Ricerca di risonanze di-bosoniche nello stato finale semi-leptonico (lvqq) in collisioni protone-protone a $\sqrt{s}= 13$ TeV collezionate con il rivelatore ATLAS.

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Dottorato di Ricerca in Fisica

Università di Pisa

GRADUATE COURSE IN PHYSICS UNIVERSITY OF PISA

Search for di-boson resonances in the

semileptonic final state in p- p collisions

at

√

s

= 13 TeV collected with the

ATLAS detector

Nicolò Vladi Biesuz

a

a_{Universitá di Pisa and INFN sezione di Pisa}

Supervisor: Chiara Roda

a

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Preface

With the discovery of the Higgs boson by the ATLAS [1] and CMS [2] experiments at the LHC at CERN in 2012, the Standard Model is now complete, yet unanswered questions are still present. In example the Standard Model does not explain the hierarchy between the weak and Planck scales, nor it includes a dark matter candidate, nor it explain the origin of barion asymmetry. For this reason, one of the goals of particle physics research is to find new hints of physics beyond the Standard Model that could answer some of these questions. Analyses searching for di-boson resonances are a very powerful tool to investigate many beyond the Standard Model scenarios such as extension of the Higgs sector [3, 4], Heavy Vector triplets [5] (W0

and Z0

) or excited states of Gravitons [6,7]. These searches exploit many decay channels of the two bosons allowing to select topologies with varied signal to background ratios and statistics. This thesis describes the search for new resonances decaying to a pair of massive vector bosons (X → WW, W Z) in a 36.1 fb−1 _{data sample of proton-proton collisions produced at}

a centre-of-mass energy of√s = 13TeV collected with the ATLAS detector. The final state is reconstructed through the semi-leptonic decays `νqq (` = e, µ) of the two vector bosons.

The analysis is separately optimized for the low resonance mass range MX ≤ 500 GeV

and for the high mass range MX >500 GeV. The low mass range is interesting to search

for low cross-section resonances. For low mass resonances the hadronically decaying vector boson produces two separate jets each one corresponding to one of the quarks emerging from the decay. For this reason this type of analysis is indicated as “resolved” analysis. The high mass range is instead interesting to search for new TeVscale particles (MX > 500 GeV), such a heavy resonance would decay in high pT bosons. In this pT

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Preface

detected as an unique object, that is a jet with large radius parameter R = 1.0, this analysis is therefore indicated as “merged” analysis.

I have started my analysis work by contributing to the event selection and data validation of the search in the semi-leptonic final states. The main event selection and analysis strategy of the merged and resolved analyses are described in Section 6. The final results of this analysis (Section 10.1) have been recently submitted for publication on JHEP [8].

During my analysis work I also focused on the X → W Z → `νb¯b channel that I proposed to enhance the sensitivity of the merged analysis. In the merged regime the standard technique used to discriminate between the hadronic decays of high pTbosons

and light jets, namely boson tagging [9], gives a signal efficiency of ≈ 50% for a background rejection of ≈ 25 − 50. The standard b-tagging algorithm can instead give 70% efficiency for a light jet rejection of ≈ 380 yielding a better signal to background ratio and therefore allowing for an improved sensitivity. Furthermore, in the high boost regime (jet pT > 250 GeV) the boson tagging relies on a broad mass window cut around

the boson mass, typically MJ ∈ MV ±15 GeV, and on the two prong jet substructure

variable. This implies that it cannot easily discriminate between Z and W bosons. Meanwhile the double b-tag used in Z → b¯b selection can achieve a high W boson rejection giving a clear signature of the resonance charge. The studies that I carried out on the application of Z → b¯b-tagging techniques to the selection of large-R jets in the high pTregime are described in Section 5.3. The strategies to include the Z → b¯b

tagged events in the overall analysis are discussed in Section7. Once the event selection for the Z → b¯b tagged events was defined I revised the analysis part that allows to establish the evidence for new resonance and the cross-section limit in case no evidence is found. The expected upper limits on σ(pp → X) × BR(X → W Z) using 36.1 fb−1_of

proton-proton collisions at√s= 13 TeV, obtained with the modified event selection are shown in Section10.2.

The data-sample of the newly introduced b-tagged categories could be increased by improving the trigger selection that presently introduces a 5-30% loss. The trigger signatures of `νb¯b final states will greatly benefit from the introduction of the Fast Tracker trigger upgrade that is presently being commissioned in ATLAS. This system, on

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which I am working, will provide full detector track and vertex reconstruction at trigger level thus helping in b-tagging, in isolation requirements and in pile-up suppression. One of the board of this custom track processor has been designed and built in Pisa. I participated both in the testing of the board prototypes both in realizing the classes needed for the online board configuration during data-taking. A short description of the Fast Tracker system is given in Section2.2.6.

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1 Theoretical models

One of the goals of particle physics research at the LHC is to find hints for physics beyond the Standard Model (BSM), both through precision tests of the Standard Model itself and through direct search of possible new phenomena. Di-boson resonances are predicted by several new physics models, such as extension of the Higgs sector [3, 4], Supersymmetry [10], the Extended Gauge Model (EGM) [11], Extra Dimensions [6,7], and Technicolor1_{models [}₁₂_–₁₄_].

Given the wide variety of possible models only three representative signal models are used to optimize the event selection, assess the sensitivity of the search and interpret the data: an additional heavy Higgs boson predicted by multiple beyond-SM theories, a Heavy Vector Triplet (HVT) parametrization based on a simplified phenomenological Lagrangian [5, 15, 16] and a bulk Randall-Sundrum (RS) graviton [6, 7]. The three chosen models allow to cover a wide variety of models with particles with spin 0, 1 and 2.

This chapter gives a short introduction to the status of the Standard Model (Section1.1) and of the main motivations to search for new physics (Section1.2). It will then briefly describe the characteristics of the three models used as benchmark and it will discuss the motivation behind their construction. The searches for such models will be described in Section1.3.

1_{Technicolor theories proposed to solve electroweak symmetry breaking problem without the}

intro-duction of an Higgs boson, thus Technicolor models can be considered excluded by the good match of the Higgs boson properties measured at LHC to the Standard Model predictions. Nevertheless they provide a model for spin-1 resonances that can accommodate also other models thus will be considered as valid for the present scope.

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1 Theoretical models

1.1 The Standard Model

The goal of particle physics is to identify the fundamental components of matter and to understand the forces acting between them. By keeping in mind this scope, the birth of this field can be traced back to the Maxwell’s formulation of electromagnetism (1864) and to the Thomson’s discovery of the electron (1897). With the beginning of the 20t h

century this goal was pursued with the development of quantum mechanics. This theory was pioneered by Max Planck to solve the ultraviolet catastrophe (1900), then it evolved during the 20t h_{century giving born to what is now called Quantum Field Theory. Indeed,}

during the last century new layers of matter were discovered, firstly the nuclei, then the nucleons, then new elementary particles. Furthermore, two new forces were discovered and studied, the strong force and the weak force. With all those discoveries it became ever clearer that there exist a fundamental duality between the matter components and the forces acting between them. Thus it became apparent that particles and forces have to be described in a similar way, that is by quantum fields. It also became clear that such fields did respect defined symmetries that were therefore to be considered as an intrinsic characteristic of the theory. The resulting collective theory describing all known forces and the interaction between particles takes the name of Standard Model, an extensive description of which can be found in Reference [17].

In brief, in the Standard Model, matter is composed by two types of fundamental particles, leptons and quarks. They both have spin equal to1/2~ and are structureless down to the smallest distance currently probed. There are two types of leptons with different electric charge, charged leptons (e, µ, τ) like the electrons have electric charge2

−1 e while neutral leptons or neutrinos (νe, νµ, ντ) have null electric charge. There are

also two types of quarks with different electric charge, the “up-type” (u, c, t) with charge +2/₃ e and the “down-type” (d, s, b) with charge −1/₃ e. Quarks have an additional property called colour charge, that can assume the values “red”, “green” or “blue”. In Quantum Field Theory those particles are described as quantum fields and the in-teractions between them is derived by requiring the Lagrangian to be invariant under a set of local transformations defined by the group SU(3)c× SU(2)L × U(1)Y. These

2_{here e denotes the absolute value of the electron charge. It must not be confused with e indicating}

the electron itself.

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1.1 The Standard Model transformations are gauge transformations, meaning that the symmetry is preserved only at the cost of introducing new fields in the Lagrangian of the model. These new fields are associated with new spin-1 particles (in units of ~) representing the mediator of a force. In particular the SU(3)cgroup describes the strong force and it is associated with

the gluons that carry themselves a colour charge and mediate the interaction between coloured objects. The SU(2)L× U(1)Y is the group associated to the electroweak part of

the Standard Model. The three gauge boson fields of SU(2)L and the one of U(1)Y are

combined in linear combinations through the mechanism of the electroweak symmetry breaking. Two out of three new fields arising from the linear combinations, W±_{and Z, are}

the mediator of weak interactions, while the third field the photon (γ) is responsible for the electromagnetic interaction. The resulting Lagrangian contains all renormalizable3

terms that are invariant under both the gauge group and the Lorentz group. However these fields describe only massless particles. While for quarks and leptons masses could be introduced as parameters, introducing a mass for the W± _{and Z gauge bosons would}

violate the symmetry requirements. To give mass to these fields the Higgs mechanism is used, it foresees the introduction of a spin-0 scalar field associated to the Higgs boson. The new scalar field acquires a non-null vacuum expectation value through electroweak symmetry breaking which in turns generates the masses of fermions and bosons. The Standard Model Lagrangian gives all the rules governing possible interaction between the known particles. The strength of known processes can be given in terms of experimentally measurable coupling constants that fix the intensity of each interaction. Once those are fixed the theory can be used to predict the probability of a given process, that is its cross-section. Comparing the experimentally measured rates measured by the ATLAS Collaboration with the ones predicted by the Standard Model as done in Figure 1.1 gives an idea on the level of accuracy this theory has reached and on the variety and precision of the experimental tests.

3_{Renormalizable means that the physics happening at an energy scale much greater than the one for}

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1 Theoretical models pp 500µb−1 500µb−1 80µb−1 W Z t¯t t t-chan WW H total VBF VH t¯tH Wt 2.0 fb−1 WZ ZZ t s-chant¯tW t¯tZ tZj σ [p b] 10−1 1 101 102 103 104 105 106 1011 Theory LHC pp√s= 7 TeV Data 4.5 − 4.9 fb−1 LHC pp√s= 8 TeV Data 20.3 fb−1 LHC pp√s= 13 TeV Data 0.08 − 36.1 fb−1

Standard Model Total Production Cross Section Measurements Status: July 2017

ATLAS Preliminary Run 1,2√s= 7, 8, 13TeV

Figure 1.1: Summary of several Standard Model total production cross-section measure-ments [18], corrected for leptonic branching fractions, compared to the corresponding theoretical expectations. Not all measurements are statistically significant yet.

1.2 Going beyond the Standard Model

With the discovery of the Higgs boson by the ATLAS and CMS experiments in 2012, the Standard Model is now complete, yet unanswered questions are still present. Indeed, the Standard Model cannot account for the nature and origin of dark matter, nor does it address the puzzling hierarchy between the electroweak and Planck scales. The hierarchy problem can be solved introducing new models that often foresee the presence of TeV scale di-boson resonaces.

A hierarchy problem in Quantum Field Theory occurs when the effective value of a parameter, that is the value measured by the experiment, is vastly different with respect

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1.2 Going beyond the Standard Model to its fundamental value provided by the theory. The cited values are related. Indeed, the effective value can be predicted starting from the fundamental value of the theory and dressing it up with all possible high order diagrams. In the present context, the question is why the Higgs boson mass in much smaller than the reduced Planck mass ( ¯MP). 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 cutoff scale at which the Standard Model is no longer valid and a new physics appears. This happens unless there is an incredible fine-tuning cancellation between the quadratic radiative corrections and the bare mass. Those cancellations look somehow un-natural and force us to ask whether there is a reason why they cancel out or if the cutoff scale is much smaller than ¯MP.

Indeed, the Higgs boson Lagrangian can be written as: L = 1

2 ∂µφ2+ 1₂µ2φ2+ 1₄λφ4 (1.1)

where the first two terms describe the kinetic term of a scalar particle φ which has an additional four legs self-interaction with coupling λ given by the third term. In this lagrangian there appear two constants µ and λ assuming real values. The interesting case fo the standard model is µ < 0 in which the vacuum status has value φ0=

q

−µ_λ2 = v In this case, by shifting the field to the minimum with the transformation η = φ − v, we can see that at first order the so obtained Higgs boson has a mass given by: mH =

p −2µ2. The problem occurs from contributions that include loops of virtual particles, at first order we have to include the graphs in Figure1.2.

Without going into the details of the calculation the Higgs mass obtained summing up all 1-loop contributions is divergent and can be expressed as:

m2_H = m2_pole+ 3Λ 2 8π2_v2 h m2_Z + 2m_W2 + m2_pole−4m_t2i + o log Λ mpole (1.2) where the first term (mpole) is the Higgs boson pole mass, the second term indicates the

main contribution given by 1-loop diagrams and the third term indicates the contribution of ignored diagrams. mZ, mW, mtare the Z, W and top masses respecively. The fermion

diagrams included in Equation1.2are only those from the top quark since, given the large top mass, they are the dominant contributions. As shown in Equation1.2, the integrals

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Figure 1.2: 1-loop corrections to the Higgs boson propagator. Here H is the Higgs field, S are scalar particles, V stands for vector bosons and F are fermions. Taken from Reference [19].

renormalization introduces the cutoff scale Λ on the momenta of the virtual particles in the loops. This cutoff scale can be taken as the scale at which the theory is expected to breakdown, that is the Plank scale. Therefore considering the value of reduced Planck mass (MP =

q

~c

8πG = 2.435 × 1018 GeVc2 ) as the cutoff scale value, then the Higgs mass

would naively be of the order of 1018 GeV

c2 . On the contrary the experimental value has

been measured to be equal to 125.09 ± 0.24 GeV [20]. Therefore, in order for the Higgs mass to remain finite, all high order corrections to the Higgs propagator must somehow cancel out one another, that is the factor hm2_Z + 2m_W2 + m2_pole−4m2_ti is almost null. The latter requirement imposes a fine tuning of fundamental parameters that might look artificial.

Many different theoretical models propose alternative solutions to the hierarchy prob-lem. Most of these solutions foresee a widening of the Higgs sector as explained in Section 1.2.1. Other possible solutions arise in the context of 5-dimensional theories that introduce a new cutoff scale while including gravitation in the model Lagrangian. One of this type of models is the Randall-Sundrum model which will be described in

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1.2 Going beyond the Standard Model Section1.2.2. Nevertheless multidimensional models foresee the presence of multiple particles among which there are spin-1 particles that can be modeled with the HVT Lagrangian described in Section1.2.3.

1.2.1 A model with additional Higgs bosons: the two-Higgs-doublet

model

As mentioned above, the existence of an elementary scalar particle brings to the fore the problem of naturalness of the Standard Model and strongly motivates new physics at the weak scale. In particular, extensions of the Standard Model that address the naturalness problem generally require an extension of the Higgs sector. Searching for additional Higgs bosons is therefore an important part of the program of probing naturalness at the LHC. As reported, a model for an additional neutral Higgs boson decaying to W±_W∓ _is

used as benchmark to asses the analysis ability of detecting spin-0 resonances.

The simplest possible extensions of the Standard Model Higgs sector is the two-Higgs-doublet model, of which a complete description can be found in References [3,4]. While this model can not solve directly the hierarchy problem it arises in many models that try to do so, of which the best known is Supersymmetry [10]. Other motivations include the generation of the baryon anti-baryon asymmetry observed in the universe, which can be achieved thanks to the flexibility and the additional sources of CP violating terms. It must be noted that the Standard Model in its orthodox formulation assumes the simplest possible scalar structure containing just one SU(2) doublet. Nevertheless the introduction of additional scalar doublets does not violate the Standard Model structure.

The most general scalar potential for two SU(2) doublets contains 14 parameters and can have CP-conserving, CP-violating, and charge-violating minima. For the present discussion CP will be considered to be valid and not to be spontaneously broken, and that discrete symmetries eliminate from the potential all quartic terms odd in either of the doublets. Then, the most general scalar potential for two doublets φ1 and φ2 with

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1 Theoretical models hypercharge +1 is: V = m2₁₁φ†₁φ₁+ m2₂₂φ†₂φ₂− m₁₂2 φ†₁φ₂+ φ†₂φ₁ + λ1 2 φ†₁φ₁2+ +λ2 2 φ†₂φ₂2+ λ₃φ†₁φ₁φ†₂φ₂+ λ₄φ†₁φ₂φ†₂φ₁+ λ5 2 φ†₁φ₂2+ φ†₂φ₁2 (1.3) here m11, m12, m22 and, λ[1,5] are real parameters. The minima of such potential are

given by hΦ_ai₀= 0_v a √ 2 ! , a = 1, 2. (1.4)

With two scalar SU(2) doublets there are eight associated fields: φa= φ+a va+ρ_√a+iηa 2 ! , a = 1, 2. (1.5)

as in the Standard Model three of them are removed while giving mass to the W± _and

Z bosons. The remaining five fields indicate the presence of one charged scalar field (φ±_{), two neutral scalar fields (ρ}

1,2) and, a neutral pseudoscalar field (η). At this point

the values of the α and β angles are obtained by requiring that they define a rotation that diagonalize the mass-squared matrix of the neutral scalars and, the rotation angle that diagonalise the mass-squared matrix of the charged scalars and of the pseudoscalar, respectively. Given those angles the physical fields can be expressed as rotation of the fields in Equation1.5, in particular the two neutral scalar fields are indicated with h, the one with lower mass, and H, the one with higher mass and given by:

h = ρ₁sin α − ρ₂cos α; (1.6)

H= ρ₂sin α + ρ₁cos α. (1.7)

The Standard Model Higgs boson can be described as a function of h and H as: HSM = ρ₁cos β + ρ₂sin β = h sin (α − β) + H cos (α − β)

It is therefore clear that the two parameters α and β determine the interactions of the

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1.2 Going beyond the Standard Model various physical Higgs fields with the vector bosons and with the fermions. In particular in the present discussion we are interested in the presence of an additional heavy neutral Higgs decaying into W±_W∓_.

The different models can be obtained imposing additional symmetries on the Higgs and fermionic fields in order to fix the interactions between the Higgs sector and the fermions. In example, in type I models all quarks couple to just one of the two Higgs doublets (by convention φ2) corresponding to the symmetry φ1→ −φ1, while in type II

the “up-type” right handed quarks couple to φ2while “down-type” right handed quarks

couple to φ1, corresponding to φ1 → −φ1, diR → −d i

R. Other models can be generated

changing the coupling of right/left handed components of leptons. The phenomenology of those models is quite different and it is fully analysed in Reference [3].

1.2.2 The Randall-Sundrum model

A new mechanism to solve the hierarchy problem is proposed in Reference [6,7]. In this model the weak scale is generated by embedding the 4-dimensional space-time inside a 5-dimensional bulk space with one warped extra dimension. The new cutoff scale is generated from a large scale of order the Planck scale through an exponential hierarchy which is obtained from the modified metric of the 5-dimensional bulk.

In the Randall-Sundrum model the modified metric is obtained by adding one extra dimension in a non-factorizable way. The new metric is obtained adding the new dimension and multiplying the standard four-dimensional space by a rapidly changing function of the new dimension and is given by:

ds2= e−2κ rcϕ_ηµν_dx

µdxν+ rc2dϕ2 (1.8)

Here ηµν _{is the Minkoski metric, dx}

µare the 4-dimensional coordinates, κ is a constant

having the dimension of an energy, rcis the warp radius of the warped extra dimension

and ϕ is the coordinate on the additional dimension (0 ≤ ϕ ≤ π). The only real scale in this bulk is ¯MPhowever, when at a distance y from the origin of the extra dimension, all

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This space has two boundaries; the boundary at ϕ = 0 is called the Planck brane and the boundary at ϕ = π is called the TeV brane. Then, if all Standard Model fields, except gravity, were confined in the TeV brane then the local cutoff would not be ¯MP but:

Λπ = e−2κ rcπM¯P

Therefore at this stage the requirement of Λπ ≈ TeV can be expressed as k rc = O(10)

which does not constitute a very significant constrain. In the case of the model used by ATLAS the ratioκ_/M¯P is fixed to 1.

However, constraining SM fields in the TeV brane introduces large contributions to flavour-changing neutral current processes and observables in electroweak precision measurements [7] which are in contradiction with their current limits and measurement. The RS model was then extended to allow as well the SM gauge bosons and fermions to propagate in the additional dimension and is referred to as bulk RS model. Indeed it is the Higgs that must remain localized on the TeV brane, or it would receive large quadratically divergent corrections of order of MP.

This model has clear experimental consequence, in example, since gravity propagates in the bulk then there are observable gravitons. In particular for each particle propagating in the bulk there exist Kaluza-Klein excitations. In the case of a massless graviton, the corresponding excited spin-2 neutral KK gravitons G∗ _{are close to the TeV scale.}

Those Kaluza-Klein gravitons couple to particles in the TeV brane and can be produced at accelerators with significant cross-sections (fixed by the choice of k

¯

MP), reported in

Table1.1.

1.2.3 The Heavy Vector Triplet

The HVT triplet model is based on an effective Lagrangian [5] that allows predicting the main observables (essentially the coupling strength and the mass) of the resulting resonance as a function of a limited set of effective parameters. Those parameters are linked to the fundamental parameters of a theory and may be tuned to accommodate the prediction of different theories. This model foresees the presence of three additional heavy spin-one particles: one charged boson and its anti-particle (V±

c ) and a neutral

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1.2 Going beyond the Standard Model particle (V0). These states must be mass degenerate in this model in order to reproduce

the relation between the masses of SM bosons.

The new heavy vectors couple to the Higgs and the Standard Model gauge bosons via a combination of parameters gVcH and to the fermions via the combination g2/gV cF.

The parameter gV represents the typical strength of the vector boson interaction, while

the parameters cH and cF are explicitly introduced to accommodate different models and

they are expected to be of the order of unity in most models. The resulting decay width to Standard Model bosons is proportional to g2

vc2HmV giving a large branching ratio in

di-bosons that depends only on the direct Higgs coupling and on the exotic boson mass. For the scope of the present analysis two models where considered, the first, namely model-A, sets g2

vc2H = 1, while the second model, called Model-B, sets g2vc2H = 3. The

cross-sections and signal width obtained for Model-B are reported in Table1.1.

This parameterized Lagrangian is implemented in MadGraph (Section3), and a web interface [21] is provided by the authors for generating the MadGraph parameter cards and calculating the widths, branching ratios, and cross-sections for a given set of para-meters. Results will be given for a specific set of Lagrangian parameters reported in Section3An exclusion region in the parameter space will be obtained as a function of resonance mass. HVT W’ and Z’ RS G∗ m Γ σ × BR(Z0 → WW) σ × BR(W0 → W Z) Γ σ × BR(G∗ → WW) [T eV ] [GeV ] [ f b] [ f b] [GeV ] [ f b] 0.8 32 354 682 46 301 1.6 51 38.5 79.3 96 4.4 2.4 74 4.87 10.6 148 0.28

Table 1.1: The resonance width (Γ) and the product of cross-section times branching ratio (σ × BR) for di-boson final states, for different values of the pole mass m of the resonances for a representative benchmark for spin-1 and spin-2 cases. The table shows the predictions by model-B of the HVT parameterisation (gV = 3) and by the graviton model (κ/MPl = 1).

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1.3 Searches for narrow di-boson resonances:

experimental status

Experimental indication that new physics may appear at the multi-TeV scale can be found in some results on precision measurements that show tensions between SM predictions and experimental results. Presently the largest deviations from SM predictions are at the level of a more than 2 σ disagreement and have been found in two very different type of experiments: the measurement of the bottom meson branching ratios [22, 23] and the measurement of the muon anomalous magnetic dipole [24]. In both cases new experiments or more data will allow to verify the measurements with increased precision.

Even if there are strong theoretical motivations for the presence of BSM physics, direct searches for BSM particles did not lead to any discovery yet. The exclusion limits in almost all the Beyond Standard Model (BSM) scenarios are largely dominated by the results of the ATLAS and CMS experiments. Indeed, those results take advantage of the unprecedented centre of mass energy and integrated luminosity delivered by the Large Hadron Collider. A summary of the main results of BSM searches performed by the ATLAS are shown in Figure1.3. The BSM scenarios shown include extra dimension, i.e. the Randall-Sundrum model in Section1.2.2, and additional gauge bosons, i.e. the HVT model of Section1.2.3. As reported in Figure1.3, for the warped extra dimensions model presented in Section1.2.2limits are dominated by the search in the WW → `νqq final state. In this model, the Bulk Randall-Sundrum G∗

k k is excluded by the WW → `νqq

analysis for masses mG∗ < 1.75 TeV. Regarding models including the presence of extra

gauge bosons, Figure1.3shows that the HVT W0

and Z0

highest exclusion limit is given by di-boson searches in the fully hadronic final states and it sits at 3.5 TeV.

As stated in Section1, di-boson TeV scale narrow resonances are a promising detection channel for many signals predicted by SM extensions. We can therefore use them as a tool to discover the new physics whatever it might be. These searches exploit the many decay channels of the two bosons allowing to select topologies with varied signal to background ratios and statistics. Table1.2 summarizes the final states analysed by the ATLAS Collaboration, the most relevant channels are briefly described in AppendixB.

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1.3 Searches for narrow di-boson resonances: experimental status The search for di-boson resonances in the WV → `νqq final state will be detailed in Section6. The results of the searches for resonances in the two gauge bosons final states in different channels are periodically combined in a unique results.

The combined result for the searches for massive weak di-bosons carried out by the ATLAS Collaboration with a 20.3 fb−1 _{data-set collected at}√

s = 8 TeV has excluded Extended Gauge Model W’ with masses up to 1.81 TeV and Bulk Randall-Sundrum Gravitons G* with masses up to 810 GeV [25]. Nevertheless an excess of events with respect to the predicted mass spectrum with local p-value of ∼ 2σ was observed in the mass region around 2 TeV. A similar situation was found by the CMS Collaboration that observed an excess of events of ∼ 1.8σ with respect to the background only hypothesis for the mass region around 1.8 − 2 TeV [26].

The observation of those mild excesses renewed the interest on these searches pushing to an improvement of the data-analysis. The exclusion limits on the cross-section times branching ratio for an HVT W0

→ W Zobtained by the all the di-boson resonance serches performed by ATLAS Collaboration using 36.1 fb−1_{of p-p collisions at}√

s= 13 TeV are reported in Figure1.4. As shown no peak is found by any of the di-boson analyses and the 2 TeV region is now in the reach of most of the di-boson analyses.

V → q¯q(qq0) W →`ν Z →`` Z →νν H → b ¯b

V → q¯q(qq0) VV → qqqq WV →`νqq ZV →``qq ZV →ννqq V H → qqb ¯b

SectionB.2 Section6 SectionB.1 SectionB.1 SectionB.5

W →`ν -_- W Z →_- `ν`` -_- W H →_Section`νb ¯b_B.6

Z →`` Z Z →```` Z Z →``νν V H →``b ¯b

Z →νν -_- V H →_Sectionννb ¯b_B.6

H → b ¯b HH → b ¯bb ¯b

SectionB.4

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Figure 1.3: Reach of ATLAS searches for new phenomena other than Supersymmetry [18]. Only a representative selection of the available results is shown. Yellow (green) bands indicate 13 TeV (8 TeV) data results. Updated in July 2017.

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1.3 Searches for narrow di-boson resonances: experimental status

Figure 1.4: Expected and observed limits on the cross-section times branching fraction to W Z for a new heavy vector boson W0

[18]. Line colours refer to results extracted from different di-boson final state. The solid lines show the observed limit on the cross-section times branching fraction while dashed lines show the expected cross-section times branching fraction for an HVT W0 as a function of its mass.

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2 Experimental setup

This chapter describes the ATLAS detector and its data taking system highlighting the features relevant for the present analysis. The ATLAS detector records particles emerging from the proton-proton collisions produced by the Large Hadron Collider (LHC). Protons are accelerated through a system of accelerators, described in Section2.1. Protons are then brought into collision at interaction points where the experiments sit. The ATLAS detector is designed to take advantage of the unprecedented energy available at the LHC in order to observe phenomena that involve production of highly massive particles or with very low cross-sections which were out of reach of earlier lower-energy accelerators. A description of the ATLAS detector is given in Section2.2.

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2 Experimental setup

Mean Number of Interactions per Crossing

0 5 10 15 20 25 30 35 40 45 50 /0.1] -1 Delivered Luminosity [pb 0 20 40 60 80 100 120 140 160 180 200 220 240 =13 TeV s Online, ATLAS

∫

Ldt=42.7 fb-1 > = 13.7 µ 2015: < > = 24.9 µ 2016: < > = 23.7 µ Total: < 2/17 calibration

Figure 2.2: Luminosity-weighted distribution of the mean number of interactions per crossing for the 2015-2016 p-p collision data at√s= 13 TeV centre-of-mass energy [18].

Day in 2015

23/05 20/06 18/07 15/08 12/09 10/10 07/11

]

-1

Total Integrated Luminosity [fb

0 1 2 3 4 5 = 13 TeV s ATLAS Online Luminosity

LHC Delivered ATLAS Recorded -1 Total Delivered: 4.2 fb -1 Total Recorded: 3.9 fb (a) Day in 2016 18/04 16/05 13/06 11/07 08/08 05/09 03/10 31/10 ] -1

Total Integrated Luminosity [fb

0 10 20 30 40

50 ATLAS Online Luminosity s = 13 TeV LHC Delivered ATLAS Recorded -1 Total Delivered: 38.5 fb -1 Total Recorded: 35.6 fb 2/17 calibration (b)

Figure 2.3: Cumulative luminosity versus time delivered to (green) and recorded by (yellow) the ATLAS experiment for p-p collisions at √s = 13 TeV centre-of-mass energy [18] during 2015(a)and 2016(b).

2.1 The Large Hadron Collider

The LHC [27] is a circular collider with a circumference of 27 km situated in the tunnel once occupied by the Large Electron Positron collider based at CERN in Geneva, Switzerland. Both protons and lead ions can be used in collisions, however this thesis

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2.1 The Large Hadron Collider will focus on proton-proton collisions. In the case of proton-proton (p-p) collisions the design centre-of-mass energy is 14 TeV. Before being injected in the LHC and brought to collision, the protons are pre-accelerated up to 450 GeV in a chain of different accelerators depicted in Figure2.1. In LHC the radio frequency cavities accelerate the beams, consisting of several hundreds of bunches each, to its final energy of 3.5 TeV (2010-2011), 4.0 TeV (2012), 6.5 TeV (2015-2017) or the design energy of 7 TeV (2020). 1232 superconducting dipole magnets with a maximum magnetic field strength of 8.33 T assure that the protons are kept on their circular path, while 392 superconducting quadrupole magnets are used to focus the beams.

The event rate (dNevent

dt ), defined as the number of single collision events per second, is

given by: dNevent

dt = Lσevent (2.1)

Where σevent is the process cross-section expressed in barns (1b = 10−24cm2) while the

parameter L called instantaneous luminosity is measured in cm−2_s−1_{. The instantaneous}

luminosity depends only on the beam parameters, and in the gaussian beam approxima-tion is directly proporapproxima-tional to the number of protons per bunch, the number of bunches per beam and, the revolution frequency expressed in s−1_{while it is inversely proportional}

to the beam transverse size. The LHC target luminosity is L = 1034_cm−2_s−1_.

The interaction rate at fixed number of bunches, revolution frequency and beam size parameters can vary due to the variable number of protons per bunch. It is therefore clear that given an high enough number of protons in each bunch, then for each bunch crossing there can be multiple proton-proton interactions. Since the cross-section for the interesting processes is of the order of few nb while the total cross-section is 8 order of magnitude larger, most of the interactions in each bunch crossing will not be of interest. These collisions overlaid with the studied event constitute what is called “in-time pile-up”. The distributions of the mean number of interactions observed for 2015 and 2016 beam conditions are shown in Figure2.2.

If the bunch crossing frequency is high it may happen that interactions from adjacent bunch crossings will fall inside the detector integration time and will be recorded in the same event, this phenomenon takes the name of out-of-time pile-up. In the case of the

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data used in this thesis the bunch crossing frequency is fixed to 40 MHz corresponding to a bunch crossing every 25 ns.

Given Equation 2.1, then the number of recorded events will be proportional to the integrated luminosity L = ∫ Ldt. The integrated luminosity as a function of time is shown in Figure2.3.

2.2 The ATLAS detector

A schematic view of the ATLAS detector is shown in Figure2.4. As shown, the ATLAS detector has a cylindrical shape and surrounds the proton-proton interaction point, it is 46 meters long, 25 meters in diameter, and it weighs about 7,000 tonnes. This design allows to cover a fraction of solid angle around the interaction point as large as possible, in order for the largest fraction of particles produced at the collisions to fall inside the detector acceptance. The ATLAS detector is made of different types of sub-detectors wrapped around each other in concentric layers. The design each of these sub-detectors has been optimized using specific benchmark measurements. Other principles that lead the detector design include radiation hardness and performance stability.

As shown in the schematic view of the detector in Figure2.4the region up to R ∼ 1.2 m from the beam axis contains a tracker immersed in a 2 T longitudinal magnetic field. The magnetic field is generated by a superconducting solenoid described in Section 2.2.2. This tracker, often referred as Inner Detector (ID) [28], is described in Section 2.2.3. Section2.2.4describes the calorimeters [29,30] located around the ID, also constituted by sub-systems using different technologies. The outermost part of the ATLAS detector is a muon spectrometer [31] (described in Section2.2.5) immersed in a toroidal magnetic field provided by three toroidal magnets.

The signal from all those detectors is processed using an infrastructure known as Data Acquisition (DAQ) system. The ATLAS DAQ infrastructure and the trigger infrastruc-ture, collectively known as TDAQ, will be described in Section2.2.6.

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2.2 The ATLAS detector

Figure 2.4: Schematic view of the ATLAS detector [32].

2.2.1 The ATLAS coordinates system

The ATLAS detector uses a right-handed coordinate system whose origin is placed in the interaction point. The x-axis points towards the centre of the LHC, the y-axis upwards and the z-axis along the beam pipe. Often a central coordinates system is used. The coordinates in this case are (z, φ, η), with z being the z-axis coordinate, φ the azimuthal angle in the xy-plane and η is the pseudorapidity defined as:

η= −ln

tan θ 2

where θ is the polar angle in the yz-plane. The pseudorapidity corresponds to the rapidity for massless particles. As in the case of the rapidity it transforms with a sum term under a Lorentz boost, therefore pseudorapidity differences are invariant under a Lorenz boost along the z-axis. Lorentz boost along the z-axis are to be expected due to the p-p initial state since the hard scattering products will receive a boost (mostly on the z-axis) equal to the momentum of the parton-parton centre-of-mass. In other terms the parton-parton boost is fixed by the proton parton distribution functions and does not coincide to the detector reference frame. It is therefore mandatory to use Lorentz invariant quantities like the projection of vectors on the xy-plane or transverse plane, i.e. pT = √px+ py.

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2.2.2 The Magnetic system

A central solenoid generates a 2 T field parallel to the beam axis in the tracker volume. This magnet provides a bending power of 2.1 Tm [33]. This magnet was designed to minimise the amount of inactive material in front of the calorimeters in order to minimise the degradation of the photon and electron energy resolutions. Because of this it is contained in the same cryostat of the Liquid Argon calorimeter.

The magnetic field for the muon spectrometer are provided by a system composed by three toroidal magnet systems. In the barrel region an eight air-core coils (25 m long and 4.5 m tall) are assembled radially; each coil is enclosed in its own cryostat. The peak magnetic field produced in the barrel region is about 4 T and the magnetic field has a bending power of roughly 3 Tm [33]. The magnetic field in the forward regions of the muon system is obtained with the end-cap coils (5 m long); all eight magnets are housed inside the same cryogenic unit. In the end-cap regions the bending power of the toroidal magnets is 6 Tm [33].

2.2.3 The Inner Detector

From the inside out, the first sub-detector is a 6.2 m long tracking system which covers the region from 3.3 cm up to 1.2 m in radius from the beam axis. The function of this sub-detector is to reconstruct the trajectories of charged particles emerging from the collisions and to provide an excellent momentum resolution. Because of this it is required to have a fine granularity and to be made of as little material as possible in order to minimally affect the energy measurement in the calorimeters. Furthermore the Inner Detector was designed to both reconstruct primary vertices and secondary vertices. Their precise measurement is of utmost importance to distinguish the hard-scatter vertex from pile-up vertices and for the identification of b-quarks respectively. As shown in Figure 2.5, those goals are achieved by using three different subsystems; the pixel detector, the semiconductor tracker (SCT) and the transition radiation tracker (TRT). For muon originated tracks (cosmic rays) with pT > 30 GeV, this sub-detector allows to

obtain a transverse parameter resolution σ(d0)= 22.1 ± 0.9 µm and relative transverse

momentum resolution σP

P = 0.05%pT[GeV] ⊕ 0.1%. The two terms in the relative

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2.2 The ATLAS detector momentum resolution parametrization [34] account for the intrinsic tracker resolution and multiple scattering.

The pixel detector is composed by four layers of silicon-pixel detectors covering the region |η| < 2.5. This apparatus is able to measure the trajectories of charged particles, or tracks, for pT > 500MeV. The innermost layer, called Insertable B-Layer [35] (IBL),

has been added during the long shutdown starting in 2013. The IBL consists of a unique layer of pixel modules forming a cylindrical detector of radius 3.325 cm around the interaction region covering the region |η| < 2.58. Whereas the three external layers of the pixel detector consists of pixel modules arranged in three concentric barrel layers covering the |η| < 1.5 and two end-cap systems composed of three disks of silicon modules each covering the region 1.5 < |η| < 2.5. The high resolution requirements are achieved by 1744 silicon sensors consisting of 47232 pixels each with a size of 50 × 400 µm2_{and a thickness of 250 µm that are readout individually. The addition of}

the IBL improved the resolution on the tracks impact parameter by about 40% for tracks with pT < 1 GeV, thus improving the b-tagging performances.

The pixel tracker is surrounded by the SCT which is a silicon microstrips detector spanning radial distances from 299 mm to 560 mm. As the pixel detector, the SCT consists of silicon-strip modules arranged in four concentric barrels covering the region up to |η| < 1.4 and two endcaps of nine disks each covering the region 1.4 < |η| < 2.5. Each layer is composed by single sided detector modules which are mounted back to back with a stereo angle of 40 mrad to improve spatial resolution. In this region silicon microstrip were chosen over silicon pixels due to the lower expected particle density. This allowed to maintain a good spatial resolution while containing the number of readout channels and reducing the overall detector costs.

The outermost part of the Inner Detector, called Transition Radiation Tracker, is com-posed by proportional drift straws of 4 mm in diameter filled with a gas comcom-posed by 70% Xe, 27% CO2, 3% O2, interspaced by polypropylene fibres (barrel) or foils

(end-caps). The barrel, covering the region |η| < 1.0, is composed by 144 cm long straws aligned parallel to the beam-axis, thus it does not provide information on the z-position. In the end-caps, covering the region 1.0 < |η| < 2.0, the straws are arranged radially in wheels with a length of 37 cm. The rate of photons emitted by the polypropylene

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Figure 2.5: Schematic view of a slice of the ATLAS inner detector, including IBL. Taken from Reference [31].

radiator depends on the characteristics of the particle traversing the radiator, therefore the signal in TRT straws can be used in particle identification.

2.2.4 The calorimeters

Outside the Inner Detector there is a calorimetric system shown in Figure 2.6, which measures the energy of all particles with the exception of muons and neutrinos. Indeed, muons are minimally ionizing particles, thus they do leave only a small fraction of their energy in the calorimeters. Instead neutrinos do not interact with the detector and their transverse momentum is inferred using the missing transverse energy (Section4.6) The ATLAS calorimetric system is composed by sampling calorimeters that is calorimet-ers. Different absorber and active materials are used to detect electromagnetically and strongly interacting particles in different pseudorapidity regions.

For this analysis work the two important figures of merit for the calorimeter system are

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Figure 2.6: A cut-away drawing of the ATLAS calorimetric system,and Inner Detector. Taken from Reference [30].

energy linearity and resolution. The calorimeter resolution can be parametrized as: σE E = a √ E ⊕ b E ⊕ c; (2.2)

here a, b and c are positive parameters. The parameter a accounts for the so called stochastic term that accounts for the fluctuations of the number of particles in the shower evolution. The parameter b accounts for the electronic noise in the read-out system, as expected this term is independent from the energy of the detected particle. The constant term c accounts for the systematic effects due to detector calibration and for the presence of dead material in/in front of the calorimeter. The electronic noise contributions for the two ATLAS calorimeters are found to be negligible so only statistical and constant terms are considered, the resolutions for the two calorimeters can be found in Figure2.7.

Liquid Argon Calorimeter

Liquid Argon [29] (LAr) sampling calorimeters are used for the electromagnetic calor-imeter, the end-cap hadronic calorimeter and the forward calorimeters. This calori-meter, shown in yellow in Figure 2.6, uses liquid argon as active material based on

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its radiation-hardness and intrinsic linear behaviour, while different absorbers for in different regions.

More specifically, the pseudo-rapidity region |η| < 3.2 is covered by an highly granularity electromagnetic calorimeter which uses accordion-shaped electrodes and lead absorbers immersed in liquid Argon. In this case lead is chosen as absorber due to his high atomic number (Z = 82) favouring e-e interactions. The electromagnetic calorimeter is further segmented into three coaxial section; a barrel section (EMB) covering the region |η| < 1.475 and in two end-cap sections (EMEC) covering the region 1.375 < |η| < 3.2. The overlap region between the EMC and the EMEC corresponding to 1.375 < |η| < 1.475 is known as the crack region. This region contains un-instrumented material, that is cables and pipes reaching the ID which reduce the calorimeter performances. The thickness of the electromagnecic calorimeter is comprised between 22 to 24 X0A

pre-sampler providing a measurement of the energy lost upstream is installed in front of the electromagnetic calorimeter in the central region |η| < 1.8. This pre-sampler is composed by a 1.1 cm (0.5 cm) thick LAr layer in the barrel (end-cap) region. The relative energy resolution evaluated using a test beam of electrons as a function of the beam energy for the standalone liquid argon electromagnetic calorimeter is reported in Figure2.7(a).

Behind the Electromagnetic calorimeter in the forward region lays a copper-liquid argon hadronic endcap calorimeter covering the region 1.5 < |η| < 3.2. Here the choice of absorbers is driven by the fact that in the case of hadronic calorimeters materials with higher mass number are favoured, that is hadrons interact with nucleons.

The LAr calorimeters are completed by a copper/tungsten-liquid argon forward calor-imeter covering the region closer to the beam 3.2 < |η| < 4.9. This calorcalor-imeter is segmented in three layers , the first serving as electromagnetic calorimeter uses copper as absorber, the other two layers use tungsten absorbers. In this region the calorimeter must sustain an high particle flux that lead the choice of a absorber, furthermore due to the limited angular coverage of this calorimeter tungsten was chosen to minimise the lateral spread of the hadronic showers.

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(a) (b)

Figure 2.7: Figure(a)reports the Liquid Argon electromagnetic calorimeter standalone energy resolution for electrons [18] as a function of the beam energy. Figure(b)reports The Tilecal-standalone energy resolution for pions [36] impinging on the calorimeter at |η| = 0.35 (equivalent calorimeter depth 7.9λ), as a function of the beam energy.

Tile Calorimeter

The ATLAS calorimetry is completed by the barrel hadronic calorimeter [30] known as TILE. This calorimeter, surrounding the LAr calorimeters, is a sampling calorimeter using tiles of plastic scintillator as active material and low-carbon steel (iron) as the absorber. The calorimeter scintillating tiles are coupled to photomultipliers tubes using wavelength shifting fibres. The barrel and extended barrel are segmented in three layers of different thickness. To minimise punch-through into the muon system, the hadronic calorimeter has a total thickness of more than 11 radiation lengths (λ). The TILE calorimeter is fractioned in a barrel region |η| < 1 and an extended barrel region 1 < |η| < 1.7. The relative energy resolution evaluated using a test beam of pions as a function of the beam energy for the standalone TILE calorimeter is shown in Figure2.7(b). The impact of the calorimeter resolution on the measure of the calorimetric-jets energy will be discussed in Section4.4.

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2.2.5 The muon spectrometer

The outermost sub-detector is the muon spectrometer shown in Figure2.8. This system is immersed in a magnetic field (Section2.2.2) providing a bending power of 3 Tm in the barrel and 6 Tm in the end-cap regions. The spectrometer is formed by multiple stations of muon chambers situated at different radial distances from the beam axis. The chambers are arranged such that particles emerging from the interaction point will traverse at least three stations of chambers.

In the barrel section covering the region |η| < 1.0, the structure of the air core magnets allows to put one station inside the magnet structure, hence the muons trajectories are measured at the inner field boundary, inside the field volume and at the outermost field boundary. The barrel chambers therefore form three cylinders concentric with the beam axis, at radii of roughly 5 m, 7.5 m, and 10 m allowing to determine the full sagitta of the muon track. Here Monitor Drift Tubes (MDT) chambers are used, each chamber being composed by six layers parallel layers of 30 mm drift tubes. This technology was chosen because of the very good space resolution < 50 µm. Since the collection time of MDTs is low (maximal drift time 500 ns, average drift speed 30 µm/ns), faster Resistive Plate

Chambers (RPC) are used for triggering muons in the barrel region. RPCs can achieve a typical space–time resolution of the order of 1 cm × 1 ns with digital readout. These chambers are oriented with an angle of 90 with respect to MDTs, in order to provide a measurement of the track parameter in the direction parallel to the magnetic field (φ). In the end-cap section covering the region 1 < |η| < 2.7, the magnet is enclosed in a cryostatic system that does not allow the positioning of chambers inside the field volume. Instead, the chambers are arranged to determine the momentum with the best possible resolution from a point-angle measurement. That is the muon track is reconstructed at before and after entering the magnetic field and the measure of the momentum is obtained as a function of the angle between the track segments. The end-cap chambers are arranged in four concentric disks centred on the beam axis at z distances of 7 m, 10 m, 14 m, and 21-23 m from the interaction point. In this region Cathode Strip Chambers (CSC) are used for a precise measurement of the track parameter, these chambers let cover a wide area with economically produced chambers while providing a single layer track resolution of less than 80 µm. These are multi-wire proportional chambers with

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2.2 The ATLAS detector a cathode strip readout which, by charge interpolation, provides the required spatial resolution. As for the barrel region, also in the end-cap section a different chamber technology is used for trigger chambers: in this case Thin Gap Chambers (TGC) are used. These chambers are multi-wire chambers with a wire-cathode gap smaller than the wire-wire distance. TGCs are oriented so that anode wires run the azimuthal direction, while cathode strips run in the radial direction. By reading which cathode strip was hit, TGSs are able to achieve an azimuthal (φ) granularity of 2-3 mrad. Wires are read in groups of 4 to 20 wires as a function of η, information on the hit wire-group is used to measure the track bending at trigger level.

The performance of the muon spectrometer evaluated on cosmic ray generated muons is reported in Figure2.9. As shown, the muons momentum measurement (red triangles) is performed combining the track information of both the ID (black squares) and the muon spectrometer (red dots). While the muon spectrometer is fundamental for muon reconstruction, The muon momentum measurement at low momentum is dominated by the ID due to the greater spacial resolution of this detector. The muon spectrometer dominates the momentum resolution in the high transverse momentum regime thanks to the greater lever arm available which provides a greater track bending fundamental in this pTregime.

2.2.6 The ATLAS Trigger and Data Acquisition

The ATLAS trigger and data acquisition system [38] is organized into two parallel pipelines as shown in Figure2.10. A read out system (blue) reads and transmits the elec-trical information from the detectors while a trigger system (green) receives the detector information from the read-out and decides which information should be recorded. As shown, the two systems are strictly interconnected since the read out provides informa-tion to the trigger, while the trigger refines the received informainforma-tion and sends it back to the read-out system. The trigger system is essential since the raw data rate is roughly 100TB/s which can not be written directly to disk because of the available bandwidth

and disk costs. Furthermore, it must be considered that only a small fraction of the total p-p cross-section contains the hard interesting for further data analysis, i.e. the Higgs boson production cross-section is roughly O(10−2 _{nb) while the total p-p cross-section}

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2 Experimental setup Chambers Chambers Chambers Chambers Cathode Strip Resistive Plate Thin Gap

Monitored Drift Tube

Figure 2.8: 3-D view of the muon system, indicating where the different chamber technologies are used

Figure 2.9: Relative transverse momentum resolution as a function of the measured muon transverse momentum [37] for tracks reconstructed from ID and muon spectrometer hits, and for combined muon tracks. The shaded region shows the ±1σ region of the fit to the resolution curve for the combined muon tracks.

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2.2 The ATLAS detector is of the order of 108 _{nb. In order to maintain an high efficiency on hard-scattering}

events without exceeding the available bandwidth the trigger system is divided into two decision levels. While the first decision level is a fixed latency hardware-based trigger, the second level is software based.

The first trigger level, or level 1 (L1) trigger, is formed by custom electronic boards that spy data coming from the calorimeters and muon chambers. These two detectors are chosen since they can be read with a coarser granularity and the expected particle rates are lower with respect to the Inner Detector. The usage of custom hardware allows maintaining a fixed latency of 2.5µs without introducing “dead-time”. That is intervals in which the trigger system is in a busy state and can not process further events. Due to the strong requirements on latency the L1 trigger algorithms can only perform a loose selection of events reducing the event (data) rate from 40MHz to 100kHz (from 100TB/s

to 160 GB/_s). The L1 trigger selects events and transmits to the next trigger level the positions of the detector regions where high pTobjects are located (Region Of Interests,

ROI). The data produced from the detector are collected from the front-end electronics and stored in memories that are read back synchronously with the L1 accept/reject decision. The L1 accepted events are merged into the Read Out Drivers (ROD) and then sent to a computer farm implementing the second trigger stage.

The second trigger level is called High Level Trigger (HLT), it is based on commercial CPUs, that is a computer farm running reconstruction and identification algorithms. In this case the latency requirements are relaxed (≈ 550ms) consequently the selections can be tighter and rely on complete detector information. In order to perform this high level selection the HLT collects event fragments and merges them into full-events, this process is called event-building. Event fragments are data produced from different sub-detectors belonging to the same event. Once all events fragments are collected,event selection is executed on fully reconstructed events using the full detector information. The maximum event rate expected at high level trigger output is ≈ 1KHz corresponding to 1500MB/sof data to be stored on tape for reprocessing and analysis.

Specific trigger algorithm chains (L1+HLT) are selected for each data analysis. The trigger strategy for this analysis will be described in Section6.

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Figure 2.10: Schematic view of the ATLAS trigger (left) and data acquisition (right) systems and their connections.

The FastTracKer

FastTracKer (FTK in Figure2.10) is a system able to reconstruct tracks in the full ATLAS detector at the Level one trigger accept rate.

The high LHC luminosity has the side effect of producing large pile-up. A number of pile-up event between 60 and 200 will be faced in the coming years. In this environment track reconstruction with fitting is very challenging in terms of needed CPU time and power. Nevertheless, track information at the trigger stage is required in order to achieve a background suppression compatible with the available bandwidth while keeping an high signal efficiency. Because of this, often the online track reconstruction is performed only in limited detector regions (i.e. ROIs) and/or introducing tight cuts on the track impact parameter and momentum.

The FTK system will reconstruct tracks down to 1 GeV with track reconstruction effi-ciency of about 95% thanks to the usage of massive parallel processing of data produced from the inner detector. The idea behind the FTK system is to simulate all possible

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2.2 The ATLAS detector tracks in a generic collision and extract the corresponding patterns of Inner Detector hits. The hits expected for those simulated tracks are compared with the ID hits in data, if a match is found then the event must contain a track “similar” to the simulated one. This pattern matching technique can be performed in parallel on all patterns using a suitably designed ASIC, called Associative Memory chips. These Associative Memory chips perform pattern recognition using 8 ID layers at an operating frequency of 100 MHz. In order to minimize the needed number of Associative Memory chips patterns are loaded with a coarser resolution so that more than one track will correspond to the same pattern. Once a match is found, the detector hits that fired the match are used in a two stage fit procedure giving a high quality track as output. In the first fitting procedure the 8 ID layers hits that match with a pattern are used in a linearised fitting procedure. Tracks that satisfy a χ2 _{cut are then extrapolated to the remaining ID layers. Tracks}

which successfully attach hits in the remaining layers are re-fitted. The refitted tracks that pass a second χ2_{cut are used as final tracks.}

This algorithm is implemented using a custom electronic system composed by 13 crates: 8 VME crates containing the main processing units and 5 ATCA shelves containing the boards handling the input and output of the system. The commissioning of this system, to which I participated, is currently undergoing. The commissioning of the system includes the installation of the boards in the trigger computing room and the development of the software/firmware needed for the system configuration and run.

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3 Event simulation

Searches for new resonances heavily rely on the ability to predict the kinematic dis-tributions and normalization of observed processes. Indeed, these searches look for a "bump" on top of a smooth background in the distribution of the invariant mass of the candidate resonance particle. The ability to locate such a bump requires to know both the invariant mass background distribution and the bump shape. In the case of searches in the semi-leptonic di-boson channels these shapes are extracted from simulated samples of signal and background processes. The background and signal samples used in this analysis will be described in Section3.1and Section3.2respectively. A list of the used Monte Carlo samples can be found in AppendixA.1.

Sadly it is almost impossible to predict complete distribution of events generated from a hadron collider. Theoretically, strong interactions not solved therefore event simulation relies on Monte Carlo methods. These are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical integration. Often event generators will use a different recipe in order to simulate all the processes composing an event.

At generator level the hard scattering process is represented by its differential cross-section. Taking as an example a generic scattering process h1+ h2 → X, initiated by

two protons h1and h2with four-momenta P1and P2(

√

s =p(P₁+ P₂)2 = 13TeV), with X representing some totally inclusive collection of final particles, then:

σ(h₁+ h₂→ X)=Õ i, j ∫ dx₁dx₂fh₁, i(x1, µF) fh₂, j(x2, µF)· (3.1) · N Õ m=0 α_S(m)(µ2_R) · dˆσ_{i, j}(m)(x₁x₂s, µR, µF)

Ricerca di risonanze di-bosoniche nello stato finale semi-leptonico (lvqq) in collisioni protone-protone a $\sqrt{s}= 13$ TeV collezionate con il rivelatore ATLAS.

Dottorato di Ricerca in Fisica

Università di Pisa

GRADUATE COURSE IN PHYSICS UNIVERSITY OF PISA

Search for di-boson resonances in the

semileptonic final state in p- p collisions

at

√

s

= 13 TeV collected with the

ATLAS detector

Nicolò Vladi Biesuz

Supervisor: Chiara Roda

Contents

Preface

1 Theoretical models

1.1 The Standard Model

1.2 Going beyond the Standard Model

1.2.1 A model with additional Higgs bosons: the two-Higgs-doublet

model

1.2.2 The Randall-Sundrum model

1.2.3 The Heavy Vector Triplet

1.3 Searches for narrow di-boson resonances:

experimental status

2 Experimental setup

∫

2.1 The Large Hadron Collider

2.2 The ATLAS detector

2.2.1 The ATLAS coordinates system

2.2.2 The Magnetic system

2.2.3 The Inner Detector

2.2.4 The calorimeters

2.2.5 The muon spectrometer

2.2.6 The ATLAS Trigger and Data Acquisition

3 Event simulation