
Figure 6-8: Number of jets with PT > 30 GeV for the data collected in 2011 (left)
and 2012 (right).
108
CMS Preliminary, is = 7 TeV, L = 5.0
uJU)
1015
10 5
1
fbW
CMS Preliminary, is = 8 TeV, L = 19.7 fb
--- 5xH(125 GeV)-+11
-5xH(125GV)+
(D,
------- 5xH(125 GeV)-+WW
observed
Z-*Tv
electroweak
r
-ti
r
,rep.
10
1
U)
F
-- 1-- observed
Og
rU
--
F
- electroweak
-.r
i
17
QCD
e
bkg. uncertainty
QCD
I bkg. uncertainty
105
104
4
10
103
103
102
102
r
- --.--
10
1
2
q.
.I .
3
4
0
PT >
20 GeV for the data collected in 2011
1
900
(D)
W
800
CMS Preliminary, is = 7 TeV, L = 5.0 fb7
..I
CMS Preliminary, is = 7 TeV, L =
CD)
It
.XH(1 25 heV) l
------- 5xH(125 GeV)->WW
observed
eg
4)
w:
4
SZ-m
electroweak
1000
ti
GCD
bkg. uncertainty
600
5.0 fb 1
---- '5xH1 25 GeV)%*zv
5xH(125 GeV)-+WW
-4 1- observed
1200 -eg
Z-m T
700
4
Number of b-Tagged Jets
Number of b-Tagged Jets
Figure 6-9: Number of b-tagged jets with
(left) and 2012 (right).
3
2
1=
LI -
electroweak
ti""]QCD
bkg. uncertainty
800
500
600
400
300
400
200
200
100
0
-4
-2
0
2
0
4
100
200
300
Leading jet pT [GeV]
Leading jet TI
Figure 6-10: Pseudorapidity r/ (left) and transverse momentum PT (right) for the
leading jet with PT > 30 GeV in events with at least one jet for the data collected in
2011.
109
CMS Preliminary, is =
U)
+--
w
3500
8 TeV,
L = 19.7 fb
-~
GeV)-WW
observed
-
3000
is = 8 TOV, L =
C
CMS
Preliminary,
C)
eV)-tn
5xH(125
-5xH(125
5000
eg
electroweak
-
tt
2500
4000
bkg uncertainty
2000
19.7 fb7'
--- 5xHl125 GeV)%t
----- 5xH(125 GeV)--WW
-observed
electroweak
t
QCD
Cbkg
uncertainty
3000
1500
2000
1000
1000
500
0
-4
0
-2
2
a"
4
0
300
200
100
Leading jet pT [GeV]
Leading jet rj
Figure 6-11: Pseudorapidity q (left) and transverse momentum PT (right) for the
leading jet with PT > 30 GeV in events with at least one jet for the data collected in
2012.
CMS Preliminary, is = 7 TeV, L = 5.0 fb'
(D
ci
+W
I
450
eg
400
.
Cl)
----.
5xH(125 GeV)-+n
----- 5xH(125 GeV)-4WW
-0observed
ci)
220
+uJ
W
it
-----
g-
L 5xH(125 G3eV)--+n
--------
tt
QCD
160
140
250
120
200
100
5xH(125 GeV)-WW
observed
electroweak
180
1=1QCD
bkg. uncertainty
300
Sbkg.
uncertainty
80
150
60
100
40
50
0
CMS Preliminary, is = 7 TeV, L = 5.0 fb'
200
electroweak
350
240
20
100
200
200
300
300
0
-4
-2
0
Second jet pT [GeV]
2
4
Second jet il
Figure 6-12: Pseudorapidity 77 (left) and transverse momentum PT
(right) for the sub-
leading jet with PT > 30 GeV in events with at least two jets for the data collected
in 2011.
110
CMS Preliminary,
C/)
C
2200
()
2000
w
'
is = 8 TeV, L = 19.7 fb"
1000
'5xHll125 GeV)-nTT
~JZ-nTT
1800
800
tiQCD
1b1
5xH(125 LeV)- TT
------- 5xH(125 GeV)-WW
observed
-
--
U)
electroweak
1600
is = 8 TeV, L = 19.7
C:
------- 5xH(125 GeV)--)WW
observed
e
CMS Preliminary,
electroweak
QCD
bkg. uncertainty
[2bkg.
1400
uncertainty
600
1200
et
1000
400
800
600
200
400
200
0
100
0
300
200
-4
4
2
0
-2
Second jet pT [GeV]
Second jet
1
Figure 6-13: Pseudorapidity r (left) and transverse momentum PT (right) for the subleading jet with PT > 30 GeV in events with at least two jets for the data collected
in 2012.
CMS Preliminary,
U)
w
300
is = 7 TeV,
CMS Preliminary, is = 8 TeV, L = 19.7 fb
5xH(1 25
-. GeV)-->s
------- 5xH(1 25 GeV)--WW
observed
et
250
-
200
1
L = 5.0 fb"
[
U)
C:
-
a)
electroweak
ti0
.QCDe
bkg. uncertainty
-0-
1200
5xH(1 25 GeV) -tt
5xH(1 25 GeV)->WW
observed
electroweakti
]QCD
--->bkg. uncertainty
1000
800
--
150
600
100
400
50
0
200
0
500
1000
0
500
1000
M(jj) [GeV]
M(jj) [GeV]
Figure 6-14: Invariant mass of the two leading jets in 3 for events with at least two
jets with PT > 30 GeV for the data collected in 2011 (left) and 2012 (right).
111
C)
CMS Preliminary, is = 7 TeV, L = 5.0 fb"
- --- I 5xH(125 GeV)-4rr
5xH(1 25 GeV)-4WW
observed
350
a,
-eg
300
1
CMS Preliminary, is = 8 TeV, L = 19.7 b
U)
C
LuJ
electroweak
ti
QCD
bkg. uncertainty
250
1600
------- 5xH(1 25 GeV)->rr
------ 5xH(1 25 GeV)-+WW
observed
1400
electroweak
.
QCD
1200
E---:-:3bkg. uncertainty
-
-
1000
200
800
150
600
100
400
50
0
200
0
0
0
6
4
2
6
4
2
Aq(jj)
A(jj)
Figure 6-15: Distance between the two leading jets in pseudorapidity IAqjjI for events
with at least two jets with PT > 30 GeV for the data collected in 2011 (left) and 2012
(right).
1
CMS Preliminary, is = 7 TeV, L = 5.0 fb
CMS Preliminary, is = 7 TeV, L = 5.0 fb
(D
200
W
180
ej~i
25 GeV)-+tr
5xH(1 25 GeV)->WW
observed
---0--
-i
160
140
]
[
3eV)-+rt
5xH(125
5xH(125( GeV)-4WW
observed
ci,
-5xH(1
(D
2
a,
:e
--
50 -
electroweak
electrowe ak
i
2
QCD
QCD
bkg. unce rtainty
00
kg. uncertainty
2
120
50
100
80
k+
00 -
60
40
50
20
0
-2
0
0
2
0
100
150
200
Leading b-jet pT [GeV]
Leading b-jet fl
Figure 6-16: Pseudorapidity i (left) and transverse momentum PT (right) for the
leading b-tagged jet with PT > 20 GeV in events with at least one such jet for the
data collected in 2011.
112
CMS Preliminary, is = 8 TeV, L = 19.7
C
f1b
CMS Preliminary,
----5xH(125 GeV)-+rt
------- 5xH(125 GeV)-*WW
observed
1000
LU
800
5xH(125 GeV)-:ct
C:
LU
electroweak
Is = 8 TeV, L = 19.7 fbY'
1 200
-0-
electroweak
1000
Q CD
~Zbkg.
uncertainty
-
------- 5xH(125 GeV)-rWW
observed
ei
QCD
bkg. uncertainty
800
600
600
400
400
200
200
0
-2
0
0
2
0
50
100
150
200
Leading b-jet pT [GeV]
Leading b-jet il
Figure 6-17: Pseudorapidity T1 (left) and transverse momentum PT (right) for the
leading b-tagged jet with PT > 20 GeV in events with at least one such jet for the
data collected in 2012.
113
Chapter 7
Systematic Uncertainties
The estimations obtained for the different signal and background processes under
consideration may be affected by a variety of systematic effects, which are addressed
in the analysis through the incorporation of systematic uncertainties. Both experimental and theoretical sources of uncertainty need to be considered. Uncertainties
which affect the event yield for a particular process are referred to as normalization
uncertainties, while those which affect the shapes of distributions under consideration
are referred to as shape uncertainties. Wherever possible in the analysis, data-driven
techniques or control samples in data are used to estimate background contributions
in order to reduce systematic effects due to inaccuracies in simulation.
Systematic uncertainties, propagated to uncertainties on the predicted signal and
background shapes or yields in each event category, are treated as nuisance parameters
in the maximum likelihood fit to the observed and predicted m,, distributions used
for the statistical analysis of the results, described in Chapter 8. The normalization
of a process affected by nuisance parameters representing normalization uncertainties
is assigned a probability density function based on a log-normal distribution:
P(N I No,)
1
v/2e2wu
r
in
No
eN
(
(ln(N/No))
2(lnt')
2
(7.1)
ns)2
Here No is the event yield for the process estimated by the analysis, and K represents
114
the size of the relative uncertainty. For instance, a 2% uncertainty would correspond
to a r parameter of 1.02.
The effects of systematic variations affecting the shape of the m,, distribution
are implemented using a morphing technique which interpolates between the nominal
shape estimated for a process, and alternative shapes which represent the effects of
the systematic variations on the predicted mass distribution. The event yield in each
mass bin is determined by the interpolation function, which is quadratic between the
one standard deviation upper and lower bounds, and linear beyond those bounds.
The associated nuisance parameter has a standard normal distribution, which has its
mean value of 0 at the nominal prediction for the mass distribution.
The various sources of systematic uncertainties considered for this analysis and
the methods used for evaluating them are described in the following sections.
7.1
Luminosity
The estimated yield from processes which rely solely on simulation is proportional to
the integrated luminosity corresponding to the collected data. Uncertainties on the
luminosity measurement thus result in uncertainties on the estimated yields for these
processes. The method used for luminosity calibration is described in Section 2.3.
The integrated luminosities corresponding to the data found to be usable for analysis in 2011 and 2012 were 5.0 fb-1, with an uncertainty of 2.2% [36], and 19.7 fb- 1 ,
with an uncertainty of 2.6% [37], respectively. The uncertainties arise from variations
in the effective beam widths measured during different Van der Meer scans, and the
"afterglow" effect, noise due to particles originating from previous bunch crossings.
These uncertainties translate directly into uncertainties on the yields of signal and
background processes whose estimation depends on the luminosity measurement.
115
7.2
Lepton Selection
Uncertainties on the lepton selection efficiency measurements described in Section 5.3
arise from the statistical uncertainties of the event samples used for the measurements,
and uncertainties due to the fit models used. The lepton selection uncertainty translates directly into a corresponding uncertainty on the normalization of any process
in which simulation is used to model the lepton selection. The uncertainties due to
the fit models are estimated by generating pseudo-data using reasonable alternative
models, and evaluating the bias obtained by fitting with the nominal models used for
the signal and background shapes. The overall uncertainty on the lepton selection
efficiencies, including the selection and triggering efficiencies, are estimated to be 2%
for both muons and electrons.
7.3
Lepton Energy Scale
Differences between the lepton energy scale between data and simulation can lead to
differences in the m,
shape and in the kinematic acceptance for events entering the
analysis selection, and can be measured by fitting the di-lepton mass distribution in
Z - 11 events. Such effects on the electron energy scale are found to be within 1%. To
account for this a shape uncertainty is applied on the m,, template used for the signal
and for Z
-
TT,
for which a mass peak would be affected by energy scale effects. The
electron PT is adjusted up or down on an event-event basis to account for a systematic
shift of +1% in the electron energy scale, and the
a change in the measured lepton
PT
$T is
adjusted accordingly (since
would affect the measurement of the
$T in
the
event). These changes are propagated to the computation of the SVFit mass (m,,)
and the estimated yield of events entering different event categories. Alternative shape
templates are thus obtained corresponding to systematic variations of the electron
energy scale, and the m,, shape is allowed to vary between these alternative shapes
in the combined fit. Figure 7-1 shows the alternative shapes obtained after applying
the electron energy scale variations, compared to the nominal shape. The effects of
116
the muon energy scale uncertainty are found to be negligible in comparison, and are
subsumed within the shape variation allowed for the electron energy scale uncertainty.
.U
Nominal shap e
..---- +17 shape
------- -1y shape
z0
.~o
_0
50
50
100
100
150
200
250
300
350
M, [GeV]
Figure 7-1: Alternative shapes for the m,, shape for gluon fusion signal simulation
(generated at mH = 125 GeV) with systematic variations of the electron energy
scale applied, compared to the nominal shape. The shapes are shown prior to the
classification of events into mutually exclusive event categories. The electron energy
scale is varied up (down) by 1% and the m,, recomputed for the shapes corresponding
to the +lu (-c-) variations.
7.4
Jet Energy Scale
Differences in the energy scale of jets reconstructed in data and simulation can affect
the efficiencies for processes estimated using simulation to enter the analysis event
categories which rely on the selection of jets exceeding a specified PT threshold and
on jet kinematics. These differences are corrected for by adjusting the energy scale
of simulated jets as described in Section 4.3.1. Uncertainties on the jet energy scale
measurements can affect the estimated yields in different categories and are measured
as a function of jet PT and r [78]. These uncertainties are propagated through the
117
analysis by varying the jet energies up and down by the amount of the uncertainty,
and measuring the corresponding change in event yields in each category. The effect
of the variations for each affected process in each category is taken to be the jet energy
scale uncertainty for that process in the corresponding event category. Changes in
the jet energy scale will affect categories with and without jets in an anti-correlated
manner. The additional effects of systematic variations of jet energy resolution have
been assessed to be negligible for this analysis.
For the 8 TeV analysis, the effect of the jet energy scale uncertainty on the tf yield
ranges from 2 - 3%, in the 1-Jet category, to up to 22% in the VBF loose category.
The effect on the VBF signal process is 4 - 5% in the VBF categories, while the effect
on the SM gluon fusion signal is 2 - 3% in the 0- and 1-Jet categories. For the MSSM
Higgs analysis, the effects are of the order of 1% for all processes in the No b-tag
category and range up to 7%, for tt, in the B-tag category.
7.5
Scale
1 1T
$T scale
The uncertainty on the
is obtained from the measurement of the
correction (Section 4.4.2), and affects processes in which the
in the
$T
candidate
$Tis
$T recoil
simulated. Changes
scale can affect the efficiency of the topological selection and the Higgs
PT
selection in the VBF tight category, which rely on the
the jet energy scale uncertainty, the effect of the
by shifting the
$T scale
$Tscale
$T.
As for
uncertainty is determined
up and down by the estimated uncertainty for the affected
processes, and measuring the change in the yields predicted for each event category.
The effects of the
$T
scale uncertainty are found to be within 1 - 2% for most
categories, except for the VBF tight category, where the effect is found to be 10% for
the top and di-boson backgrounds.
118
7.6
b-Tagging and Mis-Tag Rate
Uncertainties on the b-tagging efficiency and mis-tag rate and the corresponding scale
factors affect the rates estimated in event categories relying on the selection or veto of
b-tagged jets for processes which are estimated using simulation. These uncertainties
are evaluated based on jet
PT,
r/, and flavor [92,93]. Similar to the jet energy and $T
scale uncertainties, these uncertainties are propagated through the analysis by varying
the b-tag and mis-tag scale factors up and down by the measured uncertainties and
assessing the effect on the event yields in each category; the size of the effect is
determined by the composition of each signal or background process. For the 8 TeV
SM Higgs analysis, the effects of these uncertainties are negligible for most processes,
and have a 3% effect on the tt yield in the 1-Jet and VBF categories. The MSSM
Higgs analysis event categories are affected to a larger extent, with the effect of the
b-tagging efficiency uncertainty ranging from 1 -5%
and the effect of the mis-tag rate
uncertainty ranging from 2 - 5%, depending on the process.
7.7
Other Normalization Uncertainties
In addition to the uncertainties mentioned above, each background process is assigned
normalization uncertainties depending on the background estimation techniques used.
These are described below in further detail.
Z -+ r-r Normalization
7.7.1
The Z
-
TT background is estimated using the embedded sample described in Sec-
tion 6.2.1, and the inclusive normalization is determined from a control sample of
Z
-M
pp events in data. The uncertainty on the inclusive normalization comes from
the uncertainty on the Z cross section measurement [91], which amounts to 3%; this
uncertainty is applied to the Z -+
r normalization, correlated across all categories.
Additionally, there are uncertainties arising from the extrapolation into each category,
the efficiency for which is determined from the embedded sample. This uncertainty
119
corresponds to the statistical uncertainty of the embedded sample used for the extrapolation, and uncertainties due to the embedding technique. The extrapolation
uncertainties in each category, ranging from 3 - 10%, are added in quadrature to the
inclusive Z
Z
-
-
TT normalization uncertainty to obtain the overall uncertainty on the
TT normalization.
7.7.2
tt Normalization
The normalization of the tt background is determined from a tt-enriched control sample, as described in Section 6.2.2, which relies on the selection of ep events with two
or more jets, one or more b-tagged jets, and large gT.
The resultant uncertainty
on the inclusive ti normalization is found to be 10%, with contributions from the
uncertainties on the background subtraction in the control sample, jet energy scale,
b-tagging, and
$T
scale. This uncertainty is applied in a correlated manner to the
tt normalization in all event categories. An additional contribution in some event
categories arises due to the observation that the Z
-
TT embedded sample contains
a small contamination from tt events in the di-muon final state, which enter into the
di-muon selection used for producing the embedded sample. The extent of this contamination is determined by applying the embedding technique to tt simulation, and
is found to be negligible in all categories other than the B-tag category in the MSSM
Higgs analysis. The estimated contribution of this contamination is compensated for
by adjusting the tt yield estimated for this category accordingly; the uncertainty due
to this procedure gives rise to an additional 2% uncertainty on the tf yield in this
category. An additional 10% uncertainty is also assigned to the yield in the VBF
categories due to the statistical uncertainty on the evaluation of the tt contamination
in the embedded sample in these categories.
7.7.3
Fakes
The uncertainty on the fake background, which is estimated using data, arises from
the uncertainties of the fake-rate method. These uncertainties can arise due to differ-
120
ences between the phase space of the calibration sample used to determined the fake
rates and the control sample in which the fake rates are applied. The uncertainties are
estimated by varying the PT threshold applied on the jet required in the calibration
sample which in turn affects the PT spectrum of the recoiling system containing the
fakeable object, and measuring the corresponding changes in the fake-rate estimate.
The overall uncertainty on the fake background normalization in the signal region is
estimated to be 30%, correlated for all event categories. Each event category also has
an additional uncertainty on the fake estimate, arising due to the statistical uncertainty of the event sample used to extrapolate into that category. This uncertainty
ranges between 5 - 10% depending on the category, and is added in quadrature to
the overall 30% normalization uncertainty in each category.
7.7.4
Di-Boson Normalization
The uncertainty on the estimation of the di-boson background comes from the uncertainties on the cross sections used for normalization.
An overall uncertainty of
15%, correlated across all event categories, is assigned to account for the cross section
uncertainty.
7.8
Theoretical Uncertainties on SM Signal
Processes
The expected yield of selected signal events is given by
N= EAuL
(7.2)
where o- is the cross section, A, the acceptance, is the probability for produced events
to fall within the kinematic and geometric requirements of the selection, E is the efficiency for selecting those events, and L is the integrated luminosity corresponding to
the dataset being analyzed. The efficiency and luminosity are affected by experimental uncertainties which are discussed in the previous section. Theoretical uncertainties
121
on the Higgs boson production cross section and acceptance arise from a variety of
sources. One source of uncertainty on the signal production cross section is due to
uncertainties on the parton distribution functions (PDFs) used. Another source is
the effect of missing higher order corrections. Finally, there are uncertainties due to
the modeling of the underlying event and parton showering.
7.8.1
PDF Uncertainty
The Higgs boson production cross section depends on parton distribution functions,
which provide the probability densities for partons within a proton to carry a given
momentum fraction. These are determined by fits to experimental data from deep
inelastic scattering measurements, and electroweak and jet production measurements.
Several alternative approaches to deriving the PDFs result in alternative PDF sets.
Each PDF set contains a default PDF in addition to member PDFs representing the
effects of different systematic uncertainties on the derivation of the PDF. Following
the PDF4LHC prescription [97, 98], the uncertainty due to the choice of PDFs is
determined by evaluating the effect of variations within a PDF set on the signal
rate and then taking the envelope of the uncertainties provided by three different
PDF sets: CT10 [99], MSTW2008 [100], and NNPDF [101]. A 10% uncertainty is
applied to the gluon fusion signal, a 4% uncertainty to the VBF signal, and a 1 - 2%
uncertainty to the VH signal.
7.8.2
Scale Uncertainty
The signal cross section also depends on the renormalization scale ([R) and factorization scale (1F)- The default values used for these scales are
gluon fusion, and PR - PF
1R
=
IF
= mH/2 for
mH for VBF. The effects of scale variations are obtained
by varying each pR and PF to twice and one half the nominal values, and comparing
the rates obtained from each variation in order to estimate the scale uncertainty. The
uncertainty assigned to the gluon fusion signal process is 8% in the 0-Jet, 10.5- 12.5%
in the 1-Jet, and 28 - 31% in the VBF categories. The uncertainty on the VBF signal
122
process ranges from 2 - 4%.
7.8.3
Parton Shower Modeling Uncertainty
The number and kinematics of jets in the signal simulation, and consequently the
event categorization, are affected by the modeling of the underlying event and parton
shower. The uncertainty due to these effects are evaluated by varying the PYTHIA
tune from the default tune used by CMS (Z2*) to the default tune used by the ATLAS
experiment (AUET2 [102]) and measuring the corresponding change in event yield.
The parton showering uncertainty ranges up to 20% (for the gluon fusion signal in
the VBF tight category), and is anti-correlated between categories with and without
jets in the selection.
7.8.4
Higgs PT Spectrum Uncertainty
Modeling of the Higgs boson
PT
spectrum affects the efficiency of selections which rely
on the Higgs PT. The gluon fusion Higgs boson PT spectrum obtained from POWHEG at
NLO is re-weighted to the NNLO calculation obtained from the HRES program [96].
Figure 6-1 shows the effect of the re-weighting on the
PT
spectrum.
Theoretical
uncertainties on the re-weighting correspond to variations of the resummation scale
used to obtain the HRES calculation [96], and to the uncertainties oil the top quark
mass used in order to correct the infinite top-mass approximation used for obtaining
the nominal
PT
spectrum.
These uncertainties are propagated to the analysis by
obtaining alternative gluon fusion signal shapes by adjusting the re-weighting function
up and down to the alternative functions obtained through the systematic variations.
The effects of the systematic variations on the gluon fusion Higgs boson
PT
spectrum
are illustrated in Fig. 7-2 for a simulated sample produced for a hypothetical Higgs
boson mass of 125 GeV. Changes in the Higgs
and m,
PT
spectrum affect the acceptance
shape of the gluon fusion signal in different event categories. Alternative
m,, estimations are obtained in each category corresponding to the propagation of
these effects. The signal m,, shape is then permitted to float between the alternative
123
shapes thus obtained in the combined fit.
0
2.0
40
1.8:
-
Nominal re-weighting
1.6:
-
+15 re-weighting
-
-15 re-weighting
1.4
Re-weighted shape
35
-
+1Y re-weighted shape
30
-
-1o re-weighted shape
25
1.2
1.0
2C
0.8
10
1E
0.6
0.4
1.2
0.2
0
ir
000
100
200
300
400
500
Higgs p [GeV]
0.8
0
50
100
150
200
250
LI
300
Higgs p [GeV]
Figure 7-2: Re-weighting functions corresponding to the nominal and systematically
varied re-weighting applied to the Higgs PT spectrum obtained from POWHEG (left),
and the accordingly re-weighted Higgs PT spectrum obtained for a simulated gluon
fusion SM Higgs boson sample generated for mH = 125 GeV (right).
7.9
Theoretical Uncertainties on MSSM Signal
Processes
The MSTW2008 PDF set is used for calculating the nominal cross sections used for the
MSSM signal processes. PDF and scale uncertainties on the MSSM signal processes
are determined using similar procedures as for the SM signal. The estimated PDF
uncertainties range from 2 - 10% and the scale uncertainties range from 5 - 25% for
the gluon fusion production process and from 8 - 15% for the b-associated production
process.
7.10
Summary of Systematic Uncertainties
Tables 7.1 and 7.2 summarize the normalization uncertainties evaluated for each signal
and background process affected for the SM and MSSM Higgs analyses respectively.
124
The sources of uncertainty which have the largest impact for this analysis are the uncertainties affecting the normalization of the Z
-
TT
background, the electron energy
scale uncertainty, the jet energy scale uncertainty, and the theoretical uncertainties
affecting the signal processes.
Uncertainty
Value
Luminosity 7 TeV (8 TeV)
Electron efficiency
Muon efficiency
Jet energy scale
scale
b-tagging efficiency
9T
Effect propagated into categories
VBF
1-Jet
0-Jet
Experimental Uncertainties
+2.2 (2.6)% ±2.2 (2.6)% +2.2 (2.6)% ±2.2 (2.6)%
+2%
+2%
±2%
±2%
±2%
±2%
+2%
±2%
±1 - 3%
±4 - 22%
±1 - 10%
-2 - 11%
+2 - 10%
±1%
+1 - 2%
+1 - 5%
±10%
-3%
-3%
+10 - 20%
Mis-tag rate
Z - TT normalization
Z -- TT category extrapolation
tt normalization
tt category extrapolation
Di-boson normalization
Fakes normalization
Fakes category extrapolation
±3%
-
t3%
+10%
+3%
+10%
-
-
+15%
+30%
+15%
+30%
+10%
Theoretical Uncertainties
-
-
+3%
+3 - 5%
+10%
+3%
+10%
+10%
+10%
+15%
+30%
+5%
-
+15%
+30%
+5%
-
+1-10%
H)
qqH)
pR/IPF (qq -+ VH)
-
+4%
+4%
+4%
Underlying event & parton shower
-
+3 - 9%
-2%
±1 - 12%
PDF
PR/IF (gg
PR//pF (qq
-
+8%
+3%
+1-10%
- 12%
+10
+1%
+1-10%
- 31%
+2 - 3%
+23
Table 7.1: Systematic uncertainties affecting normalizations and their effects on estimates of the affected processes propagated into the different event categories used
for the SM Higgs analysis.
125
Uncertainty
Value
Effect propagated into categories
No b-tag
B-tag
Experimental Uncertainties
Luminosity 7 TeV (8 TeV)
Electron efficiency
Muon efficiency
Electron energy scale
Jet energy scale
scale
b-tagging efficiency
Mis-tag rate
Z -+ TT normalization
Z -+ TT category extrapolation
tf normalization
tt category extrapolation
Di-boson normalization
Fakes normalization
9T
PDF
P/IPF (gg -')
P/IPF (gg
-+
bb4 )
±2.2 (2.6)%
+2.2 (2.6)%
+2.2 (2.6)%
±2%
±2%
±1%
±1 - 10%
±1 - 5%
±2%
±2%
±1%
-F1%
-F2%
-F2 - 5%
F2%
±2%
±2%
±1%
±1 - 4%
±1 - 2%
±1 - 5%
±3 - 5%
±3%
±3%
±1%
±10%
±10 - 20%
±3%
-
-
±10%
±15%
±30%
±10%
±15%
±30%
Theoretical Uncertainties
±2 - 10%
±5 - 25%
±8 - 15%
-
±10%
±2%
±15%
±30%
±2 - 10%
±5 - 25%
±8 - 15%
Table 7.2: Systematic uncertainties affecting normalizations and their effects on estimates of the affected processes propagated into the different event categories used
for the MSSM Higgs analysis.
126
Chapter 8
Statistical Analysis and Results
The interpretation of the results of the analysis described in the preceding chapters
is obtained from a statistical analysis of the observed and predicted m,, distributions in the designated event categories, using a binned likelihood fit.
Systematic
uncertainties, evaluated as described in Chapter 6, are treated as nuisance parameters in the fit and varied according to their assigned probability distributions. The
likelihood fit allows these nuisance parameters and the background predictions to be
further constrained by the observed data. The aim of the analysis is to quantify any
observed excess over the total background prediction and its consistency with the
signal expectation, or, in the absence of such an excess, to place upper limits on the
signal cross section allowed by the observed data. Section 8.1 contains a discussion of
the procedure used to obtain the results of the statistical analysis. The results of the
Standard Model and MSSM Higgs boson searches are then presented in Sections 8.2
and 8.4. While the focus of this thesis is on the search in the epT -pair final state, the
results of a combination with searches in other T-pair final states are also discussed.
127
Statistical Procedure
8.1
8.1.1
Likelihood Construction
A binned maximum likelihood fit to the m,, distribution is used in order to evaluate
any excess of observed events over the background prediction [103,104]. Systematic
uncertainties enter into the fit in the form of nuisance parameters; the best estimates
for systematic variations obtained from external sources are encoded in the likelihood.
A probability distribution function p(O 10) for the nuisance parameter 0, given a
best estimate 0, reflects a prediction for the true value of 0. Using Bayes' theorem,
this can be interpreted as a posterior probability, based on external estimates of the
systematic uncertainties, and written as
0
p( 10)
p(O 10) - (0)
(8.1)
,
the posterior probability resulting from an auxiliary measurement which has a probability distribution function p(O 10). Here 7(0) is the prior probability. A "flat" prior,
corresponding to an uniform distribution, is chosen to reflect the assumption of no
prior knowledge of 0.
A likelihood function is constructed based on the expected number of signal and
background events in each bin of the m,, distribution, with the "signal strength"
p, defined as the ratio of the measured Higgs boson production cross section to the
predicted cross section, treated as a free parameter, and with nuisance parameters
distributed according to the probability distributions described in Chapter 6. The
likelihood is constructed from a product of Poisson probabilities and constraints on
the nuisance parameters:
L(data I /1, 0) =ni!
( ps2 (0) + b7 (0))n"
[
p
+
(iO
( 10))
(8.2)
where "data" implies the set of the observed numbers of events in each bin of the
mTT
distribution {n}, si and bi the numbers of predicted and background events in
128
bin i, and p(6
6) the constraints on the set of nuisance parameters. The predicted
number of background events in bin i, bi, represents the sum of the predicted numbers
of events for each contributing background process in that bin. Both si and bi are
affected by the set of nuisance parameters denoted by 6.
All event categories considered are fit simultaneously in the maximum likelihood
fit, with each bin of each category contributing to the product of Poisson probabilities in Eq. 8.2. The likelihood is maximized as a function of 6 in the fit, providing constraints on the nuisance parameters based on the information from the
observed distributions. Sources of uncertainties are treated either as fully correlated
(or anti-correlated), or as uncorrelated (independent), to allow for factorization of the
constraints in the likelihood.
8.1.2
Limit Calculation
A limit-setting procedure is used in order to quantify the absence of a signal in the
observed data. A modified frequentist (CL,) approach [105,106] is used for this purpose. The compatibility of an observation with "background-only" and "signal-plusbackground" hypotheses can be determined with the help of a test statistic defined
by the profile likelihood ratio
qp(=a-2fn
where
f
n(data
y, Ott)
6 ,0
L(data
, 0)
f
(8.3)
y,
and 0 denote the values of 1- and 6 which maximize the likelihood based on
the observed data, and b/, maximize the likelihood for a given value of p [103,104].
The signal strength is constrained to be non-negative.
restricted to be greater than or equal to
f
The tested values of /1 are
for the purpose of setting upper limits.
For a given signal strength y being tested, the observed value of the test statistic
is computed as q0s,. The values of the nuisance parameters maximizing the likelihood
~obs
based on the observed data are found for the background-only hypothesis (00 ), and
-obs
-obs
the signal-plus-background hypothesis (6o ). Probability distributions f (q,, 10, 6o )
-obs
and f(q, I p, 6o ) can be constructed for the test statistic ql, under the two hypothe129
ses using toy experiments to generate pseudo-data, with the values of the nuisance
~obs
-obs
parameters fixed to $o and bo respectively when generating the pseudo-data but
allowed to float when fitting for the test statistic. Two p-values, p, and Pb, are defined
for the signal-plus-background and background-only hypotheses respectively as
PA (p)
=
;> qPobs
P(q, P~,
P"|A,
-obs
)
(q|,
=
-obs
OP)
dqj ,
(8.4)
. bs
1-
pb(P)
-
(q,
q
b
0,
^obs
f
J
-obs
(q, 0, 0
) dq,.
(8.5)
obs
Finally, CL,(p) is calculated as the ratio
CL, (p) = 1
.
(8.6)
If CL,(p) < a for a given value of a, a signal strength of p is said to be excluded
with (1 - a)CL, confidence level (CL). The 95% CL upper limit on p is obtained by
finding the value of p for which CL, = 0.05.
For sufficiently large numbers of events, the distribution of the test statistic asymptotically approaches an analytic form [107,108. The asymptotic approximation makes
use of a single representative dataset, the "Asimov" dataset, which is composed of
the sum of expected signal and background contributions with the measured values
for the nuisance parameters.
This approximation enables a quick computation of
the probability distributions needed for the CL, computation. The median expected
limit, and the bands representing +1-
and +2-standard deviations can be computed
based on the asymptotic approximation.
8.1.3
Significance Calculation
The presence of a signal is quantified by calculating the p-value for the backgroundonly hypothesis given the observed data, which gives the probability for a fluctuation
of the background to produce an excess of events at least as large as an observed
130
excess. In this case, the test statistic is defined as
0, Oo)
L(data
C(data
qO = -2 In L~aa
The value of
f
),
ft, )
> 0 .(8.7)
is constrained to be non-negative; a zero result is obtained for the test
statistic in case there is a deficit of events rather than an excess. The distribution
-obs
f(qo 10 00
) for the test statistic is obtained, and the local p-value corresponding to
a given observation,
q bs
can be computed as
f (qo1 0 , Oobs ) dqo
Po = P(qo > qObs
.
(8.8)
The p-value can be converted into a local significance value Z for a signal-like excess
using the "one-sided" Gaussian-tail expression
P
8.1.4
exp(-x
1
2
(8.9)
/2) dx.
Coupling Fits
In order to determine the compatibility of the observed data with SM predictions,
scale factors rj are defined as modifiers of observed Higgs coupling strengths with
respect to their predicted SM values for a chosen Higgs boson mass hypothesis [109].
Thus, for instance, the observed gluon fusion cross section can be expressed as
J~ggH =
'.Uor
K
(8.10)
M
while the branching ratio for Higgs decays to tau-pairs would be given by
BR(H
-+ TT) =
2
-
BRsM(H
-
)
(8.11)
Measured deviations of Higgs couplings from their SM values could be indicators of
physics beyond the Standard Model.
The role of the Higgs boson in electroweak
symmetry breaking is linked to its couplings to W and Z bosons, while its role in
131
generating fermion masses is linked to its couplings to fermions. Certain benchmark
parametrizations are adopted in performing fits to experimental data to determine
the compatibility of an observation with the SM Higgs boson expectation. A common
parametrization used in order to derive meaningful results from the available statistics
defines two scaling factors, one for the coupling to vector bosons, tv
and one for the coupling to fermions,
Kf
(=
Kt
=
Kb =
KT).
(=
Kw
=
KZ),
With the availability of
larger datasets, measurements of individual scaling factors should be possible with
improved precision.
8.2
8.2.1
Standard Model Higgs Analysis Results
Di--r Mass Distributions
The events selected using the selection criteria described in Chapter 4 are used to
obtain the observed and expected mTT distributions which are used as inputs for
the statistical evaluation of the analysis results based on the procedures described in
Section 8.1. The observed and predicted m,, distributions obtained from the analysis
of the 2011 and 2012 data are shown for each individual event category in Fig. 8-1
and Fig. 8-2 respectively. The fit is performed in the mass region 0 < mT < 350
GeV. Variable bin widths are used in order to ensure that the mIT shape templates
provided for the maximum-likelihood fit are sufficiently well populated in each bin.
For the 0-Jet and 1-Jet categories, a 10 GeV bin width is used for mIT < 200 GeV,
while a 25 GeV bin width is used for m,, > 200 GeV. For the VBF categories, which
are affected by low numbers of events, a 20 GeV bin width is used for
mIT <
200 GeV,
while a 50 GeV bin width is used for m_, > 200 GeV. The predicted yields, shapes,
and uncertainties of the background distributions are obtained from the results of
the maximum-likelihood fit to the observed data under the signal-plus-background
hypothesis. The signal contribution shown corresponds to the prediction for a SM
Higgs boson of mH =125 GeV.
132
300
CMS.4.9fb
1
at 7TeV
40
--0-
250
E
SM H(125 GeV)-lrT
Observed
SM H(125 GeV)-WW -
100
.
.
i
.
.
.
SM H(125 GeV)->-tt
Observed
SM H(125 GeV)-4WW
--
~JZ-ITt
30
i
E
Electroweak
Misidentified e/p
uncertainty
25
e-
20
0-jet low piT
15
150
.
35
Electroweak
"" Misidentified e/p
[---- Bkg. uncertainty
200
CMS, 4.9 fb" at 7 TeV
,
[7] Bkg.
0-jet high pT
10C-
a
50
5
0'
0
0
100
0
200
300
mr, [GeV]
1
CMS, 4.9 fb at 7 TeV
60
E,
18
L]
-0-
16
E
Electroweak
40
CMS, 4.9 fb" at 7TeV
20
-SM
H(125 GeV)-tt
-0Observed
SM H(125 GeV)->WW = Z-4tT
50
300
200
100
mn, [GeV]
Misidentified e/p
Bkg. uncertainty
14
- SM H(125 GeV)-*uT
Observed
SM H(125 GeV)--WW
Electroweak
Misidentified e/p
7-Bkg. uncertainty
]
12
10 -
30
1-jet low p"T
20
1-jet high p
8
6
4
10
2
0
0
100
0
200
0
300
mn, [GeV]
100
200
300
ryT [GeV]
1
CMS, 4.9 b at 7 TeV
----- SM H(125 GeV)->tt
8- Observed
SM H(125 GeV).-aWW
0.45
0.40
"a
E
it
0.35
Electroweak
j Misidentified e/i
[-Bkg. uncertainty
0.30
0.25
0.20
VBF tag
0.15
0.10
0.05
0.00
0
100
200
300
m,, [GeV]
Figure 8-1: Observed and predicted m,, distributions for all categories used in the
7 TeV data analysis. The normalization of the predicted background distributions
corresponds to the results of the maximum-likelihood fit. The signal distribution
shown corresponds to the SM prediction for a Higgs boson of mass mH = 125 GeV.
The signal and background histograms are stacked. The distributions shown represent
the number of events per GeV, obtained by dividing the yield in each m,, bin by the
bin width.
133
CMS. 19.7 fb at 8 TeV
1000
-
800
600
Z-4T
ep
0-jet low
-
400
C,
E
I.
I .
120
100
. :
Electroweak
Misidentified e/g
Bkg. uncertainty
0
0
, .
----SM H(125 GeV)-itc
Observed
SM H(1 25 GeV)-)WW
0
Electroweak
Misidentified e/p
i 9kg. uncertainty
-
CMS, 19.7 fb' at 8 TeV
. .I
. I I I
4
. .
. .
.
.----- SM H(125 GeV)-4tt -.Observed
SM H(125 GeV)->WW
Li]
80
eg
60
0-jet high p1
pT
40
200
-
20
0'
0
100
200
0'0
300
100
200
mn,[GeV]
CA S, 19.7 fb
at 8 TeV
CMS, 19.7 fb
7n0
----
SM H(125 GeV)->tt
Observed
SM H(125 GeV)-4WW
--
0--
EM Z--+,r
0 -
20
E
0
mI, [GeV]
1
25 0
C,
MEtectroweak
0
15
Misidentified e/p
] Bkg. uncertainty
[
at 8 TeV
----SM H(125 GeV)-+11
-0- Observed
SM H(125 GeV)-+WW
60
MMZ->nc
50
ep
30
1 -jet low p
Electroweak
Misidentified e/p
kg. uncertainty
[]
40
ep
10 0
300
1-jet high p
20
I0
10
01
0
200
100
MT
3.0
CMS, 19.7
fb'
"*
"*
SM H(125 GeV)->n
Observed
2.5
E
0.4
Electroweak
Misidentified sqp
Bkg. uncertainty
-
0.3
Loose VBF tag
0.2
0.5
0.1
luu
-0-
V0
e9
0
SMH(125
4-- GeV)-*TT
Observed
MSIR H(1 25 GeV)-+WW.
CM Z-mT
0.5
.SM
1.0
0.0
300
fb" at 8 TeV
-
Etectroweak
Misidentified e/p
[---] Bkg. uncertainty
1.5
200
m, [GeV]
M(125 GeV)->WW -
2.0
100
CMS, 19.7
-0-
V
0
[GeV]
at 8 TeV
-----
C--
0
300
200
+4
g
0.0
300
0
m, [GeV]
100
200
tag
300
mnt, [GeV]
Figure 8-2: Observed and predicted mTr distributions for all categories used in the
8 TeV data analysis. The normalization of the predicted background distributions
corresponds to the results of the maximum-likelihood fit. The signal distribution
shown corresponds to the SM prediction for a Higgs boson of mass mH = 125 GeV.
The signal and background histograms are stacked. The distributions shown represent
the number of events per GeV, obtained by dividing the yield in each n, bin by the
bin width.
134
Process
Z-+ TT
tt
Fakes
Di-bosons + single-top
Total Background
H-
TT
0-Jet
± 1528
51100
110
4365
2407
± 10
± 1025
± 220
1-Jet
± 466
13202
2069
1921
1374
± 141
± 415
± 129
VBF
± 6
76
17
22
12
± 3
± 5
± 2
58030 ± 1853
126 ± 11
18614 ± 652
93 ± 6
129 ± 9
6 ± 0.3
59435
18359
141
4.18 .10-3
5.19 .10-4
8.19 .10-4
2.47 _10-3
5.37 _10-3
4.25 .10-3
4.40 .10-5
2.63 .10-3
2.01 .10-5
Data
Signal Efficiency
gg-+ H
VBF
VH
Table 8.1: Observed and expected event yields, and expected signal efficiency for
the 0-Jet, 1-Jet, and VBF categories, for a Higgs boson signal of mass TH = 125
GeV. The low PT and high PT sub-categories for both 0-Jet and 1-Jet categories are
combined in the respective columns, while the VBF loose and VBF tight categories
are combined in the VBF column.
8.2.2
Event Yields
The observed event yields and the expected yields obtained for the different contributing signal and background processes for each event category used in the analysis are
listed in Table 8.1, as are the expected efficiencies for signal events for each category,
for a Higgs boson signal of mass mH = 125 GeV. The low- and high-muon PT subcategories are combined for the 0-Jet and 1-Jet categories, as are the loose and tight
sub-categories of the VBF category. The expected yields and uncertainties on the
yields correspond to the best-fit values obtained from the results from a maximumlikelihood fit (described in Section 8.1.2) performed to the observed data under the
signal-plus-background hypothesis.
The results of the 2011 and 2012 analyses are
combined in the table. The uncertainties quoted for the expected yields represent the
quadratic sum of their statistical and systematic uncertainties.
135
8.2.3
Upper Limits on Signal Strength
The expected and observed 95% confidence level upper limits (corresponding to CL, =
0.05) on the signal strength for a SM Higgs boson are computed from a combined fit
across all event categories according to the procedure described in Section 8.1.2 for
Higgs boson mass hypotheses ranging from mH= 90 GeV to mH = 145 GeV. The
results of the limit computation are tabulated in Table 8.2 and shown in Fig. 8-3. The
analysis is most sensitive for SM Higgs boson mass hypotheses between 120 and 125
GeV. The observed 95% CL upper limit on the signal strength for a SM Higgs boson of
mass mH = 125 GeV is 2.83, while the expected limit is 1.87. For mH above 105 GeV,
the observed upper limit shows a deviation of greater than 1 standard deviation above
the expected limit, indicating a slight excess of observed events over the backgroundonly hypothesis. The best-fit signal strength value obtained for mH = 125 GeV is
f^= 0.90 t 1.03.
mH
90 GeV
95 GeV
100 GeV
105 GeV
110 GeV
115 GeV
120 GeV
125 GeV
130 GeV
135 GeV
140 GeV
145 GeV
-2u
1.19
1.16
1.25
1.15
1.01
0.97
0.95
0.96
1.02
1.14
1.36
1.74
Expected Limit
-Io
Median +lu
1.62
2.30
3.32
1.58
2.26
3.28
1.69
2.41
3.48
1.56
2.23
3.21
1.36
1.94
2.82
1.31
1.88
2.73
1.29
1.85
2.67
1.30
1.87
2.69
1.38
1.98
2.85
1.54
2.21
3.21
1.85
2.65
3.82
2.37
3.39
4.89
Observed Limit
+2u
4.63
4.58
4.85
4.48
3.94
3.80
3.72
3.75
3.95
4.46
5.32
6.82
2.18
2.76
2.98
3.15
2.96
3.10
2.67
2.83
3.37
3.64
4.25
5.60
Table 8.2: Expected and observed 95% CL upper limits on the signal strength parameter p = a/asM, representing the limit on the Higgs boson cross section relative to the
SM prediction, obtained for SM Higgs boson masses between 90 GeV and 145 GeV
in steps of 5 GeV. The median, ±1- and ±2-standard deviation results are shown for
the expected limits.
136
CMS (unpublished) H-rc, 4.9 fb-' at 7 TeV, 19.7 fb1 at 8 TeV
2
CI)
*
-
8
-
77
0
E
-1
6
i
I
I
'I
-
Observed
Expected
± 1y Expected
L
± 2(y Expected
--
I
5
4
0)
3
2
1
0L1
M
0
1
1
120
100
M
I
I
I
140
mH [GeV]
Figure 8-3: Observed 95% CL upper limits on the signal strength parameter P =
-/6TSM and expected limits obtained under the background-only hypothesis, for SM
Higgs boson masses between 90 GeV and 145 GeV. The one- and two-standard deviation uncertainty bands for the expected limit are shown in green and yellow.
8.2.4
Significance
A mild excess is seen in the observed data over the background-only hypothesis;
however, the analysis in this T-pair final state is not sensitive enough to exclude
or confirm either the signal-plus-background or the background-only hypothesis by
itself. The expected significance from this analysis reaches its maximum for a SM
Higgs boson with mass mH = 120 GeV and mH = 125 GeV, at the level of 1.2
standard deviations. The observed significance reaches its maximum value of 1.3
standard deviations at mH= 130 GeV, where the expected significance is 1.1 standard
deviations.
137
8.2.5
Combination with Other r-Pair Final States
The results of the SM Higgs boson search in the ey T-pair final state are combined
with the results of a similar search in all other T-pair final states, described in Ref. [90],
which are performed using a similar analysis strategy. The analyses in the erh,
and
Thrh
final states (the
Th
ftTh,
notation indicates a hadronic tau decay) also rely on fits
to the mIT distributions obtained in event categories which are designed to enhance
Higgs boson production through gluon fusion and vector boson fusion. In the case
of the
Thrh
final state, only 1-Jet and VBF categories are considered due to trigger
restrictions. For all three of these final states, the 1-Jet category includes a further
sub-categorization based on the Higgs boson candidate
PT
in order to further enhance
their sensitivity. The analyses in the cc and pp final states rely on fits based on a
discriminating variable built from the outputs of two multivariate Boosted Decision
Trees in 0-Jet, 1-Jet, and VBF event categories. The BDTs are based on kinematic
and topological event information.
Z
Z
-
-
TT
and Z
-±
The first is designed to discriminate between
11 events, and the second to discriminate between H
-
TT
and
TT events.
The results of the combined search are obtained using a simultaneous binned
likelihood fit to the distributions of the relevant discriminating variable obtained in
all the event categories for all of the T-pair final states, fitting for a common signal
strength modifier p using the procedure described in Section 8.1. The combined fit
shows a clear excess of events above the background-only hypothesis. The significance
of the observed excess is quantified and the results displayed in Fig. 8-4. The expected
significance for a SM Higgs boson of mass mH = 125 GeV is 3.6 standard deviations,
while the observed significance is 3.4 standard deviations. The observed significance
exceeds 3 standard deviations for mH between 110 and 130 GeV. The best-fit value
for the signal strength parameter p obtained from the profile likelihood scan for
mH=
125 GeV is y = 0.86 ± 0.29.
A visual representation of the observed excess in the mr, distribution can be found
in Fig. 8-5, which shows a weighted combination of the observed and predicted mT,
138
CMS H-+Tt, 4.9 fb' at 7 TeV, 19.7 fb 1 at 8 TeV
>I 10-1
O1
0
(mj
2o
y
3
110-2
4(3
10-5
Observed p-value
-
10-6
-------
Expected for SM H(mH)
50
10~7
10-8
eg, eT h'
Th
h
100
ee
120
140
mH [GeV]
Figure 8-4: Observed and expected local p-value and significance (in terms of standard
deviations) for SM Higgs boson mass hypotheses between mH= 90 GeV and mH
145 GeV [90].
distributions from the analyses in the prh, eT11 , TITh, and eu final states, the difference
between the observed data and the predicted background, and the expectation for a
SM Higgs boson with mass nH= 125 GeV. Distributions from each event category for
each final state are assigned a weight in the combination given by the ratio S/(S +
B), with S and B being the expected yields for a SM Higgs boson with MH =
125 GeV and for the total background prediction obtained from the results of the
combined maximum-likelihood fit respectively. These yields are obtained in an m,,
interval containing the central 68% of the expected signal distribution. Thus event
categories with a higher influence on the likelihood are assigned a larger weight in
this combination.
Finally, the results of the analysis targeting the gluon fusion and vector boson
139
CMS, 4.9 fb' at 7 TeV, 19.7 fb1 at 8 TeV
>
, h
tT 9eh
-
4)
ey
Th,
C) 2500
E
H(1I25 GeV)-+4
40 -'SM
.
Data - background
Bkg.
uncertainty
200
300
-Tm,[GeV]
20-
2000
-20-
0
1500
100
SM H(125 GeV)-+tt
1000
Observed
--
500t
Electroweak
500 --
CD
+
Cn
0
0
200
100
300
m, [GeV]
Figure 8-5: Weighted combination of the observed and predicted m,, distributions
for the pTh, eTh, ThTh, and ep final states [90]. The predicted background distributions
correspond to the results obtained from the combined maximum-likelihood fit. The
expected distribution for a SM Higgs boson with mass mH = 125 GeV is also shown.
Event categories with higher signal sensitivity are assigned higher weights in the
combination. The inset shows the difference between the observed data and the total
background prediction as well as the expected distribution for the signal.
fusion production modes in the pTh,
eTh, ThTh,
ei, ee, and pp final states are combined
with the results of an analysis targeting Higgs boson production in association with
a W or Z boson in final states with one or two additional leptons (incorporating the
leptonic decays of the associated W or Z boson). The results of this combined search
indicate an excess over the SM background expectation at the level of 3.2 standard
deviations for a SM Higgs boson of
mH
= 125 GeV, the expected significance of the
combined analysis being 3.7 standard deviations (the addition of the results of the associated production analysis reduces the combined observed significance slightly) [90].
140
CMS H--mT, 4.9 fb' at 7 TeV, 19.7 fb- at 8 TeV
2.0
j
I
-
m
I
I
I
I
I
95% CL
= 125 GeV
.
1.5-
68% CL
Best fit
SM
------------------1.0-
0.5-
0.4
0.5
.0
1.0
1.5
2.0
KV
Figure 8-6: Results of two-dimensional likelihood scan in iv - If parameter space,
where /-v and If represent the measured coupling strengths to vector bosons and
fermions relative to SM expectations. All nuisance parameters are profiled for each
point in the parameter space [90]. The contribution from H -- WW is treated as
a signal process for the purpose of measuring the coupling strengths. The observed
best-fit is shown in black and the SM expectation is shown in red for a Higgs boson
of mass mH = 125 GeV.
The best-fit signal strength obtained from this combination is p
The combined H -
7T
0.78 ± 0.27
analysis provides sensitivity to both the couplings of
the Higgs boson to fermions (through its decay to T-leptons), and to vector bosons
(through the production modes considered).
The analysis is sensitive to the vector
boson couplings through the vector boson fusion production mode as well as the
associated production mode.
The strengths of the couplings to fermions and to vector bosons measured by the
analysis are determined by a two-dimensional likelihood scan in the parameter space
141
of Kv vs
I
f, where rv
indicates the ratio of the strength of the observed coupling
to vector bosons with respect to the expected value for the SM Higgs boson, and Kf
represents the same ratio for the coupling to fermions, as described in Section 8.1.4.
In order to have a consistent treatment of any contribution from a SM Higgs boson
in the observed events, the contribution from SM Higgs boson decays to W boson
pairs is considered as part of the signal in performing this two-dimensional scan. The
contribution from H
-±
WW in the case that the Higgs boson is produced through
the VBF process provides sensitivity to the vector boson coupling through both the
production and decay mechanisms. The observed best-fit point in Kv - if
parameter
space, and the contours enclosing the regions of parameter space within 1- and 2standard deviations, are shown in Fig. 8-6 for a SM Higgs boson mass hypothesis of
125 GeV. The observation agrees with the expectation for a 125 GeV SM Higgs boson
(KV = Kf =
8.2.6
1) within 2 standard deviations.
Combined results of SM Higgs boson searches in
fermionic decay modes
The results of the SM Higgs boson search in the T-pair decay mode performed by
CMS have been combined with the results of the search in the final state with pairs
of b-quarks for a Higgs boson produced in association with W or Z boson
[110]. The
combined results indicate strong evidence, at the level of 3.8 standard deviations, for
the decay of the 125 GeV Higgs boson to down-type fermions. The combined bestfit measurement of the signal strength relative to the SM expectation is 0.83 + 0.24
for a Higgs boson of mass mH = 125 GeV. Figure 8-7 shows the results of this
combination while Table 8.3 summarizes the signal significance and best-fit signal
strength obtained by each analysis.
142
...................
.. .........
CMS
CL
10
0
is= 7TeV, L=5fb"; is= 8TeV, L= 19-20fb"
(exp.) a
(exp.)
(exp.) A
(exp.) -.-
VH -* bb
VH -> tt
H -> rT (non-VH)
Combined
:1102
. ..
101
16-
3.8
-
R
a
-6
is = 8 TeV,
..
.
L= 19-20 fb'
125 GeV
VH ---> bb
H -+ tT
Combined
12
M
1-3.2ar
10-2
10
mH=
18:-
14
a
TeV, L = 5 fb;
C
I
.....
.-
....
is =7
Ms
20
(obs.)
(obs.)
(obs.)
(obs.)
1
-
.......
......
. .
3
8-\
2.1
6-/
10 -
standard
10'6
110
I
-------
---
115
120
125
130
model
2-
N
135
mH (GeV)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Figure 8-7: Results of the combination of searches for the SM Higgs boson decaying to
T-lepton pairs and b-quark pairs [110]. The plot on the left shows the expected (exp.)
and observed (obs.) significance for the two analyses as a function of mH. The results
of the analysis in the di-r decay mode are shown separately for the analysis targeting
the associated (VH) production mode, and the analysis targeting gluon-fusion and
VBF production modes (non-VH). Contributions from non-fermionic decays of a 125
GeV SM Higgs boson are treated as background for these measurements. The plot
on the right shows a likelihood scan as a function of signal strength relative to the
expectation for a SM Higgs boson of mass mH = 125 GeV. The minimum of each
curve indicates the corresponding best-fit value of the signal strength parameter ().
Search mode
(mH
125 GeV)
VH -bb
H -+ rr
Combined
Significance (-)
Expected
Observed
2.3
3.7
4.4
2.1
3.2
3.8
Best-fit 11.0 k 0.5
0.78 ± 0.27
0.83 + 0.24
Table 8.3: Summary of results of the searches for the SM Higgs boson decaying to
T-lepton pairs and b-quark pairs and their combination for mH = 125 GeV. The
expected and observed significances are displayed in units of standard deviations (a).
The best-fit values of the signal strength relative to the expectation for a 125 GeV
SM Higgs boson are also shown.
8.3
Results from ATLAS H -+ -r-r Search
The ATLAS collaboration has also performed a search for the 125 GeV SM Higgs
boson decaying to T-lepton pairs, using 20.3 fb- 1 of proton-proton collision data col-
143
.......
. .......................
. .........
......
4
lected at V/s = 8 TeV. Preliminary results of this search are available [111].
Both
leptonic and hadronic tau decays are analyzed, and the events are classified into categories based on event kinematics in order to improve the sensitivity of the analysis.
A boosted decision tree, trained for a signal mass hypothesis of 125 GeV, is used to
discriminate between signal and background. The statistical analysis of the results is
based on a likelihood fit to the expected and observed distribution of the BDT in the
designated event categories.
The expected and observed significance obtained from this analysis correspond to
an excess of 3.2 and 4.1 standard deviations above the background-only hypothesis
respectively. The best-fit value of the signal strength parameter for a 125 GeV SM
Higgs boson is 1.4it.5. The results of this search constitute supporting evidence for
the decay of the 125 GeV Higgs boson to pairs of T-leptons.
8.4
MSSM Higgs Analysis Results
The search for MSSM neutral Higgs bosons decaying to r-lepton pairs in the ej final
state is based on ept events passing the lepton and topological selection described
in Chapter 5 which are classified into two event categories, the No B-tag and B-tag
categories. The procedure of performing a simultaneous binned likelihood fit based
on the observed and predicted mTT distributions, considering both event categories
together, is followed as for the SM analysis in order to test background-only and
signal-plus-background hypotheses. In addition to the model-dependent search for
the neutral MSSM Higgs bosons A, H, and h which tests for the presence of multiple
Higgs bosons, a model-independent search for a single narrow resonance (labeled as
4D) produced through gluon fusion or in association with b-quarks is also conducted
using the same selection and event categories. Since no significant excess of events is
observed over the predicted background, exclusion limits are computed in each case.
144
8.4.1
Di--r Mass Distributions
The observed and expected m,, distributions obtained for events selected in the B-tag
and No B-tag categories from the analysis of the 2011 and 2012 data are shown in
Fig. 8-8 in linear scale and in Fig. 8-9 in logarithmic scale. The background predictions
are adjusted based on the results of a maximum-likelihood fit to the observed data.
Since the Higgs boson mass hypotheses considered in this search extend up to 1 TeV,
the fitted m,, range extends up to 1.5 TeV to accommodate a high-mass tail for a
hypothetical signal.
Figure 8-8 restricts the m,, range shown to m,, < 350 GeV,
in order to provide a clear representation of the region around the Z -+
TT
peak.
A variable binning scheme is used, with larger bin sizes used for larger values of
mTT,
in order to ensure that the
Tm'TT
shape templates used to model the predicted
backgrounds are sufficiently well populated.
8.4.2
Event Yields
The observed and expected event yields corresponding to the events selected in the
B-tag and No B-tag categories are listed in Table 8.4. The signal yields shown include
the expected contribution from the three neutral MSSM Higgs bosons, evaluated for
mA= 160 GeV, tano = 8. The signal efficiency evaluated in each event category for
each production mode is also provided. Table 8.5 lists the signal efficiency estimated
for a neutral Higgs boson produced through gluon fusion or in association with bquarks and decaying to T-pairs for hypothetical Higgs boson masses between 90 GeV
and 1 TeV.
8.4.3
Model-Independent Single Resonance Search
For the model-independent search for a single narrow resonance, the profile likelihood
ratio test statistic is defined as in Eq. 8.3, with 6 denoting the nuisance parameters associated with the relevant systematic uncertainties, and p, the signal strength parameter, indicating the product of the cross section for a resonance 4 with its branching
ratio to T-pairs (o--BR(4
-+ TT)).
95% CL upper limits on or- BR(1
145
-+
TT)
for a single
"
8
CMS Preliminary, H-mtt,4.9 fb at 7 TeV
. -.
. . ,. .
.
0)
0
- -observed
7 -B-Tag
CMVS Preliminary, H4-m, 4.9 fb-
. . ., . ,
.
0)
Lev
No B-Tag
400
350
electroweak
Fakes
bkg. uncertainty
6
+--
5
E
300
10
250
4
at 7 TeV
observed
--
ti
electroweak
Fakes
bkg. uncertainty
200
3
150
2
100
50
0
100
0
200
0
300
100
300
200
nmi. [GeV]
mr [GeV]
CMS Preliminary,
. B .
ep
B-Tag
30
Q1
25
E
.
H-T,
, I
19.7
.
fb
CMS Preliminary, H-+t, 19.7 fb- at 8 TeV
at 8 TeV
-0-
--0--
No B-Tag
electroweak
E= Fakes
bkg. uncertainty
20
N_ep
1 400
observed
E
bserved
1200
Mt
1000
-: bkg. uncertainty
electroweak
F akes
0
800
15
600
10
400
5
0
200
0
100
200
0
300
nt, [GeV]
0
100
300
200
rn,
[GeV]
Figure 8-8: Observed and predicted m,, distributions for the B- Tag category (left)
and No B-tag category (right) obtained from the 7 TeV (top row) and 8 TeV (bottom row) data analysis shown in linear scale; the displayed m, range is restricted
between 0 and 350 GeV. The normalization of the predicted background distributions corresponds to the results of the maximum-likelihood fit. The signal prediction
is shown for mA = 160 GeV, tan # = 8. The signal and background histograms are
stacked. The distributions shown represent the number of events per GeV, obtained
by dividing the yield in each mr, bin by the bin width.
narrow resonance produced through gluon fusion or in association with b-quarks are
evaluated based on the provided signal models. The estimated signal distributions for
each of these production mechanisms are illustrated in Fig. 8-10 for three signal mass
hypotheses; the gluon fusion estimation shown is evaluated for the No B-tag category
146
CMS Preliminary, H-itt, 4.9
102
fb" at 7 TeV
-0-
B-Tag
CMVS Preliminary,
observed
a
E
electroweak
E
10
---
Fakes
bkg. uncertainty
4.9 fb-1 at 7 TeV
observed
-a
,No B-Tag
1013
tf
H-+11c,
[--J zo
tf
electroweak
Fakes
102
--
bkg.
uncertainty
A
10
10-1
10-1
10-2
10-2
0
1500
1000
500
mr., [GeV]
mr., [GeV]
CMVS Preliminary,
(D
E
H-t,19.7 fb" at 8 TeV
-0-
102
10
-B-Tag
CMS Preliminary, H-+t,
eB g
No B-Tag
1 4
observed
Z---TT
E)
tif
L----
1500
19.7 fb' at 8 TeV
-0-
observed
electroweak
electroweak
Fakes
bkg. uncertainty
E
Fakes
bkg. uncertainty
102
10
10-1
10-2
10-2
1500
rn., [GeV]
0
. 50
500
1000
1500
meT, [GeV]
Figure 8-9: Observed and predicted m,, distributions for the B- Tag category (left)
and No B- Tag category (right) obtained from the 7 TeV (top row) and 8 TeV (bottom row) data analysis, shown in logarithmic scale; the full m,, range used in the
likelihood fit is shown. The normalization of the predicted background distributions
corresponds to the results of the maximum-likelihood fit. The signal prediction is
shown for MA = 160 GeV, tan 0 = 8. The background histograms are stacked and
the signal distribution is overlaid. The distributions shown represent the number of
events per GeV, obtained by dividing the yield in each m,, bin by the bin width.
and the b-associated estimation shown for the B-tag category, both of which are fit
simultaneously in the likelihood fit. The expected signal efficiencies corresponding to
each mode are listed in Table 8.5. The contribution from b-associated production in
each category is treated as a nuisance parameter in the profile likelihood ratio when
147
Process
Z-+ TT
tt
Fakes
Di-bosons + single-top
Total Background
A+H+h-+
Tr
Data
B- Tag
826 ± 30
1496 + 156
158 ± 46
373 + 51
2853 ± 173
43 ± 2
2911
No B- Tag
60897 ± 2013
2826 ± 279
4887 ± 1289
2962 ± 387
71572 ± 2437
585 + 19
72721
Signal Efficiency
ggJ?
9.41
.10-5
9.54
bbJD
1.41
.10-3
8.18 -10-3
_10-3
Table 8.4: Observed and expected event yields, and expected signal efficiency for
the B- Tag and No B- Tag categories. The quoted signal yields are for a hypothetical
MSSM Higgs boson signal corresponding to mA = 160 GeV, tan 3 = 8 and represent
the sum of the contributions from the three neutral bosons, A, H, and h.
obtaining the limits on gluon fusion signal production, and likewise for the gluon
fusion contribution when obtaining the limits on b-associated production.
2.0
1.8
1.6
E
z0
-E
1.4
gg'D(1 60)-TT
0.30
ggID(350)-mTT
0.25
El ggID(600)->TT
1.2
z0
1.0
-
0.20
.
bbKD(350)--tt
-
LJ-
.1
0.6
-
-EibbD(600)-4Tt
0.15
-
0.8
bbCD(1 60)->,
0.10
-1...I.7
0.4
0.05
0.2
0.0
n
0
200
400
600
800
nn
0
1000 1200 1400
m, [GeV]
200
400
600
800 1000 1200 1400
m., [GeV]
Figure 8-10: Estimated signal m,, distributions for a narrow resonance (D decaying
to T-pairs produced through gluon fusion (left) or in association with b-quarks (right)
for the three mass hypotheses m4) = 160,350, and 600 GeV. The signal expectations
are shown assuming a production rate of o- -BR(b -+ TT) = 1 pb in each case.
Figure 8-11 shows the 95% CL observed and upper limits thus obtained, as well
148
M
Process
90 GeV
gg<D
100 GeV
gg<D
bb4<
120 GeV
gg4
bbJD
bbD
130 GeV
ggD
bb
140 GeV
gg4
bb<D
160 GeV
ggD
bb<D
180 GeV
200 GeV
250 GeV
gg<D
bb<D
1.03. 10-2
1.35. -1T
7.77. 10 3
1.05 - 10-2
1.23. 10-2
1.55. -1-
7.46- 10
6.56 - 10--3
9.03. 10-3
8.55- 10- 5
1.10 -10--3
9.01 - 10-7
1.32. 10-3
1.22- 10 -4
1.58. 10-3
1.36 - 10-4
1.92 - 10-3
1.832.39. 10-3
2.24 - 10-T
2.90. 10-3
5.65- 10-3
gg<D
3.57. 102
5.21 - i0-
3.10. 10-2
3.70. 10-4
bbD
2.83. 10-2
5.65. 10-
2.36. 10-2
4.51
gg<D
400 GeV
Mbb
gg4D
bb4D
1.52.
10-
2
1.83.- 10-1.58. 10-2
2.11- 10-2
1.73. 10-2
2.27. - 10-1.85. 10-2
2.40. 10-2
bbD
1.97. 102
gg<D
bb4D
2.60. 16-2
2.09. 10-2
gg4
Mbb
gg 4
bb
2.78.
2.182.82.
2.32.
700 GeV
gg<d
800 GeV
bbD
ggD
bb(D
10-2
10-2
10
10-2
3.12. -1--2
2.39. 10-2
2
3.14
2.57. 10-2
900 GeV
gg4b
3.24.
1000 GeV
2.13. 102.52- 10-3
1.46. 10-4
2.95 - 10-3
1.62.3.02. 10-3
2.62. 10-4
3.67 10--3
3.34. 10- 4
4.04. 10-3
3.24 -IT
4.59. 10-3
3.85. 10-4
4.51 - 10-3
4.07. 10-4
4.90 - 10-:'
5.13- i04.97. 10-3
9.18. 10-
2.58. 10-2
350 GeV
600 GeV
1.88. 10-3
---
4.10 - 105.36. 10-3
5.98-10
5.74. 10-3
5.78 - 10-
3
4
5.87- 10--
Mbb
300 GeV
500 GeV
8 TeV
B-tag
No B-tag
3.13- 10-3
3.45. 102.64. 10-3
3.68- 10-4
3.98. 10-3 4.37 -10-- 5
3.53- 10- 3
4.64- 10- 4
5.93- 10-3 7.44. 10-5
5.16. 10- 3
8.21 . 10-4
6.68. 10-3 7.33. 10-5
8.73. 10-3
1.17 -10-2
1.00 . 102
1.46.
1.20. 10-2
1.66. 10-2
1.37- 10-2
1.84. 10-2
1.50. 10-2
1.99.- 10
1.61 -10-2
2.15- 10-2
1.73. 10-2
2.24- 10--2
1.79. 10-2
2.48.1.93. 10-2
2.61. 10-2
2.04. 10-2
2.732.15- 10-2
2.95 - 10-2
2.31 . 10-2
gg<D
bb4b
gg
bbD
gg4
450 GeV
7 TeV
B-tag
No B-tag
4.65. 10-3
2.77. 10-5
3.96. 10-3
5.92. 10-4
5.82 -105.35. 10-5
4.82. 10-3
7.20. 10-4
8.14 -108.12. 10-5
7.09. 10-3
1.22. 10-3
9.07.- 10-3 9.32. 10-5
7.85. 10-3 1.30. 10-3
1.02-10 2
8.16. 0 5
1.45 - 10-3
9.26.- 10--3
1.21- 10-2 1.16. 10-4
2.48.- 10-4
3.07. 10-2.91 -10-4
3.41. 10-3
3.17 - 10 3.64. 10-3.19. 10- 4
3.69- 10-3
3.50- 104.05. 10-3
4.30. 10-4
4.15 - 10-3
4.24-10
4.26 - 10-3
3.73. 10-4
4.22 - 10-3
.
10-3
Table 8.5: Expected signal efficiency for each category for the 7 TeV and 8 TeV analyses for gluon fusion production and associated production with b-quarks. Efficiency
and acceptance are computed with respect to decays of neutral MSSM Higgs bosons
of mass m, to T-lepton pairs.
149
as the 1- and 2-standard deviation bands for the expected limit. The observed limit
agrees with the expected limit within one standard deviation for mass hypotheses
up to 450 GeV. The observed limit is stronger than the expected limit at a level of
over 1 standard deviation for mass hypotheses between 500 and 800 GeV, due to an
observed deficit in corresponding bins of the mr,
CMS Preliminary, H -
TT,
19.7 fb- at 8 TeV
1L-
M 102
[]±
CMS Preliminary, H -+ T , 19.7 fb" at 8 TeV
observed
expected
± 1c expected
2a expected
103
-
M02
[X
1
observed
expected
± l expected
± 2aexpected
gg-+4 profiled
10
gg->o bb profiled
,10
distributions.
C,)
CC
10T
-J 10-1
0
10
1
1
,,
0-0C
0
LO
C)
100
100
100-3~
20
200
300
400
100
1000
m,[GeV]
200
300
400
1000
m,[GeV]
Figure 8-11: Expected and observed 95% CL upper limits on o- - BR(4D -+ 7T) for
gluon fusion (left) and b-quark associated production (right) as a function of mass
hypothesis mrn obtained from the analysis of 8 TeV data. The limits obtained are
also tabulated in Appendix B.
8.4.4
MSSM Higgs Boson Search
In the context of the search for MSSM neutral Higgs bosons, the signal model implemented includes contributions from the A, H, and h calculated for each considered
point in mA - tan / parameter space. The expected signal at each point in mA - tan 3
parameter space represents the sum of the three contributions. The corresponding
values of mH and mh, the cross sections for gluon fusion and b-associated production
and branching ratios to T-pairs for each of the A, H, and h, contributions are evaluated under the mm"'
scenario as functions of mA and tan /. The expected mrn
shape
corresponding to any of these contributions with a mass for which a simulated sample
is unavailable is obtained by using a "horizontal template morphing" technique [112]
150
which interpolates between the shape templates obtained for the nearest neighboring
lower and higher mass points for which simulated samples are available. For each of
the two production mechanisms, the three Higgs boson contributions are each normalized using the appropriate product of production cross section with branching
ratio to T-pairs and the three contributions are then combined. For sufficiently large
values of mA, the mass of the light scalar h remains small while the heavier A and
H are approximately degenerate in mass. Figure 8-12 shows the expected signal contribution from the three neutral Higgs bosons decaying to 7-pairs produced through
gluon fusion or in association with b-quarks in the No B-tag and B-tag categories
respectively for two points in mA - tan / parameter space.
A profile likelihood test statistic is constructed as in Eq. 8.3, parametrized in mA
and tan 13 instead of p, using the signal model obtained as described above. The
results of the limit calculation can be interpreted as a 95% CL exclusion contour in
mA-
tan
/
parameter space by determining the set of points ill an mA
-
tan / grid for
which the computed value of CL, (Eq. 8.6) is less than or equal to 0.05. Figure 8-13
shows the observed and expected 95% CL exclusion regions in mA - tan / parameter
space obtained for the m"ax benchmark scenario, as well as the 1- and 2-standard
deviation bands around the expected exclusion contour. The downward fluctuation
in the observed limit relative to the expected limit for mA > 450 GeV corresponds to
the observed deficit of events in the corresponding bins of the muTT distributions.
8.4.5
Combination with Other -r-Pair Final States
The results of the search in the ep T-pair final state are combined with the results
of a similar search in other 7-pair final states (erm,
/ITt, TTh,
and fpi), described in
Ref. [113], which are performed using a similar analysis strategy. The analyses in the
cT,
pTh,
and TITh final states also rely on fits to the mTT distributions obtained in B-
tag and No B-tag event categories. In the case of the pp final state, a two-dimensional
fit to the mTT and mvis distributions is performed for additional discriminating power
against the large Z
-+
ypp background.
The results of the combined search are obtained using a simultaneous binned
151
X:10-'
(,
gg
3.5
ED ggh (mh
ggA (mA
3.0
= 124
GeV)
=160
GeV)
0
z
~0
No B-Tag
1.5
MA = 160 GeV,
tan = 8
0.15
MA
0.05
300
400
0.00
500
bbH (mH = 164 GeV)
B-Tag
0.5
200
bbA (mA =160 GeV)
0.20
0.10
100
bb(D
0.25
1.0
0.01
0
o-
bbh (m = 124 GeV)
2.5
2.0
-A
0.30
ggH (m, = 164 GeV)
'
z
~0
0.35
0
100
160 GeV, tan= 8
200
300
400
m, [GeV]
(,
mr,
2.4
5,
Sgge
2.2
'ggA
1.8
z
'0
(mA =350
~0
GeV)
1.6
z
1.4
"a
No B-Tag
1.2
1.0
mA
=
350 GeV, tan p = 45
0.8
bbA (mA =30 GeV)
bbH (mH = 350 GeV)
0.30
0.25
B-Tag
0.20
MA
350 GeV, tan P= 45
0.15
0.6
0.10
0.4
0.05
0.2
0.0
bbh (m = 130 GeV)
0.40
0.35
ggH (m = 350 GeV)
[GeV]
E3bb(D
0.45
ggh (mh = 130 GeV)
2.0
500
0
200
400
600
800
1000
0.00
0
200
400
600
800
1000
m.r., [GeV]
m, [GeV]
Figure 8-12: Expected contributions from A/H/h - TT, and the combined expectation for 4b --4 TT for neutral MSSM Higgs bosons 1D produced through gluon fusion in
the No B-tag category (left) and in association with b-quarks in the B-tag category
(right). The contributions are estimated for mA = 160 GeV, tan 3 = 8 (upper row)
and for mA = 350 GeV, tan = 45 (lower row). The corresponding values for mh,
mH, and the cross sections and branching ratios for decays to T-pairs for each of the
three neutral Higgs bosons are evaluated using the mm"' benchmark scenario.
likelihood fit across all the event categories for all of the T-pair final states using
the procedures described in Sections 8.1 and in the previous sub-sections. Figure 814 shows the combined 95% CL observed and expected limits for a single narrow
resonance produced through gluon fusion or in association with b-quarks. The interpretation of the results of the MSSM neutral Higgs boson search as a 95% CL
152
CMS. H-+t t. 4.9 fb~ at 7 TeV. 19.7 fb-'at 8 TeV
cOU
95% CL Excluded:
CU
50
-observed
-- expected
40
la expected
2(y expected
30
20
10
MSSM max
scenario
h
200
400
600
mA
[GeV]
Figure 8-13: Observed and expected 95% CL exclusions in the mA - tan 3 parameter
space for the MSSM mnax scenario. The observed and expected exclusion regions are
also tabulated in Appendix B.
exclusion in mA - tan 3 parameter space is shown for the m"x scenario in Fig. 8-15.
Since the presence of a SM Higgs boson of mass mH = 125 GeV decaying to T-pairs is
evidenced in the results described in Section 8.2.5, and would affect the composition
of events selected for the non-SM analysis as well, the expected limits obtained when
a 125 GeV SM Higgs boson is included as part of the background expectation are
also shown in both contexts.
8.4.6
Intepretation of MSSM Higgs Boson Search Results
As discussed in Section 1.4, the existence of a Higgs-like state at 125 GeV has significant implications for searches in the context of the MSSM. For certain regions
153
of parameter space, the light scalar MSSM h might behave like a SM Higgs boson,
and the 125 GeV boson could be interpreted as the MSSM light scalar Higgs boson
while searching for the presence of additional, non-SM-like Higgs bosons predicted by
the MSSM. It is to be noted that in the max scenario, large regions of mA - tan3
parameter space would be ruled out by such a restriction on mh since this scenario
was designed to allow the light scalar Higgs boson to approach its maximal mass of
~ 135 GeV in the decoupling limit (mA >> mz). However, the interpretation of the
search results in this scenario is still useful since it allows for a direct comparison
with previous MSSM search results which have been traditionally presented in the
scenario. Existing results can also be re-interpreted in the context of a variety
of other models [114].
mhax
Outside the framework of the max scenario, the interpretation of the 125 GeV
particle as one of the MSSM scalar Higgs bosons remains compatible with large regions of parameter space. Several benchmark scenarios have been proposed for future
studies which maintain such a compatibility by adjusting parameters which, through
radiative corrections, affect the light scalar Higgs boson mass [30, 31]. The largest
radiative corrections arise from loops containing third generation quarks or squarks;
the related parameters thus play an important role in determining mh.
One such scenario features a slight modification of the mjax scenario by adjusting
the stop mixing parameter Xt which is related to the Higgs-stop quark coupling. A
change in this parameter affects positive contributions to radiative corrections which
influence the Higgs boson mass; tuning this parameter allows mh to remain lighter
than its maximal value.
This scenario is referred to as the mnod scenario.
Two
versions of the mnod scenario are proposed, one which features a positive stop mixing
parameter and one which proposes a negative Xt. These adjustments result in a
scenario compatible with the interpretation of the 125 GeV particle as the light scalar
h for large portions of mA - tan 3 parameter space. In these scenarios, the branching
ratios for decays of the heavy MSSM Higgs bosons to 7-pairs (and to b-quark pairs)
may be reduced due to increased rates for decays to charginos and neutralinos for
small and moderate values of tan 3.
154
The amplitude of gluon fusion Higgs boson production is affected by corrections
whose magnitude is determined by the physical stop masses and the stop mixing
parameter. A "light stop scenario" allows the light scalar Higgs boson mass to be in
the appropriate range by choosing a sufficiently large Xt and allowing the presence
of a light stop and would lead to a reduced rate for gluon fusion production relative
to the expected SM rate. The light stop could be within the direct experimental
search reach of the LHC. On the other hand, a "light stau scenario" would lead to a
modified rate for the decay of the light scalar h to two photons. The corrections to
the di-photon decay amplitude of the Higgs boson are determined by the stau masses
and XT, the mixing parameter in the stau sector.
Corrections due to mixing between the two MSSM CP-even Higgs bosons, the h
and the H, could lead to a modified Higgs coupling to down-type fermions for large
values of the mixing parameters, tan#3, and p (the Higgsino mass parameter). One
such scenario is referred to as the "tau-phobic Higgs scenario".
The decay rates of
the h to T-pairs and to b-quark pairs are modified in this scenario. At low values of
tan 0, Higgs boson decay rates to charginos and neutralinos are reduced with respect
to the rates expected in the mr4,od scenarios.
Another possibility would be to identify the 125 GeV boson as the heavy CP-even
H of the MSSM, in which case all of the MSSM Higgs bosons would be required to
be light. The light h would, in such a scenario, have significantly reduced couplings
to gauge bosons. The restrictions of such a phenomenology should make such a "low
mH scenario" relatively easy to confirm or rule out.
Future interpretations of MSSM Higgs boson search results in the context of such
alternative scenarios can be presented in a slightly modified fashion as tests of compatibility with the following alternative hypotheses: the existence of only a 125 GeV
SM Higgs boson without additional Higgs bosons, or the existence of a signal in
accordance with MSSM expectations including a 125 GeV scalar Higgs boson.
155
CMS, H-mr,
.-
Observed
1----
12
[
1
10
%.C
0
-i0
1
3
Observed
SM H(125 GeV) injected
Expected
SM H(125 GeV) injected
Expected
± lo Expected
102
± I Expected
2a Expected
X
± 2o Expected
gg->0 profiled
10
gg->bb profiled
10
C)
CMIS, H-+4TT, 19.7 fb-1 at 8 TeV
19.7 fb"at 8 TeV
10
C0)
11M3
..0
1
0 10-1
E 1-1
-JE
10-2
10-2
L00
0> 10-3-
1
100
0 0- 10-3-
,1
200
300 400
g
1000
m, [GeV]
1
100
200
300 400
1000
m. [GeV]
Figure 8-14: Expected and observed 95% CL upper limits on u- - BR(D -* Tr)
for
gluon fusion (left) and b-quark associated production as a function of mass hypothesis
m. obtained from the analysis of 8 TeV data combining the results for five T-pair
final states. The expected limits obtained in the presence of a SM Higgs boson of
mass mH - 125 GeV are also shown.
156
CMS Preliminary, H-m, 4.9 fb' at 7 TeV, 19.7 fb'1 at 8 TeV
MSSM M max scenario Msusy=1 TeV
I
10
95% CL Excluded:
observed
SM H injected
expected
±1(y expected± 2a expected
LEP
100
200
300
400
1000
mA [GeV]
Figure 8-15: Observed and expected 95% CL exclusions in the mA - tan 3 parameter
space for the MSSM mj"x scenario combining the results for five T-pair final states.
The expected exclusion obtained in the presence of a SM Higgs boson of mass mH
125 GeV are also shown.
157
Chapter 9
Perspective
Since the observation of a ~ 125 GeV Higgs boson decaying to final states with pairs
of vector bosons, one of the most pressing concerns has been to determine if evidence
for this particle can also be seen in fermionic final states. Confirmation of its decay to
fermions would provide support for the Standard Model nature of the Higgs boson,
while evidence to the contrary would be a strong indicator of physics beyond the
Standard Model. The current level of evidence in the di-T decay mode indicating the
leptonic decay of the 125 GeV boson is an important step towards establishing that
the new particle is the Standard Model Higgs boson.
Thus far, the signal strengths measured in different Higgs boson decay modes,
both bosonic and fermionic, agree with the Standard Model expectation within the
measured uncertainties [12, 21, 115, 116]. Tests of hypotheses which posit different
spin-parity possibilities for the observed boson also thus far provide no indications of
a deviation from the expectation for a pure CP-even, spin-0 scalar [13,14].
The LHC is currently scheduled to resume proton-proton collisions in 2015 at
a planned center-of-mass energy of 13 TeV and at instantaneous luminosities close
to the design value. A dataset corresponding to 300 fb--'should be delivered to the
ATLAS and CMS experiments by 2022. Following another shut-down period and
upgrades requisite for higher-luminosity operations, the LHC should then resume
operation in a high-luminosity phase (the High Luminosity LHC or HL-LHC), and
158
deliver 3000 fb-lby 2030. One of the principal goals of the LHC physics program in
upcoming years will be to measure the properties of the 125 GeV particle as precisely
as possible with the large datasets foreseen. Projections have been performed, using
extrapolations based on the performance of existing CMS analyses, to assess the
potential level of sensitivity to the Higgs boson couplings which could be achieved
with such datasets collected at vs = 14 TeV [117.
The results of these projections
are presented in terms of the expected precision which could be achieved on the
ratios of measured Higgs boson coupling strengths to the SM values (t) for different
particles. Two scenarios were considered for these studies: in the first, Scenario 1,
existing systematic uncertainties are assumed to be unchanged in the future analyses,
while in the second, Scenario 2, theoretical uncertainties are assumed to be halved
while other systematic uncertainties are assumed to evolve according to the integrated
luminosity. Figure 9-1 shows the results of these extrapolations for the two scenarios,
for datasets corresponding to integrated luminosities of 300 fb-'and 3000 fb- 1 . Based
on these projections, the coupling of the Higgs boson to taus could be known to
within a precision of 2-5% with 3000 fb-lof accumulated data. Adopting an effective
field theory approach and making certain model assumptions, a deviation A of the
measured coupling strength ratios from 1 could indicate physics beyond the SM at
a characteristic scale A such that A
O(v2 /A 2 ) [118], with v
246 GeV being
the vacuum expectation value of the SM Higgs field. Thus, a 2% precision on the
measurement of , could provide sensitivity to new physics at scales of beyond 1 TeV.
One of the goals of future Higgs studies is to test for CP violation in the Higgs
sector by determining if the Higgs state contains a mixture of CP-odd and CP-even
contributions. The Higgs analysis in the di-T final state is especially valuable in this
regard because of its sensitivity to Higgs boson production through vector boson
fusion. The study of the VBF Higgs production mode could be used to measure a
CP-odd contribution to the Higgs state once a clear signal has been established in
this mode, using observables such as the angular correlation between the two tagging
jets characterizing the VBF topology [119].
The decay of the Higgs boson to taus
could also potentially allow a measurement of CP violation in the coupling of the
159
Higgs to fermions through the use of spin correlations in the T decay. An accuracy
of ~ 110 could be achieved on measurements of the CP phase with a dataset of 3000
fb-'according to a recent study [120].
The years ahead should be a rewarding time for particle physics by providing a
deeper experimental understanding of the Higgs sector of the Standard Model, or
indeed by opening up possibilities for exploring physics beyond the Standard Model
in case more precise measurements lead to indications of a deviation from Standard
Model expectations.
160
CMS Projection
I
I
I
I
I
I
I
I
I
Expected uncertainties on
H
Higgs boson couplings
H
Kw7
KW
I
300 fbil at (s = 14 TeV Scenario 1
300 fbl at (s = 14 TeV Scenario 2
I
Kz
Kg
Kb
Kt
I
0.00
0.05
0.10
I
i
i
I
I
I
0.15
expected uncertainty
CMS Projection
Expected uncertainties on
Higgs boson couplings
KyI
H
H
3000 fb-' at (s =14 TeV Scenario 1
3000 fb at s =14 TeV Scenario 2
I
KW
KZ
Kg
Kb
Kt
I
II,
0.00
0.10
0.05
0.15
expected uncertainty
Figure 9-1: Estimated precision on measurements of Higgs boson coupling strengths
relative to their SM expectations with datasets corresponding to 300 fb- 1 (top) and
3000 fb- 1 (bottom) collected at Vfs = 14 TeV [117]. The estimations are based on
extrapolations from existing analyses and consider two scenarios for the evolution of
systematic uncertainties.
161
Chapter 10
Conclusion
The results of a search for Higgs bosons decaying to pairs of T-leptons using protonproton collision data collected by the CMS experiment in 2011 and 2012 have been
presented. This thesis focuses on the search through the subsequent T-pair decay
to an electron, a muon, and neutrinos. The results of the analysis in the electronmuon T-pair final state are combined with the results of similar analyses in other
T-pair final states in order to achieve the best possible sensitivity to a Higgs boson
decaying to taus. The search is challenging because of the poor signal-to-background
ratio, and the difficulty of reconstructing the invariant mass of the full di-T system
due to the presence of neutrinos in the final state which cannot be detected directly.
Nevertheless, the T-pair decay mode is essential in order to establish whether the
newly observed Higgs boson with a mass near 125 GeV couples to fermions through
Yukawa interactions as expected for the Standard Model Higgs boson. This mode also
provides an excellent opportunity to search for physics beyond the Standard Model,
since couplings to taus are expected to be enhanced in several scenarios such as the
MSSM.
In the case of the SM Higgs boson analysis, which is performed in the 90 - 145
GeV mass range, a mild excess above the SM background-only expectation with a
maximum observed significance of 1.3 standard deviations is seen in the electronmuon final state, consistent with the expectation for a 125 GeV SM Higgs boson.
162
The analysis in the electron-muon final state alone would not be sufficiently sensitive
to confirm the presence of a SM Higgs boson in the available data. The combined
results of the SM Higgs boson search in all 7-pair final states yield evidence, at the
level of over 3 standard deviations, for a Higgs boson decaying to T-lepton pairs,
consistent with the expectations for a SM Higgs boson of mass near 125 GeV. For
a SM Higgs boson mass hypothesis of 125 GeV, the observed significance of the
combined search is 3.4 standard deviations, compared to an expected significance of
3.6 standard deviations. The combined results of the MSSM Higgs boson search do
not indicate the presence of any additional Higgs bosons for mass hypotheses in the
range 90 - 1000 GeV.
These results constitute the first evidence for a Higgs boson to decay into leptons.
They represent a significant milestone towards establishing its nature and properties.
The first period of LHC operations has brought about a paradigm shift for particle
physics, marking a transition from Higgs boson searches to more precise measurements
of an observed Higgs boson which thus far agrees with the predictions for the longsought-after Standard Model Higgs boson. With the addition of more data when the
LHC resumes operation, the Higgs analysis in the di-T final state should continue
to provide one of the most important sources of insight towards understanding the
properties of the Higgs boson.
163
164
Appendix A
Lepton Efficiencies
[GeV] / r; bin
MC efficiency
0.4980 ± 0.0041
0.5097 ± 0.0034
0.2326 ± 0.0025
0.6694 + 0.0022
0.6574 ± 0.0021
0.3831 ± 0.0019
Data efficiency
0.4975 ± 0.0083
0.5664 ± 0.0528
0.2203 ± 0.0163
0.6434 ± 0.0099
0.6378 ± 0.0271
0.3946 ± 0.0131
Scale factor
0.9990 ± 0.0187
1.1113 ± 0.1038
0.9471 ± 0.0706
0.9611 ± 0.0152
0.9702 ± 0.0413
1.0299 ± 0.0345
< 0.8
0.9096 ± 0.0002
0.8979 + 0.0011
0.9871 ± 0.0013
20.0 <PT , 0.8
1rj1 < 1.5
20.0 < PT ,1.5 < Ir/1 < 2.3
0.8630 + 0.0002
0.6376 + 0.0004
0.8456 ± 0.0007
0.6463 ± 0.0022
0.9799 ± 0.0008
1.0136 + 0.0035
PT
10.0
10.0
10.0
15.0
15.0
15.0
< PT <
<
<
<
<
PT
PT
PT
PT
< PT
15.0
,
0.0 <
< 15.0 , 0.8
< 15.0 ,1.5
JrT,
< 0.8
< I/ < 1.5
< JTIr < 2.3
< 20.0 , 0.0 < JrT, < 0.8
< 20.0 0.8 < |Jr/ < 1.5
< 20.0 ,1.5 < Jr/l < 2.3
20.0 <PT , 0.0
Jr/I
Table A.1: Electron identification and isolation efficiencies in 7 TeV data and simulation and the corresponding scale factors measured in different bins of PT and rI.
Only statistical uncertainties and uncertainties from the likelihood fit are included in
the displayed uncertainties; a discussion of the systematic uncertainty can be found
in Section 7.2.
165
PT
10.0
10.0
10.0
15.0
15.0
15.0
20.0
20.0
20.0
[GeV]
< PT < 15.0
< PT < 15.0
< PT < 15.0
< PT < 20.0
< PT < 20.0
< PT < 20.0
< PT < 25.0
< PT < 25.0
< PT < 25.0
25.0 < PT < 30.0
25.0 < PT < 30.0
25.0 < PT < 30.0
/
?j
0.0
0.8
1.5
0.0
0.8
1.5
0.0
0.8
1.5
bin
< 1j1
< qI|
< ITI
< TIJ
< I}I
< I}I
<
<
<
<
<
<
< IyI <
< 1q7 <
< IyI <
MC efficiency
0.8
1.5
2.3
0.8
1.5
2.3
0.8
1.5
2.3
0.4489
0.4524
0.1931
0.6190
0.6190
0.3461
0.7344
0.6489
0.3785
± 0.0047
± 0.0038
± 0.0028
± 0.0026
± 0.0023
± 0.0022
+ 0.0015
± 0.0016
± 0.0016
Data efficiency
0.3436
0.3481
0.1104
0.5196
0.5235
0.2431
0.6442
0.5535
0.2888
±
±
±
±
+
+
+
±
±
0.0057
0.0068
0.0020
0.0017
0.0032
0.0021
0.0010
0.0022
0.0019
Scale factor
0.7654
0.7693
0.5719
0.8394
0.8457
0.7024
0.8772
0.8530
0.7631
±
±
±
±
±
±
±
±
+
0.0149
0.0164
0.0131
0.0045
0.0061
0.0075
0.0023
0.0039
0.0061
0.0 < Iy/ < 0.8
0.7984 ± 0.0010
0.7191 + 0.0011
0.9006 ± 0.0018
30.0 < PT < 35.0
30.0 < PT < 35.0
0.8
1.5
0.0
0.8
0.7294
0.4630
0.8443
0.7854
0.6472
0.3746
0.7819
0.7224
0.8874
0.8092
0.9261
0.9199
30.0
1.5 < 1j1 < 2.3
< PT
< 35.0
< 177 < 1.5
< TIJ < 2.3
< TIJ < 0.8
< jq < 1.5
35.0 <PT , 0.0 < TIJ < 0.8
35.0 <PT , 0.8 < 177 < 1.5
35.0 < PT ,1.5 < Jq < 2.3
± 0.0012
± 0.0013
± 0.0007
± 0.0009
±
±
±
±
0.0007
0.0003
0.0001
0.0001
±
±
±
+
0.0017
0.0024
0.0007
0.0010
0.5345 ± 0.0011
0.4527 ± 0.0011
0.8469 ± 0.0027
0.9092 ± 0.0002
0.8683 ± 0.0003
0.6625 ± 0.0005
0.8650 ± 0.0000
0.8201 ± 0.0000
0.6015 ± 0.0001
0.9514 ± 0.0002
0.9445 ± 0.0003
0.9078 ± 0.0007
Table A.2: Electron identification and isolation efficiencies in 8 TeV data and simulation and the corresponding scale factors measured in different bins of PT and 71.
Only statistical uncertainties and uncertainties from the likelihood fit are included in
the displayed uncertainties; a discussion of the systematic uncertainty can be found
in Section 7.2.
PT [GeV] / q bin
10.0 < PT < 15.0 , 0.0 < 171 < 0.8
10.0 < PT < 15.0 , 0.8 < JqI < 1.2
10.0 < PT < 15.0 , 1.2 < q I < 2.1
15.0 < PT < 20.0 , 0.0 <
15.0 < PT < 20.0 , 0.8 <
15.0 < PT < 20.0 , 1.2 <
20.0 < PT , 0.0 < 177
20.0 < PT , 0.8 < rJ|
jiI < 0.8
TIJ < 1.2
Iy| < 2.1
< 0.8
< 1.2
20.0 < PT , 1.2 < TIJ < 2.1
MC efficiency
0.6478 + 0.0044
0.6951 ± 0.0041
Data efficiency
0.6027 ± 0.0190
0.7038 t 0.0133
Scale factor
0.9303 ± 0.0300
1.0125 ± 0.0200
0.6459
0.7334
0.7908
0.7350
0.9340
0.9340
0.6455
0.7463
0.7940
0.7396
0.9338
0.9346
0.9994
1.0176
1.0040
1.0063
0.9998
1.0006
±
±
±
±
±
±
0.0023
0.0021
0.0021
0.0014
0.0001
0.0002
0.9085 + 0.0002
±
±
±
±
+
±
0.0130
0.0098
0.0017
0.0034
0.0005
0.0007
0.9126 ± 0.0003
±
±
+
±
±
±
0.0205
0.0137
0.0034
0.0050
0.0005
0.0008
1.0045 ± 0.0004
Table A.3: Muon identification and isolation efficiencies in 7 TeV data and simulation
and the corresponding scale factors measured in different bins of PT and 7.
Only
statistical uncertainties and uncertainties from the likelihood fit are included in the
displayed uncertainties; a discussion of the systematic uncertainty can be found in
Section 7.2.
166
[GeV] / r/ bin
10.0 < PT < 15.0 , 0.0 < JrTI < 0.8
10.0 < PT < 15.0 , 0.8 < Jr;I < 1.2
10.0 < PT K 15.0 ,1.2 < ITr/ < 1.6
10.0 < PT < 15.0 , 1.6 < IrTI < 2.1
15.0 < PT < 20.0 0.0 < iJr/ < 0.8
15.0 < PT < 20.0 , 0.8 < Jr/ < 1.2
15.0 < PT < 20.0 ,1.2 < r/1 < 1.6
15.0 < PT < 20.0 ,1.6 < T11 < 2.1
MC efficiency
0.6121 t 0.0048
0.6749 ± 0.0047
0.6987 ± 0.0042
0.6315 + 0.0039
0.7059 + 0.0024
0.7534 ± 0.0028
0.7594 ± 0.0028
0.7030 ± 0.0027
20.0 < PT < 25.0
0.7808 ± 0.0014
0.7533 ± 0.0012
0.9648 + 0.0023
0.8047
0.8144
0.7637
0.8414
0.8519
0.8559
0.8146
0.7915
0.7997
0.7567
0.8141
0.8364
0.8462
0.8051
0.9836
0.9820
0.9909
0.9676
0.9817
0.9886
0.9883
PT
20.0
20.0
20.0
25.0
25.0
25.0
25.0
< PT
< PT
< PT
< PT
< PT
< PT
< PT
<
<
<
<
<
<
<
,
0.0 < Trj < 0.8
25.0 , 0.8 < Ir/ < 1.2
25.0 , 1.2 < I < 1.6
25.0 ,1.6 < Ir;I < 2.1
30.0 , 0.0 < jqrI < 0.8
30.0 , 0.8 < Jrq < 1.2
30.0 ,1.2 < Ir/I < 1.6
30.0 , 1.6 < Ir/I < 2.1
30.0 < PT < 35.0
,
0.0 < 'r| < 0.8
30.0 < PT < 35.0 0.8 < rjl < 1.2
30.0 < PT < 35.0 ,1.2 < r,, < 1.6
30.0 < PT < 35.0 ,1.6 < r < 2.1
35.0 <PT , 0.0
1r/ < 0.8
,
0.8
<
IrTI < 1.2
35.0 <PT
35.0 < PT ,1.2 < Ir I < 1.6
35.0 < PT ,1.6 < rj I < 2.1
±
±
±
+
±
±
±
0.0018
0.0018
0.0018
0.0008
0.0012
0.0012
0.0013
Data efficiency
0.5981 ±
0.6578 ±
0.6738 ±
0.6246 ±
0.6740
0.7309
0.7416
0.6954
±
±
+
±
±
±
±
±
±
±
±
Scale factor
0.0045
0.9771 + 0.0107
0.0041
0.0037
0.0032
0.0022
0.0025
0.0025
0.0022
0.9746
0.9644
0.9891
0.9548
0.9701
0.9766
0.9892
0.0016
0.0016
0.0014
0.0007
0.0010
0.0009
0.0009
+ 0.0091
+ 0.0078
± 0.0080
± 0.0046
± 0.0049
± 0.0049
± 0.0049
±
±
±
+
±
±
±
0.0030
0.0029
0.0030
0.0012
0.0018
0.0018
0.0019
0.8845 + 0.0005
0.8606 ± 0.0004
0.9730 ± 0.0008
0.8827
0.8824
0.8483
0.9418
0.9398
0.9385
0.9129
0.8680
0.8745
0.8399
0.9255
0.9249
0.9291
0.9025
0.9833
0.9910
0.9900
0.9826
0.9841
0.9900
0.9886
±
±
±
±
±
+
+
0.0009
0.0009
0.0010
0.0002
0.0003
0.0003
0.0003
±
±
±
+
±
±
±
0.0007
0.0007
0.0010
0.0004
0.0002
0.0002
0.0002
±
+
±
±
±
+
±
0.0012
0.0013
0.0016
0.0005
0.0004
0.0003
0.0004
Table A.4: Muon identification and isolation efficiencies in 8 TeV data and simulation
and the corresponding scale factors measured in different bins of PT and I. Only
statistical uncertainties and uncertainties from the likelihood fit are included in the
displayed uncertainties; a discussion of the systematic uncertainty can be found in
Section 7.2.
167
/
MC efficiency
Data efficiency
Scale factor
10.0
10.0 < PT < 15.0 , 0.8 < 1j1 < 1.5
0.5573 ± 0.0071
0.5560 ± 0.0085
0.9256 + 0.0155
0.9018 ± 0.0214
1.6608 + 0.0348
1.6220 ± 0.0458
10.0
PT [GeV]
< PT < 15.0
q bin
, 0.0 < IT| < 0.8
15.0 , 1.5 < 1j1 < 2.3
0.4804 ± 0.0148
0.9333 ± 0.0426
1.9427 ± 0.1070
15.0 < PT < 20.0 , 0.0 < 1j1 < 0.8
0.6144 ± 0.0063
0.9565 ± 0.0114
1.5569 + 0.0243
15.0
15.0
0.6074 ± 0.0078
0.5529 ± 0.0120
0.9844 ± 0.0104
0.9643 ± 0.0234
1.6208 ± 0.0270
1.7441 ± 0.0563
0.9694
0.9892
0.9693
0.9770
0.9954
0.9729
0.9839
0.9941
0.9858
0.9799
0.9938
0.9858
0.9863
0.9850
1.0000
0.9873
0.9959
0.9864
1.0108
1.0046
1.0171
1.0095
0.9895
1.0278
1.0035
1.0018
1.0006
< PT K
< 20.0 , 0.8 < ij < 1.5
< 20.0 , 1.5 < Jil < 2.3
20.0 < PT < 25.0 , 0.0 < IT4 < 0.8
< PT
< PT
20.0 < PT < 25.0 , 0.8 <
20.0 < PT < 25.0 , 1.5 <
25.0 < PT < 30.0 , 0.0 <
25.0 < PT < 30.0 , 0.8 <
25.0 < PT < 30.0 , 1.5 <
30.0 < PT , 0.0 < TIJ
30.0 < PT , 0.8 < lql
30.0 < PT , 1.5 < Inj
177 <
rjj <
Iq <
1j1 <
Ij1 <
< 0.8
< 1.5
< 2.3
1.5
2.3
0.8
1.5
2.3
±
±
±
±
±
±
+
±
±
0.0026
0.0023
0.0053
0.0025
0.0018
0.0050
0.0018
0.0014
0.0033
±
±
±
±
±
±
±
±
±
0.0091
0.0082
0.0184
0.0081
0.0117
0.0160
0.0034
0.0032
0.0080
+
±
±
+
+
±
±
+
±
0.0097
0.0086
0.0198
0.0087
0.0119
0.0173
0.0039
0.0035
0.0088
Table A.5: Electron trigger leg efficiencies in 7 TeV data and simulation and the
corresponding scale factors measured in different bins of PT and TI. Only statistical
uncertainties are shown; a discussion of the systematic uncertainty can be found in
Section 7.2.
168
[GeV] / r bin
10.0 < PT < 15.0 , 0.0 < 'qj <
10.0 < PT < 15.0 , 0.8 < Ir/j <
10.0 < PT < 15.0 ,1.5 < Ir,1 <
15.0 < PT < 20.0 , 0.0 < Irq <
15.0 < PT < 20.0 , 0.8 < Irq <
15.0 < PT < 20.0 ,1.5 < iJrI <
20.0 < PT < 25.0 , 0.0 < IrTJ <
20.0 < PT < 25.0 , 0.8 < jrq <
20.0 < PT < 25.0 ,1.5 < Ir/| <
25.0 < PT < 30.0 , 0.0 < I/ <
25.0 < PT < 30.0 , 0.8 < Jr <
25.0 < PT < 30.0 ,1.5 < Tr1 <
30.0 < PT < 35.0 , 0.0 < Tr1 <
30.0 < PT < 35.0 0.8 < iT1 <
30.0 < PT < 35.0 ,1.5 < Ir/I <
35.0 <PT , 0.0
IrTI < 0.8
35.0 <PT , 0.8 < JrTI < 1.5
35.0 <PT , 1.5 < jri, < 2.3
PT
0.8
1.5
2.3
0.8
1.5
2.3
0.8
1.5
2.3
0.8
1.5
2.3
0.8
1.5
2.3
MC efficiency
0.7615 ± 0.0128
0.8186 ± 0.0150
0.7652 ± 0.0312
0.8903 ± 0.0090
0.9367 ± 0.0091
0.9126 ± 0.0162
0.9419 ± 0.0072
0.9746 + 0.0069
0.9654 ± 0.0120
0.9591 ± 0.0072
0.9757 ± 0.0071
0.9732 + 0.0140
0.9454 ± 0.0088
0.9748 ± 0.0100
0.9875 + 0.0095
0.9629 ± 0.0073
0.9763 ± 0.0069
0.9787 ± 0.0131
Data efficiency
0.7270 + 0.0086
0.7380 ± 0.0100
0.6899 ± 0.0224
0.8752 ± 0.0052
0.9059 + 0.0057
0.8635 ± 0.0118
0.9142 + 0.0042
0.9484 ± 0.0045
0.9356 ± 0.0089
0.9368 + 0.0038
0.9630 + 0.0041
0.9466 + 0.0079
0.9499 ± 0.0037
0.9642 ± 0.0042
0.9735 ± 0.0059
0.9689 t 0.0012
0.9809 ± 0.0013
0.9802 ± 0.0021
Scale factor
0.9548 ± 0.0197
0.9015 + 0.0205
0.9017 ± 0.0470
0.9830 ± 0.0115
0.9672 + 0.0113
0.9463 ± 0.0212
0.9707 ± 0.0087
0.9731 ± 0.0083
0.9691 ± 0.0149
0.9768 t 0.0084
0.9870 ± 0.0083
0.9727 ± 0.0162
1.0047 ± 0.0100
0.9891 ± 0.0111
0.9858 ± 0.0112
1.0063 ± 0.0078
1.0047 ± 0.0073
1.0015 ± 0.0135
Table A.6: Electron trigger leg efficiencies in 8 TeV data and simulation and the
corresponding scale factors measured in different bins of PT and /. Only statistical
uncertainties are shown; a discussion of the systematic uncertainty can be found in
Section 7.2.
169
PT [GeV] / Tj bin
10.0 < PT < 15.0 0.0 < 1j7 <
10.0 < PT < 15.0 0.8 < qI| <
10.0 < PT < 15.0 1.2 < IrJ <
15.0 < PT < 20.0 0.0 < IT| <
15.0 < PT < 20.0 0.8 < IyI <
15.0 < PT < 20.0 1.2 < TJ| <
20.0 < PT < 25.0 0.0 <
<
20.0 < PT < 25.0 0.8 < IrI <
20.0 < PT < 25.0 1.2 < ITI <
25.0 < PT < 30.0 0.0 < 171 <
25.0 < PT < 30.0 0.8 < TIJ <
25.0 < PT < 30.0 1.2 < Inj <
30.0 <PT , 0.0 < ITl < 0.8
0.8
MC efficiency
0.9849 ± 0.0021
Data efficiency
0.9660 ± 0.0164
Scale factor
0.9808 ± 0.0167
1.2
2.1
0.8
0.9678 ± 0.0049
0.9589 ± 0.0039
0.9857 ± 0.0021
0.9314 ± 0.0350
0.9207 ± 0.0271
0.9668 ± 0.0148
0.9623 ± 0.0365
0.9602 ± 0.0285
0.9808 ± 0.0152
1.2
0.9759 ± 0.0043
0.9556 ± 0.0256
0.9791 ± 0.0266
2.1
0.8
1.2
2.1
0.9663
0.9843
0.9799
0.9674
0.9613
0.9878
0.9495
0.9379
0.9948
1.0035
0.9690
0.9694
0.8
1.2
2.1
0.9865 ± 0.0027
0.9761 ± 0.0059
0.9707 ± 0.0044
0.9680 ± 0.0154
0.9550 ± 0.0293
0.9416 ± 0.0255
0.9812 ± 0.0158
0.9783 ± 0.0306
0.9700 ± 0.0266
30.0 <PT , 0.8 < Ir| < 1.2
0.9885 ± 0.0020
0.9827 ± 0.0044
0.9671 i 0.0044
0.9502 ± 0.0089
0.9783 ± 0.0049
0.9669 ± 0.0101
30.0 < PT ,1.2
0.9699 ± 0.0040
0.9383 ± 0.0083
0.9674 ± 0.0094
IriI
<
TIJ
< 2.1
±
±
+
±
0.0037
0.0025
0.0040
0.0040
±
±
±
±
0.0202
0.0118
0.0327
0.0239
±
±
+
±
0.0213
0.0122
0.0336
0.0250
Table A.7: Muon trigger leg efficiencies in 7 TeV data and simulation and the corresponding scale factors measured in different bins of PT and 71.
Only statistical
uncertainties are shown; a discussion of the systematic uncertainty can be found in
Section 7.2.
170
PT [GeV] / rj bin
10.0 < PT < 15.0 , 0.0 < |ij
10.0 < PT < 15.0 , 0.8 < JrTI
10.0 < PT < 15.0 , 1.2 < Jrq
10.0 < PT < 15.0 ,1.6 < Ir/I
15.0 < PT < 20.0
,
0.8
1.2
1.6
2.1
MC efficiency
0.9870 ± 0.0048
0.9666 + 0.0104
0.9357 ± 0.0136
0.9415 ± 0.0140
Data efficiency
0.9701 ± 0.0033
0.9419 ± 0.0064
0.9303 + 0.0074
0.8623 ± 0.0105
Scale factor
0.9829 + 0.0058
0.9745 + 0.0124
0.9943 ± 0.0164
0.9158 ± 0.0176
0.0 < q/ < 0.8
0.9868 ± 0.0046
0.9720 ± 0.0030
0.9850 ± 0.0056
0.9445
0.9512
0.9638
0.9812
0.9822
0.9640
0.9657
0.9853
0.9618
0.9538
0.9287
0.9826
0.9454
0.9247
0.9305
0.9267
0.8995
0.9764
0.9439
0.9366
0.9134
0.9725
0.9405
0.9218
0.8824
0.9785
0.9342
0.9184
0.9852
0.9743
0.9333
0.9951
0.9610
0.9716
0.9459
0.9869
0.9779
0.9665
0.9501
0.9959
0.9881
0.9932
15.0 < PT < 20.0 , 0.8
15.0 < PT < 20.0 ,1.2
15.0 < PT < 20.0 ,1.6
20.0 < PT < 25.0 , 0.0
20.0 < PT < 25.0 , 0.8
20.0 < PT < 25.0 ,1.2
20.0 < PT < 25.0 ,1.6
25.0 < PT < 30.0 , 0.0
25.0 < PT < 30.0 , 0.8
25.0 < PT < 30.0 ,1.2
25.0 < PT < 30.0 ,1.6
30.0 < PT < 35.0 , 0.0
30.0 < PT < 35.0 , 0.8
30.0 < PT < 35.0 ,1.2
<
<
<
<
<
<
<
<
<
<
<
<
<
<
r/ < 1.2
r/ < 1.6
r1 < 2.1
iT/ < 0.8
'r/ < 1.2
r/ < 1.6
r1 < 2.1
r1 < 0.8
i/ < 1.2
r/ < 1.6
r/ < 2.1
< I < 0.8
< JrjI < 1.2
< IrIj < 1.6
30.0 < p, < 35.0 ,1.6 <
Jr/T
< 2.1
35.0 < PT , 0.0
Tr1 < 0.8
35.0 < PT , 0.8 < iTj < 1.2
35.0 < PT ,1.2 < iTj < 1.6
35.0 < PT ,1.6 < rj < 2.1
±
±
±
±
±
±
±
±
±
±
±
±
±
+
0.0149
0.0155
0.0133
0.0053
0.0097
0.0123
0.0131
0.0067
0.0170
0.0163
0.0214
0.0078
0.0202
0.0234
0.9573 ± 0.0289
0.9692
0.9759
0.9522
0.9606
+
±
±
±
0.0083
0.0166
0.0206
0.0208
±
+
h
±
±
+
±
±
±
±
±
±
±
±
0.0068
0.0078
0.0094
0.0028
0.0066
0.0071
0.0091
0.0031
0.0068
0.0086
0.0114
0.0030
0.0078
0.0094
±
±
±
±
+
+
±
±
±
±
±
±
±
±
0.0171
0.0179
0.0162
0.0060
0.0116
0.0141
0.0159
0.0074
0.0187
0.0184
0.0251
0.0085
0.0227
0.0271
0.8990 ± 0.0111
0.9679 ± 0.0014
0.9391 ± 0.0307
0.9986 ± 0.0087
0.9310 ± 0.0031
0.9092 ± 0.0041
0.9016 ± 0.0049
0.9540 + 0.0165
0.9549 ± 0.0211
0.9386 ± 0.0209
Table A.8: Muon trigger leg efficiencies in 8 TeV data and simulation and the corresponding scale factors measured in different bins of PT and rl. Only statistical
uncertainties are shown; a discussion of the systematic uncertainty can be found in
Section 7.2.
171
Appendix B
Tables of Exclusion Limits
[GeV]
90
100
120
140
160
180
200
250
300
350
400
450
500
600
700
800
900
1000
Observed limit
Expected limit [pb]
me
-2u
24.88
24.52
4.84
2.17
1.64
1.33
1.16
0.47
0.33
0.25
0.20
0.17
0.15
0.11
0.09
0.07
0.06
0.08
-1a
33.11
32.74
6.48
2.89
2.18
1.78
1.47
0.63
0.44
0.33
0.27
0.23
0.20
0.14
0.12
0.09
0.07
0.09
Median
46.16
45.16
8.95
3.84
2.97
2.33
1.87
0.86
0.62
0.46
0.38
0.32
0.28
0.20
0.16
0.13
0.10
0.12
+1
64.74
62.98
12.42
5.12
3.86
2.97
2.38
1.20
0.86
0.64
0.53
0.44
0.39
0.28
0.23
0.18
0.15
0.16
+2(7
86.30
83.59
16.52
6.53
4.85
3.73
3.04
1.64
1.17
0.87
0.72
0.60
0.53
0.38
0.31
0.25
0.20
0.21
[pb]
54.51
52.39
11.92
4.89
3.38
2.50
1.78
0.74
0.48
0.41
0.37
0.26
0.17
0.08
0.08
0.10
0.12
0.13
Table B.1: Expected and observed 95% CL upper limits on o - BR(1D -4 TT) for a
single resonance <D produced through gluon fusion as a function of mq, obtained from
the analysis of data collected at V/ = 8 TeV.
172
m4
[GeV]
90
100
120
130
140
160
180
200
250
300
350
400
450
500
600
700
800
900
1000
-2u
5.32
4.55
2.61
2.24
1.97
1.66
1.50
1.25
0.58
0.45
0.35
0.29
0.25
0.23
0.17
0.14
0.11
0.12
0.14
Expected limit [pb]
-1a Median +-l
7.13
9.98
14.08
6.06
8.47
12.01
3.48
4.86
6.85
2.99
4.17
5.75
2.64
3.64
4.90
2.22
3.01
3.88
2.00
2.59
3.28
1.53
1.93
2.46
0.77
1.07
1.50
0.60
0.83
1.16
0.47
0.65
0.91
0.38
0.53
0.74
0.33
0.46
0.65
0.30
0.42
0.59
0.22
0.31
0.44
0.17
0.25
0.35
0.14
0.20
0.28
0.15
0.20
0.27
0.17
0.22
0.28
+2j
19.11
16.25
9.18
7.51
6.28
4.85
4.05
3.09
2.04
1.55
1.23
0.99
0.86
0.78
0.58
0.48
0.38
0.35
0.35
Observed limit
[pb]
12.47
9.15
4.19
3.72
3.89
3.63
2.95
2.24
1.10
0.83
0.65
0.53
0.37
0.24
0.13
0.12
0.13
0.17
0.19
Table B.2: Expected and observed 95% CL upper limits on u-BR((D -+ TT) for a single
resonance 4D produced in association with b-quarks as a function of 'mT, obtained from
the analysis of data collected at s = 8 TeV.
173
mA
[GeV]
90
100
120
130
140
160
180
200
250
300
350
400
450
500
600
700
-2o5.32
5.42
4.15
3.95
4.28
5.23
5.93
7.05
11.49
16.47
21.51
26.26
32.32
39.27
53.20
70.70
Expected limit
Median
-Io8.22
6.68
7.06
8.81
5.54
7.20
5.21
6.66
5.34
6.58
5.96
7.40
7.17
8.49
8.28
10.17
13.52
15.90
18.70
21.66
24.39
28.38
29.72
34.43
36.76
42.59
52.53
44.81
72.62
61.04
94.26 131.62
(tan /)
+1o10.34
11.09
8.97
8.31
8.16
8.84
10.53
11.94
18.87
25.18
32.86
39.93
49.41
60.68
101.86
185.66
Observed limit (tan /)
+212.14
13.30
11.07
10.28
10.03
10.77
12.10
14.19
21.81
29.10
37.49
45.91
57.13
69.53
138.58
250.21
10.52
11.04
7.84
7.73
8.27
10.33
11.54
12.69
15.19
21.51
29.29
35.97
40.19
42.64
49.81
68.91
Table B.3: Expected and observed 95% CL limits on tan /3 as a function of
mA,
obtained in the mjax scenario. For each value of mA, values of tan 0 greater than
those listed in the table are expected or observed to be excluded.
174
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