Search for H->mu mu in the VBF production channel with the CMS experiment at LHC

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DIPARTIMENTO DI

FISICA

"ENRICO

FERMI"

CORSO DI

L

AUREA

MAGISTRALE IN

FISICA

Search for H → µµ

in the VBF production channel

with the CMS experiment at LHC

CANDIDATA:

RELATORE

:

Agnese Bonavita

Prof. Paolo Azzurri

Prof. Andrea Rizzi

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Se non potete essere un pino sulla vetta del monte, siate un cespuglio nella valle, ma siate il miglior piccolo cespuglio sulla sponda del ruscello. Siate un cespuglio se non potete essere un albero. Se non potete essere una via maestra siate un sentiero. Se non potete essere il sole siate una stella piccina, non con la mole vincete o fallite. Siate il meglio di qualunque cosa siate. Cercate ardentemente di scoprire

a cosa siete chiamati e poi mettetevi a farlo appassionatamente.

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Introduction

Understanding the mechanism that breaks the electroweak symmetry and generates the masses of the known elementary particles has been one of the fundamental endeavors in particle physics. The breaking of the electroweak symmetry is allowed if at least one new particle with well defined properties is added to the ensemble of the elementary particles. Such a particle has long been know as the Higgs boson. Its discovery at the Large Hadron Collider (LHC) at Cern in 2012 by the ATLAS and CMS collaborations [1] represents therefore a major achievement in the field. Starting in 2012, the properties of the Higgs boson have been measured in many of the accessible final states originating from its decay. The mass of the Higgs boson has been determined to be 125.09 ± 0.21 (stat) ±0.11 (syst) GeV, from a combination of the ATLAS and CMS measurements [2]. Several results from both experiments established that its measured properties, including its spin, CP properties, and coupling strengths to fermions and bosons, are consistent with the Standard Model (SM) expectations.

As new data is collected, the properties of the Higgs boson can be measured with increasing precision and rarer decay modes become accesible. Such measurements are interesting because any deviation from the prediction of the theory might be a hint of new physics beyond the SM. Among the rare decay modes currently under investigation, the Higgs boson decay into two muons (H → µµ) is the object of study of this thesis.

For a Higgs boson with mass of approximately 125 GeV, the probability to decay into a muon pair is expected to be B(H → µµ) = 2.2 × 10−4 _{[3], making it one of}

the smallest accessible at the LHC. On the other hand, the H → µµ signature is one of the cleanest to detect experimentally. Higgs boson decays in two muons are of particular importance because they extend the study of its couplings from the third generation to the second generation of fermions, where deviations from the SM predictions [4], [5] due to new physics are predicted to be larger.

The search for H → µµ presented in this work is performed selecting the vector-boson fusion (VBF) production mode. The cross section is about 10% of the cross section for the gluon-gluon fusion, which is the most important production mode. However, the VBF process gives a cleaner experimental signature. In fact, in the VBF process, a quark coming from each colliding proton radiates a W or Z bosons

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that subsequently interacts. The two quarks therefore slightly deviated from their original flight direction and typically fall inside the detector acceptance, while a Higgs is emitted.

Restricting the scope of the search to the VBF production mode, makes the process even rarer but the peculiar signature of the VBF production mode can be exploited to effectively reduce the experimental backgrounds. The VBF quarks are revealed as jets: two back to back high momentum narrow cones of hadrons and other particles produced by the hadronization of a quark or gluon. Generally the two VBF jets are expected to have high pseudorapidity and large invariant mass while the Higgs decay products are expected to be in the central region of the detector. Imposing the constraints to the invariant mass and the rapidity of the jets as addi-tional cut one reaches an impressive improvement of the signal-to-background ratio. The data used for this search were collected using proton-proton collision at √

s = 13 TeV by the CMS experiment in 2016, corresponding to an integrated luminosity of 35.9 fb−1_{. Only 30 event are expected during the entire data taking}

period. It is therefore essential to have a high signal efficiency, both in the online and the offline selections, while greatly reducing the backgrounds. The dominant sources of background in these studies are production of top quark pairs (tt) and Drell-Yan leptons with associated jets (referred to as DY+jets). These have a good probability to decay into muons, whose tracks risk to be misclassified as coming from a Higgs decay. The DY+jets background is the hardest to discriminate because it is characterized by two real prompt leptons from a virtual Z or γ boson in addition to two jets, either from initial state radiation.

A multivariate approach is used to further discriminate signal from background. As background processes are many orders of magnitude larger than the signal, a Machine Learning (ML) classifier with an extremely good signal acceptance versus background rejection performance is required. For this purpose two different ma-chine learning techniques are used: Boosted Decision Trees (BDTs) and Deep Neural Networks (DNNs). Such systems "learn" (i.e. progressively improve performance on tasks) by considering examples, generally without task-specific programming. The toolkits used in this thesis to implement the multivariate classifier algorithm are TMVA [6] for the BDT method and the Keras library, running on top of Theano, for the NN one. Both are integrated into the ROOT analysis framework.

My personal contribution has been the development of these dedicated multivariate techniques, including the search and selection of the most discriminant variables. In order to improve the suppression of the background sources and to obtain the maximum sensitivity a particular attention was given to the choice of the variables starting with the definition of an extensive set of kinematic observables. Several tests were made to search the best discriminant variables checking also the cor-relation between all the features. Seven variables are considered as the inputs of the BDT. The same input variables are sent to the NN with the addition of other five. After several network configurations the best one results using a pretraining step without the muon invariant mass mll (that is the most discriminant variable)

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vii and then a training with the previous weights with the complete features set. In this way is possible to exploit the discriminating power of all the selected variables. The expected final goal is an improvement of the branching ratio upper limit of the process. The current results are still preliminary but encouraging: for a Higgs boson decaying to two muons, the upper limit on the decay rate at 95% confidence level (CL) is expected to be approximately 2.5 times the SM value.

The present thesis is organized in six chapters. Chapter 1 presents the physics of the Higgs boson including the state of the art of the experimental studies performed by CMS and ATLAS. In Chapter 2, the main features of the Large Hadron Collider (LHC) and the CMS Detector are described. Chapter 3 shows the details of the reconstruction techniques used by the CMS experiment making an emphasis on the physics objects used in this analysis. After a detailed description of the VBF H → µµ event topology, the analysis strategy is explained. The techniques developed to identify and select the input variables are presented in Chapter 4, focusing on the experimental signature of the signal processes and on the main background sources. A description of the machine learning techniques adopted in this work, including all the tests made to find the best options settings is discussed in Chapter 5. Finally, the results are presented in Chapter 6.

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Chapter

1

Standard Model and Higgs Boson

Evolving over the course of decades of theoretical insights and experimental discoveries, the Standard Model (SM) of particle physics can be viewed as a success of the scientific method. In its current incarnation, the SM describes three of the four fundamental forces. It predicts with surprising accuracy all the elementary particles, as well as the form and the strength of their interactions. All the elementary particles predicted by the Standard Model have been observed in high energy experiments, but we know that this is not the end of the story: there are several experimental observations and theoretical questions that cannot be addressed within the SM, such as the dark matter evidence, the acceleration of the universe, the hierarchy problem and the baryon asymmetry problem.

In this chapter, the theoretical framework behind the Higgs boson measurement presented in this thesis is laid out, starting with a description of the SM.

From there, the properties of the SM Higgs boson and the previous experimental results are described.

1.1 The Standard Model

The Standard Model(SM) [7] describes with high precision all known phenomena in particle physics. A detailed description of the SM can be found in [8].

The particles are grouped in two categories: particles with integer spin are called bosons and half-integer spin particles are called fermions. Among bosons, there are the spin-1 gauge bosons which carry the fundamental interactions of nature and the spin-0 Higgs boson that is related to the electroweak symmetry breaking. Among fermions, there are two classes of particles: quarks and leptons. Each class is divided into three generations, and each one is composed of a doublet of particles.

The first generation of leptons is formed by the electron (e), with charge Q=-1 and mass 0.511 MeV, and the electronic neutrino (νe), that is electromagnetically

neutral and almost massless [9]. The first generation of quarks is composed by 1

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the quark up(u), with electric Q=+2/3, and the quark down(d), with Q=-1/3. The masses of both particles are of few MeV. The other generations of particles are similar to the first one, but with higher mass. Quarks exist in three types, with different color charge: red(r), green(g), and blue(b).

Summarizing, in the SM there are three doublets of leptons: ν_e e ν_µ µ ν_τ τ

and nine doublets of quarks: u d r,g,b c s r,g,b t b r,g,b

Fig. 1.1.1: The particles of the standard model: in green the quarks are shown, in yellow it is possible to see the leptons, whereas the gauge bosons appear in the blue boxes.

For each fermion exist an antiparticle with opposite quantum numbers, same mass, and same spin.

1.2 Electroweak Unification

The SM is a gauge theory that contains three local gauge symmetries:

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1.3. SPONTANEOUS SIMMETRY BREAKING 3 The strong nuclear interaction is described by SU (3)C while the electroweak

inter-action by SU (2)L⊗ U (1)Y . This chapter presents only the electroweak interaction

since it is related to the Higgs boson physics.

Given the symmetry group SU (2)L⊗ U (1)Y, the field transformations are defined by

the representation of the group. Each fermionic field is composed by a left-handed and a a right-handed component:

ψ = ψR+ ψL (1.2.2)

Under SU (2)L, left-handed quarks and leptons transform like doublets in the

fun-damental representation (T = 1 2).

Right-handed quarks and leptons are singlets under SU (2)L(T = 0). Each field has

a quantum number, named weak isospin, that is T3 = 0 for singlets and T3 = ±1/2

for doublets. The gauge bosons associated with the three generators of SU (2)L are

called Wi. Under U (1)Y, all fields are singlets and have an associated quantum

number, called hypercharge, that is defined as Y = Q − T3. Using this definition,

the fields contained in each SU (2)Ldoublet have the same weak hypercharge. The

gauge boson associated with the generator of U (1)Y is called B.

We can then write the covariant derivative of SU (2)L⊗ U (1)Y :

Dµ = ∂µ− 1 2igW i µσ i_{− ig}0 Bµ (1.2.3)

where g e g0_{are the two coupling constants, and σ}i _{are the Pauli matrices. Applying}

the substitution ∂µ→ Dµ, the Lagrangian becomes

LHiggs= ¯ψi(iγµDµ− mi)ψi− 1 4F a µνF aµν _(1.2.4)

Still, it has two problems: the gauge bosons are massless, contrary to observation, and the mass term ¯ψimiψi is not gauge invariant. Both problems are solved by the

Higgs-Brout-Englert mechanism [10].

1.3 Spontaneous simmetry breaking

Spontaneous symmetry breaking occurs when a Lagrangian is invariant under a symmetry, but the vacuum state breaks this symmetry. To explain the concept, an example with a U(1) gauge invariance is discussed. It will be then extended to the Standard Model, by considering the more complex group SU (2)L⊗ U (1)Y. Let us

consider the Lagrangian of a gauge theory for a complex scalar field φ: L = −1 4F µν_F µν + (Dµφ)?(Dµφ) + µ2φ?φ − λ 4(φ ?_φ)2 _(1.3.1)

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where Dµφ = ∂µφ − ieAµφ. In this example, the Lagrangian describes a massless

vector Aµ, and the Lagrangian is thus U(1) gauge invariant. If µ2 < 0, it describes

the kinematic of a particle having mass p−µ2 _{. In case µ}2 _{> 0, the minimum of}

the potential is no longer in φ = 0, but it is in the circumference |φ|2 ₌ 2µ2

λ ≡ v 2_.

A sketch of the potential in the case µ2 _{> 0} _{is drawn in Fig. 1.3.1. In this case,}

there are an infinite number of possible potential minima (vacuum states) and each minimum is no longer U(1) invariant.

Parameterizing the field φ(x) as φ(x) = ρ(x)eiθ(x)_{, and expanding around v, the}

covariant derivative becomes

Dµφ(x) = [∂µρ(x) − iρ(x)(∂µθ(x) − eAµ(x) − ieAµ(x)(ρ(x) − v)]eiθ(x) (1.3.2)

In this regard, ρ is a massive excitation, along the radial axis of the potential, whereas θ is a massless excitation, schematically, they are moving along the contin-uum minima of the potential, and thus they do not require additional energy as a massive excitations. A gauge transformation of parameter Λ transforms fields as θ(x) → θ(x) + eΛand Aµ(x) → Aµ(x) − ∂µ. Hence, we can choose Λ(x) to eliminate

θ(x) from the |Dµφ|2 term in the Lagrangian:

|Dµφ(x)|2 = (∂µρ(x))2+ e(ρ(x) − v)2Aµ(x)Aµ(x) (1.3.3)

Using this parametrization, the Lagrangian does not depend on θ(x) and the gauge boson is massive since e2_v2_A

µ(x)Aµ(x)is a mass term. However, the number of

degrees of freedom is unchanged: φ is a complex scalar, but after the gauge fixing we are left with only one massive real degree of freedom. The massless part has become the longitudinal part of the vector Aµ, which is now massive, and

conse-quently has three degrees of freedom. The Lagrangian contains also trilinear and quadrilinear vertices ρA2 _{and ρ}2_A2_{, which give the interactions between the gauge}

boson and the scalar field.

This mechanism of giving mass to the gauge bosons through the spontaneous symmetry breaking is generic and valid for other symmetry groups too. It was conceived in 1964 by P. Higgs [11], R. Brout and F. Englert [10].

1.4 The origin of the mass: the Higgs mechanism

Mass problem for gauge bosons

The Higgs-Brout-Englert mechanism is used in the SM to give mass to the elec-troweak gauge bosons (W± , Z0 ). This is achieved by adding two new complex

scalar fields which form a SU (2)Ldoublet: Φ(x) =

φ(x)†

φ(x)

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1.4. THE ORIGIN OF THE MASS: THE HIGGS MECHANISM 5

Fig. 1.3.1: A sketch of the Higgs potential, usually called Mexican hat potential, due to its shape. The minimum of the potential is represented by continuum values, hence there is a continuous infinity of degenerate vacuum states, distinguished by the value of the phase. The underlying symmetry is exact and all the vacua are in fact physically equivalent. The choice of one of the vacua breaks the symmetry, and the Higgs field can be rewritten with a physical Higgs boson h, that represents the excitation along the "radial" axis, and three πiGoldstone bosons. The πiare mass-less excitations: schematically, they

are moving along the continuum minima of the potential, and thus they do not require additional energy as a massive excitations.

The potential of the new field Φ(x) has a minimum in Φ(x) =0 v

, and this breaks spontaneously the SU (2)L⊗ U (1)Y symmetry.

The field Φ(x) can be expressed as a function of v and θ(x) as:

Φ(x) = e12iθ

a_σa 0

v + h(x)

(1.4.1) After the spontaneous symmetry breaking, the Lagrangian no longer depends on the fields θa _{and contains the mass terms for the gauge bosons:}

|Dµφ(x)|2 = 1 4[g 2 (|W1|2+ |W2|2) + (gW_µ3− g0Bµ)2][v2+ h(x)2 2 + 2vh(x) √ 2 ] (1.4.2) Finally, we can rotate the field (W1_{, W}2_{) and (W}3 _{, B) to find the mass eigenstates}

of the gauge bosons:

W_µ± = √1 2(W 1 µ± iW 2 µ) (1.4.3) Z_µ0 = 1 pg2_{+ g}02(gW 3 µ − g 0 Bµ) (1.4.4)

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Aµ= 1 pg2_{+ g}02(gW 3 µ+ g 0 Bµ) (1.4.5)

and the mass eigenvalues: mW± = gv

2, mZ =pg

2_{+ g}02 v

2, mA = 0.

Note that Eq. 1.4.2 predicts also the interaction between the Higgs field h(x) and the massive gauge bosons Z0 _{and W}±_.

Mass problem for quarks and leptons

The fermionic mass term m ¯ψi_ψi _{is not SU (2)}

L invariant. This problem is solved by

adding a new interaction between the Higgs field and fermions. The electron mass can be introduced by adding to the Lagrangian the following term:

− Ge[ ¯ψe,LΦψe,R+ ¯ψe,RΦψ¯ e,L]

= −Ge[( ¯νe, ¯e) · ϕ† ϕ0 eR+ ¯eR(ϕ−, ¯ϕ0) · (νee)] = −√Ge 2v[ ¯eLeR+ ¯eReL] − Ge √ 2[ ¯eLeR+ ¯eReL]h(x) = −me[¯ee] − me v h(x)[¯ee] (1.4.6) where Ge = √

2me/v. Likewise, we can add the mass term for the other charged

leptons and up-type quarks. Down-type quark masses can be obtained by a similar method using the doublet ΦC _{= −iσ}2_Φ? _{that has the expectation value(}v

0). In

addition, the down-type quark mass eigenstates are rotated with respect to the SU (2)L eigenstates by the Cabibbo-Kobayashi-Maskawa matrix [12]. Therefore,

the quark mass term in the Lagrangian appears as follows:

− Gij_d[(¯ui, ¯d0i)L· ϕ† ϕ0 djR − Giju(¯ui, ¯d0i)L − ¯ϕ0 ϕ− ujR + hc. = −mi_dd¯idi(1 + h(x) v ) − m i uu¯iui(1 + h(x) v ) = −mi_dd¯idi− mi d v ¯ didih(x) − miuu¯iui− mi u v u¯iuih(x) (1.4.7)

Note that both Eq. 1.4.6 and 1.4.7 predict the interactions between the Higgs field and the fermions. The terms mid

v and mi

u

v show that the coupling between the

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1.5. THE HIGGS BOSON AT THE HADRON COLLIDERS 7

1.5 The Higgs boson at the hadron colliders

1.5.1 Production channels

At the LHC, the main Higgs boson production channels are four: the gluon-gluon fusion(ggH), the vector-boson fusion (VBF), the vector-boson associated produc-tion (VH) and the top pair associated producproduc-tion (ttH). The cross secproduc-tions of the production channels at √s = 13 TeV are reported in Table 1.5.1 and shown in Fig.1.5.3 and they are in the range from 0.5 pb to 40 pb for a Higgs mass of 125 GeV.

• The gluon-gluon Fusion (ggF) in Fig. 1.5.1 is the dominant production

mode with a cross section of approximately 85% of the total. The leading diagram involves a quark loop: the main contribution to the SM amplitude arises from the top quark loop, though the amplitude is potentially sensitive to the presence of new massive particles with non zero color charge.

• The Vector Boson Fusion (VBF), in Fig.1.5.1, has a cross section of about

a tenth of that of gluon-gluon fusion. The leading diagrams involve a qq scattering in the t or in the u channel, with a vector boson exchange and the emission of a real Higgs. Since the momentum exchange is typically lower than the center of mass energy of the two quarks, the channel is characterized by two separated high-rapidity quarks in the final state, detectable as high rapidity jets. Their presence can therefore serve as a signature of the VBF production channel.

• The Higgs-Strahlung (VH) has an even smaller cross section, but the

pres-ence of a vector boson when the Higgs decays to two quarks in the final state helps to separate Higgs events from background. The presence of final state charged leptons or neutrinos is currently exploited in H → b¯b searches. H → b¯b searches take into account also the contribution of gluon initiated processes (Fig. 1.5.2 b, c) whose contribution to the total ZH cross-section is around 8%, but they can help to increase the sensitivity to high-pT Higgs

bosons.

• Thetop pair associated production (t¯tH) allows a direct measurement of Higgs coupling to the top quark. Its contribution to the total cross-section is about 1%. Other processes, namely the bbH associated production and the single-top associated production are also object of direct searches and their contribution is taken into account in global Higgs properties measurements.

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Process Cross section (pb)

Gluon-gluon fusion 43.9 ± 4.4

Vector-boson fusion 3.75 ± 0.12

Vector-boson associated production 2.25 ± 0.06 Top-pair associated production 0.51 ± 0.05

Table 1.5.1: SM Higgs boson production cross section at mH= 125.0GeV and

√

s = 13TeV

Fig. 1.5.1: Leading Feynman diagrams for Higgs boson production via ggF (a) and VBF (b).

Fig. 1.5.2: Leading diagrams for the VH production channel. Gluon initiated processes (b,c) are important when looking for a high-pT Higgs decaying to hadrons.

1.5.2 Decay channels

The Higgs boson is short-lived, with a lifetime on the order of 10−22_seconds1_and

decays close to the interaction point in the CMS detector. It must therefore be identified from its decay products.

It couples to all massive fermions and massive vector bosons, including self-couplings. Couplings to gluons and photons are possible indirectly, through inter-mediate loops of other particles. An exception to this is the direct decay of the Higgs boson to the top quark, since the top quark is too heavy. The Higgs boson can decay into W and Z bosons, via off-shell contributions for W/Z bosons. The

1_{The lifetime is given by τ =} }

Γ. For a Higgs boson of mass 125.09 GeV the predicted decay

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1.5. THE HIGGS BOSON AT THE HADRON COLLIDERS 9

Fig. 1.5.3: Higgs production cross sections at the LHC for the various channels

branching ratios for the decay modes as a function of the Higgs boson mass are shown in Figure 1.5.4.

As it is possible to see in Table 1.5.2, the dominant decay channel is H → b¯b, with a branching ratio of 57.5%. Other significative decay modes are: H → W W and H → γγ followed by , H → τ τ , H → c¯cand H → ZZ, while H → Zγ and H → µµ have even smaller rates such that in the first run of the LHC no events were detected.

Since the decays into gluons, diphotons and Zγ are loop induced, they provide information on the Higgs couplings to W W , ZZ and t¯tin different combinations [14]. Some of these channels are excellent candidates to show possible deviations from the SM predictions and might open the door to the observation of physics beyond the SM.

The agreement between the SM prediction and the relative measurement is de-scribed by the signal strength parameter µ. For each production and decay channel i → H → f the production and decay signal strengths are defined as:

µi = σi σi,SM and µf = BR f BRf_SM

For a given value of mH , the search sensitivity depends on the production cross

section, the decay branching ratio into the selected final state, the signal selection efficiency, the mass resolution and the level of background of similar or identical

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final state topologies.

Combining the Higgs boson search results requires a simultaneous analysis of the data selected by the individual decay modes, accounting for their correlations and for all the statistical and systematic uncertainties. The statistical methodology used for this combination was developed by the ATLAS and CMS Collaborations in the context of the LHC Higgs Combination Group.

Fig. 1.5.4: Branching fractions as a function of the Higgs boson mass. The width of the lines represents the total theoretical uncertainty.

Decay Channel Branching Ratio [%] H → b¯b 57.5 ± 1.9 H → τ τ 6.30 ± 0.36 H → c¯c 2.90 ± 0.35 H → µµ 0.022 ± 0.001 H → W W 21. ± 0.9 H → gg 8.56 ± 0.86 H → ZZ 2.67 ± 0.11 H → γγ 0.228 ± 0.011 H → Zγ 0.155 ± 0.014

Table 1.5.2: SM predicted branching ratios for a Higgs boson of mass 125.09 GeV. Some of the decay channels reported are beyond reach of the current experiments.

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1.6. HIGGS EXPERIMENTAL RESULTS 11

1.6 Higgs experimental results

1.6.1 Previous experimental searches for the Higgs boson

LEP

The first extensive search for the Higgs boson took place at CERN in the 1990’s, with the LEP (Large Electron-Positron Collider) accelerator [15]. Four experi-ment collected collision data at LEP: ALEPH, OPAL, DELPHI and L3. These four collaborations have collected a total of 2461 pb−1 _{of e}+_e− _{collision data at}

center-of-mass energies between 189 and 209 GeV. At LEP the SM Higgs boson was mainly searched in the associated Z boson production mode through the Higgs Strahlung process e+_e− _{→ HZ and mainly in the decay into bb quark pairs. Although no}

evidence of the Higgs boson was found, a lower limit of 114.4 GeV was established, at the 95% confidence level on the mass of the SM Higgs boson.

Tevatron

The search for the SM Higgs boson continued at Fermilab with the Tevatron collider with two experiments: D0 and CDF [16]. The amount of data collected was 10 fb−1 _pp _{collision data at center-of-mass energies up to} √_s _{= 1.96 TeV. The}

decay modes studied were H → bb, H → τ+_τ−_{, H → W}+_W− _{and H → γγ.}

Both CDF and D0 observed an excess of signal-like events in the mass range 115 < mH < 140GeV, compatible with the experimental resolution and the local

significance corresponds to 3.0σ at mH = 125 GeV. The resulting fitted signal

strength is µ = σ/σSM = 1.44 ± 0.59. The results obtained are shown in Figure

1.6.1.

1.6.2 Experimental results after the LHC Run 1

After the announcement of the observation of a new particle with a mass of approx-imately 125 GeV with Higgs-like properties [17], a great effort has been made to characterize the newly-discovered object.

During the first LHC run, the CMS and ATLAS experiments have collected an inte-grated luminosity of proton-proton collision of about5 fb−1_{each at a center-of-mass}

energy of √s = 7TeV, and 20 fb−1 _at√_{s = 8}_{TeV .}

All direct and indirect measurements on the Higgs boson properties are compatible with the SM Higgs boson.

The Higgs boson mass measurement has been performed by both experiments in two of the most sensitive channels, H → ZZ? _{→ 4l and H → γγ which have a}

typical mass resolution of 1-2% [18]. The results are obtained from a simultane-ous fit in the two channels and for the two experiments to obtain the combined

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Fig. 1.6.1: Exclusion plot for the Higgs mass obtained at Tevatron [16].

measurement of the Higgs boson mass:

mH = 125.09 ± 0.21(stat) ± 0.11(syst)GeV (1.6.1)

The total uncertainty is dominated by the statistical term; the systematic uncertain-ties are dominated by effects related to the photon, electron, and muon energy or momentum scales and resolutions.

The global signal strength measurement, performed assuming the same µi and µf

for each process, gives as a result a best-fit value of µ = 1.09+0.11_−0.10

Analogous measurements are performed treating independently each production signal strength, assuming SM branching ratios, and each branching ratio signal strength, assuming SM production cross-sections. The best fit results are reported in 1.6.5. Among the signal strengths the observed µttH value of 2.3+0.7−0.6differs from the

expected by more than 2σ, while the combined µbb _{strength of 0.69}+0.29

−0.27 is slightly

lower than the expected.

The coupling to each SM particle individually is tested assuming the consistency of the loop amplitudes (γγ final state, ggF production mode) with the SM.

At the lowest order the Higgs is expected to couple to fermions with a strength proportional to their mass and to vector boson proportionally to mass square. Coupling modifiers

yv,i =pkv,i·

mv,i

v and yf,i= kf,i· mf,i

v

are thus introduced to test each vertex agreement with the SM. The result is re-ported in 1.6.3.

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1.6. HIGGS EXPERIMENTAL RESULTS 13

Finally, the spin and parity of the Higgs boson have been tested exploiting the H → γγ, H → ZZ → 4l and H → W W → 2l2ν channels [19], [20]. The observa-tions disfavor spin-2 hypothesis and, assuming that the boson has spin zero, are consistent with the pure scalar hypothesis, JP _{= 0}+ _{as predicted by the SM, while}

disfavoring the pseudoscalar hypothesis.

Fig. 1.6.2: Best-fit results for the production signal strengths combining ATLAS and CMS measurements. The error bars indicate the 1σ and 2σ intervals.

1.6.3 First results after Run2

In 2016, an integrated luminosity of 35.9 fb−1 _{data was recorded by the CMS}

ex-periment at the center of mass of 13 TeV. Compared to Run 1, this provides a Higgs production with larger cross-section in an almost doubled integrated luminosity. It not only gives a great opportunity to examine the Higgs properties in better precisions, but also to probe some rare processes like Higgs boson pair production. Among the most relevant results of CMS during the Run2 period we can un-derline the VH H → b¯b and H → τ τ . About the former an excess of events is observed in data compared to the expectation in the absence of a H → b¯b and the signal strength corresponding to this excess, relative to that of the SM Higgs boson production is 1.2 ± 0.4. Combining this result with the one from the search for the same processes performed during the Run 1, the observed signal significance is 3.8

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Fig. 1.6.3: Best fit result for the coupling modifiers measurement for each SM particle; the dashed line indicates the expected value as function of the SM particle mass.

standard deviations, where 3.8 are expected from a SM signal [21].

For the latter, the τ leptons decay semi-hadronically, or leptonically to an electron or a muon, and the four final states with the largest branching fractions were con-sidered. An excess of events was observed over the expected background prediction with a significance of 4.9 standard deviations for the scalar boson mass of 125 GeV, to be compared to an expected significance of 4.7 standard deviations. The best fit of the observed H → τ τ signal cross section times branching is 1.06+0.25_−0.24 times the standard model expectation [22].

Some other interesting decays are briefly described in the following sections, in-cluded H → µµ process.

H → ZZ? → 4l

The event selection in the H → ZZ? _{→ 4l decay channel is characterized by the}

selection of high-quality leptons, including final-state-radiation recovery, with high efficiency; the background estimate is based on Monte Carlo (MC) simulations for the ZZ? _{and from control region in data for the so-called reducible backgrounds}

(mainly Z+X). The signal extraction in ATLAS [23] is performed via a fit to the m4l distribution after a kinematic fit with a constrained Z mass while in CMS [24]

two signal categories are defined (VBF-tagged events and other events) and the bare m4l plus a matrix-element-based kinematic discriminant are used to perform

the analysis. Of course the results are limited by the very small statistics recorded. Figure 1.6.4 (right) shows the m4l distribution observed by CMS with the early 13

TeV dataset. The global signal strength measured by CMS is µ4l _{= 0.89}+0.62 −0.46.

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1.6. HIGGS EXPERIMENTAL RESULTS 15 H → γγ

The key points of the H → γγ decay channel are the very good energy resolution and photon selection. The ATLAS analysis [25] uses a cut-based approach for this selection, while CMS [26] uses a multivariate approach and various signal categories for a measurement of the signal strength in different production modes. The variables used are based on the shape and the expected containment of the showers, track and calorimeter isolation, and the rejection of π0 _{decays. Another}

important aspect of the di-photon mass reconstruction is the identification of the primary vertex, where CMS adopts a multivariate analysis using the P p2

T of tracks

in the vertex and their balancing with respect to the di-photon system and ATLAS uses a similar technique supplemented with photon trajectory estimates from the pointing calorimeter. Both experiments fit the distribution of mγγ in signal

categories of different purity. Figure 1.6.4 (left) shows the inclusive distribution as observed in ATLAS 13 TeV data.

Fig. 1.6.4: (left) Diphoton invariant-mass spectrum observed in the 13 TeV ATLAS data. The solid red curve shows the fitted signal plus background model when the Higgs boson mass is fixed at 125.09 GeV. The background component of the fit is shown with the dotted blue curve. The bottom plot shows the residual of the background-subtracted data. (Right) Distribution of the four-lepton invariant mass observed in the 13 TeV CMS data.

H → µµ

The branching fraction in the H → µµ channel is 2.2 × 10−4_{, about ten times}

smaller than that for H → γγ. The dominant and irreducible background arises from the Z/γ → µµ process which has a rate several orders of magnitude larger than that from the SM Higgs boson signal. Due to the precise muon momentum measurement achieved by ATLAS and CMS, the mµ+_µ− mass resolution is excellent

(' 2 − 3%). A search is performed for a narrow peak over a large but smoothly falling background. For optimal search sensitivity, events are divided into several categories. Either taking advantage of the superior muon momentum measurement in the central region, events can be subdivided by the pseudorapidity of the muons,

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Fig. 1.6.5: Summary of the CMS and ATLAS mass measurements in the γγ and ZZ channels in Run 1 and Run 2 Expected Observed γγ 4.6σ (ATLAS) 5.3σ(CMS) 5.2σ (ATLAS) 4.6σ(CMS) ZZ 6.2σ (ATLAS) 6.3σ(CMS) 8.1σ (ATLAS) 6.5σ(CMS) WW 5.9σ (ATLAS) 5.4σ(CMS) 6.5σ (ATLAS) 4.7σ(CMS) τ+_{τ −} _{3.4σ (ATLAS) 3.9σ(CMS)} _{4.5σ (ATLAS) 3.8σ(CMS)} b¯b 2.6σ (ATLAS) 2.5σ(CMS) 1.4σ (ATLAS) 2.1σ(CMS) τ+τ−(combined) 5.0σ 5.5σ b¯b (combined) 3.7σ 2.6σ

Table 1.6.1: Summary of the significances of the excesses observed for the main decay processes. The

γγ, ZZ, and W+_W− _{decay modes have been established at more than 5σ by both the ATLAS and CMS}

experiments individually, the combined observation significance therefore exceeds 5σ and is not reported here.

or designing selections aiming at specific production processes such in particular as the vector boson fusion.

No excess in the µ+_µ− _{spectrum is observed near 125 GeV. From an analysis of}

their Run 1 data, ATLAS sets [27] an observed (expected) 95% CL upper limit on the signal strength µ<7.0 (7.2). The CMS analysis [28] of their 7 and 8 TeV data sets an observed (expected) limit of µ <7.4 (6.5). A search carried out by the ATLAS experiment using the 2015 an d 2016 data showed no excess at 125 GeV. A signal strength of µ = −0.1 ± 1.4 was measured, yielding an observed (expected) 95% CL upper limit on the signal strength of µ<2.8.

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Chapter

2

The CMS experiment at the LHC

The search described in this thesis uses a data sample collected by the CMS detector during the LHC Run 2 in 2016. The following chapter provides a brief description of the experimental apparatus which is composed by the collider and the detector.

2.1 The Large Hadron Collider

The Large Hadron Collider (LHC) is a circular proton-proton collider in the Geneva area (Switzerland). It is hosted by the European Organization for Nuclear Research (CERN). The purpose of the LHC is to collect data that could help answering open questions in fundamental physics. It provides experimental condition suitable to explore high energy phenomena up to TeV scale. The LHC is the biggest particle accelerator ever built: it can reach an unprecedented energy of the collision and luminosity.

The LHC is located in a 27 km long tunnel that previously hosted the Large Electron-Positron collider (LEP). It was designed to collide protons at the center of mass energy of√s = 14TeV at the instantaneous luminosity of L = 1034 _cm−2 _s−1_.

The center of mass energy reached in 2011 proton run was of 7 Tev, in 2012 it was raised to 8 TeV and it eventually reached 13 TeV, which is very close to its nominal value of 14 TeV, in 2015.

Before entering the LHC, protons need to be accelerated and are grouped in bunches of about 1011 _{particles and accelerated to a minimum energy of 450 GeV,}

because of magnetic field constraints. This is achieved through a chain of 4 accel-erators present in the CERN site. The protons start from the LINAC2, then they are injected in the Booster(PBS), followed by the Proton Synchrotron(PS) and the Super Proton Synchrotron(SPS) that injects them in the LHC, as shown in Fig. 2.1.1. The LHC is composed by two rings with four crossing points, flanked by long straight sections. Each straight section has a length of 528 m and can serve as

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Fig. 2.1.1: The LHC acceleration complex, in which protons are accelerated in different stages: LINAC, Booster, PS and SPS are the four stages before entering the LHC.

an experimental or utility insertion. The four crossing points are occupied by the experiments: A Toroidal LHC ApparatuS (ATLAS), Compact Muon Solenoid (CMS), Large Hadron Collider beauty (LHCb) and A Large Ion Collider Experiment (ALICE). CMS and ATLAS are two multi-purpose experiments: they have been designed to investigate many fundamental physical processes, such as the search for the Higgs boson and new physics particles, as well as precision measurements of the SM quantities.

The beam is not continuous but organized in bunches. They are 8 cm long, with a transverse section of about 10x10 µm at the interaction points, and they are interspersed by 25 ns, corresponding to roughly 7.5 m at the speed of light.

The bunch structure of the beam is important for two main reasons. First of all, this makes possible to accelerate them in radio frequency cavities: if the bunch revolution frequency matches the oscillation frequency of the electric field inside the cavities, the bunches always feel an electric field in their direction of motion and they are always accelerated. Next, the collisions only occur during the "bunch crossings". A bunch crossings usually last for about 200ps. This has the advantage of reading the detector just over a small time around this instant, classifying the collisions in events. An event is a complete read-out of the detector. However, because of the transit time of the particles through the detector and because of the integration time of sensors electronics used for the read-out, signals related to particles produced in few previous and subsequent bunch crossings might overlap with the read-out of the current bunch crossing.

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2.1. THE LARGE HADRON COLLIDER 19 One of the most important feature of a collider is the luminosity, defined as:

L = R

σ (2.1.1)

where R is the rate of events of a given process and σ is the cross section for that given process. It is usually expressed in cm−2 _s−1 _{. The rate of}

produc-tion of a given process is proporproduc-tional to L through the cross secproduc-tion σ. Therefore, if the process is very rare, it is necessary to maximize L to collect enough statistics1_.

For circular machine with approximately Gaussian bunches with transverse di-mensions σx, σy, it can be proved that:

L = f N1N2 4πσxσy

(2.1.2)

where we assumed two bunches containing N1 and N2 particles colliding with

frequency f . For the LHC N1,2 = 1.5 × 10−11, f = 40MHz, σx= 100 µm σy = 10µm:

these features lead to L ' 3 × 1033_cm−2_s−1_.

A huge amount of instantaneous luminosity has also an important collateral effect: the increase of pile-up collisions (PU). Indeed, if the instantaneous luminosity is large enough, the number of inelastic proton-proton interactions in each bunch crossing can be larger than one. This is to say, multiple proton-proton interactions take place per bunch crossing, enlarging the number of particles measured in each event and creating ambiguity in separating them in the various collisions. In Fig 2.1.2 the integrated luminosity trend during the last 8 years is presented.

Reference Frame

For later convenience we report the CMS coordinate system. It is a right-handed coordinate system, with the origin at the nominal interaction point, the x-axis pointing to the center of the LHC, the y-axis pointing up, perpendicular to the LHC plane, and the z-axis along the anticlockwise beam direction. The polar angle, θ, is measured from the positive z-axis and the azimuthal angle φ, is measured from the x axis.

It is usually more convenient to consider a different set of variables instead of energy and angle or Cartesian coordinates. In fact, the one particle invariant phase space can be written as:

d4pδ(E2− p2_{− m}2_{) = p}

TdpTdφdY (2.1.3)

1_{The integrated luminosity is defined as}_{L = R Ldt and it is usually quoted to show the amount}

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Fig. 2.1.2: Integrated luminosity delivered by the LHC as a function of the day of the year, for the various LHC runs. As it is possible to see, during 2017 the delivered luminosity exceeded 50 fb−1_,

significantly larger than the expectation. This was possible thanks to the achievement and following overtaking of the instantaneous design luminosity.

where pT is the component of the momentum perpendicular to the beam axis

(transverse momentum) while Y is the rapidity (along the beam axis) and it is defined as: Y = 1 2log( E + pZ E − pZ ) (2.1.4)

where pZ is the component of the momentum along the beam axis. In case of

massless particles (E m), that goes produced at large angles with respect to 1/γ(|sin(θ/2| (1/γ)), the rapidity coincides with the pseudorapidity defined as:

η = − log(tan θ/2) (2.1.5)

and it is a biunivocal correspondence with the polar angle θ. This choice is due to the fact that pT is invariant under boosts along the beam axis, whereas Y is additive

for the same boosts.

2.2 The Compact Muon Solenoid

The Compact Muon Solenoid (CMS) detector, is located at the 5th access point of the LHC tunnel in the vicinity of the town of Cessy, in France. It was designed to withstand the LHC running conditions and at the same time exploiting the collected data to fulfill a rich physics program. This comprehends Higgs boson, SM, etc. A

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2.2. THE COMPACT MUON SOLENOID 21

Fig. 2.2.1: Picture of CMS in its location at point 5 of LHC. This section of the detector shows in full the 15 m of the outer diameter.

more detailed description can be found in Ref [29].

The main features of the detector, needed to operate in the LHC environment, are: radiation hardness, good time resolution, and capability to recognize interesting events in very short amount of time. These requirements are imposed by the large proton-proton total cross section, the high beam intensity and the high frequency of the collisions. A further necessity is a high granularity, both to reconstruct single particles with high efficiency and to be able to operate with a high number of PU interactions.

CMS is made of several sub-detectors: by combining the information collected by all of them it is possible to identify and measure with high precision the momentum and the energy of the particles produced in the event. An illustration of the various CMS sub-detectors is presented in Fig. 2.2.2.

The detector is designed according to the cylinder shape of its superconducting solenoid, which provides a uniform magnetic field of 3.8 T. The structure consists of two regions, the barrel, made of subdetectors positioned at increasing values of the cylinder radius, and the endcaps, where subdetectors are layered along the z axis, to ensure hermeticity. The solenoid itself is 13 m long with a 6 m diameter. It contains, from inside out, the tracker and the electromagnetic and hadronic calorimeters. Outside the magnet coil, the iron return yoke of the magnet hosts the muon spectrometer, used for reconstruction of muon tracks.

In the following sections a brief summary of the main features of the CMS sub-detectors is given; a detailed description can be found in the CMS official design report [30].

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Fig. 2.2.2: An illustration of the various sub-detectors inside CMS.

2.2.1 The Tracker

The tracker of CMS constitutes the inner part of CMS and it is designed to provide a precise and efficient measurement of the charged particle tracks and of the primary and secondary interaction vertices.

The tracker is aimed to work in a high-radiation environment, therefore high gran-ularity and fast response are mandatory to ensure an efficient vertex and track reconstruction. On the other hand finely segmented detectors require a large num-ber of readout channels and an efficient cooling system, which, as dead material, are expected to worsen the tracking performance. As a consequence different kind of technologies are employed depending on the detector-beam distance.

A silicon pixel detector is installed in the inner region, closest to the interaction point, while silicon microstrip detectors are used in the outer region.

The total length of the tracker is of 5.8 m and its diameter is 2.5 m, while the angular coverage reaches up to |η| = 2.5, for a total active surface of 200 m2_{. The}

pixel detector is formed by three barrel layers positioned at radii of 4.4, 7.3 and 10.2 cm and two endcap disks for each side. It provides three dimensional position measurements. The inner detector provides at least two hits for tracks coming from within few cm of the nominal interaction point, with an angular acceptance of |η| < 2.4 .

Each pixel has a surface of 100 × 150µ m2 _{to obtain low cell occupancy (order 10}−4

per collision) and a spatial resolution of about 10µm in the r − φ plane and 15 µm in the z coordinate.

The inner silicon microstrip detector is made of 4 barrel layers, called tracker inner barrel (TIB), positioned at radii ranging from 20 to 55 cm and 3 disks at each

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2.2. THE COMPACT MUON SOLENOID 23

Fig. 2.2.3: An illustration of the CMS tracking system. The acronyms TIB, TID, TOB, and TEC stand for "tracker inner barrel", "tracker inner disks", "tracker outer barrel", and "tracker endcaps",respectively.

side called tracker inner disks (TIDs). The strips are oriented along the z axis in the barrel and along the r coordinate in the endcaps. The microstrip detector design spatial resolution is of about 20-50 µm in the r − φ plane and about 200-500 µ m along the z axis.

Figure 2.2.4 shows the mean channel occupancy in strip and pixel sensors in data collected with a "zero-bias" trigger, with about nine proton-proton interactions on average per bunch crossing. The high granularity of the inner pixel detector results in a lower channel occupancy is 0.002-0.02% compared to the one in the strip detector 0.1-0.8%.

Fig. 2.2.4: Channel occupancy for CMS silicon detectors in events taken with unbiased triggers with an average of nine p-p interactions per beam crossing, displayed as a function of r and z

Tracker Update

The elements of the tracker are exposed to large radiation and have a finite lifetime. The pixel system is very close to the interaction region and sees the largest flux

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of particles. For this reason the CMS pixel detector designed for a luminosity of 1034_cm−2_s−1 _{was replaced during the 2016-2017 end-of-the-year shutdown. The}

current 3-layer barrel, 2-disk endcap system is replaced with a 4-layer barrel, 3-disk endcap system for four hit coverage. Moreover, the addition of the fourth barrel layer at a radius of 16cm provides a safety margin in case the first silicon strip layer of the TIB degrades more rapidly than expected, but its primary role is in providing redundancy in pattern recognition and reducing fake rates and reconstruction time with high pile-up.

Fig. 2.2.5: Comparison between the position of layers and disks in the existing (below the beam pipe) and the new (above the beam pipe) pixel trackers.

2.2.2 The Electromagnetic Calorimeter

The electromagnetic calorimeter (ECAL) measures the energy and the direction of photons and electrons. ECAL is a hermetic homogeneous calorimeter composed of 61200 lead-tungstate crystals (P bW O4) in the barrel and 7324 crystals in each

end-gap. The ECAL has a barrel section and two endcaps for a total coverage up to |η| = 3. The thickness is 23 cm in the barrel and 22 cm in the endcaps.

The ECAL granularity is very high: the angular size of each barrel crystal is ∆η × ∆φ = 0.0174 × 0.0174.

When photons or electrons hit a crystal they produce an electromagnetic shower. The P bW O4 is a scintillating material and a fraction or the ionization energy

re-leased by the charged particles in the shower is collected in a visible light signal. It has been chosen because it has a short radiation length (X0 = 0.89cm) and a small

Molière radius (RM = 2.2cm)2. The light is measured by avalanche photodiodes

(APD) in the barrel and vacuum phototriodes (VPT) in the endcaps. Thanks to the very big S/N ratio, the crystals are also sensitive to the primary scintillation of non showering particles as muons.

The resolution of the calorimeter, measured with electron beams, is parametrized

2_{The radiation length X}

0expresses the fraction of energy a particle loses when crossing through

a certain amount of material and correspond to the average distance covered by an electron before its energy is reduced through bremsstrahlung by a factor 1/e. The Molière radius RM characterizes

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2.2. THE COMPACT MUON SOLENOID 25 as a function of the energy:

σ(E) E = 2.8% pE/GeV + 12% E/GeV + 0.30% (2.2.1) where E is in GeV.

The first term in the resolution formula is the so called stochastic term, and it is

Fig. 2.2.6: Layout of the CMS electromagnetic calorimeter [30]

related to the intrinsic fluctuations of the shower. The behavior ∼ 1/√E reflects the stochastic fluctuations in a Poisson process that go like ∆N/N ' 1/√N. As a property of homogeneous calorimeters, the stochastic term is very small. This allows an excellent energy resolution in the typical range of the photon energy inside jets, normally between 1 and 50 GeV.

In the endcaps, the internal face of the calorimeter is equipped with a preshower. It is composed of two silicon detectors planes with a 1 cm lead plate in the middle. The preshower is useful to discriminate the isolated photon or electron signals from the π0 −→ γγ background.

2.2.3 The Hadron Calorimeter

The Hadron Calorimeter (HCAL) is used to measure the energy of hadron jets and neutrinos or exotic particles resulting in missing transverse energy. It is an heterogeneous calorimeter: the absorber is brass and the energy is measured through plastic scintillators crossed by the particles of the hadronic shower. The HCAL can detect hadrons up to |η|=3, so an additional calorimeter (HF) in quartz and scintillating fibers is installed to extend the acceptance up to |η|=5 . Its thickness in the barrel amounts to 1.2 m and is limited by the requirement to fit inside the coil. The hadrons energy resolution obtained using this detector is about

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10-20% for high energy jets.

The HCAL resolution, measured with a pion test beam, results to be: σ

E =

110%

pE/GeV ⊕ 9% (2.2.2)

Although the resolution is not the best feature of the HCAL, thanks to the possibility of using the particle flow algorithm to measure the charged tracks and the photons inside jets, the poor resolution of the HCAL affects only the measurement of the neutral hadrons, that are responsible for around 10% of the typical jet energy. This detector, given its fast read-out is also very important for L1 trigger, where it is possible to set up triggers on the energy of a jet as well as on the missing transverse momentum.

2.2.4 The Muon System

The CMS muon chambers [31] are located in the external part of the detector, precisely in the steel return yoke of the magnet. Their angular acceptance reaches up to |η| < 2.4, providing information to identify muons and to measure the mo-mentum and charge of high pT muons.

Muons are very important tools in CMS. Together with the electrons they are the only particles that can traverse the whole detectors essentially unharmed and leave clear signatures in the muon chambers. Moreover, they can not be produced directly in QCD interactions that dominate the physics production at LHC and constitute a hint for more interesting events. For this reason, they are a main tool for triggering. On average, a muon in the barrel loses 3 GeV of energy before it reaches the first muon station and another 3 GeV between the first and the last muon station. Muons with lower energy can therefore not be reconstructed. The muon system is shown schematically in figure 2.2.7 . It is composed of different types of gas detectors organized in layers in the return yoke of the magnet. In the barrel, up to |η| = 1.3, the muon system consists of four layers occupied by drift tube chambers (DTs). These measure the position of the muon by converting their ionization electrons drift time to the anode wire to a distance. In the endcaps, between 0.9 < |η| < 2.4 where the flux of muons is higher, cathode strip chambers (CSCs) are used. They are organized in four layers where closely spaced anode wires are stretched between two cathodes. The ionization electrons drift towards the closest anode wire which provides the measurement point. The magnetic field is almost completely confined inside the steel return yoke and the trajectories are not bent within the layers of the muon system. Each layer measures the straight track and provides a vector in space called track segment. The segments are then extrapolated between the stations to reconstruct the full track. In order to get a faster signal for triggering, resistive plate chambers (RPCs) are installed in most

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2.2. THE COMPACT MUON SOLENOID 27 of the detector, up to |η|= 2.1. These are parallel plate gaseous detectors that combine an adequate position resolution with a very fast response time.

Fig. 2.2.7: Layout of one quadrant of CMS.

2.2.5 The Trigger system

A fundamental feature of the experiments at hadron collider is the trigger: that is a system that rapidly decides which events to record since only a small fraction of the total produced events can be stored. As mentioned before, the LHC provides proton-proton collisions at high rates. The bunch crossing interval is 25 ns, corresponding to a frequency of 40 MHz. At peak luminosity an average of 27 collisions per bunch crossing occur, making impossible to store and process all the information provided by the detector. The data needs to be reduced and selected so the crucial aspect is a fast and efficient real-time selection to keep track of the useful events. In CMS the data reduction happens in two steps: The Level-1 Trigger [32] and the High Level Trigger (HLT) [33].

Level-1 Trigger

The Level-1 Trigger consists of programmable electronics which processes coarsely segmented information coming from the calorimeters and from the muon system. It reduces the event rate from an input of 40 MHz to an output of about 100 kHz, through a synchronous pipelined structure of processing elements. At every bunch crossing, each processing element sends its results to the next element and receives

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a new event to analyze. During this process, the full detector data are stored in pipeline memories with limited depth (128 bunch crossings).

High Level Trigger

The HLT further decreases the event rate from about 100 kHz to about 1 kHz for data storage. The HLT is implemented by a computer farm composed of 16000 CPUs running the same software framework used for the offline reconstruction. The full detector readout is available at HLT, but in order to meet the timing requirements given by the input rate from L1, events are reconstructed in multiple steps and rejected as soon as there is enough reconstructed information to make a decision.

A list of reconstruction algorithms and filters for one or more physics objects is called HLT Path. A "HLT Menu" represents the set of trigger paths that, if enabled, contribute to a final OR of decisions which determines whether to reject or store an event. A single trigger path can require the presence of one or more physics objects of a particular type that pass specific kinematic thresholds, and it can also mix physics objects.

The event rate of each trigger path should be maintained within the allowed limits given the expected instantaneous luminosity. Trigger paths with lower thresholds than those necessary to reduce the event rate are kept in the HLT Menu with a "prescale" factor applied. They are usually employed to measure the efficiencies of higher threshold triggers.

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Chapter

3

Physics objects

The reconstruction and identification of all the particles coming from the interaction point between the two proton beams is performed using the informations provided by the CMS subdetectors. First the detectors readout is processed to extract the physical information and to build objects such as vertices, tracks and calorimeter clusters. Secondly the reconstructed objects are combined together in order to identify high level objects such as electrons, muons and jets. The identification procedure of physics objects is described in this chapter.

3.1 The Reconstruction Process

In CMS the standard reconstruction process uses information coming from different subdetectors as input. Each subdetector gives a set of locally reconstructed objects that are used to perform the global reconstruction of the physics objects. Therefore the "standard" reconstruction consists in a software process that is can be broadly divided in three steps: local reconstruction, global reconstruction and combination of these reconstructed objects [34].

The local reconstruction occurs in an individual subdetector module. The module uses real data coming from the DAQ system or from simulated data. The data format at this level is called "digis". After the reconstruction algorithms are applied, one goes from "digis" to reconstructed hits (RecHits). The reconstructed hits contain information about positions and energy clusters of the particles signatures in each subdetector. In the tracker, for instance, the reconstructed hits have information coming from pixels or strips in which the signal threshold is exceeded while in the calorimeters the reconstructed hits store position, time and localized energy deposit information. All this information is added to the event and is used in the global reconstruction.

The global reconstruction uses the reconstructed hits coming from the different 29

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subdetector systems to obtain the best version of this kind of objects. For example in the tracker system, the combination gives tracks with low or high pT or in the

calorimeter system, the different clusters are linked to created projective towers, useful in the jet reconstruction. The objects obtained in this step are added to the event.

The last reconstruction step combines local and global reconstruction to obtain higher-level objects based on the information of the whole detector. Some examples are a combination of the ECAL and HCAL clusters to produce jet candidates; tracks produced by the muon system are extrapolated into the tracker to match with tracks reconstructed by this subdetector. The resulting objects are stored and are used for direct physics analyses.

3.1.1 Track reconstruction

Tracks are the reconstructed trajectories of charged particles. They play a funda-mental role in the event reconstruction in CMS and are the main component of the Particle Flow and b-tagging algorithms that will be described in this chapter. Each trajectory is defined as a sequence of hits in different layers of the tracker. The position of a hit is obtained by fitting the deposited charge distribution, both in the pixel detector and in the strip detector. The tracking algorithms assign hits to tracks aiming to measure with the best possible resolution the five parameters which identify the trajectory: three for the momentum vector (pT, η,φ), and two for

the impact parameter (r, z), where the impact parameter is defined as the distance between the primary vertex and the point of closest approach of the track to it.

Iterative Tracking

Tracks are reconstructed in CMS through multiple iterations of the Combinatorial Track Finder (CTF) algorithm sequence, which is based on the combinatorial Kalman Filter ([35]) technique. In the first stages, the iterative tracking searches for tracks of relatively large pT or small impact parameter, that are easier to find.

After each iteration the hits associated with the reconstructed tracks are removed from the hit collection, reducing the combinatorial complexity of the subsequent iterations. Each iteration of the CTF algorithm is composed of four steps:

• Seeding: Track seeds are identified from triplets of hits or pairs of

3D-hits plus the beam spot. Only 3D-hits measured by the pixel and double strips detectors are used at this stage. Pixel hits are preferred because of the higher resolution, the lower occupancy and the smaller amount of material before the active detector layers. Double strip hits are useful to recover efficiency for displaced tracks, coming from outside the beam spot.

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3.1. THE RECONSTRUCTION PROCESS 31 • Pattern Reconstruction:The seeds are extrapolated up to the whole tracker

using a combinatorial Kalman filter: the hits from the different tracker layers are added to the suitable tracks, and at each iteration the track parameters are updated. In case multiple compatible hits are found when extrapolat-ing the trajectory to a sextrapolat-ingle layer, the algorithm will create one trajectory candidate for each hit and they will be propagated independently. Once the track is completed another search is performed backwards starting from the outermost hit to improve the hit collection efficiency.

• Track Fitting: Track-associated hits are fitted considering also the effects

neglected by the Kalman filter, like the non-uniformity of the magnetic field, the dependence of the hit resolution from the track parameters, and the presence of outlier hits (delta-rays etc.).

• Track Selection: Only the fitted tracks that fulfil a minimum quality

require-ment (number of layers that have hits, the track normalized χ2_{, longitudinal}

distance from the closest pixel-only vertex) are kept, the others are discarded. The hits associated with the reconstructed tracks are then removed from the hits collection.

The average track-reconstruction efficiency for promptly-produced charged particles with transverse momenta of pT > 0.9GeV is 94% for pseudorapidities of |η| < 0.9

and 85% for 0.9 < |η| < 2.5 are shown in Fig. 3.1.1. The momentum resolution σ(pT)/pT for muons is of about 1.3% in the barrel and 2 − 5% in the endcaps up to

pT values of 100 GeV [36], Fig.3.1.2.

Fig. 3.1.1: Track reconstruction efficiencies for single, isolated muons passing the high-purity quality requirements. Results are shown as a function of η (left), for pT=1, 10, and 100 GeV. They are also

shown as a function of pT (right), for the barrel, transition, and endcap regions, which are defined by

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Fig. 3.1.2: Resolution, as a function of pT, in the four track parameters for single, isolated muons

in the barrel, transition, and endcap regions, defined by η intervals of 0-0.9, 0.9-1.4 and 1.4-2.5, respectively. From top to bottom and left to right: transverse and longitudinal impact parameters, φ and cot θ. For each bin in pT, the solid (open) symbols correspond to the half-width for 68% (90%)

intervals centered on the mode of the distribution in residuals.[36]

Primary vertex reconstruction

The primary vertices are the proton-proton collision points and they are is recon-structed using the available tracks in the event. First tracks consistent with being produced in the primary interaction region are selected. These are then clustered on the basis of their z-coordinates at their point of closest approach to the beam line. Track clusters are eventually fitted using the Adaptive Vertex Fitter [37] algorithm. This algorithm is an iterative reweighed Kalman filter that fits a candidate vertex starting from a collection of tracks. Tracks are reweighted at each iteration so that the contribution of fake tracks gradually diminishes.

The reconstructed interaction vertex with the largest sum of squared transverse mo-menta for each track(P

ip 2

T ,i), is selected as a candidate for the origin of the hard

interaction. The primary vertex resolution depends on the number of associated tracks: in x and z the resolution is of order of 20-50 µm.

Search for H->mu mu in the VBF production channel with the CMS experiment at LHC

DIPARTIMENTO DI

FISICA

"ENRICO

FERMI"

CORSO DI

L

MAGISTRALE IN

FISICA

Search for H → µµ

in the VBF production channel

with the CMS experiment at LHC

CANDIDATA:

RELATORE

:

Agnese Bonavita

Prof. Paolo Azzurri

Prof. Andrea Rizzi

Introduction

Contents

Chapter

1

Standard Model and Higgs Boson

1.1

The Standard Model

1.2

Electroweak Unification

1.3

Spontaneous simmetry breaking

1.4

The origin of the mass: the Higgs mechanism

1.5

The Higgs boson at the hadron colliders

1.5.1

Production channels

1.5.2

Decay channels

1.6

Higgs experimental results

1.6.1

Previous experimental searches for the Higgs boson

1.6.2

Experimental results after the LHC Run 1

1.6.3

First results after Run2

Chapter

2

The CMS experiment at the LHC

2.1

The Large Hadron Collider

2.2

The Compact Muon Solenoid

2.2.1

The Tracker

2.2.2

The Electromagnetic Calorimeter

2.2.3

The Hadron Calorimeter

2.2.4

The Muon System

2.2.5

The Trigger system

Chapter

3

Physics objects

3.1

The Reconstruction Process

3.1.1

Track reconstruction