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UNIVERSITA DEGLI STUDI DI BARI
Aldo Moro
FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALIDipartimento Interateneo di Fisica M. Merlin
Tesi di Laurea
SEARCH FOR THE STANDARD MODEL HIGGS BOSON
IN THE DECAY CHANNEL H→ ZZ→ 4l
WITH THE CMS EXPERIMENT AT√
s = 7 TeV
Relatori:Ch.mo Prof. Mauro de PalmaDott. Nicola De Filippis
Laureanda:Giorgia Miniello
Anno Accademico 2011-2012
Index
Introduction 1
1 The Standard Model Higgs Boson 3
1.1 Electroweak Interactions . . . . . . . . . . . . . . . . . . . . . 3
1.2 Gauge Symmetries . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Electroweak Spontaneous Symmetry Breaking: The Higgs Mech-
anism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Renormalizability of the Standard Model . . . . . . . . . . . . 16
1.4.1 The Higgs Field Choice . . . . . . . . . . . . . . . . . . 16
1.4.2 Standard Model free parameters: Gauge Boson Masses,
Fermions Masses . . . . . . . . . . . . . . . . . . . . . 18
1.4.3 Renormalization . . . . . . . . . . . . . . . . . . . . . . 20
1.4.4 The Final S.M. Lagrangian . . . . . . . . . . . . . . . . 22
2 The Large Hadron Collider and the CMS Detector 25
2.1 The Large Hadron Collider at CERN . . . . . . . . . . . . . . 25
2.1.1 Performance Goals . . . . . . . . . . . . . . . . . . . . 27
2.1.2 LHC Collision Detectors . . . . . . . . . . . . . . . . . 29
2.2 The Compact Muon Solenoid (CMS) Detector . . . . . . . . . 32
2.2.1 Coordinate System . . . . . . . . . . . . . . . . . . . . 32
2.2.2 The CMS detector structure and the Magnet . . . . . . 33
2.2.3 Inner Tracking System . . . . . . . . . . . . . . . . . . 34
2.2.4 Electromagnetic Calorimeter . . . . . . . . . . . . . . . 37
2.2.5 Hadron Calorimeter . . . . . . . . . . . . . . . . . . . . 41
2.2.6 The Muon System . . . . . . . . . . . . . . . . . . . . 42
2.2.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
i
2.3 Lepton Reconstruction . . . . . . . . . . . . . . . . . . . . . . 48
2.3.1 Electron Reconstruction . . . . . . . . . . . . . . . . . 48
2.3.2 Muon Reconstruction . . . . . . . . . . . . . . . . . . . 53
3 The Higgs Boson Production and Simulation at LHC 57
3.1 Higgs Production Mechanism . . . . . . . . . . . . . . . . . . 58
3.1.1 The higher-order corrections and the K-factor . . . . . 58
3.2 Decays of the SM Higgs boson . . . . . . . . . . . . . . . . . . 61
3.2.1 Decays into electroweak gauge bosons: two body decay 64
3.3 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Monte Carlo generator studies . . . . . . . . . . . . . . . . . . 71
4 Data Analysis 75
4.1 Experimental Data samples . . . . . . . . . . . . . . . . . . . 76
4.2 Physics Objects: Electrons and Muons . . . . . . . . . . . . . 78
4.2.1 Lepton Identification . . . . . . . . . . . . . . . . . . . 78
4.2.2 Electrons and Muons Isolation . . . . . . . . . . . . . . 82
4.2.3 Pile-up Corrections . . . . . . . . . . . . . . . . . . . . 84
4.2.4 Primary and Secondary leptons: the significance of the
impact parameter . . . . . . . . . . . . . . . . . . . . . 86
4.3 Selection cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 Selection Efficiency . . . . . . . . . . . . . . . . . . . . 89
4.4 Data to MC comparison . . . . . . . . . . . . . . . . . . . . . 93
4.5 Studies about the best four-lepton algorithm . . . . . . . . . . 106
4.5.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . 112
4.6 Background Evaluation and Control . . . . . . . . . . . . . . . 120
4.7 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 121
4.7.1 Theoretical uncertainties . . . . . . . . . . . . . . . . . 121
5 Results 127
5.1 Mass Distributions and Kinematics . . . . . . . . . . . . . . . 127
5.2 Statistical interpretation: The CLs Method . . . . . . . . . . . 129
5.2.1 The Likelihood function and the test statistics . . . . . 133
5.2.2 Determination of the exclusion limits . . . . . . . . . . 136
5.3 Latest Results of the Standard Model Higgs Search in the
H→ ZZ→ 4` channel at√s = 8 TeV with 2012 data. . . . . 139
Conclusions 147
Bibliography 151
Introduction
The aim of particle physics is to study the fundamental constituents and
interactions of matter. In the twentieth century, from this theoretical branch
of physics a new experimental one came up, the high energy physics, which
studies the interactions between elementary particles at very high energy.
These high energy interactions allow the production of new particles, not
existing in nature in ordinary conditions, by means of particle accelerators
(colliders).
The Standard Model (SM) of the electroweak and strong interaction is the
quantum field theory which has the greatest number of experimental veri-
fications, with some exception like the proton lifetime and the existence of
the Higgs boson. In particular, the Higgs boson mass, like those of quarks,
leptons and gauge bosons, is a free parameter of the theory.
The SM predicts the existence of a unique physical Higgs scalar boson as-
sociated to the spontaneous electroweak symmetry breaking, the so called
Higgs mechanism. The motivation for introducing the Higgs scalar boson
is completely theoretical and takes as foundation the fact that it allows to
generate the weak boson masses without spoiling the renormalizability of the
electroweak gauge theory. So far, no evidence of the existence of SM Higgs
has been found, although both theoretical and experimental constraints have
been put on Higgs mass.
Direct searches for SM Higgs boson have been already performed at the e+e−
collider LEP and at the pp collider Tevatron. A lower bound of mH ≥ 114.4
GeV/c2 at 95% CL (Confidence Level) has been found for the Higgs mass
at LEP, while the experiments D0 and CDF at Tevatron excluded the mass
range 158 ≤ mH ≤ 173 GeV/c2 (95% CL).
The search of Higgs boson is one of the main goals of CMS and ATLAS
1
experiments at the Large Hadron Collider (LHC) located at CERN since it
started to provide pp collision on November 2009. These two experiments
have been designed to cover a large spectrum of signatures in LHC eviron-
ment and the Higgs search has been the major guide criterion followed to
define the detectors requirements and performances.
The aim of this thesis work is to develop a physics analysis to search for
the SM Higgs boson in the decay channel H → ZZ(∗) for which each vector
boson Z decays into a di-electron or di-muon object, by using data collected
by the experiment in 2010 and 2011 at center of mass energy of 7 TeV.
In the first chapter a wide view on the theoretical basis of the SM and the
spontaneous symmetry breaking mechanism generating the Higgs boson is
presented. The second chapter shows a description of the LHC and the
whole CMS detector along with an overview of the subdetectors. The third
chapter is focused on the SM Higgs boson production and decay channels in
hadron colliders. It also contains a detailed description of all the samples
of real and simulated data used for this analysis. In the fourth chapter the
analysis selection is detailed along with the description of the physics objects
and the main physics observables used. For a better understanding of the
goodness of event selection criteria, a study of the vector boson recostruction
efficiency is also presented. The results are then shown in the last chapter.
Not any clusterization has been found by the analysis of the 2010 and 2011
data. First collisions at√s = 8 TeV started the 5th of April 2012. During
the last period, extremely important results have been derived at that en-
ergy, showing an excess of about 3σ in the H → ZZ → 4` analysis and a 5σ
excess overall when combining all the Higgs analyses for the different chan-
nels. Some details about those amazing results are given in the last section
of my thesis.
2
Chapter 1
The Standard Model Higgs
Boson
In the early 1970’s, a new quantum field theory was enounced by Wein-
berg and Salam and later completed by ’t Hooft: the Standard Model for
electroweak interactions. This soon turned out to be a very powerful tool,
being the only model able of explaining a wide variety of physics phenomena.
Through many decades and a lot of experiments, the Standard Model has be-
come the one which has the greatest number of experimental confirmations.
It was developed starting from the need of finding a single unified symmetry
group describing both electromagnetic and weak interactions. It’s no useless
to remind that one of the most fascinating ideas in particle physics is that
the interactions are dictated by simmetry principles, the so-called local gauge
symmetries. This insight is deeply connected with the fact that conserved
physical quantities are conserved in local (not global) regions of space.
All the treatise presented in the following sections was sourced from [26] and
[42].
1.1 Electroweak Interactions
The problem of finding a common symmetry group structure rose already
within the weak currents themselves. It’s worth reminding that the forms
for the weak charged currents are
3
Jµ ≡ J+µ = uνγµ
1
2(1− γ5)ue ≡ νγµ
1
2(1− γ5)e = νLγµeL (1.1)
and
J†µ ≡ J−µ = ueγµ1
2(1− γ5)uν = eLγµνL, (1.2)
where ue and (as well as e in a more compact form) and uν (as well as ν) are
the four component spinors relative to electron e and neutrino ν respectvely,
γµ’s are the 4× 4 Dirac matrices and γ5 is a matrix obtained by the product
of the four previous γ-matrices
γ5 = iγ0γ1γ2γ3. (1.3)
The apices + and - indicate the charge raising and charge lowering char-
acter of the currents respectively, while the subscript L stands for “left” and
is used to denote the left-handed spinors, attesting the V-A nature of the
charged currents. The form of the Dirac γ-matrices depends on the repre-
sentation chosen to state them. In the Dirac-Pauli representation they have
the following form:
γ0 =
(I 0
0 −I
), γ =
(0 σ
−σ 0
), γ5 =
(0 I
I 0
). (1.4)
Introducing a two-dimensional form for the previous spinors
χL =
(ν
e−
)L
, (1.5)
along with the step-up and step-down operators τ± = 12(τ1 ± iτ2), where
τ+ =
(0 1
0 0
), τ− =
(0 0
1 0
)(1.6)
and the τ1,2 are the spin Pauli matrices, the two charged currents can be
rewritten as
J+µ (x) = χLγµτ+χL , (1.7)
4
J−µ (x) = χLγµτ−χL. (1.8)
Supposing a SU(2) group structure for the weak current, a neutral one
of the same form can be introduced
J3µ(x) = χLγµ
1
2τ3χL =
1
2νLγµνL −
1
2eLγµeL . (1.9)
Nevertheless, it can be noticed that the last one cannot be identified with
the weak neutral current, whose costumary definition is
JNCµ (q) =
(uqγµ
1
2(cqV − c
qAγ
5)uq
), (1.10)
because in general the neutral current JNCµ , unlike the charged ones that are
pure V-A currents in which cV 6= cA, has a right-handed component. Just
for trying to solve this puzzle and attempting to save the SU(2)L simmetry
supposed for the neutral currents, it can be reminded that the electromag-
netic current has both right- and left-handed components. For example, the
electromagnetic current for an electron can be written as
jemµ (x) = −eγµe = −eRγµeR − eLγµeL. (1.11)
Including the coupling costant e omitted until now, the last equation
becomes
jµ ≡ ejemµ = eψγµQψ, (1.12)
where Q is the charge operator and it can be considered the generator of
the group U(1)em simmetry group of electromagnetic interactions. It can be
noticed that, even if the the two neutral currents JNCµ and jemµ do not respect
the SU(2)L simmetry, these two combinations do have definite transforma-
tion properties under this group and allow us to complete the weak isospin
triplet J iµ, keeping the jYµ (where Y stands for hypercharge) unchanged un-
der SU(2)L transformations. As the operator charge Q generates the sym-
metry group U(1)em, the hypercharge operator Y generates the symmetry
group U(1)Y and so, including the electromagnetic interactions, the symme-
5
try group we are dealing with has become SU(2)L ×U(1)Y . That is why we
can say that, using this approach, we unified the electromagnetic and the
weak interactions.
This theory was proposed for the first time by Glashow in 1961 and later
modified by Weinberg and Salam just to include the vector bosons W± and
Z0. The assumption made at this point is that, as in QED the interactions
are based on photon exchange, the electroweak interactions are based on
the exchange of massive vector bosons and just as electromagnetic current is
coupled to the photon, the electroweak currents are coupled to vector bosons
W± and Z0. The electroweak interaction can be written as
− ig(J i)µW iµ − i
g′
2(jY )µBµ, (1.13)
where W iµ is an isotriplet of vector fields, whose components W 1
µ and W 2µ are
connected by the relation
W±µ =
√1
2
(W 1µ ∓ iW 2
µ
), (1.14)
which describes massive charged bosons W+and W−, Bµ, along with W 3µ ,
is a neutral field, g is the coupling constant by which these vector fields are
coupled to the weak isospin current J iµ and Bµ is a vector field coupled to
the weak hypercharge current jYµ
with the coupling constant g′/2.
1.2 Gauge Symmetries
As we pointed out at the beginning of this chapter, the interactions between
particles are ruled by gauge symmetries. We have already mentioned that
we are interested in local gauge symmetries rather than global ones. As
an example, it can be shown how the imposition of the gauge invariance
of the lagrangian connected to a particular kind of interaction, e.g. the
electromagnetic one, could bring to conditions on the gauge particles. In
this case, an electron can be described by a complex field ψ(x), and the
6
associated lagrangian
L = iψγµ∂µψ −mψψ (1.15)
is found to be invariant under global phase trasformation
ψ(x)→ eiαψ(x). (1.16)
It can be easily found that this is not the most general kind of invariance. To
make it more general, the phase factor α should assume different values in
different space-time points and the previous trasformation should be written
as
ψ(x)→ eiα(x)ψ(x). (1.17)
In this case, it could be easily demonstrated that the previous lagrangian
is no more invariant under (local) phase trasformation. To compensate for
this liability trying to preserve the goal of keeping the gauge invariance of
the lagrangian, this last can be modified using the “covariant derivative”
Dµ ≡ ∂µ − ieAµ instead of the simple derivative form ∂µ, where Aµ is a
vector field added just for the purpose. Therefore, demanding the local
phase invariance for the lagrangian, this last vector field, called gauge field, is
necessarily included. It can be identified with the physical photon field and
the new expression for the Quantum Electro-Dynamics (QED) lagrangian
becomes
L = ψ(iγµ∂µ −m)ψ + eψγµAµψ −1
2FµνF
µν , (1.18)
where last term is the kinetic energy corresponding to the vector field and it
is constructed from gauge invariant field strenght tensor
Fµν = ∂µAν − ∂νAµ (1.19)
for preserving its Uem(1) local gauge invariance. It can be noticed that no
mass term connected to Aµ can be found in the last expression, because it
would be prohibited by the gauge invariance. This bring us to the conclusion
that the photon, as a gauge particle, is massless within this theory.
Following the same criteria, the structure of Quantum Chromo-Dynamics
7
(QCD) can be deduced using local gauge invariance again, extending the
previous procedure and using the SU(3) group of the phase transformations
on quark colored fields instead of the U(1) one. From a physical point of view,
the starting point is a bit different from the previous QED case because this
time SU(3) is not an abelian group, since not all its generators Ta commute
each other. The Ta’s are a set of eight (a = 1, .., 8) linearly indipendent
traceless 3× 3 matrices, which satisfy the commutation relation
[Ta, Tb] = ifabcTc, (1.20)
where fabc are real constants and they are called the structure constants of
the group. If an invariance under local α phase tranformation of the free
lagrangian
Lq = qj (iγµ∂µ −m) qj, (1.21)
(where qj=1,2,3 are three color fields) is required, it can be written in the
following form
q(x)→ Uq(x) ≡ eiαa(x)Taq(x), (1.22)
where U is an arbitrary unit matrix. Imposing the SU(3) gauge invariance
on the Lagrangian and following steps very similar to the previous case, we
come to a new form for the lagrangian for interacting colored quarks q and
vector gluons Gµ
L = q (iγµ∂µ −m) q − g(qγµTaq)Gaµ −
1
4GaµνG
µνa , (1.23)
where Gµa represents the eight gauge fields introduced to preserve the invari-
ance of L, trasforming as
Gaµ → Ga
µ −1
g∂µαa, (1.24)
the last term is the kinetic energy term for each of the Gµa fields, and g is the
coupling costant associated to this interaction. Not even in the QCD case
we can find in the lagrangian a mass term and then we can deduce that, by
imposing the local gauge invariance, the gluons (as the photons previously)
8
are forced to be massless.
It can be worth underlying that the QCD kinetic energy term is not only
purely kinetic as in QED. It includes an induced self-interaction between
gauge bosons, accordingly to the non-Abelian nature of the group and, con-
sequently, of the theory. Therefore in the QCD theory, unlike QED, the
gauge particles (the gluons) interact each other exchanging color charge.
If we want to apply the same procedure for the electroweak interactions, we
have just to keep in mind that the gauge bosons which mediate those interac-
tions are massive and then the procedure to get a lagrangian which includes
a mass term will be different. It can be seen through calculations that pre-
serving the lagrangian gauge invariance is not just an option, because, if
we do not take it into account, unrenormalizable divergences will appear in
the propagators and the theory would become physically meaningless. The
mechanism by which the massive bosons could be included without breaking
the gauge invariance is called Spontaneous Symmetry Breaking.
1.3 Electroweak Spontaneous Symmetry Break-
ing: The Higgs Mechanism
Let us consider the simplest form for a lagrangian
L = T − V =1
2(∂muφ)2 −
(1
2µ2φ2 +
1
4λφ4
)(1.25)
in which φ describes a scalar field. Skipping the trivial case for µ2 > 0 which
describes a scalar field with mass µ, we can focus on µ2 < 0 case. In the
previous lagrangian the relative sign of the φ2 term and the kinetic one is
positive, determining a mass term 12µ2φ2 with the “wrong” sign. This time,
the potential V has two minimum values
φ = ±v with v =√−µ2/λ. (1.26)
9
Applying perturbative expansions around these two classical minima, the
field φ could be written in the form
φ(x) = v + η(x), (1.27)
where η(x) is the quantum fluctuation around the minimum +v. Considering
that translating the field φ to φ = +v does not involve any loss of generality,
we can substitute the last relation in the lagrangian obtaining
L′ = 1
2(∂µη)2 − λv2η2 − λvη3 − 1
4λη4 + const. (1.28)
The mass term λv2η2 associated to the field η has the correct sign. This
mass mη can be calculated comparing the last lagrangian with the one for a
scalar field
L =1
2(∂µφ)(∂µφ)− 1
2m2φ2 (1.29)
obtaining
mη =√
2λv2 (1.30)
Even if the two lagrangians L and L′ are completely equivalent (because the
choice φ(x) = v + η(x) does not change the physics), we have to choose the
second one. The use of L would imply that the perturbation series does not
converge because φ = 0 (the value around which the expansion would be
performed) is an unstable point. The correct way to proceed is expanding
L′ around a stable point (called vacuum point). This last lagrangian is the
one which offers the correct picture of the physics and the scalar particle
associated to η field is massive. We use to say that choosing one of the
possible vacuum point breaks the symmetry and so we refer to this mechanism
as Spontaneous Symmetry Breaking. Iterating an analogous procedure for a
complex scalar field φ = (φ1 + φ2)/√
2 and the relative lagrangian
L =1
2(∂µφ)∗(∂µφ)− µ2φ∗φ− λ(φ∗φ)2 =
=1
2(∂µφ1)2 +
1
2(∂µφ2)2 − 1
2µ2(φ1
2 + φ22)− 1
4λ(φ1
2 + φ22)2,(1.31)
10
which possesses a U(1) global gauge symmetry, and considering the same
case as before µ2 < 0 and λ > 0, we now have a circle of minimum points
(see Fig. 1.1) for the potential V (φ) such that
φ21 + φ2
2 = v2 v2 = −µ2/λ. (1.32)
Fig. 1.1: The potential V (φ) for a complex scalar field for the case µ2 < 0 eλ > 0.
A perturbative expansion of the lagrangian can be performed about the
vacuum point chosen in terms of η and ξ fields
φ(x) =
√1
2[v + η(x) + iξ(x)] . (1.33)
The lagrangian then becomes
L′ = 1
2(∂µξ)
2 +1
2(∂µη)2 + µ2η2 + const.+ cubic and quadratic terms in η, ξ
(1.34)
We can see that only the mass term connected to the scalar field η is in-
cluded and, on the contrary, the scalar particle related to ξ has no mass.
11
This massless scalar particle is called Goldstone boson. So, we can say that
spontaneously symmetry broken gauge theories are someway biased by the
presence of a massless scalar particle which is producted along with the mas-
sive particle we were looking for in attempting to find the way to generate
the mass for the gauge vector bosons. Obviously, the problem is that this
massless particle is unwanted because not observed.
Now we move to study the spontaneous symmetry breaking of a local gauge
transformation in U(1) group. Following the same procedure performed be-
fore, we have to impose the gauge invariance under the phase transformation
φ→ eiα(x)φ. (1.35)
The gauge invariant lagrangian can then be written as
L = (∂µ + ieAµ)φ∗(∂µ + ieAµ)φ− µ2φ∗φ− λ(φ∗φ)2 − 1
4FµνF
µν . (1.36)
Also in this case, we have to consider µ2 < 0, since we want to generate the
gauge boson masses through spontaneous symmetry breaking. Making the
same vacuum choice as before, we can translate the field φ without changing
the physics. The lagrangian then becomes
L′ =1
2(∂µξ)
2 +1
2(∂µη)2 − v2λη2 +
1
2e2v2AµA
µ
− evAµ∂µξ − 1
4FµνF
µν + interaction terms. (1.37)
It can be noticed that there is a mass term associated to the scalar field η
mη =√
2λv2, another one associated to the vector field Aµ, mA = ev, and
we can still observe the presence of the massless Goldstone boson associated
to ξ.
In attempting to eliminate this disturbing element, we can focus on the off-
diagonal term Aµ∂µξ present in L′ and try to understand if the particle
spectrum assigned it is correct.
Owing to the mass assigned to the vector boson associated to the Aµ field, the
polarization degrees of freedom are now three instead of two and this could
12
not just be due to a simple translation of the field. So it can be deduced
that the fields in the last lagrangian are not associated to distinct physical
particles.
What we will see is that this extra degree of freedom, due to the longitudinal
polarization, simply corresponds to the freedom to make a choice about the
gauge transformation. Indeed, to sidestep the problem we can notice that
we can write the vacuum chosen in a different form using the expansion at
the lowest order in ξ
φ(x) =
√1
2[v + η(x) + iξ(x)] '
√1
2(v + η)eiξ/v. (1.38)
From this last equality it can be deduced that a different set of real fields
h, θ, Aµ can replace the previous three ξ, η, Aµ in the previous lagrangian,
where
φ→√
1
2(v + h(x))eiθ(x)/v, (1.39)
and
Aµ → Aµ +1
ev∂µθ. (1.40)
The field h(x) is real, owing to the particular choice of θ field. Substituting
these transformations in the lagrangian, the new one obtained will be
L” =1
2(∂µh)2 − λv2h2 +
1
2e2v2A2
µ − λvh3 − 1
4λh4
+1
2e2A2
µh2 + ve2A2
µh2 + ve2Aµh−
1
4F µνµν (1.41)
In this last version of the lagrangian the Goldstone boson does not exist
anymore and only a massive vector boson Aµ and a massive scalar boson h
can be observed. The mechanism by which the Goldstone boson is turned
in the longitudinal polarization of the massive gauge particle is the so called
Higgs Mechanism.
Since in the previous section we found that the electroweak symmetry
group is the SUL(2)×UY (1) group, the last step will be extending the study
of the spontaneous simmetry breaking to the SU(2) gauge symmetry. Also
13
in this case, we will see another example of Higgs mechanism.
Considering φ as a SU(2) doublet of complex scalar fields
φ =
√1
2
(φ1 + iφ2
φ3 + iφ4
), (1.42)
the lagrangian can be written as
L = (∂µφ)†(∂µφ)− µ2φ†φ− λ(φ†φ)2 (1.43)
As done previously, we are interested in a lagrangian invariant under local
gauge transformation. This goal can be achieved using the covariant deriva-
tive
Dµ = ∂µ+ igτa2W aµ , (1.44)
where W aµ (x) are three gauge fields (a=1,2,3), the τ ’s are the SU(2) group
generators introduced in the first section, and αa(x)’s are three parameters
related to the phase transormation. Under an infinitesimal gauge transfor-
mation, the W aµ (x) fields transform as
Wµ →Wµ −1
g∂µα−α×Wµ. (1.45)
Considering that, under this sort of transformation, the field φ transforms as
φ(x)→ (1 + iα(x) · τ/2)φ(x), (1.46)
the lagrangian 1.43 becomes
L =
(∂µφ+ ig
1
2τ ·Wµφ
)†(∂µφ+ ig
1
2τ ·W µφ
)− V (φ)− 1
4Wµν ·W µν ,
(1.47)
where
V (φ) = µ2φ†φ+ λ(φ†φ)2 (1.48)
14
and the last term is the kinetic energy of the gauge fields with
W µν = ∂µWν∂νWµ − gWµ ×Wν . (1.49)
If µ2 < 0 and λ > 0, it can be seen that the potential V (φ) has its minimum
at a value of |φ| such that
φ†φ ≡ 1
2(φ2
1 + φ22 + φ2
3 + φ24) = −µ
2
2λ. (1.50)
By choosing a particular minimum value of the potential about which the
field φ(x) can be expanded
φ1 = φ2 = φ4 = 0, φ32 = −µ
2
λ≡ v2, (1.51)
the spontaneous symmetry breaking is now applied to SU(2) group. We can
now follow a procedure analogous to the previous case. The fluctuations
about another particular value of the vacuum
φ0 =
√1
2
(0
v
), (1.52)
whose expansion φ(x) about this value is
φx =
√1
2
(0
v + h(x)
), (1.53)
can be parametrized using four real fields θ1, θ2, θ3, and h, so that the field
φ can be written as follows
φ(x) = eiτ ·θ(x)/v
(0
v+h(x)√2
), (1.54)
Studying this case for small pertubations it can be observed that the four
fields are totally independent and that, choosing this particular value for
vacuum, makes the lagrangian locally SU(2) invariant.
15
Operating a gauge choice, we can impose θ1(x), θ2(x), θ3(x) = 0 (related
to the massless Goldstone boson) and so the only scalar field remained is
the Higgs field h(x). Inserting the value of the vacuum φ0 in the lagrangian
the three gauge boson masses can be determined. It can be said that the
Higgs mechanism, in this case, allows the gauge fields “to eat” the Goldstone
bosons becoming massive.
The Higgs Mechanism allow us to bypass the presence of massless particles
in the lagrangian, enabling us to obtain a massive gauge boson and the Higgs
boson. Nevertheless, it must be noticed that one more problem still remains:
obtaining a theory in which the weak bosons are no more massless particles
preserving the renormalizability of the theory.
1.4 Renormalizability of the Standard Model
In the previous section we pointed out that the S.M. of the electroweak
interactions has been built starting from a gauge theory. It includes four
gauge fields, whose associated particles are the massless photon and the three
massive bosons W± and Z0. The aim of this section is just to highlight that
such a theory is renormalizable and so it does not contain any unmanageable
divergence in it.
1.4.1 The Higgs Field Choice
It has been shown that in order to generate particle masses in a gauge in-
variant way we have to use the Higgs mechanism which enables us also to
remove massless scalar particle physically not existing. This mechanism can
be reformulated so that the bosons W± and Z0 are massive, making sure that
the photon remains massless. For this purpose, it can be observed that the
complete expression of the SM lagrangian is composed of several contributes.
One of them is SU(2)×U(1) gauge invariant lagrangian that can be written
as follows
L2 =
∣∣∣∣(i∂µ − gT ·Wµ − g′Y
2bµ
)φ
∣∣∣∣2 − V (φ), (1.55)
16
where the field φ has four scalar components φi.
Repeating the usual steps, for keeping 1.55 invariant under gauge transfor-
mation, we can say, making the simplest choice, that the fields φi must belong
to an isospin doublet with Y = 1:
φ =
(φ+
φ0
)with φ+ ≡ (φ1 + iφ2)/
√2, φ+ ≡ (φ1 + iφ2)/
√2. (1.56)
This is the model originally established by Weinberg in 1967. In order to
trigger the Higgs mechanism, we can use the expression 1.48 for the potential,
always considering only the case µ2 < 0 and λ > 0. The vacuum value
choosen is
φ0 ≡√
1
2
(0
v
). (1.57)
This choice can be justified by the fact that, if φ0 is left invariant under a
subgroup of gauge transformation, the gauge bosons associated to this group
will be kept massless while generating a mass for the corresponding gauge
boson. In this case φ0, being neutral, is invariant under Uem(1) trasformation,
because, for its generator Q, we can write the equation
Qφ0 = 0, (1.58)
where Q can be evaluated by the Gell-Mann-Nishijima relation
Q = T 3 +Y
2(1.59)
and T = 1/2, T 3 = −1/2.
So the corresponding symmetry remains unbroken, ensuring the photon to
be massless. The other three generators T and Y do not satisfy a rela-
tion like 1.58 and the symmetry breaking allows the mass generation for the
corresponding bosons.
17
1.4.2 Standard Model free parameters: Gauge Boson
Masses, Fermions Masses
The gauge bosons and fermions masses could be obtained just substituting
the φ0 chosen in the corresponding term of the SM full lagrangian and com-
paring the mass term with the one expected for a charged boson and for a
fermion respectively. For the gauge boson masses we have
MW =1
2vg. (1.60)
By considering the off-diagonal term of the lagrangian, we can also write the
expression of the physical fields Zµ and Aµ
Aµ =g′W 3
µ + gBµ√g2 + g′2
withMA = 0 (the photon is massless) (1.61)
Zµ =gW 3
µ − g′Bµ√g2 + g′2
withMZ =1
2v√g2 + g′2 (the Z boson is massive). (1.62)
Using the relation correlating g and g′
g′
g= tanθW , (1.63)
where θW is the Weinberg or weak mixing angle, and substituting it into 1.61
and 1.62, we haveMW
MZ
= cosθW , (1.64)
where the difference between the MW and MZ values is due to the the mixing
between W 3µ and Bµ in the off-diagonal term of the lagrangian.
It can be stressed that the only prediction of the SM is about the ratio
between the vector bosons MW and MZ expressed in 1.64, along with the
parameter ρ
ρ ≡ M2W
M2Zcos
2θW. (1.65)
18
Using analogous procedures, we can obtain the electron mass
me =Gev√
2, (1.66)
where Ge is arbitrary and so the electron mass is not predicted by the SM.
Moreover, examining the gauge invariant term which generats the electron
mass
L3 = −meee−me
veeh, (1.67)
where e belongs to the doublet ( ν, e )L, we can find that there is an inter-
action term which couples the Higgs scalar to the electron.
Since v is fixed (v = 246 GeV), we can notice that this coupling is very
small. Again, iterating the same steps, it can be found that also the quark
masses depend on the arbitrary coupling constants called Gu,d and so, like
me, cannot be predicted.
The diagonal form of the quark Lagrangian can be written as
L4 = −middidi
(1 +
h
v
)−mi
uuiui
(1 +
h
v
), (1.68)
where u and d belong to the quark doublet ( u, d )L, and mu and md are
the masses of up and down quark respectevely.
It can be observed that, also in this case, the Higgs coupling to the quarks is
proportional to their masses. This is another feature that could be considered
a prediction of the SM.
In addition to that, analyzing the potential 1.48, we can get the following
expression for the Higgs mass
m2h = 2v2λ. (1.69)
To find the upper and lower limits on mh, it can be noticed that it depends on
λ and, along with the bosons and the fermions masses, it is a free parameter
of the theory. Due to the need to make a perturbative expansion, λ could
not be very large, and so also the Higgs mass has not to be so high. In
19
particular, the upper limit for mh can be a few hundred GeV (up to mh < 1
TeV) . For the lower theoretical limits, based on correction to loop diagrams,
it has been found that m > 10 GeV [26]. Finally, it can be commented
that light fermions (electrons, u and d quarks in protons and neutrons) are
the most experimentally accessible particles. Since the Higgs boson has the
property of coupling to fermions in proportion to their mass, its discovery
turned out to be very difficult in the past.
1.4.3 Renormalization
The renormalizability of the SM theory can be observed in a more direct way
just studying the cross sections of the interactions we are interested in. For
example, the cross section of a neutrino-electron scattering (Fig. 1.2) can be
written as
σ(νee→ νee) =G2s
π, (1.70)
where s is the center of mass energy squared, and so if s → ∞ the cross
section will diverge.
Fig. 1.2: The Feynman diagram for the e− ν scattering
When the W charged boson is included in the theory, it can be demon-
strated that the divergence for high values of s is removed and the corre-
sponding cross section will be
σ(νee→ νee) =G2M2
W
π. (1.71)
Unfortunately, introducing the W boson, other diagrams have to be consid-
20
ered (see Fig. 1.3), whose corresponding cross section is
Fig. 1.3: The Feynman diagram for the divergence introduced with W boson.
σ(νee→ νee) =G2s
3π. (1.72)
It is quite evident that this contribute diverges at high values of s as well.
We can now observe that this last deficiency can be removed just by consider-
ing the contribution of the neutral current to νeW−. However, in other cases,
Fig. 1.4: The Feynman diagram for the νeW− scattering contribution
considering neutral currents do not delete the divergences that can appear
in the cross sections. For example we can consider the charged W bosons
scattering. In this case, it can be seen that the corresponding cross section
diverges as s2/M4W and the introduction of Z0 vector bosons exchange will
cause only that the cross section will diverge proportionally to s. To com-
pletely eliminate the divergence, the scalar Higgs particle must be introduced,
21
Fig. 1.5: The Feynman diagram for charged W bosons scattering.
adding a contribution like that in Fig. 1.6.
Fig. 1.6: The Feynman diagram contribution of the Higgs to WW scattering.
So we can say that the Higgs introduction allows us to ensure the renor-
malizability of the S.M. theory.
1.4.4 The Final S.M. Lagrangian
Finally, we can summarize the terms which compose the final SM lagrangian
LSM = L1 + L2 + L3 + L4 (1.73)
where L1 is the contribution of W±, Z and γ kinetic energies (and self interac-
tion), L2 is the contribution of fermions kinetic energies and their interactions
with W±, Z and γ, L3 is the contribution coming from W±, Z, γ and Higgs
masses (and couplings) and L4 is the contribution of fermions masses (and
22
Chapter 2
The Large Hadron Collider
and the CMS Detector
In the previous chapter, it has been pointed out that the Higgs particle is not
easy to detect just because of its peculiar feature of coupling with fermions
proportionally to their masses. In order to produce heavier fermions, which
couple stronger with the Higgs, or igniting its production, a large amount
of energy is required. For this purpose several particles accelerators and
colliders have been projected. LHC (Large Hadron Collider) is one of these
giant machines which hold the responsability of discovering new particles.
The Higgs boson is one of them.
2.1 The Large Hadron Collider at CERN
The CERN (European Organization for Nuclear Research) was established in
1954 as the world’s largest particle physics laboratory. The acronym CERN
originally stood, in french, for Conseil Europen pour la Recherche Nuclaire
(European Council for Nuclear Research), which was a provisional council for
setting up the laboratory, established by twelve European countries in 1952.
It is located in the northwest part of Geneva, on the franco-swiss border, and
currently the organization includes twenty European member states. One of
the CERN main function has been to provide the particle accelerators and
other infrastructures needed for high-energy physics research. Since its birth,
25
many experiments have been built at CERN by international collaborations
but, at present, most of the activities at CERN are directed towards operating
the new Large Hadron Collider (LHC), and the experiments for it. The LHC
[16, 17] represents a large-scale worldwide scientific cooperation project. It
is placed in a tunnel located approximately 100 metres underground, in the
region between the Geneva airport and the nearby Jura mountains. This
tunnel was previously occupied by the LEP (The Large Electron-Positron
Collider) experiment, which also made important headway in hunting for the
Higgs boson. It was closed down in November 2000. The LHC inherited from
LEP some advanced devices as the Proton Synchrotron (PS) and the Super
Proton Synchrotron (SPS) accellerator systems (fig.2.1).
Fig. 2.1: The LHC accelerator complex.
The acceleration of protons starts from a linear accelerator (LINAC) that
injects the protons to the Proton Synchrotron (PS), which accelerates them
to 25 GeV. In the following stage, the Super Proton Synchrotron (SPS)
accelerates the beams to 450 GeV and then injects them into the LHC ring.
26
The main experiments ATLAS, CMS, ALICE and LHCb, are located at the
four interaction regions. Two of them, CMS and ATLAS, are particulary
focused on the Higgs boson search within the SM context and on physics
beyond it. LHC has been designed for two kinds of collisions: collisions of
protons, and collisions of heavy ions.
2.1.1 Performance Goals
The LHC was designed to investigate the scalar sector, and the physics be-
yond the Standard Model in case of the failed discovering of the Higgs boson.
The number of events per second of a given physics process is related to the
cross section1 of the corresponding process, via the luminosity L of the ma-
chine, by the following relation
N = Lσ. (2.1)
The relevant events for physics searches, such as Higgs physics and physics
beyond the Standard Model, are predicted to have a quite low production
cross sections in proton-proton collisions. Fig. 2.2 shows that the cross sec-
tion for the production of a Higgs boson is several orders of magnitude smaller
than the total inelastic cross section. Besides, it increases significantly more
than the other ones with the center-of-mass energy of the collisions. That is
the reason why, for reaching the expected high researched event rate, both
the collision luminosity and the center-of-mass energy must be as high as
possible. For the LHC the choice focused on a very high collision luminos-
ity. The nominal center-of-mass energy for LHC collisions is√s = 14 TeV (7
TeV per beam), and the nominal peak luminosity is L = 1034 cm−2s−1 for the
CMS and ATLAS experiments. For these values (see the right axis on Fig.
2.2), a Higgs boson with a mass of 500 GeV/c2 would be produced approx-
imately every 100 s. Since LHC is a proton accelerator with a constrained
circumference, the maximal energy per beam is related to the strength of
1In particle physics, the cross section is used to express the normalized rate or prob-ability of a given particle interaction. It has the dimension of a surface and is usuallyexpressed in barns (b): 1b=10−28m2.
27
the dipole field that maintains the beams in orbit. A high technology global
magnet system allows to reach the nominal LHC beam energy of 7 TeV. The
system uses a total of about 9600 magnets.
The 1232 dipole magnets use niobium-titanium (NbTi) cables. By pumping
superfluid helium into the magnets, they are brought to a temperature of 1.9
K. For this purpose, a total of 120 t of superfluid helium is used. At that
temperature, the dipoles are in a superconducting state and a field of 8.33 T
can be provided. Such a magnetic field is necessary to bend the 7 TeV beams
around the 27-km ring of the LHC. Among the other magnets, quadrupoles
play a major role at collision points: they are used to focus the beam, and
maximize the probability of collision.
The very high LHC design luminosity implies many constraints on the pro-
ton beam parameters. The nominal luminosity can be reached with a num-
ber of bunches per beam nb = 2808 and a number of prototons per bunch
Nb = 1.15 · 1011. Such a high beam intensity could not be reached with
antiproton beams, hence a simple particle-antiparticle accelerator collider
configuration cannot be used at LHC.
The LHC has therefore been designed with two separate rings. The common
sections are located at the insertion regions, which are equipped with the
experimental detectors.
The configuration is presented in Fig. 2.3. A summary of the machine pa-
rameters [33] is given in Tab. 2.1. The numbers indicated correspond to the
nominal values.
In addition to the previously mentioned parameters, the luminosity lifetime
is an important parameter at LHC and colliders in general. The luminos-
ity tends to be reduced during a physics run, because of the degradation of
intensities and emittances of the circulating and colliding beams.
2.1.2 LHC Collision Detectors
Reaching the high luminosity values previously discussed imposes tight con-
straints on the design of the detectors. Under nominal conditions, the LHC
29
Cironference 26.659 kmCenter-of-mass energy (
√s) 14 TeV
Nominal Luminosity (L) 1034 cm−2s−1
Luminosity lifetime 15 hrs.Time between two bunch crossings 24.95 nsDistance between two bunches 7.48 mLongitudinal max. size of a bunch 7.55 cmNumber of bunches (nb) 2808Number of protons per bunch (Nb) 1.15× 1011
beta function at impact point (β?) 0.55 mTransverse RMS beam size at impact point (σ?) 16.7 µmDipole field at 7 TeV (B) 8.33 TDipole temperature (T) 1.9 K
Tab. 2.1: List of the nominal LHC parameters, for proton-proton collisions,relevant for the detectors.
can produce 109 inelastic collision2 events per second. The corresponding
bunch crossing rate is 40 MHz (i.e. a bunch crossing spacing of 25 ns), with
∼ 20 collisions events expected per bunch crossing. A significant number of
inelastic collisions are so expected to occur at each crossing (corresponding to
∼ 1000 particles per bunch), due to the large number of protons per bunch.
To distinguish one event from another, a high detector granularity is manda-
tory. Besides, for a good pile-up control, the detectors must provide a fast
response (i.e. a response concentrated in a single bunch spacing) along with a
good time resolution (few ns) in order to distinguish the events coming from
two consecutive bunch crossings. The limit where two consecutive signals
start to overlap is called out-of-time pile-up and it affects the shape of the
signal.
Considering the elevated number of events per second, which can be hardly
handled even by the very high perfomance facilities of the LHC, it must be
noticed that events can be recorded only at a rate of ∼ 300 Hz. Hence, an
online selection system, which could determine if an event is worth to be
considered, is mandatory. In this way, an event reduction of seven orders of
magnitude can be performed.
2An inelastic collision is the collision of two partons, one from a proton of the first beamand one from a proton of the second beam. The energy of each parton is an unknownfraction of the proton energy and so it can be observed that the collision energy is not afixed parameter.
31
2.2 The Compact Muon Solenoid (CMS) De-
tector
2.2.1 Coordinate System
The coordinate system of the CMS detector is illiustrated in Fig.2.4. The
Fig. 2.4: The CMS coordinate system.
detector has a cylindrical shape around the beam axis (z axis). As origin,
the nominal collision point inside the experiment is considered. The x axis
points horizontally towards the center of the LHC, and the y axis points
vertically upwards, while the z (longitudinal) axis, horizontal and colinear to
the beam trajectory, points to the direction of the vector perpendicular to xy
plane, considering the anticlockwise rotation of the x axis towards the y axis.
In the transverse (x-y) plane, the azimuthal angle φ is measured from the x
axis and the radial coordinate is denoted r. The polar angle θ is measured
from the z axis. The pseudorapidity variable η can be defined as
η = −ln tan(θ/2). (2.2)
32
A particle trajectory direction at production point is then described by the
coordinates (η, φ). Two parts of the subdetectors can be considered relying
on the cylindrical shape of the detector:
1. the ‘barrel’, which corresponds to the central cylindrical region
2. the ‘endcaps’, which are two disks at the extremities closing the detector
along the beam axis.
The parton momentum, before the collision, is expected to be longitudinal
(along the beam axis). Being the transverse momentum of each parton neg-
ligible and the total transverse momentum conserved during an interaction,
the transverse momentum of the collision is expected to be negligible too.
2.2.2 The CMS detector structure and the Magnet
The CMS detector is a multi-purpose detector. Its lenght is 21.6 m and it has
a diameter of 14.6 m. It contains two calorimeters: an electromagnetic one
and a hadronic one. In the first, electromagnetic particles are stopped and
measured, while hadronic particles are stopped in the second but measured
in both of them. The trajectories of all the charged particles are measured
by an inner tracking device. Charged particles crossing both the calorimeters
(i.e. muons) are measured instead by an outer tracking device.
The tracking devices are exposed to a magnetic field which curves the trajec-
tories of charged particles. As reminded by its denomination, CMS detector
has been designed [9] paying a particular attention to muons: their energy
is measured through their track curvature information combined in both the
inner and the outer tracking devices. The charge and the transverse momen-
tum (pT ) measurements are performed by using the curvature radius of the
trajectory that is inverse proportional to the pT .
For the Higgs boson search in the decay channel H → ZZ → 4µ, an ex-
tremely precise measurement of the four-lepton mass is mandatory, so a pre-
cise measurement of the muon momentum is necessary, at least for pT values
up to 100 GeV/c and, along with it, a precise measurement of the muon track
curvatures. Hence, a large bending power in the tracker region is mandatory.
33
For this purpose, a 4 T superconducting solenoid is used. The tracker, and
both calorimeters are located inside the solenoid, and exposed to its longitu-
dinal magnetic field. The magnetic flux is returned through a 10000 t iron
yoke comprising 5 wheels and 2 endcaps, composed of three disks each. Four
muon stations are included along the detector’s length. The geometry of the
CMS detector [44] is illustrated in Fig. 2.5. The subdetectors and the online
Fig. 2.5: A perspective view of CMS detector.
selection (‘trigger’) system are presented in the next sections.
2.2.3 Inner Tracking System
The CMS tracker is a fundamental tool for the charge and momentum mea-
surements of charged particles. It has a length of 5.8 m and a diameter
34
of 2.5 m around the interaction point. It covers a pseudorapidity range of
|η| < 2.5. Since it is located directly around the collision point, the tracker
material must be very resistant to radiation. The very fine granularity in
the innermost part is an essential feature for the identification of the differ-
ent vertices in a bunch crossing. While the primary vertex corresponds to
the interaction point of the collision, secondary vertices can indicate other
interactions that can occur during the same bunch crossing (pile-up), or the
presence of long-live particles3. A tracker design entirely based on silicon
detector technology has therefore been chosen. However this very powerful
system has some disadvantages:
• it implies a high density of detector electronics, which requires an effi-
cient cooling system;
• the particles coming from collisions may interact with this dense ma-
terial while crossing the tracker detector. It implies a complicated
recostruction procedure (see section 2.3) and a loss in the detector ef-
ficiency.
The high hit occupancy, which imposes constraints to the detector granular-
ity, is the result of the high number of particles crossing the tracker. The
CMS tracker is made of two kinds of silicon sensors:
1. silicon pixels, which constitute the pixel detector in the most inner
part;
2. silicon strips, which constitue the rest of the tracker.
The outer tracker region is made of thicker silicon sensors since the spatial
density of tracks decreases far from the interaction point.
In Fig. 2.6 a schematic cross section of the CMS tracker is presented. Each
line represents a detector module. The double lines indicate back-to-back
modules which deliver stereo hits. The pixel detector contains barrel and
3Leptons coming from late decays indicate a background event in the H → ZZ(∗) → 4`,where ` = e, µ
35
endcap modules; the silicon strip detector contains two collections of bar-
rel modules, the Tracker Inner Barrel (TIB) and the Tracker Outer Barrel
(TOB), and two collections of endcap modules, the Tracker Inner Discs (TID)
and the Tracker EndCaps (TEC). The tracker structure contains several parts
Fig. 2.6: Schematic cross section through the CMS tracker.
of central barrel layers and are completed by endcap discs on both sides. The
pixels have to:
• provide the three first hits of the track of a primary particle;
• allow a precise measurement of a particle impact parameter (see chapter
4 subsection 4.2.4);
• allow secondary vertices identification.
The silicon tracker is coupled to a cooling system made of liquid Perfluoro-
hexane (C6F14) and operate only at temperature below −10◦C to prevent
thermal risks. The transverse momentum resolution varies according to the
tracker modules crossed. A ∼1% resolution in the most central region, rais-
ing to ∼3% for high pseudorapidity values, is expected in the pT range of W
and Z boson decays (pT ∼ 40 GeV/c).
36
2.2.4 Electromagnetic Calorimeter
The Electromagnetic Calorimeter (ECAL) [13] has been calibrated according
to the requirements of the H → γγ search.
It is the only subdetector to provide information about photons. For an ac-
curate di-photon mass reconstruction (∼ 0.1 GeV/c2), a very precise position
and energy measurement is provided by the ECAL.
The ECAL is also of primary importance for the electron reconstruction in
a Higgs boson analysis in a multi-lepton final state. The combination of its
information with the one from the tracker can ensure a very precise mea-
surement of electron position and momentum and a significant background
removal.
A good segmentation is essential to distinguish the energy deposit shape of
an electromagnetic particle from the one belonging to a hadronic particle.
The CMS ECAL is a hermetic and homogeneous calorimeter, that covers
the rapidity range |η| < 3 . It is made of lead tungstate (PbWO4) crystals,
mounted in a barrel (|η| < 1.479) and two endcaps (1.479 < |η| < 3.0).
A longitudinal view of the detector is shown in Fig. 2.7. The crystals are
followed by photodetectors that read and amplify their scintillation.
Avalanche photodiodes (APDs) are used in the barrel. In the endcaps a very
high resistivity to radiation and to the magnetic field is mandatory.
In the forward region the pion population becomes particularly important,
and the π0 decaying into two photons is hard to distinguish from a single
photon. Hence, a better photon identification is ensured by a preshower de-
tector installed in front of the ECAL endcaps (see Fig. 2.7).
The preshower is a 20-cm thick sampling device, made of two parts located
at both ends of the tracker, in front of the ECAL endcaps, covering the pseu-
dorapidity range 1.653 < |η| < 2.6 (see Fig. 2.8).
Electromagnetic showers from incoming electrons and photons are initiated
by its absorber, made of lead radiators. Two layers of silicon strip sensors
are positioned, orthogonally oriented, behind each radiator. These sensors
measure the deposited energy and the transverse shower profiles for better
identication of electromagnetic particles.
37
Fig. 2.7: Longitudinal view of part of CMS electromagnetic calorimeter show-ing the ECAL barrel and an ECAL endcap with the preshower in front.
An electron or a photon emitted in the direction of the preshower, deposits
5% of its energy in the preshower, and the rest in the ECAL endcap.
The choice of the lead tungstate crystals relies on some constraints as-
signed to the detector:
• the compactness of the ECAL, needed to include both calorimeters
inside the magnet;
• the good separability of electromagnetic showers due to the smallness
of Moliere radius4 (2.2 cm) of lead tungstate;
• the scintillation decay time of the crystals, which is fast enough relying
on the LHC necessities.4The Moliere radius Rµ is a characteristic costant of a material, giving the scale of
the transverse dimension of the fully contained electromagnetic showers initiated by anincident high energy electron or photon. It is defined as the mean deflexion of an electronof critical energy after crossing a width 1X0, where X0 is defined as the radiation lenght,i.e. the average distance covered by an electron in a material through which it loose afraction of its energy equal to 1/e. A cylinder of radius Rµ contains on average 90% ofthe shower’s energy deposition.
38
Fig. 2.8: Layout of the CMS ECAL showing the arrengement of crystalmodules, supermodules and endcaps, with preshower in front.
The ECAL barrel is made of 36 identical Supermodules, each covering
half the barrel length (−1.479 < η < 0 or 0 < η < 1.479), with a width of
20◦ in φ . Each Supermodule is composed by four Modules in the η direction
(see Fig. 2.8). The presence of acceptance gaps, called cracks, between the
Modules, makes the energy reconstruction more complicated. At η = 0 a
larger crack is present between Supermodules, and an even larger one marks
the barrel-endcap transition.
Each ECAL endcap is made of two semi-circular plates called Dees (Fig.
2.8). Small cracks are also present between the endcap Dees, but they can
be considered negligible.
The energy loss can be measured by comparing the energy measured in the
39
ECAL with the momentum measured in the tracker on electrons with little
bremsstrahlung, considering that the difference is due to energy loss in cracks.
To cancel these losses a recovery method has been conceived, except for the
border corresponding to η = 0 and the barrel-endcap transition, where energy
losses are 5% and 10% respectively.
Finally, a quick focus on energy resolution has to be introduced. It has
been measured on one barrel supermodule, using incident electrons, during
a beam test in 2004 [40]. It is made of a stochastic, a noise and a constant
contribution: (σ(E)
E
)2
=
(2.8%√E
)+
(0.12%
E
)2
+ (0.30%)2. (2.3)
and the result is shown in Fig. 2.9. A resolution higher than 1% is achieved
Fig. 2.9: ECAL barrel energy resolution, σ(E)/E, as a function of electronenergy as measured from a beam test (see text). The points correspond toevents taken restricting the incident beam to a narrow (4 × 4 mm2) region.The stochastic (S), noise (N), and constant (C) terms are given.
40
for electrons of energy higher than 15 GeV; for 40 GeV electrons it is of 0.6%.
2.2.5 Hadron Calorimeter
The hadron calorimeter (HCAL) plays a major role in the detection of hadron
jets. It is located behind the Tracker and the Electromagnetic Calorimeter
(from interaction point of view). Its purpose is then to provide a sufficient
containment of the hadron showers. Moreover, a wide extension in pseudora-
pidity is mandatory to have a precise description of the total collision event,
allowing a reliable measurement of the missing transverse energy.
The importance of the HCAL from the point of view of a Higgs boson analy-
sis in a multi-lepton final state, is that it allows to distinguish electrons from
hadron jets, which can be mis-identified as leptons (see chapter 4, section
4.2.1). It is a sampling calorimeter.
Such as the ECAL, it is composed of a barrel part (HB) and an endcap part
(HE).
The HCAL Barrel covers the pseudorapidity range |η| < 1.3. It is limited in
radial dimension, between the outer extent of the ECAL and the inner extent
of the magnet coil (1.77 m < R < 2.95 m). Moreover, the HCAL is extended
outside the solenoid with a tail catcher called the outer calorimeter, HO, just
to ensure adequate sampling depth for |η| < 1.3.
The HCAL Endcaps cover a wide rapidity range: 1.3 < |η| < 3. The forward
hadron calorimeters (HF) are placed at 11.2 m from the interaction point
extend. They extend the pseudorapidity coverage down to |η| < 5.2. The
structure of the Hadron Calorimeter is illustrated in Fig. 2.10.
The HB effective thickness increases with polar angle (θ) as 1/ sin θ. It
results in 10.6 λI at η = 1.3, where λI is the radiation lenght5.
The HO uses the solenoid coil as an additional absorber equal to 1.4/ sin θ in-
teraction lengths and is used to identify late-starting showers and to measure
the shower energy deposited after HB. The material in the HCAL Endcaps
must resist to the radiation, and handle high counting rates.
5Nuclear interaction length is defined as the mean path length in which the energy ofrelativistic charged hadrons is reduced by the factor of 1/e as they pass through matter.
41
HF
HE
HB
HO
Fig. 2.10: Longitudinal view of the CMS detector. The locations of thehadron barrel (HB), the endcap (HE), the outer (HO) and the forward (HF)calorimeters.
Because of the magnetic field, the absorber must be made from a non mag-
netic material.
Finally, the HE has to fully contain hadronic showers. The calorimeter bar-
rel energy resolution (EB + HB + HO) has been measured on pions which
energy varies in a range of 3-500 GeV by test beams. It has been found to
be: (σ(E)
E
)=
(84.7%√
E
)⊕ 7.4%. (2.4)
It can be observed that the energy resolution is dominated by the HCAL
contribution.
2.2.6 The Muon System
The topology of the final state of H → ZZ → 4µ analysis give reasons for
the construction of a muon system with a wide angular coverage and no ac-
ceptance gap.
Muons are particularly easy to identify and distinguish from backgrounds
42
with CMS detector, thanks to the absorbing function played by the calorime-
ters.
The muon systems are divided into a cylindrical barrel section and two pla-
nar endcap regions. Less background, a low muon rate and a uniform 4-T
magnetic field, mostly contained in the steel yoke, is measured in the barrel.
A longitudinal view of the muon detectors can be found in Fig. 2.11.
Fig. 2.11: Longitudinal view of the muon detectors: DT, RPC and CSC.
Muon System Subdetectors
Drift tube (DT) chambers have been used. They cover the pseudorapidity
region |η| < 1.2. Chambers measuring the muon coordinate in the r − φ
bending plane are alternated with chambers providing a measurement in the
z direction. Each of the four stations contains four chambers of each kind.
The most relevant problem of this design is the presence of ‘cracks’, i.e. dead
efficiency spots between the chambers. It has been solved by the presence of
43
an offset of the drift cells between neighbor chambers.
The endcaps cover a region of higher rates. In this region the magnetic field
appears large and non-uniform.
Cathode strip chambers (CSC) are instead used to cover the pseudorapidity
region 0.9 < |η| < 2.4. Each of the four stations contains six layers of
chambers and anode wires.
The chambers are positioned perpendicular to the beam line and provide a
precision measurement in the r − φ bending plane, while the anode wires
provide measurements of the beamcrossing time of muons.
Other tools are included to reject non-muon backgrounds and to match hits
to those in the other stations and in the inner tracker.
A system of resistive plate chambers (RPC) has been added in barrel and
endcap regions, over a large portion of the pseudorapidity range (|η| < 1.6).
They consists of double-gap chambers, operated in avalanche mode to ensure
good operation at high rates.
Six layers are present in the barrel and three in each endcap. They produce
a fast response, with good time resolution but coarser position resolution
than the DTs or CSCs. They provide an independent trigger system with an
optimal time resolution. Moreover, they help to reduce ambiguities in track
reconstruction.
The muon momentum resolution is optimized by a high technology alignment
system, which measures the relative positions of the muon detectors along
with their positions respect with the inner tracker system.
2.2.7 Trigger
The Trigger system can be considered as the first event selection step. The
main feature of this step, which makes it different from the other selection
steps, is that it is not reversible. It indeed performs a fast selection of the
events which seem to be of interest for physics analysis among the huge
amount of those produced by LHC collisions.
This selection can drastically reduce the extremely high event rate (the LHC
nominal bunch crossing rate is ∼ 40 MHz) to a reasonable rate, more suit-
44
able for data recording (∼ 300 Hz). Obviously, all collision data must be
kept untill the trigger decision has been taken, so requiring a fast response.
To fulfill these requirements, a two-level trigger system has been designed.
The Level-1 (L1) Trigger is a hardware system made of largely programmable
electronics. It provides a first rate reduction to 100 kHz, scanning events
fastly in 3.2 µs. This timing constraint are satisfied considering coarse gran-
ularity objects from the calorimeters and from the muon system.
A positive L1 decision is converted in a transfer of the complete event infor-
mation to the next level: the High Level Trigger (HLT). Unlike the previous
one, the HLT is a software system which is based on algorithms of increasing
complexity that use the fine granularity of the event. So, the HLT decision
time is not a fixed value as the L1 trigger one. It may vary according to the
event, with a mean value of 50 ms.
In the case of the Higgs boson analysis in multi-lepton final state here pre-
sented, the trigger relies on events containing electron and muon signals. For
the Level-1 Trigger, an electron signature can be identified with a narrow
and highly energetic deposit in the ECAL, while a muon signature is based
on a track segment or a hit pattern in muon chambers.
The High-Level Trigger considers higher granularity objects, because it re-
constructs the total energy deposits in the calorimeters and muon tracks, and
combines them with the tracker and preshower information.
Level-1 Trigger
The Level-1 Trigger architecture is described in Fig. 2.12.
It is divided into two parallel trigger systems, one corresponding to the
calorimeters and the other to the muon chambers.
Each system is composed of a local, a regional, and a global part, then merged
into a Global Trigger for the final L1 decision.
The candidate categories of the Level-1 Trigger are:
• Muons, built in the Muon Trigger;
• Electrons/Photons (isolated and non-isolated: e− γ);
45
Fig. 2.12: Level-1Trigger Architecture.
• Central and forward Jets;
• Taus, built in the Regional Calorimeter Trigger;
• Total Transverse Energy (∑ET ), Missing Transverse Energy Emiss
T ,
Scalar Trasverse Energy Sum of all Jets (above a given threshold: HT ),
built in the Global Calorimeter Trigger;
Local Triggers
The local trigger creates coarse-granularity information . In the calorime-
ters, this information is a collection of Trigger Primitives.
Regional Triggers
The Regional Calorimeter Trigger collects the local information to build
Level-1 Trigger candidates, combining all the information of both calorime-
ters. A DT track finder and a CSC track finder collect the local DT and
46
CSC information to build Level-1 Trigger Candidates as tracks for the muon
trigger. The RPC trigger is directly regional. The four most relevant Candi-
dates of each category are sent to the Global Calorimeter Trigger or to the
Global Muon Trigger respectively. The regional summed transverse energy
is also sent to the Global Calorimeter Trigger by the Regional one.
Global Calorimeter Trigger and Global Muon Trigger
The Global Calorimeter Trigger has finally the task of sorting the Level-1
Trigger Candidates to send the four most relevant ones of each category to
the Global Trigger. It also calculates the summed ET and the EmissT infor-
mation of the event, as well as the scalar transverse energy sum of all jets
above a given threshold (HT). The Global Trigger riceives this information
as well. The Global Muon Trigger collects and compares the candidates from
the DT, CSC and RPC Triggers and combines them into four Muon Candi-
dates. It also uses some information from the Regional Calorimeter Trigger
for isolation considerations. The Global Trigger finally collects the informa-
tion about the four Muon Candidates.
Global Trigger
The Global Trigger collects the candidates produced by the Global Calorime-
ter Trigger and the Global Muon Trigger, and compares them to the Level-1
Trigger Menu. This menu is a list of Level-1 enabled triggers. If at least one
of the listed triggers is satisfied by a candidate collection, the Level-1 Trigger
response is positive and the fine granularity event information can be sent to
High-Level Trigger. The Level-1 Trigger also follows some rules to prevent
memory overload (e.g. L1 Trigger cannot accept two events separated by
only one single bunch crossing).
The trigger algorithms consist in a threshold applied to the highest ener-
getic candidate of each category. For background reduction, a combination
of triggers is often required.
47
High-Level Trigger
The higher and last level trigger step is the High-Level Trigger which builds
candidates corresponding to all kinds of reconstructed objects considered in
the offline analyses. The algorithms used are very similar to the previous
ones. Its inner sub-structure is made of several increasing complexity levels,
starting from Level 2.
The Level 2 starts generally with the Level-1 Trigger information, and builds
fine granularity objects around the Level-1 candidates, using only the infor-
mation from the calorimeters and the muon system. The tracker information
is also used, only when necessary, at the next 2.5 Level.
2.3 Lepton Reconstruction
2.3.1 Electron Reconstruction
The electron reconstruction [59] combines the information from the elec-
tromagnetic calorimeter (ECAL) and the silicon tracker. It starts by the
recostruction of clusters seeded by hot cells in the ECAL.
Electron seeds are then used to form superclusters (clusters of clusters) to
collect the electron energy radiated by bremsstrahlung in the tracker and
spread in φ by the solenoidal magnetic field and to initiate a track building
and a fitting procedure.
The superclusters are first preselected using a hadronic veto (defined by the
ratio H/E of the hadronic energy estimated by summing HCAL towers en-
ergy within a cone of ∆R = 0.15 behind the supercluster position over the
supercluster energy) and applying a 4 GeV cut on the supercluster transverse
energy.
The superclusters are also used to search for hits in the innermost tracker
layers which are used to accomplish the seeding of the tracks.
The ECAL driven seeding algorithm has been used. It has been optimised
for isolated electrons in the peT range relevant for Z or W decay, down to 5
GeV/c. For lower electron peT values the φ window used for the superclus-
ters becomes too small and the electrons which radiate lead to electron and
48
photon clusters separated by a distance greater than 0.3 rad (the maximum
limit) in the magnetic field.
Moreover, for electrons in jets, the energy collected in the superclusters could
include neutral contribution from jets so biasing the energy measurement
used to seed the tracks.
For these reasons, the driven seeding strategy has been complemented by
a tracker driven seeding algorithm. It can be illustrated with two extreme
cases:
• electrons which do not radiate energy by bremsstrahlung while crossing
the tracker;
• electrons which undergo a significant energy loss by bremsstrahlung.
In the first case, the electron creates a single cluster in the ECAL and its
track may be recostructed well enough by the standard Kalman Filter, which
is able to collect hits up to ECAL.
The track recostructed is then matched with a particle flow6 [25] cluster and
the ratio E/p of the cluster energy over the track momentum can be eval-
uated. If the value of this ratio is close to unity, the seed of the track is
considered as an electron seed.
Instead, in the second case, the Kalman Filter cannot follow the change of
curvature and a small number of hits belongs to the track. In this case,
the electron tracks are selected using the silicon tracker as a preshower and
evaluating the different characteristics of a pion track and an electron track
recostructed by Kalman Filter.
A merging procedure of the seeds of the two algorithms is then carried out so
keeping the track of seed provenance. It can be also noticed that the tracker
driven algorithm for non-isolated electrons brings, if applied, an efficiency
enhancement on isolated electrons too, in particular in the ECAL cracks re-
gions (η ' 0 and |η| ' 1.5) and as expected, at low peT values.
6The aim of the CMS particle flow event-reconstruction algorithm is to identify andreconstruct individually each particle arising from the LHC proton-proton collision, bycombining the information from all subdetectors. The resulting global event descriptionleads to an improved performance for the reconstruction of jets and for the identificationof electrons, muons, and taus.
49
The trajectories in the silicon tracker volume are recostructed using a dedi-
cated modelling of the electron energy loss and fitted with a Gaussian Sum
Filter, which relies on a modelling of electron radiative energy loss. The
seeding algorithm combines the information from pixel and TEC layers so to
get an efficiency gain in the forward region where the coverage by the pixel
layers is limited. To perform the selection, a matching between superclusters
and trajectory seeds built from hit pairs or triplets is required.
The electron momentum is estimated by combining the tracker and ECAL
mesurements. The electron candidates preselection is performed applying
loose cuts on track-cluster matching observables, so preserving a high effi-
ciency value while removing part of QCD background. To resolve ambiguous
cases (due to conversion legs of radiated photons) in which several tracks are
recostructed, a cleaning procedure is carried out.
The mis-identification arising from the early conversions of radiated photons
is coped with electron charge determination which is performed compar-
ing different charge measurement observables. Electrons are classified using
observables sensitive to the bremsstrahlung emission and showering in the
tracker material.
For the analysis presented here, the electron candidates have been required
to have transverse momentum peT larger than 7 GeV/c and a reconstructed
|ηe| <2.5.
The reconstruction efficiency for isolated electron is expected to be above
≈ 90% over the full ECAL acceptance, apart from some narrow ”crack” re-
gions.
The one for basic electron objects integrated over the acceptance rises to
reach ≈ 90% at pT = 10 GeV/c, and then more slowly to reach a plateau of
≈ 95% for peT = 30 GeV/c. The application of identification requirements on
top of the recostructed electron objects collection allows the enhancement of
the purity of the sample of electron candidates.
The electron objects are separated into classes according to the amount of
energy lost by bremsstrahlung processes. A series of different cuts are then
applied to each category.
The variables used, which are sensitive to bremsstrahlung processes, are the
50
fraction of radiated energy as measured from the innermost and outermost
state of the electron track and the ratio E/p between the supercluster energy
and the measured track momentum at the vertex. This procedure allows
to handle the non gaussian fluctuations induced on the ECAL and on the
tracker mesurements by the presence of material in the tracker.
Three different categories are defined with quite different measurement char-
acteristics and purity:
• “brem”;
• “lowbrem”;
• “badtrack”.
In addition, two others categories are defined to separate electron objects in
transition regions:
• ”pure tracker-driven objects”;
• ”crack objects”.
Subcategories are also defined for “brem”,“ lowbrem”, “badtrack” and “pure
tracker-driven” objects according to pseudorapidity regions (barrel and end-
cap), leading to a total number of nine categories. The cuts on each category
are applied just to optimize the signal to background ratio (s/b).
As previously mentioned, the shape of most of the discriminating variables
strongly depends on the transverse energy (ET ) of the electron, and so the
selection cuts are made ET -dependent.
The cuts are defined for the following variables:
• |∆ηin| = |ηsc − ηextrap.in |, where ηsc is the energy weighted position in η
of the supercluster and ηextrap.in is the η coordinate of the position of
closest approach to the supercluster position, extrapolating from the
innermost track position and direction;
• |∆φin| = |φsc−φextrap.in |, where ∆φin is a quantity similar to the previous
one but in azimuthal coordinates;
51
• Eseed/pin, where Eseed is the seed cluster energy and pin the track mo-
mentum at the innermost track position;
• H/E: ratio of energy deposited in the Hadronic Calorimeter directly
behind the ECAL cluster (H) and the energy of the electron superclus-
ter (E);
• σiηiη: supercluster η width taken from cluster shape covariance.
A list of all the cut values is presented in Table 2.2.
Electron charge mis-identification has been measured on 2010 data using Z
|∆ηin| < |∆φin| < Eseed/pin < H/E < σiηiη <
[EminT -Emax
T ] [EminT -Emax
T ] [EminT -Emax
T ] [EminT -Emax
T ]
”brem” EB [8.92-9.23]×10−3 [0.063-0.069] 0.65 [0.171-0.222] [1.16-1.27]×10−2
”lowbrem” EB [3.96-3.77]×10−3 [0.153-0.233] 0.97 [0.049-0.052] [1.07-1.08]×10−2
”badtrack” EB [8.50-8.70]×10−3 [0.290-0.296] 0.91 [0.146-0.147] [1.08-1.13]×10−2
”crack” EB [13.4-13.9]×10−3 [0.077-0.086] 0.78 [0.364-0.357] [3.49-4.19]×10−2
”brem” EE [6.27-5.60]×10−3 [0.181-0.185] 0.37 [0.049-0.042] [2.89-2.81]×10−2
”lowbrem” EE [10.5-9.40]×10−3 [0.234-0.276] 0.70 [0.145-0.145] [3.08-3.02]×10−2
”badtrack” EE [11.2-10.7]×10−3 [0.342-0.334] 0.33 [0.429-0.326] [0.99-0.98]×10−2
”crack” EE [30.9-62.0]×10−3 [0.393-0.353] 0.97 [0.420-0.380] [3.37-4.28]×10−2
”pure tracker-driven” [18.8-4.10]×10−3 [0.284-0.290] 0.59 [0.399-0.132] [4.40-2.98]×10−2
Tab. 2.2: The definition of cuts used in the electron identification for electronscategories in the barrel (EB) and in the endcaps (EE). Where a range isspecified the cuts are made ET -dependent between Emin
T = 10 GeV andEmaxT = 40 GeV.
events and a charge mis-ID of 0.004 ± 0.001 (0.028 ± 0.003) has been mea-
sured in the ECAL barrel (ECAL endcaps) in very good agreement with the
simulation and no significant pT dependency has been observed in the range
of on-shell Z boson decays.
The electron classification also allows the identification of electrons accom-
panied by low bremsstrahlung with smallest measurement error.
52
2.3.2 Muon Reconstruction
Muon detection and reconstruction [27] requires an excellent detection of
muons over the full acceptance of the CMS detector.
The muon recostruction is performed combining the information of the track-
ing and the calorimeter devices.
Three are the high level physics objects (particles travelling through the de-
tector) involved, depending on the muon track reconstruction step:
• stand-alone muons ;
• global muons ;
• tracker muons.
The reconstruction starts in the muon spectrometer with the reconstruction
of the hits positions in DT, CSC and RPC chambers.
A hit corresponds to a signal from a particle recorded by detector com-
ponents. So the signal is recostructed as individual points in space called
recHits. The hits in DT and CSC are then associated together to form ”seg-
ments” (track stubs).
The seeding procedure is then accomplished collecting and matching the seg-
ments. The seeds are so used to perform the actual track fit using also the
RPC hits. The reconstructed track that results in the muon spectrometer
is called stand-alone muon. The stand-alone muon tracks are then matched
with those from the silicon tracker, generating global-muon tracks.
The third high level object, the tracker muon, is recostructed with an al-
gorithm which starts from the silicon tracker tracks and then requests the
matching with segments in the muon chambers. In the studies performed for
the analysis at√s = 8 TeV it has been noticed that the use of the tracker
muons improves the expected limited and so they have been included. From
all these three kinds of objects a unique collection of muons is obtained.
The muon system in CMS has three distinct functions:
• muon identification
• momentum measurement
53
• triggering over the whole kinematic range
The hits are analyzed using a recognition algorithm to associate measure-
ments with trajectories. The procedure used to extract tracks from hits
consists of the following steps:
• trajectory seeding: the determination of the track recostruction initial
point is accomplished using an estimated trajectory state or collection
of hits compatible with the assumed physics process;
• trajectory building: it starts from the position specified by the trajec-
tory seed, proceeding in the direction specified by the seed and search-
ing for compatible hits on the subsequent detector layers. The track
finding and fitting procedure is performed using a Kalman Filter. This
last method uses an iterative approach to update the trajectory esti-
mate, using track parameters and covariance and propagating them to
the next detector layer;
• trajectory cleaning: the trajectory building procedure produces a large
amount of possible trajectories, sharing a lot of hits. This step is then
finalized to remove the ambiguities, keeping a maximum number of
tracks candidates;
• trajectory smoothing: in this step a backward fitting is performed. The
Kalman filter is also used in this case because of its feature of being
linear in the measurements and its backward complement capability to
use the whole information package;
Once the hits are fitted and the fake trajectories are removed, the remaining
tracks are extrapolated to the point of closest approach to the beam line,
where the information from the track is measured in the transverse plane.
In order to improve the pT resolution, a beam spot constraint has been ap-
plied. It can be observed that the muon tracks are not re-fitted to the
common vertex.
The reconstructed muons are required to have transverse momentum pµT
54
larger than 5 GeV/c and |ηµ| < 2.4: the first requirement ensures an ef-
ficiency for the reconstruction of muons above the 80%, while the second
relies on the geometric acceptance of the tracker detector in where the muon
reconstruction is fully efficient.
For ensuring an accurate measurement of the track momentum, more than
ten silicon tracker hits (Nhits > 10) have to be included in the track fit.
55
Chapter 3
The Higgs Boson Production
and Simulation at LHC
In this work a search for a Higgs boson in the dacay channel H → ZZ(∗) → 4`
using pp collisions from LHC at√s = 7 TeV is presented. From now on Z
can stand for the real particle Z, for the virtual one Z∗, and, eventually, also
for γ∗.
For the event generation, ` stands for any charged lepton, e, µ or τ but the
analysis here discussed will focus on reconstructed final states with only elec-
trons or muons. In this section a theoretical overview of the production and
decay channels of the SM Higgs boson [22] along with a quick view on the
signal and background MC samples used will be discussed.
The total cross section at hadron colliders is extremely large (about 100 mb
at the LHC), resulting in an interaction rate of ≈ 109 Hz at the design lu-
minosity [22]. In this difficult environment, the detection of processes with
signal to total hadronic cross section ratios (of about 10−10), as is the case
for the SM Higgs production in most channels, is challenging.
The huge QCD-jet backgrounds prevents from the detection of the produced
Higgs boson, or any particle in general, in fully hadronic modes.
For the purpose of this analysis, it can be worth to remind that in the
SM Higgs decay mode H → ZZ/WW, at least one of the W/Z bosons has
to observed in its leptonic decays which have small branching ratios (e.g.
BR(Z→ l+l−) ≈ 6%) but a clear signature of leptons in the final state.
57
For this reason a very good detection of isolated high transverse momentum
muons and electrons and high performance calorimetry are required.
3.1 Higgs Production Mechanism
In the SM, while studying the main production mechanisms for the Higgs
production in the hadronic collisions, one must take into account that the
Higgs boson couples preferentially to heavy particles, i.e. the massive W
and Z bosons and the top and bottom quarks. Four main Higgs production
processes can be identified (see Fig. 3.1). They are:
• the associated production with W/Z bosons: qq → V +H
• the weak vector boson fusion processes: qq → V ∗V ∗ → qq +H
• the gluon gluon fusion mechanism: gg → H
• the associated Higgs production with heavy quarks (top and bottom
quarks): gg, qq → QQ+H
3.1.1 The higher-order corrections and the K-factor
For a process involving strongly interacting particles, as in this case, the
lowest order (LO) cross sections are affected by large uncertainties coming
from higher-order (HO) corrections. Hence, the total cross sections can be
derived properly if at least next-to-leading order (NLO) QCD corrections to
the process are included. The impact of higher-order QCD corrections is
quantified by defining the K-factor as the ratio of the cross section for the
process (or its distribution) at HO with the value of the coupling costant αs
and the parton distribution functions (PDFs, see subsection 3.1.1) evaluated
also at HO, over the cross section (distribution) at LO with αs and the PDFs
consistently evaluated at LO:
K =σHO(pp→ H +X)
σLO(pp→ H +X). (3.1)
58
Fig. 3.1: The dominant SM Higgs boson production mechanisms in hadroniccollisions.
Hence, all the main Higgs procuction processes are required to be studied
at least at NLO. The QCD corrections to the transverse momentum and
rapidity distributions are also available in the case of vector-boson fusion and
gluon-gluon fusion. In this latter case, that is the one of main interest for this
work, the resummation of the large logarithms for the PT distribution has
been performed at the next-to-next-to-leading-logarithm (NNLL) accuracy.
In the gluon-gluon fusion mechanism the calculation of the cross sections at
next-to-next-to-leading order (NNLO) is also necessary [28].
The parton distribution functions: PDFs
The PDFs describe the momentum distribution of a parton in the proton and
so they play a central role at hadron colliders. A detailed knowledge of the
PDFs over a wide range of the proton momentum fraction x carried by the
parton and the squared center of mass energy Q2 at which the process to be
studied takes place is absolutely mandatory to well predict the production
cross sections of the signal and background processes
59
The cross sections for a centre of mass energy√s = 7 TeV corresponding
to the value currently adopted by the LHC, are shown in fig.3.2.
Fig. 3.2: Higgs production cross sections at√s = 7 TeV as a function of the
Higgs mass.
A quick overview of all the production mechanisms is here provided.
The gluon-gluon fusion (gg fusion)
In this work we will consider mainly the gg fusion mechanism which is the
dominating one for the Higgs production at the LHC over the whole Higgs
mass spectrum because of the high luminosity of gluons at the nominal centre
of mass energy. It can be considered the most efficient production channel in
the search for the Higgs boson at the LHC. Considering QCD corrections of
order greater than the leading one (NLO), the cross section for this process
increases by a factor of 2.
Searches in the dominant hadronic H → bb and H → WW/ZZ → 4j (in
which j stands for jet) decay channels are extremely difficult because of the
60
large QCD jet backgrounds. That is the reason why one has to rely on rare
Higgs decays which provide clean signatures involving photons and/or lep-
tons for which the backgrounds are smaller but far from being negligible.
Vector-boson fusion
The Vector-boson fusion is the second main contribution to the Higgs
production cross section. It is about one order of magnitude lower than the
gg fusion for a wide range of Higgs mass values and the two processes become
comparable only for very high Higgs masses (O(1TeV)). The main feature of
this production mechanism is that it has a very clear experimental signature.
The presence of two jets with high invariant mass can be considered a very
powerful tool for tagging the signal events and discriminate the backgrounds.
The W and Z associated production (Higgsstrahlung process)
In the W/Z associated production process the Higgs boson is produced
in association with a W or Z boson that are used for tagging the event. The
cross section corresponding to this process is several orders of magnitude
lower than the ones associated to the mechanisms previously described.
3.2 Decays of the SM Higgs boson
In the SM the profile of the Higgs particle is uniquely determined, once the
Higgs mass is fixed. As already pointed out (see chapter 1), the Higgs cou-
plings to gauge bosons and fermions are directly proportional to the masses
of the particles and so the Higgs boson tends to decay into the heaviest
ones allowed by the phase space. Since the masses of the gauge bosons and
fermions are known:
MZ = 91.187, GeV/c2
61
MW = 80.425 GeV/c2, mτ = 1.777 GeV/c2,
mµ = 0.106 GeV/c2, mτ = 178± 4.3 GeV/c2,
mb = 4.88± 0.07 GeV/c2, mc = 1.64± 0.07 GeV/c2, (3.1)
all the partial widths for the Higgs decays into these particles1 can be pre-
dicted. The decay widths into massive gauge bosons V = W,Z are directly
proportonal to the HV V couplings. In terms of field they can be written as
follows [22]:
L(HV V ) = (√
2Gµ)1/2M2VHV
µVµ, (3.2)
where Gµ is the Fermi coupling costant2. The decay widths into fermions are
proportional to the Hff couplings:
gHff ∝ (√
2Gµ)1/2mf , (3.3)
The SM Higgs boson has many decay channels: quarks and leptons, real or
virtual gauge bosons and loop induced decays into photons and gluons. The
branching ratios for each Higgs decay channel vs different Higgs masses are
shown in Fig. 3.3.
It can be easily observed that fermion decay mode dominates at low
masses (up to 150 GeV/c2). In this region the branching ratio is dominated
by the Higgs decay into bb. However, the di-jet background makes it a quite
difficult channel to use for a Higgs discovery. Instead, for mH > 130 GeV/c2
the channel of the Higgs decaying into two photons seems to be the main
one, because, in spite of its lower branching ratio, the two photons emitted
are very energetic, and provide a very clear signature.
For the intermediate mass region (140 < mH < 180 GeV/c2), the Higgs de-
cays into WW (∗) and ZZ(∗) are the main ones.
1the electron and light quarks are not included since their masses are to small to berelevant.
2the universal value of G is G = 10−5m−2N , where mN is the nucleon mass. It is obtained
from β- or µ-decay.
62
Fig. 3.3: The Higgs Branching Ratio vs Higgs mass for main decay channels.
For mass values greater than 160 GeV/c2 the decay mode into vector-boson
pairs starts to dominate.
It can be noticed that the branching ratio of the decay mode H → WW (∗) is
higher, because of the higher coupling of the Higgs boson to charged current
with respect to neutral current, but the Higgs recostruction in this channel
is compromised by the presence of two neutrinos in the final state. That
is the reason why the H → ZZ → 4`, despite its lower branching ratio, is
considered the one which played a major role for SM Higgs boson discovery
in this region. It presents a clearer experimental signature, still preserving
a high signal to background ratio. In the high Higgs mass region (approxi-
mately above the 2mZ threshold), it can be observed that the Higgs boson
can decay into a real ZZ or WW pair. Though in H → ZZ decay mode the
branching ratio is still lower than H → WW one, the first remains still the
63
golden channel for a high mass Higgs discovery.
With theoretical constraints related to the violation of unitarity condition
dictated by the SM, it can be said that 1 TeV can be considered an upper
limit for Higgs boson mass.
3.2.1 Decays into electroweak gauge bosons: two body
decay
Above the WW and ZZ kinematical thresholds, the Higgs boson will decay
mainly into a pair of massive gauge bosons (see Fig. 3.4).
Fig. 3.4: Diagrams for the Higgs boson decays into real and/or virtual gaugebosons.
The decay widths are directly proportional to the HV V couplings given
in eq. 3.2. The partial width for a Higgs boson decaying into two real gauge
bosons, H → V V , in which V = W or Z are given by [22]:
64
Γ(H → V V ) =GµM
3H
16√
2πδV√
1− 4x(1− 4x+ 12x2) (3.4)
where x = M2V /M
2H , δW = 2 and δW = 1. It can be noticed that for large
Higgs boson mass values, the decay width into WW bosons is two times
larger than the decay width into ZZ and the respective branching ratios for
the decays would be 2/3 and 1/3 if other decay channels are kinematically
forbidden. One can also observe that a heavy Higgs boson would be “obese”
since its total decay width would become comparable to its mass
Γ(H → WW + ZZ) ∼ 0.5 TeV[MH/1 TeV]3 (3.5)
and behaves as a resonance.
3.3 Monte Carlo samples
Both Higgs boson signal samples and a large number of electroweak and
QCD-induced SM background processes have been simulated using Monte
Carlo (MC) techniques.
The signal and background samples have been used for the definition and
the optimization of the event selection strategy prior to the analysis of the
experimental data, for comparisons with the real measurements, for the eval-
uation of acceptance corrections and for studies about systematics.
The backgrounds for this analysis include indistinguishable 4` contributions
from di-boson production, via the production mechanisms qq → ZZ(∗) and
gg → ZZ(∗), as well as instrumental backgrounds. For instrumental back-
ground we mean the background that has to be considered because of the
limitations in the performance of the detectors. These can cause hadronic
jets or secondary leptons from heavy meson decays to be misidentified as
primary leptons.
The analysis discussed in this work will focus on reconstructed final states
with only electrons or muons in the final state.
The main possible sources of instrumental background are:
65
• Z + light jets production with Z→ `+`− decays;
• Zbb (and Zcc) associated production with Z→ `+`− decays;
• the production of top quark pairs in the decay mode tt → WbWb →`+`−ννbb.
Other contributions to multiple jet production from QCD hard interac-
tions need also to be considered in early stages of the analysis, as well as
other di-boson (WW, WZ, Zγ) and single top backgrounds.
Signal and background processes cross sections are all re-weighted, at least, to
NLO. For the Higgs production mechanism via gluon fusion, NNLO+NNLL
calculations of the cross sections are included.
Several Monte Carlo event generators has been used:
• The multi-purpose generator PYTHIA [57], for example, has been used
for reproducing several processes such as QCD multijet production and
hard process at leading order (LO). For hard processes generated at
higher orders, it is used only for the showering, the hadronization, the
decays, and the simulation of the underlying event 3. In general, PYTHIA
can be used to generate high-energy ‘events’, i.e. sets of outgoing par-
ticles produced in the interactions between incoming particles. An
accurate representation of event properties in a wide range of reactions
can so be provided.
• The MadGraph (MadEvent) Monte Carlo event generators [23] has been
used to generate multi-parton amplitudes and some background events.
• The POWHEG NLO generator [53] has been used for the Higgs boson
signal and for the ZZ and tt background.
• The dedicated tool GG2ZZ [55] has been used to generate the gg → ZZ
contribution to the ZZ cross section.
3The “underlying event (UE) is defined as those aspects of a hadronic interactionattributed not to the hard scattering process, but rather to the accompanying interactionsof the rest of the proton.
66
The tool “PYTHIA tune Z2” [54], which relies on pT -ordered showers, has been
used for the underlying event. The tools CTEQ6M [34] and CT10 [30] have
been used for the parton density function of the colliding protons.
They are summerized along with the datasets in table 3.1.
In the following paragraphs some details about MC signal and background
samples is provided.
Signal: H→ ZZ(∗) → 4`
The Higgs boson samples used are generated with POWHEG, which includes
NLO gluon fusion (gg → H) and weak-boson fusion qq → qqH. Additional
samples with WH, ZH and ttH associated production are also used and pro-
duced with PYTHIA event generator.
The Higgs boson is forced to decay into two Z-bosons, which are allowed to
be off-mass shell, and both Z-bosons are forced to decay into two leptons
via Z→ 2`. A re-weighting procedure has been applied to generated events
according the total cross section σ(pp→ H) which includes the gluon fusion
contribution up to NNLO and NNLL [34, 8, 20, 21, 39, 46, 7, 58, 52, 48] and
the weak-boson fusion contribution at NNLO [34, 36, 37, 56, 32, 41]. The
total cross section is scaled by the BR(H → 4`) [34, 2, 1, 4, 49]. Figure 3.5
shows the number of MC expected events with an integrated luminosity of
L = 5 fb−1 as a function of the Higgs mass.
The current analysis has been performed using only samples for gluon fusion
production mechanism and rescaled to the total cross section including all
other production processes (weak-boson fusion, WH, ZH and ttH associated
production).
The POWHEG MC program used to simulate the gg → H process results in
a Higgs Boson pT spectrum which differs significantly from the theoretical
calculation that is available at NNLL+NLO. A theoretical estimate of this
pT spectrum is computed using the HqT [29] program, which implements such
NNLL+NLO calculation.
A re-weighting procedure has also been applied to the simulated events, but
the total effect has been found very small. In this analysis, indeed, no direct
67
Process MC σ(N)NLO Comments and samples
generator
Higgs boson H→ ZZ→ 4`
gg → H POWHEG [1-20] fb mH = 110-600
V V → H POWHEG [0.2-2] fb mH = 110-600
W H; Z H; ttH PYTHIA [0.01-0.05] fb mH = 110-180
ZZ continuum
qq → ZZ→ 4e(4µ, 4τ) POWHEG 15.34 fb ZZTo4e(4mu,4tau) 7TeV-powheg-pythia6
qq → ZZ→ 2e2µ POWHEG 30.68 fb ZZTo2e2mu 7TeV-powheg-pythia6
qq → ZZ→ 2e(2µ)2τ POWHEG 30.68 fb 2e(2mu)2tau 7TeV-powheg-pythia6
gg → ZZ→ 2`2`′ gg2ZZ 3.48 fb GluGluToZZTo2L2L 7TeV-gg2zz-pythia6
gg → ZZ→ 4` gg2ZZ 1.74 fb GluGluToZZTo4L 7TeV-gg2zz-pythia6
Other di-bosons
WW→ 2`2ν PYTHIA 4.88 pb WWTo2L2Nu TuneZ2 7TeV pythia6 tauola
WZ→ 3`ν PYTHIA 0.595 pb WZTo3LNu TuneZ2 7TeV pythia6 tauola
tt and single t
tt→ `+`−ννbb POWHEG 17.32 pb TTTo2L2Nu2B 7TeV-powheg-pythia6
t (s-channel) POWHEG 3.19 pb T TuneZ2 s-channel 7TeV-powheg-tauola
t (s-channel) POWHEG 1.44 pb Tbar TuneZ2 s-channel 7TeV-powheg-tauola
t (t-channel) POWHEG 41.92 pb T TuneZ2 t-channel 7TeV-powheg-tauola
t (t-channel) POWHEG 22.65 pb Tbar TuneZ2 t-channel 7TeV-powheg-tauola
t (tW -channel) POWHEG 7.87 pb T TuneZ2 tW-channel-DR 7TeV-powheg-tauola
t (tW -channel) POWHEG 7.87 pb Tbar TuneZ2 tW-channel-DR 7TeV-powheg-tauola
Z/W + jets (q = d, u, s, c, b)W + jets MadGraph 31314 pb WJetsToLNu TuneZ2 7TeV-madgraph-tauola
Z + jets MadGraph 3048 pb DYJetsToLL TuneZ2 M-50 7TeV-madgraph-tauola
QCD inclusive multi-jets, binned pminT
b, c→ e+X PYTHIA QCD Pt-XXtoYY BCtoE TuneZ2 7TeV-pythia6
EM-enriched PYTHIA QCD Pt-XXtoYY EMEnriched TuneZ2 7TeV-pythia6
MU-enriched PYTHIA QCD Pt-XXtoYY MuPt5Enriched TuneZ2 7TeV-pythia6
Tab. 3.1: Monte Carlo simulation datasets used for the signal and back-ground processes; Z stands for Z, Z∗, γ∗; ` means e, µ or τ ; V stands for Wand Z; pT is the transverse momentum for 2 → 2 hard processes in the restframe of the hard interaction.
constraints are imposed on the transverse momentum of the 4` system, or on
the hadronic recoil against this system (e.g. no jet veto or missing transverse
68
Fig. 3.5: Expected events as a function of the Higgs mass in H → 4` in ppcollision at
√s = 7 TeV for a luminosity L = 5 fb−1.
momentum cut).
Irreducible background: qq → ZZ(∗) → 4`
The samples qq → ZZ(∗) → 4l has been produced with POWHEG which in-
cludes the complete NLO simulation, interfaced to PYTHIA for showering,
hadronization, decays and the underlying event.
69
Irreducible background: gg → ZZ(∗) → 4`
The gluon-induced ZZ background constitues a non-negligible fraction of the
total irreducible background at masses above the 2MZ threshold.
The contributions have been estimated by using the dedicated tool gg2ZZ
which computes the gg → ZZ at LO, which is of order α2s , compared to α0
s
for the LO qq → ZZ.
The hard scattering gg → ZZ(∗) → 4` events are then showered and hadronized
using PYTHIA.
The gg2ZZ tools has been used to compute the cross-section after ap-
plying a cut on the minimally generated invariant mass of the same-flavour
lepton pairs (which can be interpreted as the Z/γ invariant mass) mmin`` =
10 GeV/c2. The gg2ZZ generator gives the contribution for final states with
different flavours of the lepton pairs, but it has been also used to estimate
the same-flavour background. This is an approximation which is only strictly
valid when m4` ≥ 2mZ. Below this threshold the relative amount of like-
flavour events increases compared to unlike-flavour events. The total cross
section for events with different-flavour lepton pairs in the final state is 3.48 fb
at 7 TeV.
Background: Z+jets→ 2`+jets
The Z+jets→ 2`+jets samples have been generated with MadGraph tool, with
a statistics of ≈ 30 million events corresponding to an integrated luminosity
above O(10) fb−1. Both light (q = d, u, s) and heavy-flavor (q = c, b) jets
have been included in the sample. A cut on two-lepton invariant mass of
m2` > 50 GeV/c2 has been imposed in the simulation and a total NNLO
cross section of 3048 pb has been used for 7 TeV.
Background: tt→ 2`2ν2b
The tt→ 2`2ν2b sample has been generated with POWHEG event generator.
The theoretical NLO cross-section for the process is σNLO(pp→ tt→ 2`2ν2b) =
17.32 pb [35]. A sample of about 10 milion events corresponding to an inte-
grated luminosity of more than 600 fb−1 has been simulated.
70
3.4 Monte Carlo generator studies
In this section some MC generator studies are presented.
In Fig. 3.6 the pT distribution for muons coming from the Higgs decay
H → ZZ → 4µ for Higgs masses mH = 120 GeV/c2, mH = 200 GeV/c2,
mH = 350 GeV/c2, as derived from MC simulation, is shown.
It can be noticed how the spectrum of the lepton pT moves towards higher
values as the Higgs mass grows.
Hence, it can be observed that imposing cuts on the two highest pT leptons,
pT,1 > 20 GeV/c, pT,2 > 10 (7) GeV/c for electron (muon) objects (see
chapter 4, section 4.1), does not cut signal events.
In Fig. 3.7 Higgs mass distribution for Higgs masses mH = 120 GeV/c2,
mH = 200 GeV/c2, mH = 350 GeV/c2 is shown. At very low masses the
distribution tends to be a Dirac δ one because of the very small Higgs width,
while at higher mass values the distribution appears to be wider around the
nominal sample value, since the Higgs total width increases with the Higgs
mass.
Fig. 3.8 shows how the Z2 tends to be off-mass shell in the low Higgs
mass region and on-mass shell as the mass grows.
Studying the event generated by MC simulation, we can also observe that,
for low mH values, also the Z1 could be off mass-shell (see the left-tail of the
Z1 mass distribution in Fig. 3.8, (a)). This phenomenon must be taken into
account during the recostruction phase.
71
(a) (b)
(c)
Fig. 3.6: pT distribution for muons coming from MC samples H → ZZ → 4µfor Higgs masses mH = 120 GeV/c2 (a), mH = 200 GeV/c2 (b), mH = 350GeV/c2 (c). The event number is rescaled for an integrated luminosity ofL = 4.71 fb−1.
72
(a) (b)
(c)
Fig. 3.7: Higgs mass distribution from MC samples H → ZZ → 4µ for Higgsmasses mH = 180GeV/c2 (a), mH = 300 GeV/c2 (b), mH = 400GeV/c2 (c).The event number is rescaled for an integrated luminosity of L = 4.71fb−1.
73
(a) (b)
(c) (d)
Fig. 3.8: Z1/Z2 mass distributions from MC samples H → ZZ → 4µ forHiggs masses mH = 120 GeV/c2 (a), mH = 160 GeV/c2 (b), mH = 350GeV/c2 (c), mH = 500 GeV/c2 (d). The event number is rescaled for anintegrated luminosity of L = 4.71 fb−1.
74
Chapter 4
Data Analysis
In this chapter the analysis selection developed to perform an experimental
search for the Higgs boson in the decay channel H → ZZ(∗) → 4`, with each
Z boson decaying into a muon or electron pair, is presented. It is carried out
using proton-proton (pp) collisions from LHC at√s = 7 TeV. The data col-
lected correspond to an integrated luminosity L = 4.71± 0.21 fb−1 recorded
by CMS detector during 2010 and 2011.
The Higgs boson mass window covered by this analysis is 110 < mH < 600
GeV/c2. Dealing with Higgs bosons with masses mH < 2mZ , at least one
lepton pair can be coupled to an off-mass shell Z∗ boson. The softest lepton
in that pair typically has p`T < 10 GeV/c for masses mH < 140 GeV/c2.
Because of the presence of four leptons in the final state, a high-performance
lepton recostruction, identification and isolation, along with excellent lepton
energy-momentum mesurements, is mandatory. A substantial reduction of
QCD-induced sources of mis-identified (“fake”) leptons has been realized by
identifying isolated leptons coming from the event primary vertex.
High precision energy-momentum measurements allow to obtain a good res-
olution on the reconstructed mass m4`, which is the most important observ-
able for the Higgs boson search. It can be noticed that preserving the highest
possible reconstruction efficiency and ensuring, at the same time, sufficient
discrimination against hadronic jets is particulary challenging for the recon-
struction of leptons with low p`T .
A special method called “tag-and-probe” [12] allows us to measure that ef-
ficiency from data and MC and keep full control of the behaviour at very
75
low p`T values. In this range the combined information from the tracker and
the electromagnetic calorimeter (for electrons) and from the tracker and the
muon spectrometer (for muons) plays the most important role for lepton
reconstruction, identification and isolation.
4.1 Experimental Data samples
The data sample used for this analysis has been recorded by the CMS exper-
iment during 2010 and 2011.
The CMS standard selection of runs and luminosity sections has been ap-
plied, since it assures high quality data.
The validation of the data used for the analysis of the 4e, 4µ and 2e2µ chan-
nels has been guaranteed by detector operation conditions. Only certified
data have been used.
The monitoring and certification of the quality of the CMS data consists
of a multi-step procedure, which goes from online data taking to the offline
reprocessing of data recorded earlier.
The quality assessment is based both on visual inspection of data distribu-
tions by monitoring shift persons and on algorithmic tests of the distributions
against references.
The Run Registry (RR) is the central workflow management and tracking
tool used for collected data certification. It keeps track of the certification
results and make them available to the whole CMS collaboration. It is reg-
ularly used for the creation of official good-run list files which are used as
input to downstream selection of the data for re-processings and for physics
analyses.
Events have been required to pass double lepton (ee, eµ, µµ) High Level Trig-
gers (HLT) with a transverse momentum (pT ) threshold on each lepton and
additional selection criteria that changed during the data taking according
to the instantaneous luminosity and the available data taking bandwidth.
Given the high probability of jets to fake electrons, double electron events
have been selected with more complicated criteria based not only on the elec-
trons transverse momentum but also on their isolation and identification.
76
The analysis presented in this work relies on primary datasets (from now
on in this chapter, the short form “PDs” will stand for primary datasets)
produced centrally, which combine various collections of HLT selections1.
For the 2010 data, the analysis relies on the so-called ”EG” and ”MU” PDs
for the data taking with instantaneous luminosities L in the range 1029 −1031 cm−2s−1 and on ”Electron” and ”MU” PDs [6] for L > 1031 cm−2s−1.
For the 2011A data, the analysis relies on the so-called ”DoubleElectron” and
”DoubleMuon” PDs [43]. These latter PDs are formed by a ”OR” between
various triggers with symmetric or asymmetric trigger thresholds for the two
leptons. They also include triggers requiring a condition on three leptons
above a low pT theshold. The PDs and trigger paths used for this analysis
are summarized on Table 4.1.
Tab. 4.1: Summary of data samples and trigger paths used.Period Dataset Name Trigger Name
2010A /Mu/Run2010A-Apr21ReReco-v1/AOD DoubleMu3
2010A /EG/Run2010A-Apr21ReReco-v1/AOD Ele10 LW ”OR”Ele15 SW
2010B /Mu/Run2010B-Apr21ReReco-v1/AOD DoubleMu3
2010B /Electron/Run2010B-Apr21ReReco-v1/AOD Ele17 SW CaloEleId ”OR”Ele17 SW TightEleId ”OR”Ele17 SW TighterEleIdIsol
2011A /DoubleElectron/Run2011A-05Jul2011ReReco-ECAL-v1AOD Ele17 CaloIdL CaloIsoVL
Ele8 CaloIdL CaloIsoVL
2011A /DoubleElectron/Run2011A-05Jul2011ReReco-ECAL-v1AOD Mu13 Mu8
2011A /DoubleElectron/Run2011A-05Aug2011-v1/AOD Ele17 CaloIdT CaloIsoVL TrIdVL TrIsoVL
Ele8 CaloIdT CaloIsoVL TrIdVL TrIsoVL
2011A /DoubleMu/Run2011A-05Aug2011-v1/AOD Mu13 Mu8
2011A /DoubleElectron/Run2011A-03Oct2011-v1/AOD Ele17 CaloIdT CaloIsoVL TrIdVL TrIsoVL
Ele8 CaloIdT CaloIsoVL TrIdVL TrIsoVL
2011A /DoubleMu/Run2011A-03Oct2011-v1/AOD Mu13 Mu8
2011B /DoubleElectron/Run2011B-PromptReco-v1/AOD Ele17 CaloIdT CaloIsoVL TrIdVL TrIsoVL
Ele8 CaloIdT CaloIsoVL TrIdVL TrIsoVL
2011B /DoubleMu/Run2011B-PromptReco-v1/AOD Mu17 Mu8
On these PDs a skimming procedure common to all the three 4` channels
has been applied to perform a reduction of the data. This procedure requires:
• at least two reconstructed lepton candidates, either an electron basic
track-supercluster object or global muon object, or a tracker muon
1To enable the most effective access to CMS data, the data are first split into PDsand then the events are filtered. The division into the PDs is done relying on the triggerdecision. The primary datasets are structured and placed to make life as easy as possible,e.g. to minimize the need of an average user to run on very large amounts of data.
77
object;
• pT,1 > 20 GeV/c, pT,2 > 10 (7) GeV/c for electron (muon) objects;
• an invariant mass M1,2 > 40 GeV/c2
In the next section an overview of the physics objects involved in the
analysis will be shown, paying attention to the recostruction, identification
and isolation for each of them.
4.2 Physics Objects: Electrons and Muons
4.2.1 Lepton Identification
Electrons
A high electron identification efficiency [51] is required in physics analysis
with multi-electron final states just to improve signal selection, in particular
at low ET , where the background and, consequently, the fake rate (rate of
jets reconstructed as electrons, “fake” electrons) increases.
The electron identification largely depends on some CMS detector features,
such as high magnetic field, a thick tracker and lower ECAL response to
pions with respect to electrons.
The electron categories, already presented in the subsection 2.3.1, have been
originally proposed for electron selection and used for the best momentum
determination in the electron recostruction. For instance, electrons coming
from W and Z can be distinguished from other particles due to their feature
of being primarily measured in the ECAL and tracker. The electron track
would match pretty well in position and momentum with the cluster of en-
ergy found in the ECAL.
The electron identification makes use of a set of variables to distinguish be-
tween real electrons and electrons from background. Some of them have
been already mentioned in the reconstruction section (the hadronic to elec-
tromagnetic ratio H/E, the energy-momentum matching variables between
the energy of the supercluster or of the supercluster seed and the electron
78
track momentum at the vertex or at the calorimeter, the geometrical match-
ing between the electron track parameters at the vertex extrapolated to the
supercluster and the supercluster position, see chapter 2 subsection 2.3.1).
In addition to them, the calorimeter shower shape variables can be included.
To cope with the high photon conversion rate due to the material budget in
front of the ECAL, cuts on the impact parameter d0 (the distance between
the track at the point of closest approach and the reconstructed primary ver-
tex) and on missing hits (number of crossed layers without compatible hits
in the back-propagation of the track to the beam line) are applied. Finally,
the performance of electron identification depends on the degree of isolation
imposed on the electron candidates.
Not isolated electrons, i.e. electrons in jets, are reconstructed and identi-
fied using a dedicated particle-flow clustering algorithm which, exploiting
the good ECAL granularity, can saparate overlapping showers. The low pT
electrons are better reconstructed and identified using the same technique
developed for non-isolated electrons.
Muons
Many phenomena can lead to an incorrect muon identification [38]. They
can be classified under several categories.
Fake muon signatures are typically produced by light hadron such as pions
and kaons which are abundantly present in any high energy collision final
state. We call fake muon any reconstructed muon, passing whatever cuts
applied, that is recostructed in single pion or kaon events. Thus, a muon
from a K → µ decay in flight is a fake muon. Fake muon signals in the muon
chambers can also be originated from the leakage of secondary particles pro-
duced in hadronic interactions in the calorimeter. This case is denoted as
punch-through.
The need of establishing the muon identification (muon-ID) can be well
enough illustrated in plots in Fig. 4.1. Here the probability that a gen-
erated kaon/pion of |η| < 2.4 results in a reconstructed muon versus global
and tracker muon pT is presented.
79
0 20 40 60 80 100 120 140 160 180 2000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Kaon fakeratevs PtGLOBALMUONS
0 20 40 60 80 100 120 140 160 180 2000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Pion fakeratevs PtGLOBALMUONS
0 20 40 60 80 100 120 140 160 180 2000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Kaon fakeratevs PtTRACKERMUONS
0 20 40 60 80 100 120 140 160 180 2000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Pion fakeratevs PtTRACKERMUONS
Fig. 4.1: Out-of-the-box Global Muon and Tracker Muon fake rates as afunction of pT . Black histograms: total. Red histograms: decays in flight.
Global Muon requirements
A series of cuts are applied to some variables just to reject these fake
muons. For example, the global muon normalized-χ2 is a powerful tool to
reject both decays in flight and punch through. Usually, a normalized-χ2 <
10 is requested. Furthermore, track quality cuts can be used to reject decays
in flight. The quantity to be looked at for this purpose are:
• Impact parameter of the silicon or global fit.
• Normalized-χ2 of the silicon fit.
• Number of hits of the silicon fit.
80
It can be worth to remind that a set of five helix parameters can describe a
track in the solenoidal magnetic field:
• the transverse momentum pT
• the azimuthal angle φ
• the pseudorapidity η
• the transverse impact parameter d0, which is the distance of the tra-
jectory from the origin (conventionally the origin is the primary inter-
action vertex) calculated in the point of closest approach (poca)
• the logitudinal impact parameter r0
A loose d0 cut is very efficient for prompt muons, i.e. muons coming from
primary vertex, because it allows to reject a significant fraction of decays in
flight. High-pT muons penetrate deeply into the muon detector and very few
of the global fits for real muons end in the first layer of the barrel detec-
tor. On the contrary, this just often happens for kaons and pions, even after
all the requirements. Rejecting these muons almost a 20% reduction of the
fake rate can be obtained with little cost in efficiency. The muon segment
compatibility is also checked for ensuring muon-ID: in cases in which an ex-
trapolated track passes through a muon station but no associated segment is
found, the muon object stores the distance between the extrapolated track
position and the closest chamber edge. The value of this distance divided by
the multiple scattering uncertainty is used as a measure of the probability
for a trajectory of a given track to deflect from inside to outside of a chamber
boundary or viceversa.
Tracker Muon requirements
Two approaches have been developed to Tracker Muon identification:
• a cut-based approach
81
• an approach based on the costruction of a continous variable, “com-
patibility”
In both cases, the algorithm performs a procedure called “arbitration”.
It has been already pointed out that the tracker muons are built by associat-
ing segments in the muon chambers with the silicon track. A given segment
can be associated to more than one silicon track, so that it can be said that
Tracker Muon can share segments. The arbitration procedure allow to assign
each segment to a unique Tracker Muon.
The arbitration algorithm is relied on the calculation of the quantity ∆R2 =
∆X2 + ∆Y 2, where ∆X and ∆Y are the distance between the extrapolated
silicon track and the segment in local X and Y coordinates. The smallest
∆R value corresponds to the segment uniquely associated to the Tracker
Muon. On the other hand, the aim of the muon compatibility algorithm is to
build a continous variable which can quantify the compatibility of a Tracker
Muon object with the muon hypothesis. Two such variables are constructed,
one based on calorimeter information and the other based on muon chamber
information. The two variables are then combined into a single one. The
cut-based requirements are found to be quite different from the compatibil-
ity ones because they do not require that energy in the towers crossed by
muons be compatible with minimum ionizing.
In the context of this analysis tracker muons have been only used for studies
about the background estimate.
4.2.2 Electrons and Muons Isolation
To establish an isolation criterium for leptons, a lepton track relative isolation
variable has been introduced. This is defined as the sum of the pT of the
tracker tracks within a cone of radius ∆R =√
∆η2 + ∆φ2 < 0.3 around the
lepton candidate direction. The standard veto regions have been used just
to remove the lepton footprint (called “Jurassic” veto in case of electrons).
Finally, other leptons that fall in one lepton isolation cone are also vetoed.
For the ECAL or HCAL, the isolation variable is defined as the sum that is
computed using the transverse energy ET from energy deposits in cells with
82
geometrical centroids situated within a cone of radius ∆R =√
∆η2 + ∆φ2 <
0.3.
For electrons the cone axis is taken as the ECAL supercluster centroid viewed
from the electron vertex taken at (0,0,0). For muons the cone axis is taken
from the direction of the associated inner track, with the apex of the isolation
cone set at the nominal vertex position.
The selection of tracker tracks, energy deposits in ECAL and HCAL used
in isolation cones and veto regions are specified in Table 4.2.
ElectronType ∆R Deposits Veto region Thresholds
Tracker 0.3 CTF tracks |∆η| < 0.015 pT > 0.7 GeV/c,|∆z| < 0.2 cm
ECAL 0.3 RecHits |∆η| < 1.5 crys. ∆R < 1.5 crys. ET > 0.08 GeV (EB)E > 0.1 GeV (EE)
HCAL 0.3 Towers ∆R < 1.5Muon
Type ∆R Deposits Veto region ThresholdsTracker 0.3 CTF tracks ∆R < 0.015 pT > 1.0 GeV/c,
|∆z| < 0.2 cm, ∆R < 0.1 cmECAL 0.3 RecHits ∆R < 0.07 E > 0.25 GeVHCAL 0.3 Towers ∆R < 0.1
Tab. 4.2: List of parameters for electron and muon isolation. ∆η is thedifference in pseudo-rapidity with respect to the direction of the cone axis,∆R is the radius of the veto cone, pT is the transverse momentum of thetracks in the cone, E is the energy deposited in each ECAL rechit within thecone, ET = E · sin(θ) is the transverse energy , ∆z, ∆R are the minimumdistances from a track to the cone apex in the longitudinal and in the radialdirection, respectively. CTF tracks stands for Combinatorial Track Finderand EE and EB stand for ECAL endcap and ECAL barrel respectively.
To preserve the best signal efficiency and background rejection [50], a
relative isolation variable for selected leptons is defined as
Riso = (Isotrack + IsoECAL + IsoHCAL) /pT ,
where Isotrack is defined as the sum of the pT of the tracks in an isolation cone
with ∆R = 0.3 around the lepton, and IsoECAL and IsoHCAL are the trans-
83
verse energies measured by the electromagnetic and the hadronic calorimeters
respectively in the same cone. The denominator represents the value of the
lepton pT .
Combining the measurements around two lepton legs ensures the best per-
formance for 4` physics. Hence, a cut on the sum of Riso for pairs of two
leptons i, j has been used, Riso,i +Riso,j < 0.35. Since the combined relative
isolation makes use of the information from the ECAL calorimeter within the
isolation cone of radius ∆R < 0.3, the efficiency loss caused by the presence
of a bremsstrahlung, or an initial state (ISR) or final state (FSR) photon
from the hard collision process must be taken into account.
The working point found for this analysis is sufficiently loose to minimize
the efficiency loss. The combined relative isolation used in the analysis cor-
responds on average to a cut per lepton of Riso ∼ 0.25.
The overall efficiency loss from FSR photons caused by an isolation veto is
estimated to be at most at the % level for the sum of the 4e, 4µ and 2e2µ
channels.
The ambiguities between reconstructed electrons and muons that arise from
the emission from an electron of a FSR photon above the superclustering
threshold of 1 GeV are resolved by discarding electron candidates whose
tracks are found fully shared with a muon candidate (a cone of ∆R = 0.05
around the muon candidate is used).
4.2.3 Pile-up Corrections
Isolation variables are among the mostly pile-up sensitive variables in this
analysis.
The pile-up is responsible for the increasing of mean energy deposited in
the detector, leading to the rise of the mean isolation values. So, it can be
observed that the efficiency of a cut on isolation variables strongly depends
on pile-up conditions. The effect is observed to have a very deep impact in
both the calorimeters (ECAL, HCAL) and to be very feeble in the tracking
system, mostly due to the requirement that the tracks contributing to the
isolation cone originate from a common vertex (∆z cut). Thus the isolation
84
variable has to be corrected in order to take into account the pile-up phe-
nomena.
Among several correction methods, the one using the so-called FastJet en-
ergy density (ρ) in the event has been chosen to estimate the mean pile-up
contribution within the isolation cone of a lepton.
A ρ variable is defined for each jet in a given event and the median of the ρ
distribution for each event is taken. The correction to the isolation variable
is then applied according to the formula
Σ Isocorrected = Σ Iso− ρ · A (4.1)
where A is the area of the cone in the (η,φ) space. Since ρ is given in
1/(∆η∆φ) units, it has the dimension of an angle. An effective area is then
considered to avoid dealing with different thresholds in the isolation and
FastJet algorithms. It is defined as the ratio of the slope obtained from
linearly fitting Σ Iso(Nvtx). In this way the isolation cut efficiencies are
made stable with respect to changing pile-up conditions.
Table 4.3 shows the most recent results along with the reference ones, which
have been used in the following steps of the selection.
Electrons
Region AEcalIso AHcalIsoBarrel 0.078 (0.101) 0.026 (0.021)
Endcaps 0.046 (0.046) 0.072 (0.040)
Muons
Region AEcalIso AHcalIsoBarrel 0.087 (0.074) 0.042 (0.022)
Endcaps 0.049 (0.045) 0.059 (0.030)
Tab. 4.3: The values of effective areas as evaluated from Run2011B data,from Z → e+e− and Z → µ+µ− tag-and-probe. The corresponding valuesobtained from MC (without the requirement of leptons matched to the on-line trigger objects) are listed in parentheses. The choice of the separationbetween the barrel and the endcap region (|η| = 1.479) has been driven bythe ECAL layout.
It has been noticed that the average values of IsoECAL/pT , after ρ correc-
85
tion, are higher in the barrel than in the endcaps. It leads to a lower isolation
efficiency in the barrel than in the endcaps for a given threshold. This effect
is related to the way vetoes are applied when isolating the electrons in ECAL.
4.2.4 Primary and Secondary leptons: the significance
of the impact parameter
For leptons originating from a “common primary vertex” we mean that each
individual lepton has an associated track with a small impact parameter with
respect to the event primary vertex.
For the purpose of the event selection (see section 4.3), the significance of
the impact parameter to the event vertex, |SIP3D = IPσIP| is used where IP is
the lepton impact parameter in three dimensions at the point of closest ap-
proach with respect to the primary interaction vertex, and σIP the associated
uncertainty.
The condition for a lepton to be called a ”primary lepton” is to satisfy
|SIP3D| < 4.
In the background enhanced regions, hereafter referred as control regions, for
the Zbb and tt reducible backgrounds, the |SIP3D| cuts are reverted.
On the other hand, a “secondary lepton” is a lepton which satisfy the con-
dition |SIP3D| > 4. For the background control this is further restricted to
secondary leptons with 5 < |SIP3D| < 100.
4.3 Selection cuts
The selection steps of this analysis act on loosely track isolated lepton can-
didates: the electron reconstructed objects have been requested to be within
the geometrical acceptance of |ηe| < 2.5, with peT > 7 GeV/c and Isotrack/pT <
0.7, while the muons have to satisfy the conditions |ηµ| < 2.4, pµT > 5 GeV/c
and Isotrack/pT < 0.7.
The event selection has been performed after the skimming procedure of
relevant primary datasets and Monte Carlo samples as was described in sec-
tion 4.1.
86
The events have also been requested to have fired the relevant electron and
muon triggers, consistently in data and MC (see section 4.1).
The sequence of selection requirements consists of the following steps:
• 1. First Z reconstruction: a pair of lepton candidates of opposite charge
and same flavour (e+e−, µ+µ−) satisfying m1,2 > 50 GeV/c2, pT,1 > 20
GeV/c and pT,2 > 10 GeV/c; the sum of the combined relative isolation
for the two leptons has to satisfy Riso,j +Riso,i < 0.35; the significance
of the impact parameter with respect to the primary vertex, SIP3D, has
been required to satisfy |SIP3D = IPσIP| < 4 for each lepton; the lepton
pair with reconstructed mass closest to the nominal Z boson mass has
been retained and denoted Z1.
• 2. Three or more leptons: at least another lepton candidate of any
flavour or charge.
• 3. Four or more leptons and a matching pair: a fourth lepton candidate
having the same flavour (SF) of the third lepton candidate from the
previous step, and with opposite charge (OC).
• 4. Choice of the “best 4`” and Z1, Z2 assignments: a second lepton
pair is kept, denoted Z2, among all the remaining `+`− combinations
with mZ2 > 12 GeV/c2 and such that the reconstructed four-lepton
invariant mass satisfies m4` > mmin4` . For the 4e and 4µ final states,
at least three of the four combinations of opposite sign pairs have to
satisfy m`` > 12 GeVc2. If more than one Z2 combination satisfies all
the criteria, the one built from leptons of highest pT has been chosen.
The set of cuts applied up to this step are referred hereafter as preselection
cuts. Further cuts are used after the preselection to further suppress the
remaining contribution of Zbb and tt background events:
• 5. Relative isolation for selected leptons: for any combination of two
leptons i and j, irrespective of flavour or charge, the sum of the com-
bined relative isolation Riso,j +Riso,i < 0.35.
87
• 6. Impact parameter for selected leptons: the significance of the impact
parameter to the event vertex, SIP3D, is required to satisfy |SIP3D =IPσIP| < 4 for each lepton, where IP is the lepton impact parameter in
three dimensions at the point of closest approach with respect to the
primary interaction vertex, and σIP the associated uncertainty.
• 7. Z and Z(∗) kinematics: with mminZ1 < mZ1 < 120 GeV/c2 and mmin
Z2 <
mZ2 < 120 GeV/c2, where mminZ1 and mmin
Z2 are defined below.
The first step ensures that the leptons in the selected events are on the
high efficiency plateau for the trigger. The second step enables the control of
the three-lepton event rates which include WZ di-boson production events.
The first four steps have been designed to reduce the contribution of the
instrumental backgrounds from QCD multi-jets and Z+jets, preserving, at
the same time, the maximal signal efficiency and the phase space for the
evaluation of background systematics. The combinatorial ambiguities which
arise assigning the leptons to candidate Z bosons can be drastically limited
by reducing the number of jets which can be mis-identified as leptons. The
four first steps are completed by the choice of the best combination of four
leptons with m4` > mmin4` . The mmin
4` for this analysis has been set at 100
GeV/c2.
As already mentioned, the subsequent steps further suppress the reducible
backgrounds from Zbb/cc, tt and the remaining WZ+jet(s), and define the
phase space for the Higgs boson signal.
Three sets of kinematic cuts corresponding to three different analysis ty-
pologies are introduced to maximize the sensitivity in different ranges of
Higgs boson mass hypothesis. A baseline analysis is defined by requiring
mminZ2 ≡ 12 GeV/c2 and mmin
Z1 ≡ 50 GeV/c2. This provides a best sensitiv-
ity at low mass values, i.e. mH < 130 GeV/c2. An intermediate-mass
analysis is defined by requiring mminZ2 ≡ 20 GeV/c2 and mmin
Z1 ≡ 60 GeV/c2.
Finally, a high-mass analysis is defined by requiring mminZ2 ≡ 60 GeV/c2 and
mminZ1 ≡ 60 GeV/c2.
The enlarged phase space of the baseline selection for the Higgs boson signal
is needed at very low masses given the very small cross section × branching
88
ratio, at the price of a larger background. The increased acceptance for the
signal becomes small (< 10% compared to the baseline selection) for mass
above ≈ 130 GeV/c2. For Higgs boson masses above ≈ 2 × mZ, a further
restriction of the phase space of the pair of Z boson can be made without
significant loss of acceptance for the signal and with the benefit of a slight
reduction of the ZZ background.
4.3.1 Selection Efficiency
In Fig. 4.2 the signal efficiency versus Higgs mass for 4e, 4µ and 2e2µ
channels at main selection steps for baseline selection is presented. In all cases
the efficiencies are calculated using the events which pass the acceptance cuts
which are pT > 7 GeV/c and |ηe| < 2.5 for electrons and pT > 5 GeV/c and
|ηµ| < 2.4 for muons.
It can be noticed that the efficiency at the last step, i.e. after applying
the kinematics cuts, is evaluated to be raising from about 33% / 69% / 45%
at mH = 120 GeV/c2 to about 63% / 83% / 73% at mH = 400 GeV/c2 for
the 4e / 4µ / 2e2µ channels; this is strictly related to the kinematic of the
Higgs production that enhances the increase of lepton pT when the mass is
large.
It can be also observed that in the low mass region, very low efficiency values
are reached expecially in 4e- (∼ 30% at the kinematics step for mH = 120
GeV/c2) and 2e2µ-channel (∼ 40% at the kinematics step for mH = 120
GeV/c2); the loss is related to the efficiencies of leptons reconstruction and
identification that tends to go down at low pT so degradating the efficiency
to select good four-lepton candidates.
Table 4.4 summarizes the events yields as a function of the selection steps
for the main backgrounds, one Higgs mass hypothesis (mH = 200 GeV/c2)
and data for 4e, 4µ and 2e2µ channels
The events yields as a function of the selection steps are shown in Figs. 4.3,
4.4 and 4.5 for the baseline, intermediate and high-mass selection in the 4e,
4µ and 2e2µ channels. In the plots a fairly good agreement between data and
MC background expectation can be observed generally. It can be noticed how
89
(a) (b)
(c)
Fig. 4.2: Signal Efficiency Plots for Baseline Selection in (a) 4e, (b) 4µ, (c)2e2µ channels respectively. The 4` step corresponds to the step at which afourth lepton candidate SF and OC respect with the third lepton is chosen.at the “best 4`” step the best 4` object is chosen, with m4` > mmin andmZ2 > 12 GeV/c2. For 4e and 4µ channels m`` > 12 GeVc2 for at least threeof the four combinations of opposite sign pairs. The Iso step correspondsto Riso,j + Riso,i < 0.35 for any combination of two leptons; the IP stepcorresponds to |SIP3D| < 4 for each lepton; the Kin step corresponds tommin
Z1 < mZ1 < 120 GeV/c2 and mminZ2 < mZ2 < 120 GeV/c2 (for mmin
Z1 andmmin
Z2 see text).
90
(a)
Cu
tQ
CD
ttZ
+je
tsZ
bb
/cc
WZ
ZZ
mH
=200
Tota
lD
ata
HLT
6.1
1×
104
6.8
0×
103
1.3
9×
106
6.6
3×
105
588.9
1179.2
28.9
9(2
.12±
0.0
03)×
106
2.2
4×
106
Z1
4.7
0×
103
4.6
5×
103
1.2
1×
106
5.7
2×
105
506.8
5148.3
25.8
2(1
.79±
0.0
05)×
106
1.7
8×
106
Z1+`
19.1
2198.3
92.7
8×
103
2.1
8×
103
138.9
746.5
8.3
9(5
.38±
0.0
4)×
103
6.0
9×
103
“b
est
4`”
-1.6
51.1
93.1
80.2
517.4
3.8
027.5
1±
1.3
224
Isola
tion
-0.0
6-
0.3
90.1
116.4
3.5
320.5
1±
0.4
012
SIP3D
-0.0
2-
-0.0
915.2
3.2
918.5
9±
0.0
512
base
line
-0.0
2-
-0.0
614.5
3.2
917.8
5±
0.0
312
inte
rm
ediate
-0.0
2-
-0.0
613.9
3.2
717.2
5±
0.0
512
high-m
ass
-0.0
1-
-0.0
212.2
3.0
515.2
8±
0.0
49
(b)
Cu
tQ
CD
ttZ
+je
tsZ
bb
/cc
WZ
ZZ
mH
=200
Tota
lD
ata
HLT
1.8
8×
106
1.2
5×
104
1.6
8×
106
8.2
1×
105
658.3
2208.6
32.9
5(4
.39±
0.0
2)×
106
4.5
5×
106
Z1
655.7
05.3
9×
103
1.4
2×
106
6.6
9×
105
581.0
9168.1
28.6
7(2
.09±
0.0
2)×
106
2.1
4×
106
Z1+`
-432.2
3839.5
03.6
8×
103
175.1
456.3
9.6
7(5
.19±
0.0
5)×
103
6.3
9×
103
“b
est
4`”
-5.8
8-
13.8
90.1
625.5
5.1
950.6
6±
2.3
645
Isola
tion
-0.0
9-
1.1
90.0
424.1
4.8
930.2
9±
0.6
930
SIP3D
-0.0
2-
-0.0
323.6
4.7
928.3
8±
0.0
524
base
line
-0.0
2-
-0.0
222.6
4.7
827.4
1±
0.0
223
inte
rm
ediate
-0.0
2-
-0.0
220.7
4.7
624.4
2±
0.0
321
high-m
ass
--
--
0.0
03
17.5
4.4
220.9
1±
0.0
514
(c)
Cu
tQ
CD
ttZ
+je
tsZ
bb
/cc
WZ
ZZ
mH
=200
Tota
lD
ata
HLT
1.9
6×
106
1.9
3×
104
3.0
7×
106
1.4
8×
106
1.2
4×
103
347.5
53.3
9(6
.54±
0.0
2)×
106
6.8
2×
106
Z1
5.3
6×
103
1.0
0×
104
2.6
4×
106
1.2
4×
106
1.0
9×
103
287.2
47.8
5(3
.89±
0.0
2)×
106
3.9
1×
106
Z1+`
44.1
2520.8
24.7
9×
103
5.6
9×
103
287.3
996.6
917.2
(1.1
5±
0.0
06)×
104
1.2
9×
104
“b
est
4`”
-6.9
20.3
917.4
70.4
144.2
59.0
978.5
4±
2.6
868
Isola
tion
-0.1
20.3
92.7
70.1
940.7
48.0
452.2
7±
1.1
345
SIP3D
-0.0
6-
1.1
90.1
638.9
67.6
948.0
7±
0.6
940
base
line
-0.0
3-
1.1
90.1
337.4
77.6
946.5
9±
0.6
937
inte
rm
ediate
-0.0
3-
1.1
90.1
035.2
17.6
744.2
1±
0.6
933
high-m
ass
-0.0
1-
0.3
90.0
530.8
67.2
839.0
0±
0.0
830
Tab
.4.
4:E
vent
yie
lds
inth
e(a
)4e
,(b
)4µ
and
(c)
2e2µ
chan
nel
for
the
trig
ger
and
the
seve
nev
ent
sele
ctio
nst
eps,
(see
text)
wit
hst
eps
thre
ean
dfo
ur
regr
oup
edas
”Z1
+`+`−
”fo
rth
ech
oice
ofth
eb
est
four
lepto
ns
and
Z1,
Z2
assi
gnm
ents
.T
he
sam
ple
sco
rres
pon
dto
anin
tegr
ated
lum
inos
ity
ofL
=4.
71.
The
MC
yie
lds
are
not
corr
ecte
dfo
rbac
kgr
ound
exp
ecta
tion
.
91
the background is progressively reduced at each selection step. In particular
QCD background disappeared completely after the second (4µ channel) or
the third step (4e and 2e2µ channels). The Isolation and SIP3D cuts concur
mainly to the reduction of Z+light and Zbb/cc background reduction.
As expected, the main background contribution in the last steps is due to
the irreducible ZZ background (see also Tab. 4.4).
Fig. 4.3: Event yields in the 4e channel as a function of the event selectionsteps. The MC yields are not corrected for background expectation. Thesamples correspond to an integrated luminosity of L = 4.71 fb−1
92
Fig. 4.4: Event yields in the 4µ channel as a function of the event selectionsteps. The MC yields are not corrected for background expectation. Thesamples correspond to an integrated luminosity of L = 4.71 fb−1
4.4 Data to MC comparison
In this section a data to MC comparison of the most important observables
used in this analysis will be presented.
In Fig. 4.6 the recostructed di-electron mass fitting after the best Z1 choice
is presented for 4e channel. At this step of selection (see section 4.3) a cut
of m1,2 > 50 GeV/c2 on the invariant di-lepton object has been applied. A
quite good agreement between data and MC background expectation can be
noticed. A peak corresponding to the nominal value of the Z boson mass can
also be observed.
93
Fig. 4.5: Event yields in the 2e2µ channel as a function of the event selectionsteps. The MC yields are not corrected for background expectation. Thesamples correspond to an integrated luminosity of L = 4.71 fb−1
Fig. 4.7 shows a comparison between data and MC before preselection,
for the recostructed masses Z1 and Z2 in the 4µ channel at the end of the step
3 presented in section 4.3. At this step, the all four-lepton objects matching
the best Z1 dilepton object have been chosen and cuts on the leptons belong-
ing to each 4`-object have been applied, but the Z1 and the Z2 assignements
have not been yet performed.
It can be noticed that the data are in reasonable agreement with MC back-
ground expectation also in this case. Comparing these plots with those after
preselection, in Figs.4.8 and 4.9 for 4e and 4µ final state, i.e. after the best
four-lepton candidate choice and when the two Z’s have been assigned, we
94
Fig. 4.6: Recostructed Z1 mass after best Z1 choice in 4e channel. The eventnumber is re-scaled for an integrated luminosity of L = 4.71 fb−1
can see a drastically reduction of the Zbb/cc, Z+ligt jets, WW and QCD
background. Well shaped peaks corresponding to the nominal Z value mass
can be noticed, with data mainly distributed around them. The data to MC
comparison is reasonably good.
In the Z2 mass distributions after preselection for both 4e and 4µ channel a
double peak can be noticed at ∼ 90 GeV/c2 (see Figs. 4.8 and 4.9).
This weird feature may be due to an uncorrect recostruction of the Z2, also
considering that it can be off mass-shell, expecially at low masses.
A preliminary study about the Z1 and Z2 mis-matching has been performed
and presented in section 4.5.
In Figs. 4.10 and 4.11 the distributions of the recostructed lepton pT of
all the lepton in the event and of only the highest-pT lepton are shown for
the 4e channel after the skim selection and after the choice of the best Z1.
95
Fig. 4.7: Recostructed Z1 / Z2 mass distributions before preselection in 4echannel. The event number is re-scaled for an integrated luminosity of L =4.71 fb−1
96
Fig. 4.8: Recostructed Z1 / Z2 mass after preselection in 4e channel. Theevent number is re-scaled for an integrated luminosity of L = 4.71fb−1
97
Fig. 4.9: Recostructed Z1 / Z2 mass after preselection in 4µ channel. Theevent number is re-scaled for an integrated luminosity of L = 4.71fb−1
98
At these two steps a cut on the highest pT lepton belonging to the di-lepton
recostructed object (pT,1 > 20 GeV/c ) is applied.
By comparing the top and bottom plots in each figure, it can be seen that
this cut allows us to reject a background excess presented at low pT values.
Figs. 4.12 and 4.13 show the lepton pT distributions before and after the
preselection in 4e and 4µ channels respectively. A quite good agreement
between data and MC expectation can be noticed in both channels. A small
reduction of background can be observed at low pT values for the 4e channel,
while a greater one can be notice for Zbb and tt for the 4µ channel in the
same pT region.
Fig. 4.14 shows the Riso12 distributions for the worst isolated pair of leptons
after the choice of the best Z1 and after the preselection in the 4e channel,
while in Fig. 4.15 the Riso distributions for all the leptons after the skimming
step and after the preselection step are shown for the 4µ channel.
At the step of the choice of best Z1 level, a cut (Riso,j +Riso,i) < 0.35 on the
lepton pair coming from best Z1 has been applied.
The same final cut has been applied at the end of the full selection for any
combination of two lepton i and j to accomplish a reduction of the main
reducible background sources.
The relative isolation variable for data is well described by the MC Truth both
for electrons and for muons. This gives us confidence in performing a quite
good lepton isolation control. Leptons coming from reducible backgrounds
have generally high relative isolation values. Hence, a cut on this variable
allows a drastic reduction of these background sources.
In Figs. 4.16 and Fig. 4.17, the SIP3D distributions after best Z1 choice
and after preselection both in 4e and 4µ channels are presented.
At the level of best Z1 choice the cut |SIP3D| < 4 is applied only on the two
leptons coming from Z1 best candidate. The effect of this cut appears quite
evident in the top plot of Fig. 4.16 . It can be noticed that the reducible
background in that energy range is considerably reduced. Hence, at the end
of selection, the same cut is applied to all the recostructed selected leptons
survived (see step 7 of the section 4.3).
Generally, a quite good agreement between data and MC expectation, in
99
Fig. 4.10: Recostructed lepton pT [top] and recostructed lepton highest pTdistributions [bottom] after Skim in 4e channel. The event number is re-scaled for an integrated luminosity of L = 4.71 fb−1
100
Fig. 4.11: Recostructed lepton pT [top] and recostructed lepton highest pTdistributions [bottom] after best Z1 in 4e channel. The event number isre-scaled for an integrated luminosity of L = 4.71 fb−1
101
Fig. 4.12: Recostructed lepton pT distributions before preselection [top] andafter preselection [bottom] in 4µ channels. The event number is re-scaled foran integrated luminosity of L = 4.71 fb−1.
102
Fig. 4.13: Recostructed lepton pT distributions before preselection [top] andafter preselection [bottom] in 4e channels. The event number is re-scaled foran integrated luminosity of L = 4.71 fb−1.
103
Fig. 4.14: Recostructed lepton relative isolation Riso12 distributions for the
worst isolated lepton pairs after best Z1 choice [top] and after the preselection[bottom] in 4e channel. The event number is re-scaled for an integratedluminosity of L = 4.71 fb−1.
104
Fig. 4.15: Recostructed lepton relative isolation Riso distributions after theskimming step [top] and after the preselection [bottom] in 4µ channel. Theevent number is re-scaled for an integrated luminosity of L = 4.71 fb−1.
105
particular at low SIP3D values, can be observed. A good control of the
significance of the impact parameter can be performed using data both for
electrons and for muons.
As can be observed from the after preselection plots, applying the SIP cut
allows a good rejection of Z+jets and tt reducible background.
In Figs. 4.18 and 4.19 the invariant mass distibutions after preselection
for all the channels and that for the sum of the 4e, 4µ and 2e2µ channels is
presented.
It’s worth to remind that at this level a cut m4` > 100 GeV/c2 is applied
on the recostructed four-lepton objects survived. It can be noticed that,
expecially for 4µ and 2e2µ channels, a relevant contribution of Zbb/cc and
tt reducible background is still presented.
Comparing these plots with those after full selection (see chapter 5 section
5.1), i.e. after applying relative isolation and impact parameter cuts on the
selected leptons and kinematics cuts previously described (see section 4.3),
it can be observed that the reducible background is strongly reduced (� 1%
over the total yield in the baseline selection as can be derived from Tab 4.4).
4.5 Studies about the best four-lepton algo-
rithm
During my thesis work, an original preliminary study about the efficiency of
reconstruction algorithm for the Z1 and Z2 di-lepton pairs has been studied
by matching the reconstructed masses with the generated ones.
It has already been explained in the event selection subsection that the 4` best
candidate algorithm builds the Z1 looking for opposite sign (OS) and same
flavour (SF) di-leptons candidates with di-lepton mass mll > 50 GeV/c2,
lepton transverse momenta pT1 > 20 GeV/c and pT2 > 10 GeV/c, sum of
the lepton relative isolation Riso,j +Riso,i < 0.35 and 3D significance impact
parameter |SIP3D| < 4.
After applying these cuts, the algorithm selects the di-lepton object with
invariant mass closest to the nominal one (mZ = 91, 1876 GeV/c2).
106
Fig. 4.16: Recostructed lepton 3D Significance Impact Parameter distribu-tion after best Z1 choice [top] and after preselection [bottom] in 4e channel.The event number is re-weighted for an integrated luminosity of L = 4.71fb−1.
107
Fig. 4.17: Recostructed lepton 3D Significance Impact Parameter distribu-tion after best Z1 choice [top] and after preselection [bottom] in 4µ channel.The event number is re-weighted for an integrated luminosity of L = 4.71fb−1.
108
Fig. 4.18: Distribution of the four-lepton reconstructed mass after preselec-tion cuts in the (a) 4e, (b) 4µ, (c) 2e2µ, and (d) the sum of the 4` channels.The samples correspond to an integrated luminosity of L = 4.71 fb−1.
109
Fig. 4.19: Distribution of the four-lepton reconstructed mass after prese-lection cuts (a) 2e2µ, and (b) the sum of the 4` channels. The samplescorrespond to an integrated luminosity of L = 4.71 fb−1.
110
The Z2 selection is performed applying among the other OS and SF di-lepton
objects the cuts mll > 12 GeV/c2 on the di-lepton mass and m4l > 100
GeV/c2 on the four-lepton mass. If more than one combination is found, the
one built from leptons with highest pT is chosen.
It can be noticed, however, that for Higgs mass values mH < 2mZ at least
one between the two Z tends to be off-mass shell and the algorithm can fail to
select the best di-lepton mass. As it is shown in Fig. 3.8 (chapter 3, section
3.4), which represents the MC generated Z1 and Z2 mass distributions for
an Higgs mass mH = 120 GeV/c2, the Z2 mass distribution is peaked at a
lower value than the nominal Z boson mass one. In such a case the algorithm
Fig. 4.20: Monte Carlo Z1 and Z2 mass distributions for Higgs mass mH =120 GeV/c2
previously described becomes inefficient and so possible consequences of this
biased procedure on the final 4` candidates selection have been investigated
at low masses.
111
4.5.1 The Method
The procedure followed for checking the algorithmic efficiency for the Z1 and
Z2 reconstruction has been developed through the following steps:
• comparing the information of the recostructed di-lepton candidates and
the Z’s from the MC Truth by applying a matching procedure between
the reco- and MC Truth objects
• matching the recostructed leptons objects coming from Z1 and Z2 with
those from MC Truth
• searching for alternative recostructed di-lepton objects which could
eventually match with the Z at MC Truth level
• evaluating the rate of fake Z1 and Z2 objects related to a wrong leptons
assignment to the two Z’s
The variables used for testing the matching perform a check on
• isolation matching ∆R < 0.15
• mass matching
• pT matching ∆prelT < 0.5
• η matching
• φ matching
Z Recostrucion Algorithm Efficiency
In order to check the matching between the recostructed Z1 and Z2 di-lepton
objects built in baseline analysis with the Z1 and Z2 objects from MC Truth,
a study of the efficiency of the Z1/Z2 matched over the number of total events
passing the baseline selection at the level of best Z1 and Z2 choice has been
performed.
The corresponding plots for 4e, 4µ and 2e2µ are shown below in Figg. 4.21,
4.22 and 4.23 respectively.
112
Fig. 4.21: Z1/Z2 Recostruction Algorithm Efficiency for 4e-channel vs Higgsmass.
It can be noticed that in each channel the two Z’s are not matched with
those from MC Truth for a not negligible fraction of events (up to 30% for
the 4e channel and up to 25% for 4µ and 2e2µ channels) in the low mass
region. Fig. 4.24 shows the Z1/Z2 recostruction algorithm efficiency as a
function of the MC Truth Higgs trasversus momentum in 4µ channel for an
Higgs mass mH = 120 GeV/c2.
It can be noticed that the efficiency of choosing the best Z1 decreases with
lowering pT of the Higgs boson, while that for Z2 remains pretty constant.
Matching leptons from Z1 and Z2
The next step of this study was to check if the leptons coming from the
recostructed Z’s are matched with leptons from MC Truth.
The corresponding plots are presented in Fig. 4.25 for 4µ channel and in Fig.
4.26 for 4e channel.
The lepton matching efficiency is found to be very close to unity for both
113
Fig. 4.22: Z1/Z2 Recostruction Algorithm Efficiency for 4µ-channel vs Higgsmass.
Z1 and Z2 in the 4µ channel, while it reaches lower values for 4e channel at
high masses, keeping anyway always above 80%.
The quite good agreement in lepton matching even when the corresponding
Z1 and Z2 are not matched could reveal a possible wrong pairing of the
leptons coming from the two Z’s.
Impact of Z1 and Z2 mis-match on final selection
After the preliminary studies presented above on the Z1 and Z2 mismatch at
Z1/ Z2 choice level, further investigations about the impact on final selection
have been performed. These have been carried out by
• checking the events in which both Z1 and Z2 are matched with those
from MC Truth after passing the full selection
• checking the events in which neither Z1 nor Z2 are matched with those
coming from MC Truth after passing the full selection
114
Fig. 4.23: Z Recostruction Algorithm Efficiency for 2e2µ-channel
Fig. 4.24: Z1 [left] and Z2 [right] Recostruction Algorithm Efficiency for 4µ-channel vs Higgs pT .
115
Fig. 4.25: Z1 [left] and Z2 [right] Muon Matching Efficiency for 4µ channel.
Fig. 4.26: Z1 [left] and Z2 [right] Muon Matching Efficiency for 4e channel.
116
• checking if in those in which the matching has failed there exist any
di-lepton pair different from the recostructed Z1 /Z2 pairs which match
with the MC Truth corresponding object
In Fig. 4.27 the efficiency, built as the number of events for which the two
Z’s are both matched and pass the full selection over the number of events
passing the full selection, has been plotted against the Higgs mass for 4e and
4µ channels.
Fig. 4.27: Z1 and Z2 Matching Efficiency for 4e [left] and 4µ [right] after fullselection
We can notice that at low mass values (mH < 300 GeV/c2) about 10-
25 % for 4µ channel and 10-40 % for 4e channel of the events passing the
full selection do not have the two Z’s matched with those from MC Truth.
So at low masses a mis-match between the reconstructed Z1 and Z2 and
the corresponding MC Truth objects seems evident. Then, the next step
has been to check if alternative matched di-lepton objects exist among the
remaining reconstructed ones. In Fig. 4.28 the number of events passing the
full selection for which there is an alternative choice of Z1 and Z2 matching
the MC Truth over the number of events passing the full selection versus
Higgs mass for 4e and 4µ channels are presented.
It is clear from these last plots that for about 15-20 % of events that pass
the full selection there is an alternative choice of reconstructed di-lepton ob-
117
ject that can match Z at MC Truth, confirming the wrong pairing hypothesis.
Bias in final selection:“fake” events ratio
In previous subsections it has been established that, at least at low masses,
we can reconstruct events with wrong pairing. These events can pass the full
selection but they should have not if the correct pairing had been applied.
So this events can be labelled as “fake” events. Consequently, the last step
of this analysis has been checking the percentage of these fake events, i.e.
the number of events passing the full selection for which Z1 and Z2 are not
matched and for which there is no other di-lepton object with mll > 50
GeV/c2 matching the MC Truth over the number of events passing the full
selection. The events have been selected following the baseline selection
because of wrong assignment of Z1 and Z2. These “fake” signal events can
be responsible for an over-estimation of the signal rate in the low mass region.
The plots showing the percentage of fake events versus Higgs mass in 4e and
4µ channels are presented in Fig. 4.29.
As it can be observed, in the low mass region the 8% of events for the
4e channel and the 12% of events for the 4µ channel is passing the full se-
lection, even if the Z reconstructed objects are not matched, so they can be
Fig. 4.28: Z1 and Z2 Matching Efficiency for 4e [left] and 4µ [right] after fullselection
118
considered as fake events.
From this preliminary study we can conclude that the Z1/Z2 matching is
less efficient at low mass values.
It has been found that it has an impact on signal events passing the full
selection at the level of 8%/12% of signal rate overestimation in 4e and 4µ
channels. The impact on ZZ background is expected to be almost the same,
but the one for Z+jets still needs to be investigated. Possible improvements
for the baseline analysis are currently under study. They could be
• changing the event selection strategy keeping all the di-lepton/4` com-
binations until the end of the full selection.
• lowering the cut at mll > 50 GeV/c2 on Z1. This procedure could cut
the tail of the Z1 distribution.
Finally, it can be underlined that in this context, where the two Z’s could
be both off-mass shell, the distinction between Z1 and Z2 at low Higgs mass
becomes meaningless and loose justification.
Fig. 4.29: Fraction of “fake” events (see text) which pass the full selectionversus Higgs mass in 4e [left] and in 4µ [right] channel.
119
4.6 Background Evaluation and Control
No specific studies on background estimation from data have been performed
for this thesis. Nevertheless, a quick overview of the background evaluation
and control has been included.
The total number of signal-like background events surviving the baseline se-
lection is quite small for the integrated luminosity reached in this analysis
(see section 5.1).
A precise evaluation of the background, using only the side-bands method
[45], is then not possible because of the small number of observed events
in the relevant narrow signal-like region. Then, for background control and
systematics evaluation, other data driven methods have been used.
According to the event yields evaluated from MC simulations and shown in
Table 4.4, the background is overwhelmingly composed of the ZZ(∗) contin-
uum with just a small contamination from the reducible and instrumental
backgrounds.
The tt and WZ backgrounds appear negligible, i.e. they both represent� 1%
of the total background rate expected for the baseline selection. Only a few
events survive for Z+γ but these are actually Z+γ+jets events. The Z de-
cays in a pair of muons while at least one jet fragment is mis-identified as an
electron, and one electron at most comes from the photon conversion. This
background is then treated in common with the Z+jets background.
Unfortunately, the MC event yield in Table 4.4 does not allow to get conclu-
sive results on the the situation for Z+jets, and Zbb backgrounds because of
the low statistics. Hence, these backgrounds must be evaluated from data. It
could be observed in this way, that only a small contamination from Z+jets,
and Zbb remains for the baseline selection, concentrated mostly at low m4`.
The typical procedure for the background evaluation from data consists of
choosing a background control region outside the signal phase space, which
becomes populated with background events, by relaxing some cuts of the
event selection. Then it has to be verified that the event rates change ac-
cording to the Monte Carlo expectation.
The control region has to be chosen carefully for any given background since
120
any other reducible backgrounds might rapidly become dominant if the event
selection is relaxed, thus making the extrapolation to the signal phase space
difficult.
4.7 Systematic uncertainties
4.7.1 Theoretical uncertainties
Signal theoretical uncertainties
Systematic errors from the theory on the signal total cross section for each
production mechanism and for all Higgs boson masses are computed in Ref.
[34]. They come from PDF+αs choice and from the theoretical uncertainties
related to the QCD renormalization and factorization scales (µR and µF ).
The uncertainty on BR(H → 4l) is taken to be 2% [3, 2, 1]. It has been
assumed to be mH-independent.
As the Higgs boson total width ΓH becomes very large, additional uncer-
tainties related to the theoretical treatment of running Higgs width and
due to non-negligible effects of the signal-background interference between
gg → H → ZZ and gg → ZZ must be considered.
Following Ref. [11], one more uncertainty has been added on the Higgs boson
cross sections (all sub-channels) just to cover for all systematic errors specific
to high mass Higgs bosons. Depending on the Higgs boson mass, the lepton
kinematic cuts restrict the signal acceptance to A ∼ 0.6− 0.9 [24].
2e2µ final state has been used for the calculation of the impact of the previous
scales on the acceptance and the following cuts have been applied:
• electrons satisfying |ηe| < 2.5 and with peT > 7
• muons satisfying |ηµ| < 2.4 and pµT > 5
• opposite sign same flavour pairs satisfy m`` > 12
The results are shown in Table 4.5.
It can be noticed that the acceptance errors are very small (0.1-0.2%)
and, therefore, can be neglected.
121
Higgs boson mass mH (GeV) 120 200 400 500 600Default A0 (µR = µF = mH/2) 0.5421 0.7318 0.8120 0.8421 0.8637Aup (µR = µF = mH) 0.5417 0.7317 0.8128 0.8427 0.8644Adown (µR = µF = mH/4) 0.5430 0.7328 0.8119 0.8418 0.8632δA /A = max |∆A| /A0 0.17% 0.14% 0.11% 0.07% 0.08%
Tab. 4.5: Signal acceptance A for different QCD scales.
For an estimate of the effect of the harder Higgs pT spectrum in POWHEG than
the one predicted by the theoretical calculation at NNLL+NLO, Higgs boson
events in MC have been re-weighted to make their pT spectrum matching
the one obtained in HqT program [29] and then the change in the signal
acceptance arising from the lepton kinematic cuts used in the analysis has
been evaluated.
It has been find that, before the complete selection cuts, the relative change
in the H → ZZ → 4` acceptance, shown in Fig. 4.30, is (1%). It has been
checked that this effect is negligible at the end of the analysis, or, at least,
much smaller than the theoretical errors on the gg → H cross section, (10%).
Thus, this correction is neglected in the H → ZZ → 4` search.
/ ndf 2χ 5.134e-06 / 4const 32.32± 56.22 scale 32.79± 55.14 p2 0.4± 0
2 , GeV/cHm150 200 250 300 350 400 450 500
unw
eigh
t/A
wei
ght
A
0.97
0.975
0.98
0.985
0.99
0.995
1
/ ndf 2χ 5.134e-06 / 4const 32.32± 56.22 scale 32.79± 55.14 p2 0.4± 0
unweight/Aweight2e2mu: A
unweight/Aweight4mu: A
unweight/Aweight4e: A
-55.14)H
-56.22)/(mH
Fit: (m
Fig. 4.30: The change in the H → 4` acceptance due to the Higgs pHT re-weighting in POWHEG to match the HqT calculations.
122
ZZ background theoretical uncertainties
PDF+αs and QCD scale uncertainties for qq → ZZ→ 4` at NLO and gg →ZZ→ 4` have been evaluated using MCFM [19].
The 2e2µ final state has been used and the following cuts applied:
• electrons satisfying |ηe| < 2.5 and with peT > 7GeV/c
• muons satisfying |ηµ| < 2.4 and pµT > 5
• opposite sign same flavour pairs satisfy m`` > 12 GeV/c2.
The cuts on the jet energy ET and the minimal jet-lepton ∆R-distance have
been relaxed also in this case.
To estimate QCD scale systematic errors, variations in the differential cross
section dσ/dm4` with changing the renormalization and factorization scales
by a factor of two up and down from their default setting µR = µF = mZ
have been calculated.
Instrumental uncertainties
The uncertainty on the luminosity measurement has been estimated as 4.5% [10].
The pile-up effect has also been evaluated re-weighting the Monte Carlo sim-
ulation to match the number of reconstructed vertices found in data. The
difference between re-weighting and not weighting at all has been taken as
an upper limit of this effect.
The estimate uncertainty on the efficiency is very small and it has been ne-
glected.
The trigger efficiency for signal-like events is very close to 100% within the
acceptance defined by the baseline cuts. Therefore the overall data/MC
discrepancy in trigger efficiency for the signal and for the irreducible back-
grounds turns to be negligible and a systematic uncertainty of 1.5% has
been assigned. The observed data/Monte Carlo discrepancy in the lepton
reconstruction and identification efficiencies measured with the data-driven
technique has been used to correct the Monte Carlo on an event-by-event
basis.
123
The uncertainties on this efficiency correction have been propagated inde-
pendently to obtain a systematic uncertainty on the final yields for signals
and backgrounds. A systematic uncertainty on the efficiency of this cut in
MC cannot be properly determined from the discrepancy of efficiencies for a
fixed isolation cut just because the isolation cut is applied on the sum of the
isolation values of pairs of leptons.
It is then estimated by considering the cut on the sum as a variable cut on
the worst-isolated lepton of the pair, and propagating the largest data/Monte
Carlo discrepancy observed while varying the cut in the full range [0.0, 0.35].
Background normalization
Additional statistical uncertainties derive from the data driven methods used
to estimate the amount of background from ZZ, Zbb, tt and Z+jets.
In Tab.4.6 a summary of the magnitude of theoretical and phenomenological
systematic uncertainties for H → ZZ → 4` and ZZ → 4` is presented,
while Tab.4.7 shows a summary of the magnitude of instrumental systematic
uncertainties in percent for H → ZZ → 4` and ZZ → 4`.
2*Source of uncertainties Error for different processesggH VBF WH ZH ttH ZZ ggZZ
gg partonic luminosity 8 8-10 10qq/qq partonic luminosity 2-7 3-4 3-5 5
QCD scale uncert. for gg → H 5-12QCD scale uncert. for VBF qqH 0-3QCD scale uncert. for V H 0-1 1-2QCD scale uncert. for ttH 3-114`-acceptance for gg → H negl. negl. negl. negl. negl.Wide Higgs uncertainties 1 + 1.5× (mH/1TeV )3
Uncertainty on BR(H → 4`) 2 2 2 2 2
QCD scale uncert. for ZZ(NLO) 2-6QCD scale uncert. for gg → ZZ 20-45
Tab. 4.6: Summary of the magnitude of theoretical and phenomenologicalsystematic uncertainties in percent for H → ZZ → 4` and ZZ → 4`. Errorsare common to all 4` channels.
124
Source of uncertainties Error for different processesH → ZZ → 4` ZZ/ggZZ → 4`
4e 4µ 2e2µ 4e 4µ 2e2µ
Luminosity 4.5 4.5 4.5 4.5 4.5 4.5
Trigger 1.5 1.5 1.5 1.5 1.5 1.5
electron reco/ID 3.8-1 - 2-0.5 1.7 - 1.1muon reco/ID - 2-0.8 1.2-0.4 - 1. 0.5
electron isolation 2 - 1 2 - 1muon isolation - 1 1 - 1 1
electron ET scale (error on ET scale) 0.3-0.4 - 0.3-0.4 0.3-0.4 - 0.3-0.4muon pT scale (error on pT scale) - 0.5 0.5 - 0.5 0.5
Tab. 4.7: Summary of the magnitude of instrumental systematic uncer-tainties in percent for H → ZZ → 4` and ZZ → 4`. The instrumentalsystematic uncertainties for all five Higgs boson production mechanisms areassumed to be same, similarly on ZZ → 4` (NLO) and gg → ZZ → 4`.The uncertainties assigned for the lepton reconstruction, identification andisolation apply to the event yields. The uncertainty assigned to the elec-tron/muon scale is further propagated through the shape of the expectedsignal and background reconstructed mass distributions.
125
Chapter 5
Results
5.1 Mass Distributions and Kinematics
The reconstructed four-lepton invariant mass distributions after full selec-
tion (baseline) obtained in the 4e, 4µ, and 2e2µ channels is shown in Figs.
5.1 and 5.2 for the data, and compared to expectations from the SM main
backgrounds. A plot for the sum of the three 4` channel is also shown in
Fig. 5.3. The combination of the three channels does not reveal a particular
clusterization of data around any given mass.
The number of events observed, as well as the background rates in the sig-
nal region within a mass range from m1 = 100 GeV/c2 to m2 = 600 GeV/c2,
are reported for each final state in Table 5.1 for the baseline selection. It can
be seen that, at this last selection step, only a very small fraction (< 1%) of
the reducible Zbb/Zcc, tt, WZ and Single Top backgrounds survived to the
full selection. The main contribution comes obviously from the irreducible
ZZ continuum. The total backgroud after all the selection steps (see chapter
4, section 4.3) is considerably reduced with respect to that presented in Figs.
4.18 and 4.19 in chapter 4, section 4.4, after the preselection step.
A zoom on the low mass range (mH < 160 GeV/c2) is shown in Fig. 5.4 for
the combination of the three channels. It can be observed that the reducible
and instrumental backgrounds have found to be very small or negligible.
127
Fig. 5.1: Distribution of the four-lepton reconstructed mass after full selectioncuts in4e [top] and 4µ [bottom]. The samples correspond to an integratedluminosity of L = 4.71 fb−1.
128
Fig. 5.2: Distribution of the four-lepton reconstructed mass after full selectionin 2e2µ channel. and the sum of the 4` channels [bottom]. The samplescorrespond to an integrated luminosity of L = 4.71 fb−1.
5.2 Statistical interpretation: The CLs Method
A statistical method has been used in order to quantify the sensitivity of the
experiment to the presence of a Higgs boson signal. It is called the modified
frequentist method (also referred to as CLs or hybrid frequentist-bayesian)
[31, 47, 18].
To fully define this method, the choice of the test statistic and how to treat
nuisance parameters in the construction of the test statistic and in generating
pseudodata have to be specified.
In this section, the expected SM Higgs boson event yields will be generically
denoted as s and total background as b. These stand for event counts in one
or multiple bins or for unbinned probability density functions; the latter ,
exploiting the four-lepton mass spectrum, is the approach used for this anal-
129
Fig. 5.3: Distribution of the four-lepton reconstructed mass after full selectionfor the sum of the 4` channels. The samples correspond to an integratedluminosity of L = 4.71 fb−1.
130
Baseline 4e 4µ 2e2µZZ 14.46 ±0.04 22.55 ±0.05 37.47 ± 0.08
Zbb/cc - - 1.19 ± 0.69tt 0.02± 0.01 0.02±0.01 0.03 ± 0.01
WZ 0.06± 0.01 0.02±0.01 0.13 ± 0.02Single Top - 0.05±0.04 -
All background 14.54± 0.04 22.64± 0.07 38.82± 0.69mH = 120 GeV/c2 0.26 0.67 0.79mH = 140 GeV2 1.30 2.51 3.57mH = 350 GeV/c2 1.95 2.61 4.64
Observed 12 23 37
Tab. 5.1: Number of event candidates observed, and background and signalrates for each final state for 100 < m4` < 600 GeV/c2 for the baselineselection.
ysis.
In absence of a clear signal it is common to express null results of the SM-like
Higgs searches as an exclusion limit on a signal strength modifier µ that is
taken to change the SM Higgs boson cross sections of all production mech-
anisms by exactly the same scale. The parameter µ is defined as the ratio
between the observed cross section and the cross section expected from the
SM.
Predictions for both signal and background yields, prior to the scrutiny of
the observed data entering the statistical analysis, are exposed to multiple
uncertainties that are handled by introducing nuisance parameters θ, so that
signal and background expectations become functions of the nuisance param-
eters: s(θ) and b(θ).
The systematic error pdfs (probability density functions) ρ(θ|θ), where θ is
the default value of the nuisance parameter, take into account the degree of
belief on what the true value of θ might be.
Next, a conceptual step has to be followed, in which ρ(θ|θ) have to be re-
interpreted as posteriors, i.e. as if it arises from some real or imaginary
measurements of θ .
The connection between the a priori and a posteriori probability is stated
131
Fig. 5.4: Distribution of the four-lepton reconstructed mass for the sumof the 4` channels in the low-mass domain with mH < 160 GeV/c2. Pointsrepresent the data, shaded histograms represent the signal and backgroundexpectations. The results are presented for an integrated luminosity of 4.71fb−1
by the Bayes’ theorem [5]:
ρ(θ|θ) = p(θ|θ) · πθ(θ) (5.1)
where the πθ(θ) functions are hyper-priors for those “measurements”. The
pdfs chosen to work with (normal, log-normal, gamma distribution) can be
easily re-formulated in such a context, while keeping πθ(θ) flat. This shift in
the point of view allows one to represent all systematic errors in a frequentist
132
context. A list of the main steps to derive the exclusion limits for this analysis
is presented in the next section.
5.2.1 The Likelihood function and the test statistics
1. Firstly, a likelihood L(data |µ, θ)fuction has to be built.
L(data |µ, θ) = Poisson(data|µ · s(θ) + b(θ)) · p(θ, θ)(5.2)
where “data” could represent either the actual experimental observa-
tion or the pseudo-data (toy experiment) used to construct sampling
distributions. The parameter µ is the signal strenght modifier, as al-
ready mentioned, and θ represents the whole suite of nuissance param-
eters.
Poisson(data|µ · s(θ) + b(θ)) stands either for a product of the Poisson
probabilities to observe ni events in bins i:
∏i
µsi + bini
ni!e−µsi−bi (5.3)
or for an unbinned likelihood in the data sample:
∏i
(µSfs(xi) +Bfb(xi)) · e−µS+B (5.4)
where in the equation 5.4 fs(x) and fb(x) are the pdf s of signal and
background of some observables x, while S and B are the total event
rates expected for signal and background respectively.
2. A test statistic qµ has to be costructed to compare the compatibil-
ity of the data with the background-only (null hypothesis) and sig-
nal+background hypotheses. It can be defined as
qµ = −2 lnL(data|µ, θµ)
L(data|µ, θ)where 0 ≤ µ ≤ µ. (5.5)
133
where θµ is the maximum likelihood estimators of θ, given the sig-
nal strength parameter and “data” which, as before, may refer to the
experimental observation or pseudo-data (toys). The parameter esti-
mators µ and θ correspond to the global maximum of the likelihood.
The lower constraint 0 ≤ µ is dictated by the fact that the signal rate
must be positive while the upper constraint µ ≤ µ is imposed by hand
to guarantee a one-side confidence interval.
3. The observed value of the test statistic qobsµ for the given µ under test
has to be derived.
4. The values of nuisance parameters θobs0 and θobsµ which best describe the
experimentally observed data have to be derived for the background-
only and signal+background hypothesis respectevely.
5. The fifth step consists in generating toy Monte Carlo pseudo-data
to construct the pdfs f(qµ|µ, θobsµ ) and f(qµ|0, θobs0 ) , where a signal
strenght µ is assumed in the signal+background hypothesis and a null
signal strenght is assumed in the background-only hypothesis. An ex-
ample of this distributions is shown in Fig. 5.5.
6. After the costruction of the pdf s, two p-values to be associated to the
actual observation in the two hypotheses have to be defined, pµ and pb:
pµ = P (qµ ≥ qobsµ |signal + background) =
∫ ∞qobsµ
f(qµ|µ, θobsµ )dqµ, (5.6)
1−pb = P (qµ ≥ qobsµ |background−only) =
∫ ∞qobs0
f(qµ|0, θobs0 )dqµ, (5.7)
The CLs can be then expressed as the ratio:
CLs(µ) =pµpb. (5.8)
134
7. The next step is the evaluation of CLs for µ = 1. If CLs ≤ α it can
be stated that the SM Higgs-boson is excluded at (1-α) CLs confidence
level (C.L.).
8. Finally, to quote the 95% confidence level upper limit on µ, which we
are interested in, the signal strenght modifier is adjusted until the value
of CLs=0.05 is reached.
Fig. 5.5: Test statistic distributions for ensambles of pseudodata generatedfor signal+background and background-only hypotheses.
To quantify an excess of events, we use the test statistic q0, defined as
follows:
q0 = −2 lnL(data|0, θ0)
L(data|µ, θ)and µ ≥ 0. (5.9)
This test statistic is known to have a χ2 distribution for one degree of
freedom, which allows us to evaluate significances (Z) and p-values (p0) from
135
the following asymptotic formula, derived from the asymptotic properties of
the test statistic based on the profile likelihood ratio [18]:
Z =√qobs
0 , (5.10)
p0 = P (q0 ≥ qobs0 ) =
∫ ∞Z
e−x2/2
√2π
dx =1
2
[1− erf
(Z/√
2)], (5.11)
where qobs0 is the observed test statistic calculated for µ = 0 and with only
one constraint 0 ≤ µ, which ensures that data deficits are not counted on an
equal footing with data excesses. The “erf” stands for the error function.
The approximation has been tested for the range of expected background
and signal yields. The data can be, as usual, the actual experimental obser-
vation or pseudo-data. As previously pointed out, both the numerator and
the denominator are maximized and θ0, µ, θ are the values corresponding to
this maximum.
The p-value variable is used to quantify the consistency of the observed ex-
cess with the background only hypothesis. Whilst the p-value characterizes
the probability of observing a given excess of events, it does not give any
information about the compatibilty of the excess with the expected signal.
A measure of this compatibility is given by a best fit of µ variable. Two
kinds of p-value can be defined: a local p-value, defined for a particular mass
value or a very restricted range of mass, and a global p-value, which takes
into account the look-elsewhere effect for the entire search mass range (see
Ref. [5]). It can be defined as the probability for a background fluctuation
to match or exceed the observed excess anywhere in a specified mass range
[15].
5.2.2 Determination of the exclusion limits
To define the expected median upper limit and ±1σ and ±2σ bands for the
background-only hypothesis a set of background-only pseudo-data must be
generated. Then, CLs and µ95%CL can be calculated as they were real data.
The µ95%CL is the value of the signal strenght modifier at which the 95%
confidence level upper limit is reached.
136
Hence, a cumulative probability distribution of the results can be built start-
ing to the side corresponding to low event yields (see Fig. 5.6, right).
The median expected value is the point at which the cumulative distribu-
tion crosses the quantile 50%, while the ±1σ (68%) band is defined by the
crossing of the 16% and 84% quantiles and the ±2σ (95%) is defined by the
crossing of the 2.5% and 97.5%.
Fig. 5.6: [Left] An example of differential distribution of possible limits onµ for the background-only hypothesis (s=0, b=1, no systematics). [Right]Cumulative probability distribution of the plot with 2.5%, 16%, 50%, 84%,97.5% quantiles (horizontal lines), defining both the median expected limitand the ±1σ (68%) and ±2σ (95%) bands for the expected values of µ in thebackground-only hypothesis.
The observed and mean expected 95% CL upper limits on Higgs σ(pp→H + X) × B(ZZ → 4`), obtained for Higgs masses in the range 110-600
GeV/c2, are shown in Fig. 5.7. It can be seen that upper limits at 95 % CL
on the product of the cross section and branching ratio exclude the SM Higgs
boson in the ranges 134 < mH < 158 GeV/c2, 180 < mH < 305 GeV/c2 and
340 < mH < 465 GeV/c2.
The limits are made using a CLs approach. The bands represent the 1σ and
2σ probability intervals around the expected limit.
The expected background yield is small, hence the 1σ range of expected
outcomes includes pseudo-experiments with zero observed events. The lower
edge of the 1σ band therefore corresponds already to the most stringent limit
137
on the signal cross section, as fluctuations below that value are not possible.
As already pointed out, the systematic uncertainties have been taken into
account in the form of nuisance parameters with a log-normal probability
density function. The exclusion limits extend at high mass beyond the sen-
sitivity of previous collider experiments.
It can be observed that the differences between the observed and the expected
limits are fairly consistent with statistical fluctuation, as the observed limits
fall generally within the green and yellow bands. We can also see that the
expected limits reflect the dependence of the branching ratio B(H→ZZ) on
mH .
The significance of the local excesses relative to the standard model ex-
pectation as a function of mH is shown in Fig. 5.8, obtained both without
or with individual candidate mass measurement uncertainties1 for the com-
bination of the three channels.
Event-by-event mass errors are evaluated starting from the errors on the in-
dividual lepton momenta.
For muons, the full error matrix, as obtained from the muon track fit, as
been used.
For electrons, the estimated error on the momentum magnitude, as obtained
from the combination of the ECAL and tracker measurement is used, ne-
glecting the uncertainty on the track direction from the Gaussian Sum Filter
fit. The lepton momentum measurement errors are then propagated to the
4l mass error and to the Z1 and Z2 mass errors using an analytical error
propagation including all correlations.
Excesses are observed for masses near 120 GeV/c2 and 320 GeV/c2. The
small 2σ excess near 320 GeV/c2 includes three events with p4`T >50 GeV/c.
The most significant excess is present near 120 GeV/c2 and corresponds to
about 2.5σ [2.7σ] significance, not including [or including] candidate mass
1The precision on the estimation of the mH and mZ∗ masses can vary significantly onevent-by-event depending on the p`T and η`. In the case of electrons, energy measurementuncertainties can furthermore vary significantly depending on the “category” of the re-constructed electron object, i.e. depending if the electron initiates a shower early in thetracker volume (“showering” electrons) or reaches the ECAL surface largely unperturbed(”golden” electrons). Overall, uncertainties on the measured ∆mH and ∆mZ∗ can varyby a factor up to three or so for the same initial mass mH.
138
uncertainties.
The significance is less than 1.0σ [about 1.6σ] when the look-elsewhere [5] ef-
fect is taken into account for the full mass range (100 < m4` < 600 GeV/c2).
Hence, we can remark that the data do not reveal a significant clustering of
events at any mass value.
5.3 Latest Results of the Standard Model Higgs
Search in the H → ZZ → 4` channel at√s = 8 TeV with 2012 data.
Even if the 2012 data samples have not been used to develop the selection
cuts for this thesis work, the importance of the 2012 results deserves to be
here presented.
The latest analysis has been designed for a Higgs boson in the mass range
100 < mH < 800 GeV/c2.
It used the data collected by CMS in 2011, combining them with the new
data collected in 2012 at√s = 8 TeV which corresponds to an additional
integrated luminosity of 5 fb−1 [14].
The reconstructed four-lepton invariant mass distribution for the 4` is shown
in Fig. 5.9. It combines the 4e, 4µ and 2e2µ channel information. We fo-
cused only on low mass values which represent the region of main interest.
A good agreement between data and MC background expectation can be
observed. The main background contribution after applying all the selection
cuts, is due to the irreducible background ZZ, with a smaller contribution of
Z+X, calculated by data driven techniques, at low masses.
The measured distributions are compared with the SM background expecta-
tion and exclusion limits at 95% CL on the µ ratio of the production cross
section for the Higgs boson to the SM expectation have been derived.
The upper limits obtained for the 4` and 2`2τ channel combination are shown
in Fig. 5.10. It can be observed that upper limits at 95% CL exclude the
presence of SM Higgs boson in the range 130-520 GeV/c2.
An excess of events has been observed in the low mass range in the 4` chan-
139
nel.
In Fig. 5.11, the local p-values in the full mass range and in the low mass
range region are shown as a function of mH . It can be observed that a lo-
cal minimum is reached approximately for the Higgs boson mass hypothesis
mH = 126 GeV/c2, corresponding to a local significance of 3.2σ.
140
[a] ]2 [GeV/cHM200 300 400 500
SM 4
l)(H
/
(95%
CL)
4l)
(H
-110
1
10
4l, Asym CLs ZZ Observed Limit, H 4l, Asym CLs ZZ Expected Limit, H
68% expectation95% expectation
SM / CMS Preliminary 2011 -1 = 7 TeV, L = 4.7 fbs
110 600
Expected ± 1σ
Expected ± 2σ
Observed
CutHLT Z1 Z1 + l
Presel.Iso IP Kin (basel.)
Kin (int.)Kin (high)
Even
ts/1
Eve
nts
-110
1
10
210
310
410
510
610
710 DATAQCDtt
Z+light jetsc/cbZb
W+jetsSingle topWWWZZZ 2=350 GeV/cHm
2=200 GeV/cHm2=140 GeV/cHm
CMS Preliminary 2011 -1 = 7 TeV L = 4.71 fbs
[b] ]2 [GeV/cHM120 140 160 180
SM 4
l)(H
/
(95%
CL)
4l)
(H
-110
1
10
4l, Asym CLs ZZ Observed Limit, H 4l, Asym CLs ZZ Expected Limit, H
68% expectation95% expectation
SM / CMS Preliminary 2011 -1 = 7 TeV, L = 4.7 fbs
110
Expected ± 1σ
Expected ± 2σ
Observed
CutHLT Z1 Z1 + l
Presel.Iso IP Kin (basel.)
Kin (int.)Kin (high)
Even
ts/1
Eve
nts
-110
1
10
210
310
410
510
610
710 DATAQCDtt
Z+light jetsc/cbZb
W+jetsSingle topWWWZZZ 2=350 GeV/cHm
2=200 GeV/cHm2=140 GeV/cHm
CMS Preliminary 2011 -1 = 7 TeV L = 4.71 fbs
Fig. 5.7: The mean expected and the observed upper limits at 95% C.L.on σ(pp → H + X) × B(ZZ → 4`) for a Higgs boson (a) in the mass range110-600 GeV/c2, (b) zoom in the low mass range (110-180 GeV/c2), for anintegrated luminosity of 4.71fb−1 using the CLs approach. The results areobtained using a shape analysis method.
141
[a] ]2 [GeV/cH
Higgs mass, m200 300 400 500 600
p-v
alue
-410
-310
-210
-110
1-1= ~4.7 fbint=7 TeV LsCMS Private
4l ( without event-by-event mass resolution ) ZZ H
4l ( with event-by-event mass resolution ) ZZ H
MH [GeV/c2]110
CutHLT Z1 Z1 + l
Presel.Iso IP Kin (basel.)
Kin (int.)Kin (high)
Even
ts/1
Eve
nts
-110
1
10
210
310
410
510
610
710 DATAQCDtt
Z+light jetsc/cbZb
W+jetsSingle topWWWZZZ 2=350 GeV/cHm
2=200 GeV/cHm2=140 GeV/cHm
CMS Preliminary 2011 -1 = 7 TeV L = 4.71 fbs
1σ
2σ
3σ
[b]
14
p-value
FOR PRL inside the enlarged
Inclusive analysisZOOM
]2 [GeV/cH
Higgs mass, m110 115 120 125 130 135 140 145 150 155 160
p-v
alue
-410
-310
-210
-110
1-1= ~4.7 fbint=7 TeV LsCMS Private
4l ( without event-by-event mass resolution ) ZZ H
4l ( with event-by-event mass resolution ) ZZ H
]2 [GeV/cH
Higgs mass, m110 115 120 125 130 135 140 145 150 155 160
p-v
alue
-410
-310
-210
-110
1-1= ~4.7 fbint=7 TeV LsCMS Private
4l ( without event-by-event mass resolution ) ZZ H
4l ( with event-by-event mass resolution ) ZZ H
1σ
2σ
3σ
p-va
lue
16
p-value
Without vs. With event-by-event mass errors
Inclusive analysisZOOM
]2 [GeV/cH
Higgs mass, m110 115 120 125 130 135 140 145 150 155 160
p-v
alue
-410
-310
-210
-110
1-1= ~4.7 fbint=7 TeV LsCMS Private
4l ( without event-by-event mass resolution ) ZZ H
4l ( with event-by-event mass resolution ) ZZ H
100 110 120 130 140 150 160100 110 120 130 140 150 160100 110 120 130 140 150 160100 110 120 130 140 150 160100 110 120 130 140 150 160100 110 120 130 140 150 160
]2 [GeV/cH
Higgs mass, m110 115 120 125 130 135 140 145 150 155 160
p-v
alue
-410
-310
-210
-110
1-1= ~4.7 fbint=7 TeV LsCMS Private
4l ( without event-by-event mass resolution ) ZZ H
4l ( with event-by-event mass resolution ) ZZ H
MH [GeV/c2]
Fig. 5.8: Significance of the local fluctuations with respect to the standardmodel expectation as a function of the Higgs boson mass for an integratedluminosity of 4.71 fb−1, with the default average (blue) and event-by-event(red) resolutions, (a) in the mass range 110-600 GeV/c2. (b) in the low massrange (110-160 GeV/c2).
142
[GeV]4lm80 100 120 140 160
Eve
nts
/ 2 G
eV
0
2
4
6
8
10
12
Data
Z+X
ZZ
=126 GeVHm
CMS Preliminary -1 = 8 TeV, L = 5.26 fbs ; -1 = 7 TeV, L = 5.05 fbs
Fig. 5.9: Four-lepton reconstructed mass distibution for the sum of the 4e,4µ, and 2e2µ channels in low mass range.
143
Fig. 5.10: [Top] Observed and expected 95% CL upper limit on the ratio ofthe production cross section to the SM expectation in the full mass range .2011 and 2012 data-samples are used. The 68% and 95% ranges of expecta-tion for the background-only model are also shown in green and yellow bandsrespectively. [Bottom] Zoom in the low mass region. The final version of theplot includes the contribution of 2`2τ channel.
144
Fig. 5.11: [Top] Significance of the local fluctuations with respect to the SMexpectation vs Higgs boson mass for an integrated luminosity of 5.05 fb−1 at7 TeV and 2.97 fb−1 at 8 TeV in the mass range 100-600 GeV/c2. [Bottom]Zoom of the local p-value in the low mass range. Dashed line shows meanexpected significance of the SM Higgs signal for a given mass hypothesis.
145
Conclusions
The results of a search for the Standard Model Higgs boson produced in
pp collisions at√s= 7+ 8 TeV and decaying in ZZ(∗), based on data col-
lected during 2010-2011, have been presented in the leptonic Z decay channel
ZZ(∗) → 4`, with ` = e, µ.
The procedure to get them has followed the simple sequential sets of lepton
reconstruction, identification and isolation cuts and a set of kinematic cuts,
already described in chapter 4, to define a common baseline for the search
at any Higgs boson mass mH in the range 100 < mH < 600 GeV/c2 at√s =
7 TeV and 100 < mH < 800 GeV/c2 at√s = 7 and 8 TeV, respectively.
The instrumental background from Z+jets and the reducible backgrounds
from Zbb and tt, with mis-identified primary leptons, have been shown to be
negligible over most of the mass range, with a small contamination remaining
at low masses.
For the analysis which used only 2010-2011 data samples at√s = 7 TeV,
72 events, 12 in 4e channel, 23 in 4µ channel e 37 in 2e2µ channel, have
been totally observed for an integrated luminosity of 4.71± 0.21 fb−1, while
67.1± 5.5 events are expected from SM background processes.
The distribution of events is compatible with the expectation from the SM
continuum production of Z boson pairs from qq annihilation and gg fusion.
The most significant excess is near 120 GeV/c2, corresponding to about 2.5σ
significance. Taking into account the look-elsewhere effect the significance is
lowered down to about 1.0σ.
The significance values are further lowered when candidate mass uncertain-
ties are not included.
No clustering of events is observed in the measured m4` mass spectrum. Thir-
teen of the candidates are observed within 100 < m4` < 160 GeV/c2 while
147
9.8± 0.8 background events are expected.
Upper limits obtained at 95% CL on the cross section×branching ratio for
a Higgs boson with standard model-like decays exclude cross sections pre-
dicted by the standard model in the mass ranges 134 < mH < 158 GeV/c2,
180 < mH < 305 GeV/c2 and 340 < mH < 465 GeV/c2.
A major fraction of the mass range 100 to 600 GeV/c2 is so excluded at 95%
CL.
At low mass, only the region 114.4 < mH < 134 GeV/c2 remains consistent
with the expectation of the Standard Model.
An original preliminary study about the best 4` algorithm has also been
presented. It revealed a general inefficiency of the reconstructed Z1 and Z2
matching with MC Truth objects (up to 30% for the 4e channel and up to
25% for 4µ and 2e2µ channels) in the low mass region.
A quite good matching (∼ 100% for muons and > 80% for electrons) of the
recostructed lepton objects coming from Z1 and Z2 has also been found.
At low mass values (mH < 300 GeV/c2) about 10- 25 % for 4µ channel and
10-40 % for 4e channel of the events passing the full selection do not have
the two Z’s matched with those from MC Truth.
In this region the 8% of events for the 4e channel and the 12% of events
for the 4µ channel is passing the full selection, even if the Z reconstructed
objects are not matched (fake events).
It can be concluded that a wrong lepton pairing has been performed in the
low energy range.
For the analysis performed at√s = 8 TeV and combined with that at 7
TeV, the invariant mass distribution m4` is found quite consistent with the
SM background expectation over almost all the mass range. In this case,
upper limits calculated at 95% CL enlarge the exclusion mass window to
130-520 GeV/c2.
An excess of event can be observed in the mass range 120 < m4` < 130
GeV/c2. This excess makes the observed limits weaker than expected in the
null hypothesis (only-background hypothesis).
A clusterization of events can be seen at m4` ' 126 GeV/c2, giving rise to
a local excess with the respect to the background expectation. The corre-
148
sponding significance calculated for the SM Higgs boson hypothesis is 3.2σ.
More statistics is required to confirm definitely this amazing result.
149
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