Keywords: LHC, CMS, Higgs boson, photon identication, Higgs coupling, vector boson fusion

The Standard Model Higgs boson at LHC Table 1.1: Classication of the three families of fundamental fermions.

Titre: Production du boson de Higgs dans le canal de désintégration en 2 photons au LHC dans l'expérience CMS: première mesure de la section ecace inclusive dans des collisions proton-proton à 13 TeV, et étude du couplage de m H = 125.09 GeV est 5.6 σ, pour une signication attendue de 6.2 σ, et la signication maximale de 6.1 σ est observée à m H = 126.0 GeV. Enn une étude de faisabilité ayant pour but de contraindre les couplages anomaux du boson de Higgs aux bosons de jauges est présentée. Pour cette analyse les données à 8 TeV collectées pendant le Run 1 du LHC, correspondant à une luminosité intégrée de 19.7 fb -1 sont utilisées. Cette analyse exploite la production du boson de Higgs par fusion de bosons-vecteurs (VBF), avec le Higgs se désintégrant ensuite en 2 photons. Les distributions cinématiques des jets et du Higgs, qui dépendent de l'hypothèse de spin-parité, sont utilisées pour construire des discriminants capables de séparer les diérentes hypothèses de spin-parité. Ces discriminants permettent de dénir diérentes régions de l'espace des phases enrichies en signaux de spin-parité diérent. Les diérents nombres d'événements de signal sont extraits dans chaque région par un ajustement de la masse invariante diphoton, permettant de déterminer les contributions respectives des diérents signaux et permettant ainsi de contraindre la production de boson de Higgs pseudo-scalaire (spin-parité 0 -).

Mots-clés: LHC, CMS, boson de Higgs, identication de photons, couplage de Higgs, fusion de bosons-vecteurs Contents i Title: Higgs boson production in the diphoton decay channel with CMS at the LHC: rst measurement of the inclusive cross section in [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] TeV pp collisions, and study of the Higgs coupling to electroweak vector bosons Abstract: In this document two analyses of the properties of the Higgs boson in the diphoton decay channel with the CMS experiment at the LHC (Large Hadron Collider) are presented. The document starts with a theoretical introduction of the Standard Model and the Higgs boson physics, followed by a detailed description of the CMS detector. Then, photon reconstruction and identication algorithms are presented, with a particular focus on the dierences between the rst and the second run of the LHC, where the rst run (Run 1) took place from 2010 to 2012 with a centre-of-mass energy of 7 and then 8 TeV, while the second run (Run 2) started in 2015 with a centre-of-mass energy of 13 TeV. Performances of Run 1 and Run 2 reconstructions from the photon identication point of view are compared. Then the photon identication algorithm for the H → γγ analysis optimised for Run 2 is presented. To do that a multivariate analysis method is used. Performances of the photon identication at 13 TeV are nally studied and a data-simulation validation is performed. Afterwards, the H → γγ analysis using the rst Run 2 data is presented.

The analysis is performed with a dataset corresponding to an integrated luminosity of 12.9 fb -1 . An event classication is performed to maximize signal signicance and to study specic Higgs boson production modes. The observed signicance for the Standard Model Higgs boson at m H = 125.09 GeV is 5.6 σ, while 6.2 σ was expected, and the maximum signicance of 6.1 σ is observed at m H = 126.0 GeV.

Finally a feasibility study, having the aim of constraining the anomalous couplings of the Higgs boson to the vector bosons, is presented. This analysis is performed using the data collected at 8 TeV during Run 1 at the LHC, corresponding to an integrated luminosity of 19.7 fb -1 . This analysis exploits the production of the Higgs boson through vector boson fusion (VBF), with the Higgs decaying to 2 photons. The kinematic distributions of the dijet system and the Higgs, which depend from the spin-parity hypothesis, are used to build some discriminants able to discriminate between dierent spin-parity hypotheses. These discriminants allow to dene dierent regions of the phase-space enriched with a certain spin-parity process. The Higgs boson signal yield is extracted in each region from a t to the diphoton mass, allowing to determine the contributions of the dierent processes and then constrain the production of a pseudo-scalar (spin-parity 0 -) Higgs boson.

Introduction

The Standard Model is, up to now, the most successful theory of subatomic elementary particles. Developed in the early 1970s, it provides an elegant mathematical framework which describes how the fundamental constituents of the matter interact between each other, through the electromagnetic, weak and strong forces. Furthermore, it has successfully explained several experimental results and precisely predicted a wide variety of phenomena.

The Standard Model of particle physics predicts the existence of a unique physical Higgs scalar boson associated to the spontaneous electroweak symmetry breaking, whose mass is a free parameter of the theory, and which is regarded as the responsible for the masses of all known elementary particles. This particle, whose search is one of the main goals of the LHC collider and its experiments installed at the CERN laboratory in Geneva, was discovered by both ATLAS and CMS experiments in 2012, with a measured mass of ∼ 125 GeV. After the Higgs boson discovery the main objectives are the measurement of its properties and the tests of consistency with the Standard Model.

The inclusive production of SM Higgs boson followed by the decay to two photons is one of the most sensitive channels for the Higgs search at ∼ 125 GeV. In fact, despite its very small rate, it has a clear experimental signature thanks to an excellent diphoton mass resolution.

The general context of this thesis is therefore the measurement of the Higgs boson properties in the H → γγ decay channel. The analysed datasets were collected in proton-proton collisions at a center-of-mass energy of √ s = 8 TeV and √ s = 13 TeV, recorded with the CMS detector, comprising a total integrated luminosity of 19.7 fb -1 and 12.9 fb -1 respec- tively.

In Chapter 1, a theoretical introduction of the Standard Model and the Higgs boson physics is given, along with the presentation of the main Higgs results achieved at the LHC during Run 1.

In Chapter 2, after an introduction to the LHC performances, the CMS detector is described, with particular focus on the electromagnetic calorimeter, the sub-detector used to identify and reconstruct photons.

In Chapter 3 photon reconstruction and identication algorithms are presented, concenvii viii Introduction trating in particular on the dierences between the rst and the second run of the LHC.

The rst run (Run 1) took place from 2010 to 2012 with a centre-of-mass energy of 7 and then 8 TeV, while the second run (Run 2) started in 2015 with a centre-of-mass energy of [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] TeV. Performances of Run 1 and Run 2 reconstructions from the photon identication point of view are compared. Then the photon identication algorithm for the H → γγ analysis optimised for Run 2 is presented. To do that a multivariate analysis method is used. Performances of the photon identication at 13 TeV are nally studied and a datasimulation validation is performed.

Chapter 4 presents the H → γγ analysis using the rst Run 2 data. The analysis is performed with a dataset corresponding to an integrated luminosity of 12.9 fb -1 . An event classication is performed to maximize signal signicance and to study specic Higgs boson production modes.

Finally a feasibility study, having the aim of constraining the anomalous couplings of the Higgs boson to the vector bosons, is presented in Chapter 5. This analysis is performed using the data collected at 8 TeV during Run 1 at the LHC, corresponding to an integrated luminosity of 19.5 fb -1 . This analysis exploits the production of the Higgs boson through vector boson fusion (VBF), with the Higgs decaying to 2 photons. The kinematic distributions of the dijet and diphoton systems, which depend from the spin-parity hypothesis, are used to build some discriminants able to discriminate between dierent spin-parity hypotheses. These discriminants allow to dene dierent regions of the phase-space enriched with a certain spin-parity process. The Higgs boson signal yield is extracted in each region from a t to the diphoton mass, allowing to determine the contributions of the dierent processes and then constrain the production of a pseudo-scalar Higgs boson.

Chapter 1

The Standard Model Higgs boson at LHC

The fundamental components of matter and their interactions are nowadays best described by the Standard Model of Particle Physics (SM) [START_REF] Halzen | Quarks and leptons: An introductory course in modern particle physics[END_REF][START_REF] Glashow | Partial Symmetries of Weak Interactions[END_REF][START_REF] Weinberg | A Model of Leptons[END_REF], a quantum eld theory which describes the electroweak interaction (Glashow-Weinberg-Salam model or GWS) and the strong interaction (Quantum Chromo-Dynamics or QCD). The SM predicts the existence of a single physical scalar boson, the Higgs boson, associated to the spontaneous electroweak symmetry breaking via the Brout-Englert-Higgs (BEH) mechanism [START_REF] Englert | Broken Symmetry and the Mass of Gauge Vector Mesons[END_REF][START_REF] Higgs | Broken Symmetries and the Masses of Gauge Bosons[END_REF]. The mass m H of this boson is a free parameter of the theory. The BEH mechanism gives origin to the mass of both fermions and gauge bosons, in agreement with experimental results. This occurs without explicitly breaking the gauge invariance, thus preserving the renormalizability of the theory.

After a brief introduction of the theoretical framework, in the following the BEH mechanism, the Higgs boson phenomenology at the LHC collider and the main Higgs results of the Run 1 at the LHC (data recorded from 2010 to 2012) are described.

The Standard Model of elementary particles

The SM describes the matter as composed by twelve elementary particles, the fermions, all having half-integer spin. Fermions can be divided into two main groups, leptons and quarks, whose classication is given in Table 1.1. Leptons can just interact via electroweak bosons, while quarks are subject to both strong and electroweak interactions. Moreover, quarks do not exist as free states, but only as elementary constituents of a wide class of particles, the hadrons, such as protons and neutrons.

In the SM the interactions between elementary particles are mediated by bosons, integerspin particles. The main characteristics of bosons and of the corresponding interactions are summarised in Table 1.2.

The gravitational interaction is not taken into account, as it is not relevant at the typical energy scales of particle physics.

This complex phenomenology arises from a mathematical formalism according to which the SM is a perturbatively renormalizable quantum eld theory (QFT) based on the local gauge symmetries of its Lagrangian. According to Noether's theorem, a conservation law corresponds to each of these local invariances, explaining why they are so important. The SM is therefore a local gauge quantum eld theory describing three of the four fundamental interactions: electromagnetic, weak and strong interaction. It is based on the symmetry group

SU (3) C ⊗ SU (2) I ⊗ U (1) Y ,
the direct product of SU (3) C , the color symmetry group upon which Quantum Chromo Dynamics (QCD) is built, the gauge groups of weak isospin, SU (2) I , and hypercharge, U (1) Y . Electromagnetic and weak interactions are unied in the electroweak gauge group SU (2) I ⊗ U (1) Y , upon which the Glashow-Weinberg-Salam Model is built.

Despite this symmetry predicts with precision and accuracy the phenomenology of particle interactions, it is broken by both fermion mass term and gauge boson mass term of the Lagrangian. A necessary ingredient of the SM is therefore that the electroweak symmetry is broken, which allows to introduce mass terms to the Lagrangian.

1.2 The electroweak theory 3

The electroweak theory

From a historical point of view, the starting point of the study of electroweak interactions is the Fermi's theory of muon decay [START_REF] Fermi | Trends to a Theory of beta Radiation[END_REF], which is based on an eective four-fermion Lagrangian:

L = - 4G F √ 2 νµ γ α 1 -γ 5 2 µēγ α 1 -γ 5 2 ν e , (1.1)
where G F is the Fermi coupling constant reported in Table 1.2, e, µ, ν e and ν µ are the fermionic elds of the electron, muon and electron and muon neutrinos respectively, while γ α and γ 5 are Dirac matrices. Fermi's Lagrangian is not renormalizable and it results in a non-unitary scattering matrix.

Both problems of renormalizability and unitarity are overcome, as already said, requiring the weak interaction Lagrangian to be invariant under local transformations generated by the elements of a Lie group (gauge transformations). The resulting Lagrangian must reduce to Equation 1.1 in the low energy limit.

A gauge theory for weak interactions is conceived as an extension of the theory of electromagnetic interaction, the Quantum Electro-Dynamics (QED), which is based on the gauge group U (1) EM , associated to the conserved quantum number Q (electric charge). In this case, the condition of local invariance under the U (1) EM group leads to the existence of a massless vector boson, the photon.

A theory reproducing both the electromagnetic and weak interaction phenomenology is achieved by extending the gauge symmetry to the group SU (2) I ⊗ U (1) Y . In this sense, the weak and electromagnetic interactions are said to be unied. The generator of SU (2) I is the weak isospin operator and the generator of U (1) Y is the weak hypercharge Y operator. The corresponding quantum numbers satisfy the Gell-Mann-Nishijima formula

Q = I 3 + Y 2 ,
where I 3 is the third component of the weak isospin. Fermions can be divided in doublets of left-handed particles and singlets of right-handed particles, as follows:

L L = ν ,L L , R , Q L = u L d L , u R , d R , (1.2)
where = e, µ, τ, u = u, c, t and d = d, s, b. In Table 1.3, I 3 , Y and Q quantum numbers of all fermions are reported. As well as for QED, the requirement of local gauge invariance 1. The Standard Model Higgs boson at LHC Table 1.3: Isospin (I 3 ), hypercharge (Y ) and electric charge (Q) of all fermions.

I 3 Y Q u L d L 1 2 -1 2 1 3 -1 3 2 3 -1 3 u R , d R 0, 0 4 3 , -2 3 + 2 3 , -1 3 ν ,L L 1 2 -1 2 -1 -1 0 -1 R 0 -2 -1
with respect to the SU (2) I ⊗U (1) Y group introduces now four massless vector elds (gauge elds), W 1,2,3 µ and B µ , which couple to fermions with two dierent coupling constants, g and g . Note that B µ does not represent the photon eld. The gauge-invariant Lagrangian for fermion elds can be written as follows:

L = ΨL γ µ i∂ µ + gt a W a µ - 1 2 g Y B µ Ψ L + ψR γ µ i∂ µ - 1 2 g Y B µ ψ R , (1.3)
where

Ψ L = Ψ 1 L Ψ 2
L and where Ψ L and Ψ R are summed over all the possibilities in Equation 1.2. As already stated, W 1,2,3 µ and B µ do not represent physical elds, which are given instead by linear combinations of the four mentioned elds: the charged bosons W + and W -correspond to:

W ± µ = 1 √ 2 W 1 µ ∓ iW 2 µ , (1.4)
while the neutral bosons γ and Z correspond to

A µ = B µ cosθ W + W 3 µ sinθ W (1.5) Z µ = -B µ sinθ W + W 3 µ cosθ W (1.6)
obtained by mixing the neutral elds W 3 µ and B µ with a rotation angle being named the Weinberg angle θ W . In terms of the elds in Equations 1.4 to 1.6, the interaction term between gauge elds and fermions, taken from the Lagrangian in Equation 1.3, becomes

L int = 1 2 √ 2 g(J + α W (+)α + J - α W (-)α ) + 1 2 g 2 + g 2 J Z α Z α -eJ EM α A α , (1.7)
where J EM is the electromagnetic current connected to the photon eld, while J + , J -and J Z are the three weak isospin currents. A α can then be identied with the photon eld, yielding g sin θ W = g cos θ W = e.

(1.8)

The Higgs mechanism 5

The GWS model thus predicts the existence of two charged gauge elds, which only couple to left-handed fermions, and two neutral gauge elds, which interact with both left-and right-handed components. Note that the Z boson interacts dierently with right and left part, while the photon does not.

The Higgs mechanism

In order to correctly reproduce the phenomenology of weak interactions, both fermion and gauge boson elds must acquire mass, in agreement with experimental results. Up to this point, however, all particles are considered massless: in the electroweak Lagrangian, in fact, a mass term for the gauge bosons would violate gauge invariance, which is needed to ensure the renormalizability of the theory. Masses are thus introduced with the BEH mechanism [START_REF] Englert | Broken Symmetry and the Mass of Gauge Vector Mesons[END_REF][START_REF] Higgs | Broken Symmetries and the Masses of Gauge Bosons[END_REF][START_REF] Dawson | Introduction to electroweak symmetry breaking[END_REF], which allows fermions and W ± , Z bosons to be massive, while keeping the photon massless. Such mechanism is accomplished by means of a doublet of complex scalar elds,

φ = φ + φ 0 = 1 √ 2 φ 1 + iφ 2 φ 3 + iφ 4 , (1.9)
which is introduced in the electroweak Lagrangian within the term

L BEH = (D µ φ) † (D µ φ) + V (φ † φ), (1.10)
where D µ = ∂ µ -igt a W a µ + i 2 g Y B µ is the covariant derivative. The Lagrangian in Equation 1.10 is invariant under SU (2) I ⊗ U (1) Y transformations, since the kinetic part is written in terms of covariant derivatives and the potential V only depends on the product φ † φ. The φ eld is characterised by the following quantum numbers:

I 3 Y Q φ + φ 0 1 2 -1 2 1 1 1 0
Writing the potential term as follows (see also Figure 1.1 for a graphical representation)

V (φ † φ) = -µ 2 φ † φ -λ(φ † φ) 2 , (1.11)
with µ 2 < 0 and λ > 0, it results to have a minimum for

φ † φ = 1 2 (φ 2 1 + φ 2 2 + φ 2 3 + φ 2 4 ) = - µ 2 2λ ≡ v 2 2 .
(1.12)

This minimum is not found for a single value of φ, but for a manifold of non-zero values. The choice of (φ + , φ 0 ) corresponding to the ground state, i.e. the lowest energy state or vacuum, is arbitrary, and the chosen point is not invariant under rotations in the (φ + , φ 0 )

1. The Standard Model Higgs boson at LHC plane: this is referred to as spontaneous symmetry breaking. If one chooses to x the ground state on the φ 0 axis (if not the vacuum would be charged), the vacuum expectation value of the φ eld is

< φ > = 1 √ 2 0 v , v 2 = - µ 2 λ .
(1.13)

The φ eld can thus be rewritten in a generic gauge, in terms of its vacuum expectation value:

φ = 1 √ 2 e i v φ a ta 0 H + v , a = 1, 2 , 3, (1.14)
where the three elds φ a are called Goldstone elds and H is the Higgs boson scalar eld. These 3 Goldstone bosons are massless and in the SM can actually be eliminated by choosing an ad hoc gauge named the unitary gauge, given by the transformation

φ → φ = e -i v φ a ta φ = 1 √ 2 0 H + v .
(1.15)

The remaining eld, the Higgs eld, has now a zero expectation value.

Rewriting the Lagrangian in Equation 1.10 with the φ eld in the unitary gauge, L BEH can be written as:

L BEH = 1 2 ∂ µ H∂ µ H - 1 2 m 2 H - λ 2 m H H 3 - λ 4 H 4 + m 2 W W +µ W - µ + m 2 Z 2 Z µ Z µ 1 + H v 2 , (1.16)
where m H = 2µ 2 = √ 2λv.

(1.17 Summarizing, the BEH mechanism is used to explain weak boson masses without explicitly breaking the gauge invariance and thus preserving the renormalizability of the theory.

When a symmetry is spontaneously broken, it is only hidden by the choice of the ground state. It can be shown that the minimum of the Higgs eld is still invariant under the U (1) EM group. The electromagnetic symmetry is therefore unbroken and photons do not couple to the Higgs boson at tree level and remain massless.

Vector boson masses and couplings

The masses of vector bosons W ± and Z are related to the parameter v, characteristic of the BEH mechanism, and to the electroweak coupling constants:

m W = 1 2 vg m Z = 1 2 v g 2 + g 2 → m W m Z = g g 2 + g 2 = cosθ W .
(1.18)

The couplings of vector bosons to the Higgs are found to depend on the square of m W and m Z :

g HW = 1 2 vg 2 = 2 v m 2 W (1.19) g HZ = 1 2 v(g 2 + g 2 ) = 2 v m 2 Z .
(1.20)

A relation between the decay ratios of the Higgs boson to a W pair and to a Z pair can be derived from Equations 1.19 and 1.20:

BR(H → W + W -) BR(H → ZZ) = g HW 1 2 g HZ 2 = 4 m 2 W m 2 Z 2 2.4.
Finally, the electroweak symmetry breaking energy scale can be determined from the relation between the v parameter and the Fermi constant

G F : v = 1 √ 2G F 1 2
246 GeV.

(1.21)

Fermion masses and couplings

Fermion elds can be split into a left-handed and right-handed part, that are chirality eigenstates, according to:

ψ = ψ L + ψ R , ψ L,R = 1 ∓ γ 5 2 ψ (1.22)

The Standard Model Higgs boson at LHC

Left and right part of fermion elds ll dierent multiplets of electroweak gauge group, to account for parity violation of weak interactions. For the rst generation one can write:

q L ≡ u L d L , u R , d R , l L ≡ ν L e L , e R (1.23)
It is not possible to introduce in the fermion lagrangian an explicit mass term like m ψψ because it is not gauge invariant: from Equation (1.23) it is clear that ψ L and ψ R behave dierently under SU (2) transformations. However, with a Higgs doublet as introduced in the GWS model there is a gauge invariant interaction that looks like a fermion mass term when the Higgs gets its vacuum expectation value, that is called Yukawa coupling. For the electron:

L Y uk = -Y e lL φe R + h.c., (1.24) where h.c. is the hermitian conjugate. Using unitary gauge (Equation 1.15) one gets, for the terms proportional to v:

-

Y e v √ 2 ( ēL e R + ēR e L ) = Y e v √ 2 ēe ⇒ m e = Y e v √ 2 (1.25)
From Equation 1.25 one can see that electron has acquired a mass, proportional to v. Like for vector bosons W and Z, also fermions get mass from spontaneous symmetry breaking: the mass is proportional to Y f , which is the strength of the coupling of the fermion f to the Higgs.

For the down quarks (d, s, b), the Yukawa coupling term is the same as for electron:

L Y uk = -Y d qL φd R + h.c.

(1. [START_REF] Randall | A Large mass hierarchy from a small extra dimension[END_REF] but for the up quarks (u, c, t) something dierent is needed, because the vacuum expectation value of the Higgs eld is placed in the down part of the doublet (see Equation 1.13).

Dening:

φ C = 1 √ 2 H + v 0 (1.27)
one can get a new Yukawa invariant interaction for the up quarks:

L Y uk = -Y u qL φ C u R + h.c.
(1.28)

Finally the mass terms also for up and down quarks can be derived:

m u = Y u v √ 2 , m d = Y d v √ 2 .
In this brief description we have omitted all the cross terms which give couplings and which are eliminated by means of the CKM matrix giving rise to CP violation. Note that this important mechanism is the only known source of CP violation in the electroweak sector of the SM.

Higgs boson production

While the Higgs boson mass cannot be predicted by the theory, the Higgs couplings to the fermions and bosons are predicted to be proportional to the corresponding particle mass. For this reason the Higgs production and decay processes are dominated by channels involving the coupling of Higgs boson to heavy particles, especially to W ± and Z bosons and to the third generation of fermions. About the other gauge bosons, the Higgs does not couple to photons and gluons at tree level, but only by one-loop diagram, where the main contribution is given by t loops, for the gg → H channel, and by W + W -and t loops for the γγ → H channel.

In proton-proton collisions at Below the main Higgs production mechanisms are described.

Gluon-gluon fusion

The gluon gluon fusion (ggF) mechanism, pp → gg → H, pp → qq → qqH, (1.30) is the second-most important mechanism at the LHC. For the Higgs boson at m H = 125

GeV, its contribution to the total cross section is of the order of 8%. However, this channel is very interesting because of its clear experimental signature: the presence of two spectator jets with high invariant mass in the forward region provides a powerful tool to tag the signal events and discriminate the backgrounds, improving in this way the signal to background ratio, despite the low cross section. The VBF cross section has been calculated up to NNLO.

Associated production

The associated production mechanism (VH), described by the process pp → q q → V H,

is smaller due to the presence of an antiquark that, in a pp machine, does not come from the valence but from the sea. In this case, the selection of an event can be performed by reconstructing the original boson that radiated the Higgs. The VH cross section has been calculated including the QCD corrections up to NNLO, whereas the electroweak corrections are known at NLO.

Associated production with a t t pair

The production mechanism of the Higgs boson associated with a t t pair, pp → q q → t tH, (1.32) is the production mechanism with the smallest yield, but the presence of a t t pair in the nal state provides a clean experimental signature. Furthermore, going from 8 to 13 TeV its cross section increases by a factor of 4, and this production mode, giving a direct access to top quark coupling, plays an important role in testing the SM. This process has been computed with a precision up to NLO.

Higgs boson decay

The branching ratios of the dierent Higgs decay channels are shown in [START_REF] Dittmaier | Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables[END_REF][START_REF] Dittmaier | Handbook of LHC Higgs Cross Sections: 2[END_REF].

the H → W + W -channel is visible around 160 GeV, when the production of two on-shell W bosons becomes possible and the production of a real ZZ pair is still not allowed. At high masses (about 350 GeV) the t t channel opens. As shown in Figure 1.4, the branching ratios change dramatically across the possible mass range, requiring dierent strategies for the Higgs identication depending on its mass. The most promising decay channels for the Higgs discovery do not only depend on the corresponding branching ratios, but also on the capability to experimentally distinguish signal from background. Fully hadronic events are the most copious nal states from Higgs boson decays, but they cannot be easily distinguished from QCD background. For this reason topologies with leptons or photons are preferred, even if they have smaller branching ratios.

Such channels are illustrated in the following, depending on the Higgs mass range:

• High mass region (180 GeV < m H < 1 TeV). This range is characterised by the fact that m H > 2m • Low mass region (110 GeV < m H < 130 GeV). In the low mass range, the main decay channel is b b, then τ + τ -, cc and gg (even if not accessible experimentally).

In spite of its high value of σ × BR, the b b mode is not easily accessible because of the overwhelming QCD background. The decay channels that are characterised by a virtual top or bottom loop, namely H → γγ and H → Zγ, are much rarer than b b or τ + τ -although they are experimentally precious because of their very distinctive signature due to two high energetic photons forming a narrow invariant mass peak.

Furthermore, H → γγ decay channel only suers from the q q → γγ and Z → e + e - backgrounds or jets faking photons. The expected signal rate is at least one order of magnitude smaller than the SM background rate.

Higgs boson to two photons decay channel

The photon is massless while the

m γγ = 2E γ1 E γ2 (1 -cos(θ γγ )), (1.33)

The Standard Model Higgs boson at LHC

where E γ1 and E γ2 are the measured single photon energies and θ γγ is the measured angle between the momenta of the two photons.

A good resolution of both the measured photon energy and the measured open angle therefore leads to a narrow peak of diphoton mass spectrum associated to the Higgs resonance.

Since the distribution of the background events is expected to be continuously falling, this narrow peak provides an eloquent evidence of the existence of the Higgs boson.

From the amplitude and the location of the peak, the relative total Higgs production cross section times the branching ratio to two photons with respect to the Standard Model Higgs expectation, the signal strength, and the Higgs mass are measured precisely. The rate of the decay, mediated through a loop of particles involving W boson and top quark, is sensitive to the magnitudes of both k V and k f as well as their relative sign, same sign for destructive interference between W loop and top quark loop as expected by the SM while opposite sign for constructive interference (see Section 1.5.4 for more details and for the denition of k V and k f ). It is also sensitive to any possible new heavy charged particles in the loop, whose existence is quantied through measuring the eective Higgs coupling strength to photon, k γ [START_REF] J R Andersen | Handbook of LHC Higgs Sections: 3[END_REF].

As explained in detail in Chapter 3, the dominant background consists of irreducible and reducible components. The irreducible component is real (prompt) diphoton events.

The reducible component includes dijet and γ + jet events, in which jets are misidentied as photons. A jet typically fakes a photon when it results in a narrow concentration of photonic energy in the detector due to the decay of high energy neutral mesons, especially π 0 's. The π 0 decays into two photons with small opening angle, which may appear as a single photon.

Higgs boson total width

The total width of the Higgs boson resonance is shown in Figure 1.6 as a function of m H . Below the 2m W threshold, the Higgs width is of the order of a few MeVs, then it rapidly increases, but it remains lower than 1 GeV up to m H 200 GeV. The region at low mass is therefore the most challenging one, because the Higgs boson width is dominated by the experimental resolution. At 125 GeV, the Higgs boson width is expected to be 4 MeV.

Main Higgs results from LHC Run 1

As mentioned above, the Higgs boson was discovered by both ATLAS and CMS experiments at the LHC in 2012, with a measured mass of about 125 GeV [START_REF] Serguei Chatrchyan | Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC[END_REF][START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF]. In this section the main results on the Higgs boson properties from LHC Run 1 are presented.

Mass measurement

The H → γγ and H → ZZ → 4 channels are used to determine the Higgs boson mass, thanks to their very good mass resolution (of about 1%) [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF] Chatrchyan | Measurement of the properties of a Higgs boson in the four-lepton nal state[END_REF]. Figure 1.7 shows the mass measurement for the two channels indipendently: the H → γγ analysis, on the left, measures a narrow signal mass peak on top of a smoothly falling background mainly due to events from prompt nonresonant diphoton production. The plot on the right shows the four-lepton mass peak (in red) over a small continuum background mainly due to nonresonant ZZ production.

The mass measurements with H → γγ and H → ZZ → 4 data are combined assuming a single state [START_REF] Vardan Khachatryan | Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV[END_REF]. Figure 1.8 on the left shows the scan of the test statistic as a function of the mass m H separately for the H → γγ and H → ZZ → 4 channels, and for their combination. The production rates and decay ratios are left free in the m H t. The intersections of the likelihood curves with the 2 horizontal lines dene the 68% and 95%

CL condence intervals for the mass of the observed particle. The mass is measured to be m H = 125.02±0.27(stat.)±0.15(syst.) GeV. The ATLAS+CMS combined result is: 125.09±0.21(stat.)±0.11(syst.) GeV [START_REF] Aad | Combined Measurement of the Higgs Boson Mass in pp Collisions at √ s = 7 and 8 TeV with the ATLAS and CMS Experiments[END_REF].

Metastability of the EW vacuum

The discovery of the Higgs boson [START_REF] Serguei Chatrchyan | Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC[END_REF][START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF] was expected to be the herald of new physics soon to be found at the TeV scale, but so far no signal of new physics nor any clear deviation from the SM Higgs properties have been detected at the LHC. Furthermore, the Higgs mass did not provide clear indications for new physics. The measured value (see previous section) is a bit high for supersymmetry and a bit low for composite models, making theoretical

Higgs boson width

The width of the SM Higgs boson is expected to be ∼4 MeV. Some upper limits on the width can be obtained through direct measurement from the mass peak, but they are limited by the experimental resolution (∼1 GeV). Another possibility is to use the o-shell/on-shell production and decay to 2 Z bosons ratio [START_REF] Vardan Khachatryan | Constraints on the Higgs boson width from o-shell production and decay to Z-boson pairs[END_REF]. From this equation

dσ gg→H→ZZ dm 2 ZZ ∼ g 2 ggH g 2 HZZ (m 2 ZZ -m 2 H ) 2 + m 2 H Γ 2 H (1.34)
one can see that the gluon fusion production cross section depends on Γ H through the Higgs boson propagator, where g ggH and g HZZ are the couplings of the Higgs boson to gluons and Z bosons, respectively. It was found that a measurement of the relative o-shell and on-shell production in the H → ZZ channel provides direct information on Γ H , as long as the evolution of ggH and HZZ couplings as a function of the mass is the SM one.

In Figure 1.10, the indirect measurement of the Higgs width, using the o-shell/on-shell ratio, is shown. CMS was able to put an upper limit of 22 MeV on the Higgs width, 5.4

times the expected value in the SM.

(

Spin-parity measurement

Concerning the spin-parity measurement, CMS was able to test some reasonable benchmark models for alternative J CP hypotheses [START_REF] Vardan Khachatryan | Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV[END_REF]. To do that, the angular distributions 1.5 Main Higgs results from LHC Run 1 19 were used, and the bosonic channels are the most sensitive: for example the ZZ → 4 system is fully reconstructed, and thanks to a Matrix Element Likelihood Approach that uses the kinematics of the decay products it is possible to distinguish between dierent spin-parity hypotheses. The W W nal state is not fully reconstructed, but some kinematic variables, like M and M T , are sensitive to the Higgs spin/CP. The γγ system can be used for spin determination through p T and cosθ * and it allows to exclude the spin-1 hypothesis.

The most general expression that one can write for HV V scattering amplitude is this one

A(HVV) ∼ a VV 1 + κ VV 1 q 2 V1 + κ VV 2 q 2 V2 Λ VV 1 2 m 2 V1 * V1 * V2 + a VV 2 f * (1) µν f * (2),µν + a VV 3 f * (1) µν f * (2),µν , (1.35)
where a 1 is the scalar SM term, a 2 indicates a scalar anomalous, while a 3 corresponds to the pseudo-scalar component. In the SM a 1 = 1 and a 2 = a 3 = 0. Beyond the SM a 2 and a 3 can be dierent from zero.

The SM hypothesis 0 + was tested against many alternative ones. Figure 1.11 shows the distributions of the test-statistic for the spin 2 J P models tested against the SM Higgs boson hypothesis in the X → ZZ analyses. The expected median and the 68%, 95% and 99.7% CL regions are shown for the SM Higgs boson in orange and for the alternative J P hypotheses in blue. The observed q values are indicated by the black circles. Finally the 0 + hypothesis is preferred to all the alternate tested models at more than the 3σ level. 2 19.7 fb gg production production q q decay-only discriminants Observed Expected

+ h3 2 + h 2 + b 2 + h6 2 + h7 2 - h 2 - h9 2 - h10 2 + m 2 + h2 2 + h3 2 + h 2 + b 2 + h6 2 + h7 2 - h 2 - h9 2 - h10 2 + m 2 + h2 2 + h3 2 + h 2 + b 2 + h6 2 + h7 2 - h 2 - h9 2 - h10 2 CMS ZZ → H ( 7
σ 1 ± + 0 σ 1 ± P J σ 2 ± + 0 σ 2 ± P J σ 3 ± + 0 σ 3 ± P J Figure 1
.11: Distributions of the test statistic q = -2ln(L J P /L 0 + ) for the spin-two J P models tested against the SM Higgs boson hypothesis in the X → ZZ analyses. The expected median and the 68.3%, 95.4%, and 99.7% CL regions for the SM Higgs boson (orange, the left for each model) and for the alternative J P hypotheses (blue, right) are shown. The observed q values are indicated by the black dots.

The Standard Model Higgs boson at LHC

Higgs couplings

The couplings of the Higgs boson were also probed for deviations in magnitude from the SM predictions, and no signicant deviations were found [START_REF] Vardan Khachatryan | Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV[END_REF]. To test the observed data for possible deviations from the rates expected for the SM Higgs boson in the dierent channels, coupling modiers were introduced, denoted by the scale factors k i . The scale factors are dened for production processes by

k 2 i = σ i /σ SM i , for decay processes by k 2 i = Γ ii /Γ SM ii ,
and for the total width by k 2 H = Γ tot /Γ SM . It is possible to group the Higgs boson couplings into vectorial and fermionic sets tting 2 parameters, k V and k f , which indicate the Higgs couplings with vector bosons and with fermions respectively. The H → γγ is the only channel sensitive to the relative sign of k V and k f , because the partial width Γ γγ is induced via loops with virtual W bosons or top quarks and scales as a function of both k V and k f . Figure 1.12 (left) shows the results of this combined analysis in the dierent decay channels and for the combination. One can see that the H → γγ region is the only not symmetric in the 2 quadrants. It is thought that more than 95% of the known universe consists of dark matter (∼ 27%) and dark energy (∼ 68%) [START_REF] Sullivan | Snls3: Constraints on dark energy combining the supernova legacy survey three-year data with other probes[END_REF]. Since there is currently no way to explain either dark matter or dark energy within the SM, the latter can only attempt to explain about 5% of the energy of the universe.

Furthermore, the overabundance of matter, as opposed to anti-matter, in the universe, is a phenomenon known as the baryon asymmetry. It was shown by Sakharov [21] that a model of baryogenesis must satisfy three necessary conditions: baryon-number violation, chargesymmetry and charge-parity-symmetry violation (CP-violation), and interactions which are out of thermal equilibrium at early stages of the universe. Even if it has been shown that the SM contains the three necessary conditions for baryogenesis, it is believed to be insucient to explain the degree of baryonic asymmetry in the visible universe [START_REF] Jarlskog | Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Violation[END_REF][START_REF] Shaposhnikov | Possible Appearance of the Baryon Asymmetry of the Universe in an Electroweak Theory[END_REF].

Additional sources of CP-violation in the SM would therefore provide a promising solution to the baryon-asymmetry problem.

The hierarchy problem, linked to the expected naturalness of electroweak symmetry breaking, is also often cited as a big reason to expect physics beyond the SM. The question is why the Higgs boson is so much lighter than the Planck mass: one would expect that the large quantum contributions to the square of the Higgs boson mass would inevitably make the mass huge, comparable to the scale at which new physics appears, unless there is an incredible ne-tuning cancellation between the quadratic radiative corrections and the bare mass [START_REF] Aitchison | Supersymmetry in Particle Physics: An Elementary Introduction[END_REF]. Since the Higgs measured mass is ∼ 125 GeV, it should exist some kind of physics able to explain this 10 17 ne-tuning of our SM parameters. For this reason, we expect there to be some kind of new physics accessible at TeV energies to explain why the Higgs should be right around that scale rather than being at the Planck mass.

It exists a number of proposed solutions to the ne-tuning problem, some of which could also provide solutions to some of the problems noted above, for example, Supersymmetry (SUSY) [START_REF] Aitchison | Supersymmetry in Particle Physics: An Elementary Introduction[END_REF]. Since SUSY predicts that all fermions have a symmetry with a corresponding boson, all Feynman diagrams which provide quantum corrections to the Higgs boson mass have a canceling partner which removes the large quantum corrections. SUSY is also thought to provide a natural dark matter candidate and is a prerequisite for string theory, which naturally incorporates gravity. Finally, it is possible for SUSY to allow for additional CP-violation in the Higgs sector. Recently this idea was studied in the more generic framework of type-II 2 Higgs doublet models (2HDM) and found that the amount of additional CP-violation possible in the Higgs sector could provide a reasonable model for baryogenesis [START_REF] Shu | Impact of a CP Violating Higgs Sector: From LHC to Baryogenesis[END_REF].

The Standard Model Higgs boson at LHC

Other explanations of ne tuning include composite Higgs models or Randall-Sundrum models of gravity. Composite Higgs models interpret the Higgs mechanism as only an eective theory and introduce a new strongly interacting QCD-like force above the electroweak scale. It was shown by Randall and Sundrum [START_REF] Randall | A Large mass hierarchy from a small extra dimension[END_REF] that higher-dimensional models with warped space-time metrics can provide a natural explanation of the hierarchy problem and thus ne-tuning.

Summary

In this chapter a theoretical introduction of the Standard Model and the electroweak symmetry breaking is given. The Higgs boson phenomenology at the LHC is then presented, with particular attention to the Higgs to two photons decay channel, main subject of this thesis. Finally the main Higgs results achieved at the LHC during Run 1 are summarised.

After the discovery of the Higgs boson and the rst measurements of its properties, it is important to perform more precise measurements of this particle, in order to detect possible small deviations from the Standard Model, hints of new physics.

Chapter 2 LHC and the CMS detector

The Large Hadron Collider restart

The Large Hadron Collider (LHC) [START_REF] Sim | LHC Design Report[END_REF] is the world's biggest particle accelerator. Proposed and realized by the European Organization for Nuclear Research (CERN), it was designed to collide protons, as well as lead ions, at an unprecedented energy and rate, in order to answer some of the most fundamental questions of physics.

On 23 november 2009, the accelerator produced the rst proton-proton collisions. After few pilot runs at energies of 450 GeV and 1.18 TeV per beam, the energy was ramped up to 3.5 TeV and, on 30 march 2010, the rst collisions at a centre-of-mass energy of 7 TeV, the highest ever reached at a particle collider, were recorded by the experiments ATLAS, CMS and LHCb. During these years the LHC has performed beyond expectations and the total integrated luminosity delivered in 2011 was 6.13 f b -1 (see Figure 2.1). In 2012 the centre-of-mass energy has been incremented up to 8 TeV, and an integrated luminosity of 23.30 f b -1 was reached (see Figure 2.1). The Run 1, concluded in february 2013, has been rich of scientic results, such as the discovery of the Higgs Boson and of several hadrons (like the χ b (3P ) bottomonium state) and the rst observation of the very rare decay of the B s meson into two muons, which severely constrains supersymmetry models for instance.

After these three very fruitful years of collisions at the LHC started a two-year break, the LHC's rst long shutdown (LS1). This period without beam aimed at improving the accelerator as well as the detectors towards the restart for Run II at a centre-of-mass energy of 13 TeV. During the technical stop about 10.000 electrical interconnections between the magnets were consolidated, magnet protection systems were added, while cryogenic, vacuum and electronics were improved and strengthened. Furthermore, the beams have been set up in such a way that they will produce more collisions by bunching protons closer together, with the time separating bunches being reduced from 50 ns to 25 ns.

In this second period of operation at an unprecedented energy of 13 TeV, after the discovery of the Higgs boson in 2012 by the ATLAS and CMS collaborations, physicists will be After the technical stop, beams started circulating again in 2016, and the LHC performed very well, delivering about 22 fb -1 so far, as shown in Figure 2.1. The dataset used for the H → γγ analysis presented at ICHEP amounts to 12.9 fb -1 , recorded in 2016.

The CMS detector

The Compact Muon Solenoid (CMS) [28] is one of the two general-purpose detectors which operate at LHC. Its main physics goals are the search for the Higgs boson, the search for new physics beyond the SM and precision measurements of already known physics processes. For these reasons an excellent lepton reconstruction and particle identication are required.

The main characteristics of the CMS detector are a compact design with a strong magnetic eld, which is obtained using a 3.8 T superconducting solenoid, a robust and redundant muon system, a good electromagnetic calorimeter and a high quality central tracking system.

CMS is composed by a cylindrical barrel, with several layers coaxial to the beam axis, closed at both ends by endcap disks orthogonal to the beam direction. Its full length is 28.7 m, the diameter 15 m and the total weight about 14.000 t.

As already mentioned, the core of the apparatus is the magnet, which contains, from inside out, the following detectors:

• the tracker, made of a silicon pixel detector in the inner region, closest to the beam, and of silicon microstrip detectors in the outer region, used to reconstruct charged particle tracks and primary and secondary interaction vertices,

• the electromagnetic calorimeter (ECAL), which allows for precise measurement of electron and photon energies; it is made of lead tungstate (P bW O 4 ) scintillating crystals, both in the barrel and in the endcaps, and extended by a forward preshower detector in the endcap region,

• the hadron calorimeter (HCAL), used for jet direction and transverse energy measurements, extended in the forward region with the very forward calorimeter.

Outside the magnet coil, the iron return yoke of the magnet hosts the muon spectrometer, used for reconstruction of muon tracks: drift tubes (DT) in the barrel and cathode strip chambers (CSC) in the endcaps, complemented overall by resistive plate chambers (RPC), In the following we will give a brief description of each subdetector, developing in particular the electromagnetic calorimeter section, since this thesis work is focused on photons.

Coordinate conventions

The CMS coordinate system (see Figure 2.2) used to describe the detector geometry is a right-handed Cartesian frame, with the x axis pointing to the centre of the LHC ring, the z axis parallel to the beam and the y axis directed upwards.

Because of the cylindrical symmetry of the CMS design, the reconstruction algorithms use a cylindrical coordinate system: the azimuthal angle Φ is measured in the xy plane from the x axis, while the polar angle θ is measured from the z axis. Instead of θ, the pseudorapidity η is used, which is dened as:

η = -ln tan θ 2 .
The transverse momentum p T is dened from x,y components of the momentum as:

p T = p 2 x + p 2 y .
The transverse energy is dened as E T = Esinθ and the missing transverse energy is denoted with E miss T .

Finally, the ∆R parameter is dened as:

∆R = ∆Φ 2 + ∆η 2 .

The tracker

The tracker [29] is the innermost subdetector and the closest to the interaction point.

Its goal is to reconstruct charged tracks with high eciency and momentum resolution, to measure their impact parameter and to reconstruct primary and secondary vertices.

The tracker is solely based on several layers of silicon detectors and its dimensions are |z| < 270 cm and r < 120 cm. Close to the interaction point, the rst layers, composed by nely segmented pixel detectors, are fundamental for the measurement of the impact parameters and have to cope with a very high particle ux. The rest of the tracker is made

LHC and the CMS detector

The CMS detector

29 up of single-sided and double-sided silicon strip detectors.

In order to limit the radiation damage to silicon sensors due to the high particle ux, both pixel and microstrip detectors have to be kept at a working temperature of -10 o C.

Pixel detector

The pixel detector (see Figure 2.5) provide high-resolution three-dimensional measurements, that are used for charged track reconstruction. Its excellent resolution allows the measurement of track impact parameters, the identication of b-and τ -jets and the reconstruction of vertices in three dimensions. This detector consists of three barrel layers and two endcap disks for each side. The barrel layers, extending from z = -26.5 cm to z = +26.5 cm, are placed at mean radii of 4.4 cm, 7.3 cm and 10.2 cm. The two disks of the endcaps, placed on each side at z = 34.5 cm and 46.5 cm, have the inner radius of 6 cm and the outer of 15 cm.

The pixel detector consists of 66 million pixel elements, each 100 µm × 150 µm in dimension, spread across 1440 modules. Each pixel consists of a p-n semiconductor junction.

When a charged particle crosses the junction, it excites electron-hole pairs, and the charge is collected by the readout electronics connected to the junction. In order to keep the data volume reasonable given the very large number of channels, zero suppression is performed by electronics on the sensor modules, in which only pixels with signal above a set threshold are read out. A charged particle crossing the module will generally deposit charge in at least two adjacent pixels, with the amount of charge deposited in each pixel inversely related to the distance between the particle position and the pixel. A measurement of the charge sharing between adjacent pixels therefore allows a single hit position resolution substantially smaller than the dimensions of a single pixel. In order to exploit the shar- ing of charge among adjacent pixels, the signal amplitude is digitized with 5 to 8 bits of information, allowing a single hit position resolution of 15 -20 µm.

LHC and the CMS detector

Microstrip detector

The outer part of the tracking detectors, the silicon microstrip detector, provides measurements precisely localized in only two-dimensions, with most strips oriented perpendicular to the φ direction. In the barrel, this consists of the Tracker Inner Barrel (TIB) region, comprised of four layers between 20 and 55 cm in radius, as well as the Tracker Outer Barrel (TOB) region, consisting of an additional 6 layers between 50 and 116 cm in radius.

In the endcap region, the strip tracker consists of the Tracker Inner Disk (TID) region of The combined tracking detector system provides coverage up to |η| = 2.5, with an average of 13-17 measurements per charged particle, depending on the pseudorapidity region.

The silicon strip detector consists of about 9.3 million strips across 15148 modules, with strips as well consisting of p-n junctions across which charge carriers are ionized by charged particles as they cross the strip. Depending on the region of the detector, the strip pitch varies between 80 and 184 µm. By exploiting charge sharing between strips, analogous to charge sharing between adjacent pixels, the single hit resolution along the φ direction ranges from 23 to 53 µm.

The large amount of silicon in the inner tracking detectors, combined with the sophis-

The electromagnetic calorimeter

The goal of the Electromagnetic Calorimeter (ECAL) [30] [31] is the accurate measurement of the position and energy of electrons and photons. In particular, one of the main objectives of this subdetector is the search for the Higgs boson in the channel H → γγ, considered as the golden channel for low Higgs masses. Thus the electromagnetic calorimeter performance has to deal with the diphoton mass resolution, which depends both on energy and angular resolution:

σ M M = 1 2 σ E 1 E 1 ⊕ σ E 2 E 2 ⊕ σ θ tan θ 2 ,
where E 1,2 are the energies of the two photons, θ is the photon angular separation and ⊕ indicates a quadratic sum.

LHC and the CMS detector

The energy resolution σ E E can be parametrized as

σ E E = a √ E ⊕ b E ⊕ c,
where a, b, c are respectively the stochastic, noise and constant term and will be discussed in details later in this section.

In order to achieve the best possible energy resolution, the CMS calorimeter is homogeneous, nearly hermetic and made of lead tungstate (P bW O 4 ) crystals, coupled to photodetectors. There are about 76000 crystals in total, divided between the ECAL barrel detector (EB) and the ECAL endcap detector (EE). Incident electrons and photons initiate showers inside the crystals, and the showering particles produce scintillation light as they interact with the crystal. This scintillation light is then measured by photodetectors, and the amount of scintillation light is used to determine the energy deposited in each crystal.

In the endcap region, in the η range 1.653 < |η| < 2.6, a sampling preshower detector made of lead and silicon active layers is installed in front of the ECAL in order to improve angular resolution for photon/π 0 separation.

Lead tungstate has been chosen for the crystal material because of its high density, corresponding short radiation length (X 0 = 0.89 cm) and small Molière radius (2.2 cm), thus having a high compactness, allowing a very ne granularity. Moreover, the very short scintillation decay time of these crystals allows to collect about 80% of the light within 25 ns, so that they can be used at the crossing rate of 40 MHz.

The use of high density crystals has allowed the design of a calorimeter which is fast, has ne granularity and is radiation resistant, all important characteristics in the LHC environment.

Lead tungstate crystals

The main parameters of the P bW O 4 crystals compared to other crystals typically used for electromagnetic calorimetry are summarized in Table 2.1. The crystals emit blue-green The scintillation decay time of these crystals is of the same order of magnitude as the LHC bunch crossing time: about 80% of the light is emitted in 25 ns. The light output is relatively low and varies with temperature (variations of -2%/

• C at room temperature).

The temperature dependence of the light yield is represented in Figure 2.8. For this reason the detector cooling system, which much stabilize the crystal temperature to 0.05 • C, is fundamental.

To exploit the total internal reection for optimum light collection on the photodetector, the crystals are polished after machining, on all but one side for EB crystals. Since the truncated pyramidal shape makes the light collection non-uniform along the crystal length, the needed uniformity is achieved by depolishing one lateral face. On the contrary, for endcap crystals the light collection is naturally more uniform because the crystal geometry is nearly parallelepipedic. Pictures of barrel and endcap crystals with their photodetectors attached are shown in gure 2.9. The crystals have to withstand the radiation levels and particle uxes present throughout the duration of the experiment. For this reason lead tungstate is intrinsically radiation hard. Nevertheless crystals suer from radiation damage: ionizing radiation produces absorption bands through the formation of colour centres due to oxygen vacancies and impurities in the lattice. As a consequence the lead tungstate transparency is altered within a few percent, while the scintillation mechanism is not aected. The loss in the transmission eciency can be corrected for by monitoring the optical transparency with injected laser light, as briey described later. In this way most of the radiation damages are recovered. The ECAL layout and mechanics

LHC and the CMS detector

The CMS electromagnetic calorimeter consists of a barrel part and of two endcaps; a three dimensional view of the calorimeter is given in

The CMS detector 35

The EB detector consists of 61200 crystals arranged in a 90 × 360 η -φ grid, with coverage up to |η| = 1.479. In order to have an hermetic coverage of the detector, the crystals must be tightly packed. Moreover, to minimize the leakage of the electromagnetic shower in the small gaps between crystals, the EB geometry is such that crystals are tilted at an angle of 3

• with respect to the trajectory of particles incident from the nominal interaction point. In order to obtain this tilt, together with the tight packing requirement, EB crystals are shaped as truncated pyramids, with a number of dierent particular variations needed depending on the precise location in EB. The crystals surface is 22 × 22 mm 2 at their front face, and 26 × 26 mm 2 at their back face, comparable to the Molière radius, such that a large fraction of the energy from an electromagnetic shower is expected to be contained within a radius of a few crystals with respect to the crystal on which the electron or photon was incident. Each crystal is 23 cm long, corresponding to 25.8 radiation lengths of material, such that longitudinal leakage of the electromagnetic showers is negligible.

The back of each crystal is attached to an Avalanche Photodiode (APD), that detects the scintillation light from the crystal. The EB crystals are arranged into 36 supermodules, 18 for each of the +z and -z sides of the detector, such that each supermodule subtends 20

• in φ. Each supermodule is composed of 4 modules, ranging from η = 0 to η = ±1.479.

These modules are enumerated 1-4 from the center of the detector outwards. Module 1 in each supermodule consists of 25 × 20 crystals in the η × φ direction, whereas modules 2, 3 and 4 in each supermodule consist of 20 × 20 crystals. The barrel granularity is of ∆η × ∆Φ = 0.0175 × 0.0175.

All supermodules are provided with a cooling system supplying a stability of the crystal array and readout devices within a tight spread of 0.05 • C.

The EE detectors consist of 15000 crystals. The geometry in the endcap is dierent from that in the barrel, with crystals arranged in an x-y grid in groups of 5 × 5 crystals, such that all EE crystals share the same geometry. In this way the angle between the crystal axes and the trajectory of particles from the interaction point is between 2 and 8 degrees.

EE crystals are 25 × 25 mm 2 at the front and 30 × 30 mm 2 at the back, with a length of 22 cm, corresponding to 24.7 radiation lengths. Because of the higher radiation dose in the endcap region, Vacuum Photo Triodes (VPT's) are used as photodetectors for the EE crystals instead of APD's. The EE coverage extends from |η| = 1.479 to |η| = 3.0.

The preshower detector is located in front of the EE in the region 1.653 < |η| < 2.6.

It consists of two alternating layers of passive lead and active silicon, acting as a sampling calorimeter. The rst lead layer corresponds to two radiation lengths of material, whereas the second layer corresponds to one additional radiation length. The silicon layers consist of active silicon strips with a pitch of 1.9 mm. The additional spatial resolution provided by the preshower is designed in principle to improve the separation between prompt photons and neutral mesons in the endcap region.

A longitudinal section of the electromagnetic calorimeter is shown in Figure 2.11.

Photodetectors

Due to the crystals low light yield, the choice of the readout devices used to extract the crystal signal is very important. Photodetectors with an internal gain are needed, in order to give a rst amplication stage for the signal before the injection in the electronic readout chain. Furthermore the photodetectors need to be fast, radiation tolerant, and be able to operate in the longitudinal 4-T magnetic eld. The requirement of radiation hardness and the presence of a strong magnetic eld lead to the choice of Avalanche PhotoDiodes (APDs) for the barrel region and of Vacuum PhotoTriodes (VPTs) in the endcaps. Two dierent devices are needed in order to face up the dierent radiation level and magnetic eld conditions.

Barrel: avalanche photodiodes

The use of APDs presents several advantages: they are fast detectors (≈ 2 ns of rise time), they have a very good quantum eciency of 70%-80% around λ = 420 nm and they are higly insensitive to the magnetic eld. They are compact devices (overall thickness of 2 mm) with a high radiation resistance, and can be manufactured in large quantities with a small spread in the performance parameters. Each APD has an active area of 5 × 5 mm 2 .

Two of them are glued to the back of each crystal. The APD basic structure is shown in Figure 2.12.

The light enters via the p + layer and is absorbed in the p layer behind, where electron-hole pairs are generated if the photon energy is higher than the gap energy. A drift in the p-n transition region is followed by an amplication stage in the n volume (with a gain tunable between 50 and more than 10 3 ) and by an intrinsic drift region before the charge is collected by the cathode.

The APD is supplied by a reverse voltage: by changing its value, the charge multiplication gain can vary from 0 to 200, but the optimum gain to operate with the CMS front-end electronics sits between 50 and 100 and it has been decided to operate at gain 50.

Not only the P bW O 4 light yield, but also the APD gain is temperature dependent: for this reason, one tenth of the APD pairs glued to the crystals has a sensor for the temperature measurement.

Endcap: vacuum phototriodes

The APDs used in the barrel are insuciently radiation-hard to be used also in the endcap region, where VPTs are employed. The VPT basic structure is represented in Figure 2.13.

LHC and the CMS detector

The photocathode is semitransparent and made of a radiation-hard glass: the photoelectrons produced are accelerated by an ultra ne mesh (100 wires/mm) placed 4 -5 mm far from the photocathode, and impact on a dynode producing secondary electrons (emission factor of about 20). The secondary electrons are attracted back to the anode mesh where a substantial fraction is captured, leading a total eective gain for the VPT greater than 8 in a magnetic eld of 4 T. The VPTs lower quantum eciency with respect to the APDs is compensated by a larger active area of about 280 mm 2 , so that the total detector response is almost the same for barrel and endcap regions.

Trigger tower and readout electronics

The CMS Electromagnetic Calorimeter needs a very fast electronics readout, in order to match the bunch crossing time of 25 ns and to provide very precise energy measurements over a wide range. The additional requirement of radiation hardness and large amount of channels are two other aspects to take into account.

The signal produced by photodetectors is amplied and then digitized, passing through 3 dierent boards as shown in Figure 2.14. The Mother Board is a totally passive board located beneath the cooling system for the electronics; it is necessary to route the signals from the photodetectors to the VFE cards, to distribute high voltage to the photodetectors and low voltage to the VFE cards.

The LVRBs are connected directly to the external Low Voltage power supplies which sit in the CMS racks attached to the outside of the CMS iron yoke, approximately 20 metres from the supermodule. Each LVRB contains radiation-hard voltage regulators which provide the 2.5 V needed by the front end electronics. This regulated 2.5 V is distributed to the FE card by a small connector on the LVRB, and to the 5 VFE cards in a trigger tower via the MB.

The CMS detector 39

The VFE board is needed to amplify the signal and convert it from analog to digital, using very fast components (40 M Hz) compatible with the 25 ns time that separates two LHC bunch crossings. Each VFE contains amplication and digitization for the signals from 5 crystals adjacent in Φ.

The VFE board feeds the digitized outputs to a FE board, which stores and processes the data during the Level-1 trigger latency of ∼ 3 µs. The trigger data are then transmitted to the o-detector electronics through an optical link operating at 800 Mbyte/s. After a L1-trigger reception, the data stored on the FE card corresponding to the triggered event are transmitted through a second optical link to the o-detector electronics for further trigger analysis (High-Level Trigger).

CMS trigger and data acquisition

At the LHC expected energy and instantaneous luminosity, the interaction rate (≈ 40M Hz) leads to ≈ 10 9 interactions/sec, that is orders of magnitude larger than what can be reasonably processed by the readout system and archived for later o-line analysis. In fact, data from only about 100 crossings/sec can be written to archival media. For this reason a very good online selection is needed and a rejection of nearly 10 7 with respect to the active bunch crossings at the LHC has to be achieved. In CMS this selection is performed in two physical steps: the Level-1 Trigger and the High Level Trigger (HLT). The L1 Trigger is based on processors which perform fast selections (≈ 3 µs) for each 25-ns bunch crossing; it is built of mostly custom-made hardware and it performs detector analysis in a coarse way.

On the contrary, the HLT can operate on longer timescales, it is basically a processor farm which inspects the events that have already passed the L1 trigger and executes software algorithms. In Figure 2.15 the data ow in the CMS trigger and data acquisition system is shown. In this section a brief description of L1 trigger and HLT is provided; then, a particular attention is paid to the calorimeter trigger.

Level 1 Trigger versus High Level Trigger

The total time allocated for the L1 trigger decision to keep or discard data from a particular beam crossing is 3.2 µs. This time includes the transit time for signals from the front-end electronics to reach the services cavern housing the Level-1 trigger logic and return back to the detector front-end electronics. During this time, the detector data must be held in buers, while trigger data are collected from the front-end electronics and decisions are performed. The Level-1 triggers involve the calorimetry and muon systems, as well as some correlation of information between them. The Level-1 decision is based on the presence of "trigger primitive" objects such as photons, electrons, muons, and jets above E T or p T thresholds. It also employs global sums of E T and E miss T . The L1 trigger reduces event rates from 40 M Hz to 100 kHz (design value). The HLT reduces event rates furthermore, down to 100 Hz, running the reconstruction algorithms and performing more sophisticated selections. The HLT code is developed starting from the idea of partial reconstruction: rather than reconstruct all possible objects in an event, whenever possible only those objects and regions of the detector that are actually needed are reconstructed. Moreover, since events have to be discarded as soon as possible, many virtual trigger levels are provided: calorimeter and muon information are used, followed by the tracker pixel data and nally the use of the full event information (including full tracking). HLT selection can then be seen as a sequence of lters of increasing complexity, using the information of calorimeters, pixel association and track reconstruction.

LHC and the CMS detector

The Electromagnetic Calorimeter Trigger

The ECAL front end electronics is in charge of:

• amplifying and shaping the signal from the sensors,

• digitizing the signal at 40 M Hz,

• using the digitized data to calculate trigger primitives for the Level-1 Trigger decision,

• buering the data until reception of the Level-1 trigger decision,

• transmitting the data to the o-detector electronics for insertion in the CMS data stream.

The building block of the front end electronics is the Trigger Tower, previously described.

At each bunch crossing, trigger primitive generation is rst started in the Front End boards, and then nalized and synchronized in an electronic board (called Trigger Concentration Local calorimeter trigger information refers to energy depositions in the trigger towers of the electromagnetic and hadronic calorimeters. The Regional Calorimeter Trigger uses the trigger primitives to nd candidate electrons or photons, jets and isolated hadrons from the decay of τ s and to calculate transverse energy sums in dierent detector regions. All calorimeter trigger objects described so far are forwarded to the Global Calorimeter Trigger, which sorts the electrons or photons, τ s and jets according to energy and quality, and sends the four objects with the highest rank in each category to the Global Trigger. The input for the physics trigger algorithm calculations are the trigger objects ordered by rank:

an algorithm is dened as a logic combination of the trigger objects together with a set of energy or momentum thresholds, windows in η and/or Φ and topological conditions.

All thresholds and space parameters, except for some exceptions, are only applied at the Global Trigger stage.

Energy resolution

As already mentioned at the beginning of this section, the energy resolution of an homogeneous electromagnetic calorimer can be parametrized as:

σ E E = a √ E ⊕ b E ⊕ c,
where a, b, c are respectively the stochastic, noise and constant term. The individual contributions are discussed below.

The stochastic term

The stochastic term a is a consequence of the statistics associated with the electromagnetic shower development in the calorimeter and the following scintillation light collection. This term represents the intrinsic resolution of an ideal calorimeter, that is a calorimeter of innite size and without response deterioration caused by instrumental eects. The initial energy E 0 of a particle incident in the calorimeter is directly proportional to the total track length T 0 , dened as the sum of all ionization tracks due to the charged particles in the electromagnetic shower. Since T 0 is proportional to the number of track segments in the cascade and the shower development is a stochastic process, the intrinsic resolution, from purely statistical arguments, can be written as:

σ E E ∝ √ T 0 T 0 ∝ 1 √ E 0 .
In the case of a real calorimeter, this term also absorbs the eects related to statistical uctuations in the scintillation light collection due to geometry eects, quantum eciency and electron multiplication processes inside the photodetectors.

For the CMS ECAL calorimeter, the contribution due to uctuations on the lateral containment of the shower is of 1.5% considering the energy deposited in a cluster of 5 × 5 crystals. The contributions due to the photostatistics are kept below 2.3% if the photodetectors produce more than 4000 photoelectrons per GeV . In the endcap regions, where a preshower is present in front of the calorimeter, an additional contribution of ∼ 5%, related to the uctuations on the energy deposited in the absorber, needs to be taken into account.

The noise term

The noise term is strongly related to the features of the readout circuit (detector capacitance, devices, cables etc.). In ECAL photodetectors contribute because of their intrinsic capacitance and leakage currents. Furthermore there are the noise introduced by the preamplier stage of the electronic readout and the one introduced in the digitization step:

the rst one is ∼ 30 -40 M eV in the barrel and 150 M eV in the endcaps, while the second one is negligible. A nal contribution to the noise term comes from pileup: in a cluster of 5 × 5 crystals the contribution is of ∼ 30 M eV in the barrel and of ∼ 175 M eV in the endcaps, thus compatible with the total electronic noise.

The CMS detector 43

The constant term

The constant term c is very important since it is the asymptotic value of the energy resolution at high energies. All the defects connected to the detector construction and assembly, as well as the instability of temperature, voltage etc. during its operation, contribute to this term. The main contributions are described below:

• Non-uniformity of the longitudinal light collection: as a consequence of the truncated pyramid-shape of the crystal and the high refractive index (n = 2.16), a strong focusing eect on the scintillation light causes non-uniformity in the light-yield. One of the lateral faces of the crystals is depolished during the production process to avoid this eect. In this way the contribution is kept below 0.3%,

• Longitudinal shower containment and uncorrected geometrical eects: thanks to an accurate simulation and to test beam studies has been shown that the constant term contribution due to these eects is lower than 0.2%,

• Inter-calibration errors: inter-calibration of the channels is a crucial issue for physics performance. The main source of channel-to-channel response variation is the crystalto-crystal variation of scintillation light yield, together with readout variations,

• Temperature stability: as already discussed, both the emission of scintillation light and the APD gain are temperature dependent.

A temperature stability within 0.05 • C is needed over the full detector volume in order to keep the contribution to the constant term below 0.1%,

• High voltage stability: the APD gain strongly depends on the bias voltage. In order to keep this contribution below 0.1% the stability on the high voltage has to be better than 30 mV .

Calibration

In order to achieve a constant term contribution of 0.5% in the energy resolution, a big eort has to be made to obtain the best possible calibration of the calorimeter [START_REF] Chatrchyan | Energy Calibration and Resolution of the CMS Electromagnetic Calorimeter in pp Collisions at √ s = 7 TeV[END_REF]. ECAL calibration is naturally seen as composed of a global component, giving the absolute energy scale, and a channel-to-channel relative component, which is referred to as intercalibration.

The essential issues are uniformity over the whole ECAL and stability, so that showers in dierent locations in the ECAL in data recorded at dierent times are accurately related to each other.

The intercalibration is principally done using π 0 events in the barrel and W → eν events in the endcap. Concerning the absolute energy scale, physics events in which a particle (namely a Z boson) decays into an electron-positron couple are used. The kinematical 2. LHC and the CMS detector constraint given by the invariant mass of the particle gives the absolute calibration of the calorimeter.

Monitoring

The crystal transparency is expected to decrease with the amount of radiation absorbed, and then recover after a certain time. For this reason it is fundamental to continuously monitor the light transmission of each crystal during the LHC operation. For this purpose a laser-based monitoring system is designed to inject pulses into each single crystal to measure the light transmission near the scintillation spectrum peak (λ ≈ 440 nm) and, as a crosscheck, at a longer wavelength (λ ≈ 800 nm). The loss in transparency due to irradiation for the laser light (R) and for the scintillation light (S) are related by

S S 0 = R R 0 α ,
where R 0 and S 0 are the signal intensity, respectively for laser light and scintillation light, before irradiation. Specic test beam studies have shown that the coecient α for the dierent crystals has the same value within 5%. The irradiation damage being small (< 6%) in Run 1 for crystals in the barrel, it is possible to use one single value of α for all the crystals in order to correct the crystal response for the transparency loss. This allows to keep the contribution to the constant term in the resolution < 0.3%, within the design specication.

The hadronic calorimeter

The hadronic calorimeter (HCAL, see Figure 2.16) [START_REF]The Hadronic Calorimeter[END_REF] plays an essential role measuring the direction and energy of jets, the total transverse energy and the imbalance in the transverse energy (missing E T ). To achieve this goal a high hermeticity is required. In particular, the HCAL angular coverage must include the very forward region, since the identication of forward jets is very important for the rejection of many backgrounds.

The Hadronic Calorimeter can be divided in four regions, which provide a good segmentation, a moderate energy resolution and a full angular coverage up to |η| = 5. The magnet and an additional layer of scintillation detectors, which is referred to as the outer hadronic calorimeter (HO), installed outside of the coil increase the material thickness in the barrel pseudorapidity region, such that the hadronic showers are fully absorbed before reaching the muon system. The HB and HE are sampling calorimeters with active plastic scintillators interleaved with brass plates. This absorber material has been chosen because of its reasonably short interaction length and because it is non-magnetic. The read-out system is constituted by wavelength-shifting bres. The rst layer is read out separately, while all others are read out together in towers of ∆η × ∆Φ = 0.087 × 0.087 rad.

The energy resolution (expressed in GeV) is:

• σ E E ∼ 65% √ E ⊕ 5% in the barrel, • σ E E ∼ 85% √ E ⊕ 5% in the endcaps, • σ E E ∼ 100% √ E ⊕ 5% in the very forward calorimeter.

The CMS solenoid

In order to achieve a good momentum resolution for momenta up to 1 TeV/c, CMS needs a high magnetic eld. The CMS solenoid is the central device around which the experiment is built and its dimensions limited the size of the total apparatus. Its purpose is to bend the paths of particles emerging from high-energy collisions. The higher the particle momentum is, the less its trajectory is curved by the magnetic eld. A higher strength eld, combined with high-precision position measurement in the tracker and muon system, gives accurate measurement of momentum.

The CMS magnet [START_REF] Acquistapace | the magnet project[END_REF] is a 13 m long superconducting solenoid, the largest ever built. It is

LHC and the CMS detector

able to generate a uniform magnetic eld of 4 T in the inner region, storing about 2.5 GJ of energy (Figure 2.17). It operates at a temperature of 4 K, ensured by a sophisticated Figure 2.17: Layout of the magnetic eld of CMS.

helium cooling system. At such temperature, the at NiTb cable becomes superconducting, allowing a 20 kA current to ow without appreciable loss. The whole magnet is then contained in an enormous vacuum cylinder, which isolates it from the external environment.

Outside, an iron structure composed by ve barrel layers and three disks for each endcap constitutes the iron yoke, needed to return the magnetic ux.

The muon system

The aim of the muon spectrometer [START_REF]The CMS muon project[END_REF] is to identify muons and measure, in combination with the inner tracker, their transverse momentum accurately. As a matter of fact, since high-p T muons provide a clean signature for many processes, the muon system plays an important role in the trigger. The muon spectrometer, placed outside the magnet, is embedded in the iron return yoke, so that the magnetic eld bends the tracks and allows muon p T measurements. The muon system consists of 3 types of gaseous particle detectors (see Figure 2.18):

• Drift Tube (DT) Chambers in the barrel, covering the region (|η| < 1.2),

• Cathode Strip Chambers (CSC) in the endcaps, covering the region (0.9 < |η| < 2.4),

• Resistive Plate Chambers (RPC) in both the barrel and the endcaps, covering the region (|η| < 1.6).

These dierent technologies are used because of the dierent particle rates and occupancies, both higher in the endcaps, and the intensity of the residual magnetic eld, which is lower in the barrel.

The CMS detector

LHC and the CMS detector

The internal volume is lled with a gas mixture of Ar (85%) and CO 2 (15%) at atmospheric pressure, which provides good quenching properties and a saturated drift velocity of about 5.6 cm/µs. A single cell has an eciency close to 100% and a resolution of about 180 µm.

Cathode strip chambers

Because of the large occupancy of the endcap regions, from few Hz/cm 2 to more than 100 Hz/cm 2 , and the intense and inhomogeneous magnetic eld, cathode strip chambers were chosen in this region. resolution is of the order of about 0.5 cm, while for the strips is of about 50 µm.

Resistive plate chambers

Resistive plate chambers are installed both in the barrel and in the endcap regions, in order to add robustness and redundancy to the muon trigger. They have a limited spatial resolution, but an excellent time resolution, of the order of few nanoseconds. They operate in avalanche mode rather than in the more common streamer mode. This is obtained with a moderate electric eld across the gap which allows to sustain higher rate. However the gas multiplication is reduced, and improved electronic amplication is needed.

Summary

This chapter gave an overview of the LHC performances since its start and the structure of the CMS experiment. The electromagnetic calorimeter is presented in more detail with respect to the other subdetectors, since it plays a fundamental role in the detection of photons. The LHC data taking is going on very smoothly, so for the end of the year more than 40 fb -1 of data should be collected.

Chapter 3

Photon reconstruction and identication

One of my main contribution to the H → γγ analysis concerns the study of photon recon- 3. Photon reconstruction and identication

Photon reconstruction

A photon, produced at the interaction point, rst passes through the tracker, then enters ECAL and loses all its energy through electromagnetic shower, which can be spread over several neighbouring crystals. The photon can have two dierent behaviours. In about 75%

of the cases the photon is unconverted, it goes through the tracker without interacting and deposits about 94% (97%) of its energy into 3×3 (5×5) crystal matrix in the ECAL.

In the remaining cases the photon converts to an electron-positron pair before entering the ECAL, the electron and positron bend under the magnetic eld and deposit their energies in a larger region in φ. To include all the photon energy deposits, photons are thus reconstructed by clustering the energy deposits in the ECAL crystals into so-called superclusters, which are a collection of EM clusters close together [START_REF] Vardan Khachatryan | Performance of photon reconstruction and identication with the CMS detector in proton-proton collisions at √ s =8 TeV[END_REF][START_REF] Vardan Khachatryan | Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at √ s = 8 TeV[END_REF][START_REF] Meschi | Electron Reconstruction in the CMS Electromagnetic Calorimeter[END_REF].

The clustering algorithm used in Run 2 is dierent from that used in Run 1, allowing for a ner reconstruction of the photon energy. In the following section a more detailed description of the clustering algorithm is given, with a particular attention to the dierences between Run 1 and Run 2. Clustering in the endcaps uses xed matrices of 5×5 crystals. After a seed cluster has been dened, further 5×5 matrices are added if their centroid lies within a small η window and within a φ distance roughly equivalent to the 17 crystals span used in the barrel. The 5×5 matrices are allowed to partially overlap one another. For unconverted photons, the superclusters resulting from both the barrel and endcap algorithms are usually simply 5×5 matrices.

Clustering

The raw photon energy E RAW is obtained by summing the calibrated energy deposits in the crystals of the supercluster, and the energy deposited in the preshower detector is added for photons in the endcap. The photon position in η -φ is obtained from the mean position of basic clusters weighted by energy, and the position of basic clusters is calculated from mean positions of crystals corresponding to the shower depth weighted by the logarithm of the crystal energy [START_REF] Meschi | Electron Reconstruction in the CMS Electromagnetic Calorimeter[END_REF].

Clustering in Run 2

The algorithm for the photon reconstruction in Run 2 is quite dierent, allowing for a ner reconstruction of the photon energy. The main changes applied to the reconstruction are listed below:

• Particle Flow clustering: the particle ow technique, which consists in a combination of the information from all sub-detectors, allowing the improvement of the global event description, was just partially used during Run 1. In Run 2 the potential of this technique is fully exploited, with the so-called particle ow (PF) clusters grown from the seed by aggregating crystals with at least one side in common with a cell already included in the cluster, and with an energy above a given threshold (zero suppression method). This threshold represents about two standard deviations of the electronic noise in the ECAL, that is 80 MeV in the barrel and up to 300 MeV in the endcaps. Furthermore, an energy-sharing algorithm was developed. It consists

Photon reconstruction and identication

in sharing the energy of each cell among contiguous clusters according to the cellcluster distance with an iterative determination of the cluster energies and positions assuming a gaussian shower prole.

A more detailed description of the particle ow algorithm is given in Section 3.1.2, where it is explained how this technique plays an important role not just in the cluster growing, but also in the supercluster building.

• Dynamic Superclustering: PF clusters are dynamically merged into superclusters.

Dynamic superclustering allows good energy containment, robustness against pileup and takes into account the detector geometrical variations with η (e.g. endcap crystal size). Clusters lying in the area between two parabolas, function of η and centered around the most energetic cluster, are dynamically gathered giving to the supercluster a mustache-like shape. This is important especially moving to higher |η| regions and for low energy clusters, as the shape of the shower starts to extend also in η. A xed supercluster size, as was used in Run 1, would suer from pileup in low-pseudorapidity region and miss some bremsstrahlung electron at high-η. In Figure 3.2 the mustacheeect is shown. The ∆φ and ∆η distances between each cluster and the max-energy cluster are shown for |η| going from 0 to 3, in slices of |η| = 0.25. It is evident that moving to higher |η| the shower shape becomes dierent and starts to extend not only in φ but also in η. The mustache shape depends from the cluster energy and it is more pronounced for clusters with low energy, of about 1 GeV. The clusters recovered with the mustache clustering are originating from electrons coming from converted photons, the latter probably being low energy bremsstrahlung.

In Run 2 variables describing shower shapes can be computed in two manners:

• Particle Flow: only crystals from PF clusters are used,

• full5×5: all crystals in a 5×5 matrix around the seed are used and both the energy sharing fraction and the zero suppression are ignored (zero suppression excludes crystals with an energy lower than a certain threshold). This is very similar to Run 1.

I performed some comparison studies between the Run 1 reconstruction (called RECO in the following), the standard particle ow reconstruction (called GED) and the full5×5 one (called GED5×5). These studies are presented in Section 3.3.1 of this chapter.

Particle ow

The particle ow algorithm [START_REF] Weng | A Global Event Description using Particle Flow with the CMS Detector[END_REF] allows to exploit the versatility of the CMS apparatus in an attempt to identify and reconstruct individually each particle arising from LHC protonproton collisions with a combination of the information from all sub-detectors. This can lead to a better global event description. The reconstruction and the identication of each particle are optimised, allowing to avoid redundancy while keeping a good level of precision.

An important ingredient for the success of the particle ow technique is the ne spatial granularity of the sub-detectors. Indeed, if the sub-detectors are coarse-grained the signals from dierent particles could merge, reducing the identication and reconstruction capability for the dierent types of particles. If the granularity is instead sucient to provide a good separation between individual particles, a complete event description becomes possible.

The particle ow algorithm proceeds in steps, associating clusters and tracks with a newly reconstructed particle at each progressive step. In the following the dierent steps of the particle ow algorithm are briey described:

• rst, clusters and tracks are gathered in a list called unassociated objects;

• tracks and clusters identied as being associated with hits and segments in the muon chambers are tagged as muons and removed from the list of unassociated objects;

• then, tracks and clusters identied as being associated with electrons (and all the possible individual bremsstrahlung photons) are tagged and removed from further processing;

• next, in the case of HCAL clusters linked to a track, the calibrated HCAL cluster energy is compared with the track momentum. If the cluster energy is compatible 56

Photon reconstruction and identication

with the track momentum, a charged hadron is created with energy determined from a weighted average of the track momentum and the cluster energy. If the dierence between the cluster energy and the track momentum is signicant (with respect to the expected calorimeter energy resolution and the measured track momentum uncertainty), a neutral hadron is created from the cluster energy in excess;

• similarly, if an ECAL cluster and an HCAL cluster are linked together with a track, the calibrated combined energy of the ECAL cluster and HCAL cluster is compared with the track momentum. If the combined ECAL and HCAL calorimeter energy is compatible with the track momentum, a charged hadron is created, otherwise either a neutral hadron or a photon is created from the excess of calorimeter energy. This is done with a multivariate analysis that takes into account the track momentum, the relative energy deposits in ECAL and HCAL, the cluster-track link quality and the transverse cluster shapes;

• once these tracks and clusters have been removed from the list of unassociated objects, only clusters not linked to any track remain uncleaned from the event. In this case any ECAL clusters are assumed to be photons and any HCAL clusters (or HCAL clusters linked with ECAL clusters) are assumed to be neutral hadrons.

The particle ow algorithm allows to improve in particular the jets and taus reconstruction, along with the missing transverse energy and isolation computation. For instance, jets are commonly reconstructed by clustering the energy deposits observed in the calorimeters.

The particle ow algorithm, on the other hand, makes it possible to build jets of reconstructed particles, thereby resolving the jet constituents and providing unique insight on the jet substructure and the parton fragmentation process.

An example of the benet brought by the particle ow approach is shown in Figure 3.3, where it can be seen that the tau jets PF reconstruction is characterised by an improved energy and angular resolution with respect to the calorimeter-based algorithm. In fact, the limited energy and angular resolution of the calorimeter-based jets is dominated by the hadron calorimeter resolution and granularity. Since the tau decays mostly in photons and charged pions, the particle ow-based jets benet from the tracker and electromagnetic calorimeter better resolutions.

Photon identication 3.2.1 Principles of photon identication

The great challenge of the Higgs to diphoton decay channel, as shown in Figure 3.4, is to identify a small peak in the diphoton mass distribution over a background that is several orders of magnitude larger. Diphoton events include potential Higgs signal events but mostly 3. Photon reconstruction and identication a mixture of background events. The backgrounds can be separated in two components, irreducible and reducible. The irreducible component consists of prompt diphoton events, where a prompt photon originates from the hard scatter vertex. The reducible component includes dijet and γ + jet events, in which jets are misidentied as photons (fake). The primary mechanism for a jet to fake a photon involves the fragmentation of the majority of the jet energy into a leading π 0 or η meson, which subsequently decay to two photons. For the energy range of interest, the π 0 or η are signicantly boosted, such that the two photons from the decay are nearly collinear and are dicult to distinguish from a prompt photon.

The goal of photon identication is to reduce these backgrounds, in general applying isolation requirements against additional energy from jet fragmentation, as well as exploiting dierences in shower prole in the calorimeter to distinguish between a prompt incident photon and a pair of incident photons from a neutral meson decay.

In Section 3.2.2 the variables able to discriminate between prompt and fake photons are presented. The discriminating power of these variables can be used through several methods, as explained in Section 3.2.3.

Discriminating variables

In general two groups of variables can be used for discrimination between prompt and fake photons, because of their connection with the two intrinsic dierences between a prompt photon and a fake photon: the electromagnetic shower shape variables and the isolation variables. As discussed, the most photon-like jets result from fragmentation into a leading π 0 or η, which subsequently decay into a pair of photons with small opening angle. Even if the two photons cannot be cleanly distinguished, such objects have wider shower proles on average than a single photon in the calorimeter. This is true in particular along the η axis of the cluster, since the discriminating power resulting from the Φ prole of the shower is partially washed out by the eect of the magnetic eld, which can expand the electromagnetic cluster in the Φ direction for both converted photons. In addition, because π 0 or η result from jet fragmentation, there are in general additional charged and neutral particles produced. Since jets tend to be collimated objects, these additional particles are likely to be produced close to the reconstructed photon in the detector. This leads to a class of discriminating variables called isolation, which generally consist of the sum of some particular type (EM, charged...) of energy in a cone around the reconstructed object. To do this, it is convenient to dene cones around the direction of the photon, with cone radius dened by R = ∆η 2 + ∆Φ 2 , where ∆η and ∆Φ are the distances in η and Φ, respectively, between the photon direction and the direction of selected objects in the cone. In order to ensure that the energy from the photon itself is not included in this sum, we dene a smaller veto region inside the cone, which is excluded from the isolation cone.

Two isolations are included:

Photon identication 59

• one with respect to the best estimate of the primary vertex,

• one which is the worst isolation of a photon among all isolations computed with respect to all reconstructed vertices. This is due to the fact that a prompt photon is generally isolated with respect to all vertices, while fake photons are not.

Event-level variables are also included such that the distributions of shower shape and isolation variables are used dierentially as function of pileup contamination measured by ρ, and photon kinematics measured by η SC and E RAW .

In order to reduce the photon kinematic dependence of the photon identication BDT and the associated mass dependence in the diphoton BDT, explicit use of kinematic dierences between prompt photons and fake photons in the training sample is avoided by reweighting the 2D p T -η SC distribution of the signal to that of the background.

The input variables for the photon identication BDT are given below, with their denition:

• Shower shape cluster variables: R 9 : E 3×3 /E SC , where E 3×3 is the energy sum of the 3×3 crystals surrounding the supercluster seed crystal and E SC is the energy sum of the supercluster.

Photon reconstruction and identication

These variables have also the full 5×5 version, which uses only 5×5 matrix around the seed crystal, and does not use PF energy sharing neither zero suppression (this means that all crystals are included).

• Particle ow-based isolation variables: PF Photon ISO: transverse energy sum associated with all particles identied as photons by the particle ow algorithm falling inside a cone of size R = 0.3 around the photon candidate direction. For photons in the barrel, an inner veto strip of |∆η| < 0.015 is excluded from the isolation sum, and for photons in the endcap instead an inner veto cone of ∆R < 0.07 is excluded.

PF Charged ISO (selected vertex): transverse energy sum associated with all particles identied as charged hadrons by the particle ow algorithm falling inside a cone of size R = 0.3 around the photon candidate direction, excluding an inner veto cone of R < 0.02. It is measured with respect to the selected primary vertex.

PF Charged ISO (worst vertex): transverse energy sum associated with all particles identied as charged hadrons by the particle ow algorithm falling inside a cone of size R = 0.3 around the photon candidate direction, excluding an inner veto cone of R < 0.02. It is measured with respect to the worst vertex, that is the one which yields the largest isolation sum.

• Auxiliary variables: ρ: the estimate of transverse energy per unit area in the η -Φ plane contributed by the pileup interactions and underlying-event eects in the event. This is constructed from the median transverse energy density of all anti-k T -reconstructed jets in the event, where the anti-k T algorithm [40] tends to produce a large num- ber of soft jets such that the median of this distribution is relatively insensitive to the hard interaction. SC η: the η of the supercluster corresponding to the reconstructed photon, computed from the pseudorapidity of the vector joining the point (0,0,0) to the reconstructed supercluster position in the electromagnetic calorimeter. SC E RAW : the sum of crystal energy in the supercluster corresponding to the reconstructed photon.

Other variables are interesting because used in the preselection of the H → γγ analysis (see Section 4.4):

• H/E: the energy collection by the HCAL towers within a cone of R=0.15 centered on the supercluster position, divided by the supercluster energy.

Methods for photon identication

Cut-based technique

The goal of photon identication is to discriminate as well as possible prompt from fake photons. The rst ones are thus considered as signal, the second ones as background. A simple approach to this problem is to encode information about the photons present in the event into a set of one-dimensional variables, and then apply simple cuts on those variables.

In the analysis photons which pass the cuts are kept, those which fail are discarded. This approach, called cut-based identication, is easy to understand and to describe, but has a few important drawbacks:

• events are either retained or discarded. In principle events can be used in a more ne-grained way, according to how signal-like or background-like they are,

• correlations between variables are neglected. Generally it is dicult to encode all of the relevant information into fully uncorrelated variables, and therefore neglecting correlations between variables leads to a loss of discriminating power,

• the selection of cut values which optimize the performance of an analysis is a complex problem, especially with a large number of variables. Most cut-based analyses therefore rely on a relatively small number of variables and/or use suboptimal cut values, again neglecting potentially useful information.

Boosted Decision Trees (BDT)

The optimal separation between two classes of events given a set of variables x, is given by the likelihood ratio [START_REF] Pearson | On the Problem of the Most Ecient Tests of Statistical Hypotheses[END_REF] L

R = L s (x) L s (x) + L b (x)
where L s (x) and L b (x) represent the full multidimensional likelihood functions for signal and background events respectively. If the set of variables x encodes all of the relevant information, then this likelihood ratio contains all of the relevant information for distinguishing the two classes of events. This ratio quanties the probability that a given event with features x is a signal event as opposed to a background event.

In high energy physics, the input variables x are the output of a complicated detector response, and therefore there is no known analytic form for the multidimensional likelihood 62 [START_REF] Weinberg | A Model of Leptons[END_REF]. Photon reconstruction and identication functions above. Therefore this likelihood is estimated using a nite sample of events representing each class, either from Monte Carlo simulation or from carefully dened control regions in data. There are many techniques designed to estimate the multidimensional likelihood ratio from a nite set of training events in this case. One such technique is the Boosted Decision Tree, able to address some of the limitations listed for the cut-based technique.

Boosted Decision Trees [START_REF] Hoecker | TMVA -Toolkit for Multivariate Data Analysis[END_REF][START_REF] Friedman | Greedy Function Approximation: A Gradient Boosting Machine[END_REF][START_REF] Yang | Observation and Measurement of a Standard Model Higgs Boson-like Diphoton Resonance with the CMS Detector[END_REF] is one of the MVA (multivariate analysis) techniques employed in experimental particle physics to estimate a multidimensional function. If the function has discrete values, like signal or background, this is called classication. If the output is continuous, like energy corrections, this is called regression. We use a BDT in this analysis for its ability to handle large number of input variables and their correlations, as well as its simple mechanism and robustness against overtraining. BDT are used to combine all the relevant information in an event into a single variable which discriminates signal from background for classication (for example for the photon identication) or precisely estimates a particular target property (for the regression, see Section 5.11). Whereas a cut-based technique is able to select only one hypercube of the phase space, the decision tree is able to split the phase space into a large number of hypercubes, each of which is identied as either signal-like or background-like.

To train a BDT we provide two simulated samples with known identity, one for the signal and one for the background, and a set of input variables with discriminating power x = {x 1 , x 2 , ..., x n }. A single decision tree, which is a binary tree structured classier like the one sketched in Figure 3.5, is rst trained. Starting from the root node representing the entire variable phase space, a sequence of binary splits using the discriminating variables x i is performed. Every split uses the variable that at this node gives the best discrimination between signal and background when 3.2 Photon identication 63 being cut on. The same variable may be used at several nodes, while others might not be used at all. The terminal nodes at the end of the tree are labeled S for signal and B for background depending on the majority of events that end up in the respective nodes.

In more detail, the tree building starts from the root node, with the number of signal and background events reweighted such that both total weights for signal and for background are equal. The node is then split by selecting a single variable and a cut value on it. The splitting continues iteratively until a predetermined limit is reached, such as a maximum depth of the tree or a minimum number of events in a node. The limit is chosen to reduce the bias due to statistical uctuation of the training samples, the overtraining.

A shortcoming of the single decision trees is their instability with respect to statistical uctuations in the training sample from which the tree structure is derived. This instability can cause an overtraining and a misclassication for some of the events in the nal nodes. This problem is overcome by constructing a forest of decision trees, all derived from the same training sample, with the events undergoing subsequently so-called boosting, a procedure which modies their weights in the sample. With this method we train a set of trees and we assign a score to an event as the weighted average of the scores of all the trees.

For the photon identication studies we use the boosting procedure called Gradient Boost, whose expression is as following:

F ( x; P ) = M m=1 β m f ( x; α m ),
where F ( x; P ) represents the function with the set of parameters P corresponding to the BDT made up of M trees, f ( x; α m ) is the function corresponding to the m th tree, α m represents the parameters of the m th tree including the splitting variables and cut values at each node, and β m is the weight of the m th tree. The parameter set P is determined by minimizing the deviation between the estimates provided by F ( x; P ) and the true identities of the training events, given by the loss function:

L(F ( x; P ), y) = N n=1 ln(1 + e -2Fn( x;P )yn ),
where F n ( x; P ) is the estimated value for the n th event, and y n represents the true value +1 or -1 of the n th event, and N is the total number of events.

The trained BDT function is then used to assign a score to each event, given its values of the input variables. The score is a continuous variable varying from -1 to +1, the more signal-like an event is, the higher value it gets.

A classier based on a Boosted Decision Tree trained on a set of variables containing all of the relevant information itself contains all of the information needed to discriminate between signal and background. The simplest possible usage of such a BDT is to place a 3. Photon reconstruction and identication cut on the output. Cutting on the BDT output rather than on the input variables directly addresses two of the three limitations listed for cut-based technique, namely that it properly exploits correlations among the input variables and is relatively simple to optimize. This cut-based usage still retains the drawback of completely accepting or discarding events. In the case of the H → γγ analysis, the photon identication multivariate discriminator is fed forward to the per-event multivariate discriminator described in Section 4.8, after a very loose cut on it.

For the photon identication studies we use a Toolkit for Multivariate Data Analysis (TMVA) [START_REF] Hoecker | TMVA -Toolkit for Multivariate Data Analysis[END_REF] within CERN's ROOT framework [START_REF] Antcheva | ROOT: A C++ framework for petabyte data storage, statistical analysis and visualization[END_REF] to train the BDT.

Training samples

The BDT technique is thus used in the H → γγ analysis to perform the photon identication. As mentioned in Section 3.2.3, to train a BDT we provide two simulated samples, one signal and one background, each sample containing the set of input variables with discriminating power x = {x 1 , x 2 , ..., x n }. The prompt and fake photons for training, used as signal and background respectively, are both taken from the γ + jet Monte Carlo samples listed in Section 4.1.6. The events in these samples generally contain one prompt photon and one electromagnetically enriched object originating from a jet (more details on the EM-enrichment applied to some background MC samples can be found in Section 4.1.6).

In order to properly cover the phase-space, there are two γ + jet samples used for the training. They are weighted according to the cross-section since they cover dierent p T ranges. Prompt photons and non-prompt photons are required to pass the H → γγ analysis preselection as dened in Section 4.4. Just the p T requirement on the leading (subleading) photon is loosen from 30 [START_REF] Sullivan | Snls3: Constraints on dark energy combining the supernova legacy survey three-year data with other probes[END_REF] GeV to 18 GeV with respect to the preselection, which gives a p T threshold of 18 GeV for both photons.

The signal sample consists of reconstructed photons which match prompt photons at the generator level, which means they originate from a quark. The fake photons belonging to the background sample are all the remaining photons. 50% of the γ + jet samples is used for the training, while the remaining is used for testing, that is to recompute the photon identication output variable using the trained BDT.

Results

In the next two sections my studies concerning the dierent photon identication algorithms and the relevant results on the photon identication are presented. Monte Carlo samples might dier from one study to another, yielding some slight dierences in the variable shapes or in the performances achieved.

Results

65

Results of photon reconstruction study

The rst part of my study was dedicated to the comparison between Run 1 and Run 2 photon reconstruction from the identication point of view. These two reconstructions are called RECO (Run 1) and GED (Run 2) in the following. In addition, as explained in Section 3.1.1, a third identication was studied for Run 2 reconstruction, and it is called GED5×5 in the following. We will refer to RECO, GED and GED5×5 as dierent reconstructions, though strictly speaking GED and GED5×5 have the same clustering.

There are three main steps: rst I analysed the shower shape and isolation variables for the dierent reconstructions. Then I compared the performances of the dierent reconstructions using, for all of them, the BDT trained for Run 1 conditions. Finally I compared the performances of the reconstructions, this time after having performed a dedicated training at 13 TeV for each of them.

In Figures 3.6 In general the variable distributions of the three reconstructions are quite similar. The variables that show the biggest discrepancies between RECO and particle ow-based reconstructions are SC η-width and SC Φ-width. This is expected because these are supercluster level variables, whereas most of the others are related only to the seed cluster.

In fact the superclusters are dierent between Run 1 and Run 2, because of the dierence in the geometry of the clustering (mustache prole versus simple rectangular η-Φ region).

Looking at the dierences in the variables is not sucient to compare the three reconstructions. It is indeed necessary to compare the photon identication performances in the three cases. As a rst step, the photon identication (in the following ID MVA) output variable for the three reconstructions was computed using the Run 1 training. This is clearly a rough approach, since this training was obtained with the RECO reconstruction at 8 TeV, so it is non-optimized for the GED and GED5×5 reconstructions. Nevertheless in this way it is possible to have a rst idea of the performances of the dierent reconstructions without doing a new training.

Once the ID MVA output variable, like the one in Figure 3.18, is obtained, it can be used to calculate the so-called ROC curve, which is the background eciency as a function of the signal eciency obtained for several cuts of the ID MVA output variable. The more the curve is on the bottom right part of the plot, the better is the ID MVA performance, because in this region the signal eciency is high while the background eciency is low.

Results

69

The ROC curve is a good gure of merit for the photon identication discriminating power.

Therefore the ROC curves for each reconstruction are obtained, starting from the ID MVA output obtained applying the Run 1 training. Figure 3.9 shows the ROC curves obtained, in blue for RECO, in grey for GED and in red for GED5×5 reconstruction, for both barrel and endcap. From these plots it is evident that the Run 1 reconstruction has a better performance than the GED one, while the use of GED5×5 variables allows to have performances similar to RECO.

Nevertheless one has to remember that the training used in this case is optimised for RECO, so it is possible that the loss in performance of the particle ow-based reconstructions is just an artifact; furthermore, GED5×5 has a better performance than GED because it is more similar to RECO algorithm. It was eventually decided to use the GED5×5 reconstruction in the nal H → γγ analysis, which is slightly better than GED (see Figure 3.10).

Results of photon identication study Discriminating variables and training tests

Photon reconstruction and identication

each individual tree to fully explore the multidimensional phase space. The depth (number of terminal nodes) of each of the individual trees in the boosting series, referred to as the forest, can thus be limited. An additional handle for reducing overtraining is the addition of a shrinkage factor, which represents the learning rate of the gradient boost algorithm.

Empirically for classication problems it has been found that optimal performance is obtained with a large number of small trees, and using a small shrinkage factor, of about 0.1. Boosted decision trees constructed in this way are extremely robust to the addition of variables which are either redundant, or only contribute additional information in a limited region of the input variable space. In general this allows the selection of variables based on the physical information which they contain, with the nal performance being relatively insensitive to the precise denition or particular combination of variables.

Taking into account all these prescriptions, a shrinkage factor of 0.1 was used. Several trainings with dierent number of trees and depth were tested. I started with 700 trees, each one with a depth of 3; then I varied the number of trees for 500, 1000, and nally doubled the depth of the trees. These changes in the parameters have small eect on the training performances, as one can see in Figure 3. [START_REF] Aad | Combined Measurement of the Higgs Boson Mass in pp Collisions at √ s = 7 and 8 TeV with the ATLAS and CMS Experiments[END_REF], where the ROC curve with the initial parameters is shown along with the ROC curves obtained increasing the number of trees to 1000 and the depth of the trees to 6. Figure 3.16 shows also the ROC curve obtained adding in the training the variable H/E, which was tried since it has a good discriminating power between prompt and fake photons. But it does not seem to improve the training performances.

Several MVA techniques dierent from BDT were also tried. The more interesting is the Articial Neural Network (ANN), that is any simulated collection of interconnected neurons, with each neuron producing a certain response at a given set of input signals. By applying an external signal to some (input) neurons the network is put into a dened state that can be measured from the response of one or several (output) neurons. The neural network can therefore be seen as a mapping from a space of input variables x 1 , ..., x nvar onto a, in case of a signal-versus-background discrimination problem, one-dimensional space of output variables y. The mapping is nonlinear if at least one neuron has a nonlinear response to its input.

The neural network MLP (Multilayer Perceptron) was used. While in principle a neural network with n neurons can have n 2 directional connections, the complexity can be reduced by organizing the neurons in layers and only allowing directional connections from one layer to the immediate next one. This kind of neural network is called multilayer perceptron. The rst layer of a multilayer perceptron is the input layer, the last one the output layer, and all others are hidden layers. For a classication problem with n var input variables and 2 output classes the input layer consists of n var neurons that hold the input values, x 1 , ..., x nvar , and one neuron in the output layer that holds the output variable, the neural network estimator y M LP . Each directional connection between the output of 3. Photon reconstruction and identication one neuron and the input of another has an associated weight. The value of the output neuron is multiplied with the weight to be used as input value for the next neuron. The number of hidden layers can be tuned, keeping in mind that for a multilayer perceptron a single hidden layer is theoretically sucient to approximate a given continuous correlation function to any precision, given an arbitrary large number of neurons in the hidden layer.

If the available computing power and the size of the training data sample are sucient, one can thus raise the number of neurons in the hidden layer until the optimal performance is reached.

Another parameter useful to tune is the number of training cycles, that has to be not too low, to exploit all the information available, but neither too high, to avoid overtraining.

Keeping in mind all these aspects I decided to use one hidden layer with several neurons, n var + 5, and to perform trainings with a dierent number of cycles. The more adequate number of cycles was found to be 3000, and Figure 3.17

Final training and relevant results

The nal training, used in the public H → γγ analysis, along with the relevant results is presented in this section. The BDT technique is used, because quicker and easier to handle than neural network. The photon identication BDT output is a score assigned to each photon which ranges from -1 to 1. The higher the score assigned to a photon, the more likely the photon is a prompt photon rather than a fake photon. The BDT output for the double EM-Enriched photon plus jet simulated samples is shown in Figure 3.18, for barrel and endcap respectively. The signal (blue) and background (red) training samples (solid circles), and the corresponding testing samples (histograms) are shown. From this gure one can see that the discriminating power between prompt and fake photons is very good.

Furthermore, good agreement between the distributions of the testing samples and those of the training samples is found, which proves the statistical stability of the BDT output.

The BDT output has been checked also for signal samples and for the others H → γγ backgrounds (photon plus jet, jet-jet and diphoton). is expected as a result of using ρ as an input variable.

In the analysis a selection at -0.9 is applied on the BDT output as a further preselection which guarantees 99% eciency on signal photons. The BDT output values for each photon are used as an input to a diphoton event-level multivariate classier, described in Section 4.8. A validation of the extent to which the MVA inputs and output in data are well modeled by simulation can be performed using electrons reconstructed as photons in Z → ee events. Even if the Z boson diers from a Higgs signal in many aspects, a comparison for Z → ee events in simulation and data constitutes an important check to be sure that the modeling of the BDT input variables and their correlations in the simulation is suciently accurate.

Photon reconstruction and identication

Contrary to the standard analysis, in the validation events are selected with the inverted electron veto applied as part of the preselection, in order to keep both electrons decaying from the Z boson. In addition to the sliding p T /m γγ criteria applied in the preselection (see Section 4.4), the leading and subleading photons are also required to satisfy p T > 35 and 25 GeV, respectively, in order to prevent transverse momentum thresholds falling below trigger thresholds for low diphoton invariant masses. Finally, to have a purer dielectron sample, each pair is required to have an invariant mass between 86 and 94 GeV.

Data-simulation comparison showed a reasonable agreement for the photon identication input variables, except for three of them: important discrepancies arose for some shower shape variables, in particular for R 9 , S 4 and SC η-width. These discrepancies are present especially for photons in the barrel, and their origin is still under investigation. In order to improve the data/MC agreement these variables were corrected using a histogram remapping method with a sample of probes from Z events. Figure 3.22 shows the data/MC comparison before the correction is applied, both for barrel and endcap. The nal training of the photon identication, presented in Section 3.3.2, was done using shower shape variables after the correction.

Some discrepancies between data and simulation were observed also for the photon identication output, and they were included in the systematic uncertainty. As a rst step, the treatment of systematic uncertainty for the photon identication output variable was done in a way similar to Run 1 [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF], shifting its value for every photon in the simulation by ±0.03. In spite of that, a small discrepancy was observed in the low score tail. Since one of the main sources of systematic uncertainty on the diphoton MVA output derives from the photon ID MVA (see Section 4.8.2), the imperfect coverage on the photon ID tail is reected in the diphoton BDT tail. In order to take this into account, it was decided to be conservative and to estimate systematic uncertainty combining the shift of ±0.03

Photon reconstruction and identication

This way of estimating the systematic uncertainty is quite coarse, but before proceeding with more complex studies we need to understand the origin of the discrepancies between data and MC. The corrections applied to R 9 , S 4 and SC η-width brought some improvement, but it is possible that little discrepancies present in other variables entering the photon identication training can aect the nal output.

Summary

In this chapter the photon reconstruction and identication algorithms of CMS are presented, with a particular focus on the dierences between the rst and the second run of the LHC. Performances of Run 1 and Run 2 reconstructions from the photon identication point of view are compared and found to be very similar. The optimisation of the photon identication algorithm for the Run 2 H → γγ analysis is then described. Performances of the photon identication at 13 TeV and a data-simulation validation are nally presented.

The treatment of the systematic uncertainties is for the moment quite coarse and can be improved in the future. First of all it would be important to understand the origin of the discrepancies between data and MC. After that, it would be interesting to nd a method for the systematics estimation that takes into account the correlations between the variables entering the photon ID MVA. Some work was started for that, but it is far from a conclusive result. Another important contribution I gave to this analysis, as MC contact of the H → γγ group, concern the production of all the simulation samples needed to perform the analysis. This is the rst H → γγ analysis performed at 13 TeV after the restart of the LHC, and its results have been presented at ICHEP 2016. The main goal of the analysis is the rediscovery of the Higgs boson, waiting for more data to perform property studies.

Summary

Despite its small branching ratio of 0.23% for an Higgs boson mass of 125 GeV, the H → γγ decay channel provides a clean nal-state topology with an invariant mass peak that is reconstructed with great precision. For this reason the H → γγ was one of the most important channels used in the discovery and rst measurements of the Higgs boson, and in the LHC Run 2 this channel remains one of the best to perform a precise characterization of the Higgs properties.

The analysis strategy is similar to that used in Run 1. The sensitivity of the analysis is improved by categorizing events by mass resolution, signal-to-background ratio and production mechanism. Higgs production mechanisms other than gluon-gluon fusion (ggH) can be identied by selecting nal state objects in addition to the diphoton pair. The events with additional objects are tagged as exclusive categories, while those that remain untagged are the inclusive categories identied as the gluon-gluon production mechanism.

The inclusive events are categorized using a multivariate classier, that creates categories based on photon kinematics, mass-resolution, as well as other inputs to indicate the signalto-background ratio.

After the event classes are determined, the diphoton mass spectrum for each event class, The analysis is performed on 12.9 fb -1 of data collected during 2016 with 25 ns bunch spacing and magnetic eld of 3.8 T. The analysis is performed in the invariant mass region 100 GeV < m γγ < 180 GeV, blinding the region 115 GeV < m γγ < 135 GeV.

Principles of Monte Carlo simulation and H → γγ Monte Carlo samples

During the last two years I was in charge of the simulated samples production for the H → γγ group.

In this section a detailed description of the techniques to simulate a hadronic collision event, based on the factorisation of hard and soft components, is given, along with the presentation of the simulated samples of the H → γγ analysis.

High energy processes, hadron collisions

A hadronic collision is a complex phenomenon, which evolution can be described as follows:

1. The two beams collide at the intersection points. Each hadron is composed of quarks of dierent avours and gluons, which carry fractions of its momentum. The hadron composition in terms of avour and energy sharing is modelled by parton distribution functions (PDF);

2. The partons inside the colliding hadrons emit radiations, initiating a sequence of branching processes q → qg, g → q q, g → gg. Because of the large value of the strong coupling constant α S , these splittings have a high probability to occur and this gives rise to the formation of initial-state parton cascades;

3. Two partons in the cascade enter the hard interaction, at a momentum transfer scale Q 2 . The products of the hard scattering are the nal-state elementary particles, partons, leptons and bosons, that characterise the event topology. Short-lived resonances, such as Z, W ± and Higgs bosons, instantly decay into partons, leptons or photons. Even if the hard scattering subprocess is not observable, it determines the main properties of the collision event;

4. The outgoing partons (quarks and gluons) start branching and initiate nal-state cascades;

5. After every branching in the initial and nal-state showers, the momentum scale decreases down to the cuto scale Λ QCD ∼ 1 GeV, where the perturbative theory is no more valid;

4.1 Principles of Monte Carlo simulation and H → γγ Monte Carlo samples 89 6. Below Λ QCD , the strong interaction connes the partons into colourless hadrons. The connement process is followed by the decay of the unstable particles. Therefore, through fragmentation and decay, the parton cascades evolve into jets of stable and meta-stable particles which are observable in particle physics detectors.

The modelling of a hadronic collision is factorized into subprocesses, each of them relatively easy to handle with the appropriate technique. This approach is adopted in the Monte Carlo generators, the main tool to describe and reproduce the phenomenology at a hadronic collider.

To do that, the factorisation theorem allows the independent treatment of the hard scattering and of the soft non-perturbative processes. For a proton-proton collision p A p B → X, where X is a generic nal state, it can be expressed by the formula:

σ AB = dx a dx b f a (x a , Q 2 )f b (x b , Q 2 ) • σab→X (4.1)
where σ AB is the total cross-section, x a and x b are the fractions of the proton momentum carried by the two partons a and b involved in the interaction, and σab→X is the hard partonic scattering cross section. Calculating the latter with the perturbative expansion, Equation 4.1 can be written as:

σ AB = dx a dx b f a (x a , µ 2 F )f b (x b , µ 2 F ) • [σ 0 + α S (µ 2 R )σ 1 + α 2 S (µ 2 R )σ 2 + ...] ab→X (4.2)
The f a (x a , µ 2 F ) and f b (x b , µ 2

F terms are the parton distribution functions described in Sec- tion 4.1.2. The momentum transfer Q 2 is replaced by the factorisation scale parameter µ F , which indicates the separation between the hard scattering and the soft process. In the perturbative expansion, the strong coupling constant α S is evaluated at the renormalisation scale µ R . This two scale parameters are unphysical. The µ F and µ R dependence of the parton density functions and of α S is exactly compensated by the σi coecients at all perturbative orders, resulting in the invariance of the σ AB cross section under changes of their values. At a xed order, instead, the dependences do not cancel out, and a specic choice of the scale parameter values is necessary for a cross section estimation. The sensitivity of the σ AB prediction to variations of the scale parameters has to be accounted for as theoretical uncertainty.

Qualitatively, the factorisation theorem states that the hard scattering and the soft components of a hadronic collision can be disentangled, and independently modelled. The hard-scattering component for a specic process of interest can be solved in the context of the well known perturbation theory. Dierent methods are available, as described in Various PDF sets are available: their main dierence is the number of parameters of the model and the series of data used to t the processes. The most common ones are CTEQ [START_REF] Nadolsky | Progress in CTEQ-TEA PDF Analysis[END_REF], MSTW [START_REF] Martin | Parton distributions for the LHC[END_REF] and NNPDF [START_REF] Ball | Impact of Bibliography 199 Heavy Quark Masses on Parton Distributions and LHC Phenomenology[END_REF].

Steps in the event generation process

Monte Carlo event generation is used to simulate the nal states of high-energy collisions in full detail down to the level of individual stable particles. The aim is to generate a large number of simulated collision events, each consisting of a list of nal-state particles and their 4-momenta, such that the probability to produce an event is proportional to the probability that the corresponding actual event is produced in the real data. The event generation for a hadron-hadron collision is generally split into dierent steps by taking advantage of factorization theorem. An overview of the steps needed to obtain such a complete event is given in Figure 4.1. More details about the single steps in the event generation will follow in the subsequent paragraphs.

The computation of the hard subprocess (Matrix Element ME)

The rst step in the event generation is the simulation of the hard subprocess. The hard process is dened by the collision of two particle beam constituents which interact with each other at a high momentum scale. Thus the strong coupling constant α S is rather small for the hard subprocess, which can be described with perturbation theory and by a matrix element.

To describe the computation of the hard subprocess in more detail the collision of two protons, each consisting of partons (quarks and gluons, each with a colour charge), is

The parton shower step (PS)

After the hard collision a parton shower is used to evolve the event further. Due to the large momentum transfers during the hard subprocess step, the nal-state particles gluons. This leads to a parton shower which does not stop until the involved partons have decreased their energy by collinear parton splitting and/or soft gluon emission so much that they enter the hadronization phase. Dierent approximation schemes exist to describe the parton shower and, in principle, the showers represent higher-order corrections to the hard subprocess. However, we should keep in mind that the parton shower generally produces only low-energy additional radiation due to the collinear parton splitting and soft gluon emission and that for non-collinear parton splitting the parton shower approximation diverges. For this reason, the parton shower can ll phase-space for higher orders of perturbation theory, which are not covered by the matrix element of the hard process, but the emission of additional hard radiation is suppressed. Furthermore, a matching between the matrix element computation for the hard process and the parton shower is needed, otherwise some parts of the phase-space would be lled twice (see Section 4.1.5). The splitting of partons in the initial-state (before the hard interaction took place) and in the nal-state (after the hard interaction) by emitting gluons is schematically illustrated in

The hadronization process

During the parton shower the involved partons lose energy by splitting and gluon emission, at the same time the strong coupling constant α S rises due to its running. In this evolution

The underlying event

In the previous steps the interactions of the partons, which were part of the colliding protons but not participating in the hard subprocess, were neglected. As a rst approximation it was assumed that these beam remnants keep on ying undisturbed. However they can also split and emit gluons themselves and take part in the hadronization process together with their emitted daughter partons. In This ends the event generation per-se. However, in a full analysis the Monte Carlo event generation continues with the following steps:

Pile-up simulation

In the same bunch crossing there are multiple p-p interactions, which constitute the socalled pile-up. The pile-up is reproduced adding to the underlying event additional simulated events.

Detector simulation

In order to represent the response of the CMS detector with respect to the nal state particles, a full detector simulation is performed, including the propagation of each particle in the magnetic eld and the interactions of each particle with the passive and active elements of the detector. This simulation is performed using Geant 4 [START_REF] Agostinelli | GEANT4: A Simulation toolkit[END_REF] and a detailed implementation of the CMS geometry. Interactions with the material are simulated for each particle, including energy loss, Bremsstrahlung and photon conversions. For active detector elements, the simulated energy deposits are processed through a simulation of the readout electronics for each subdetector, including eects such as simulated noise.

Reconstruction and identication step

In a rst step a particle detector only measures hits of the nal-state particles in the single detector cells of their subdetectors. Afterwards tracks and particle objects can be reconstructed by using these informations applying reconstruction algorithms which make use of the specic properties of dierent particle types. In a last step, the obtained information is gathered and the particle objects are identied as particles.

Types of event generators

Monte Carlo event generators play an essential role in QCD modelling and in data analysis for high-energy physics. Dierent types of event generators exist, and in particular two types of event generators are used in the event generation for the LHC and will be explained in more detail.

GPMC event generators

The so-called general-purpose Monte Carlo (GPMC) event generators allow the complete simulation of high-energy physics processes. For this purpose, the GPMC event generators include low-order (LO and/or NLO) matrix elements for 2 → 1 and 2 → 2 process as well as parton shower, in which the shower evolution has to be independent from the details of 96 4. H → γγ analysis at 13 TeV the hard scattering and relies only on a few features of the matrix element: the energies and avours of incoming and outgoing partons in the matrix element as well as the overall energy scale Q 2 of the hard subprocess must be known by the successive parton shower.

GPMC event generators include beside parton shower algorithms also hadronization models and, therefore, allow to describe physics processes starting from the matrix element up to the hadron formation and decay. Dierent GPMC event generators can be mainly distinguished by their choice of the evolution scale t (which models the progression of the parton shower), the implemented hadronization and hadron decay models, and the available matrix elements.

The main generators of this type are Herwig, Pythia and Sherpa. The last two are used in the H → γγ analysis to model the background (see Section 4.1.6). In particular we used Pythia8 [START_REF] Skands | A Brief Introduction to PYTHIA 8[END_REF], which contains a wide range of hard-coded subprocesses and a highly developed multiple-interaction model for the underlying event. Sherpa [START_REF] Gleisberg | Event generation with SHERPA 1.1[END_REF] has two built-in matrix-element generators, AMEGIC++ and Comix, which allow to generate LO and NLO matrix elements for a wide range of subprocesses and are not limited to 2 → 2 processes.

Additionally, Sherpa contains a multiple-interaction model which is loosely based on that of Pythia.

ME+PS and NLO+PS event generators

GPMC event generators have a big disadvantage: they rely on parton shower algorithms which are based upon a combination of collinear (small-angle) and soft (small-energy) approximations. This approximation proves to be inaccurate for hard, large-angle emissions.

Thus the GPMC event generators make use of the so-called Matrix Element Corrections (MEC), which correct the emission of the hardest jet at large angles in a 2 → 1 or 2 → 2 process. Nevertheless, in the past decade, so-called Matrix Element and Parton Shower matching (ME+PS) event generators together with NLO and Parton Shower matching (NLO+PS) event generators were developed to improve the parton shower description of the hard scattering process and to get rid of the limitation to 2 → 1 and 2 → 2 processes. The main focus of these programs lays on the use of exact matrix elements for the hard subprocess. Due to the accurate description of the hard subprocess these generators strive for more advanced techniques for the generation of the matrix elements and the phase space calculation have to be applied resulting in more dicult computations. The matrix element event generators still depend on GPMC generators for the parton shower and hadronization, so that elaborated matching procedures between the matrix element generator and the parton shower are needed (see Section 4.1.5). In contrast to the ME+PS event generators, the NLO+PS event generators extend the accuracy of the generation of the basic process at NLO in QCD. For this purpose, the NLO+PS event generators contain also real emission and virtual loop matrix elements beside the Born matrix elements.

Two of the most common event generators of this type, MadGraph5_aMC@NLO [56] and 4.1 Principles of Monte Carlo simulation and H → γγ Monte Carlo samples 97 POWHEG Box [START_REF] Alioli | A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX[END_REF], are used in the H → γγ analysis, in particular to generate signal samples. These two event generators have a ME+PS operation mode as well as a NLO+PS operation mode.

MadGraph5_aMC@NLO is a fusion of the LO ME+PS event generator MadGraph5 and the NLO+PS event generator aMC@NLO. At the end of 2013 it was the rst public event generator which allowed to perform a NLO computation and optional matching with a GPMC event generator without the need to include further external dependencies. Mad-Graph5_aMC@NLO additionally includes the MadSpin tool [START_REF] Artoisenet | Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations[END_REF] for the proper treatment of the decay of parton-level events. If MadSpin is applied to the particle decay spin correlations between the decaying particles are preserved with very good accuracy.

POWHEG Box is a general framework for implementing NLO matrix element computations in GPMC event generators and makes use of the POWHEG method [59]. The particularity of POWHEG Box is that it cannot be used for arbitrary processes because for each process the LO and NLO matrix element computation of the hard subprocess has to be provided in the form of a program package. A large number of processes of general interest for high-energy physics were implemented and are now available in POWHEG Box.

Combining matrix element and parton shower: the jet matching

As previously discussed, the matrix element and parton shower techniques are appropriate for modelling dierent phase-space: the matrix element calculation is the most reliable for the hard scattering subprocess, while the parton shower is more suitable for soft and collinear radiation emissions and jet formation. Under these premises, it is evident that a combination (matching) of these two approaches would be the best solution for the extraction of theoretical predictions to compare to data.

The main obstacle to the practical implementation of the matching is the denition of the separation between the hard component of the process, to be solved with the matrix element calculation, and the soft and collinear emissions that instead have to be done by the parton shower. There is in fact an intrinsic ambiguity: an event with a given number N of jets can be produced either from a matrix element with N outgoing partons or from a matrix element with (N-1) outgoing partons plus a jet coming from parton shower.

The two approaches are equivalent and lead to the same result. Since factorisation theorems are not rigorously applicable to complex nal state topologies, a specic factorisation prescription, the matching scheme, is introduced, identifying on an event-by-event basis the approach that provides the best description of a given conguration. The aim of the matching scheme is to avoid double counting in the phase-space regions of overlap between the matrix element calculation and the parton shower. The most natural solution is to apply a cuto, called matching scale: branchings occurring at a scale harder than the 4. H → γγ analysis at 13 TeV cuto are handled by the matrix element calculation, while softer radiation emissions are left to the shower program. The matching scale being unphysical, the resulting theoretical predictions should not depend, or at least show a small dependence on the choice of the cuto.

Several matching schemes have been developed, such as the CKKW [START_REF] Catani | QCD matrix elements + parton showers[END_REF], the MLM [START_REF] Alwall | Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions[END_REF] and the FxFx [START_REF] Frederix | Merging meets matching in MC@NLO[END_REF]. In MadGraph5_aMC@NLO the matching between the NLO matrix element computation and the parton shower is done by introducing so-called MC counterterms and a subtraction scheme. By adding or subtracting these MC counterterms during the computation of the parton-level short-distance cross sections the overlaps are taken into account and the parton shower can later be applied to the parton-level events. The necessary MC counterterms can be computed in a process-independent manner, but they depend on the particular parton shower and lead to a specic set of MC subtraction terms for each specic parton shower. Because of the MC counterterms, event samples generated by MadGraph5_aMC@NLO consist of a large number of events with positive weight, but also include a small number of events with negative weights. As a rule of thumb, the fraction of events with negative weights increases for processes with higher multiplicities.

On the other hand, in POWHEG the hardest emission is generated with NLO accuracy at rst and independently from the subsequent parton shower which is matched to the matrix element generator part. In this way, also for NLO event generation no subtraction terms are required.

H → γγ Monte Carlo samples

The data sample used for this analysis corresponds to an integrated luminosity of 12.9 f b -1 , recorded at the LHC in pp collisions at a center-of-mass energy of 13 TeV.

Monte Carlo simulation is used to model Higgs to diphoton signal, after appropriate validation and corrections, in order to measure signal properties. Monte Carlo simulations of the background processes are used only to optimize the selection requirements and to train various multivariate discriminators, but are not used for the nal analysis, and the results do not depend on a proper description of the background processes by the corresponding Monte Carlo simulation.

The signal samples produced for the standard H → γγ analysis consist of all the four production modes, for seven dierent mass points (120, 123, 124, 125, 126, 127 and 130 GeV).

The dierent mass points are used for the construction of a parametric signal model, as explained in Section 4.12.

Concerning the background, as already mentioned in Section 3.2.1, a large irreducible background is present from QCD diphoton production in both quark and gluon initial states.

Leading order diagrams for the quark-initiated Born diphoton production and the gluon initiated box di-photon production are shown in Figure 4.7.

Despite the fact that the gluon-induced process does not exist at tree-level, the contribution is comparable to the The software used for the matrix element step varies according to the availability of implementations for each desired process, using a mixture of POWHEG [START_REF] Alioli | A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX[END_REF], MadGraph5_aMC@NLO [START_REF] Alwall | The automated computation of tree-level and next-to-leading order dierential cross sections, and their matching to parton shower simulations[END_REF] and Pythia 8 [START_REF] Skands | A Brief Introduction to PYTHIA 8[END_REF], where POWHEG and MadGraph5_aMC@NLO use NLO matrix elements, while Pythia uses LO matrix elements. In particular MadGraph5_aMC@NLO is the new version of both MadGraph5 and aMC@NLO that unies the LO and NLO lines of development of automated tools within the MadGraph family.

The signal samples are generated both with POWHEG and MadGraph5_aMC@NLO, although it was decided to use MadGraph5_aMC@NLO in the analysis. The parton level samples are interfaced to Pythia 8 for parton showering and hadronization.

Dierent generators are used to generate the simulated samples for the background: Pythia 8, MadGraph5_aMC@NLO interfaced with Pythia 8, and the matrix element Sherpa generator which also generates the particle shower. The QCD diphoton prompt-prompt background, for example, is modeled with the Sherpa generator. It includes the born processes with up to 3 additional jets at LO accuracy as well as the box processes at LO. Prompt-fake and fake-fake backgrounds are instead modeled with Pythia 8.

In order to select the events which are likely to pass the later diphoton selection of the analysis, I developed a double EM-enriched lter for the production of the QCD di-jet and γ+jet samples. In this way computing power for the further simulation of interactions between the particles and the detector was saved. This lter requires a potential photon signal (electromagnetic activity), coming from photons, electrons, or neutral hadrons, with p T > 15 GeV. In addition it is required that this potential photon signal has no more than two charged particles in a cone ∆R < 0.2, mimicking a tracker isolation. These charged particles consist of electrons, muons, taus, pions and kaons. They are required to have p T > 1.6 GeV and |η| < 2.2. For each event, the potential photon signals are coupled together to form double EM enriched objects. Just the couples passing particular cuts are kept.

The DY sample is simulated with MadGraph5_aMC@NLO.

A complete list of simulated processes, generated at 13 TeV, as well as the corresponding matrix element generators are given in Table 4.1 Since the parton shower step may add additional photons to the event with respect to the matrix element, some care must be taken to avoid double counting of background processes. In particular, QCD photon + jet events with one additional photon added by the parton shower are already included in the Sherpa diphoton + jets sample. Because the matrix element is expected to describe the

Process Matrix Element

Gluon Fusion Higgs MadGraph5_aMC@NLO -POWHEG Vector Boson Fusion Higgs MadGraph5_aMC@NLO -POWHEG W/Z Associated Production Higgs MadGraph5_aMC@NLO -POWHEG t t Associated Production Higgs MadGraph5_aMC@NLO -POWHEG Drell-Yan di-lepton + 0-2 jets MadGraph5_aMC@NLO QCD di-photon (gluon-gluon box and Born diagrams) Sherpa QCD Photon + jet Pt-20to40 Pythia QCD Photon + jet Pt-40toInf Pythia QCD Di-jet Pt-30to40 Pythia QCD Di-jet Pt-40toInf Pythia kinematics of such events better than the parton shower, these events need to be removed from the Pythia sample at analysis stage. Similarly, QCD di-jet events with two photons added by the parton shower are already included in the Sherpa diphoton + jets sample, and need to be removed from the Pythia sample.

The cross-sections for signal processes have been computed up to NNLO+NNLL and are documented in Reference [START_REF]LHC Higgs Cross Section Working Group[END_REF]. The cross-sections for background processes, where used for optimization, are computed from the LO matrix element generators.

Pile-up conditions are simulated such that the running conditions of the 2016 run are covered. The pile-up scenario accounts for multiple pp collisions happening in the same bunch crossing as well as for 25 ns out-of-time pile-up in a window of [-12,+4] bunch crossings. The average number of pile-up events in data is 18.5. Events in the simulated samples are weighted such that the resulting pile-up distribution matches that of data. To validate the weighting technique that is applied to the simulation in order to match the actual pile-up events distribution observed in the data, the comparison of the number of reconstructed vertices is done between the data and the simulation after reweighting for a sample of DY → ee events. The distribution is shown in Figure 4.9.

Trigger

The events entering in this analysis must rstly pass a hardware level trigger (L1) followed by a software level trigger (HLT) decision. Since a certain number of events would be able to pass the analysis selection but not the diphoton trigger one, the trigger has an eciency smaller than one, reducing the number of events which can enter the analysis. To measure the trigger eciencies, one needs to evaluate separately the eciency of the L1-seeding (L1 eciency) and the eciency of the HLT lters, provided that the L1 requirement has been satised. For eciency measurements the tag and probe method on Z → ee data is used (see Appendix A for a description of the tag and probe method). The diphoton trigger and the measurement of its eciency are described below.

Level 1 trigger

Each high level trigger diphoton path is seeded by at least one hardware level 1 electromagnetic candidate. Because of bandwidth limitations at the L1, 40 GeV is the lowest transverse momentum of single electromagnetic L1 candidates, giving a few percent ineciency at the lowest transverse energy of the analysis selection. This is mitigated seeding the HLT paths also by a L1 pair of 22 and 10 GeV respectively. Figure 4.10 shows the L1

eciency measured with the tag and probe technique on Z → ee data, as a function of the probe p T .

Given an L1 seed, the ECAL clustering algorithm is performed by the HLT from the readout units overlapping a rectangle centered on the L1 candidate, extended from the rectangle of the L1 segment by ∆η × ∆Φ = 0.14 × 0.4. The requirements of the HLT diphoton path are then applied.

High level trigger

The • general variables: E T of both photons, m γγ , H/E (with modied cone size R = 0.14),

• variables used in Iso+CaloId paths: σ iηiη (full5x5), ECAL PF Cluster ISO, Tracker isolation in a hollowcone (with modied R = 0.29 outer and R = 0.06 inner radii),

• variables used in R 9 paths: R 9 (full5x5).

The L1-seeded leg of the HLT is required to have E T > 30 GeV. The cluster must have |η| < 2.5 and R 9 > 0.5 (0.8) in EB (EE). In addition the cut H/E < 0.12(0.1) in EB (EE) is applied. After that, the clusters are ltered by an R 9 > 0.85 (0.9) EB (EE) selection; if passing, the clusters continue to the unseeded step without going through the Iso+CaloId lters, if failing, the clusters must pass the Iso+CaloId selection, which consists of σ iηiη < 0.015 (0.035) EB (EE) and ECAL isolation < 6.0 + 0.012 E T .

If at least one cluster passes the previous criterion, the entire ECAL is clustered. Two clusters, with one corresponding to the seeded HLT cluster, are now required on the unseeded leg: an E T > 18 GeV cut is applied, the remainder of the selection is the same as for the seeded leg with the addition that both legs are required to pass tracker isolation < 6.0 + 0.002 E T .

The mass of the diphoton object is nally required to be above 90 GeV.

H → γγ analysis at 13 TeV

Trigger performance

The eciency of the trigger selection is studied using the tag and probe technique. The eciency of both the seeded and unseeded leg of the diphoton HLT path is measured on Z → ee data events. It is possible to select high purity Z → ee events requiring events to pass a tag and probe trigger and requiring an additional oine selection. Since the tag and probe trigger only requires a single electron, the second electron is an unbiased probe to measure the eciency of the diphoton path. To account for the shower shape dierence between electrons and photons (as well as the dierent η distributions for Z → ee and H → γγ), due to the material upstream of the ECAL, the entries to the eciencies are weighted in R 9 and η from the respective simulated samples in order to match the H → γγ distributions. This brings to an event migration to higher R 9 values, which gives an overall increase of the measured eciency of the Z → ee events. The HLT eciency of both the seeded and unseeded leg of the diphoton trigger with respect to the oine photon p T is shown in Figure 4.11. For the majority of simulated samples used in this analysis the analysis trigger was not simulated. This means that there is no trigger applied on the simulated events in our analysis. After the analysis preselection is applied the trigger is reasonably ecient, but corrections must still be applied to the simulation to replicate the ineciency of the trigger in data.

The eciency measured on data, binned in E T , R 9 and η, is used to scale the simulation.

The scale factors are a combination of the HLT and L1 eciency presented earlier in this section to properly simulate the seeding of the HLT by the L1. These scale factors are applied to the simulation to replicate the eect of the trigger.

Since the application of trigger scale factors aects both the signal and background yields 4.3 Photon energy correction 105 from simulation, a log-normal asymmetric uncertainty calculated from the tag and probe ts to the Z-peak is applied.

Photon energy correction

Dierent sets of corrections are necessary in order to achieve the best photon energy resolution. The rst consists of crystal-level corrections needed to equalize the channel-to-channel response variations. The second, an high-level correction method called photon energy regression, takes into account ner eects, like the containment of the shower and the energy losses. This method is based on a multivariate approach and it provides a per-photon energy resolution estimator, which is used for the diphoton BDT as described in Section 4.8.

Further dierences between data and simulation are resolved using Z → ee with electrons reconstructed as photons. The energy scale is corrected in data and a smearing is applied to MC in order to have the best agreement between data and simulation for photon energy scale and resolution. Figure 4.12 shows the comparison of simulation to data for the Z invariant mass plots in η, R 9 categories after all the energy corrections described above have been applied. A more detailed description on the photon energy corrections is given in Appendix B.

Event preselection

For each event with at least two reconstructed photons, the diphoton pairs are rst reconstructed by grouping the photons into all possible two photon combinations. A primary vertex is assigned to each diphoton pair, as described in Section 4.5. The momentum of each photon is built with its magnitude obtained from the corrected photon energy as described in Section 4.3 and its direction pointing from the selected vertex to the supercluster. A preselection designed to match the HLT requirements is then applied on each photon, in order to keep the same phase space in data and in simulation (where the HLT is not applied). The preselection, tuned to be tighter than the trigger, includes a cut on the acceptance of supercluster pseudorapidity measured with respect to the origin of the detector coordinate η SC , a set of loose photon identication cuts against jets faking photons and an electron veto:

• the cuts on the acceptance of the supercluster pseudorapidity, which aim to exclude the transition region between the ECAL barrel and endcap and the region outside the tracker acceptance, are |η SC | < 1.442 in the barrel or 1.566 < |η SC | < 2.5 in the endcap,

• the ECAL shower shape and isolation variables used in the loose photon identication cuts are the following: H/E, σ iηiη (full5x5), R 9 (full5x5), Photon ISO and Tracker ISO (both the isolations with a ρ correction applied to match the HLT).

To apply these cuts, the photons are classied into four categories according to the photon supercluster location in the ECAL (barrel or endcap) and the value of R 9 (> 0.85 or ≤ 0.85 in the barrel, > 0.9 or ≤ 0.9 in the endcap). The photons in the barrel and endcap are treated separately because the geometry of the crystals and the amount of tracker materials in front are dierent in the two cases. The values of the loose photon identication cuts are summarised in Table 4.2,

• the electron veto is used to distinguish electrons from photons. A photon candidate is removed if its supercluster is matched to an electron track. To avoid rejecting the converted photons, the electron track is required to have no missing hits in the tracker before its rst hit, and not to match an identied conversion.

In addition the leading photon (photon with the largest p T ) is required to have p T > 30 GeV, while the subleading one (photon with the second largest p T ) must have p T > 20

GeV.

Finally we apply a set of diphoton kinematic acceptance cuts, determined to select the phase space right above the trigger threshold and to dene a region for the diphoton mass t. The cuts include m γγ > 95 GeV, 100 GeV < m γγ < 180 GeV, p γ1 T /m γγ > 1/3 and p γ2 T /m γγ > 1/4, for the leading photon γ1 and the subleading photon γ2 respectively. Preselection eciencies in the four photon categories are evaluated with the tag and probe technique using electrons from Z → ee events, for which the electron R 9 is rescaled to match photon R 9 distribution in H → γγ simulation. Data and simulation eciencies are then compared in order to calculate the appropriate scale factors. By denition the tag and probe technique using Z → ee events does not allow to measure the electron veto eciency, which is instead measured independently using Z → µµγ events. Table 4.3 shows the eciencies calculated on Z → ee events for data, simulation, and their ratio in four η, R with Z → ee events (for all preselection criteria except electron veto).

Diphoton vertex identication 107

Diphoton vertex identication

In the decay of the Higgs boson into two photons the determination of the primary vertex associated with the signal is very important, because the vertex choice has a direct impact on the diphoton mass resolution (a wrong choice would worsen the resolution by about 1

GeV on average), and it is not trivial for two main reasons. Firstly, the nal state unconverted photons are not detected in the tracker and the electromagnetic calorimeter alone 4. H → γγ analysis at 13 TeV cannot be used for pointing, as it does not have a longitudinal segmentation. Secondly, the diphoton production vertex needs to be selected from an average of 18.5 pp collision vertices distributed in z with an RMS of about 4 cm. In order to discriminate between the diphoton production vertex and the pileup vertices, we use the knowledge that the total transverse momentum of the recoiling tracks associated with the diphoton production vertex roughly balances the diphoton transverse momentum plus the fact that a hard vertex produces high p T tracks compared to a minimum bias one. Even if the balance is not exact as we do not have the association between neutral particles and vertices, it is possible to build some variables having dierent distributions for the recoiling tracks of the diphoton production vertex and those of the pileup vertices. The discrimination power provided by these variables can nally be exploited using a multivariate tool. In addition to the correlation between the kinematics of the recoiling tracks and that of the diphoton, when at least one of the photons is converted in the tracker the position of the conversion vertex, together with either the direction of the conversion momentum or the position of the ECAL supercluster, provides an extrapolation of the position of the diphoton vertex, which is used for the vertex selection. Therefore we train a BDT using the above information, to distinguish between the prompt vertex and the pileup vertices. The BDT assigns a score to each vertex according to how likely it is to be the γγ vertex, and the vertex with the highest score is selected. The eect of the vertex selection on the diphoton mass resolution is negligible with respect to the single photon energy resolution if the selected diphoton vertex is required to be within 1 cm in z from the actual diphoton vertex. A per-event probability to choose the right vertex is also determined, giving the full benet of the excellent ECAL resolution.

A more detailed description on the diphoton vertex identication is given in Appendix C.

Photon identication

Photon identication for the H → γγ analysis is explained in detail in Chapter 3.

Event classication

In order to improve the sensitivity of the analysis, diphoton events passing the preselection and having an output value of the photon identication BDT greater than -0.9 (see Section These events with additional objects are tagged as exclusive categories, while the untagged ones belong to the inclusive categories and identify the gluon fusion production mechanism.

If more than one diphoton candidate is present, the candidate with the highest priority tag is selected. In the case of multiple diphotons with equal tag priority, the diphoton with the maximum scalar sum of photon transverse momentum is used for the analysis. The event tagging priority sequence is based on the signal purity and is as following:

• rst, events with leptons from the leptonic or semi-leptonic top decays are selected (ttH leptonic tag),

• second, remaining events with jets from hadronic top decays are selected (ttH hadronic tag),

• then events with two forward jets are selected and divided into two VBF categories,

• nally remaining events, without additional objects, are classied in four dierent untagged categories (see later).

The inclusive events are categorized using a multivariate classier. The multivariate diphoton classier, described in the next section, divides the untagged events in four categories based on photon kinematics, mass-resolution and other inputs indicating the signal-tobackground ratio.

Diphoton BDT

Classier setup and performance

As already said in the previous section, an increase of the sensitivity of the analysis is obtained categorizing the events. In this way the high-perfomance categories are characterised by a higher signal-to-background ratio and a better mass resolution.

The untagged events are categorized using the output of a multivariate event classier, implemented using a BDT, which goal is to assign high scores to events with two photons fullling the following criteria:

• signal-like kinematic characteristics,

• good diphoton mass resolution,

• photon identication BDT score in the photon-like region.

H → γγ analysis at 13 TeV

The events with two photons entering the diphoton classier, must satisfy the preselection criteria described in Section 4.4, with an additional loose cut on the photon ID BDT output (> -0.9) which is 99% ecient on signal events. In addition photons have to pass a diphoton mass-dependent requirement on the transverse momentum, that is p T > 1/3 (1/4) m γγ for the leading (subleading) photon.

The set of input variables is chosen such that the diphoton system mass cannot be inferred from these variables, in this way the classier result cannot be biased by the specic mass of the signal used as training sample. For this purpose, dimensional variables are rescaled by the mass of the diphoton system.

The variables entering the diphoton event classier are therefore the following:

• the transverse momenta of both photons, rescaled for the diphoton mass, p

1(2) T /m γγ ,
• the pseudorapidities of both photons, η 1(2) ,

• the cosine of the angle between the two photons in the transverse plane, cos(∆Φ γγ ),

• the identication BDT score for both photons,

• the per-event relative mass resolution estimate, under the hypothesis that the mass has been reconstructed using the correct primary vertex (σ rv ),

• the per-event relative mass resolution estimate, under the hypothesis that the mass has been reconstructed using an incorrect primary vertex (σ wv ),

• the per-event probability estimate that the correct primary vertex has been used to reconstruct the mass, based on the event-level vertex selection BDT as described in Section 4.5.

The per-event relative mass resolution estimate assuming the correct vertex is computed as the sum in quadrature of the per-photon energy resolution estimators of the leading and subleading photon as:

σ rv = σ right m /m γγ = 1 2 σ E1 E 1 2 + σ E2 E 2 2
.

In order to correctly estimate the mass resolution for those events where an incorrect primary vertex is selected, the estimator of the mass resolution includes an additional term σ vtx given by the displacement between the correct and the selected primary vertex.

The distance between the selected vertex and the true one is distributed as a Gaussian with width √ 2σ beamspot Z and the term σ vtx can be computed analytically given the impact positions of the two photons in the calorimeter. The relative mass resolution under the incorrect vertex hypothesis is therefore computed as:

σ wv = σ wrong m /m γγ = σ right m /m γγ 2 + σ vtx m /m γγ 2 .

Diphoton BDT 111

In order to provide to the BDT training the information that signal-to-background is inversely proportional to mass resolution, the signal events entering the training are weighted as follows:

w sig = p vtx σ rv + 1 -p vtx σ wv ,
where p vtx is the probability of the selected vertex being the right one estimated from vertex probability BDT, while σ rv and σ wv are the relative mass resolutions assuming the correct/wrong vertex is selected. In this way the events with better mass resolution get higher weights and appear more signal like.

The diphoton BDT is trained on samples simulating signal and background processes at 13 TeV. The signal sample consists of H → γγ events at a Higgs mass of 125 GeV, with all four production processes weighted by cross section. The background sample consists of a proper mixture of prompt-prompt (from diphoton+jets sample), prompt-fake (from photon+jet and QCD di-jet samples) and fake-fake (from QCD di-jet samples) events.

The diphoton BDT discriminating power between signal and background events is summarised in Figure 4.13, where the ROC curve of the classier and the normalised BDT output variable for signal and background are shown. Figure 4.14 shows the diphoton have a at distribution for the cross-section weighted sum of the four signal samples, allowing to have a more immediate visualisation of the BDT performances. From the signal processes distribution it is evident that VBF, VH, and ttH processes tend to accumulate at higher BDT scores compared to gluon fusion, because of the harder Higgs p T spectrum.

On the other hand the distribution for the dierent background components shows that events contained in the diphoton+jets sample cluster in a region at high values of BDT score, since they are characterised by photons with good photon ID values and better resolution compared to prompt-fake and fake-fake components coming from γ+jet and QCD di-jet samples.

Systematic uncertainties

In the H → γγ analysis the background is modelled in a fully data-driven manner, so the result does not depend on the simulation prediction for the diphoton BDT output shape of the dierent background components. The signal modelling is driven instead by the simulation prediction, where corrections from simulation to data are applied. The two main sources of systematic uncertainty on the diphoton BDT output derive from the photon ID BDT and the per-photon energy resolution estimate from the regression.

The photon ID BDT output ranges from -1 to 1, with prompt photons tending to have values close to 1. The systematic uncertainty to this variable is assigned shifting its value for every photon in the simulation according to a transformation combining a shift of ± 0.03 with a linear increase of the uncertainty for events having a low photon ID BDT score.

Since larger values of the photon ID BDT tend to lead to a larger value of the diphoton BDT, the simultaneous translation of the photon ID BDT for both photons produces the maximal migration of events in the diphoton BDT output, which is then considered as a migration of the signal yield among the nal event classes.

The per-photon resolution estimate is aected by imperfect modelling of the electromagnetic shower shape in the simulation. The diphoton BDT output is inuenced by this quantity because of its impact on the mass resolution estimates, both under the right and wrong vertex hypotheses (σ rv and σ wv ). The systematic uncertainty from imperfect modelling of σ E /E is assigned shifting its value by ±5% for each photon. The diphoton BDT is expected to have lower values for larger energy resolution estimates and thus to produce the maximum event migration for simultaneous shifts.

The impact of these two sources of systematic uncertainty on the transformed diphoton BDT output variable is shown in Figure 4. [START_REF] Aad | Combined Measurement of the Higgs Boson Mass in pp Collisions at √ s = 7 and 8 TeV with the ATLAS and CMS Experiments[END_REF]

Event categorisation using diphoton BDT output

The diphoton BDT is used to split the untagged events in categories. The boundaries of the categories in the BDT output spectrum are chosen as a result of an optimisation method, and it is found that splitting the events into four categories increases the expected signicance of the analysis, while further splitting does not bring substantial additional gain.

The optimisation method, for an n-category analysis, initially places n boundaries at equal distances in signal quantiles from each other, given the two xed boundaries at the edges of the spectrum -1 and 1. n + 1 categories are dened by the n boundaries, and only n are selected for the analysis and for the calculation of the expected signicance, while the events falling in the lowest-BDT score category are not used. The positions of the boundaries are free to vary and are dened minimising the combined p-value 1 . In each category, signal and background simplied models are extracted from simulation. Both models are extracted through a t to the diphoton invariant mass distribution in simulated samples. 1 The p-value is the probability P , under assumption of a null hypothesis H0, of obtaining a result as compatible or less with H0 than the one actually observed. If H0 is the background-only hypothesis, the p-value is the probability that the background uctuates to the observed value. In case of an observed excess above the expected background, the p-value is used to estimate the signicance of that excess.

VBF tag 115

The procedure is repeated from n = 2 up to n = 6; no larger values of n are explored since the gain in expected signicance is only of the order of few 0.1% increasing n from 5 to 6, as shown in Figure 4.17. Given also the small gain achievable going from n = 4 to 5, the analysis is split into 4 generic categories. The positions of boundaries are shown in Figures 4. [START_REF] Vardan Khachatryan | Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV[END_REF]

VBF tag

The events produced through the vector boson fusion (VBF) mode are characterised by the presence of two energetic jets, originating from the two scattering quarks, with large separation in η in addition to the photon pair in the nal state. Even if the cross section of this production mode is more than ten times smaller than for gluon fusion, with an appropriate selection and the use of multivariate analysis tool, two categories of events with excellent signal-to-background ratio can be dened.

The VBF candidates are rst preselected from the diphoton events by applying a set of loose cuts on dijet kinematics. To each VBF candidate is assigned a score from a kinematic dijet BDT, which provides a kinematic discriminator between the VBF events and both the background and the ggH events. Finally, events are further classied according to a BDT combining the output of the kinematic dijet BDT and of the diphoton BDT.

The jet denition, the dijet preselection cuts for the VBF candidates and the details about the kinematic dijet BDT and the combined BDT are provided below.

Jet denition

Jets are reconstructed from all particle ow candidates, clustering them through the anti-k T algorithm [START_REF] Cacciari | The anti-k t jet clustering algorithm[END_REF] with a size parameter of ∆R = 0.4. Furthermore, among the jet constituents the charged candidates associated with a vertex other than the selected vertex for the event are excluded (this is the so-called CHS technique).

For jets having |η| > 2.5, the tracker is no longer present and the CHS technique cannot be used. To cope with this problem a selection on the width of the jet is introduced: RMS < 0.03, with

RM S = constituents p 2 T ∆R 2 constituents p 2 T ,
where ∆R = (∆η) 2 + (∆φ) 2 is between the constituent and the jet axis.

The value of 0.03 is chosen by maximising the signicance of the kinematic dijet BDT.

Dijet preselection

As already said, in order to be tagged as VBF-like, the events are required to have at least 2 jets in addition to the photons. Only the two highest p T jets are considered in the selection. The dijet preselection consists of a set of loose cuts: both jets are required to have |η| < 4.7, the p T must be greater than 30 GeV for the leading jet and greater than 20 GeV for the subleading jet. Finally there is a requirement on the invariant mass of the dijet system, m jj > 250 GeV.

Kinematic dijet BDT

The goal of the kinematic dijet BDT is to provide a kinematic discriminator between the VBF events and both the background and the ggH events. It is trained on simulated events: VBF H → γγ sample with m H = 125 GeV as signal, prompt-prompt, prompt-fake and fake-fake samples as background. The gluon fusion H → γγ with m H = 125 GeV is also used in the training as an additional background, in order to improve the purity of the dijet signal.

The variables entering the kinematic dijet BDT are the following:

• the transverse momenta of the leading and subleading photons divided by the invariant mass of the di-photon candidate: p γ1 T /m γγ and p γ2 T /m γγ ,

• the transverse momenta of the leading and subleading jets: p j1 T and p j2 T ,

• the dijet invariant mass m jj ,

• the dierence in pseudorapidity between the two jets ∆η jj ,

• the Zeppenfeld variable, dened as the separation between the diphoton pseudorapidity and the average pseudorapidity of the dijet system: |η γγ -(η j1 + η j2 )/2|,

ttH tag 117

• the dierence in azimuthal angle between the dijet and the diphoton system, ∆Φ jjγγ .

Combined BDT and categorisation

The combined BDT is built using the kinematic dijet BDT, the diphoton BDT, and p γγ T /m γγ as input variables. Its goal is to maximally discriminate the VBF dijet signal from backgrounds using the information from all the relevant objects tagged in the event.

p γγ T /m γγ is used as an input because it has a strong correlation to both the dijet BDT and the diphoton BDT.

The BDT is trained on simulated events: the signal sample is the same as for the kinematic dijet BDT, while the background sample consists of the same background events as for the dijet BDT but not the ggH events.

ttH tag

The study of the ttH production channel is very important because it allows access to the coupling of the Higgs boson to the top quark, which, thanks to its high mass, might play a special role in the context of electroweak symmetry breaking.

Since the top quark decays almost always in a W boson and a b quark, the ttH nal state is composed, in addition to the photon pair, by two b-jets along with additional jets or leptons coming from the decay of W bosons. Thus two dierent sets of selection criteria are used, optimised for the leptonic and hadronic W decays, corresponding to the leptonic and hadronic ttH tags.

The jets selected are as described for the VBF tag and are required to have p T > 25 GeV and |η| < 2.4. In order to avoid the overlapping between the jets and one of the photons belonging to the photon pair, the jets must be separated from the photons with R(jet, γ) > 0.4. Finally the Secondary Vertex algorithm is used for the b-jets identication. Since the simulation for events with two photons and multiple jets in the nal state is not reliable, a control sample in data is dened to perform studies for the expected background. This control sample is built by selecting diphoton events where one of the photons is required to pass the preselection and photon ID BDT criterion (ID BDT > -0.9), while for the other photon, the photon ID BDT criterion is inverted and the preselection is not applied.

Leptonic tag

The leptonic tag is optimised for semi-leptonic and leptonic t t decays in ttH events, that is t t → b ν bq q and t t → b ν b ν , where can be either a muon or an electron. The background is fairly low thanks to an high p T isolated lepton in the nal state. The electrons are vetoed if they are found to match converted photons.

The event selection for ttH leptonic category also requires additional criteria on the number of jets along with the presence of at least one isolated lepton. Events are rst required to pass analysis preselection described in Section 4.4 and then:

• leading photon p T > m γγ /2,
• subleading photon p T > m γγ /4,

• at least one selected lepton with p T > 20 GeV,

• specic to the leptonic channel: the lepton should have R( , γ) > 0.4,

• specic to the electron channel: |m e,γ -m Z | > 10 GeV, where m Z refers to the mass of the Z boson,

• at least 2 selected jets in the event with p T > 25 GeV, |η| < 2.4, R(jet, γ) > 0.4 and R(jet, ) > 0.4,

• at least one of the jets in the event has to be b-tagged with p T > 25 GeV, • diphoton BDT > -0.4, which gives a signal eciency of 89%.

Hadronic tag

The hadronic tag is optimised for hadronic t t decays in ttH events, that is t t → bqq bqq .

Events passing the full analysis preselection described in Section 4.4 are required to pass the following selection requirements:

• photon pair selection with the highest sum of p T ,

• leading photon p T > m γγ /2,

• subleading photon p T > m γγ /4,

• no leptons (dened according to the leptonic tag),

• at least 5 jets in the event with p T > 25 GeV,

• at least one of the jets in the event has to be b-tagged with p T > 25 GeV,

• diphoton BDT > 0, which gives a signal eciency of 90% and a background eciency of 35%. These values were checked on control samples (see Figure 4.20).

4. H → γγ analysis at 13 TeV

Statistical analysis

As already mentioned in previous sections, events are classied into eight exclusive categories. Two categories allow to classify events produced in association with two jets, likely to originate from vector boson fusion (VBF), and are labelled VBF Tag 0 and VBF Tag 1, with the former being the most sensitive. Two further categories, TTH Leptonic Tag and TTH Hadronic Tag, are used to classify events likely to have been produced in association with top quarks, decaying either leptonically or hadronically. Remaining events are categorised into four inclusive categories, labelled Untagged 0, Untagged 1, Untagged 2, Untagged 3, ordered from the most to the least sensitive. Events which do not enter any of the above categories are discarded.

The overall strategy to interpret the data and to extract the Higgs signal is to perform maximum likelihood ts to the diphoton mass distribution simultaneously across all of the event categories. This requires models for the probability density functions (PDFs) of both the expected signal and the background in each category.

Simulated signal samples corresponding to each of the allowed Standard Model Higgs production processes (VBF, ttH, ggH, WH and ZH) are used to produce the signal model.

Each sample is analyzed using the procedure described in the previous sections and is divided into the categories described above. This process is repeated for seven Higgs boson mass scenarios, 120, 123, 124, 125, 126, 127 and 130 GeV, referred to as the mass points.

These simulated signal samples are used to produce a parametric signal model, described in Section 4.12.

The background model is extracted directly from data, using the discrete proling method described in Section 4.13.

Signal model

In each category MC simulation is used to extract signal eciency × acceptance and signal mass PDF. A parametric signal model is built continuously for any value of the Higgs mass between 120 and 130 GeV. The signal model is derived from the signal simulation using an analytic function, the parameters of which are determined by tting the simulated events in each category and at each of the seven Higgs mass points. Finally, the full signal model is dened by a linear interpolation of each t parameter between the tted mass values.

For each category, the simulated events for each of the four production mechanisms are used as input to the ts. The analytic functions for each production mechanism are added together according to their relative cross-sections in the Standard Model to give the nal function in each category. Furthermore it is important to take into account that the m γγ distribution changes considerably depending on whether the vertex associated with the diphoton candidate was correctly identied or not. In eect, when the correct vertex is identied the shape of the m γγ distribution is dominated by the detector resolution and reconstruction, while when the incorrect vertex is chosen the signal shape is smeared signicantly by the variation in the z position of the selected primary vertex with respect to the true Higgs production point. The cases where the right vertex (RV) and wrong vertex (WV) were chosen are tted separately when constructing the signal model.

For each production mode, category and RV/WV scenario, the m γγ distributions are tted using a sum of at most four Gaussians. The width, mean and relative size of each Gaussian are left free in the ts to the simulation. A representative set of ts for events with correct and incorrect primary vertex selection, in one particular category for gluon-fusion production are shown in Figure 4.21.

The combined shape in each category for correct and incorrect vertex selection is constructed by adding the shapes for the two sub-components together, according to the correct vertex selection eciency determined from each simulated sample. This eciency is treated as another model parameter for the purposes of interpolation between mass points, although in practice the vertex selection eciency does not vary much as a function of Higgs mass.

In order to facilitate the interpretation of the signal model in terms of a Standard Model Higgs production cross-section, and in order to facilitate the use of the signal model simultaneously across all of the event categories, the signal yield is parametrized in terms of a per class acceptance times eciency, computed from each Monte Carlo sample. Systematic uncertainties corresponding to the smearing and scale of the individual photon energies, the fraction of events where the RV was correctly identied, the material corrections and ECAL crystal light yields are incorporated into the signal model as additional parameters to be treated as nuisances.

Background model

Since the level of background after selection is large, and a comprehensive Monte Carlo description is not available at NLO or beyond, the background is instead modelled in an entirely data driven manner. The model used to describe the background is produced by tting various analytic functions to the m γγ distribution, in the 100 to 180 GeV range.

The data are then classied into the eight categories described previously. The method used to do that is the discrete proling or envelope method [START_REF] Dauncey | Handling uncertainties in background shapes: the discrete proling method[END_REF]. The discrete proling method is designed as a way to determine the systematic uncertainty associated with choosing a particular analytic function to t to the background m γγ distribution.

CMS Simulation Preliminary

The method treats the choice of the background function as a discrete parameter in the likelihood t to the data.

For each event category, four families of analytic functions are considered:

• Sums of exponentials:

f N (x) = N i=0 p 2i e p 2i+1 x ,
• Sums of polynomials (in the Bernstein basis):

f N (x) = N i=0 p i b (i,N ) , where b (i,N ) := N i x i (1 -x) N -i ,
• Laurent series:

f N (x) = N i=0 p i x -4+ i j=1 (-1) j (j-1) , 126
4. H → γγ analysis at 13 TeV

• Sums of power-law functions:

f N (x) = N i=0 p 2i x -p 2i+1 ,
where for all k, the p k are a set of oating parameters in the ts.

These functions cover a range of possible shapes for the background. For each event category, each functional form is tted to the data, with the number of degrees of freedom being determined by an F-test [START_REF] Fisher | On the Interpretation of χ 2 from Contingency Tables, and the Calculation of P[END_REF], where terms are only included if they signicantly improve the χ 2 probability of the t.

When tting these functions to the background m γγ distribution, the value of twice the negative logarithm of the likelihood (2NLL) is minimized. A penalty is added to 2NLL to take into account the number of oating parameters in each candidate function. When making a measurement of a given parameter of interest, the discrete proling method determines the envelope of the lowest values of 2NLL proled as a function of the parameter of interest. The envelope obtained through this method will yield a broader curve than the 2NLL curve obtained from a single function choice. These bands are obtained using an extended likelihood t parametrised in terms of the background yield in a 1 GeV window, which is the size of the bins in the showed histogram.

The signal model assuming m H = 125 GeV is also overlaid on the background distribution.

Systematic uncertainties

Several types of systematic uncertainty are considered in this analysis. A summary of all the systematic uncertainties along with their treatment is presented in this section.

The systematic uncertainties related to the signal shape are treated dierently depending on how they aect the m γγ distribution. Those which modify the shape of the m γγ distribution are generally built directly into the signal model as parametric nuisance parameters.

If the shape of the m γγ distribution is instead unaected, the systematic variations are treated as log-normal uncertainties on the eciency. Finally, for cases where the systematic has an eect on the input to one of the classication BDTs, the variation takes the form of a correlated log-normal uncertainty on the category yield, that is it is considered as a category migration systematic.

The systematic uncertainties considered in this analysis are listed below:

• Theory systematics: 12.9 fb On the top, the set of functions chosen to t the background using the discrete proling method is shown, for the Untagged 1 (left) and VBFTag 1 (right) categories considered in this analysis. Four families of functions are considered. An F-test [START_REF] Fisher | On the Interpretation of χ 2 from Contingency Tables, and the Calculation of P[END_REF] is used to select representative functions from each of these four families in order to proceed with the discrete proling. On the bottom, the best t background parametrization plotted alongside the data is shown in the same two categories. The green and yellow bands give a measure of the statistical uncertainty in each 1 GeV bin. The corresponding signal model for each category is also shown.

CMS Preliminary

H → γγ analysis at 13

TeV parton density functions (PDF) uncertainties: the uncertainty coming from the choice of PDF is assessed by estimating the relative yield variation in each process and category, after re-weighting the events of the simulated signal sample. The re-weighting is done according to PDF4LHC15 combined PDF set and NNPDF30 [START_REF] Demartin | The impact of PDF and alphas uncertainties on Higgs Production in gluon fusion at hadron colliders[END_REF] using the MC2hessian procedure [START_REF] Carrazza | An unbiased Hessian representation for Monte Carlo PDFs[END_REF]. The category migrations are found to be less than 2%. The overall normalization variation is taken from [START_REF] J R Andersen | Handbook of LHC Higgs Sections: 3[END_REF]. α s uncertainty: the uncertainty on the value of the strong force coupling constant α s is evaluated following the PDF4LHC prescription [START_REF] Butterworth | PDF4LHC recommendations for LHC Run II[END_REF]. The overall variation in the relative event yield due to the α s uncertainty is found to be at most 3.7%.

Underlying event and parton shower uncertainty, corresponding to the choice and tuning of the generator: this systematic uncertainty is treated as an event migration systematics as it will mainly aect the jets in the analysis. The possibility that an event could move from one VBF Tag to another or from either VBF Tag to an inclusive category is assigned a systematic uncertainty of 7% and 9% respectively.

QCD scale uncertainty, related to varying the renormalization and factorization scales: the uncertainties are taken as variations on the QCD parameters µ R and µ F . The overall eect on the normalisation is taken from [START_REF] J R Andersen | Handbook of LHC Higgs Sections: 3[END_REF] and eect on the relative category yield is found to be about 5-10%.

Uncertainty on the H→ γγ branching ratio: it is estimated to be about 2% [START_REF] J R Andersen | Handbook of LHC Higgs Sections: 3[END_REF].

Gluon fusion contamination in VBF and ttH tagged categories: the theoretical predictions for gluon fusion are not reliable in a regime where the Higgs boson is produced in association with a large number of jets. The uncertainty on the yield of gluon fusion events in the VBF tagged classes is estimated using the Stewart-Tackmann procedure, according to the LHC Higgs Cross Section Working Group [START_REF] J R Andersen | Handbook of LHC Higgs Sections: 3[END_REF] recommendations. The overall normalization is found to vary by 39% while migrations between the two VBF categories are of about 10%. The systematic uncertainty on the gluon fusion contamination in the t tH tagged classes is estimated taking into account the following contributions: * the uncertainty due to the limited size of the simulated sample is computed to be 10%. * the uncertainty coming from the parton shower modelling is estimated as the observed dierence in the jet multiplicity between MADGRAPH5_aMC@NLO predictions and data in t t +jets events, with fully leptonic t t decays. This uncertainty is found to be of about 45% in the bins with the largest discrepancy (N jets ≥ 5) [START_REF]First measurement of the dierential cross section for t¯t production in the dilepton nal state at √ s = 13 tev[END_REF].

Systematic uncertainties

129 * the uncertainty on the gluon splitting modelling is estimated by scaling the fraction of events from gluon fusion with real b-jets by the observed dierence between data and simulation in the ratio σ(t tb b)/σ(t tjj) at 13

TeV. This uncertainty implies a variation of about 18% in the yield of gluon fusion events.

• Integrated luminosity: the uncertainty on the integrated luminosity is estimated from data, and it is found to be of 6.2% on the signal yield.

• Trigger eciency: the trigger eciency is measured from Z → ee events using the tag-and-probe technique; the size of the eect on the event yields is of less than 0.1%.

• Photon preselection: the systematic uncertainty on the photon preselection is taken as the uncertainty on the ratio between the eciency measured in data and in simulation; it ranges from 0.1% to 2.3% according to the photon category and results in an event yield variation up to 4% depending on the event category.

• Vertex selection eciency: the systematic uncertainty in the vertex nding eciency is taken from the uncertainty in the measurement of the corresponding data/simulation scale factor obtained using Z → µµ events. It is handled as an additional nuisance parameter built into the signal model which allows the fraction of events in the right vertex/wrong vertex scenario to change. The size of the uncertainty of the vertex selection eciency is 1.5%.

• Energy scale and resolution: scale and resolutions are studied with electrons from Z → ee events and then applied to photons. The main source of systematic uncertainty is the dierence between electrons and photons in the interaction with material upstream the ECAL . Uncertainties are assessed by changing the R 9 distribution, the regression training (using electrons instead of photons) and the electron selection used to derive the corrections. The uncertainty on the additional energy smearing is computed propagating the uncertainties on the various |η| and R 9 bins to the Higgs boson signal phase space. In both cases dedicated nuisance parameters are included as additional systematic terms in the signal model and result in less than 0.5% depending on the photon category.

• Non-uniformity of the light collection: the uncertainty on the response of the ECAL crystals has been slightly amplied with respect to Run 1 to account for the eect of larger transparency loss of the ECAL crystals. The size of the eect on the photon energy scale for 2016 data is estimated to be 0.07%.

• Non-linearity: the uncertainty associated with the non-linearity of the photon energy between MC simulation and data is estimated using Z boson decays to electron-130 4. H → γγ analysis at 13 TeV positron pairs. The eect is found to be 0.1% on the photon energy in all categories, except Untagged 0 in which it is 0.2%.

• Geant4: a small uncertainty is added to account for imperfect electromagnetic shower simulation in GEANT 4 [START_REF] Agostinelli | GEANT4: A Simulation toolkit[END_REF]. A simulation made with an improved shower description, changes the energy scale for both electrons and photons. Although mostly consistent with zero, the variation is interpreted as a limitation on our knowledge of the correct simulation of the showers, leading to a further uncertainty of 0.05% on the photon energy.

• Modeling of the material budget: the uncertainty on material budget between the interaction point and the vertex, which aects the behaviour of electron and photon showers, is estimated with special simulation samples where the material budget is uniformly varied by ±5%. Its eect on the energy scale is at most 0.17%.

• Shower shape corrections: the uncertainty deriving from the imperfect shower shape modelling in simulation is estimated using simulated H → γγ and Z → ee samples with and without shower shape corrections. The eect on the photon energy scale is found to be at most 0.064%.

• Photon identication BDT score: in order to cover the observed discrepancies between data and simulation, the uncertainty on the signal yields in the dierent categories of the analysis is estimated conservatively by propagating the uncertainty described in Section 3.3.3.

• Per photon energy resolution estimate: it is parametrized as a rescaling of the resolution estimate by ±5% about its nominal value.

• Jet energy scale and smearing corrections: this uncertainty is implemented as migration within VBF categories, within t tH categories and from tagged to untagged categories. Jet energy scale corrections (JEC) account for a 4-15% migration within VBF categories and 4-15% from VBF to untagged categories. The migration due to energy scale in t tH categories is about 5%. The jet energy resolution has an impact on the event migration smaller than 2%.

• b-tagging eciency: the systematic uncertainty on the b-tagging eciency is evaluated by varying the ratio between the measured b-tagging eciency in data and simulation within their uncertainty [START_REF] Chatrchyan | Identication of b-quark jets with the CMS experiment[END_REF]. The resulting uncertainty on the signal yield is found to be of about 2% in the lepton-tagged category and 5% in the hadronic-tagged category.

• Lepton identication eciency: the uncertainty is computed, for both electrons and muons, by varying the ratio of the eciency measured in data and simulation by its • Background modelling: the choice of background parametrization is handled using the discrete proling method. This automatically leads to an uncertainty on the choice of background function as described in Section 4.13.

Results

Results are extracted performing a simultaneous binned maximum-likelihood t to the diphoton invariant mass distributions in all the event classes over the range 100 < m γγ < 180 GeV. The signal PDF is that described in Section 4.12, where the shape and normalization for each production mode are separately tracked and dened. The background is evaluated by tting the m γγ distribution in data, without reference to the MC simulation.

Thus the likelihood to be evaluated in a signal-plus-background t is

L = L(data|s(p, m γγ ) + f (m γγ )),
where p comprises those parameters of the signal, such as m H or the signal strength, that are allowed to vary in the t, s(p, m γγ ) is the parametric signal model, and f (m γγ ) the background t function.

The test statistic, used to determine how signal-like or background-like the data are, is based on the prole likelihood ratio. The systematic uncertainties are integrated in the analysis via nuisance parameters and treated according to the frequentist paradigm. A description of the general methodology used in this analysis can be found in References [START_REF]Procedure for the LHC Higgs boson search combination in Summer[END_REF][START_REF] Chatrchyan | Combined results of searches for the standard model Higgs boson in pp collisions at √ s = 7 TeV[END_REF]. Table 4.6 shows the expected number of signal events for each category. The total number is broken down by percentage contribution of each production mode. Also listed are the σ ef f and σ HM . The former represents the smallest interval in the distribution which contains 68.3% of the entries. The latter represents the full width at half maximum divided by 2.355. Also listed in the table is the expected number of background events per GeV in the corresponding σ ef f window around 125 GeV, which is taken from the best-t candidate 4. H → γγ analysis at 13 TeV

Events / GeV Data S+B fit B component σ 1 ± σ 2 ± Untagged 0 =0.95 µ =126.0 GeV, H m - - Preliminary CMS TeV) (13 -1 12.9 fb γ γ → H (GeV)

Results

133 GeV is 5.6 σ, while 6.2 σ was expected, and the maximum signicance of 6.1 σ is observed at m H = 126.0 GeV. A likelihood scan of the signal strength (µ = σ/σ SM ) proling all the nuisances is performed and it is shown in Figure 4.29. In this scan, the Higgs boson mass was proled in the same way as other nuisances in the t. The best-t signal strength measured for all categories combined using this method is μ = 0.95 ± 0.20 = 0.95 ± 0.17 (stat.) +0.10 -0.07

Events / GeV Data S+B fit B component σ 1 ± σ 2 ± VBF Tag 0 =0.95 µ =126.0 GeV, H m - - Preliminary CMS TeV) (13 -1 12.9 fb γ γ → H (GeV)
(syst.)
+0.08 -0.05 (theo.). If the Higgs boson mass is xed to the Run 1 best-t value m H = 125.09 GeV, then the resulting signal strength is measured to be 0.91 ± 0.20 = 0.91 ± 0.17 +0.08 -0.05 (theo.). Figure 4.30 shows the signal strength separately for each of the categories used in the analysis (top) and the signal strength split by process (bottom). Since this analysis does not have any categories which specically target the VH production mode, µ V H is set to 1. In addition a two-dimensional likelihood scan of the signal strength µ ggH,t tH for fermionic production modes (ggH and t tH) and µ V BF,V H for vector boson production modes (VBF, ZH, WH), with the value of the parameter m H proled in the t, is performed. Figure 4.31 shows the 68% and 95% condence level contours, the best-t values are µ ggH,t tH = 0.80 +0. 14 -0.18 and µ V BF,V H = 1.59

Summary

In this chapter a general overview of the H → γγ analysis using the rst Run 2 data is presented. A particular focus is dedicated to the important role that Monte Carlo simulations have in the signal model building, selection optimisation and training of dierent multivariate analyses. This analysis brought to a rediscovery of the Higgs boson, with a signicance greater than 5 σ. For the future, the VH tag and detailed studies to dene the Higgs mass with its uncertainty should be included. Furthermore, studies of the Higgs spin-parity in the diphoton channel at 13 TeV could appear in the near future.

Chapter 5

Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

Introduction

In this section, we will describe a preliminary study of the possibility to constrain HVV couplings in the VBF production, using the Higgs boson decay to 2 photons. This is done with the 8 TeV Run 1 CMS dataset (19.7 fb -1 ), following closely the analysis designed to discover the Higgs boson in the 2 photons decay channel [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF]. In this dataset, the sensibility to the VBF production per-se is small and therefore we do not expect to have strong constraints. Nevertheless this is an alternate and complementary approach to the one usually employed which is to study this coupling in the decay of the Higgs boson H → ZZ * or H → W W * . We will see that despite the low event yield in the VBF channel, this new approach has an interesting sensitivity and should be pursued with larger dataset and a larger number of VBF events.

Theory

The observation of a new boson consistent with the Standard Model (SM) Higgs boson has been reported by ATLAS and CMS Collaborations in 2012 [START_REF] Serguei Chatrchyan | Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC[END_REF][START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF]. Even if this discovery is an important step to complete the SM, there are still many questions to be answered and new physics may exist beyond the SM. There are two ways of performing searches for beyond the SM physics: the rst one through direct searches for new physics, the second one by detailed studies of the properties of known particles. The precise study of the Higgs 140 5. Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ boson properties allows to better understand its connection to the rest of the SM particles and can give a hint of the presence of some deviations to the SM.

In spite of a low branching ratio, the H → γγ channel is very interesting because of the clear experimental signature thanks to an excellent diphoton mass resolution. This channel is important not only for the Higgs boson observation, but also to study the properties of this particle. In particular, as shown in Figure 5.1, if we consider the vector boson fusion production (VBF), this channel contains a coupling to the vector bosons HVV (where V is either a W or a Z boson) which can be studied. q q V V q q H 0 γ γ Previous studies of anomalous couplings of the Higgs boson to vector bosons [START_REF] Vardan Khachatryan | Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV[END_REF][START_REF] Chatrchyan | Measurement of the properties of a higgs boson in the four-lepton nal state[END_REF][START_REF] Chatrchyan | Measurement of Higgs boson production and properties in the WW decay channel with leptonic nal states[END_REF][START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF] Aad | Evidence for the spin-0 nature of the Higgs boson using ATLAS data[END_REF][START_REF]Combined CDF and D0 Constraints on Models for the Higgs Boson with Exotic Spin and Parity[END_REF], which aimed to measure the spin and parity of this new particle, have concluded that the Higgs is likely to be spin-0 with SM-like couplings. Thanks to these studies we know that the Higgs couplings are SM-like (within 30 % of the SM predictions), but the precision needs to be improved.

In this analysis we use a model-independent approach to determine anomalous couplings;

we dene a generic amplitude for a spin-zero boson coupling to vector bosons and we scan the coupling parameter space in order to determine the most likely value. Following the notation of previous CMS results [START_REF] Vardan Khachatryan | Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV[END_REF], it is possible to write the general scattering amplitude that describes interactions of a spin-zero boson with gauge bosons, such as ZZ, WW, Zγ, γγ or gg, as

A(HVV) ∼ a VV 1 + κ VV 1 q 2 V1 + κ VV 2 q 2 V2 Λ VV 1 2 m 2 V1 * V1 * V2 + a VV 2 f * (1) µν f * (2),µν + a VV 3 f * (1) µν f * (2),µν , (5.1)
where f (i),µν = µ i q ν i -ν i q µ i is the eld strength tensor of a gauge boson with momentum q i and polarization vector i , while f (i),µν = 1 2 µναβ f αβ is the conjugate eld strength tensor. m V is the mass of the vector boson, and Λ 1 is the scale of new physics which is a free parameter of the model. The tree-level SM-like contribution corresponds to a ZZ 1 = 0 and a WW 1 = 0, while there is no tree-level coupling to massless gauge bosons, that is a VV 1 = 0 for Zγ, γγ and gg. In the SM a VV 1 = 1 for ZZ and W W , and a 2 = a 3 = 0.

The pseudoscalar interaction (CP-odd state) corresponds to the a VV 3 terms, while the other terms describe the parity-conserving interaction of a scalar (CP-even state). The a VV 3 terms appear in the SM only at a three-loop level and are extremely small. The a VV 2 and Λ VV 1 terms appear in loop-induced processes and give small contribution O(10 -3 -10 -2 ) due to radiative corrections.

Since a 2 and a 3 are expected to be small, they can be studied separately. In this analysis we consider only the eects of the pseudoscalar coupling a 3 , assuming a 2 = 0.

To scan the allowed hypotheses, the physical eects of such anomalous couplings are parameterized as eective cross-sections and phases. Following again the convention of previous CMS studies it is possible to dene:

f a3 = |a 3 | 2 σ 3 |a 1 | 2 σ 1 + |a 3 | 2 σ 3 , φ a3 = arg a 3 a 1 , (5.2)
where σ i is the cross section of the process corresponding to a i = 1, a j =i = 0. f a3 = 0 corresponds to a pure scalar hypothesis, while f a3 = 1 corresponds to a pure pseudoscalar. In the absence of additional anomalous Higgs couplings, the signal strength parameter (µ = σB/σB| SM ) is given by

µ = |a 1 | 2 σ 1 + |a 3 | 2 σ 3 σ 1 .
(5.3)

Analysis strategy

For this analysis we follow as closely as possible the CMS 8 TeV SM H → γγ search in the VBF production mode [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF]. We use the same techniques to ensure accuracy of the results; the photon energy regression, background modeling and the objects selected are unchanged, but the event selection, though similar, has been adapted: VBF events are selected with looser cuts with respect to Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF]. The event selection will be presented hereafter. An important aspect to take into account is that the events satisfying VBF selection criteria are partly real VBF events, but also coming from ggH production with two additional emitted partons. As shown in Figure 5.2, the latter event topology has the same nal state as the real VBF one, with two forward jets and two isolated photons.

We will see in the following that the ggH processes are treated as a background, since in this event topology it is dicult to discriminate between 0 + and 0 -events. Therefore the analysis has to cope with the following processes: VBF scalar (0 + ), VBF pseudoscalar (0 -) and their interference, the ggH and the continuum background. For each event selected two dierent kinematic discriminants are built, using the Matrix Element Likelihood Approach (MELA), one to discriminate between VBF and ggH scalar components and one to distinguish VBF 0 + from VBF 0 -hypotheses. Thanks to these discriminants it is possible to determine dierent regions of the phase-space enriched with a certain process and extract their Higgs signal yield from a t to the diphoton mass. In this way we can infer the yields due to the dierent productions: VBF 0 + , VBF 0 -, ggH and the continuum. Finally we perform a scan of f a3 , comparing these yields to data, in order to constrain f a3 .

Data sample and simulated events

The data sample used in this analysis was recorded by the CMS experiment during the LHC Run 1 at a centre-of-mass energy of 8 TeV. A total of 19.7 fb -1 of data is analyzed, collected with diphoton triggers with asymmetric transverse energy thresholds and complementary photon selections, as in the SM search [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF].

The signal MC samples are generated with the LO matrix element generator JHUGen [START_REF] Anderson | Constraining anomalous HVV interactions at proton and lepton colliders[END_REF][START_REF] Bolognesi | On the spin and parity of a single-produced resonance at the LHC[END_REF][START_REF] Gao | Spin determination of single-produced resonances at hadron colliders[END_REF], both for gluon fusion and vector boson fusion production mode, under the assumption of a SM-like, purely scalar (0 + ) HVV coupling structure, as well as an anoma- lous, purely pseudoscalar (0 -) HVV coupling structure, and a 50/50 mix. In the mixed sample, 50% of the cross section comes from the a 1 term, and the other 50% of the cross section comes from the a 3 term in Equation 5.1. The phase Φ a3 is chosen to be zero.

The parton level samples are interfaced to PYTHIA6 [START_REF] Mrenna | Pythia 6.4 physics and manual[END_REF] for parton showering and hadronization. Detector simulation is performed with GEANT4. Two additional signal samples are produced with POWHEG interfaced to PYTHIA6, for

Object and event selection

143 the scalar hypothesis 0 + and both for ggH and VBF production modes. These samples are used in the analysis and in the study for the systematic uncertainties. All the signal MC samples are listed in Table 5.1.

Object and event selection

We follow closely the object selection used in the cut-based SM analysis for VBF categories [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF]. The cut-based analysis does not use a multivariate techniques for selection or classication of events. The identication selection requirements are specic to the category, and use a subset of the discriminating variables that are used in the multivariate photon identication described in Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF].

In our analysis we use a looser VBF category than the one described in Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF].

First a selection on the two jets p T and invariant mass is applied. In a second step several cuts are added, in order to improve the purity of the VBF selection: we cut on the dierence between the pseudorapidities of the two jets, |∆η jj |, the absolute dierence in the azimuthal angle between the diphoton system and the dijet system, |∆Φ γγjj | and the dierence between the average pseudorapidity of the two jets and the pseudorapidity of the diphoton system, |η γγ -(η j1 +η j2 )/2|. The values of the second set of cuts have been tuned in order to obtain the best expected sensitivity. The selection requirements are listed in 5.2, for four dierent production/spin-parity hypotheses, VBF 0 + , VBF 0 -, ggH 0 + and ggH 0 -. It is evident that a good discrimination between VBF 0 + and VBF 0 - processes is present, followed by a fair discrimination between VBF 0 + and ggH 0 + . It is therefore possible to exploit these dierences in kinematic distributions building kinematic discriminants to distinguish any two spin-parity hypotheses. These discriminants, calculated with the Matrix Element Likelihood Approach (MELA) [START_REF] Gao | Spin determination of single-produced resonances at hadron colliders[END_REF][START_REF] Bolognesi | On the spin and parity of a single-produced resonance at the LHC[END_REF][START_REF] Anderson | Constraining anomalous HVV interactions at proton and lepton colliders[END_REF], take as input the diphoton and dijet kinematics and have the form D 12 = P 1 /(P 1 + P 2 ), where P 1 and P 2 are the probability densities corresponding to the two spin-parity hypotheses we wish to discriminate. Therefore we dene two kinematic discriminants: M 0 -for the discrimination between a SM Higgs boson and a pure pseudoscalar state J P = 0 -in the VBF production mode; M V BF for the discrimination between VBF and ggH production under the hypothesis of a scalar Higgs boson. The discriminant calculation takes the diphoton and dijet systems kinematics as input, and for each event it calculates the theoretical dierential cross section for the dierent processes (i in Equation 5.4) given the event kinematics x, obtaining the probability density P i ( x):

P( x |i) = 1 σ i dσ i d x .
(5.4)

The two discriminants that we obtain can thus be expressed as:

M 0 -( x) = P( x |V BF 0 + ) P( x |V BF 0 + ) + P( x |V BF 0 -) , M V BF ( x) = P( x |V BF 0 + ) P( x |V BF 0 + ) + P( x | ggH 0 + ) . (5.5)
The distributions for these two discriminants, for simulated samples, are shown in Figures It can be seen from Figure 5.5 that the separation between VBF 0 + (blue histogram) and VBF 0 -(green histogram) hypotheses is very good. By construction the 0 + distribution peaks at 1, and the 0 -distribution peaks at 0. In Figure 5 In a rst step we calculated these discriminants also for ggH scalar and pseudoscalar processes, in order to try to distinguish the two parity hypotheses also in the case of gluon fusion production mode. But as shown in Figure 5.7 the two parity distributions, in magenta (ggH 0 -) and in red (ggH 0 + ), have very similar shapes for all discriminants. Therefore no attempt was made to separate ggH 0 + and ggH 0 -. These two contributions were estimated together and simulated as ggH 0 + .

2D MELA

The two discriminants described in Section 5.4.1 can be used simultaneously to build 2D maps that allow us to determine dierent regions of the phase-space enriched with a certain process. The discriminant between VBF and ggH hypotheses constitutes the x axis, while the one between VBF scalar and pseudoscalar processes constitutes the y axis. In Figure 5.8 the 2D maps are presented for the dierent simulated processes and for data (in data the mass region between 115 and 135 GeV is excluded). From Figure 5.8 one can see VBF 0 + simulated events (top left plot) populate the region on the top right of the 2D map, while the VBF 0 -events (top right plot) dominate the bottom right region. The ggH 0 + simulated events are in the same region as VBF 0 + , but they have a broader distribution, as already seen for the 1D discriminants (Figure 5.6). The data are also distributed in the top right part of the 2D map, with a broad distribution.

As explained in the next section, thanks to the separation of the processes in dierent regions of the phase-space, the latter can be divided in 2D categories enriched with a certain process. The number and borders of these categories are optimised in order to maximize the analysis sensitivity, as explained in Section 5.7.

Treatment of the scalar -pseudoscalar interference

Since the 2 VBF production 0 + and 0 -give raise to identical nal states, the interference between the 2 has to be simulated. To infer the interference term we used three MC samples: pure VBF 0 + , pure VBF 0 -and 0 + /0 -mixed.

We dene:

σ 1 = |Amp 1 | 2 σ 3 = |Amp 3 | 2 , (5.6)
where σ 1 and σ 3 are the cross sections, Amp 1 and Amp 3 are the amplitudes of the VBF 0 + (a 1 = 1, a 3 = 0) and VBF 0 -(a 1 = 0, a 3 = 1) process respectively.

The amplitude of a generic 0 + /0 -mixed process can be written as:

Amp mix = a 1 Amp 1 + a 3 Amp 3 ,

Treatment of the scalar -pseudoscalar interference 151

where a 1 and a 3 are the coupling constants of the 0 + and 0 -processes, from Equation 5.1. The square of Equation 5.7 gives the cross section of a generic 0 + /0 -mixed process:

|Amp mix | 2 = σ mix = |a 1 | 2 |Amp 1 | 2 + |a 3 | 2 |Amp 3 | 2 + 2|a 1 ||a 3 ||Amp 1 ||Amp 3 |cos(δ + Φ), (5.8)
where δ = arg Amp 3 Amp 1 , Φ = arg a 3 a 1 .

(5.9)

In the following we will use Φ = 0. Using Equation 5.6 one can write σ mix as function of σ 1 and σ 3 :

σ mix = σ 1 |a 1 | 2 + σ 3 |a 3 | 2 + 2|a 1 ||a 3 | √ σ 1 σ 3 cosδ.
(5.10)

After acceptance cuts from the analysis, the ducial cross section is therefore given by replacing

σ i → σ i A i , (5.11)
where A i are the acceptances for the dierent processes.

Taking the acceptances into account, Equation 5.10 can be written, for any value of a 1 and a 3 :

σmix ( x) = σ mix ( x)A mix ( x) = σ 1 A 1 ( x)|a 1 | 2 + σ 3 A 3 ( x)|a 3 | 2 + 2|a 1 ||a 3 | √ σ 1 σ 3 A int ( x), (5.12)
where A i ( x) are the acceptances for the dierent processes in each point of the phase-space, and cosδ has been absorbed by A int ( x).

If we perform the integration on the phase-space, we obtain:

σmix ( x)dx = σ 1 I A 1 |a 1 | 2 + σ 3 I A 3 |a 3 | 2 + 2|a 1 ||a 3 | √ σ 1 σ 3 I A 1 I A 3 , (5.13)
where I A i are the integrals of the acceptances on the phase-space, and is dened as:

= A int ( x) I A 1 I A 3 dx.
(5.14)

Using the integrals of the acceptances, Equation 5.12 can be expressed as:

σmix ( x) = σ 1 I A 1 A 1 ( x) I A 1 |a 1 | 2 + σ 3 I A 3 A 3 ( x) I A 3 |a 3 | 2 + 2 σ 1 I A 1 |a 1 | 2 σ 3 I A 3 |a 3 | 2 A int ( x) I A 1 I A 3 .
(5.15)

Before going on, we dene the fraction of the pseudoscalar component that takes into account the acceptances as:

fa3 = σ 3 I A 3 |a 3 | 2 σ 1 I A 1 |a 1 | 2 + σ 3 I A 3 |a 3 | 2 .
(5.16)

Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF

production with H → γγ

Dening s = σ 1 I A 1 |a 1 | 2 + σ 3 I A 3 |a 3 | 2 , (5.17)
one can obtain:

σ 3 I A 3 |a 3 | 2 = fa3 s σ 1 I A 1 |a 1 | 2 = (1 -fa3 )s.
(5.18)

Now, inserting Equation 5.18 in Equation 5.15 and keeping in mind that

A i ( x) I A i
are probability densities, we obtain:

σmix ( x) = s (1 -fa3 )P 1 ( x) + fa3 P 3 ( x) + 2 (1 -fa3 ) fa3 A int ( x) I A 1 I A 3 , (5.19)
where P 1 ( x) and P 3 ( x) are the probability densities of pure 0 + and pure 0 -process respectively (after cuts).

Similarly we can write Equation 5.13 as:

σmix ( x)dx = s 1 + 2 (1 -fa3 ) fa3 .

(5.20)

Finally we can obtain the probability density for a generic 0 + /0 -mixed process:

P mix ( x) = σmix ( x) σmix ( x)dx = (1 -fa3 )P 1 ( x) + fa3 P 3 ( x) + 2 (1 -fa3 ) fa3 P int ( x) 1 + 2 (1 -fa3 ) fa3
, (5.21)

P mix ( x) = (1 -fa3 )P 1 ( x) + fa3 P 3 ( x) + 2 (1 -fa3 ) fa3 P int ( x) 1 + 2 (1 -fa3 ) fa3 , (5.22)
where P int ( x) = A int ( x) √

I A 1 I A 3
is the probability density of the interference in each point of the phase-space, while , as dened in Equation 5.14, is its integral.

Equation 5.22 is valid for any fa3 . Therefore we can use any mixed sample to infer P int ( x). This will allow to simulate P mix ( x) for any f a3 . We used a mixed sample with f a3 = 0.5. We found that I A 1 = 0.4 and I A 3 = 0.27, and knowing that in the mixed MC sample a 1 = 1 and a 3 = 3.2, we found fa3 = 0.4. This value of fa3 was used in Equation 5.22 to compute the contribution of the interference P int ( x).

Starting from P mix ( x), P 1 ( x) and P 3 ( x), which are the 2D maps of the mixed f a3 = 0.5, pure 0 + and pure 0 -sample respectively, we computed in an iterative way, nding it very close to 0. P int ( x) is shown in Figure 5.9. From Figure 5.9 one can see that P int ( x) P 1 ( x), P 3 ( x) in all the phase-space and it will be neglected in the following.

Analysis strategy and signal extraction 153

As mentioned above, because of our acceptance cuts, the fraction of pseudoscalar component that we observe ( fa3 ) is slightly dierent from that dened in Equation 5.2. Com- paring Equations 5.2 and 5.16, one can obtain the expression of f a3 as a function of fa3 :

f a3 = fa3 I A 3 I A 1
(1 -fa3 ) + fa3 .

(5.23)

So constraining fa3 corresponds to constraining f a3 .

Figure 5.9: 2D map of P int ( x), that is the value of the interference in each bin of MELA.

Analysis strategy and signal extraction

In order to extract the dierent signal, we use M V BF ≡ Mela VBF vs gg to discriminate VBF from ggH production, M 0 -≡ Mela VBF 0 + vs 0 -to discriminate VBF 0 + from VBF 0 -productions and the invariant mass of the two photons m γγ to discriminate Higgs production from diphoton background.

Starting from Equations 5.17 and 5.19, the number of expected VBF events can be written as

N V BF ( x) L ≡ |a 1 | 2 1 1 -fa 3 × σ 1 I A 1 × P mix ( x) ≡ µ V BF × σ 1 I A 1 × P mix ( x) (5. 24
)
where L is the luminosity and µ V BF is dened as

µ V BF ≡ |a 1 | 2 1 1 -fa 3
in such a way that in the SM, µ V BF = 1 and fa 3 = 0.

Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

Therefore the total number of expected events in the sample can be parametrized in the 3 dimensional space (M V BF , M 0 -and m γγ ) and can be written as:

N (m γγ , M V BF , M 0 -)/L = µ V BF × σ SM V BF × I A 1 × (1 -fa 3 )P 1 (m γγ , M V BF , M 0 -; θ) + fa 3 P 3 (m γγ , M V BF , M 0 -; θ) + µ ggH × σ SM ggH × I A ggH × P ggH (m γγ , M V BF , M 0 -; θ)+ N bkg × P bkg (m γγ , M V BF , M 0 -; θ) (5.25)
where we have redened σ SM V BF = σ 1 , σ SM ggH is the number of expected events from ggH production in the Standard Model and µ ggH is a potential deviation to this expectation (due to theoretical uncertainties for instance or to the contribution of new processes), the interference term has also been neglected as aforementioned.

In order to simplify the extraction we do not t the number of events in the 3D space, but rather we will dene categories in the 2D space of (M V BF ,M 0 -) and t the m γγ mass distribution in each of these categories. This does not change substantially Equation 5.25, but the 2D space (M V BF ,M 0 -) is replaced by a 1 dimensional discrete function, the cate- gory number.

The model described by Equation 5.25 will be used as input to the standard CMS statistical treatment to extract the constraints on the dierent parameters. In addition several systematics need to be added, either aecting the total yield, or the migration in the 2D space (M V BF ,M 0 -), or practically the migration of events between categories.

The following section describes the optimisation of these categories.

Categories optimisation

For each MELA discriminant separately we rst performed 1D optimisation to obtain the best sensitivity, dividing the phase-space in two or more categories. The values obtained for the 2x1D optimisations are then combined to form the 2D categories. In the following the optimisation procedure is explained in more detail for the two discriminants.

Optimisation of VBF vs ggH discriminant M V BF

We performed the optimisation of the 1D discriminant between VBF SM and ggH SM hypotheses. To do that, referring to the physics model presented in Equation 5.25, we set these conditions: 5.7 Categories optimisation 155

• f a3 xed at 0, since with this discriminant we want to distinguish between the VBF and ggH,

• µ ggH is constrained to 1 within a theoretical systematic uncertainty of 32% (this value was taken from Reference [START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF][START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF]),

• µ V BF is left oated,

• the sensitivity to µ V BF is considered as gure of merit.

The full range is rst cut in 2 categories, trying several cuts between 0 and 1. For each cut value we compute the expected sensitivity performing a prole likelihood scan as a function of µ V BF with Asimov toys [START_REF] Cowan | Asymptotic formulae for likelihood-based tests of new physics[END_REF], and we kept the value for which we obtained the best sensitivity. The sensitivity here was dened as the value of the statistical test (likelihood ratio) when testing µ V BF = 0, the higher is this number, the more likely it is to observe a VBF production signal. The best value for this rst cut was found to be 0.91. After that, we took the best category of the two, that is the one with the highest signal over background ratio, and we performed a further split cut, dividing in this way the discriminant range in three 1D categories. Doing this we saw a little improvement in the expected sensitivity, in particular for the cut at value 0.97. We veried that the addition of more than three categories does not bring any improvement to the expected sensitivity.

The nal cut values kept for the VBF SM vs ggH SM discriminant are therefore 0.91 and 0.97. In Figure 5.10 the prole likelihood scan as a function of µ V BF is shown for two 1D categories, with a cut at 0.91, and for three 1D categories, with cuts at 0.91 and 0.97. The optimisation of the 1D discriminant between VBF 0 + and VBF 0 -hypotheses was done similarly. In Equation 5.25, we set the following conditions:

• µ ggH is constrained to 1 within a theoretical systematic uncertainty of 32% (this value was taken from Reference [START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF]),

• µ V BF is left oated,

• f a3 is left oated between 0 and 1 in the t, while f a3 = 0 in the true underlying model.

As for the VBF vs ggH discriminant, we started dividing the discriminant range in two 1D categories, trying several cuts between 0 and 1. For each cut value we computed the expected sensitivity performing a prole likelihood scan as a function of f a3 with Asimov toys, and we kept the value for which we obtained the best sensitivity, that is 0.1. This sensitivity is dened as the value of the likelihood obtained when probing f a3 = 1, the higher is this number the more likely it is to exclude an anomalous production (when the VBF production is pure SM). A further categorisation does not bring any improvement to the expected sensitivity, so 0.1 is the only value kept as boundary of the nal 2D categories.

Optimised 2D categories

After the independent optimisation of the two 1D discriminants, the discriminant values that give the best expected sensitivity are combined in 2D to form the nal optimised categories. Given that the boundaries are 0.91 and 0.97 for the discriminant VBF vs ggH, and 0.1 for the discriminant VBF 0 + vs VBF 0 -, we should have 6 categories. Nevertheless, the categories in the phase-space region delimited by (MELA VBF 0 + vs VBF 0 -) < 0.1 were gathered in a single category, in order to increase the statistic in this region, where the background is already extremely small. Therefore we ended up with 4 categories, shown in Figure 5.11. Their numbering, from 0 to 3, will be maintained in the following.

Optimisation of the diphoton MVA cut

Once dened the 4 categories, we added a cut on the diphoton MVA. This quantity is very similar to the one presented in chapter 4 and allows to make the best use of the quality of the photons in the event, hence improving our sensitivity. To do this we performed a scan for diphoton MVA values going from -1 to 0.4. For this optimisation we set these conditions:

• f a3 xed at 0, • µ ggH is constrained to 1 within its theoretical systematic uncertainty of 32% (this value was taken from Reference [START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF]),

• µ V BF is left oated.

We then use the same procedure as for the 1D optimisation of M V BF . As one can see in Figure 5.12, the sensitivity reaches a plateau for a cut on the diphoton MVA of 0. It was decided to cut at 0.2 on the diphoton MVA output, which retains a lot of statistic while having a high sensitivity.

diphoton MVA cut

Bias study for the background function

Since we do not rely on MC to predict the background distribution, we follow the same procedure as the one described in the analysis [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF], and we use a polynomial to t the background. The order of the polynomial is chosen following the same procedure as in Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] and is described below.

Suppose we obtain a set of measurements of a parameter τ , whose true or generated value is τ g . The measurements are statistical uctuations around τ g and could, for example, follow an exponential time distribution In our study we generated the expected number of background events, in a diphoton mass range between 100 and 180 GeV, according to a particular functional form, power law, exponential and polynomial of order between 1 and 4. Then we tted this generated mass distribution with other functions. This procedure was repeated several thousands of time to get the distribution

N f itted -N expected , (5.28)
where N f itted is the number of events that the t was able to extract, while N expected is the number of generated events. From this distribution we computed the bias as mean(N f itted -N expected ) RM S(N f itted -N expected ) .

(5.29)

The more the tting function is appropriate to t the generated distribution, the more the bias value is close to zero. So by construction when we generate and we t the distribution with the same function, the bias value is zero.

As already mentioned, we were interested in choosing the best order of the polynomial function for each category. Therefore, in each category, we computed the bias for a model generated both with a power law and with an exponential, and tted with a polynomial of order 1, 2, 3 and 4. The polynomial function with the lowest order which gives a bias < 0.15 is chosen. The polynomials nally chosen for the dierent categories are the following:

• category 0: polynomial of order 3,

• category 1: polynomial of order 1,

• category 2: polynomial of order 1,

• category 3: polynomial of order 1.

The polynomial order decreases with the statistic present in the category. In Figure 5.13, as an example, the distribution N f itted -N expected is shown, for category 0, for events generated according to an exponential function and tted with an exponential, a power law, a polynomial of order 1 and 3. As expected, if the t was done with an exponential or with a polynomial of order 3, the mean of the distribution is closer to zero. ing to an exponential function and tted with an exponential (violet), a power law (green), a polynomial of order 1 (red) and a polynomial of order 3 (blue).

Systematic uncertainties

Systematics can have 2 dierent eects: they can aect the overall yields of expected signal or the signal shapes, either via the mass distribution or via migration between the dierent signal categories. It has to be noted that for this analysis we are not sensitive to systematics aecting the overall yield of µ V BF , since it is left oated in the extraction of the results. Nevertheless, main systematics aecting the overall yield have been also considered in order to extract µ V BF for the case of f a3 = 0.

A summary of the systematic uncertainties considered is presented in this section.

Integrated luminosity

A 2.6% uncertainty was assigned to the overall luminosity [START_REF]Absolute Calibration of the Luminosity Measurement at CMS: Winter 2012 Update[END_REF][START_REF]CMS Luminosity Based on Pixel Cluster Counting -Summer 2013 Update[END_REF].

ggH + 2jets cross section uncertainty, QCD scale

The theoretical uncertainty on the ggH + 2 jets process cross section, coming from both uncertainties due to the missing higher orders and uncertainties related to the parton distribution functions, is of about 32% in the VBF categories (see Reference [START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF]). This is the dominant source of systematic uncertainty.

Systematic uncertainties 161

H+2jets kinematics description

For the nal results we use the JHU MC sample for the VBF 0 -process, and the Powheg MC samples for the ggH 0 + and VBF 0 + .

The distributions of the dierent discriminants for several generators (powheg, JHU, MiNLO,aMC@NLO) have been studied and are shown in Figures 5.14 and 5.15. This was done both at the generator and reconstruction level. The dierences present between dierent generators create event migrations between categories, and leads to a large source of systematic uncertainties. To estimate this systematics we computed the ratio of the four categories yield from an alternate generator to the reference one. The deviation of the ratio from 1 in each category is taken as systematics (blue line in Figure 5.16). This was done at reconstruction level for VBF 0 + , VBF 0 -and ggH 0 + , comparing JHU and Powheg generators. Figure 5.16 shows the event yield in the 4 categories for the two generators and their ratio, for the dierent processes.

Since the Powheg 0 -sample was not available, we performed a 2D reweighting of the 2 kinematic discriminants in the VBF 0 + JHU sample in order to match the distributions of the VBF 0 -JHU sample. Then we applied the 2D weights to the VBF 0 + Powheg sample, obtaining in this way a VBF 0 -Powheg sample.

One may notice on distributions from Figures 5.14 and 5.15 that JHU generator is quite dierent from others especially for ggH production. This has been traced back to the factorisation scale, setup too high for JHU, which yields more radiations in JHU than in other MCs used in CMS. Therefore, the systematic uncertainty estimated as the dierence between JHU and powheg is conservative.

Jet energy correction and jet energy resolution

The signal eciency is aected both by the uncertainty on the jet energy scale and by the uncertainty on the jet energy resolution. We varied the jet energy scale (JEC) by shifting the scale by ±1σ, where σ is the full jet energy scale uncertainty. The uncertainty is evaluated as prescribed for the 2012 dataset.

The jet energy resolution is smeared by the level of disagreement between the resolution measured in data and in MC. The uncertainty on this over-smearing is taken as systematics.

Both the JEC and JER uncertainties aect the analysis causing events to migrate from one category to another. We computed the ratio of the four categories yield for the shifted sample (both for shift up and down) over the four categories yield for the nominal sample.

The deviation of the ratio from 1 in each category is taken as systematics. This was done for VBF 0 + , VBF 0 -and ggH 0 + . Figure 5.17 shows the event yield in the 4 categories for the shifted and nominal samples and their ratio, for the dierent processes, both for JEC and JER.

Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

Systematics on diphoton MVA Since our selection contains a cut on the diphoton MVA, we evaluated its systematic uncertainty. The two main sources of systematic uncertainty on the diphoton MVA output derive from the photon ID MVA and the per-photon energy resolution. Following prescription in Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] the systematic uncertainty to photon ID MVA was assigned varying the photon ID MVA score of ± 0.01. The uncertainty in the per-photon energy resolution estimate was parameterized as a rescaling of the resolution estimate by ±10%

about its nominal value. These systematics are varied correlated for both photons. Figure 5.18 shows the event yield in the 4 categories for the shifted and nominal samples and their ratio, for the dierent processes, both for photon ID MVA and for photon energy resolution.

Systematics on photon preselection and jet identication

Following Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF], we assigned a systematics on the photon eciency of 1%(2.6%) in the barrel (endcap). In a similar way, the eciency on the jet identication is estimated to be known at 3-5% level from the CMS collaboration. Note that these sources of systematics aect mostly the total yield of µ V BF and therefore not the nal constraint on fa3 .

Systematics on photon energy scale and photon energy resolution

An uncertainty of 0.1% on the electromagnetic calorimeter energy scale is assigned, following prescription in Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] and is correlated over all signal categories.

An additional smearing is applied as an additional constant term of the energy resolution, as reported in Table 5.3. The systematic error on this smearing is used to infer the systematics due to potentital data/MC disagreement on the photon energy resolution. The eect on the experimental width was found to be of the order of 0.1% correlated over the categories. 5.4 shows the expected number of signal events and the corresponding number of events in data for each category. In Table 5.5 we provide the expected number of signal events and the corresponding number of events in data also for the cut-based analysis of Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF] compared to the expected and observed number of events that we nd making the same categorisation (2 VBF categories, one tight and one loose). One can see that we are able to reproduce the results of the standard analysis at 8 TeV [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF].

Fit to the diphoton mass

After the denition of the 4 nal 2D categories and the choice of the background function for each of them, a t to the diphoton mass was performed in each category. The simulated signal, for the processes VBF 0 + , VBF 0 -and ggH 0 + , is tted with a double Gaussian.

The data, that constitute our background, are instead tted with a polynomial function of dierent order according to the category. The analysis was performed in the invariant mass range 100 GeV < m γγ < 180 GeV, blinding the region 115 GeV < m γγ < 135 GeV.

With the t to the diphoton mass we extracted simultaneously the yield for each process in each category. In Figure 5.19 the ts to the signal simulated samples in the 4 categories are shown, for the dierent processes, VBF 0 + , VBF 0 -and ggH 0 + . Figure 5.20 shows instead the unblinded t to the data, along with the diphoton mass shapes of the simulated signals.

Parameter scan

We performed a scan over f a3 values from 0 (pure scalar) to 1 (pure pseudoscalar). At each point in the scan, we maximised the binned likelihood

L = N i=1 n sig i ( ζ) + n bkg i n i ! e -n sig i ( ζ)-n bkg i , (5.30)
where n sig i (n bkg i ) is the expected number of signal (background) events and n i is the observed number of events in bin i of N bins. The expected number of signal events depends on the anomalous coupling parameters, ζ. Systematic uncertainties described in Section 5.9 are introduced with nuisance parameters. Deviations from the global minimum in the negative log likelihood distribution, -2∆lnL, are used to quantify consistency of the pseudoscalar hypothesis with the data. Expected results are determined from a t to an Asimov dataset with the SM Higgs included (µ = 1). categories with the one of Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF] shown in the plot at the bottom, one can see that we obtain similar results. Figure 5.22 shows the likelihood scan as a function of µ V BF for our analysis, performed with the cut-based categorisation of Reference [START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF][START_REF]Measurements of the Higgs boson at 125 GeV in the two photon decay channel in the Full LHC Run 1 Data at CMS[END_REF] (blue line) and with the categorisation done with the MELA discriminants (red line). Plot on the left shows the expected results, plot on the right the observed results. From the plot on the left one can see that the categorisation with the MELA discriminants has a better expected sensitivity, while plot on the right shows that the analysis with the cut-based categorisation has an observed result closer to the expected. Figure 5.23 shows the likelihood scan as a function of fa3 on the left, and as a func- tion of f a3 on the right, where f a3 was obtained applying the transformation described in Equation 5.23. The dashed line represents the expected result, the solid line the observed result. One can see that we do not reach any exclusion of a pure pseudo-scalar state (which would be -2∆N LL = 3.84), nevertheless the analysis has some sensitivity to f a 3 despite the fact that we do not have sensitivity to observe SM VBF signal.

Results

We also performed a projection for the Run 2 LHC data. Figure 5.24 shows the ratios of LHC parton luminosities, as a function of the mass, for dierent initial states. We are interested in the blue dashed curve (13 TeV/ 8TeV ratio for q q initial state) at a mass of around 700 GeV, that is the mass of the Higgs + dijet system. For this value of the mass, the parton luminosity ratio 13 TeV / 8 TeV is ∼ 2.5. From that we can deduce that 250 fb -1 at 8 TeV correspond roughly to 100 fb -1 at 13 TeV, if we assume that the background scales as the signal. We scale our process yields accordingly and we obtain the projection of the likelihood scan as a function of fa3 for 250 fb -1 at 8 TeV, shown in Figure 5. 25. From this gure one can see that it would be possible to exclude fa3 > 0.22 at 95% CL. In Figure 5.26 we show, as a reference, the likelihood scan as a function of f a3 obtained by the H → ZZ channel combining data at 8 and 7 TeV. From this gure one can see that with our analysis at 13 TeV it would be possible to reach results similar to the H → ZZ ones at 7+8 TeV.

Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF

production with H → γγ 5. Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

Summary

In this last chapter a feasibility study, having the aim of constraining the anomalous couplings of the Higgs boson to the vector bosons, is presented. The peculiarity of this study is the use of the Higgs boson production through vector boson fusion (VBF), instead of exploiting the decay of the Higgs in two vector bosons, as was done so far in other analyses. For this reason this is an alternate and complementary approach to the one usually employed. It was proven that despite the low event yield in the VBF channel, this new approach has an interesting sensitivity and should be pursued with larger dataset and a copier number of VBF events at 13 TeV.

Conclusions

The work presented in this thesis was carried out within the CMS Saclay group, working in the search of the Higgs boson in the decay channel H → γγ.

The main contributions of my studies throughout the period 2013-2016 are reported in Chapters 3, 4 and 5.

After the description of the Standard Model framework and the CMS detector, Chapter 3 describes in detail the photon reconstruction and identication at CMS. Despite many changes of the reconstruction algorithm between Run 1 and Run 2, the performance of the reconstruction from the photon identication point of view is found to be very similar between the two runs. The photon identication algorithm for the H → γγ analysis is optimised for Run 2, using a multivariate analysis method, and its performance and validation studies are presented.

In Chapter 4 the H → γγ analysis using the rst Run 2 data is presented, with a particular accent on the simulation methods used to simulate the Monte Carlo samples used in this analysis. The analysis is performed with a dataset corresponding to an integrated luminosity of 12.9 fb -1 at 13 TeV. The observed signicance for the standard model Higgs boson at m H = 125.09 GeV is 5.6 σ, while 6.2 σ was expected, and the maximum signicance of 6.1 σ is observed at m H = 126.0 GeV. The best-t signal strength relative to the Standard Model prediction is μ = 0.95 ± 0.20 = 0.95 ± 0.17 (stat.) +0.10 -0.07 (syst.) +0.08 -0.05 (theo.) when the mass parameter is proled in the t, and 0.91 ± 0.20 = 0.91 ± 0.17 Furthermore it provides a per-photon energy resolution estimator, which is used for the diphoton BDT as described in Section 4.8. The regression is trained, separately for barrel and endcap, on photons in a sample of simulated events.

The input variables to the regression are the following (with more details in Section 3.2.2):

• shower shape variables: R 9 , the number of reconstructed clusters, energy weighted η-width and Φ-width of the supercluster, cov iηiΦ , the ratio of the seed cluster energy to the supercluster energy and H/E. In the endcaps, preshower σ RR is used as well.

These variables are sensitive to global containment eects and provide information on the conversion probability and on the degree of showering,

• energy ratios within the seed cluster: these are sensitive to the local energy distribution and to the local containment eects,

• absolute position variables: seed crystal indices iη and iΦ, the dierence between the seed crystal position and the supercluster position, variables comparing the seed crystal indices to the modules and supermodules boundaries in the barrel. These variables are sensitive in particular to the gap and crack energy loss,

• pile-up variables: number of reconstructed vertices and ρ, used to take into account potential energy additions due to pile-up.

A BDT is used to implement this regression, and it is trained to reproduce the probability density of E T rue /E Raw for any photon with input variables x. In each leaf of the BDT the output E T rue /E Raw is tted by a double-sided Crystal Ball function, whose parameters are functions of the input variables x. The advantage of this technique is to be able to estimate simultaneously the energy of the photon and its median uncertainty. An example of the performance of the regression method is given in Figure 27, which shows the comparison of the ratios of the photon raw and corrected energies to the true energy, for photons from a simulated sample of Higgs to gamma-gamma events with m H = 125 GeV.

Energy correction between data and simulation

The imperfect simulation of detector eects causes discrepancies in the scale and resolution of regression photon energy between data and Monte Carlo simulation. These discrepancies are dealt with by correcting the energy scale in data and by then determining a smearing to be applied to the simulated samples in order to have the best agreement between data and simulation for photon energy scale and resolution. The corrections are derived from Z → ee events from data and simulation with the electron energy esitmated in the same way as a photon energy, and performed in a multi-step procedure.

The supercluster energy scale is corrected for by varying the scale in the data to match the simulation in Z → ee events. The extraction of the energy scale corrections is done using two methods: the t method and the smearing method. The rst one consists in performing an analytic t to the Z invariant mass peak, built with the supercluster energies corrected by the regression. The t is performed using a Breit-Wigner function convoluted with a Crystal Ball, where the Breit-Wigner function models the intrinsic distribution of Z → ee, with the peak mass and width parameters xed to the Particle Data Group values (m Z = 91.188 GeV and Γ Z = 2.495 GeV). The Crystal Ball function gives a reasonable description of the calorimeter resolution eects and bremsstrahlung losses in front of the calorimeter, and its parameters are left free during the t. Data and simulated distributions are tted separately and the t results are compared to extract the scale oset. The relative shift between data and simulation is given by:

∆P = ∆m data -∆m M C m Z ,
where ∆m M C(data) is the tted mean of the Gaussian core of the Crystal Ball function for simulation (data).

Since the data-simulation dierence is time dependent and the time dependence is not the same in dierent pseudorapidity regions, the scale correction is extracted, with the t method, per run range and per pseudorapidity region (4 bins, two in EB and two in EE).

Then, once the scale has been corrected in the dierent categories, the residual data-MC dierence is addressed looking separately at the two R 9 bins (non-showering and showering electrons), in every pseudorapidity region, in order to factorize the eect of the material in front of the calorimeter. In this second step the scale corrections and the smearing of the MC energies are derived using the smearing method.

The aim of the smearing method is to estimate more precisely the smearing to be applied to the MC energies. This method uses the invariant mass shape in the simulation as a pdf for a maximum likelihood t instead of using an a-priori chosen function. The advantage is that all the known detector eects, reconstruction ineciencies and Z kinematic behaviour are already taken into account in the simulation. The discrepancies between data and simulation are found to be successfully covered by a Gaussian smearing function. Another big advantage of this method with respect to the rst one is that a larger number of electron categories can be handled, allowing to include also the events with the two electrons having dierent properties. The method is based on the maximization of the likelihood between the data and the smeared simulation in the Z → ee invariant mass distribution in each electron category. In the likelihood maximization, the electron supercluster energies are modied by applying a Gaussian multiplicative factor centered in 1 + ∆P and with a ∆σ resolution, where ∆P is the energy scale correction and ∆σ is the additional constant term in the energy resolution.

The nal energy scale correction is therefore derived as the product of the two corrections in the number of run ranges × 4 (pseudorapidity regions) × 2 (R 9 ) categories.

Systematic uncertainties

The systematic uncertainty in the determination of the energy scale correction and the additional energy smearing to be applied to the H → γγ simulation is dominated by the dierence between electrons and photons.

A variable particularly sensitive to this dierence is R 9 : its variation as a function of η reects qualitatively the variation of the tracker material budget and is an indication of how much the material upstream from the calorimeter aects dierently electrons and photons.

The lower R 9 requirement is thus varied both for the R 9 > 0.94 and the R 9 < 0.94 categories. The maximum absolute dierence among all these variations with respect to the nominal value, dened as ∆ R 9 , is then used in the evaluation of the systematic uncertainty.

Furthermore, one can apply to electrons the regression trained for electrons, and apply to electrons reconstructed as photons the regression trained for photons, in order to account for possible dierences between electrons and photons (this systematic uncertainty is dened as ∆ pho ).

Other possible sources of systematic uncertainty are investigated: in particular the event selection is varied using the medium and tight working points for the electron identication and the requirement on electron E T is varied from 20 GeV to 25 GeV. These systematic uncertainties are called respectively ∆ sel and ∆ E T .

The nal estimate of the systematic uncertainty is obtained adding all these eects in quadrature:

∆ tot syst = ∆ 2 R 9 + ∆ 2 pho + ∆ 2 sel + ∆ 2 E T
The systematic uncertainty is computed in the dierent R 9 -η categories, both for the energy scale and the energy resolution. Its values vary between 0.15% and 0.5%.

Appendix C Details on diphoton vertex identication

Vertex Selection BDT

The vertex selection BDT is trained to select the diphoton production vertex in an event, which has an average of 18.5 pp collision vertices as a consequence of pileup interactions.

The training is performed using simulation for all Higgs production modes weighted according to their expected cross sections. The signal sample consists of right vertices, matched to the Higgs MC truth vertices, while the background sample consists of the pileup vertices.

The most discriminating variables for the vertex identication, entering the BDT, are the following:

• i | p i T | 2 : the sum of the square of transverse momentum of each track associated with the vertex, p i T . This quantity is expected to be larger for the diphoton vertex than for pileup vertices,

• -i p i T • p γγ T | p γγ T |
: the negative sum of projections of the p T of the tracks on the diphoton p T . This quantity tends to be positive for the true vertex, as tracks recoil against the diphoton, and centered on 0 for wrong vertices,

• (| i p i T | -p γγ T )/(| i p i T | + p γγ T ): the asymmetry between the total momentum of the tracks attached to a given vertex and the modulus of the diphoton p T . This quantity tends to have higher values for the true vertex and to peak at -1 for wrong vertices,

• |z PV -z conv PV |/σ conv , only for cases with at least one converted photon: the distance between the z position of the vertex and the estimated position of diphoton vertex from the conversion and normalized by the uncertainty of the estimation. This quantity is expected to be near 0 for the diphoton vertex while larger for pileup vertices.

Figure 28 shows the eciency of choosing the vertex within 1 cm of the true vertex from Higgs to two photons simulation as a function of the p T of the diphoton pair and as a function of the number of vertices. This gure also shows separately the eciencies for events with at least one converted photon (red) and for events where no photon is converted (blue). It is evident that the use of converted photons allows to improve the eciency of the vertex identication algorithm.

Vertex probability BDT

Vertex probability BDT is trained to estimate the probability that the selected vertex is the correct diphoton vertex for each event. The criterion for being correct is that the distance between the selected vertex and the true diphoton vertex is within 1 cm in the z direction, in which case the resolution on the photon opening angle makes a negligible contribution to the diphoton mass resolution. Figure 29 shows the mass resolution worsening as a function of the z distance to the true vertex. For the events with the best energy resolution (two photons in the ECAL barrel with high R 9 ), the resolution worsens by about 15% when the vertex is between 1 cm and 1.5 cm of the true one, and by more than 20% between 1.5 cm and 2 cm.

The probability to choose the vertex within 1 cm of the true vertex is computed from the output of a second MVA obtained using a BDT method, as for vertex identication. It • the p T of the diphoton system,

• the number of vertices,

• the values of the vertex identication BDT discriminant for the best three vertices,

• the ∆z between the best vertex and the second and third choices,

• the number of converted photons (0, 1, or 2).

The BDT is then transformed to a probability computed for both converted and unconverted photons.

To measure the performance of both the vertex selection BDT and the vertex probability BDT, the diphoton vertex selection eciency and the average vertex probability are evaluated on Monte Carlo simulated H → γγ events at a Higgs mass of 125 GeV, in bins of p γγ T .

As shown in Figure 30, the average vertex probability along with uncertainty (blue band) predicts well the measured vertex selection eciency (data points), and both increase with the increasing p γγ T . The total vertex selection eciency is ∼82% for the H → γγ events at a Higgs mass of 125 GeV.

Systematic uncertainties

The systematic uncertainty in the vertex nding eciency is taken from the uncertainty in the measurement of the corresponding data/simulation scale factor obtained using Z → µµ events. In eect Z → µµ events are used to validate the H → γγ vertex identication algorithm for the case of unconverted photons. To do that the vertices are rst retted without the muon tracks, mimicking a diphoton system. Then the muon tracks are removed from the tracks used by the identication algorithm and the eciency of nding the good vertex is estimated both in data and simulation. Thus the vertex is selected within the vertex collection without muon tracks, while the true vertex is determined from the muon tracks.

Events with 2 muons are selected if they satisfy all tight identication criteria, except the ones involving vertex, and in addition the dimuon mass is required to be within 70 GeV and 110 GeV.

The data/simulation eciencies ratio as a function of p T , shown in Figure 31, is used to correct the eciencies in H → γγ simulation, and it is varied within uncertainties to estimate the associated systematics. 12.9 fb et du Higgs, qui dépendent de l'hypothèse de spin-parité, sont utilisées pour construire des discriminants capables de séparer les diérentes hypothèses de spin-parité. Ces discriminants permettent de dénir diérentes régions de l'espace des phases enrichies en signaux de spin-parité diérente. Les diérents nombres d'événements de signal sont extraits dans chaque région par un ajustement de la masse invariante diphoton, permettant de déterminer les contributions respectives des diérents signaux et permettant ainsi de contraindre la production de boson de Higgs pseudo-scalaire (spin-parité 0 -). Cette analyse utilise les données collectées pendant le Run 1 du LHC, correspondant à une luminosité intégrée de

CMS Preliminary

  photons sont présentés, avec une attention particulière aux diérences entre le premier et le deuxième run du LHC, le premier run (Run 1) ayant été pris entre 2010 et 2012 avec une énergie dans le centre de masse de 7 puis 8 TeV, le deuxième (Run 2) ayant commencé en 2015 avec une énergie dans le centre de masse de 13 TeV. Les performances des reconstructions du Run 1 et du Run 2 en ce qui concerne l'identication des photons sont comparées. Ensuite l'algorithme d'identication des photons pour l'analyse H → γγ et optimisé pour le Run 2 est présenté. Pour ce faire une méthode d'analyse multivariée est utilisée. Les performances de l'identication des photons à 13 TeV sont enn étudiées et une validation données-simulation est eectuée. Ensuite l'analyse H → γγ avec les premières données du Run 2 est présentée. Les données utilisées correspondent à une luminosité intégrée de 12.9 fb -1 . Une catégorisation des événements est faite, an de rendre maximale la signi- cation statistique du signal et d'étudier les diérents modes de production du boson de Higgs. La signication statistique observée pour le boson de Higgs du Modèle Standard à

Equation 1 . 1 2 ( 1 -γ 5 )

 1115 1 represents a point-like interaction, with only one vertex and without any intermediate boson exchanged. It is usually referred to as V -A interaction, being formed by a vectorial and an axial component. The term that appears in it is the left-handed projector. Only the left-handed component of fermions takes part to this interaction.

Figure 1 . 1 :

 11 Figure 1.1: Shape of the Higgs potential of Equation 1.11.

) Equation 1 .

 1 16 now contains mass terms for elds W ± and Z: each of the three gauge bosons has acquired mass and an additional degree of freedom, corresponding to the longitudinal polarization. At the same time, the three Goldstone bosons have disappeared from the Lagrangian L BEH , thus preserving the total number of degrees of freedom: the degrees 1.3 The Higgs mechanism 7 related to the missing Goldstone bosons have become the longitudinal degrees of the vector bosons. Only the H scalar eld is still present and has acquired mass itself: it is the Higgs boson.

1. 4 9 1. 4

 494 The Higgs boson phenomenology at the LHC The Higgs boson phenomenology at the LHC The electroweak theory has been extensively tested in the last thirty years of the 20th century, proving that the Standard Model oers a valid explanation of the nature of particle interactions. The Higgs boson has been the only missing piece for more than three decades and has been searched by experiments at LEP, Tevatron and LHC until it was discovered by both ATLAS and CMS experiments at the LHC in 2012, with a measured mass of about 125 GeV[START_REF] Serguei Chatrchyan | Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC[END_REF][START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF].

√ s = 7 -

 7 14 TeV, like those at the Large Hadron Collider, the main processes contributing to the Higgs boson production are represented by the Feynman diagrams in Figure 1.2. In Figure 1.3 (left) the Higgs cross section for the dierent production mechanisms is shown as a function of the centre-of-mass energy for a Higgs mass of 125 GeV.Figure 1.3 (right) shows how the total Higgs production cross section increases going from 7-8 TeV to 14 TeV.

( 1 .

 1 29)is dominant at the LHC in the whole Higgs mass range. The coupling of the gluons to the Higgs boson is mediated through a triangular loop of virtual quarks where the t contribution plays the dominant role because of the large top mass. The theoretical cross section has been computed including the QCD corrections up to next-to-next-to-next-to-leading-order (N3LO) and next-to-next-to-leading-log (NNLL), whereas the electroweak corrections are known at next-to-leading order (NLO).

1 .Figure 1 . 2 :

 112 Figure 1.2: Higgs boson production mechanisms at tree level in proton-proton collisions: (a) gluon-gluon fusion; (b) VV fusion; (c) W and Z associated production (or Higgsstrahlung); (d) t t associated production.

Figure 1 . 3 :

 13 Figure 1.3: On the left, cross section for the dierent Higgs boson production mechanisms, as a function of the centre-of-mass energy for a Higgs mass of 125 GeV. On the right, total cross section for pp → H + X for √ s = 7 TeV, √ s = 8 TeV and √ s = 14 TeV, in the Higgs mass range 100 < M H < 300 GeV.

Figure 1 .Figure 1 . 4 :

 114 Figure 1.4: On the left, branching ratio of dierent Higgs boson decay channels as a function of the Higgs boson mass. On the right, Standard Model Higgs boson production cross section times branching ratio at √ s = 8 TeV in the whole mass range up to 1 TeV [10, 11].

  Higgs boson only couples to massive particles. Nevertheless the Higgs boson decays to two photons through a loop of massive charged particles, mainly W bosons and top quarks. The leading order Feynman diagrams, where the W loop and top quark loop interfere destructively, are shown in Figure 1.5.

Figure 1 . 5 :

 15 Figure 1.5: Leading order Feynman diagrams for Higgs boson decaying to two photons.

1. 5 15 Figure 1 . 6 :

 51516 Figure 1.6: Total decay width of the Higgs boson as a function of its mass [10].

Figure 1 . 7 :Figure 1 . 8 :

 1718 Figure 1.7: On the left, diphoton mass spectrum together with the background subtracted mass spectrum. On the right, distribution of the four-lepton reconstructed mass for the sum of the 4e, 2e2µ and 4µ channels. Shaded histograms represent the backgrounds, and the unshaded histogram represents the signal expectation for a mass hypothesis of m H = 125 GeV.

Figure 1 . 9 :

 19 Figure 1.9: SM phase diagram in terms of Higgs and top pole masses in the region of the preferred experimental range of m H and m t . The plane is divided into regions of absolute stability, meta-stability and instability of the SM vacuum. The grey areas denote the allowed region at 1, 2, and 3σ.

Figure 1 . 10 :

 110 Figure 1.10: Scan of the negative log-likelihood, -2∆lnL, as a function of Γ H for the combined t of the 4 and 2 2ν channels (blue thick lines), for the 4 channel alone in the o-shell and on-shell regions (dark red lines), and for the 2 2ν channel in the o-shell region and 4 channel in the on-shell region (light red lines). The solid lines represent the observed values, the dotted lines the expected values.

Figure 1 .

 1 12 (right) shows the scaling of the coupling of the Higgs as a function of the particle mass. Both plots indicate that the observation is compatible with the SM expectation.

Figure 1 . 12 : 1 . 6

 11216 Figure 1.12: On the left the 68% CL condence regions for individual channels (coloured swaths) and for the overall combination (thick curve) for the k V and k f parameters are shown. The cross indicates the global best-t values. The dashed contour bounds the 95% CL condence region for the combination. The diamond represents the SM expectation,(k V ,k f ) = (1,1). On the right the scaling of the coupling of the Higgs is shown as a function of the particle mass.

))s = 13 TeVFigure 2 . 1 :

 1321 Figure 2.1: Cumulative luminosity versus day delivered (blue) to, and recorded (orange) by CMS during stable beams and for p-p collisions at 7 TeV centre-of-mass energy in 2011 (top), 8 TeV centre-of-mass energy in 2012 (middle) and 13 TeV centre-of-mass energy in 2016 (bottom).

2. 2

 2 The CMS detector 25 putting the Standard Model of particle physics to its most stringent test yet, searching for new physics beyond this well-established theory describing particles and their interactions. Run 2 will be also the occasion to perform more precise studies of the physics processes already known, and in particular it will be possible to analyze more in detail the Higgs boson properties.The rst beams started circulating in april 2015 at an energy of 450 GeV, to reach gradually the expected energy of 13 TeV. The rst part of Run 2 nished in november 2015 and it was followed by a brief technical stop during winter. The total integrated luminosity delivered was 4.22 fb -1 , out of which CMS recorded 3.81 fb -1 .

  to ensure redundancy and robustness to the muon trigger. Schematic views of the CMS detector are shown in Figures 2.3 and 2.4.

Figure 2 . 2 :

 22 Figure 2.2: A three dimensional view of the CMS detector with the conventional coordinate system.

Figure 2 . 3 :

 23 Figure 2.3: Longitudinal view of one quarter of the CMS detector.

Figure 2 . 4 :

 24 Figure 2.4: Transverse view of the CMS barrel region.

Figure 2 . 5 :

 25 Figure 2.5: The pixel detector: the barrel section and the two disks of the endcaps are visible.

  three layers between |z| of 80 and 90 cm, plus a Tracker EndCap (TEC) region of nine layers located between |z| of 124 and 280 cm. A fraction of the layers includes double layered modules, with a second set of strips oriented at an angle of 100 mrad with respect to the rst. The combination with these stereo measurements can give a position measurement in the third dimension with a precision ranging from 230 to 530 µm. A schematic view of the tracking detectors, labeled by region, is shown in Figure 2.6.

Figure 2 . 6 :

 26 Figure 2.6: A diagram of the CMS inner tracking detectors, showing the layers of the silicon pixel and strip tracking detectors.

Figure 2 . 7 :

 27 Figure 2.7: The amount of material in the inner tracking detectors, measured in units of radiation lengths, and broken down by detector regions.

Figure 2 . 8 :

 28 Figure 2.8: Temperature dependence of the P bW O 4 light yield.

Figure 2 . 9 :

 29 Figure 2.9: P bW O 4 crystals with photodetectors attached. Left gure: a barrel crystal with the upper face depolished and the APD capsule. In the insert, a capsule with the two APDs. Right gure: an endcap crystal and VPT.

Figure 2 . 10 .

 210 The main design characteristics are strongly prescribed by the need to have accurate measurements of electrons, photons and missing energy. The mechanical design should in particular minimize the amount of material in front of the calorimeter, optimize the interface with the tracking system and with the Hadron Calorimeter, ensure the best possible hermeticity by minimizing the gaps between crystals and the barrel/endcaps transition region, stabilize the crystal temperature within a tenth of a degree.

Figure 2 . 10 :

 210 Figure 2.10: The layout of the barrel and endcap ECAL subdetectors, along with the preshower detector.

Figure 2 . 11 :

 211 Figure 2.11: Pseudorapidity coverage of a quarter of the CMS electromagnetic calorimeter.

2.2 The CMS detector 37 Figure 2 . 12 :

 37212 Figure 2.12: On the left, structure of a barrel APD; on the right, pair of APDs to be installed on a crystal rear face.

Figure 2 . 13 :

 213 Figure 2.13: On the left, structure of an endcap VPT; on the right, picture of a VPT detector.

Figure 2 . 14 :

 214 Figure 2.14: ECAL readout chain, from the crystal light emission to the digitized signal.

Figure 2 . 15 :

 215 Figure 2.15: Data ow in the CMS Trigger/DAQ system. The software-based High-Level Trigger lters via the Data Acquisition system (DAQ) the events passing hardware-based Level-1 trigger. Time axis goes from upside down.

  The barrel hadronic calorimeter (HB) surrounds the electromagnetic calorimeter and covers the central pseudorapidity region up to |η| = 1.3. The endcap regions are covered up to |η| = 3 by the two endcap hadron calorimeters (HE). The HB and HE are located inside the solenoid magnet. To satisfy the hermeticity requirements, two forward hadronic calorimeters (HF) surround the beam pipe at |z| = 11 m, extending the pseudorapidity coverage up to |η| = 5.

Figure 2 . 16 :

 216 Figure 2.16: The layout of the various HCAL subdetectors showing their respective coverage in pseudorapidity.

Figure 2 . 18 :Figure 2 . 19 :

 218219 Figure 2.18: Longitudinal view of one quarter of the muon system.

Figure 2 . 20 :

 220 Figure 2.20: Orthogonal sections of a cathode strip chamber.

2. 3 49 Figure 2 . 21 :

 349221 Figure 2.21: Section of a double gap resistive plate chamber.

  photons in Z → ee events. Finally the photon identication systematics were assessed. The data-simulation comparison and the treatment of systematic uncertainties are presented in Section 3.3.3.

52

 52

Clustering in Run 1

 1 Photons are reconstructed in the detector pseudorapidity range |η| < 1.479 in the barrel and 1.479 < |η| < 2.5 in the endcap. Clustering of ECAL shower energy is performed on intercalibrated, reconstructed signal amplitudes. The clustering algorithm collects the energy from radiating electrons and converted photons that get spread in the φ direction by the magnetic eld. This algorithm evolves from xed matrices of 5×5 crystals, which provide the best reconstruction of unconverted photons, by allowing extension of the energy collection in the φ direction, to form superclusters. Clusters are built starting from a seed crystal, which is the crystal with highest E T above a certain threshold among the crystals not included in any other cluster yet. In the barrel, where the crystals are arranged in an (η, φ) grid, the clusters have a xed width of ve crystals centered on the seed crystal, in the η direction. Then, 5×1 matrices of crystals (bars) each centered at the same η of the seed crystal are built, within the range ± 17 crystals in φ from the seed crystal. The bars with total energy above a certain threshold connected in φ are further grouped into clusters called basic clusters. The basic clusters with the highest bar energy above a certain threshold are nally grouped to form a supercluster. In Figure3.1 a schematic view of the η -φ window opened to build the supercluster in the barrel is shown.

Figure 3 . 1 :

 31 Figure 3.1: A supercluster algorithm collects all calorimetric clusters, satisfying a given geometric condition (e.g. lying in a certain region around the main cluster), into a collection of clusters.

3. 1 reconstruction 55 Figure 3 . 2 :

 15532 Figure 3.2: Representation of ∆φ and ∆η distances between each cluster and the max-energy cluster for |η| going from 0 to 3, in slices of |η| = 0.25. The simulation is done using a photon gun with p T between 10 and 100 GeV. Taken from an internal presentation.

3. 2 identication 57 Figure 3 . 3 :Figure 3 . 4 :

 2573334 Figure 3.3: Comparison between particle ow reconstruction (red) and calorimeter-based (black) reconstruction of single taus with p T = 50 GeV. In the left plot the dierence, in GeV, between the reconstructed and the true visible transverse momentum is shown. The right plot shows the dierence, in radian, between the reconstructed and the true azimuthal angle. Taken from Reference [39].

58

 58

S 4 :

 4 E 2×2 /E 5×5 , the ratio of the maximum energy 2×2 crystal grid and the energy in a 5×5 crystal grid centered on the seed crystal.

σ

  iηiη : the log-energy weighted standard deviation of single crystal η in crystal index within the 5×5 crystals centered at the seed crystal. The weight percrystal is 4.7 plus the logarithm of the ratio between the energy in the crystal and the energy in the 5×5 crystals. If the weight is negative then 0 is used instead. cov iηiΦ : the log-energy weighted covariance of single crystal η -Φ in crystal index within the 5×5 crystals centered at the seed crystal. • Shower shape supercluster variables: SC η-width (σ η ): the energy-weighted standard deviation of single crystal η in detector coordinate within supercluster. The weight per-crystal is the ratio of the single crystal energy to the supercluster energy. SC Φ-width (σ Φ ): the energy-weighted standard deviation of single crystal Φ in detector coordinate within supercluster. The weight per-crystal is the ratio of the single crystal energy to the supercluster energy. Preshower σ RR (endcap only): the sum in quadrature of the energy-weighted standard deviation of the strip index in the x and y planes of the preshower detector.

3. 2 identication 61 •

 261 Photon Tracker isolation in a hollow cone (TrackerIso in Table4.2): transverse momentum sum associated with all tracks falling in a cone size of R=0.3 around the photon candidate direction. Tracks falling in an inner cone of size R=0.04 are not included in the p T sum.

Figure 3 . 5 :

 35 Figure 3.5: Schematic view of a decision tree.

  , 3.7 and 3.8 the distributions of shower shape and isolation variables are shown, for prompt photons (signal) and fake photons (background) belonging to γ + jet simulated sample and for the dierent reconstructions. These distributions are obtained applying the preselection cuts of Run 1 analysis. These cuts are in general quite similar to those presented in Section 4.4, and are responsible for discontinuity in the distribution of PF Charged ISO (worst vertex) and R 9 .

Figure 3 . 6 : 67 Figure 3 . 7 :

 366737 Figure 3.6: Distributions of shower shape variables σ iηiη (top row), σ iηiΦ (middle row) and S 4 (bottom row) for signal prompt photons (solid line) and background fake photons (dashed line) in the barrel (left) and in the endcap (right). The distributions are shown for the three reconstruction algorithms, RECO (blue), GED (grey) and GED5×5 (red). Photons are from γ + jet samples passing the Run 1 preselection.

68 3 .

 3 Figure 3.8: Distributions of isolation variables PF Photon ISO (top row), PF Charged ISO (selected vertex) (middle row) and PF Charged ISO (worst vertex) (bottom row) for signal prompt photons (solid line) and background fake photons (dashed line) in the barrel (left) and in the endcap (right). The distributions are shown for the three reconstruction algorithms, RECO (blue), GED (grey) and GED5×5 (red). Photons are from γ + jet samples passing the Run 1 preselection.

  For this reason a dedicated training at 13 TeV for each reconstruction was performed, and the resulting ROC curves were compared. The result is quite dierent with respect to the previous one; as shown in Figure3.10, with three dedicated training the dierent reconstructions have similar performances (solid lines represent the ROC curves coming from the dedicated trainings, while dashed lines represent the ROC curves obtained in the previous study). It has thus been shown that the photon identication has the same performances for the Run 1 reconstruction and for the particle ow-based ones. The little dierences between the three reconstructions present in the variable distributions seem to have no impact on the nal performances of the photon identication and the MVA training is able to compensate by the correlations between variables.

Figure 3 .

 3 Figure 3.11 shows the p T and η SC distributions, for both barrel and endcap, for fake photons and for prompt photons before and after the 2D p T -η SC reweighting mentioned in Section 3.2.2. The distributions of the input variables for the signal and background training samples after the 2D reweighting are shown in Figures 3.12, 3.13, 3.14 and 3.15. The

  photons have a shower prole wider than prompt photons, and the isolation values are in general larger for the fake photons.

Figure 3 .

 3 Figure 3.10: ROC curves obtained applying the Run 1 weights in the computation of ID MVA output variable (dashed lines) and ROC curves obtained with a dedicated training at 13 TeV for each reconstruction (solid lines), in blue for RECO, in grey for GED and in red for GED5×5, for both barrel (left) and endcap (right).

Figure 3 .

 3 Figure 3.11: p T and η SC distributions, for both barrel (left) and endcap (right), for fake photons (dashed red histogram) and for prompt photons before (green) and after (blue) the 2D p T -η SC reweighting, where the 2D p T -η SC distribution of the signal is reweighted to that of the background.

Figure 3 . 12 :

 312 Figure 3.12: Distributions of photon identication BDT input variables σ iηiη (top row), cov iηiΦ (middle row) and S 4 (bottom row) for signal prompt photons (blue) and background fake photons (red) in the barrel (left) and in the endcap (right) from pp collisions at 13 TeV. Photons are from the training samples passing the preselection with p T > 18 GeV and after p T -η SC reweighting.

3. 3 73 Figure 3 . 13 :

 373313 Figure 3.13: Distributions of photon identication BDT input variables R 9 (rst row), SC η-width (second row) and SC Φ-width (third row) for signal prompt photons (blue) and background fake photons (red) in the barrel (left) and in the endcap (right), along with the distribution of preshower σ RR (fourth row) for photons in the endcap only, from pp collisions at 13 TeV. Photons are from the training samples passing the preselection with p T > 18 GeV and after p T -η SC reweighting.

Figure 3 . 14 :

 314 Figure 3.14: Distributions of photon identication BDT input variables PF Photon ISO (top row), PF Charged ISO (selected vertex) (middle row) and PF Charged ISO (worst vertex) (bottom row) for signal prompt photons (blue) and background fake photons (red) in the barrel (left) and in the endcap (right) from pp collisions at 13 TeV. Photons are from the training samples passing the preselection with p T > 18 GeV and after p T -η SC reweighting.

3. 3 75 Figure 3 . 15 :

 375315 Figure 3.15: Distributions of photon identication BDT input variables η SC (top row), SC E RAW (middle row) and ρ (bottom row) for signal prompt photons (blue) and background fake photons (red) in the barrel (left) and in the endcap (right) from pp collisions at 13 TeV. Photons are from the training samples passing the preselection with p T > 18 GeV and after p T -η SC reweighting.

3. 3 77 Figure 3 .

 3773 Figure 3.16: ROC curves obtained doing the training with dierent parameters/variables. In red the default training with Ntrees = 700 and depth = 3, in grey the training with Ntrees = 1000, in blue the training with depth = 6 and in green the training with the addition of the variable H/E.

78

 78

  shows the performance comparison between the training done with the neural network and the training done with the BDT.The performances are very similar, so the BDT was chosen for the nal training, since neural network is very computing and time consuming.

Figure 3 .

 3 Figure 3.17: ROC curves obtained doing the training with dierent MVA techniques, with a BDT in red and with a neural network MLP in blue.

  Figure 3.18: Output distribution of the BDT: barrel (left) and endcap (right). The blue histograms represent the prompt photons, the red histograms the fake photons. The points correspond to training samples, the histograms to test samples.

Figure 3 .

 3 [START_REF] Vardan Khachatryan | Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV[END_REF] shows the photon identication BDT score of the lower-scoring photon in diphoton pairs with an invariant mass, m γγ , in the range 100 < m γγ < 180 GeV, for events passing the preselection, in data and simulated background events. The sum of all the backgrounds is consistent with data, even if some discrepancies are visible in the high-score region. These discrepancies are taken into account in the treatment of the systematic uncertainties, presented in the next section.

Figure 3 .Figure 3 . 19 :Figure 3 . 20 :

 3319320 Figure 3.20 shows background eciency versus signal eciency of the identication performances for the new ID MVA (in blue) and for identication used in the 8 TeV analysis (in red) applied in the 13 TeV environment. Eciencies are relative to the preselection

Figure 3 . 21 : 3

 3213 Figure 3.21: Signal and background eciency versus p T (top), supercluster η (middle) and number of vertices (bottom). Left plots refer to the barrel, right plots to the endcap.

  with a linear correction that expands the uncertainty at low BDT scores. The photon ID MVA score distribution, for data and MC, with the nal systematic uncertainty is shown in Figure3.23.

Figure 3 . 22 :

 322 Figure 3.22: Data/MC comparison distribution for three shower-shape variables, R 9 , S 4 and SC η-width, for both barrel (left) and endcap (right). Some discrepancies between data and MC are evident, in particular in the barrel.

  Photon ID BDT score 0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Data/MC 0.5 1 1.5

Figure 3 . 23 : 4 H

 3234 Photon ID BDT score 0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Data/MC 0.5 1 1.5

  and the corresponding Higgs signal model and background model, are constructed. The signal model is obtained from Monte Carlo simulated Higgs events, while the background 88 4. H → γγ analysis at 13 TeV one directly from the data. The Higgs signal is nally extracted by statistical procedures based on simultaneous likelihood t to the diphoton mass spectra over all event classes.

Section 4 . 1 . 3 .

 413 Part of the soft process, namely hadronisation and quark connement, occurs instead at the momentum scales of non-perturbative QCD. Phenomenological models have to be used in this context, based on experimental data. Because of the processindependence of the soft-process phenomenology, these models have a general validity.

90 4 .

 4 H → γγ analysis at 13 TeV4.1.2 Parton distribution functionsThe PDF functions in Equations 4.1 and 4.2 relate the dynamics of the partons entering the hard scattering to that of the colliding hadrons, by modelling the probability that a parton carries a fraction x of the momentum of the proton. The PDF depend on the momentum transfer Q 2 , because of higher-order corrections from real and virtual gluon emission within the colliding protons. In good approximation, the PDF evolution as a function of the energy scale Q 2 of the process can be calculated by the Altarelli-Parisi, or DGLAP, equations, developed in the perturbative theory[START_REF] Altarelli | Asymptotic Freedom in Parton Language[END_REF][START_REF] Dokshitzer | Calculation of the Structure Functions for Deep Inelastic Scattering and e+ e-Annihilation by Perturbation Theory in Quantum Chromodynamics[END_REF][START_REF] Gribov | e+ e-pair annihilation and deep inelastic e p scattering in perturbation theory[END_REF].The x dependence is extracted from a global t to data, including few thousands measurement points from deep inelastic scattering (DIS), Drell-Yan and jet production. Results are available at the tree-level, at the next-to-leading (NLO) and, only partially, at the next-to-next-to-leading (NNLO) order. The PDF extrapolations are aected by uncertainties, accuracy of the experimental data and of the analysis, uncertainty on the coupling constant α S , and have to be taken into account as source of uncertainty in all theoretical predictions.

4. 1 Figure 4 . 1 :

 141 Figure 4.1: Overview of the steps in event generation.

Figure 4 . 2 :

 42 Figure 4.2: The hard subprocess in the event generation: two protons (displayed by gray ellipses) collide with each other. Thus one high energetic parton from each proton interacts with the other one in a hard interaction and produces two further fundamental objects (shown by two red outgoing lines). The other partons (displayed by two black arrows) from each proton are unaected by the collision and keep on ying. Taken from Reference [52].

4 .

 4 H → γγ analysis at[START_REF] Vardan Khachatryan | Observation of the diphoton decay of the Higgs boson and measurement of its properties[END_REF] TeV obtained from the matrix element have high energies. The strongly interacting partons (quarks and gluons) carrying a colour charge can emit QCD radiation in the form of gluons, similar to the electromagnetic shower generated by electrically charged particles. However, in contrast to QED radiation in which the uncharged photons, being the gauge bosons of QED, can produce only pairs of electrons, the gluons, being the gauge bosons of QCD, carry a colour charge themselves and hence can interact among each other by emitting further

Figure 4

 4 Figure 4.3.

Figure 4 . 3 :

 43 Figure 4.3: The parton shower step during the event generation: splitting of partons in the initial-state (before the hard interaction shown in red took place) and in the nal-state (after the hard interaction) by emitting gluons (displayed in blue color) is shown. The newly emitted gluons (blue color) can radiate further gluons (green color). Taken from Reference [52].

4. 1

 1 Principles of Monte Carlo simulation and H → γγ Monte Carlo samples 93 the dynamics reach a non-perturbative phase and at some point the coupling between the individual colour charged partons becomes strong enough to bound partons in colorless hadrons. The hadronization process begins roughly at an energy of 1 GeV (the exact value depends on the hadronization model) and cannot be described by the perturbative techniques currently available. For this reason, hadronization models based on empirical data are needed for the description of this formation of hadrons.The cluster hadronization approach is represented in Figure4.4: the quarks and gluons from the previous parton shower step form colour neutral clusters with corresponding colour partners (displayed as white ellipsoid objects). In a second step the clusters are rearranged and, if necessary, split into smaller clusters in a way that the clusters have a limited cluster mass and can decay into hadrons (shown in yellow color) using a simple decay model. The produced hadrons are the rst particles in the event generation process which could theoretically be observed in nature. But most of these hadrons have only a short mean life time τ . Because of that only a small fraction of these hadrons is observed by particle detectors while most of them decay beforehand.

Figure 4 . 4 :

 44 Figure 4.4: The hadronization process in the event generation: colourless clusters are formed by colour charged partons which have reached the hadronization scale by parton splitting and soft gluon emission. The clusters are rearranged and, if necessary, split into smaller clusters in a second step before the cluster decays to observable hadrons. Taken from Reference [52].

4. H → γγ analysis at 13 TeVFigure 4 . 5 :

 1345 Figure 4.5: The hadron decay stage during the event generation: the excited and unstable hadrons, formed in the previous hadronization, decay into further hadrons until only longliving or stable hadrons are left over. Taken from Reference [52].

Figure 4 .

 4 [START_REF] Fermi | Trends to a Theory of beta Radiation[END_REF] the so-called underlying event is represented: the undisturbed ying beam remnants (shown in brown colour), consisting of partons, can split and emit gluons (blue colour) while they form hadronization clusters (white ellipsoidal objects), also with the partons originating from the hard subprocess and the subsequent parton shower step, before decaying into additional hadrons (displayed in yellow colour).

4. 1 Figure 4 . 6 :

 146 Figure 4.6: The underlying event in the event generation process: the beam remnants (shown in brown colour) consisting of partons which do not participate in the hard subprocess (red point) can split and emit gluons (in blue) while they form hadronization clusters (white ellipsoidal objects). Such hadronization clusters can also include partons from the hard subprocess and decay into hadrons (yellow colour). Taken from Reference [52].

Figure 4 . 7 :

 47 Figure 4.7: Leading order Feynman diagrams for QCD diphoton production from quark (left) and gluon (right) initial states.

Figure 4 . 8 :

 48 Figure 4.8: Example of tree-level Feynman diagrams for QCD diphoton production in association with one or two additional jets.

4. H → γγ analysis at 13 Figure 4 . 9 :

 1349 Figure 4.9: Distribution of the number of reconstructed vertices for Z → ee events in data (black dots) and simulation after having applied the re-weighting on the number of simulated pile-up events (blue histogram).

Figure 4 . 10 :

 410 Figure 4.10: Trigger eciency, as a function of oine probe p T , measured on data for Z → ee events using the tag and probe technique. Eciency of photons in the 4 cut-based analysis categories are shown. The plots correspond to the dierent p T thresholds used to seed the diphoton HLT trigger, 22 GeV (on the left) and 10 GeV (on the right).

Figure 4 . 11 :

 411 Figure 4.11: Trigger eciency measured on data for Z → ee events using the tag and probe technique. The four untagged cut-based categories are shown for the seeded (left) and unseeded (right) HLT leg of the diphoton trigger.

Figure 4 . 12 :

 412 Figure 4.12: Comparisons of data to simulation for the invariant mass of di-electrons from Z boson decay reconstructed as photons. The events are splitted in η, R 9 categories. The comparison between the simulation (lled histograms) and data (black points) is shown.

106 4 .

 4 H → γγ analysis at 13 TeV

3. 3 . 2 )

 32 for both photons are categorized by mass resolution, signal-to-background ratio and production mechanism. The production mechanisms which dier from gluon fusion can be identied by selecting nal state objects in addition to the diphoton pair. The Vector Boson Fusion production is characterized by the presence of a pair of jets separated by a large rapidity gap. The tagging of VBF events increases the overall sensitivity of the analysis and the precision on the measured signal strength, and allows to measure the 4.8 Diphoton BDT 109 coupling to vector bosons. The tagging of the ttH production mode, which is accompanied by b-quarks and possible charged leptons or additional jets, increases the sensitivity of the measurement of the coupling to vector bosons and top quark, and further probes the compatibility of the observed signal with a SM Higgs boson.

  110

Figure 4 . 13 :Figure 4 . 14 :

 413414 Figure 4.13: The diphoton classier ROC curve (left) and the BDT output variable, normalised to unity, for simulated signal and background events (right).

Figure 4 .

 4 15 also shows data-simulation comparison and the denition of the diphoton BDT-based untagged categories (described later in Section 4.8.3), with the black dashed lines showing the boundaries of the categories and the grey shaded area identifying the region of low BDT values where events are excluded from the analysis. The data and simulation are in good agreement.

Figure 4 . 15 :

 415 Figure 4.15: The transformed BDT output distribution is compared between simulation (stacked histograms) and data (black points). The transformation is done in order to have a at distribution for signal events.

  .

Figure 4 . 16 :

 416 Figure 4.16: Data-simulation comparison for diphoton BDT output for electrons reconstructed as photons from the decay of the Z boson. The red band indicates the impact on the BDT output variable of the systematic uncertainties on the photon ID BDT variable and on σ E /E.

  and 4.16 and depend on the luminosity.

Figure 4 . 17 :

 417 Figure 4.17: Expected signicance as a function of the number of categories. The estimate of the expected signicance is approximated since it is extracted from a simplied signal+background t. It can be seen how the relative gain in expected signicance is of the order of 1% after n = 4.

Figure 4 .

 4 Figure 4.18, which shows the ROC curves for VBF signal eciency vs eciency for various backgrounds for both the dijet BDT and the combined BDT, demonstrates that the combined BDT is better than the dijet BDT at rejecting the background, especially QCD. In Figure 4.19 the dijet and the combined BDT outputs are shown for VBF signal, gluon fusion, the background simulation and data.

4. H → γγ analysis at 13 Figure 4 . 18 :Figure 4 . 19 :

 13418419 Figure 4.18: Eciency in VBF signal simulation versus QCD eciency (top left), versus gluon fusion eciency (top right), versus preselected data eciency (bottom left) and versus SM diphoton background eciency (bottom right). All samples passed through the VBF preselection before entering the calculation. The combined BDT is better than the kinematic dijet BDT at rejecting backgrounds containing fake photons from QCD.

120 4 .

 4 H → γγ analysis at 13 TeV

Figure 4 . 20 :

 420 Figure 4.20: Distribution of diphoton BDT for signal, data sidebands and control samples in the hadronic (left) and leptonic (right) categories. The histograms are normalized to the area of the sidebands to compare the shape of the distributions.

Figure 4 . 21 :

 421 Figure 4.21: Fit results for the signal shape of simulated ggH events in the Untagged 1 category. The plots show the case when the right vertex (left) or the wrong vertex (right) is chosen. The black points are weighted events from simulated data and the lines represent the ts when 1 (blue), 2 (red), 3 (green) or 4 (pink) Gaussians are included in the t. The mean, width and relative size of the Gaussians are allowed to vary independently. Similar plots are used to determine the number of Gaussians to use to t each process and category.

Figure

Figure 4 . 22 :

 422 Figure 4.22: The eciency × acceptance of the signal model as a function of m H for all categories combined. The yellow bands indicate the eect of the systematic uncertainties.

Figure 4 . 23 :

 423 Figure 4.23: Full parametrized signal shape integrated over all event classes for the m H = 125 GeV scenario at √ s = 13 TeV. The black points represent weighted simulation events and the blue line is the corresponding model. Also shown are the σ ef f value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution), FWHM and the corresponding interval.

Figure 4 .

 4 [START_REF] Aitchison | Supersymmetry in Particle Physics: An Elementary Introduction[END_REF] shows an example of the background t with the dierent functions and the best t background parametrization (assuming no signal), for two event categories. The uncertainties on the background shapes associated with the statistical uncertainties of the ts are shown by the 1 σ and 2 σ bands.

Figure 4 .

 4 Figure 4.24: On the top, the set of functions chosen to t the background using the discrete

4. 15

 15 Results131uncertainty. The resulting dierence in the selection eciency for the t tH leptontagged category is less than 1%.

Figures 4 .

 4 Figures 4.25 and 4.26 show the data, the background-only and the signal plus background model t for each category used in this analysis. The 1 σ (green) and 2 σ (yellow) uncertainty bands shown for the background component of the t include the uncertainty in the tted parameters.

Figure 4 .

 4 Figure 4.27 shows the diphoton mass spectrum with each event weighted proportionally to S/(S+B), where S and B are the numbers of expected signal and background events respectively.

Figure 4 . 25 :

 425 Figure 4.25: Data points (black), background-only t (dashed red) and S+B model t (red) in the four untagged categories are shown. The 1 σ (green) and 2 σ bands (yellow) include the uncertainties of the t. The bottom plot shows the residuals after background subtraction.

Figure 4 . 26 :

 426 Figure 4.26: Data points (black), background-only t (dashed red) and S+B model t (red) in VBF and ttH categories are shown. The 1 σ (green) and 2 σ bands (yellow) include the uncertainties of the t. The bottom plot shows the residuals after background subtraction.

Figure 4 . 27 :

 427 Figure 4.27: The diphoton mass spectrum where the categories are summed weighted by their sensitivity. Data points (black), background-only t (dashed red) and S+B model t (red) are shown. The 1 σ (green) and 2 σ bands (yellow) include the uncertainties of the t. The bottom plot shows the residuals after background subtraction.

4 .

 4 28 the expected and observed signicances for the observation of a standard model Higgs boson are shown as a function of m H . The local signicance for the observation of a standard model Higgs boson at m H = 125.09

Figure 4 .

 4 Figure 4.28: The observed p-value (black) is compared to the SM expectation across the t range 120-130 GeV, where the SM Higgs boson is assumed to have a mass m H = 125.09 GeV (blue). The red line shows the maximum signicance for each mass hypothesis in the range 120 GeV < m H < 130 GeV.

Figure 4 .

 4 Figure 4.29: The likelihood scan for the signal strength modier µ = σ/σ SM , where the value of the Standard Model Higgs boson mass is proled in the t.

Figure 4 . 30 :

 430 Figure 4.30: Signal strength modiers (black points) measured in each category (top) and for each process (bottom) for proled m H , compared to the overall signal strength (green band) and to the SM expectation (dashed red line).

Figure 4 . 31 :

 431 Figure 4.31: The 2-D best-t (black cross) of the signal strength modiers (µ = σ/σ SM ) for fermionic (ggH, t tH) and bosonic (VBF, ZH, WH) production modes compared to the SM expectations (red diamond). The Higgs boson mass is proled in the t. The solid (dashed) line represents the 1 σ (2 σ) condence region.

Figure 5 . 1 :

 51 Figure 5.1: Higgs boson produced through the vector boson fusion and decaying to two photons.

5 .Figure 5 . 2 :

 552 Figure 5.2: Vector boson fusion production (left), and gluon fusion production with two additional jets (right), with the H decaying to two photons.

5. 4

 4 Classifying Higgs boson production processes 5.4.1 Discriminating variables and 1D kinematic discriminants As briey described in Section 5.1, the analysis has to discriminate on one hand VBF (0 + ) from VBF (0 -) processes, on the other hand ggH from VBF scalar processes. The kinematics of the production of the Higgs boson and the 2 jets in the H → γγ channel are sensitive to its spin and parity. This is illustrated in Figures 5.3 and 5.4, where some kinematic variables of the system H → γγ + 2 jets are shown after the VBF selection described in Table

5. 5

 5 and 5.6.

MFigure 5 . 3 :146 5 .Figure 5 . 4 :Figure 5 . 5 :Figure 5 . 6 : 5 .

 5355455565 Figure 5.3: Distributions of kinematic variables of the diphoton-dijet system. The distributions are shown for four dierent production/spin-parity hypotheses, VBF 0 + (blue), VBF 0 -(green), ggH 0 + (red) and ggH 0 -(magenta). The VBF selection of the analysis was applied.

Figure 5 . 7 :

 57 Figure 5.7: Simulated distributions for the ggH 0 + and ggH 0 -processes for three kinematic discriminants: the one sensitive to ratios of scalar to pseudoscalar components in the HVV vertex assuming a VBF production (top), the one for the discrimination between VBF and ggH production under the hypothesis of a scalar Higgs boson (middle), and the one sensitive to ratios of scalar to pseudoscalar components assuming a ggH production (bottom).

5 .

 5 Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

Figure 5 . 8 :

 58 Figure 5.8: 2D maps composed by the two kinematic discriminants described in Section 5.4.1 and calculated for simulated samples, VBF 0 + , VBF 0 -, ggH 0 + , and data (the mass region between 115 and 135 GeV is excluded in data). The distributions are normalized to 1.

Figure 5 . 10 : 5 .

 5105 Figure 5.10: Prole likelihood scan for the optimisation of the VBF vs ggH discriminant.The triangles show the expected -2∆lnL value as a function of µ V BF , for two 1D categories on the left and for three 1D categories on the right.

Figure 5 . 11 : 5 .

 5115 Figure 5.11: 2D maps composed by the two kinematic discriminants described in Section 5.4.1 and calculated for both simulated samples, VBF 0 + , VBF 0 -and ggH 0 + , and data (the mass region between 115 and 135 GeV is excluded in data). The 4 categories chosen after the optimisation are delimited by red lines and are numbered from 0 to 3.

Figure 5 . 12 :

 512 Figure 5.12: Likelihood value at 0 as a function of the cut on the diphoton MVA.

  is produced, there would be Poisson uctuations on the numbers in each bin. A t to the data would give a value τ m ± σ m . Then, for a large number of events in the distribution, we would expect τ m to be approximately Gaussian distributed about τ g , 5.8 Bias study for the background function 159 even though the distribution 5.26 is non-Gaussian. For many repetitions of this procedure, the quantityg = τ m -τ g σ m(5.27)should follow a Gaussian distribution. The above denition is called a pull and can be used for checking the properties of a tting algorithm with large numbers of pseudo-experiments.

5 .Figure 5 . 13 :

 5513 Figure 5.13: Distribution of N f itted -N expected for category 0. Events are generated accord-

Figure 5 . 17 :Figure 5 . 18 : 5 .

 5175185 Figure 5.17: Distribution of the event yield in the 4 categories for the nominal sample and its variations of ±1σ. At the bottom the ratios between the nominal sample and the ±1σ samples are also shown. Plots on the left represent the JEC, plots on the right the JER. Plots are done for the dierent processes VBF 0 + (top), VBF 0 -(middle) and ggH 0 + (bottom).

Figure 5 . 19 :

 519 Figure 5.19: Fit results for the signal shape of simulated Higgs events in the 4 categories, for VBF 0 + (a), VBF 0 -(b) and ggH 0 + (c).

5 .Figure 5 . 20 :

 5520 Figure 5.20: Fit to the data, in the invariant mass region 100 GeV < m γγ < 180 GeV, in the 4 categories. The tting function (blue solid line) is a polynomial of variable order according to the category (see Section 5.8). The diphoton mass shapes of the simulated signals are also shown, VBF 0 + in red, VBF 0 -in violet and ggH 0 + in green.

Figure 5 .

 5 Figure 5.21 shows the likelihood scan as a function of µ for our analysis, where the cutbased categorisation of Reference [13, 82] has been applied, for the tight category on the left and for the loose category on the right. The black line represents the expected µ and the red line the observed one. Comparing our observed values in the two cut-based

Figure 5 . 21 :Figure 5 . 22 :

 521522 Figure 5.21: Likelihood scan as a function of µ for our analysis (top plots), where the cutbased selection of Reference [13, 82] has been applied, for the tight category on the left and for the loose category on the right. The black line represents the expected µ and the red line the observed one. The plot at the bottom shows the results of Reference [13, 82] at 8 TeV for the dierent categories. The results for the 2 Dijet Tag categories are similar to what we obtain.

Figure 5 . 23 : 5 .Figure 5 . 24 :

 5235524 Figure 5.23: Likelihood scan as a function of fa3 on the left, and as a function of f a3 on the right, where f a3 was obtained applying the transformation described in Equation 5.23. The dashed line represents the expected result, the solid line the observed result.

Figure 5 . 25 :Figure 5 . 26 :

 525526 Figure 5.25: Projection of the limit on fa3 for 250 fb -1 at 8 TeV, which would roughly correspond to 100 fb -1 at 13 TeV assuming that the background scales as the signal.

(- 1 .

 1 theo.) when it is xed to m H = 125.09 GeV.Chapter 5 nally presents a feasibility study, having the aim of constraining the anomalous couplings of the Higgs boson to the vector bosons. This analysis is performed using the data collected at 8 TeV during Run 1 at the LHC, corresponding to an integrated luminosity of 19.7 fb It exploits the production of the Higgs boson through vector boson fusion (VBF), with the Higgs decaying to 2 photons, and it is an alternate and complementary approach to the one usually employed which is to study this coupling in the decay of the Higgs boson H → ZZ * or H → W W * . It is found that even if at 8 TeV we do not reach any 180 Appendices shower in the clustered crystals, and the energy losses of photons which convert in material upstream of the calorimeter. Starting from the raw supercluster energy, this technique aims to make the best prediction of the true photon energy, based on a multivariate approach.

Figure 27 :

 27 Figure27: Ratio of photon raw energy to its true energy compared to the ratio of the photon energy corrected by the regression to its true energy, considering photons from a simulated Higgs to gamma-gamma sample (m H = 125 GeV), in the barrel (left) and in the endcaps (right). The distributions are tted with a double-sided Crystal Ball function.

Figure 28 :

 28 Figure 28: Eciency of choosing the vertex within 1 cm of the true vertex from Higgs to two photons simulation as a function of the p T of the diphoton pair (left) and as a function of the number of vertices (right).

Figure 29 :

 29 Figure 29: Mass resolution worsening in percent as a function of the z dierence between the toy vertex and the true vertex. The plot is done for the events with two photons in the barrel and high R 9 .

Figure 30 :

 30 Figure 30: Comparison between the true vertex identication eciency and the average estimated vertex probability as a function of the reconstructed diphoton p T . All the production modes are included, the reweighting is done according to the cross-sections of the dierent production modes and with respect to pileup in data.

  Résumé substantielDans ce document, deux analyses des propriétés du boson de Higgs se désintégrant en 2 photons dans l'expérience CMS située auprès du LHC (Large Hadron Collider) sont présentées.Le Modèle Standard, théorie quantique des champs qui a pour but la description des constituants élémentaires de la matière, a été testé expérimentalement de manière exhaustive. Développé dans les années 1960-1970, il fournit un élégant cadre mathématique qui décrit la façon dont les constituants fondamentaux de la matière intéragissent entre eux à travers les forces électromagnétique, faible et forte. De plus, il a expliqué et prédit avec succès nombre de résultats expérimentaux et une grande variété de phénomènes. Le Modèle Standard de la physique des particules prévoit l'existence d'un seul boson scalaire de Higgs associé à la brisure spontanée de symétrie. La masse de ce boson est un paramètre libre de la théorie. De plus le champ de Higgs est considéré comme responsable de la masse de toutes les particules élémentaires connues. Cette particule, dont la recherche est l'un des objectifs principaux du collisionneur de hadrons LHC installé au CERN de Genève et de ses expériences, a enn été découverte par les expériences ATLAS et CMS en 2012, avec une masse mesurée d'environ 125 GeV. Les objectifs principaux après la découverte du boson de Higgs sont la mesure de ses propriétés et la recherche de possibles déviations du Modèle Standard. La production inclusive du boson de Higgs du Modèle Standard, suivie par la désintégration en 2 photons, est un des canaux les plus sensibles pour la recherche et l'étude d'un boson de Higgs de masse d'environ 125 GeV. En eet, malgré sa section ecace modeste, il a une signature expérimentale très claire grâce à une excellente résolution expérimentale de la masse diphoton. L'expérience CMS est, avec ATLAS, un détecteur à large spectre. La caractéristique principale de CMS est un soléno ïde supraconducteur, de 13 m de long et 6 m de diamètre, qui fournit un champ magnétique axial de 3.8 T. Le soléno ïde contient la majorité des sousdétecteurs, alors que en déhors du soléno ïde la culasse de retour de champ est équipée de détecteurs à gaz utilisés pour identier les muons. Les trajectoires des particules chargées sont mesurées par le trajectographe, composé de pixels et strips en silicium, couvrant les pseudo-rapidités |η| < 2.5. Un calorimètre électromagnétique (ECAL), composé de crystaux de tungstate de plomb, et un calorimètre hadronique (HCAL), composé de cuivre et de scintillateurs, entourent le trajectographe et couvrent la région |η| < 3. Le calorimètre électromagnétique est composé de 75848 crystaux de tungstate de plomb, qui permettent une couverture en pseudorapidité |η| < 1.479 dans la région du tonneau et 1.479 < |η| < 3.0 dans les régions des bouchons. Un détecteur de pied de gerbe, composé par 2 couches de capteurs de silicium intercalées avec un radiateur en plomb, est placé face aux bouchons. Un calorimètre à l'avant prolonge la couverture calorimétrique jusqu'à |η| < 5. La calibration du ECAL utilise la symétrie axiale du ux d'énergie dans des événements de biais minimum, les désintégrations π 0 , η 0 → γγ, W → eν, et Z → ee. Les variations de transparence des crystaux du ECAL dûes à l'irradiation pendant les périodes de prise de données sont monitorées constamment et corrigées, en utilisant de la lumière injectée par un laser. La résolution du ECAL est de 1% à |η| = 0 pour des photons non-convertis et se dégrade jusqu'à 4% pour des photons convertis à |η| = 2.5. Le dé majeur du canal H → γγ est d'observer un signal noyé dans un bruit de fond plusieurs ordres de grandeurs plus grand. Le bruit de fond peut être séparé en 2 composantes, une irréductible et une réductible. La composante irréductible est constituée d'événements diphoton prompt, c'est à dire un photon issu du vertex de l'intéraction forte. La composante réductible contient des événements dijet et γ + jet, où les jets sont identiés comme des photons (fake). L'identication des photons est un enjeu capital de l'analyse, et elle a le but de réduire le bruit de fond réductible, en général en appliquant des conditions d'isolation et en exploitant les diérences entre les prols des gerbes dans le calorimètre pour distinguer entre un photon prompt et un couple de photons provenant de la désintégration d'un méson neutre. Dans cette thèse les algorithmes de reconstruction et d'identication des photons sont présentés, avec une attention particulière aux diérences entre le premier et le deuxième run du LHC, le premier run (Run 1) ayant été pris entre 2010 et 2012 avec une énergie dans le centre de masse de 7 puis 8 TeV, le deuxième (Run 2) ayant commencé en 2015 avec une énergie dans le centre de masse de 13 TeV. La principale nouveauté présente dans la reconstruction du Run 2 est l'utilisation de l'algorithme du ux de particules, qui permet une description globale de l'événement. Les performances des reconstructions du Run 1 et du Run 2 en ce qui concerne l'identication des photons pour le Run 2 sont comparées et on obtient des performances similaires. Ensuite l'algorithme d'identication des photons pour l'analyse H → γγ est optimisé pour le Run 2. Pour ce faire, une méthode d'analyse multivariée, qui prend en considération des variables discriminantes liées au prol de la gerbe et à l'isolation, est utilisée. Les performances de l'identication des photons pour le Run 2 sont enn étudiées et une validation données-simulation est eectuée. La Figure 32 représente l'ecacité pour le bruit de fond en fonction de l'ecacité pour le signal, en bleu pour la nouvelle identication des photons et en rouge pour l'identication utilisée dans l'analyse du Run 1 et appliquée aux échantillons du Run 2. Cette gure montre que la nouvelle identication a une meilleure performance par rapport à l'ancienne et démontre clairement l'avantage d'une identication des photons dédiée à la nouvelle énergie. La Figure 33 représente une validation données-simulation pour la variable de sortie de l'analyse multivariée. Cette variable est représentée, dans un interval de masse invariante 100 < m γγ < 180 GeV, pour les données et les diérentes composantes du bruit de fond. La somme des composantes du bruit de fond est compatible avec les données, mais quelques désaccords sont visibles pour des valeurs de la variable proches de 1. Ces désaccords sont

Figure 32 :

 32 Figure 32: Courbe de l'ecacité de l'identication des photons pour le bruit de fond en fonction de l'ecacité pour le signal, en bleu pour la nouvelle identication et en rouge pour l'identication utilisée dans l'analyse à 8 TeV et appliquée aux échantillons à 13 TeV. La gure de gauche fait référence au tonneau, celle de droite aux bouchons.

Figure 33 :

 33 Figure 33: Variable de sortie de l'analyse multivariée pour photons appartenant à couples diphoton avec une masse invariante 100 < m γγ < 180 GeV, pour les données (points) et pour la simulation du bruit de fond (histogramme cyan). Les distributions sont représentées aussi pour diérentes composantes du bruit de fond, avec 2, 1 ou 0 photons prompt. La distribution rouge correspond aux événements de signal simulés.

19. 7 fb - 1 .

 71 Avec cette quantité de données la sensibilité à la production VBF est faible, néanmoins cette approche est alternative et complémentaire à celle habituellement utilisée, qui étudie les mêmes couplages dans la désintégration du boson de Higgs H → ZZ * ou H → W W * . Bien que le lot de données du Run 1 ne soit pas susant pour exclure un état pseudo-scalaire, l'analyse montre une sensibilité intéressante à exploiter avec plus de données, en particulier car il s'agit des couplages lors de la production du boson de Higgs. La Figure 36 à gauche représente le prol du likelihood, attendu et observé, en fonction de la fraction de composante pseudo-scalaire. La gure à droite montre la projection pour 250 fb -1 à 8 TeV.

Figure 34 :

 34 Figure 34: Distribution de la masse diphoton où chaque événement est pondéré par un poids selon S/(S+B). Les données (points noirs), l'ajustement sous l'hypothèse de seul bruit de fond (ligne rouge pointillée) et l'ajustement sous l'hypothèse S+B (ligne rouge continue) sont ici représentés. Les bandes 1σ (vert) et 2σ (jaune) contiennent les incertitudes de l'ajustement. La même distribution après la soustraction du bruit de fond est montrée en bas.

Figure 35 :Figure 36 :

 3536 Figure 35: La signication observée (noir) est comparée à celle attendue dans l'interval 120-130 GeV, où on suppose que le boson de Higgs a une masse m H = 125.09 GeV (bleu). La ligne rouge indique la signication statistique attendue pour chaque hypothèse de masse dans l'interval 120 GeV < m H < 130 GeV.

  W , 2m Z . The Higgs boson decays into two massive bosons, W + , W - or ZZ pairs, with a branching ratio of ∼ 70% in the W W and ∼ 30% in the ZZ nal state. In the W W case, its σ × BR is high; however, the presence of neutrinos does not allow reconstruction of the nal state: the measurement of the rate is important but dicult since several backgrounds can mimic the signals. On the other hand, the ZZ decay channel into 4 leptons, electrons or muons, possesses an excellent mass resolution as well as a negligible background rate. The Higgs boson phenomenology at the LHC 13 virtual. As m H approaches 130 GeV, the decay channel into b b pairs is present as well, with a branching ratio ∼ 50%. When the WW threshold (m H ∼ 2m W ) is reached, the b b decay channel contribution gets less important. Until the production threshold of two real Z bosons (m H ∼ 2m Z ), the WW decay completely dominates the branching ratio.

• Intermediate mass region (130 GeV < m H < 180 GeV). The Higgs boson still decays into 4 fermions, through a pair of massive gauge bosons, one of them being

1.4

Table 2 .

 2 1: P bW O 4 compared to other crystals.

		P bW O 4 N aI(T l) BGO
	density (g/cm 3 )	8.28	3.67	7.13
	radiation length (cm)	0.89	2.59	1.12
	Molière radius (cm)	2.2	4.5	2.4
	maximum emission (nm)	440	410	480
	emission time (ns)	5-15	250	300
	scintillation light with a Gaussian-shaped distribution peaking at about 440 nm with a

Table 4 .

 4 1: List of simulated processes and the corresponding matrix element generators.

	4.2 Trigger	101

Table 4 .

 4 2: The loose photon identication cuts for single photon preselection. The photons are divided into four categories according to the photon supercluster position in the ECAL (barrel or endcap) and to the R 9 value. The cut values vary with the photon categories.

	H/E	σ iηiη (5x5) R 9 (5x5) pfPhoIso TrackerIso
	EB; R9 > 0.85 < 0.08		> 0.5
	EB; R9 ≤ 0.85 < 0.08 < 0.015	> 0.5	< 4.0	< 6.0
	EE; R9 > 0.90 < 0.08		> 0.8
	EE; R9 ≤ 0.90 < 0.08 < 0.035	> 0.8	< 4.0	< 6.0

Table 4 .

 4 categories. 3: Preselection eciencies measured in the 4 photon categories using tag and probe

			Data		Simulation	Ratio
		E.	Stat	Syst.	E.	Stat.	E.	Unc.
	Barrel; R 9 >0.85	0.9451	0.0006	0.0192	0.9374	0.0007	1.0080	0.0192
	Barrel; R 9 <0.85	0.8255	0.0012	0.0119	0.8258	0.0009	0.9960	0.0120
	Endcap; R 9 >0.90 0.9099 0.0008 0.0212 0.9127 0.0010 0.9969 0.0212
	Endcap; R 9 <0.90 0.4993 0.0018 0.0249 0.5024 0.0016 0.9938 0.0250

  The muons are requested to have p T > 20 GeV, |η| < 2.4 and to pass criteria summarised in Table 4.4. Electrons must have p T > 20 GeV and |η SC | < 1.4442 or 1.566 < |η SC | < 2.5. The electrons are also required to pass electron identication criteria summarised in Table 4.5.

Table 4 .

 4 4: Muon selection criteria for ttH leptonic tag

	Description		criterion
	χ 2 /n dof			< 10
	d 0 w.r.t. muon vertex	< 0.2 cm
	d z w.r.t. muon vertex	< 0.5 cm
	Number of pixel hits			> 0
	Number of tracker layers with hits		> 5
	Number of muon station hits		> 0
	Number of matched muon station segments		> 1
	Combined relative PF isolation		< 0.25
	Table 4.5: Electron selection criteria for ttH leptonic tag
	Description	Value in barrel	Value in endcap
	σ iηiη <	0.0103		0.0301
	abs(∆η in ) <	0.0105		0.00814
	abs(∆φ in ) <	0.115		0.182
	H/E <	0.104		0.0897
	(1/E -1/P) <	0.102		0.126
	abs(d 0 ) <	0.0261		0.118
	abs(d z ) <	0.41		0.822
	Missing Inner Hit ≤	2		1
	Relative Isolation with Eective Area <	0.0893		0.121

Table 4 .

 4 6: The expected number of signal events per category and the percentage breakdown per production mode. σ ef f and σ HM are also provided as an estimate of the m γγ resolution in that category. The expected number of background events per GeV around 125 GeV is also listed.

	4.15 Results	135

Table 5 .

 5 1: Signal MC samples used in the analysis.

	Sample	HVV coupling
	ggH+jj 0 + at 8 TeV -JHU + pythia6	0 +
	ggH+jj 0 -at 8 TeV -JHU + pythia6	0 -
	vbfH 0 + at 8 TeV -JHU + pythia6	0 +
	vbfH 0 -at 8 TeV -JHU + pythia6	0 -
	vbfH 50% 0 + -50% 0 -at 8 TeV -JHU + pythia6	50/50
	ggH 0 + at 8 TeV -Powheg + pythia6	0 +
	vbfH 0 + at 8 TeV -Powheg + pythia6	0 +

Table 5 .

 5 2.

Table 5 .

 5 2: Summary of event selection criteria. Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγAs outlined in Section 5.1, after this loose VBF selection a contamination from ggH process is still present, more precisely ∼ 60% of the selected events belong to VBF topology, while ∼ 40% derive from ggH production.

	Variable	Requirement
	p j1 T	> 30
	p j2 T	> 20
	mjj	> 250
	|∆ηjj|	> 2
	|∆Φγγjj|	> 2.6
	|ηγγ -(ηj1 + ηj2)/2|	< 2.5

Table 5 .

 5 3: The additional constant term determined from a comparison of data to Monte Search for anomalous couplings of the Higgs boson to electroweak vector bosons in VBF production with H → γγ

	Carlo.
	Photon category	∆σ(%)
	EB, |η| < 1, R9 > 0.94	0.03
	EB, |η| < 1, R9 < 0.94	0.02
	EB, |η| > 1, R9 > 0.94	0.09
	EB, |η| > 1, R9 < 0.94	0.02
	EE, |η| < 2, R9 > 0.94	0.08
	EE, |η| < 2, R9 < 0.94	0.04
	EE, |η| > 2, R9 > 0.94	0.04
	EE, |η| > 2, R9 < 0.94	0.05

Table 5 .

 5 4: The expected number of signal events and the corresponding number of events in data per category.

	Category VBF 0 + VBF 0 -	ggH	bkg
	cat 0	5.079	3.983	4.658 509
	cat 1	1.758	1.078	0.4458 39
	cat 2	1.277	0.7858	0.2181 16
	cat 3	0.2276	6.301	0.3682 42

Table 5 .

 5

	5: The expected number of signal events and the corresponding number of events
	in data per category for cut-based analysis of Reference [13, 82] and for our analysis where
	we applied the same categorisation.
	Category VBF VBF reference ggH ggH reference bkg bkg reference
	cat tight 7.199	7.19	2.127	1.95	352	353
	cat loose 5.273	5.2	5.567	5.15	1033	1029

in the barrel the trigger tower is divided into 5 Φ-oriented strips, whose energy deposits are summed by the FE board trigger pipeline to give the total transverse energy of the tower, called the main trigger primitive

LHC and the CMS detector

Remerciements

Systematics on the Higgs boson mass

In the statistical treatment we use to measure µ V BF and fa3 , we x the Higgs boson mass to its world average 125.09 ± 0.24 GeV and let this mass vary within its uncertainty (0.2%). Conclusions exclusion of a pure pseudo-scalar state, the analysis has some sensitivity to f a 3 . Because of that this new approach should be pursued with larger dataset and a copier number of VBF events. A projection done for the Run 2 LHC data is also presented, showing that with 100 fb -1 at 13 TeV it would be possible to exclude a pure pseudo-scalar state at 95% CL.

Mela SM vs PS VBF

Appendices

Appendix A Tag and probe method One well established approach to measure particle eciencies is the so called tag and probe method. The tag and probe method uses the Z resonance to select an unbiased set of particles like electrons or muons. Z → ee events are selected with triggers requiring at least one electron. The tag electron is required to match a trigger level electron and to pass a tight selection requirement. This allows to select a very pure set of unbiased electrons/positrons. Indeed the other lepton from the Z decay, named probe lepton, is selected only with very loose constraints while still having a very pure sample (the invariant mass of the 2 leptons is required to be compatible with the Z mass to improve further the purity of the sample). One can then test identication criteria on this probe lepton in both data and simulated events. This allows to correct the simulation in order to reproduce the eciency of the selection criteria observed in data.

The eciency itself is measured by counting the number of probe particles that pass the desired selection criteria:

where P pass is the number of probes passing the selection criteria and P all is the total number of probes counted using the resonance.

Appendix B Details on photon energy correction Photon energy regression

Dierent sets of corrections to ECAL reconstructed hits and photon energy are necessary in order to achieve the best photon energy resolution. The rst consists of crystal-level corrections necessary to equalize the channel-to-channel response variations. The second, an high-level correction method called photon energy regression, is applied in order to take into account ner eects. In particular this method corrects for the containment of the