UNIVERSIT ` A DEGLI STUDI DI BARI Aldo Moro FACOLT ` A DI SCIENZE MATEMATICHE FISICHE E NATURALI Dipartimento Interateneo di Fisica M. Merlin Tesi di Laurea SEARCH FOR A DOUBLY CHARGED HIGGS BOSON IN LEPTONIC FINAL STATES WITH THE CMS EXPERIMENT AT √ s =7 TeV Relatori: Ch.mo Prof. Mauro de Palma Dott. Nicola De Filippis Laureanda: Liliana Losurdo Anno Accademico 2011-2012
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UNIVERSITA DEGLI STUDI DI BARI Aldo Moro UNIVERSITA DEGLI STUDI DI BARI Aldo Moro FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALI Dipartimento Interateneo di Fisica M. Merlin Tesi
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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 A DOUBLY CHARGED HIGGS BOSON
IN LEPTONIC FINAL STATES
WITH THE CMS EXPERIMENT AT√s = 7 TeV
Relatori:Ch.mo Prof. Mauro de PalmaDott. Nicola De Filippis
Laureanda:Liliana Losurdo
Anno Accademico 2011-2012
To Mom and Dad,
my guardian angels.
”Se guardo il tuo cielo, opera delle tue dita,
la luna e le stelle che tu hai fissate,
che cosa e l’uomo perche te ne ricordi
e il figlio dell’uomo perche te ne curi?
Eppure l’hai fatto poco meno degli angeli,
di gloria e di onore lo hai coronato:
gli hai dato potere sulle opere delle tue mani,
tutto hai posto sotto i suoi piedi;
tutti i greggi e gli armenti,
tutte le bestie della campagna;
gli uccelli del cielo e i pesci del mare
che percorrono le vie del mare ...”
Salmo 8
Contents
Introduction 1
1 The Higgs Triplet Model 3
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 3
The Standard Model (SM) of particle physics is a relativistic quantum field
theory which gives a description of the behaviour of all known subatomic par-
ticles. It predicts the existence of a single scalar and neutral Higgs boson from
the spontaneous breaking mechanism of electroweak symmetry. Although the
SM has proven to be a very successful and precise theory describing the in-
teractions of fundamental particles, there are strong theoretical arguments
that lead us to think that the Standard Model is not the complete theory of
Nature.
Over the past twenty years, a large number of models has been developed
to extend the Standard Model in order to unify all fundamental interactions
and provide reasonable answers to the questions that remained unresolved
in it, like the CP violation, the exclusion of Gravity from the model, the
existence of only three generations of quarks and leptons and the neutrino
oscillations and their non-zero masses. These models, hereafter referred as
exotic models, theorize the existence of several charged and neutral Higgs
particles with different spin and parity.
This work deals with the search for a signal compatible with the pro-
duction of a doubly charged Higgs boson, Φ++, predicted in several exotic
models, in particular in the Higgs Triplet Model (HTM), with the CMS
experiment at LHC. Such model gives mass to neutrinos with the seesaw
mechanism and these masses are related to the Yukawa couplings of the lep-
tons. Thus, the Higgs boson discovery can be deduced by measuring the
fraction of its decay into leptons. The Φ++ can be produced at LHC both in
pair production process with another boson of the same type, but of opposite
charge, and in associated production process with a singlet, Φ+, giving rise to
a signature of four or three leptons (electrons, muons and taus), respectively,
1
coupled with the same sign for the reconstruction of the boson.
The purpose of this work is the development of analysis criteria for the
search for a signal compatible with the existence of the Φ++ with the data
collected by the experiment CMS during the 2011, in the case of pair pro-
duction processes.
The main background due to Standard Model processes are Z+jets, ZZ
and WZ events; they can be efficiently discriminated by the signal using
selection criteria based on the isolation, identification and transverse mo-
mentum of the leptons involved in the process.
In the first chapter we give an overview about the main features and
limitations of the Standard Model and the reasons why to go beyond it. We
then describe the seesaw mechanism that gives mass to neutrinos and the
exotic model that includes it. We summarize the previous searches for the
Φ++ at the LEP and Tevatron and then we describe the signatures of the
doubly charged Higgs production at LHC and the scenarios assumed for this
analysis.
In the second chapter we describe the LHC programme, the CMS ex-
periment, its main features, its operating logic and the performance of sub-
detector. The main reconstruction techniques involved for the analysis are
also described.
The third chapter presents the data analysis performed for this search,
by defining the selection criteria for the detection of the signatures and the
discrimination of the signal from the background, after an overview about
the main identification and isolation methods for electrons, muons and taus.
In the fourth chapter we discuss the results of the analysis. Finally we
calculate the lower limits in the different scenarios, by combining the four
lepton final state analysis with the three lepton final state analysis.
2
Chapter 1
The Higgs Triplet Model
1.1 The Standard Model
The Standard Model (SM) of particle physics is a theory which describes the
electromagnetic, weak and strong nuclear interactions of the subatomic parti-
cles. This model includes elementary particles of spin 12, known as fermions,
that are the matter particles, and particles of spin 1, known as gauge bosons,
that mediate the fundamental interactions.
1.1.1 SM features
The fermions of the Standard Model are classified according to how they
interact (or equivalently, by what type of charges they carry). There are six
quarks (up, down, charm, strange, top, bottom), and six leptons (electron,
electron neutrino, muon, muon neutrino, tau, tau neutrino). Pairs from each
classification are grouped together to form a generation, with corresponding
particles exhibiting similar physical behavior. The main property of the
quarks is that they carry color charge, and hence, interact via the strong
interaction. A phenomenon called color confinement results in quarks being
bound to each other, forming color-neutral composite particles (hadrons) con-
taining either a quark and an antiquark (mesons) or three quarks (baryons).
Quarks also carry electric charge and weak isospin. Hence, they interact with
other fermions both electromagnetically and via the weak interaction. The
remaining six fermions do not carry colour charge and are called leptons.
3
The three neutrinos are massless and do not carry electric charge either, so
they only interact with other particle by the weak force, which makes them
difficult to detect. However, by virtue of carrying an electric charge, the
electron, muon, and tau all interact also electromagnetically. In the SM,
the bosons are defined as force carriers that mediate the strong, weak, and
electromagnetic interactions. The different types of gauge bosons are: the
photons, that mediate the electromagnetic force between electrically charged
particles, the W+, the W−, and the Z gauge bosons that mediate the weak
interactions between particles of different flavors (all quarks and leptons),
and eight gluons that mediate the strong interactions between color charged
particles (the quarks).
The SM foresees the existence of a unique scalar and neutral Higgs particle
from the spontaneous electroweak symmetry breaking (EWSB) mechanism,
known as the Higgs mechanism [1]. The Higgs particle has spin 0, and for
that reason it is classified as a boson; it is the only fundamental particle
predicted by the Standard Model that has not yet been observed.
The Higgs mechanism plays a unique role in the Standard Model, by explai-
ning why the other elementary particles, except the photon and the gluon,
are massive. In particular, the Higgs mechanism would explain why the
photon has no mass, while the W and Z bosons are massive. The elementary
particle masses, and the differences between electromagnetism (mediated by
the photon) and the weak force (mediated by the W and Z bosons), are cri-
tical to many aspects of the structure of microscopic (and hence macroscopic)
matter.
1.1.2 SM restrictions
The Standard Model validity has been tested through a large number of mea-
surements. Nevertheless there are strong theoretical arguments which lead
one to think that the SM is not the ultimate theory describing the fundamen-
tal interactions. This theory in fact leaves many open questions. One of the
most serious structural problems is connected to the radiative corrections to
the Standard Model Higgs boson mass (problem of hierarchy). This problem
4
Figure 1.1: a) Diagram with a virtual fermion loop for the SM Higgs bo-son; it is generated by corrections to the m2
H that diverges quadratically; b)Diagrams with an additional field f ; they generate corrections to the m2
H
cancelling those of Diagram a).
is due to the existence of a hierarchy between the gauge boson masses and the
Plank scale (mP ≈ 1019 GeV)1, at which the gravitational interaction is of
comparable strength with the other forces. The radiative corrections are de-
rived from fermionic loops (see Fig.1.1) for which they diverge quadratically
and give a Higgs boson with a mass at least 30 orders of magnitude larger
than the values allowed by the experimental data. The conceptual structure
of the SM, indeed, is not able to explain the mass scale of vector bosons, fixed
by the Higgs mechanism at the Fermi scale m ∼ 1/√GF ∼ 250 GeV which
is about 1017 times smaller than Planck scale. This problem occurs when the
fundamental parameters (couplings or masses) of some Lagrangians are differ-
ent than the parameters measured by experiments. Therefore, a collection of
techniques used to treat divergences is introduced, and it is known as renor-
malization. Typically the renormalization parameters are connected to the
1Mass, energy and momentum are expressed in the natural units system, where c isset to a unitary adimensional constant and can thus be omitted, expressing all of thequantities in eV multiples.
5
fundamental parameters, but in some cases, it appears that there has been
a delicate cancellation between the fundamental quantities and the quan-
tum corrections to them. The hierarchy problem is related to the problems
of naturalness, or the fine-tuning problems. Studying the renormalization
in the hierarchy problem is difficult, because such quantum corrections are
usually power-law divergent. If the Standard Model was valid until the Plank
scale, the differences between the Fermi scale and the Plank scale could be
eliminated only by a not natural process of fine-tuning of the parameters.
Finally, the SM depends on a high number of free parameters: 19. Be-
sides the Higgs boson mass, they include the Weinberg angle, quark and
fermion masses, the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements
and the CP violating phase. They have values known from experiment, but
their origin is unknown. Some theorists have tried to find relations between
different parameters, for example, between the masses of particles in diffe-
rent generations. Moreover, according to the Standard Model, the neutrinos
are massless particles. However, neutrino oscillation experiments have shown
that neutrinos do have mass. Mass terms for the neutrinos can be added to
the Standard Model by hand, but these lead to new theoretical problems (for
example, the mass terms need to be extraordinarily small). Therefore, re-
searchers postulate new theories that resolve the hierarchy problem without
fine-tuning [2].
1.2 Beyond the Standard Model
While in the Standard Model the quarks, the charged leptons and the
massive gauge bosons acquire masses via the Higgs mechanism, the non-zero
neutrino masses can be derived only by using an additional mechanism to
include them [3]. According this new mechanism, neutrinos have a mass
term like other fermions, referred as Dirac mass term, by mixing left-handed
and right-handed eigenstates: right-handed neutrinos appear with the same
masses as the observed left-handed neutrinos.
Moreover, neutrinos have no electromagnetic charge and no color charge: so
6
they could be also described as Majorana particles, i.e. particles that are their
own antiparticles. This fact would imply a non-conservation of the lepton
number (νi → νi); however measurements related with the observation of
the neutrino oscillations (νi → νj) already indicate some non-conservation
laws in the lepton numbers. The interesting feature of the Majorana mass
terms is that they do not mix left-handed and right-handed components of
a particle; therefore, a description of Majorana massive neutrinos does not
require the addition of right-handed neutrinos in the model. In this scenario,
a new model beyond the SM can be introduced.
1.2.1 Type-II Seesaw Mechanism
A strongly established signal of particle physics beyond the Standard
Model is the existence of non-zero neutrino masses. Therefore, in addition to
the electroweak symmetry breaking, a seesaw mechanism is required to give
mass2 to neutrinos.
The basic principle of the seesaw mechanism consists in introducing a corre-
spondence between some high-scale phenomenon and the low-scale observed
neutrino masses [5]. Four kinds of seesaw processes can be distinguished:
1. the type-I seesaw mechanism introduces right-handed neutrinos with
a Majorana mass of the order of the grand unification scale. The ad-
dition of Dirac mass terms mixing right-handed, that sets the new
physics scale Λ3, and left-handed neutrinos, provides a very small mass
to left-handed neutrinos. The higher the right-handed neutrino mass,
the lower the left-handed neutrino mass, hence the name of “seesaw”
mechanism;
2. the type-II seesaw mechanism adds an SU(2)L Higgs triplet ∆ to the
doublet of the Standard Model. This mixing between the doublet and
triplet, via a dimensional parameter µ, allows to obtain a relation v∆ ∼2Several extensions of the Standard Model suggest the addition of a scalar triplet little
Higgs models and left-right supersymmetric models for example [4].3The cut-off Λ is a parameter introduced in the renormalization theory to take into
account the divergences.
7
µv2/M2∆, where M∆ is the mass of the triplet. In this case the scale Λ
is replaced by M2∆/µ;
3. the type-III seesaw mechanism generates neutrino masses through ad-
dition at least two extra matter fields in the adjoint representation of
SU(2)L and with zero hypercharge. Therefore, the high scale Λ is re-
placed by the mass of the extra fermions in the adjoint representation;
4. the Hybrid seesaw mechanism, a combination of type-I and type-III, in
which one SM fermionic singlet and one fermion in the adjoint repre-
sentation of SU(2) are added. This mechanism has a very simple and
unique realization in the context of grand unified theories [6].
In this work, we assume that neutrinos may obtain masses via the mi-
nimal seesaw model of type-II, an extension of the scalar sector of SM, which
introduces some new physics at large scale. To the SU(2)L Higgs doublet of
the Standard Model
Φ =
(ϕ+
ϕ0
), (1.1)
with ϕ0 = 1√2
(ϕ+ v + iχ) and hypercharge YΦ = 1, it adds a SU(2)L Higgs
triplet ∆
∆ =
(∆+/√
2 ∆++
∆0 −∆+/√
2
), (1.2)
with ∆0 = 1√2
(δ + v∆ + iη) and hypercharge Y∆ = 2. Under a gauge tran-
sformation U , these fields transform as Φ→ U(x )Φ and ∆→ U(x )∆U(x )†.
While the general SM Lagrangian can be written as
LSM = Lf + Lg + LSMY + LH , (1.3)
where Lf is the fermionic propagation term, Lg is the gauge kinetic term,
LSMY is the Yukawa term in the SM, which provides masses to the fermions,
and LH is the Higgs term, that introduces the Higgs field h, the general
Seesaw Lagrangian can be written as
Lseesaw = Lf + Lg + LseesawY + LΦ,∆, (1.4)
8
where Lf and Lg are those appearing in the Standard Model Lagrangian,
LseesawY is the Yukawa term according to the seesaw mechanism, and LΦ,∆ is
the term corresponding to the propagation of the Higgs field. This last term
is given by
LΦ,∆ = (DµΦ)†(DµΦ) + Tr(Dµ∆)†(Dµ∆)− V (Φ,∆), (1.5)
where the covariant derivatives are written as:
DµΦ = ∂µΦ− ig1YΦ
2BµΦ− ig2
τa2Waµ Φ, (1.6)
Dµ∆ = ∂µ∆− ig1Y∆
2Bµ∆− ig2
[τa2Waµ ,∆
], (1.7)
and the scalar potential is written as:
V (Φ,∆) = − m2Φ†Φ +m2∆Tr(∆
†∆) +[µ(ΦT iτ2∆†Φ) + h.c.
]+ λ1(Φ†Φ)2 + λ2[(Tr(∆†∆)]2 + λ3Tr(∆
†∆)2
+ λ4(Φ†Φ)Tr(∆†∆) + λ5Φ†∆∆†Φ, (1.8)
where m and m∆ are mass parameters in the Standard Model and Seesaw
Lagrangian, respectively, µ is a mass parameter in common between the two
Lagrangians and λi (i = 1, 2, 3, 4) are dimensionless couplings [5], Tr is the
trace over 2 × 2 matrices and τ2 is the second Dirac-Pauli matrix4 . A priori,
both scalar fields Φ and ∆ can develop a non-zero vacuum expectation value
(VEV) of their neutral components5 :
〈Φ〉 =1√2
(0
v
)and 〈∆〉 =
1√2
(0
v∆
), (1.9)
where v and v∆ are Φ and ∆ vacuum expectation values, respectively.
4τ1 =
(0 11 0
); τ2 =
(0 −ii 0
); τ3 =
(1 00 −1
).
5An electrically charged field does not acquire any vacuum expectation value, becauseotherwise charge would be spontaneously broken.
9
Finally, the Yukawa Lagrangian LseesawY contains, in addition to the com-
plete SM Yukawa Lagrangian, a coupling term between the scalar triplet ∆
and the lepton doublets Li =
(νiL
`iL
):
LseesawY = LSMY + L∆,νY , (1.10)
with
L∆,νY = −YνLTC ⊗ iτ2∆L+ h.c.
= −Yij[νiLCνjL∆0 − 1√
2(νTiLC`jL + `TiLCνjL)∆+ − `TiLC`jL∆++
]+h.c., (1.11)
where C is the charge conjugation operator, and the symmetric complex
matrix Yν is the Yukawa coupling strenght (i, j = e, µ, τ). Due to the si-
multaneous presence of the Yukawa coupling Yν in Eq. 1.11 and the term
proportional to the µ parameter in Eq. 1.8, the leptonic number is explicitly
broken in this theory.
Therefore, considering the non-zero Higgs triplet VEV of neutral component
described in Eq. 1.9, this Yukawa Lagrangian gives rise to the Majorana
mass term for neutrinos, −12Mijν
TiLCνiL, whose mass matrix is related to the
Yukawa couplings through the following relation:
Mij = 2Yij〈∆0〉 =√
2Yijv∆ , (1.12)
which is the main relation for the type-II seesaw scenario [5][7].
1.2.2 Neutrino masses
Neutrino oscillation is a quantum mechanical phenomenon for which a neu-
trino created with a specific lepton flavour (electron, muon or tau) can later
be measured with a different flavour. The probability of measuring a par-
ticular flavour for a neutrino varies periodically as it propagates. This phe-
nomenon is of theoretical and experimental interest since observation of the
10
phenomenon implies that the neutrino has a non-zero mass, which is not part
of the original Standard Model of particle physics. The flavour change may
be due to a mismatch between neutrino flavour eigenstates (|νi〉, i = e, µ, τ)
and their mass eigenstates (|νk〉, k = 1, 2, 3). This implies that neutrinos have
several different mass eigenvalues, while the SM describes them as massless
particles.
Similarly to the quark flavour mixing and the CKM matrix of Standard
Model, the mass matrix Mij for three Dirac neutrinos is diagonalized by a
unitary matrix VPMNS (Pontecorvo-Maki-Nakagawa-Sakata) [8][9]. The 3 ×3 PMNS matrix is naturally composed of three rotations, involving three
mixing angles, called the Euler angles : θ12, θ13, θ23. If neutrino oscillations
happen to violate the CP symmetry, a phase factor δ (or Dirac phase) must
be added. Finally, since neutrinos are Majorana particles, two other phase
factors, α1 and α2 (or Majorana phases) can be added. Then the mixing
matrix V becomes
V = VPMNS × diag(1, eiα1/2, eiα2/2) , (1.13)
where −π ≤ α1, α2 < π. Since we can chose to work in the basis in which
the charged lepton mass matrix is diagonal, the neutrino mass matrix is
diagonalized by VPMNS. Using Eq.1.12, the couplings Yij can be written as:
Yij =Mij√2v∆
≡ 1√2v∆
[VPMNS diag(m1,m2e
iα1 ,m3eiα2) V T
PMNS
]ij. (1.14)
Here m1, m2 and m3 are the three masses eigenvalues of the neutrinos. Such
a description of neutrino sector involves a total of nine parameters: three
mixing angles, three potential phases, and three mass eigenvalues [3].
Neutrino oscillations are sensitive to the mixing angles (θij) and the Dirac
phase (δ), and the mass-squared differences, ∆m221(≡ m2
2−m21) and ∆m2
31(≡m2
3 −m21). Since the sign of ∆m2
31 is not determined at the present, distinct
patterns for the neutrino mass hierarchy are possible.
The case with ∆m231 > 0 is referred to as normal hierarchy (NH) where
m1 < m2 < m3, and the case with ∆m231 < 0 is known as inverted hierarchy
11
(IH) where m3 < m1 < m2. Denoting the lightest neutrino mass by m0, we
can write
m0 =
{m1 (NH)
m2 (IH). (1.15)
If m0 &√|∆m2
31| ' 0.05 eV, the neutrino mass spectrum is quasi-degenerate
(QD). However, information on the mass m0 and the Majorana phases cannot
be obtained from neutrino oscillation experiments. This is because the oscil-
lation probabilities are independent of these parameters, not only in vacuum
but also in matter [10].
1.3 The Higgs Triplet Model
In order to explain the non-zero neutrino masses, several scenarios have
been proposed, for which a source of lepton flavour violation (LFV) is in-
troduced with additional Majorana neutrinos, a triplet scalar field, or triplet
fermion fields. In particular, a simple model that contains a doubly charged
scalar boson is the ”Higgs Triplet Model” (HTM) [10]. This model is an ex-
tension of the Standard Model in which only the scalar sector is augmented
with a Higgs triplet.
Assuming that the triplet scalar field carries two units of lepton number,
the lepton number conservation is violated in a trilinear interaction among
the Higgs doublet field and the Higgs triplet field. Majorana masses for
neutrinos are then generated through the Yukawa interaction of the lepton
doublet and the triplet scalar field, given by Eq. 1.12. When the electroweak
symmetry is broken and the mass of the component fields of the triplet, given
by Eqs. 1.1 and 1.2, are at the TeV scale or less, there are seven physical
massive Higgs bosons
Φ++, Φ−−, Φ+, Φ−, Φ0(= Φ or A), H,
and the model can be tested by directly detecting them, such as the doubly
12
charged (Φ±±)6 , singly charged (Φ±) and the neutral scalar bosons (Φ0)7,
which is Φ or A with Φ to be the triplet-like CP even Higgs boson and A
to be the triplet-like CP odd Higgs boson. While these Higgs states are all
∆-like (triplet), the seventh boson H generated by the EWBS is the SM-like
(doublet) one.
In addition to the appearance of these charged scalar bosons, an attractive
prediction of the HTM is the relationship among the masses of the component
fields of the triplet scalar field:
m2Φ±± −m2
Φ± ' m2Φ± −m2
Φ0(≡ ξ),
where m2Φ±± , m2
Φ± and m2Φ0 are the masses of Φ±±, Φ± and Φ0, respectively.
The mass-squared differences ξ is determined by v (' 246 GeV), the VEV
of the doublet scalar field, as well as the Standard Model VEV, and a scalar
self-coupling constant [7].
1.3.1 Constraint on the physical parameters
Solving the Lagrangian is not a simple calculation because of its com-
plex structure, so we can proceed minimizing the scalar potential, given by
Eq. 1.8, to find the stable points around which a perturbative expansion can
be performed. This minimization (vacuum condition) implies non-zero values
for both v and v∆ and the two following constraints on the parameters [5]:
m2 =1
2
[−2v2λ1 − v2
∆(λ4 + λ5) + 2√
2µv∆
], (1.16)
m2∆ = M2
∆ −1
2
[2v2
∆(λ2 + λ3) + v2(λ4 + λ5)], (1.17)
with M2∆ ≡
µv2√
2v∆.
The mass of the doubly charged scalar bosons Φ±± ( that is ∆±± in the
6The doubly charged Higgs boson is denoted also with ∆ and H alternatively, becausein the literature also these two notations have been used. Our choice of Φ for the tripletcomponents avoids possible confusion with H+ in the MSSM.
7Singly charged or neutral boson appear in many models, e.g. from scalar doublets insupersymmetric models. Doubly charged scalars are more unusual.
13
Eq. 1.2) is calculated as
m2Φ±± = M2
∆ − v2∆λ3 −
v2
2λ5
' M2∆ −
v2
2λ5, (v2 � v2
∆). (1.18)
Mass eigenstates of the singly charged states, CP odd states and CP even
states are obtained by(ϕ±
∆±
)= R(β±)
(w±
Φ±
),
(χ
η
)= R(β0)
(z
A
),
(ϕ
δ
)= R(α)
(h
Φ
),
(1.19)
R(θ) ≡
(cos θ − sin θ
sin θ cos θ
), (1.20)
where w± and z are the Nambu-Goldstone bosons which are absorbed by the
longitudinal mode of W± and Z, respectively. The mixing angles β±, β0 and
α are expressed as
cos β± =v√
v2 + 2v2∆
,
cos β0 =v√
v2 + 4v2∆
,
tan 2α ' v∆
v
4M2∆ − 2v2(λ4 + λ5)
M2∆ − 2v2λ1
. (1.21)
The masses of the other bosons are calculated as
m2Φ± = M2
∆
(1 +
2v2∆
v2
)− 1
4
(v2 + 2v2
∆
)λ5, (1.22)
m2A = M2
∆
(1 +
4v2∆
v2
)'M2
∆, (1.23)
m2Φ 'M2
∆, (1.24)
m2H ' 2λ1v
2, (1.25)
14
for v2 � v2∆
8. We can note that Eq. 1.25 is valid as long as M2∆ > 2λ1v
2.
From above mass formulae, the mass-squared difference ξ is determined by
−v2
4λ5 [7].
The neutrino masses are generated through the Yukawa interaction, given by
Eq. 1.11 and the neutrino mass matrix is obtained as
Mij =√
2Yijv∆ = Yijµv2
M2∆
. (1.26)
By this equation, the Yukawa coupling constant Yij and the ∆ vacuum ex-
pectation value v∆ are related with each other.
This simple connection between the triplet Yukawa couplings and the pa-
rameters of the neutrino mass matrix (many of which are measurable) is
an important and attractive feature of the HTM. In contrast, Eq. 1.26 does
not hold in other models with a doubly charged scalar (e.g. the Left-Right
Symmetric Model [4] in which the couplings Yij are essentially arbitrary).
A perturbative Yij can be used to obtain realistic neutrino masses pro-
vided that v∆ & 1 eV. The presence of a non-zero v∆ gives rise to ρ 6= 1
at tree level, where ρ ≡ m2W
(m2Z cos2 θW )
. Therefore a limitation of the ratio9 v∆
v
is necessary in order to comply with the measurement of ρ ∼ 1: taking the
electroweak scale and v2 + v2∆ ≈ (246 GeV)2 conditions into account, this
results in:
v ≈ 246 GeV, v∆ . 1 GeV. (1.27)
The case where the leptonic decays of Φ±± are dominating is realized when
Yij are larger than the smallest Yukawa couplings in the SM (i.e., the electron
Yukawa coupling, Ye ∼ 10−6). So taking into account Eq. 1.12 one can write
v∆Yij . 10−10 GeV , (1.28)
8In the limit of v∆ → 0, Yukawa interactions and gauge interactions of H becomecompletely the same as those of the SM Higgs boson at the tree level. This is the reasonfor which it is called the SM-like Higgs boson and denoted as H.
9The Standard Model predicts a tree-level value ρ = 1, in perfect agreement withexperiments that give ρ = 1.0002+0.0024
−0.0009. After the introduction of v∆ 6= 0, defining
x = v∆
v , the constant writes: ρ = 1+2x2
1+4x2 . This is still in agreement with experimentalresults, given that x . 0.03.
15
and from Eq.1.26 it follows that in this scenario the upper limit becomes
v∆ . 1 MeV. (1.29)
Knowing that v∆
v. 0.03, the doubly charged Higgs boson mass scale depends
mainly on the scale of µ. Besides, the comparison of Eqs. 1.18 and 1.26
shows the seesaw mechanism at work: when the vacuum expectation value
v∆ gets small, the mass of the scalar triplet increases and the neutrino masses
decrease [10].
The differences between the masses of Φ±±, Φ±, Φ and A appear through
the quartic couplings in the Higgs potential. If one assume λiv∆ � µ (i = 1,
2, 3, 4) [11], then these masses are degenerate, and H takes the same mass
as the Standard Model Higgs boson:
m2Φ±± ≈ m2
Φ± ≈ m2Φ ≈ m2
A ≈µv2
√2v∆
; m2H ≈ 2λv2 . (1.30)
1.3.2 General features of doubly charged Higgs decays
A distinctive signal of the HTM would be the observation of a doubly
charged Higgs boson Φ±±, whose mass (mΦ±±) may be of the order of the
electroweak scale. If kinematically accessible, such particles may be produced
with sizeable rates at hadron colliders in the pair production process
qq → Φ++Φ−− → `+i `
+j `−k `−l ,
as well as in the associated production process
qq′ → Φ±±Φ∓ → `+i `
+j `−k νl ,
where Φ± is a singly charged Higgs boson in the same triplet representa-
tion. The Feynman diagrams of both production processes are shown in
Fig. 1.2. Direct searches for Φ±± have been performed both by LEP10 ex-
10LEP is the acronym of Large Electron-Positron, a circular collider that acceleratedelectrons and positrons located at CERN (Switzerland-France) since 1989. The necessityto build an e+e− collider in an energy range above 200 GeV was due to characterize with
16
Figure 1.2: Feynman diagrams of both pair and associated production.
periments (OPAL, DELPHI and L3) and Tevatron11 experiments (D0 and
CDF), assuming the production channel qq → Φ++Φ−− and the leptonic de-
cays Φ±± → `±i `±j (` = e, µ, τ), and mass limits in the range mΦ±± > 110-150
GeV have been obtained.
The summary of LEP searches for doubly charged Higgs boson is presented
below:
• OPAL searched for pair production into all 6 leptonic decay channels,
assuming both doubly charged Higgs particle to decay into the same
channel. The lower mass limit is set to 99 - 100.5 GeV, depending on
the channel [12];
• DELPHI searched for 4τ signature of the pair-production. The lower
mass limit is set to 97.3 GeV [13];
• L3 searched for the pair production into all 6 leptonic decay channels.
more accuracy the gauge bosons, provide additional contributions to the confirmationof Standard Model theory. The choice of leptonic accelerators allowed the compromisebetween very high energies and extreme precision. LEP consisted of four general purposedetector with a cylindrical geometry: ALEPH, DELPHI, OPAL, L3. It worked in twophases: LEPI (from 1989 to 1995) which allowed to reach centre-of mass energies in therange 89 GeV <
√s < 93 GeV, and LEPII (from 1996 to 2000) with centre-of-mass energies
up to 209 GeV. At the end of 2000, LEP was shut down and then dismantled in order tomake room in the tunnel for the construction of the Large Hadron Collider (LHC).
11The Tevatron is a circular hadronic accelerator in the United States (Chicago), at theFermi National Accelerator Laboratory (also known as Fermilab) that accelerated protonsand antiprotons with a centre-of-mass energy equal to 1.96 TeV. It worked in two runs:the first one was from 1992 to 1995, the second one was from 2001 to 2001. Its mainexperiments were CDF and D0. Tevatron ceased operations on 30 September, 2011, dueto budget cuts.
17
The lower mass limit is set to 95.5 - 100.2 GeV, depending on the
channel [14].
The summary of Tevatron searches for doubly charged Higgs boson is as
follows:
• D0 searched for:
– µ and τ final states. The lower limit is set 128 - 168 GeV for
various model options [15];
– 4µ signature of pair production. The lower limit is set to 150
GeV [16];
– 2µ final state. The lower limit is set to 118 GeV [17];
– µτ and ττ final states. The lower limits are set to 144 GeV and
128 GeV, respectively [15].
• CDF searched for:
– leptonic final states, setting limits between 190 GeV and 245
GeV12;
– µτ and eτ final states for pair production. The lower limits are
set to 114 GeV and 112 GeV, respectively [18];
– ee, µµ and eµ final states. The lower limits are set to 133 GeV,
135 GeV and 115 GeV, respectively [19].
The LHC13, using the above production mechanism, offers improved sensi-
tivity to mΦ±± . The production of doubly charged Higgs bosons at the LHC
can give rise to following distinctive signatures:
• three or four prompt isolated leptons in the final state;
• dilepton combination with the same charge;
12The results have not been published.13LHC is the acronym of Large Hadron Collider located at CERN. It is the world’s
largest and highest-energy particle accelerator. More details are in the next chapter.
18
• final states that are combinations of all possible leptons, due to flavour
non-conservation.
The search is designed to be fully inclusive allowing for all possible combina-
tions, called model independent search in which a 100% branching ratio (BR)
into each of the six channel (namely ee, µµ, ττ, eµ, eτ, µτ) is assumed. In ad-
dition to this model, the type-II seesaw model is tested in four benchmark
points (BP1-4) which are chosen according to the different characteristics of
the neutrino mass matrix structures; they describe the following neutrino
sector:
• BP1, in which a normal hierarchy is assumed, no CP violation, normal
neutrino mass ordering and the lowest neutrino mass to be vanishing;
• BP2, same as BP1, but with the assumption of an inverted hierarchy
of neutrino masses;
• BP3, same as BP1, but the lightest neutrino mass is assumed to be 0.2
eV, giving rise to a quasi-degenerate neutrino mass spectrum;
• BP4, in which all branching ratios are assumed to be equally 16.7%.
Such a model point is called degenerate case.
The branching ratios of benchmark points are summarized in Tab. 1.1 and
they are shown in Fig. 1.3.
Benchmark point ee eµ eτ µµ µτ ττ
BP1 0 0.01 0.01 0.30 0.38 0.30
BP2 0.50 0 0 0.125 0.25 0.125
BP3 0.34 0 0 0.33 0 0.33
BP4 1/6 1/6 1/6 1/6 1/6 1/6
Table 1.1: Branching ratios of Φ++ to the various final states (τ means a taulepton before decay).
19
Figure 1.3: Benchmark points for the type-II seesaw model.
Because of the proportionality between the Φ±± Yukawa coupling matrix
Yij and the light neutrino mass matrix Mij, given by Eq. 1.26, the branching
ratios Φ±± → `±i `±j measured at the LHC test the neutrino mass mechanism
directly. Thus, the LHC experiments are able to reconstruct unknown neu-
trino parameters such as the absolute neutrino mass scale, the mass hierarchy
and CP-violating phases that are not testable in neutrino oscillations.
An inclusive search for the doubly charged Higgs boson is performed with
the CMS experiments with data collected in 2011 at the collision energy of
7 TeV corresponding to an integrated luminosity of 4.93 fb−1. It is carried
out in events with four and three final state leptons of all flavours, searching
for a same sign dilepton invariant mass peak corresponding to a Φ±±, while
decaying in the same charged lepton pairs. The three (four) lepton signature
can include maximally one (two) tau hadronic decay that implies a missing
energy related to the neutrinos from the tau decay.
The decay channels Φ±± → `±i `±j and Φ± → `±i νj are the dominant ones if
v∆ . 10−4 GeV, and give rise to multi-lepton signatures. In the HTM, one
expects v∆ . 10−4 GeV if the triplet Yukawa coupling is larger the smallest
Yukawa coupling in the SM (i.e., the electron Yukawa coupling). Various
multi-lepton signatures can be originated from the production mechanism
qq → Φ++Φ−− and qq′ → Φ±±Φ∓. Assuming that the Φ±± and Φ± are
degenerate in mass, the cross section of the associated production exceeds
the one of the pair production.
The four-lepton signature (4`) only receives a contribution from qq →Φ++Φ−−. Although this 4` signature provides a very promising way to search
20
for Φ±±, it is not necessarily the channel which offers the best sensitivity for a
given integrated luminosity and mass mΦ±± . Special attention has been given
to the three-lepton channel, which also has relatively small SM backgrounds.
Significantly, the three-lepton signature is sensitive to the production mecha-
nism qq′ → Φ±±Φ∓ that contributes to the search for Φ±± [10]. Considering
the following inclusive single Φ±± cross section (σΦ±±)
Figure 1.4: Cross sections of the inclusive doubly charged Higgs boson pro-duction (Eq. 1.31) as a function of mΦ±± .
While at the Tevatron
σ(qq′, qq → Φ++Φ−) = σ(qq′, qq → Φ−−Φ+) , (1.32)
at the LHC
σ(qq′, qq → Φ++Φ−) > σ(qq′, qq → Φ−−Φ+) . (1.33)
21
1.3.3 K-factor and QCD correction to the production
processes
For processes involving strongly interacting particles, as is the case for
the doubly charged Higgs boson, the leading order (LO) cross sections are
affected by large uncertainties arising from higher-order (HO) corrections. If
at least the next-to-leading order (NLO) QCD corrections to these processes
are included, the total cross sections can be defined properly. Besides, in this
way the renormalization scale µR, used to define the strong coupling constant,
and the factorization scale µF , used to perform the matching between the
perturbative calculation of the matrix elements and the non perturbative
part which resides in the parton distribution functions (PDFs)14, are fixed
and the generally non-negligible radiative corrections are taken into account.
The parameter, which quantifies the effects of higher-order QCD corrections,
is known as the K-factor. It is defined as the ratio of the cross section for
the process (or its distribution) at HO with the value of αs and the PDFs
evaluated also at HO, over the cross section (or distribution) at LO with αs
and the PDFs consistently also evaluated at LO. In most cases, the K-factor
is defined as the same ratio with the cross section calculated up to NLO
instead to HO, and it can written as [20]:
K =σNLO(qq → XX ′)
σLO(qq → XX ′). (1.34)
In the case of the doubly charged Higgs boson, where the dominant pro-
duction process at hadron colliders is qq → γ∗, Z∗ → Φ++Φ−−, the cross
section of this production mode only depends on the electroweak quan-
tum numbers and the mass of Φ++ states and not on further details of the
model. At both the Tevatron and the LHC, the hadronic cross section for its
pair production can be obtained from convoluting the partonic cross section
14A parton distribution function (PDF) is defined as the probability density for findinga particle with a certain longitudinal momentum fraction x at momentum transfer Q2.Because of the inherent non-perturbative effect in a QCD binding state, parton distributionfunctions cannot be obtained by perturbative QCD. Due to the limitations in presentlattice QCD calculations, the known parton distribution functions are instead obtained byusing experimental data.
22
σLO(q(q) → Φ++Φ−−) with the corresponding (anti)quark densities of the
(anti)protons:
σLO(p(p) → Φ++Φ−−) =
∫ 1
τ0
dτ∑q
dLq(q)
dτσLO(Q2 = τs) , (1.35)
where τ0 = 4m2Φ±±/s with mΦ±± being the lower mass bound of Φ±± and
s the total hadronic c.m. energy squared, Lq(q)denotes the q(q) partonic
luminosity and Q2 is the squared partonic c.m. energy.
The standard QCD corrections, with virtual gluon exchange, gluon emis-
sion and quark emission, modify the lowest order cross section in the following
way:
σ = σLO + ∆σq(q) + ∆σqg , (1.36)
with:
∆σq(q) =αs(µR)
π
∫ 1
τ0
dτ∑q
dLq(q)
dτ
∫ 1
τ0/τ
dzσLO(Q2 = τzs)ωq(q)(z)
∆σqg =αs(µR)
π
∫ 1
τ0
dτ∑q,q
dLqg
dτ
∫ 1
τ0/τ
dzσLO(Q2 = τzs)ωqg(z) (1.37)
where ωq(q)(z) and ωqg(z) are coefficient functions for quark and gluon emis-
sion, respectively, that depend on the probability of a quark emitting a quark
or a gluon, Pq(q)(z) and Pqg(z) [21].
Concerning the two production mechanisms studied at Tevatron and LHC
(see Eqs. 1.32 and 1.33), these have different QCD K-factors. Explicit cal-
culations for qq, qq → Φ++Φ−− give around K = 1.3 at the Tevatron and
K = 1.25 at the LHC, depending on mΦ±± . Actually, the K-factor for
qq′, qq → Φ±±Φ∓ is expected to be very similar (but not identical) to that for
qq, qq → Φ++Φ−−, with some dependence on the mass spitting mΦ±±−mΦ± .
Thus, since the scalar potential of the HTM gives mΦ±± ∼ mΦ± , the K-
factors are assumed to be equal [10].
23
1.4 Doubly charged scalars at the LHC
At the LHC the process
qq → Φ++Φ−− → `+`+`−`− (1.38)
provides a very spectacular signature, namely two like-sign lepton (` = e, µ)
pairs with the same invariant mass and no missing transverse momentum,
which has essentially no Standard Model background. The pair produc-
tion of the doubly charged scalar occurs by the Drell-Yan process qq →γ∗, Z∗ → Φ++Φ−−, with a subdominant contribution also from two-photon
fusion γγ → Φ++Φ−−. The cross section is not suppressed by any small
quantity (such as the Yukawa or triplet VEV) and depends only on the mass
mΦ++ .
The partial decay width for the decay Φ++ → `+i `
+j is given by
Γ(Φ++ → `+i `
+j ) =
1
4π(1 + δij)|Yij|2mΦ++ , (1.39)
with δij = 1 (0) for i = j (i 6= j). Hence, the rate is proportional to the
corresponding element of the neutrino mass matrix |Mij|2. Using Eqs. 1.26
and 1.34, the branching ratio can be expressed as
BRij ≡ BR (Φ++ → `+i `
+j ) ≡
Γ(Φ++ → `+i `
+j )∑
kl Γ(Φ++ → `+k `
+l )
=2
(1 + δij)
|Mij|2∑kl |Mkl|2
,
(1.40)
and therefore by Mij diagonalization and VPMNS unitarity:
∑kl
|Mkl|2 =3∑i=1
m2i =
{3m2
0 + ∆m221 + ∆m2
31 (NH)
3m20 + ∆m2
21 + 2|∆m231| (IH)
. (1.41)
Then, the BR of Φ++ → `+i `
+j depends on the six parameters of the neutrino
mixing matrix, V (see Eq. 1.13), the unknown mass of the lightest neutrino
(m0), the mass splittings of the neutrinos, and the ignorance of the neutrino
mass hierarchy.
In addition to the lepton channel the doubly charged Higgs can in princi-
24
Figure 1.5: Feynman graphs contributing to the production of doubly chargedHiggs boson at LHC.
ple decay also into the following two-body final states including singly charged
Higgs and/or the W :
Φ++ → W+W+, Φ++ → Φ+W+, Φ++ → Φ+Φ+, (1.42)
with the relative Feynman graphs shown in the Fig. 1.5. The last two decay
modes depend on the mass splitting within the triplet. We can assume in
the following that they are kinematically suppressed. The rate for the WW
mode is given by
Γ(Φ++ → W+W+) ≈v2
∆m3Φ++
2πv4, (1.43)
where we have used mΦ++ � mW for full expressions and a discussion of pos-
sibilities to observe this process at LHC. Hence, the branching ratio between
`+`+ and W+W+ decays depends on the relative magnitude of the triplet
Yukawas Yij and the VEV v∆. The requirement Γ(Φ++ → W+W+) �Γ(Φ++ → `+
i `+j ), together with the constraint from Eq. 1.28, implies:
v∆
v. 10−6
(100 GeV
mΦ++
)1/2
. (1.44)
The triplet VEV contributes to the ρ parameter at tree level as ρ ≈ 1 −2(v∆/v)2. The constraint from electroweak precision data ρ = 1.0002+0.0024
−0.0009
at 2σ translates into v∆/v < 0.02, which is satisfied by requiring Eq. 1.40.
It is known that the most stringent constraint on the Yukawa couplings Yij
25
comes from µ→ eee, a process which occurs at tree level via Eq. 1.11. The
branching ratio for this decay is given by:
BR(µ→ eee) =1
4G2F
|Y ∗eeYeµ|2
m4Φ++
≈ 20( mΦ++
100 GeV
)−4
|Y ∗eeYeµ|2 . (1.45)
Hence, the combination |Y ∗eeYeµ|2 . 2× 10−7( mΦ++
100 GeV
)2is constrained by the
experimental bound BR(µ → eee) < 10−12. Assuming that all Yij have
roughly the same order of magnitude, the range of Yukawa couplings can be
estimated as follows:
4× 10−7( mΦ++
100 GeV
)1/2
. Yij . 5× 10−4( mΦ++
100 GeV
), (1.46)
where the lower bound arises from Eq. 1.44 assuming the the bound, given
by Eq. 1.28, is saturated. We can see that several orders of magnitude are
available for Yukawa couplings. For Yij close to the lower bound of Eq. 1.41
the decay Φ±± → W±W± will become observable at LHC, whereas close to
the upper bound a signal in future searches for lepton flavour violation is
expected, where the details depend on the structure of the neutrino mass
matrix. The interval for the Yukawas from Eq. 1.41 implies a triplet VEV
roughly in the keV to MeV range [3][6][22].
26
Chapter 2
The LHC Collider and the
CMS Experiment
The European Organization for Nuclear Research, known as CERN , is an
international organization whose purpose is to operate the world’s largest
particle physics laboratory, which is placed in the immediate vicinity of
Geneva on the Franco-Swiss border. Founded in 1954, the organization has
twenty European member states.
Numerous experiments have been constructed at CERN by international col-
laborations for the purpose of high research. Most of the activities at CERN
are currently oriented to the operation of the Large Hadron Collider (LHC),
and the experiments along it.
2.1 The Large Hadron Collider
The LHC is the world’s largest and highest-energy particle accelerator. It is
located in a circular tunnel, with a circumference of 27 km, at a depth ranging
from 50 to 175 m underground, in the region between the Geneva airport and
the nearby Jura mountains. It is in the same tunnel previously occupied by
LEP which was closed in November 2000. CERN’s existing PS/SPS1 accele-
1The PS is the acronym of Proton Synchrotron, and the SPS means Super ProtonSynchrotron. They are particle accelerators of the synchrotron type at CERN. Startingin November 2009, the PS and SPS machines deliver protons and provide lead ion beamsfor the LHC.
27
Figure 2.1: The LHC accelerator complex.
rator complexes are used to pre-accelerate protons which will then be injected
into the LHC. Four interaction regions were equipped, and host four main
detectors: ALICE (A Large Ion Collider Experiment), ATLAS (A Toroidal
LHC ApparatuS), CMS (Compact Muon Solenoid), and LHCb (beauty) (see
Fig.2.1). Moreover, there are also TOTEM (TOTal Elastic and diffractive
cross section Measurementand) and LHCf (forward), that are smaller and are
designed for very specific research. The two experiments, ATLAS and CMS,
study Standard Model physics processes (electroweak processes, physics of
the top and bottom quarks, ...) and look for hints of physics beyond the
Standard Model. The main goal of them is the search for the Higgs boson,
and/or new particles expected in theories beyond the Standard Model.
28
Figure 2.2: View of the tunnel LHC machine.
2.1.1 LHC structure and features
The LHC [23] is designed for two kinds of collisions: collisions of protons,
and collisions of heavy ions. This section focuses on the case of proton colli-
sions.
The collider tunnel contains two adjacent parallel beam lines (or beam pipes)
that intersect at four points, each containing a proton beam, which travel in
opposite directions around the ring. Since the LHC is a proton accelerator
with a constrained circumference, its maximal energy per beam is related to
the strength of the dipole field which keeps the beam in orbit.
The nominal LHC beam energy of 7 TeV2 is made possible by a global magnet
system that uses a total of about 9600 magnets. Some 1232 dipole magnets
keep the beams on their circular path, while the 392 quadrupole magnets are
used to keep the beams focused, in order to maximize the chances of inte-
21 eV (electron volt) = 1.6× 10−19J
29
raction between the particles in the four intersection points, where the two
beams will cross. In total, over 1600 superconducting magnets are installed,
with most weighing over 27 ton each. Approximately 96 ton of liquid he-
lium is needed to keep the magnets, made of copper-clad niobium-titanium
operating at a temperature of 1.9 K (−271.25 ◦C). At that temperature,
when carrying a current of 11850 A the field of the superconducting dipole
magnets is increased from 0.54 to 8.33 T. Such a magnetic field is necessary
to bend the 7 TeV beams around the ring of the LHC. The curvilinear re-
gions are provided with radio-frequency cavities cooled to a temperature of
4.5 K. In these regions, electrical fields with a strength between 3 MVm−1
and 16 MVm−1 give the energy necessary to compensate for the energy loss
due to synchrotron radiation. Each proton beam has an energy of 7 TeV,
giving a total collision energy of 14 TeV (centre-of-mass energy). At this
energy the protons have a Lorentz factor of about 7500 and move at about
0.999999991 c, or about 3 metres per second slower than the speed of light (c).
Rather than continuous beams, the protons are accelerated into 2808 bunches,
so that interactions between the two beams, containing ∼ 1011 protons, take
place at discrete intervals never shorter than 25 nanoseconds (ns) (bunch
spacings). They provide a good time resolution (few ns), in order to di-
stinguish the events from two consecutive bunch crossing. For this reason, a
precise synchronization of all detector is requested. A bunch collision rate of
40 MHz is reached at LHC.
The LHC [24] is designed with two rings: two separate magnet fields
and vacuum chambers, in a twin-bore magnet design. The only common
sections are located at the insertion regions, equipped with the experimental
detectors. Before reaching at the LHC, the proton beams run across a chain
of acceleration (see Fig.2.3): it starts from a linear accelerator (LINAC) that
generates 50 MeV protons and injects them to the PSB3. There the protons
are accelerated to 1.4 GeV and injected into the PS, where they reach an
3The PSB is the acronym of Proton Synchrotron Booster, the first and smallest circularproton accelerator in the accelerator chain at the CERN Large Hadron Collider injectioncomplex. It was built in 1972, and contains four superimposed rings with a radius of 25meters. It receives protons from the linear accelerator Linac2 and accelerates them, toinjected them finally into the PS.
30
Figure 2.3: Chain of LHC injection.
energy of 26 GeV. In the following stage, the SPS accelerates the beams to
450 GeV before they are injected (over a period of 20 minutes) into the main
ring of LHC. Here the proton bunches are accumulated, accelerated (over a
period of 20 minutes) to their peak 7 TeV energy, and finally circulated for
10 to 24 hours while collisions occur at the four intersection points.
In addition to the centre-of-mass energy, provided by the accelerator,
another important quantity is the luminosity L4, which depends only on the
machine features, and carries out its construction.
In the general case of two colliding beams, the luminosity L is written as
follows:
L = fnbN1N2
A, (2.1)
where f is the revolution frequency, nb is the number of bunches per beam,
Ni is the number of particles in the bunches of each colliding beam, and A
4There are two kinds of luminosity: instantaneous luminosity and integrated luminosity.The instantaneous luminosity L is given by the relationship dN
dt = σL, where dNdt is the
event rate and σ is the cross section of the interaction. The integrated luminosity L isthe integral of the instantaneous luminosity over time, L =
∫Ldt. While the former
is measured in barn−1× second−1, the latter is measured in barn−1, where 1 barn =10−28cm2.
31
is the cross section of the beams. At LHC, the bunches are filled with an
identical number of protons, then we can write N1 = N2 = Nb.
The beam cross section is defined as:
A = 4πεnβ∗
γ, (2.2)
where εn is the normalized transverse beam emittance5 (with a design value
of 3.75 µm), β∗ is the beta function at collision point6, and γ is the Lorentz
relativistic factor. A further correction is required in Eq. 2.1 to account for
the geometric luminosity reduction factor, F , related to the fact that the two
beams cross at an angle at the interaction point:
L =fnbN
2b γ
4πεnβ?F. (2.3)
2.1.2 Experimental requirements
The nominal value for the luminosity, as well as the other parameters of
the LHC collider are summarized in Table 2.1. This value can be reached
with a number of bunches per beam nb = 2808 and a number of protons per
bunch Nb = 1.15 · 1011. As a high beam intensity could not be reached with
antiproton beams, a simple particle-antiparticle accelerator collider configu-
ration cannot be used at LHC.
The luminosity lifetime is an important parameter at LHC. Since the
intensities and emittances of the circulating and colliding beams degrade, the
luminosity tends to decay during a physics run. Under nominal conditions,
the LHC produces 109 inelastic collision events per second at a bunch crossing
rate of 40 MHz (i.e. a bunch crossing spacing of 25 ns), with approximately
20 collision events expected per bunch crossing. Though the very important
computing and storage facilities, events can only be recorded at a rate of
about 300 Hz. Therefore, an online selection system is necessary to determine
in a very small amount of time whether an event is worth being recorded.
5Emittance is a measure for the average spread of particles in the position-and-momentum phase space.
6It measures the beam focalization.
32
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
Table 2.1: List of the nominal LHC parameters, with their values.
This system must be fast and very selective to reduce the event rate by
seven orders of magnitude. Finally, it must keep a very high efficiency on
interesting collision events.
A significant number of inelastic collisions, due to the large number of
protons per bunch, are expected to occur at each crossing, corresponding to
an average of 1000 particles per bunch crossing. In order to distinguish such
events from one another, a large number of detector channels are needed
because a high granularity is mandatory and a precise momentum measure-
ments is necessary.
Moreover, the detector must provide a fast response with a good time resolu-
tion, in order to distinguish the events from two consecutive bunch crossings.
This requires a precise synchronization of all detector channels. The limit
where two consecutive signals start to overlap is called out-of-time pile-up.
It affects the shape of the signal, which is typically a few bunch crossings,
and must be taken into account.
2.2 The Compact Muon Solenoid Detector
The CMS detector is one of the experiments currently running at the
LHC at CERN. The main purpose of the CMS experiment is to search for
the evidence of the Higgs boson and new physics. To achieve these goals,
the experiment was designed to provide extensive information in terms of
33
Figure 2.4: The CMS coordinate system.
particle identification with high spatial resolution.
2.2.1 Coordinate System
The system of coordinates used for the CMS detector is illustrated in
Fig. 2.4.
The detector [25] has a cylindrical shape around the beam axis (z axis). The
origin is centered at the nominal collision point inside the experiment: the x
axis points horizontally towards the center of the LHC, and the y axis points
vertically upwards, so the z longitudinal axis, horizontal and collinear to the
beam trajectory, points towards the Jura mountain.
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. In experimental particle physics, the pseudorapidity η, de-
fined as η = − ln tan(θ/2), is used to describe the angle of a particle relative
to the beam axis. Hence, the direction of a particle trajectory at production
point is described by the coordinates (η, φ). The η coordinate is an important
variable because divides the subdetectors in two parts: the “barrel” and the
34
“endcaps”. The first one corresponds to the central, cylindrical region. The
last ones consist of the two discs at the extremities that close the detector
along the beam axis.
In an inelastic collision event between two partons coming from the pro-
tons, their energy is an unknown fraction of the proton energy, so the collision
energy is not fixed. However, the parton momentum, before the collision, is
expected to be longitudinal (along the beam axis): the transverse momen-
tum of each parton being negligible. Since the total transverse momentum
is conserved during an interaction, the transverse momentum of the collision
is expected to be negligible too.
A particle escaping the detection creates an unbalance in the total transverse
energy measurement, called missing transverse energy. If the detector is her-
metic, this missing transverse energy can be interpreted as the transverse
energy of the particles that the detector is not able to measure, such as
neutrinos.
2.2.2 CMS structure
The CMS [26] makes use of several subdetector systems (see Fig. 2.5)
to provide both spatial track location (precise measurement of particle mo-
mentum) and high resolution energy detection. The main subdetectors are
the two calorimeters and the tracking system. Electromagnetic particles are
stopped and measured in the first one; hadronic particles are measured in
both and stopped in the second one. In addition, an inner tracking de-
vice measures the trajectories of all charged particles, while an outer device
measures the charged particles that crossed both calorimeters, i.e. muons.
Finally, the tracking devices are submitted to a magnetic field that curve the
trajectories of charged particles.
In the design of the CMS detector, a particular attention is given to
muons: unlike other detectable particles, their energy can not be measured
by any of the calorimeters; this measurement only relies on the curvatures
of the tracks in the two tracking devices. The degree of curvature of the
trajectory of a particle decreases when its transverse momentum increases,
35
Figure 2.5: A perspective view of the CMS detector.
making the charge and pT measurements more difficult. So, a measurement
of the momentum is performed by analyzing the track bending under the
effect of the 3.8 T magnetic field provided by the superconducting solenoid
magnet which interleaves the detector systems. The flux is returned through
a 12500 ton iron yoke comprising 5 wheels and 2 endcaps, composed of three
discs each.
A longitudinal section view of the layout of the CMS detector is given in
Fig. 2.6, where the origin denotes the interaction point (IP), and the angle
specifications on the top and left are given in units of η.
2.2.3 Inner Tracking System
The CMS tracker [27] is a fundamental tool for the charge and momentum
measurements on charged particles. Surrounding the interaction point, it has
a length of 5.8 m and a diameter of 2.5 m, and covers a pseudorapidity range
of |η| < 2.5.
The CMS tracker is a full-silicon tracking system, made of a very resistant
36
Figure 2.6: Longitudinal section view of one quadrant of the CMS detector.
material to radiation, because of its position around the collision point. It
uses different technologies for achieving the requirements needed for vertex
identification7:
• requirements of high granularity and fast shaping;
• compactness allowing spatial measurements close to the interaction
point;
• necessity to operate in harsh environment, and requirement of high
reliability due to the extremely limited possibility to do maintenance
on the tracker itself.
The CMS silicon tracker is the most extended silicon tracker ever built for a
high energy physics experiment. However, it has some disadvantages:
1. an efficient cooling system is necessary because of the high power den-
sity of detector electronics;
7Besides the primary vertex, which corresponds to the IP of the spotted collision,secondary vertices can indicate another interaction that occurred during the same bunchcrossing (pile-up), or the late decay of a particle.
37
2. complications in the reconstruction of particles crossing the tracker
and loss of efficiency and precision, due to their interactions with high
amount of dense material.
The high number of particles crossing the tracker results in a high hit
density, which decreases when the distance to the center increases. So, the
granularity is dictated by the expected hit density of a given region.
The tracker is constituted by two different tracking subdetectors:
• a silicon pixel tracker;
• a silicon strip tracker;
Each of the detectors is then composed of different sections in order to ma-
ximize the η coverage, i.e. a barrel region covering the low pseudorapidity
region and two endcaps (see Fig. 2.7), one for each side, allowing high reso-
lution tracking of tracks with high pseudorapidity.
Figure 2.7: The CMS pixel detector.
The innermost part of the tracker is constituted by the pixel detector.
A schematic view of the different layers constituting the barrel and the two
endcaps is provided in Fig. 2.8, in which the schematic cross section through
38
the CMS tracker is illustrated. The pixel detector contains barrel and endcap
modules; the silicon strip detector contains two collections of barrel modules:
the Tracker Inner Barrel (TIB) and the Tracker Outer Barrel (TOB), and
two collections of endcap modules: the Tracker Inner Disc (TID) and the
Tracker EndCaps (TEC).
Figure 2.8: Schematic cross section through the CMS tracker.
The outermost part of the tracker is made of silicon strips; thicker silicon
sensors are used for this region. To prevent risks of thermal runaway, the
silicon tracker is coupled to a cooling system operating only at a temperature
below −10◦ C.
2.2.4 Electromagnetic Calorimeter
The Electromagnetic Calorimeter [28] (ECAL) was designed according
to the requirements of the search of the Higgs boson in two photons, H →γγ. It is the only subdetector to provide information about photons. For
a precise diphoton mass reconstruction, a very precise position and energy
measurement must be provided by the ECAL. The ECAL is also of primary
importance for the electron reconstruction in a Higgs boson analysis in a
39
multi-lepton final state. The combination of its information with the one
from the tracker ensures a very precise measurement of electron position and
momentum, and a significant background rejection. A good segmentation
is essential to distinguish the energy deposit shape of an electromagnetic
particle, from the one of a hadronic particle.
The CMS ECAL is a hermetic and homogeneous calorimeter, that covers
the pseudorapidity range of |η| < 3. It is made of 75848 lead tungstate
crystals, mounted in a barrel (|η| < 1.479) and two endcaps (1.479 < |η| <3). The crystals are followed by photodetectors that read and amplify their
scintillation. While in the barrel avalanche photodiodes (APDs) are used, in
the endcaps vacuum phototriodes (VPTs) are necessary to obtain a higher
resistivity to radiation.
The pion population is particularly important in the forward region, and
the decay π0 → γγ, with two photons very close to each others, is quite
difficult to distinguish from a single photon. For a better photon identifica-
tion, a preshower detector (with a thickness of 20 cm) is made of two parts
located at both ends of the tracker, in front of the ECAL endcaps, in the
pseudorapidity range 1.653 < |η| < 2.6 (see Fig. 2.9). Its absorber, made of
Figure 2.9: Longitudinal view of part of the CMS ECAL showing the ECALbarrel and a ECAL endcap, with the preshower in front.
40
lead radiators, causes electrons and muons to produce electromagnetic sho-
wers. Behind each radiator, two layers of silicon strip sensors are located,
with orthogonal orientation. These sensors measure the deposited energy
and the transverse shower profiles for better identification of electromagnetic
particles.
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 lead tungstate crystals is driven by some constraints as-
signed by the CMS detector design:
1. compactness of ECAL in order to include both calorimeters inside the
magnet;
2. good separability of electromagnetic showers due to the smallness of
Moliere radius8 (2.2 cm) of lead tungstate;
3. short time of scintillation decay of the crystal, necessary for the context
of LHC collision.
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 made of four Modules in the η direction
(see Fig. 2.10). The energy reconstruction is affected by the presence of
acceptance gaps, called cracks, between Modules. A larger crack is at η =
0 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. 2.10). Small cracks are also present between the endcap Dees,
but they can be assumed negligible.
The energy loss is measured by comparing the energy measured in the
ECAL with the momentum measured in the tracker on electrons with lit-
8The Moliere radius Rµ is a characteristic constant of a material, giving the scale ofthe 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 length,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 energy deposition.
41
Figure 2.10: Layout of the CMS ECAL showing the arrangement of crystalmoduls, supermodules and endcaps, with the preshower in front.
tle Bremsstrahlung, considering that the difference is due to energy loss in
cracks. In order to cancel these losses, a recovery method is applied for all
gaps, except at η = 0 and the barrel-endcap transition, where energy losses
are 5% and 10%, respectively.
The energy resolution has been measured on one barrel supermodule, using
incident electrons, during a beam test in 2004 [29]. 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. (2.4)
and the result is shown in Fig. 2.11. A resolution higher than 1% is achieved
for electrons of energy higher than 15 GeV; for 40 GeV electrons it is of 0.6%.
42
Figure 2.11: ECAL barrel energy resolution, σ(E)/E, as a function of elec-tron energy as measured from a beam test. The points correspond to eventstaken restricting the incident beam to a narrow (4 × 4 mm2) region. Thestochastic (S), noise (N), and constant (C) terms are given.
2.2.5 Hadron Calorimeter
The CMS hadron calorimeter (HCAL) is located behind the tracker and the
ECAL as seen from the interaction point. It is designed to do measurements
about hadron jets and single hadrons. Hence, it has:
• to provide a sufficient containment to stop hadron showers;
• to have a wide extension in |η| for a precise description of the total
collision event, a reliable measurement of the missing transverse energy.
The HCAL measurement is very useful to distinguish electrons from hadron
jets. It is a sampling calorimeter, that is made of a barrel part (HB), cove-
ring the region with |η| < 1.3, and an endcap part (HE), complementing the
barrel coverage to |η| < 3.0. In order to enhance the HCAL performance, it
is completed by two other calorimeters: the outer calorimeter (HO), that im-
proves the efficiency of the barrel region, and the forward hadron calorimeter
(HF), that covers the region 3.0 < |η| < 5.0 (see Fig 2.12).
43
HF
HE
HB
HO
Figure 2.12: Section view of the HCAL detector.
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 lenght9. The HO
uses the solenoid coil as an additional absorber equal to 1.4/ sin θ interaction
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 cope
with the radiation, and handle high counting rates. Because of the magnetic
field, the absorber must be made from a non-magnetic material. Finally,
the HE has to fully contain hadronic showers. The calorimeter barrel 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%. (2.5)
It can be observed that the energy resolution is dominated by the HCAL
contribution.
9Nuclear 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.
44
2.2.6 Muon System
The outer detector of the CMS experiment is dedicated to the detection of
muons [30]. Its design allows to identify efficiently muons momenta from a
few GeV to a few TeV. The W and Z production in the Higgs decay requires
also to have a coverage of the large pseudorapidity interval.
The muon detector is made of a cylindrical barrel and two endcaps, and is
interleaved with the return yoke of the superconducting magnet. In this case
too, the barrel region is an easier case than the endcaps: less background,
a low muon rate and an uniform 3.8 T magnetic field, mostly contained in
the steel yoke. Three different detector technologies were used in the muon
detector:
• Drift Tubes (DT): used in the barrel region (|η| <1.3);
• Cathode Strip Chambers (CSC): used in the endcap region (0.9<
|η| < 2.4);
• Resistive Plate Chambers (RPC): used in both the barrel and endcap
region (|η| < 1.6).
The DTs chambers measure the muon coordinate in the (r, φ) bending plane
and are alternate with chambers providing a measurement in the z direction.
The presence of “cracks”, i.e. dead spots in efficiency between the chambers,
is the main problem of this design, solved by an offset of the drift cells bet-
ween neighbor chambers.
In CSCs the chambers are positioned perpendicular to the beam line and
provide a precision measurement in the (r, φ) bending plane, whereas the a-
node wires provide measurements of η and the beam crossing time of a muon.
Efficient tools are used to reject non-muon backgrounds and match hits to
those in the other stations and in the CMS inner tracker.
An additional system of RPCs is placed both in the barrel and endcap regions.
These are double-gap chambers, operated in avalanche mode to ensure good
operation at high rates. They produce a fast response with good time reso-
lution but coarser position resolution than the DTs or CSCs. They provide
45
an independent trigger system with good time resolution, and a reduction
of ambiguities in the track reconstruction due to multiple hits in a cham-
ber. Finally, the muon momentum resolution is optimized by a sophisticated
alignment system, that measures the positions of the muon detectors with
respect to each other and to the inner tracker.
Figure 2.13: Section view of the Muon System: DT, RPC and CSC.
2.2.7 Trigger
The trigger system is the first step of the physics event selection process
with the purpose to reduce the data of the 40 MHz event rate down to about
300 Hz, which is the maximum amount that can be stored for offline analysis.
Hence, it performs a fast selection of events likely to be interesting for physics
analysis, among the huge amount of events produced by LHC collisions. The
selection is divided in two steps called Level-1 Trigger (L1) and High-Level
46
Trigger (HLT).
Level-1 Trigger
The L1 Trigger is a hardware system made of largely programmable electro-
nics, that provides a first rate reduction to 100 kHz in a time range of 32 µs.
To satisfy this timing constraint, it considers coarse granularity objects from
the calorimeters and the muon system. No tracker information is used during
the L1 Trigger. During this time range, the event information is stored in
so-called pipelines.
The Fig. 2.14 shows the L1 Trigger architecture: it is divided in two
parallel trigger system, one corresponding to the calorimeters, the other to
the muon system. Each system is based on a local, a regional and a global
part, after which they are merged into a Global Trigger for the final L1
decision. Several categories of Level-1 Trigger candidates are created:
Figure 2.14: Architecture of the Level-1 Trigger.
47
• Muon, built in the Muon Trigger;
• Electron/Photon, (isolated and not-isolated, e/γ);
• Tau, built in the Regional Calorimeter Trigger;
• Jet, central and forward;
• Total Transverse Energy (ΣET ), Missing Transverse Energy (EmissT ),
Scalar Transverse Energy Sum of all Jets (above a given threshold,
HT ), built in the Global Calorimeter Trigger.
Local Triggers : on each subdetector, they create coarse granularity in-
formation. In the calorimeters, this information is a collection of Trigger
Primitives.
Regional Triggers : it collects local information in order to build L1 Trig-
ger candidates and combines the information of both calorimeters or muon
system and sends them to the Global Calorimeter Trigger or the Global Muon
Trigger, respectively.
Global Calorimeter Trigger and Global Muon Trigger : the former sorts
the L1 Trigger candidates to send the four most relevant ones of each category
to the Global Trigger; the latter collects and compares the candidates from
Regional Triggers, then it combines them into four Muon candidates and
sends them to the Global Trigger.
Global Trigger : it collects the candidates produced by the Global Calori-
meter Trigger and Global Muon Trigger, and compares them to the Level-1
Trigger Menu10. If the candidate collection satisfies at least one of the listed
triggers, the L1 Trigger decision is positive and the fine granularity event
information is sent to the High-Level Trigger. Some trigger rules are also
applied at that step, to prevent any memory overload.
High Level Trigger
The High Level Trigger builds candidates corresponding to all kinds of re-
constructed objects considered in the offline analysis. Its inner substructure
10The Level-1 Trigger Menu is a list of Level-1 enabled triggers.
48
consists of several steps of increasing complexity, starting at Level-2.
The L2 starts generally with the Level-1 Trigger information, and builds fine
granularity objects around the L1 candidates, using only information from
the calorimeters and muon system. The tracker information is used, when
necessary, in order to pass on the next level: Level-2.5.
The HLT sorts the selected events into several datasets with a little overlap
as possible, accepting an event that passes at least one of these trigger se-
lection, flagging it according to the passed selections and recording it in the
corresponding datasets.
2.3 Physics Objects: Event Reconstruction
The starting point for physics analyses in CMS is based on the recon-
struction of high-level physics objects which correspond to particles travel-
ling through the detector after collisions. In this section, we will describe the
different types of high-level objects and the algorithms used by CMS for the
identification and reconstruction of these objects.
The signal of a particle going through the material of the detectors is recorded
and reconstructed as individual points in space known as recHits. In order to
reconstruct a physical particle, the recHits are associated together to deter-
mine points on the particle trajectory. The characteristics of the trajectory
are then used to define its momentum, charge, and particle identification.
2.3.1 Particle Flow
Particle Flow (PF) [31] is an algorithm used to reconstruct the physics
objects. It handles all information obtained from all subdetectors and re-
constructs the events by identifying objects as muons, electrons, photons
(converted or not), charged hadrons and neutral hadrons. Then, the list of
object/particles is used to build jets (from which the quark and gluon ener-
gies and directions are inferred), to determine the missing transverse energy
EmissT (see Sec. 2.2.1), to reconstruct and identify taus from their decay pro-
ducts, to quantify charged lepton isolation with respect to other particles, to
49
tag b jets, etc.
The PF includes an iterative algorithm for the reconstruction of the tracks
in order to obtain a high tracking efficiency and a low fake rate. Since the
purpose of the iterative algorithm is to generate tracks, it analyzes the hits
from the position sensitive detectors, giving rise to a seed. The procedure to
form tracks consists of the following steps [32]:
1. Trajectory Seeding: the track reconstruction starts by using an e-
stimate trajectory state or set of hits that are compatible with the
assumed physics process, in particular in CMS it is assumed that they
are compatible with the beam spot to provide the initial vector. Addi-
tional requirements are that the seed direction undergoes certain crite-
ria, or that the hits have to be located in a certain geometric region of
the detector.
2. Trajectory Building: the track reconstruction proceeds in the direc-
tion specified by the seed to locate compatible hits on the subsequent
detector layers. An algorithm, called Kalman Filter 11 is used to find
and fit the track: the full knowledge of the track parameters at each
detector layer provides compatible measurements in the next detector
layer, forming combinatorial trees of track candidates.
3. Trajectory Cleaning: trajectory building produces a large number of
trajectories, many of which share a large fraction of their hits. This step
resolves ambiguities among the possible trajectories keeping a maxi-
mum number of track candidates.
4. Trajectory Smoothing: a backward fitting (smoothing) allows the use
of all covariance matrices to be applied to all the intermediate points
based on all measurements used so far. This step reduces constraints
on the vertex, which allows the reconstruction of secondary charged
particles originating from photon conversions and nuclear interactions
in the tracker material and from the decay of long-lived particles.
11The Kalman Filter is a mathematical method which produces estimates of the truevalues of measurements by predicting a value, estimating the uncertainty of the predictedvalue, and computing a weighted average of the predicted value and measured value.
50
Figure 2.15: Scheme of the Particle Flow algorithm.
Calorimeter Clustering
The Calorimeter Clustering [31] is an algorithm which allows
• to detect and measure the energy and direction of stable neutral par-
ticles such as photons and neutral hadrons;
• to separate these neutral particles from energy deposits from charged
hadrons;
• to reconstruct and identify electrons and all accompanying Bremsstra-
hlung photons;
• to help the energy measurement of charged hadrons for which the track
parameters were not determined accurately, which is the case for low-
quality, or high-pT tracks.
Therefore, a specific clustering algorithm has been developed for the Particle
Flow event reconstruction; its main purpose is a high detection efficiency even
for low-energy particles, and a separation of close energy deposits. The clu-
stering is performed separately in each subdetector. The algorithm consists
of three steps:
1. identification of “cluster seed” as local calorimeter-cell energy maxima
above a given energy;
51
2. increase of ”topological clusters” from the seeds by aggregating cells
with at least one side in common with a cell already in the cluster and
with an energy in excess of a given threshold;
3. generation of “Particle Flow clusters” as seeds from topological clusters.
Link algorithm
In general, a given particle is expected to generate several Particle Flow e-
lements in the CMS subdetectors [31]: one charged-particle track, and/or
several calorimeter clusters, and/or one muon track. In order to relate these
elements to each other, a link algorithm is used to fully reconstruct each
single particle and remove any possible double counting from different detec-
tors.
This particular algorithm is performed for each pair of elements in the event
and defines a distance between any two linked elements to quantify the qua-
lity of the link. Then, it produces blocks of elements linked directly or
indirectly. These blocks typically contain only one, two or three elements,
owing to the granularity of the CMS detectors. The independence of the
algorithm performance from the event complexity is due to the smallness of
the blocks. A link between a charged-particle track and a calorimeter cluster
occurs as follows: the track is extrapolated from its last measured hit in the
tracker firstly to the two layers of the PS (Silicon-Strip Pre-shower), then to
the ECAL and finally to the HCAL.
The first reconstructed particles are muons: tracks and clusters, that are
associated with segments in the muon chambers, are labeled as muons and
deleted from the list of objects that are not associated. Similarly, if the
tracks and the clusters are compatible with the topological characteristics of
an electron, the electron is detected. Then charged hadrons are identified.
After having assigned the HCAL cluster to a track, a comparison is made
between the energy of the cluster and the momentum of the track. If there
is compatibility between the two, a charged hadron with energy given by
the weighted average of the cluster energy and momentum of the track is
52
created. Conversely, if there is a difference between the energy of the cluster
and the momentum of the track, then the block is labeled as neutral hadron.
The same procedure is repeated if there are clusters of ECAL and HCAL
associated to a track. When the associations are completed, only ECAL and
HCAL clusters remain that are not related to each other neither to a track;
they are respectively associated with photons and neutral hadrons.
More details about muon, electron and tau reconstructions are in the next
subsections.
2.3.2 Muons
The reconstruction of muons is performed by combining tracking and
calorimeter information [32] that implies an increase in performance time of
the reconstruction procedure. Muon reconstruction requires a good detec-
tion of muons over the full acceptance of the CMS detector and over the very
high background rate expected at the LHC with full luminosity. The chain of
muon reconstruction occurs in the following three steps: Local Reconstruc-
tion, Standalone, Global and Tracker Muon Reconstruction.
Local Reconstruction
The first step of muon reconstruction uses hits in the muon detectors. There-
fore, during the Local Reconstruction, only information coming from the
DTs, CSCs and RPCs are used. The muon system has three functions: muon
identification, momentum measurement, and triggering over the entire kine-
matic range of the LHC. A high-field solenoidal magnet and its flux-return
yoke make allow for an excellent muon momentum resolution and trigger
capability.
The reconstruction starts from the identification of hits involved in the cros-
sing of the particle and proceeds by creating segments according techniques
which depend on the considered subdetector.
By using algorithms that provide the hit spatial resolution for the particle
from the drift time12, in the DTs, two hits from different layers are selected,
12There are two types of algorithms which make this time-position conversion: the first
53
starting from the most distant ones. The hit pair is accepted if the incidence
angle of the relative segment is compatible with a track that points toward
the vertex of the nominal interaction point. Then, the hits compatible with
this segment are sought in the other layers and the good segments are only
those for which we have nhits > 3 and χ2/ndof < 20. Hence, the two
orthogonal projections, (r, φ) and (r, z), are arranged in order to have the
tridimensional track. The low expected rate and the relatively low strength
of the local magnetic field, which is also relatively uniform, allow to use the
drift chambers as tracking detectors for the barrel muon system.
In the CSCs, the information from cathode strips and anode wires are
arranged. Since the charge given by the passing of a ionizing particle has a
distribution that involves 3-5 strips, the geometric center of this distribution
is considered to identify the most likely passing point of the particle. An
algorithm like that described for the DTs is used to build a track segment
in each CSC, starting from the two extreme hits in the first and in the last
layer.
In both the barrel and the endcaps, the RPCs are used as part of the
trigger. The RPC consists of two gas chambers in which an ionizing particle
develops an electron avalanche picked up a read out strip in contact with the
anode. Therefore, this subdetector is able to tag the time of an ionizing event
in a much shorter time than the 25 ns between two consecutive LHC bunch
crossings. Hence, a fast appropriate muon trigger device based on RPCs can
identify unambiguously the relevant bunch crossing to which a muon track
is associated even in the presence of the high rate and background expected
at the LHC. After collecting the strips, where a signal has been generated
(clustering), and created a sets of strips, a centre of gravity of the cluster in
the RPCs, namely the reconstructed hit, is established.
one works with a constant drift velocity; the second one works with a velocity depending onthe drift time, the magnetic field and the incidence angle relative to the normal directionof the cell.
54
Standalone Muon Reconstruction
The segments obtained from the local reconstruction are the starting points
for the track fit by the Kalman algorithm (see Subsec. 2.3.1) in the offline
reconstruction and the trajectory parameters estimated by the Level-1 Trig-
ger in the online.
The track reconstruction occurs in the following stages [33]:
1. Seed Generation, in which the clusters are combined in seeds. The seed
generation allows to identify good candidates in order to completely
reconstruct the track.
2. Pattern Recognition, in which the track reconstruction occurs by means
of the Kalman Filter, that starts from a seed and moves iteratively
updating the trajectory parameters at each step. The information pro-
vided by the seeds and by each layer of the outer subdetectors is com-
bined in order to improve the precision on the track parameters.
3. Ambiguity Resolution, which takes into account the possibility that
more than one track shares the same hits to avoid double counting of
tracks. This type of procedure is first applied to all tracks from the
same seed and then to all the reconstructed tracks.
4. Track Fitting, in which the track is refitted by a Kalman filter, starting
from the inner subdetectors. Once the hits are fitted and the fake tra-
jectory removed, the remaining tracks are extrapolated to the point of
closest approach to the beam line. The final fit of the track is achieved
by a constraint to the nominal IP in order to improve the pT resolution.
The resulting reconstructed track in the muon spectrometer is so called “stan-
dalone muon”.
Global Muon Reconstruction
In this stage, the trajectories given by the muon system are extended by
the tracker hits. The algorithm starts from a standalone muon and then
develops the trajectory in the outer detectors according to the equations
55
which describe the motion of a charged particle in a magnetic field and taking
into account the Coulomb multiple scattering and the loss of energy through
material.
While at low pT , the best momentum resolution for muons is obtained from
the silicon tracker, at higher pT the improvement of the muon momentum
resolution is obtained by combining the muon track from the silicon detector,
the so called “tracker track”, with the muon track from the muon system, the
standalone muon, into a “global muon”. The reconstruction of global muon
tracks begins after the complete reconstruction of the central tracker tracks
and the muon system tracks. The first step is to identify the silicon tracker
track to combine with the standalone muon track. This process of choosing
tracker tracks to be combined with standalone muon tracks is referred to as
track matching. The method of track matching proceeds in two steps:
1. definition of a region of interest that is rectangular in (η, φ) space, and
selection of a subset of tracker tracks located in this region of interest;
2. iteration over the subset of the tracker tracks and application of more
stringent spatial and momentum matching criteria to choose the best
tracker track to combine with the standalone muon.
Tracker Muon Reconstruction
The muon track reconstruction algorithm described in previous sections starts
from the muon system and combines standalone muon tracks with tracker
tracks. If in the muon detector the quality of muon track is high, this method
works well. However, in some cases the hit and segment information in the
muon system is minimal, and standalone muon reconstruction fails. Hence,
a complementary method is introduced to consider all silicon tracker tracks
and to identify them as muons by looking for compatible signatures in the
calorimeters and in the muon system. Muons identified with this approach
are called “tracker muons”.
The main purpose of this algorithm is to reconstruct and identify muons in
CMS starting from a silicon tracker track and then searching for a compatible
segments in the muon detectors. The energy deposition in the calorimeter
56
can also be used for muon identification. All relevant information are col-
lected and stored by the algorithm into a final “muon object”. No combined
(silicon-hits + muon-hits) track fit is performed. Thus, the momentum vector
of a tracker muon is the same as that of the silicon tracker track. However, if
a global muon is reconstructed using the same silicon tracker track, the global
muon fit is stored in the same muon object and the default momentum of
the muon in the object is taken from the global muon fit. At this stage of
reconstruction, it is still possible to retrieve the momentum of the silicon
tracker track fit through the reference to the silicon tracker track which is
stored in the muon object.
The final output from the algorithms is a muon physics object together with
a compatibility value indicating the probability of the track being a muon.
2.3.3 Electrons
The electron footprints can have a complex topology, involving Bremsstra-
hlung photons that may convert into electron-positron pairs; the final parti-
cles are spread in the φ direction by effect of the 3.8 T magnetic field.
The reconstruction of electrons in CMS [34] use algorithms developed in
order to ensure a good reconstruction efficiency and high precision for the
measurement of the energy and the direction at vertex. It starts by the recon-
struction of clusters seeded by hot cells in the ECAL, and uses them to form
clusters of clusters (superclusters) to further collect the energy radiated by
Bremsstrahlung in the tracker volume. Then, the superclusters are used to
select trajectory seeds built from the combination of hits from the innermost
tracker layers. A primary superclusters preselection is performed by using a
hadronic veto cut, given by the H/E ratio (H is the hadronic energy and E is
the supercluster energy) and applying a 4 GeV threshold on the supercluster
transverse energy.
The ECAL is the essential detector to estimate the electron energy from the
deposits issued by the electromagnetic showers that are produced by elec-
trons. However, a spread in φ of the energy deposit in the calorimeter is due
to the material before the ECAL which can trigger a Bremsstrahlung process,
57
and the high magnetic field of CMS. Hence, algorithms of superclusters are
considered in order to take into account these factors. The reconstruction of
electron seeds is carried out by two seeding algorithms, an ECAL driven and
a tracker driven, that are combined into a single collection, keeping track of
the seed provenance.
Then, the electron tracks are reconstructed from electron seeds by following a
fitting procedure that takes into account the effect of Bremsstrahlung energy
loss. The hits collected in this step are passed to a Gaussian Sum Filter
(GSF)13 for the final estimation of the track parameters.
Finally, the electron candidates are built from the tracks reconstructed by
the GSF and their associated superclusters. They undergo a loose prese-
lection to reduce the rate of jets faking electrons and a further selection to
reduce ambiguous electron candidates, that arise from the reconstruction of
conversion legs from photon(s) radiated by primary electrons.
2.3.4 Taus
Tau leptons decay into other leptons about 17% of the times, while the
rest of the decays is hadronic, mainly involving pions. The detection of tau is
complicated by its short average life. So the reconstruction and identification
of taus are only based on the detection of its decay products. QCD-jets,
in particular b-jets, can be reconstructed as fake τ -jets. Since the electron
reconstruction is complex task when the electrons do Bremsstrahlung, those
can fake also τ objects. In addition, a significant fraction of the τ and
associated neutrino momentum is not detected.
The main tau reconstruction and identification algorithm developed by
CMS group is the Hadron Plus Strips (HPS) algorithm [35]. It uses Particle
Flow technique, in which the information of all the CMS subdetectors are
combined to identify and reconstruct all particles produced in the collision
13The Gaussian Sum Filter is an algorithm for electron reconstruction in the CMStracker. It is used to improve the momentum resolution of electrons compared to thestandard Kalman filter, because the Bremsstrahlung energy loss distribution of electronspropagating in matter is highly non-Gaussian and the Kalman filter relies solely on Gaus-sian probability density functions. Hence, the GSF algorithm models the Bremsstrahlungenergy loss distribution by a Gaussian mixture rather than by a single Gaussian.
58
(photons, electrons, muons, charged and neutral hadrons). Neutrinos are not
considered. The resulting list of PF candidate objects is used to reconstruct
the PF jet object.
The HPS starts from a PF jet and searches for τ lepton decay products pro-
duced by any of the hadronic decay modes with one or three charged particles
and neutral pion(s) in the final state14. Since neutral pions are produced very
often in hadronic τ decays, one of the main task in reconstructing taus, that
decay hadronically, is determining the number of π0 produced in the decay.
The HPS combines the PF electromagnetic particles in the “strips”, taking
into account possible broadening of calorimeter deposits from photon conver-
sions. In order to reconstruct the hadronic tau decay products, the neutral
objects are then combined with existing charged hadrons.
When more than one hypothesis for a possible tau decay signature exists, the
hypothesis leading to the lowest ET sum of jet constituents not associated to
τ decay products is chosen.
Figure 2.16: Scheme of tau decays into final states involving pions.
14Tau decays can be classified into those that provide a single track (1-prong) and thosethat provide three tracks (3-prong). In the leptonic case, the decay contains a singlecharged lepton, giving a single track 1-prong. In the hadronic case, the charged pionseach provide a track. Because of the charge conservation, there must be an odd numberof charged pions in the final state which gives an odd number of tracks. Generally, thetau decays into a single charged pion (1-prong) and any number of neutral pions or threecharged pions (3-prong, π− + π+ + π±) and any number of neutral pions. It is possiblefor taus to give even five or seven tracks, but these are not very frequent and they areextremely hard to identify from background process, therefore tau physics generally focuseson 1 or 3-prong taus (see Fig. 2.16).
59
60
Chapter 3
Data Analysis
In this chapter we describe the analysis about the search of the doubly
charged Higgs boson in the channel Φ++Φ−− → `+`+`−`− (` = e, µ, τ) in
proton-proton (pp) collisions at√s = 7 TeV. The data correspond to an
integrated luminosity of L = 4.93 fb−1 collected by CMS experiment at the
LHC during 2011. The doubly charged Higgs boson mass range covered by
the analysis is [130; 500] GeV.
Due to the presence of four leptons in the final state, a high-performance
lepton reconstruction, identification and isolation, along with excellent lep-
ton energy-momentum measurements, is mandatory. A substantial reduction
of QCD-induced sources of misidentified (“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 re-
solution on the reconstructed mass m(`±`±), which is the most important
observable for the search of the doubly charged Higgs boson. We can note
that preserving the highest possible reconstruction efficiency and ensuring a
sufficient discrimination against hadronic jets are particularly challenging for
the reconstruction of leptons with low pT . In this range the combined infor-
mation 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.
61
3.1 Trigger and Data samples
The data used were officially validated for trigger selection and event recon-
struction during the 2011 running period. During the data taking periods,
the instantaneous luminosity, which is known with a precision of 2.2% [36],
varied over the range 1029−1033cm−2s−1. In the 2011, CMS collected a data
set corresponding to an integrated luminosity of L = 4.93± 0.11 fb−1.
The monitoring and certification of the quality of the CMS data consists of
a multi-step procedure, spanning from online data taking to the offline re-
processing of data recorded earlier. The quality assessment is based on both
visual inspection of data distributions by monitoring shift persons as well as
algorithmic tests of the distributions against references.
The Run Registry (RR) is the central workflow management tool used to
certify collected data, to keep track of the certification results and to expose
them to the whole CMS collaboration. It is regularly used for the creation of
official good-run list files in JSON format which are used as input to down-
stream selection of the data for re-processings and for physics analyses. The
Some additional criteria on the reconstructed primary vertex are required
to select events from good collisions (discarding these from pile-up interac-
tions):
• the number of degrees of freedom > 4 for the vertex fit;
• the maximal distance of the nominal point of the pp collision along the
beam line |z(PV )| with respect to the center of CMS detector (z = 0)
is less than 24 cm;
• the maximal distance of the nominal point of the pp collision with
respect to the center of CMS detector in the transverse plane is less
than 2 cm.
1To enable the most effective access to CMS data, the data are first split into PrimaryDatasets (PDs) and then the events are filtered. The division into the Primary Datasetsis done based on the trigger decision. The PDs are structured and placed to make life aseasy as possible, e.g. to minimize the need of an average user to run on very large amountsof data.
63
In case of multiple primary vertex candidates, the one with the highest
value of the scalar sum of the total transverse momentum of the associated
tracks is selected.
Duplication of events in DoubleElectron, DoubleMuon and MuEG PDs
is avoided by selecting:
1. events in MuEG datasets that don’t fire the used double electron trig-
gers;
2. double muon events that don’t fire either the double electron or the
electron-muon cross triggers.
The Primary Datasets and the relevant run ranges for 2011 data are listed
Signal and background datasets, used in the analysis, are obtained with
detailed Monte Carlo (MC) simulations by using programs to generate high
energy physics events. These events are sets of outgoing particles produced
in the interactions between two incoming particles. The target of the simu-
lations is to provide a representation of the event properties as accurate as
possible in a wide range of reactions, within and beyond the Standard Model.
In particular those where strong interactions play a basic role, and therefore
multi-hadronic final states are produced. These programs have to take into
account a combination of analytical results and various QCD based models.
64
3.2.1 Event Generators
PYTHIA [37] is a multipurpose MC event generator used for event ge-
neration in high energy physics. It is used for the simulation of signal and
background processes, either to generate a given hard process at leading or-
der, or for simulation of showering and hadronization in cases where the hard
processes are generated at the next-to-leading order. The event generation
is carried out in some steps by factorizing the process into a number of com-
ponents, each of which can be handled reasonably accurately. As a result,
a generated event should be in the form of “event”, with the same average
behaviour and the same fluctuations as for real data.
PYTHIA6 is a particular version of PYTHIA, that has been used in order to
generate events for several new processes of beyond the Standard Model
physics, such as the production of the doubly charged Higgs boson.
CalcHEP [38] is a package for automatic calculations of elementary par-
ticle decay and collision properties in the lowest order of perturbation theory
(the tree approximation). It is used to select a model of particle interaction
and to implement some changes in the model. The CalcHEP package consists
of two parts: the first one offers to the user the possibility to select a model
of the particle interaction and to implement some changes in the model,
by specifying incoming and outgoing particles, by generating Feynman dia-
grams, etc. The main tasks of the second part are related to the possibility
to modify physical parameters (incoming momenta, couplings, masses etc.)
involved in the process, selecting the scale parameter for evaluation of the
QCD coupling constant and partonic distribution functions, calculating par-
ticle widths and decay rates, by taking into account high order QCD loop
corrections and defining the kinematic scheme for the effective MC integra-
tion.
An other program used to generate events corresponding to different pre-
cesses, such as signal(s) and backgrounds, is MADGRAPH [39]. It allows to
simulate events at the parton, hadron and detector level directly from a web
interface, for processes in the Standard Model and in several physics scenarios
beyond the SM.
65
TAUOLA [40] is a Monte Carlo program dedicated to the generation of the
tau-lepton decays. This program includes more than twenty decay chan-
nels, including leptonic, semileptonic and meson modes. Complete QED
corrections are included in the leptonic decay channels, and for other decay
channels an interface is provided to Monte Carlo generators for approximate
simulation of the QED corrections. Tau leptons may be pre-generated with
any other event generator, for example with PYTHIA6, and then passed to the
TAUOLA package for detailed decay simulation.
POWHEG [41] generator has been used for the calculation at next-to-leading
order in QCD of s and t-channel single top production.
3.2.2 MC samples
Signal and background samples, used in the analysis, are obtained with a
detailed Monte Carlo simulations by using the previous generators and the
GEANT42 [42] program to simulate the detector response and the interac-
tions of the particles with the matter. All datasets were exposed to the full
reconstruction. The signal and background samples have been used for the
optimization of the event selection strategy prior to the analysis of the ex-
perimental data.
The doubly charged Higgs signal events in the pair production mode
(Φ++Φ−−) was simulated with PYTHIA6 and the TAUOLA generator interfaced
to PYTHIA for a correct treatment of the τ decay. Concerning the single pro-
duction mode (Φ±±Φ∓), the signal samples were generated using CalcHEP.
The Fig 3.1 shows the cross section of Φ±± in the both pair and associated
production as a function of mΦ±± . The signal processes were simulated in 14
2The GEANT4 is a program which describes the passage of elementary particlesthrough matter. It includes a complete range of functionality including tracking, geo-metry, physics models and hits. The physics processes offered cover a comprehensiverange, including electromagnetic, hadronic and optical processes, a large set of long-livedparticles, materials and elements, over a wide energy range. The principal applicationsof GEANT4 in high-energy physics are the tracking of particles through an experimentalsetup for simulation of detector response and the graphical representation of the setupand of the particle trajectories.
accurate measurement of the Higgs boson mass is obtained from an accurate
measurement of the energy-momentum.
3.3.1 Muon Reconstruction and Identification
Muon candidates are reconstructed using two algorithms: the first matches
tracks in the silicon detector to segments in the muon chambers, while the
second performs a combined fit using hits in both the silicon tracker and the
muon system (see Sec. 2.3.2). Global muons are used for this analysis, di-
scarding candidates muons reconstructed only as tracker muons or standalone
muon.
Concerning the muon identification strategy, some definitions need to be
introduced in order to understand the kind of background muons we want to
reject for this analysis [43]:
• ”Fake Muon”: any muon passing whatever applied cuts that is recon-
structed in single pion or single kaon events. Thus, a muon from a
K → µ decay in flight is a fake muon.
• ”Fake Rate”: the ratio of fake muons to generated kaons and pions as
a function of the pT or η of the generated kaon or pion.
• ”Punch-Through”: a hadron which enters the calorimeter and produces
hits in the muon system. Most of the punch-through are due to kaons
and pions in the hadronic showers that decay in muons.
The global muon normalized-χ2 is used to reject both decays-in-flight and
punch-through. If χ2/ndof < 10, the muons are correctly identified with an
efficiency near to 1. Moreover, track quality cuts can be used to reject leftover
decays-in-flight. There are two other fundamental quantities to which these
cuts are applied:
1. the transverse impact parameter (d0) of the muon track with respect
to the reconstructed primary vertex;
2. the number of silicon tracker hits Nhits.
71
In this analysis, only muons with pT > 5 GeV and |η| < 2.4 are considered.
For the purpose of a tight muon identification, the muon is required to satisfy
some additional requirements:
• at least one muon chamber hit is included in the final track fit, matched
to muon segments in at least two muon stations;
• the corresponding tracker track must have Nhits > 10;
• a χ2/ndof of the global-muon track fit is required to be less than 10
for its discriminating power against decays-in-flight;
• |d0| < 2 mm, preserving the efficiency for muons from b- and c-quarks3.
3.3.2 Electron Reconstruction and Identification
In order to reject jets faking electrons and electrons resulting from con-
versions, the electron reconstruction uses a cut-based approach. It combines
the ECAL and tracker information. Electron candidates are reconstructed
from clusters of energy deposits in the ECAL, which are then matched to hits
in the silicon tracker. The standard CMS electron reconstruction algorithm,
described in Sec. 2.3.3, is used for this analysis.
The physics analysis of multi-electron final states requests a good identifica-
tion efficiency in order to enhance signal selection, in particular at low ET ,
where the Z and W background increases and the fake rate is much higher.
Efficient electron identification in CMS is quite different from identification
in many other experiments because of the large varying amount of material
in the tracker and the high magnetic field. However, thanks to a conve-
nient classification of electrons, it is possible to reach a good identification
efficiency of electrons.
Electrons are divided into categories [44]:
• brem electrons,
3A loose d0 cut is very efficient for prompt muons, coming from the primary vertex,and rejects a significant fraction of decays-in-flight. A too tight d0 cut, instead, rejectsmuons from bottom and charm decays, but too many prompt muons too.
72
• lowbrem electrons,
• badtrack electrons,
• crack electrons,
• pure tracker-driven electrons,
which are introduced to separate electrons with quite different measurement
characteristics and purity; all of them (except the last one) are split into
barrel and endcap, giving rise to nine categories. The technique that uses this
electron classification is called Cut-in-Category and it uses the following set
of variables in order to distinguish between real electrons and fake electrons:
• the H/E ratio of energy deposited in the HCAL directly behind the
ECAL cluster (H) and the energy of the electron supercluster (E);
• the energy-momentum matching variables E/pin, Eseed/pin and Eseed/
pout, where E is the supercluster energy, Eseed is the supercluster seed
energy, pin and pout are the electron track measured momentum at the
vertex and at the calorimeter, respectively;
• the geometrical matching variables ∆φin and ∆ηin, namely the diffe-
rences between the energy weighted position of the supercluster and
the position of closest approach to the supercluster position in φ and η
coordinates, respectively;
• the calorimeter shower shape variable, σiηiη.
In order to reject electrons from conversions, due to the material in front of
ECAL:
• the impact parameter d0 of the electron track computed with respect
to the reconstructed primary vertex;
• the number of “missing hits” which are the number of crossed layers
without compatible hits in the back-propagation of the track to the
beam line.
73
The algorithm gives as output a bit pattern for each electron candidate for
9 defined severity levels of cuts [45]. There is one bit for electron identifi-
cation, a second one for electron isolation, then one for conversion rejection
and the last one for impact parameter. The cut severity levels are called
Table 3.6: 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.
In addition, for this analysis, all electron candidates are required to have
pT > 15 GeV and |η| < 2.5; the first cut ensures high efficiency for the re-
construction while the second one corresponds to the geometrical acceptance
of the tracker detector.
74
3.3.3 Muon Isolation
An efficient rejection of QCD background, tt+jets and W+jets events can be
reached by using a muon isolation variable.
The isolation algorithm is based on the estimation of the total energy
deposited in a cone around the lepton, namely the isolation cone. The cone
is built around an axis (see Fig. 3.2), which overlaps the muon direction
pointing to the vertex. The value of opening angle, ∆R, is defined in the (η,
φ) space by the following equation
∆R =√
∆η2 + ∆φ2 , (3.1)
where ∆η and ∆φ are the pseudorapidity and azimuthal angle of the energy
deposit estimated respect to the cone axis. The ∆R opening angle has to
be lower than a certain value defined in the analysis; in this case, ∆R is less
than 0.3.
The contribution to the isolation variables come from the sum of the tran-
sverse momenta in the isolation cone around the lepton and the transverse
energies in the ECAL and HCAL calorimeters. The first contribution is
Figure 3.2: Representation of the isolation cone. The muon direction, esti-mated from the vertex, defines the cone axis.
75
defined as:
Isotrack =tracker∑
∆R
ptrackT . (3.2)
while the contribution from deposits in calorimeters is defined as:
Isoecal =ECAL∑
∆R
ET and Isohcal =HCAL∑
∆R
ET . (3.3)
When divided by pT , the isolation variable is defined as:
relIsoiso =Isotrack + Isoecal + Isohcal
pT, (3.4)
and we refer to it as relative isolation variable. The best performance in
terms of signal efficiency and background rejection are obtained by using the
relative isolation, as detailed in Ref. [46].
3.3.4 Electron Isolation
The isolation variables used to calculate electron isolation relying on the
information of the tracker, ECAL and HCAL are based on the sum on pT of
tracks and sum of ET depositions in cones in (η, φ) space around the lepton
and an inner veto region, called ”Jurassic” veto [45], to remove the electron
footprint coming from the path in φ due to Bremstrahlung.
Track Isolation
The sum of pT of tracks is made centered on the electron track at vertex and
it is calculated within a cone of radius
∆R =√
∆η2 + ∆φ2 < 0.3 , (3.5)
around the electron candidate direction. In the Eq. 3.5, ∆η and ∆φ are the
same variables defined in Eq. 3.1. The inner veto cone radius is set to 0.015
and the pT threshold cut on tracks is 1.0.
76
ECAL and HCAL Isolation
Electron isolation variables are summed in a cone centered on the the elec-
tron ECAL supercluster, with a footprint removal region consisting of a strip
of specified η width and an additional circular region (see Fig. 3.3). They
are computed using the ET from energy deposits in cells with geometrical
centroids situated within a cone of radius given by the Eq. 3.5, like for track
isolation. The cone axis is taken as the ECAL supercluster centroid viewed
from the electron vertex taken at (0, 0, 0). For electrons, the isolation va-
Figure 3.3: Representation of the strip of a footprint removal region in thecase of ECAL and HCAL isolation for electrons.
riables are given by Eqs. 3.2 and 3.3 and the relative isolation is given by
Eq. 3.4.
Isolation variables are among the most pile-up sensitive variables in this
analysis. An increase of the mean isolation values corresponds to an increase
of the mean energy deposited in the detector because of the pile-up. Thus,
the efficiency of a cut on isolation variables strongly depends on pile-up
conditions and a correction of the isolation variable is carried out to have a
good analysis with a reduced pile-up effects. The FastJet program [47],[48]
implements an algorithm used to estimate the mean pile-up contribution
within the isolation cone of a lepton, through the energy density (ρ) in the
event. The ρ variable is defined for each jet in a given event and the median
77
of the ρ distribution for each event is taken. The correction to the isolation
variable is given by: ∑Isocorrected =
∑Iso− ρ · A , (3.6)
where A is the area of the jet cone in the (η, φ) space. The ρ variable is
given in 1/(∆η∆φ) units; hence, A has the dimension of an angle. Rather
than computing a geometrical area, an effective area4 is considered, to avoid
dealing with different thresholds in the isolation and FastJet algorithms.
The values for the effective area have been computed in the context of the
H → ZZ → 4` analysis [49] and re-used in this analysis.
3.3.5 Tau Reconstruction, Identification and Isolation
In order to reconstruct tau leptons decaying hadronically, the HPS algo-
rithm [50], based on Particle Flow objects, is used. The main purpose is to
derive the number of pions produced in the decay (see Sec. 2.3.4).
The identification and isolation of τ leptons are carried out also by using the
HPS algorithm, in order to reduce the QCD background. The algorithm has a
modular design to facilitate building of higher analysis-specific discriminants
on top of these stable, well-measured results.
Reconstructed tau candidates are required to satisfy isolation criteria,
which are based on counting the number of charged hadrons and photons
above a certain ET threshold, not associated to the tau decay signature
within an isolation cone of size ∆R = 0.5. Three sets of ET thresholds
define “loose”, “medium” and “tight” working-points of the HPS algorithm.
The energy sum of the candidates in a solid cone of ∆R = 0.5 around the
reconstructed tau decay mode axis defines the isolation variable. Finally, pile-
up correction is applied by using three discriminators to which correspond
the three following HPS working-points:
1. Loose Isolation: no PF charged candidates with pT > 1.0 GeV and no
4Effective areas are defined as the ratio of the fit slope of the variable as a function ofthe number of reconstructed vertices Nvtx to the fit slope of ρ as a function of Nvtx.
78
PF gamma candidates with ET > 1.5 GeV;
2. Medium Isolation: no PF charged candidates with pT > 0.8 GeV and
no PF gamma candidates with ET > 0.8 GeV;
3. Tight Isolation: no PF charged candidates with pT > 0.5 GeV and no
PF gamma candidates with ET > 0.5 GeV.
For this analysis, the medium isolation is used and all taus candidates are
required to have pT > 15 GeV and |η| < 2.1.
The following additional requirements are imposed for τ -jets:
• discrimination of tau-jets against electrons and muons sharing the same
track, since these particles could fake 1-prong τ . The discriminators,
used in the analysis, are respectively
– HPSTAU discByMER (medium working-point)
– HPSTAU discByTMR (tight working-point)
• tau veto in the region 1.46 < |η| < 1.558, because of the reduced
ability to discriminate between electrons and hadrons in this portion
of the detector.
3.4 Event Selection
The analysis strategy can be divided in two steps, in addition to the
HLT trigger requirement and a basic selection of collision events described
previously.
A preliminary preselection is carried out in order to suppress most of the
QCD jet events with fake leptons. It is applied with the purpose also to keep
the events in the signal phase space.
Then, a baseline selection based on the kinematics of Φ±± production is
applied, so that the remaining background contributions can be reduced.
The production of the doubly charged Higgs boson at LHC (see Sec. 1.3.2)
can give rise to a distinctive multi-lepton signature: due to flavour non-
conservation, the final states can be combinations of all possible leptons.
79
Such different scenarios are analyzed separately in order to achieve the best
signal to background ratio. Additionally, final states are discriminated based
on the number of reconstructed τ -jets. The signal events include two pairs of
same sign leptons, hence six possible final states are looked for when searching
for the double charged Higgs in the BR=100% scenarios:
µ+µ+µ−µ−, e+e+e−e−, τ+τ+τ−τ−,
e+µ+e−µ−, µ+τ+µ−τ−, e+τ+e−τ−.
The leptonic decay of the taus in the final states including only taus are not
considered in this analysis; the final state with 4 hadronically decaying tau
is not relevant because the efficiency of the four hadronic tau reconstruc-
tion final state is too low to make the signal enhanced with respect to the
background.
3.4.1 Preselection cuts
The first condition set on the four final leptons concern the charge: two of
these leptons should be of the same charge, both coming from the same Φ±±
boson.
Then, some kinematical variables are studied to develop preselection cuts
for this analysis; the first important observable is the lepton pT . The pT
range of the leptons from the doubly charged Higgs decay depends on the
hypothesis made for the doubly charged Higgs mass, and can reach low values
down to 10-15 GeV for low Higgs masses. Anyway, since this analysis involves
at least two high pT leptons, we require that at least the two leptons with
the highest momentum in the event should have pT > 20 and 10 GeV,
respectively. This cut ensures that the background events for which the
leptons originate from the semi-leptonic b-decays (called non-prompt leptons)
are reduced as they tend to be less energetic. Moreover, it does not affect
the signal efficiency (see Sec. 3.5). The Fig. 3.4, where the distributions of
the four muons pT in the scenario BR (Φ±± → µ±µ±) = 100% are plotted in
the mΦ±± = 130 GeV (left) and mΦ±± = 300 GeV (right) hypotheses, shows
80
that in the highest mass hypothesis the pT spectrum is shifted towards higher
values of momentum because of the kinematics.
The same pT cuts are applied for the other scenarios with similar results; in
[GeV]T
Lepton p0 100 200 300 400 500 600 700
Eve
nts
/10
GeV
0
0.5
1
1.5
2
2.5
3
3.5
4CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±µ±µ→±±ΦBR (
1µ
2µ
3µ
4µ
= 130 GeV±±Φ
for signal massT
HLT Selection: lepton p
[GeV]T
Lepton p0 100 200 300 400 500 600 700 800
Eve
nts
/10
GeV
0
0.01
0.02
0.03
0.04
0.05
0.06CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±µ±µ→±±ΦBR (
1µ
2µ
3µ
4µ
= 300 GeV±±Φ
for signal massT
HLT Selection: lepton p
Figure 3.4: Distribution of the transverse momentum of the four muons in thescenario BR (Φ±± → µ±µ±) = 100%, for signal events with mΦ±± = 130 GeV(left) and mΦ±± = 300 GeV (right). The leptons are ordered in pT . Thesamples correspond to an integrated luminosity of L = 4.93 fb−1.
the final states where the taus are included, the distributions of the transverse
momentum are shifted towards lower values of pT because of the energy of
the neutrinos from the taus decay that is not detected (missing energy) and
does not contribute to the visible tau pT reconstructed by the detector.
The Figs. 3.5, 3.6, 3.7 show the distributions of the lepton pT for signal in
three different mass hypotheses (mΦ±± = 130, 300, 500 GeV), for background
and for data before and after the application of the pT cuts and by considering
different 100% BR scenarios.
The event number shown in the plots is rescaled to the integrated luminosity
of L = 4.93 fb−1 according to the cross section of the specific process.
The pairs of leptons with an invariant mass below 12 GeV are discarded in
order to suppress the background events coming from low mass b-resonances,
photon conversions and the low mass tail of the dilepton distribution for
signal and background that are generally not interesting for this analysis.
The Fig. 3.8 shows the mass distributions of the same sign dileptons for
81
Figure 3.5: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.
82
Figure 3.6: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → µ±τ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.
83
Figure 3.7: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → e±τ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.
84
signal events generated with mass mΦ±± = 130, 300, 500 GeV, for background
events and for data before and after the cut on the mass, but anyway after
the previous cut on pT . In these plots, obtained for the BR (Φ±± → µ±µ±)
= 100% scenario, the signal has a tail on the left due to probably to the
events in which the doubly charged Higgs boson tends to be off mass shell
(top). This tail is reduced after the mass cut (bottom).
In addition to the kinematic selection criteria, the following requirements
on the relative isolation and the significance of the impact parameter (SIP`)5,
are used:
• the sum of the relative isolation of the two worst isolated leptons (e,µ)
is required to be (see Eq.3.4) less than 0.35;
• all reconstructed electrons and muons are required to have SIP` < 4
with respect to the primary vertex.
The cut on the relative isolation ensures an effective reduction of the
background contribution from QCD multi-jets and misidentified leptons. In
Figs. 3.9, 3.10, the distributions of lepton isolation variable for BR = 100%
to µµ channel and eτ channel are plotted before and after applying all the
cuts previously mentioned.
Leptons arising from b-quark decays have usually a sizable impact param-
eter due to their origin from a secondary vertex. A loose cut is applied on
the significance of the impact parameter SIP`, which ensures good signal effi-
ciency while removing some reducible background as we can see in Figs. 3.11,
3.12, 3.13. In these figures the relative distributions in the different scenarios
are shown at the HLT selection level (top) and after all of preselection cuts
(bottom).
It is worth to notice that the cuts on isolation and SIP` previously men-
tioned are only applied on muons and electrons, even in the final state inclu-
ding µτ and eτ same sign pairs; indeed tau can travel through the detector
and so a cut on the SIP` can affect the signal efficiency significantly; tau
5The significance of the impact parameter is a dimensionless quantity defined as SIP` =ρPV /σρPV
, where ρPV denotes the distance from primary vertex and σρPVits uncertainty.
85
Figure 3.8: Invariant mass distribution of the same sign dileptons in thescenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) themass cut (m(`±`±) > 12 GeV). The samples correspond to an integratedluminosity of L = 4.93 fb−1.
86
Figure 3.9: Distribution of the lepton isolation variable in the scenarioBR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) the cut(relIsoworst + relIsonexttoworst < 0.35). All of previous cuts on lepton pTand same sign dilepton mass are also included. The samples correspond toan integrated luminosity of L = 4.93 fb−1.
87
Figure 3.10: Distribution of the lepton isolation variable in the scenario BR(Φ±± → e±τ±) = 100%, before (top) and after (bottom) the cut (relIsoworst+relIsonexttoworst < 0.35). All of previous cuts on lepton pT and same signdilepton mass are also included. The samples correspond to an integratedluminosity of L = 4.93 fb−1.
88
Figure 3.11: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.
89
Figure 3.12: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → µ±τ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.
90
Figure 3.13: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → e±τ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.
91
isolation cuts are instead applied at the level of the identification criteria via
the HPS algorithm, as cited in Sec. 3.3.5.
Table 3.7 summarizes the preselection criteria used for this analysis.
Table 3.8: Selection cuts applied in various four lepton final states.
In all of plots reported after cuts the background events ZZ → `+i `−i `
+j `−j
survive because they are very similar to a signal event Φ++Φ−− → `+i `
+j `−k `−l .
These backgrounds also have a higher cross section than the signal. However,
they can be distinguished from the signal by the presence of a resonance in
the same flavour opposite sign dilepton mass (Z → `+i `−i ) and not in the
same sign dilepton mass (Φ±± → `±i `±j ).
The event yields after each consecutive cut for four-lepton analysis have
been obtained for all of mass hypotheses in the five scenarios considered. The
Tables 3.9 - 3.13 report those only for masses of 130, 300 and 500 GeV. In all
cases the mass window for the particular final state has been applied. Each
cut reported in the tables includes the previous ones.
93
mΦ
++
Cu
tS
ingle
top
tt+jets
VV
+jets
Wbb
DY
+jets
Tota
lD
ata
Sig
nal
130
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.2
2±
0.0
10.0±
0.0
0.0±
0.0
0.2
2±
0.0
10.0±
0.0
375.0
5±
2.9
8∑pT
0.0±
0.0
0.0±
0.0
0.1
5±
0.0
10.0±
0.0
0.0±
0.0
0.1
5±
0.0
10.0±
0.0
367.1
5±
2.9
8
300
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
11.0
1±
0.1
7∑pT
0.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
11.0
0±
0.1
7
500
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0±
0.0
00.0±
0.0
0.7
9±
0.0
2∑pT
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0±
0.0
00.0±
0.0
0.7
9±
0.0
2
Tab
le3.9:
Cut
flow
for100%
decay
tom
uon
sw
ithm
ass130,
300an
d500
GeV
.
94
mΦ
++
Cu
tS
ingle
top
tt+
jets
VV
+je
tsWbb
DY
+je
tsT
ota
lD
ata
Sig
nal
130
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.2
0±
0.0
10.0±
0.0
0.0±
0.0
0.2
0±
0.0
10.0±
0.0
313.2
4±
2.9
6∑ p T
0.0±
0.0
0.0±
0.0
0.1
3±
0.0
10.0±
0.0
0.0±
0.0
0.1
3±
0.0
10.0±
0.0
308.2
2±
2.9
5
300
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
3±
0.0
10.0±
0.0
0.0±
0.0
0.0
3±
0.0
10.0±
0.0
10.8
2±
0.1
7∑ p T
0.0±
0.0
0.0±
0.0
0.0
2±
0.0
10.0±
0.0
0.0±
0.0
0.0
2±
0.0
10.0±
0.0
10.8
2±
0.1
7
500
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.8
6±
0.0
2∑ p T
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.8
6±
0.0
2
Tab
le3.
10:
Cut
flow
for
100%
dec
ayto
elec
tron
sw
ith
mas
s13
0,30
0an
d50
0G
eV.
95
mΦ
++
Cu
tS
ingle
top
tt+jets
VV
+jets
Wbb
DY
+jets
Tota
lD
ata
Sig
nal
130
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.4
5±
0.0
20.0±
0.0
0.0±
0.0
0.4
5±
0.0
20.0±
0.0
347.3
6±
3.0
2∑pT
0.0±
0.0
0.0±
0.0
0.2
9±
0.0
10.0±
0.0
0.0±
0.0
0.2
9±
0.0
10.0±
0.0
340.9
3±
3.0
2
300
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
2±
0.0
00.0±
0.0
0.0±
0.0
0.0
2±
0.0
00.0±
0.0
11.0
2±
0.1
8∑pT
0.0±
0.0
0.0±
0.0
0.0
2±
0.0
00.0±
0.0
0.0±
0.0
0.0
2±
0.0
00.0±
0.0
11.0
2±
0.1
8
500
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.8
3±
0.0
2∑pT
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.8
3±
0.0
2
Tab
le3.11:
Cut
flow
for100%
decay
toe-µ
with
mass
130,300
and
500G
eV.
96
mΦ
++
Cu
tS
ingle
top
tt+
jets
VV
+je
tsWbb
DY
+je
tsT
ota
lD
ata
Sig
nal
130
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.2
8±
0.0
70.0±
0.0
0.0±
0.0
0.2
8±
0.0
70.0±
0.0
7.4
2±
0.6
1∑ p T
0.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
5.5
7±
0.5
3Z
vet
o0.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
4.3
5±
0.4
7
300
GeV
SIP`4l-
10.0±
0.0
0.0±
0.0
0.0
7±
0.0
60.0±
0.0
0.0±
0.0
0.0
7±
0.0
60.0±
0.0
0.2
4±
0.0
4∑ p T
0.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.2
4±
0.0
4Z
vet
o0.0±
0.0
0.0±
0.0
0.0
1±
0.0
00.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.2
0±
0.0
4
500
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
1±
0.0
0∑ p T
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
1±
0.0
0Z
vet
o0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
1±
0.0
0
Tab
le3.
12:
Cut
flow
for
100%
dec
aytoµ
-τw
ith
mas
s13
0,30
0an
d50
0G
eV.
97
mΦ
++
Cu
tS
ingle
top
tt+jets
VV
+jets
Wbb
DY
+jets
Tota
lD
ata
Sig
nal
130
GeV
SIP`
0.0±
0.0
0.0
4±
0.0
30.2
9±
0.0
30.0±
0.0
0.0±
0.0
0.3
3±
0.0
415±
3.8
76.9
0±
0.6
0∑pT
0.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
5.3
4±
0.4
8Z
veto
0.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
0.0±
0.0
0.0
3±
0.0
00.0±
0.0
4.4
6±
0.4
8
300
GeV
SIP`
0.0±
0.0
0.0
2±
0.0
20.0
3±
0.0
10.0±
0.0
0.0±
0.0
0.0
5±
0.0
21±
10.2
9±
0.0
4∑pT
0.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.2
6±
0.0
4Z
veto
0.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.0±
0.0
0.0
1±
0.0
10.0±
0.0
0.2
6±
0.0
4
500
GeV
SIP`
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
2±
0.0
0∑pT
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
2±
0.0
0Z
veto
0.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0±
0.0
0.0
0±
0.0
00.0±
0.0
0.0
2±
0.0
0
Tab
le3.13:
Cut
flow
for100%
decay
toe-τ
with
mass
130,300
and
500G
eV.
98
3.5 Selection efficiency
The Figs. 3.14, 3.15, 3.16, 3.17 and 3.18 show the acceptance (left), e-
stimated as the ratio between the number of reconstructed events and the
number of generated events, from MC signal in the five considered scena-
rios. In the Fig. 3.14, the acceptance assumes values between the 60% and
70%, due to the pseudorapidity range (|η| < 2.4) of the global muons that
we have considered. Also the electron acceptance (see Fig. 3.15) starts from
low values, but reaches higher ones than the previous scenario because of
a larger pseudorapidity range (|η| < 2.5). For the BR (Φ±± → e±µ±) =
100% scenario (see Fig. 3.16), this ratio is a wider range (60%-90%). The
acceptances plotted in the last two figures (3.17, 3.18), that include the taus,
are generally quite lower because of the lower tau hadronic reconstruction
efficiency if compared with electron and muon ones; this is also due the fact
that a significant fraction of the τ momentum escapes undetected with the
associated neutrino’s.
[GeV]±±ΦMass of 100 200 300 400 500
Acc
epta
nce
(MM
MM
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±µ±µ→±±ΦBR (
[GeV]±±ΦMass of 100 200 300 400 500
Sel
ectio
n E
ffici
ency
(M
MM
M)
0
0.2
0.4
0.6
0.8
1
) = 100%±µ±µ→±±ΦBR (>10 GeV
T2>20 GeV, p
T1p
)>12 GeV±l±m (l
relIso
SIP
T pΣ
Mass Window
CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
Figure 3.14: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → µ±µ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.
On the right of these figures, the efficiencies for each of the selection and
for MC signal are shown for all the scenarios considered. They are estimated
99
[GeV]±±ΦMass of 100 200 300 400 500
Acc
epta
nce
(EE
EE
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±e±e→±±ΦBR (
[GeV]±±ΦMass of 100 200 300 400 500
Sel
ectio
n E
ffici
ency
(E
EE
E)
0
0.2
0.4
0.6
0.8
1
) = 100%±e±e→±±ΦBR (>10 GeV
T2>20 GeV, p
T1p
)>12 GeV±l±m (l
relIso
SIP
T pΣ
Mass Window
CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
Figure 3.15: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±e±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.
[GeV]±±ΦMass of 100 200 300 400 500
Acc
epta
nce
(EM
EM
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±µ±e→±±ΦBR (
[GeV]±±ΦMass of 100 200 300 400 500
Sel
ectio
n E
ffici
ency
(E
ME
M)
0
0.2
0.4
0.6
0.8
1
) = 100%±µ±e→±±ΦBR (>10 GeV
T2>20 GeV, p
T1p
)>12 GeV±l±m (l
relIso
SIP
T pΣ
Mass Window
CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
Figure 3.16: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±µ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.
Figure 3.17: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → µ±τ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.
[GeV]±±ΦMass of
100 200 300 400 500
Acc
epta
nce
(ET
ET
)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
) = 100%±τ±e→±±ΦBR (
[GeV]±±ΦMass of 100 200 300 400 500
Sel
ectio
n E
ffici
ency
(E
TE
T)
0
0.2
0.4
0.6
0.8
1
) = 100%±τ±e→±±ΦBR (>10 GeV
T2>20 GeV, p
T1p
)>12 GeV±l±m (lrelIsoSIP
T pΣ
Mass WindowZveto
CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs
Figure 3.18: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±τ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.
101
with respect to the acceptance. From the plots including only electrons and
muons, we can note that, after applying the cuts on the pT and same sign
dilepton mass, the efficiency is 100%, confirming the good choice of these two
kinematical cuts. From the plots including taus, the efficiencies are not flat
as a consequence of the rough tuning and the acceptance shown on the left
of the figures.
3.6 Systematic uncertainties
The impact on the selection efficiency of the uncertainties related to the
electron and muon identification and isolation algorithms and the relevant
misidentification rates, detailed in [45, 51, 52, 53, 54], are estimated to be less
than 2% by using a standard ‘tag-and-probe’ method [55] that relies on Z →`+`− decays to provide an unbiased and high-purity sample of leptons. A ‘tag’
lepton is required to satisfy stringent criteria on reconstruction, identification,
and isolation, while a ‘probe’ lepton is used to measure the efficiency of a
particular selection by using the Z mass constraint. The ratio of the overall
efficiencies as measured in data and simulated events is used as a correction
factor in the bins of pT and η for the efficiency determined through simulation,
and that is propagated to the final result.
The τhad reconstruction and identification efficiency via the HPS algo-
rithm is also derived from data and simulations, using the tag-and-probe
method with Z → τ+(→ µ+ + νµ + ντ )τ−(→ τhad + ντ ) events [52]. The
uncertainty of the measured efficiency of the τhad algorithms is 6% [52]. E-
stimation of the τhad energy-scale uncertainty is also performed with data in
the Z → ττ → µ+ τhad final state, and is found to be less than 3%. The τhad
charge misidentification rate is measured to be less than 3%.
The theoretical uncertainty in the signal cross section, which has been
calculated at NLO, is about 10-15%, and arises because of its sensitivity to
the renormalization scale and parton distribution functions [21].
The luminosity uncertainty is estimated to be 2.2% [36].
The systematic uncertainties are summarized in Table 3.14.
102
Lepton (e or µ) ID and isolation 2%τhad ID and isolation 6%τhad energy scale 3%τhad misid rate 3%
Trigger and primary vertex finding 1.5%Signal cross section 10-15%
Luminosity 2.2%Statistical uncertainty of signal samples 1-7%
Table 3.14: Source of systematic uncertainties and impact on the full selectionefficiency.
103
104
Chapter 4
Results and Statistical
Interpretation
In order to understand the results about a search of new particles or new
phenomena it is need to introduce the basic notions about the statistical
interpretation of them in terms of sensitivity to the exclusion or the discovery.
This sensitivity depends and can be compromised by some factors: a low
signal strength, the existence of a background comparable with the expected
signal and a bad experimental resolution.
4.1 Final distributions
The results of the analysis can be expressed in terms of invariant mass
distribution. They are shown in the Figs. 4.1, 4.2, 4.3, 4.4, 4.5 for each
scenario considered after applying all of cuts. The invariant mass distribu-
tions involving only light leptons (see Figs. 4.1, 4.2, 4.3) show a signal excess
for mΦ±± = 130 GeV compared to the background, but not any clustering
can be observed around the signal peak. Hence, this excess could be due
to statistical fluctuations. To understand the origin of this excess, more
data are required. We can observe that no event passes the full selection in
the invariant mass distribution of Φ±± for BR = 100% to µτ channel (see
Fig. 4.4). Moreover, we can note an obvious reduction of the background.
We find data and Monte Carlo simulations to be in reasonable agreement for
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all final states. In fact, we observe only few events at low masses, consistent
with background expectations.
Figure 4.1: Invariant mass distribution of Φ±± for BR = 100% to µµ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.
106
Figure 4.2: Invariant mass distribution of Φ±± for BR = 100% to ee channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.
107
Figure 4.3: Invariant mass distribution of Φ±± for BR = 100% to eµ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.
108
Figure 4.4: Invariant mass distribution of Φ±± for BR = 100% to µτ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.
109
Figure 4.5: Invariant mass distribution of Φ±± for BR = 100% to eτ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.
110
4.2 Statistical interpretation:
the CLs Method
The concept of the Confidence Level (CLs) is related to the fact that,
while an experiment is performed, we are interesting to confirm a new theory
or to exclude it in equal measure. For each discovery, it is necessary to
consider the hypothesis that the model from which we start can also be
wrong. Experiments are designed to be sensitive to the parameter set for
each model in a way so that the confidence levels give meaningful information.
The goal of a search is to extract the greatest possible number of information
from the data in possession, despite not having an experimental evidence of
the validity of a theory. In the case of our search, it means to exclude as
effectively as possible the existence of Higgs boson in its absence and to
confirm its existence in its presence in a mass range in which the experiment
is sensible.
The CLs, or modified frequentist method [56], is used for calculations
of exclusion limits. The analysis of the results can be formulated in terms
of a hypothesis test. The null hypothesis (H0) is that the signal is absent
and the alternative hypothesis (H1) is that it exists. This method consists in
quantifying the degree (level) to which the hypotheses are favored or rejected
by an experimental observation. It can be divided in the following steps:
• to identify the observables in the experiment of which the search con-
sists (in our case the invariant mass of the reconstructed particle pairs
that we suppose coming from the Higgs decay);
• to define a test statistic (or function) of the observables and the model
parameters for both the background and the hypothetical signal;
• to set the ranges of the values for the test statistic in which the obser-
vations will lead to the acceptance or rejection of the null hypothesis.
In practice, this means to specify a confidence level for the exclusion, like in
our case, or for the discovery. A confidence limit for exclusion is defined as
the value of a population parameter (such as a particle mass or a production
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rate) which is excluded at a specified confidence level; it is represented as a
percent value.
In order to define the method, we need to make a choice of the test stati-
stic and the treatment of the systematic uncertainties in the construction of
the test statistic and in generating data (toy Monte Carlo pseudo-data sets).
First of all, we take into account all independent sources of systematic un-
certainties, both theoretical and instrumental, and assign each of them its
own nuisance parameter θi, whose best estimate, prior data analysis, is θi.
When a nuisance parameter is taken to be distributed according to a normal
probability distribution function (p.d.f.), the effect of its variation on an ob-
servable O is propagated either as a Gaussian error, O = O0 · (1+σ ·θ) (used
only for observables that can take both positive and negative values), or as a
log-normal error, O = O0 ·κθ (used only for positive definite observables). In
this case, O0 is the observable value without error, and σ and κ characterize
the relative scale of the uncertainties [57].
In order to construct the test statistic, a likelihood function (L) is defined
where Poisson(data|µ · s(θ) + b(θ)) is the Poisson probability to observe
data, assuming that both the expected signal and background models, s(θ)
and b(θ), depend on some nuisance parameters θ. The free parameter µ is
the signal strength modifier, that is the ratio between the number of observed
events and the number of events expected by the model (process of normali-
zation). Thus, such a parameter µ takes into account how the cross section
of the Higgs boson varies with the collision energy and the decay mode, and
can be written by the σ/σmodel ratio.
The comparison between the data and the background-only (µ = 0) and
signal+background (µ) hypotheses is performed by the test statistic qµ, given
by the following likelihood ratio:
qµ = −2 lnL(data|µ, θµ)
L(data|µ, θ), (4.2)
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where data can be the actual experimental observation or pseudo-data (toys).
Assuming the independence of the measurements, both the numerator and
the denominator are maximized according to the method of maximum like-
lihood [58]. In the numerator, µ remains fixed and only θ is allowed to float
and θµ denotes the value for which L reaches the maximum. In the denomi-
nator, both µ and θ are allowed to float and µ and θ denote the values for
which L reaches the maximum. The maximization of the likelihood func-
tion is equivalent to the minimization of the logarithmic function, so the
constructed variable qµ is distributed as a χ2 variable.
The two tail probabilities (p-value), associated with the actual observa-
tion, can be estimated under the signal+background hypothesis:
pµ = P(qµ ≥ qobsµ |µs(θobsµ + b(θobsµ ))
)=
∫ ∞qobsµ
f(qµ|µ, θobsµ )dqµ , (4.3)
and under the background-only hypothesis:
p0 = P(qµ ≥ qobsµ |b(θobsµ ))
)=
∫ ∞qobs0
f(qµ|0, θobs0 )dqµ , (4.4)
where qobsµ is the observed value of the test statistic, θobs0 and θobsµ are the values
of the nuisance parameters that best describe the experimentally observed
data (i.e. maximize L), f(qµ|0, θobs0 ) and f(qµ|µ, θobsµ ) are the qµ distributions,
corresponding to the two hypothesis, generated by toy Monte Carlo pseudo-
data sets.
Then, CLs(µ) is defined as the following ratio:
CLs(µ) =P(
qµ ≥ qobsµ |µs(θobs
µ + b(θobsµ ))
)P(
qµ ≥ qobsµ |b(θobs
µ ))) . (4.5)
If CLs ≤ α for µ = 1, we say that the Higgs boson of the model is excluded
at the (1 − α) confidence level. Since we are interesting to quote the 95%
confidence level upper limit on µ, we adjust µ until we reach CLs = 0.05, so
defining µ95%CL.
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The most straightforward way for defining the expected median upper
limit and ±1σ and ±2σ bands for the background-only hypothesis is to
generate a large set of background-only pseudo-data and calculate CLs and
µ95%CL for each of them, as if they were real data (Fig. 4.6 (left)). Then, a
Figure 4.6: (Left) An example of differential distribution of possible limits onµ for the background-only hypothesis (s = 0, b = 1, no systematic errors).(Right) c.d.f. of the plot on the left with 2.5%, 16%, 50%, 84% and 97%quantiles (horizontal lines) defining the median expected limit as well asthe ±1σ (68%) and ±2σ (95%) bands for the expected value of µ for thebackground-only hypothesis.
cumulative probability distribution function (c.d.f.) of results can be built,
by starting the integration from the side corresponding to low event yields
(see Fig. 4.6 (right)). The point at which the c.d.f. crosses the quantile of
50% is the median expected value. The ±1σ (68%) and ±2σ (95%) bands
are defined by crossings of the 16% and 84% quantiles in the former case and
2.5% and 97.5% in the latter case.
In the Fig. 4.6 (right), the green and yellow bands are the ±1σ (68%) and
±2σ (95%) range in which the results are expected to fall in the background-
only hypothesis.
4.3 Exclusion Limits
A CLs method (see Sec. 4.2) is used to calculate an upper limit for the
Φ++ cross section at the 95% confidence level (CL) as a function of the Φ++
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mass hypothesis; the exclusion limits have been calculated combining the
results of this analysis with those obtained by the three lepton final state
analysis. The systematic uncertainties summarized in Table 3.14 are taken
into account, too.
The results of the exclusion limit calculations are and reported in
Figs. 4.7, 4.8, 4.9, 4.10, 4.11, in which also the previous limit exclusion at
Tevatron are shown, except for the not studied eτ channel. The observed
limits are shown by the black line; the dashed line indicates the median
expected limit on µ for the background-only hypothesis, while the green
(yellow) bands indicate the range that are expected to contain 68% (95%) of
all observed limit excursions from the median.
The exclusion limits are calculated from the intersection between the ob-
served limits from the data and the median expected limit. Lower bounds on
the Φ++ mass are established of 459 GeV in the µµ channel, 444 GeV in the
ee channel, 453 GeV in the eµ channel, 375 GeV in the µτ channel, 373 GeV
in the eτ channel; so, we exclude the doubly charged Higgs boson in mass
range below these bounds, providing significantly more stringent constraints
than previously published limits. They are summarized in Table 4.1.