Marie Hélène-Schune

Philippe Crochet

Raphael Granier

De Cassagnac

Alberto Baldisseri

Elena Gonzalez

David Rousseau

Lydia Fayard

Marie Hélène

Emma Milie

Ayyat

Asmaa, Wafa, Nawal, Mitha, Wafaa, Fatima, Najwa, Sabrine, Yafa, Jihad, Ekhlas Amal Asmaa

Keywords: Charmonia, charged-particle multiplicity, proton-nucleus collisions, ALICE, LHC

In ordinary matter, quarks and gluons can only be found in a confined state, forming hadrons. However, lattice QCD predicts the existence of the quarkgluon plasma (QGP), a deconfined state of quarks and gluons, at extremely high energy density and temperature. In nature, QGP may have existed during the first microseconds of the universe, where such extreme conditions occurred. Such conditions are reproduced in the laboratory by colliding heavy ions at sufficiently high energy. Due to its short lifetime, the QGP can not be characterized by direct observations. The influence of its formation on particle production is used to characterize it. In heavy-ion collisions, besides QGP effects, the observables might also be affected by the presence of the nuclei, the so-called cold nuclear matter (CNM) effects. To disentangle the QGP effects from the CNM effects, proton-nucleus collisions are used as a control system in which QGP is not expected to be formed. One of the main tools used to probe QGP is quarkonia. Quarkonia are bound states of heavy quark-antiquark pairs (cc or b b pairs). Due to their large mass, heavy-quark production mechanism takes place at hard scales of QCD, while the formation of the bound states involves soft QCD scales. Quarkonia are, therefore, sensitive to both per-Laure, and Bruno for all the discussions, support, and advice you gave to me. Corentin, my office mate, thank you for all our conversations in Arabic, English, and French, and for all the games you taught me.

Titre: Production de charmonium en fonction de la multiplicité de particules chargées dans les collisions p-Pb à s N N = 8. [START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF] TeV dans ALICE au LHC Mots clés: Charmonia, dépendance en multiplicité, collisions proton-noyau, ALICE, LHC Résumé: Dans la matière ordinaire, les quarks et les gluons ne peuvent être trouvés que dans un état confiné, appelés hadrons. Cependant, la chromodynamique quantique sur réseau prédit l'existence d'un état déconfiné de quarks et de gluons, le plasma de quarks et de gluons (QGP). Dans la nature, il est possible que le QGP ait pu exister pendant les premières microsecondes de l'univers, où des conditions extrêmes de haute densité d'énergie et de haute température auraient été présentes. De telles conditions peuvent être reproduites en laboratoire en faisant entrer en collision des ions lourds à des énergies suffisamment élevées. En raison de sa courte durée de vie, plusieurs observables indirectes sont utilisées pour caractériser le QGP. En plus des effets du QGP, les observables peuvent également être affectées par la présence des noyaux, appelés effets de matière nucléaire froide (CNM). Pour dissocier les effets du QGP des effets de CNM, des collisions protonnoyau, dans lequelles on ne s'attend pas à former du QGP, sont utilisées comme système de contrôle. L'une des observables les plus intéressantes pour sonder le QGP est l'étude famille des quarkonia. Les quarkonia sont des états liés de paires de quarks-antiquarks lourds (cc or b b). En raison de leur masse élevée, le mécanisme de production des quarks lourds se produit à des échelles de haute impulsion de la chromodynamique quantique (QCD), tandis que la formation des états liés implique des échelles plus basses impulsion de la QCD. Les quarkonia sont donc sen-sibles à la fois aux aspects perturbatifs et non-perturbatifs de la QCD. De plus, leur mesure dans les collisions p-Pb fournit des informations sur les effets de la matière nucléaire froide, tels que le shadowing nucléaire ou l'interaction avec les particules qui se déplacent avec elles. Des mesures récentes révèlent que les taux de production des J/Ψ augmentent avec la multiplicité des particules chargées dans les collisions pp et p-Pb au LHC. Différents mécanismes ont été proposés pour expliquer cette observation. L'un d'eux est l'influence des interactions à plusieurs partons dans l'état initial de la collision. Les mesures des états excités du charmonium, par exemple Ψ(2S), en fonction de la multiplicité des particules chargées, sont essentielles pour dissocier l'impact des éventuels effets de l'état final. Dans cette thèse, nous présentons la mesure des les taux de production du charmonium en fonction de la multiplicité des particules chargées, mesurée à rapidité centrale (|η| < 1.0). Les J/Ψ et Ψ(2S) sont reconstruits dans leur canal de désintégrations en dimuons dans les régions de rapidité 2.03 < y cms < 3.53 et -4.46 < y cms < -2.96. Cette mesure est réalisée à l'aide de collisions p-Pb à s NN = 8. [START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF] TeV dans ALICE, expérience dédiée aux ions lourds au LHC du CERN. De plus, nous présentons des résultats préliminaires pour l'incertitude systématique de l'efficacité de la reconstruction des traces dans le spectromètre à muon d'ALICE. Cette partie a été réalisée en utilisant un jeu de données de collisions pp à s = 13.6 TeV collecté en 2022.

turbative and non-perturbative aspects of QCD. In addition, their measurement in p-Pb collisions provides information on CNM effects, such as nuclear shadowing or the interaction with comoving particles. Recent measurements reveal that J/Ψ yields increase with charged-particle multiplicity in pp and p-Pb collisions at the LHC. Different mechanisms were proposed to explain this observation. One of them is the influence of multiple parton interactions in the initial state of the collision. Measurements of the excited charmonium states, e.g., Ψ(2S), as a function of charged-particle multiplicity, are essential to disentangle the impact of possible final-state effects. In this thesis, we present the measurement of charmonium yields as a function of charged-particle multiplicity, measured at central rapidity (|η| < 1.0). J/Ψ and Ψ(2S) are reconstructed in their dimuon decays within the rapidity region 2.03 < y cms < 3.53 and -4.46 < y cms < -2.96. This measurement is performed using in p-Pb collisions at s NN = 8. [START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF] TeV collected by ALICE at the LHC (CERN). In addition, we present preliminary results of the systematic uncertainty of the muon spectrometer tracking efficiency in Run 3. This study was performed using a data set of pp collisions at s = 13.6 TeV.

iii

Dedication

Mahmoud Darwish, a Palestinian poet, once said:

As you conduct your wars, think of others (do not forget those who seek peace).

As you pay your water bill, think of others (those who are nursed by clouds).

As you return home, to your home, think of others (do not forget the people of the camps).

As you sleep and count the stars, think of others (those who have nowhere to sleep).

As you liberate yourself in metaphor, think of others (those who have lost the right to speak).

As you think of others far away, think of yourself (say: "If only I were a candle in the dark")."

To the people of Palestine, one day we will be free! v

Synthèse en français

Dans la nature, les quarks et les gluons, c'est-à-dire les particules élémentaires de la matière QCD ordinaire, sont toujours confinés à l'intérieur des hadrons, un phénomène connu sous le nom de confinement de la QCD. Cependant, dans des conditions extrêmes de densité d'énergie et de température, la matière QCD subit une transition de phase vers un état où les quarks et les gluons se déplacent librement, créant ce que l'on appelle le plasma de quarks et de gluons (QGP). Ces conditions extrêmes peuvent être recréées en laboratoire grâce à des collisions d'ions lourds ultra-relativistes. En raison de sa durée de vie très courte, typiquement de l'ordre du femtoseconde par la vitesse de la lumière (fm/c), le QGP ne peut pas être détecté directement. Pour explorer et comprendre le QGP, l'étude de la production de charmonia sert d'outil précieux. Les quarks charmés sont produits au cours des premières étapes de ces collisions, avant la formation du QGP, et par la suite, ils sont influencés par l'évolution du milieu.

L'étude de la production de charmonium dans des systèmes de petite taille, tels que les collisions proton-proton ou proton-ion lourd, est essentielle car ces systèmes servent de points de référence où aucun effet du QGP n'est attendu. Néanmoins, plusieurs comportements QGP-like inattendus ont été observés dans des systèmes de petite taille lors d'événements de haute multiplicité, ce qui a conduit à considérer les interactions multipartoniques comme un scénario clé pour expliquer ces résultats. L'étude de la production de charmonium en fonction de la multiplicité de particules chargées est une méthode pour sonder ces interactions multipartoniques. L'objectif principal de cette thèse est d'analyser la production de charmonium en fonction de la multiplicité de particules chargées dans les collisions p-Pb à une énergie de centre de masse de s NN = 8,16 TeV en utilisant l'expérience ALICE au Grand Collisionneur de Hadrons (LHC).

Dans le chapitre 1, je commence par expliquer les concepts fondamentaux liés au 1 plasma de quarks et de gluons et aux méthodes utilisées pour l'étudier. Ensuite, je présente des exemples de comportements QGP-like surprenants observés dans des systèmes de petite taille. Le chapitre se conclut par un aperçu des études de quarkonium concernant la multiplicité de particules chargées.

Dans le chapitre 2, je discute de l'équipement expérimental utilisé pour recueillir l'ensemble de données utilisé pour l'analyse. Je commence par une brève explication du processus d'accélération, puis je me plonge dans la description du détecteur ALICE, en mettant l'accent sur les composants utilisés pour évaluer les rendements de charmonium et la multiplicité de particules chargées.

Le chapitre 3 fournit une explication détaillée de la procédure utilisée pour évaluer la multiplicité de particules chargées et les rendements de charmonium. La première section couvre les observables étudiés, suivie d'une présentation de l'échantillon de données utilisé pour l'analyse et des critères de sélection des traces et des événements. La troisième section décrit la méthodologie pour déterminer la multiplicité de particules chargées, notamment l'utilisation du nombre de tracelettes comme estimateur de la multiplicité. Une simulation Monte Carlo est utilisée pour mesurer les corrélations et convertir le nombre de segments de trace en multiplicité de particules chargées. Le chapitre se termine par une explication des sources d'incertitudes systématiques évaluées pour la mesure de la multiplicité de particules chargées. Dans les trois dernières sections de ce chapitre, j'explique la procédure pour mesurer les rendements de charmonium normalisés à eux-mêmes. Cela commence par l'ajustement du spectre de masse des dimuons pour extraire les rendements bruts de J/ψ et de ψ(2S). Ensuite, j'explique la correction appliquée aux rendements bruts pour obtenir les rendements de charmonium normalisés à eux-mêmes. Les incertitudes systématiques évaluées pour les rendements de charmonium sont expliquées dans la dernière section de ce chapitre.

Dans le chapitre 4, je présente les résultats de cette thèse : les résultats dépendant de la multiplicité de ψ(2S), J/ψ et ψ(2S)-sur-J/ψ. Cela est suivi de la discussion des mesures de quarkonium et de saveurs lourdes ouvertes disponibles en fonction de la multiplicité.

Pendant le deuxième arrêt prolongé (2018-2022), ALICE a subi plusieurs mises à niveau pour se préparer à la prise de données de la Run3. Dans le chapitre 5, nous discutons brièvement des mises à niveau des sous-détecteurs d'ALICE, en mettant l'accent sur ceux utilisés pour l'analyse des quarkonia. Parmi ces mises à niveau, il y a le remplacement de l'électronique des chambres de trajectographie des muons (MCH). Cela est fait pour améliorer la robustesse du détecteur afin de faire face à la luminosité accrue attendue dans la Run3. Dans cette partie, notre principal objectif est d'évaluer l'incertitude de l'efficacité de suivi du détecteur MCH. Dans le chapitre 6, j'explique la procédure pour évaluer cette incertitude et les résultats obtenus à l'aide d'un échantillon de la prise de données de la Run 3.

General introduction

In Nature, quarks and gluons, i.e., the elementary particles of ordinary QCD matter, are always found to be confined inside hadrons. This is known as QCD confinement. However, under extreme conditions of energy density and temperature, QCD matter undergoes a phase transition to a state of freely moving quarks and gluons, known as quark-gluon plasma (QGP). Such conditions can be reproduced in the laboratory using ultra-relativistic heavyion collisions. Due to its very short lifetime, typically on the order of a few fm/c, the QGP cannot be observed directly. To probe the QGP, the study of charmonia production is an excellent tool, as the charm quarks are produced during the initial stages of the collision, before the QGP formation, and experience the entire medium evolution.

The study of charmonium production in small systems, i.e., proton-proton or proton-heavyion collisions, is essential as a reference since no QGP effects are expected in small systems.

However, several surprising QGP-like behaviors have been observed in small systems in high multiplicity events. Multiple-parton interactions is one of the main scenarios proposed to understand these findings. Studying charmonium production as a function of chargedparticle multiplicity is one way to probe multiple-parton interactions. In this thesis our goal is to study the charmonium production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8. [START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF] TeV with the ALICE experiment at the LHC. In particular, the measurements reported in this thesis on both ground and excited charmonium states bring additional information on the role of final state effects at play in p-Pb collisions, as the role of initial state effects is expected to be similar for ground and excited quarkonium states.

In chapter 1, I introduce the fundamental concepts of the quark-gluon plasma and its probes.

Then, I discuss some examples of the surprising QGP-like behaviors in small systems. I close the chapter with an overview of the quarkonium studies as a function of charged-particle multiplicity.

In chapter 2, I discuss the experimental apparatus used to collect the data set used in the analysis. I start with a brief explanation of the accelerator chain process. This is followed by the description of the ALICE detector focusing on the sub-detectors used to evaluate the charmonium yields and the charged-particle multiplicity.

In chapter 3, I provide a detailed explanation of the procedure used to evaluate the chargedparticle multiplicity and charmonium yields. In the first section, I explain the observables studied in this analysis. In the second section, I present the data sample used in this analysis, as well as the track and event selections applied to this data sample. In the third section, I explain the procedure to determine the charged-particle multiplicity. The multiplicity estimator used in the analysis is the number of tracklets (or track segments) reconstructed in the Silicon Pixel Detector. A Monte Carlo simulation is used to evaluate the correlation and convert the number of tracklets into the charged-particle multiplicity. This section ends with an explanation of the systematic uncertainties evaluated for the charged-particle multiplicity measurement. In the last three sections of this chapter, I explain the procedure to measure the self-normalized charmonium yields. This starts with fitting the invariant mass spectrum of the dimuon to extract the raw J/ψ and ψ(2S) yields. Then, I explain the corrections applied to the raw yields in order to obtain the self-normalized charmonium yields. The systematic uncertainties evaluated for the charmonium yields are explained in the last section of this chapter.

In chapter 4, I present the results of this thesis: the ψ(2S) and the J/ψ self-normalized yields, as well as the ψ(2S)-over-J/ψ ratio as a function of the self-normalized chargedparticle multiplicity. This is followed by a discussion of the available quarkonium and open heavy-flavor measurements to date.

During the second long shutdown (2018-2022), ALICE underwent several upgrades in order to prepare for the Run 3 data taking. In chapter 5, we briefly discuss the upgrades of the ALICE sub-detectors focusing on those that are used for the quarkonia analysis. Among these upgrades is the replacement of the electronics of the muon tracking chambers (MCH).

This is done to enhance the robustness of the detector to cope with the increased luminosity expected in Run 3. In this part, our main goal is to evaluate the MCH detector tracking efficiency uncertainty. In chapter 6, I explain the procedure to evaluate this uncertainty and the results obtained using a sample from Run 3 data taking.

Part I quarks. The quarks carry a non-integer electric charge. The u, c, and t quarks have a +2/3 e, while the d, s, and b quarks carry a negative electric charge of -1/3 e. The quarks also have a color charge and come in a blue, red, or green color. In ordinary matter, quarks can only be found in confined colorless states called hadrons. The leptons are also grouped into three generations: the first generation contains the electron (e) and its associated neutrino (ν e ), the second generation consists of the muon (µ) and its associated neutrino (ν µ ), while the third generation is made up of the tau (τ) and its associated neutrino (ν τ ). Figure 1.1 represents this classification of elementary particles.

Our universe is governed by four forces: the strong force, the electromagnetic force, the The standard model of elementary particles [START_REF] Commons | File:standard model of elementary particles.svg -wikimedia commons, the free media repository[END_REF].

weak force, and the gravitational force. However, the SM only describes three of them, as the gravitational force carriers are not yet included in the SM. The electromagnetic interaction is described by the theory of Quantum Electrodynamics (QED). All the electrically charged fermions can interact electromagnetically by exchanging photons (γ). The weak interaction is described by the electroweak theory, which unifies the electromagnetic and the weak interactions. Within this framework, all fermions can go through a weak interaction by exchanging W ± or Z bosons. The strong interaction is described by the Quantum Chromo-Dynamics (QCD) theory. Particles with color charges, namely quarks and gluons, can interact strongly by exchanging gluons (g). In the standard model, the mass of the elementary particles arises through their interaction with the Higgs field [START_REF] Higgs | Broken Symmetries and the Masses of Gauge Bosons[END_REF]. The Higgs boson, the quantum of the Higgs field, was discovered in 2012 at CERN by two LHC experiments, ATLAS [START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF] and CMS [START_REF] Chatrchyan | Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC[END_REF].

Quantum Chromodynamics (QCD)

Quantum Chromodynamics (QCD) is the gauge field theory that describes the strong interactions of the colored particles, i.e., quarks and gluons [START_REF] Zyla | Review of Particle Physics[END_REF]. The coupling constant of QCD α s describes the strength of interaction and depends on the momentum transferred (Q). It can be obtained at the leading order from:

α s = α s (µ 2 ) 1 + α s (µ 2 ) 33-2n f 12π ln Q 2 µ 2 , (1.1)
where µ is the scale of the renormalization, n f is the number of quark flavors. Fig. 1.2 shows the behavior of α s as a function of Q. Following the figure, as Q -→ ∞, α s decreases, which means that the quarks behave as if they are free particles. This phenomenon is known as asymptotic freedom. The strong interaction can be fully described in this energy region using perturbative QCD. On the other hand, when the value of Q decreases and becomes close to the QCD scale (Λ QC D ∼ 200 MeV), the coupling increases, which implies that the quarks are strongly bound inside hadrons, and it becomes impossible to separate them. This phenomenon is known as confinement. In this regime, the perturbative QCD is no longer applicable, and other techniques like Lattice QCD are used to solve the QCD Lagrangian.

Quantum Chromodynamics under extreme conditions:

Quark Gluon Plasma

The QCD state where quarks and gluons are freely moving is known as Quark Gluon Plasma (QGP). In Fig. 1.3, the QCD phase diagram describes the state of matter as a function of temperature (T) and baryochemical potential (µ B ), which in this context can be associated to the net baryon density. For low µ B and T values, the quarks and gluons are found only in color-neutral states, the so-called hadrons. The transition from the hadron phase to the QGP phase is of cross-over type at a T ∼ 170 MeV and low µ B [START_REF]The physics of the quark-gluon plasma[END_REF] (smooth transition where the two phases coexist). Moving to a higher µ B , the transition becomes of first-order type [START_REF] Fodor | Critical point of QCD at finite T and mu, lattice results for physical quark masses[END_REF].

Evolution of a heavy-ion collision

Experimentally, the QGP can be created in the laboratory by generating conditions of high energy density and high temperature. This is achieved through high-energy heavy-ion collisions, such as Pb-Pb collisions at the LHC or Au-Au collisions at RHIC. In the following, we describe the evolution of a heavy-ion collision [START_REF] Hands | The Phase diagram of QCD[END_REF][START_REF] Strickland | Anisotropic Hydrodynamics: Three lectures[END_REF] as schematically depicted in Fig. 1.4. The collision takes place at time τ = 0 and go through the following stages:

• 0 < τ < 0.3 fm/c: hard scattering processes, i.e., scatterings with large momentum transfer between the partons of the colliding nuclei, take place;

• 0.3 < τ < 2 fm/c: rescatterings of the partons created from the inelastic collision may lead to the thermalization of the system. The energy-density of the medium reaches up to 12-20 GeV/fm 3 (these values correspond to 0-5% Pb-Pb collisions at s NN = 2.76 TeV and the correspondent expectations for the core of the collision) [START_REF] Adam | Measurement of transverse energy at midrapidity in Pb-Pb collisions at s NN = 2.76 TeV[END_REF], which is twenty times higher than the average energy-density inside a hadron [START_REF] Busza | Heavy Ion Collisions: The Big Picture, and the Big Questions[END_REF]. This can lead to the creation of non-equilibrium QGP;

• 2 < τ < 6 fm/c: the QGP is in an equilibrium stage, in which the viscous hydrodynamics can be used to model the system. Then, the system starts to expand and cool down;

Introduction

• 6 < τ < 10 fm/c: the system reaches the critical temperature in which the hadrons start to be created. The system reaches a chemical freeze-out stage where no further inelastic collisions occur, and the total number of hadrons remains constant;

• τ > 10 fm/c: the system continues to expand and cool down until it reaches the kinetic freeze-out where no more elastic collisions occur. At this stage, the kinetic properties of the particles are fixed. After that, the particles start to fly away to be detected.

Quark gluon plasma probes

Due to its extremely short lifetime of approximately 10 fm/c at the LHC collision energies [START_REF] Aamodt | Two-pion Bose-Einstein correlations in central Pb-Pb collisions at s N N = 2.76 TeV[END_REF], direct detection of the QGP is impossible. Instead, several indirect probes are employed to investigate the properties of the QGP. These probes can be classified into two categories depending on the momentum scale involved: hard and soft probes. Hard probes refer to observables that arise from processes with high momentum transfer, occurring only during the initial stages of the collision. Examples of hard probes for the QGP include jet quenching, the production of heavy flavor particles, heavy quarkonia production, and weak boson production. On the other hand, soft probes involve processes with relatively low momentum transfer. Such observables can be generated throughout all the stages of the system evolution. Examples of soft probes include the flow of charged particles and electromagnetic probes such as photons.

QGP experimental observables

Several experimental observables confirm the discovery of QGP. A complete overview of the QGP observables can be found in the following references [START_REF] Office | New State of Matter created at CERN. Un nouvel état de la matière[END_REF][START_REF] Adcox | Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration[END_REF][START_REF] Back | The PHOBOS perspective on discoveries at RHIC[END_REF][START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF][START_REF] Arsene | Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment[END_REF][START_REF]The ALICE experiment -A journey through QCD[END_REF]. In the following discussion, we present two specific observables: the elliptic flow of charged particles and the enhancement of strange hadron production. These two were among the early indicators of the formation of the QGP.

Strangeness enhancement: the strange hadron production in AA collisions serves as an essential tool for investigating the properties of the QGP in AA collisions. Unlike the up and down quarks, strange quarks are not present as valence quarks in the colliding particles. However, due to their relatively low mass, they are abundantly produced during the collision. In the initial stages of the system evolution, the strange quarks are produced from the hard partonic scattering processes via flavor creation, i.e., gg → ss and qq → ss, and flavor excitation gs → gs and qs → qs. In addition, strange quarks can be produced

Quantum Chromodynamics under extreme conditions: Quark Gluon Plasma

during the subsequent partonic evolution via gluon splitting g → ss. In the later stages of the system evolution, the soft QCD processes dominate the strangeness production. In a QGP environment, strange quarks are expected to restore their bare mass m q ∼ 0 due to the chiral symmetry restoration. Consequently, strange hadron production becomes easier in a QGP (vs. vacuum), and is expected to be enhanced in AA collisions due to the presence of the QGP. Experimentally, the enhancement of strangeness production in AA collisions has been observed by several experiments and at different collision energies [START_REF] Antinori | Strangeness enhancements at central rapidity in 40 A GeV/c Pb-Pb collisions[END_REF][START_REF] Alt | Energy dependence of Lambda and Xi production in central Pb+Pb collisions at A-20, A-30, A-40, A-80, and A-158 GeV measured at the CERN Super Proton Synchrotron[END_REF][START_REF] Abelev | Enhanced strange baryon production in Au + Au collisions compared to p + p at s(NN)**(1/2) = 200-GeV[END_REF][START_REF] Abelev | Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at s N N = 2.76 TeV[END_REF]. These studies have found that the ratio of strange hadrons to those composed of lighter hadrons (consisting of up and down quarks) is significantly higher in AA collisions compared to pp collisions.

Elliptic flow of charged particles: it refers to the preferential alignment of emitted particles in the reaction plane during non-central heavy-ion collisions. Fig. 1.5 presents a conceptual drawing for a heavy-ion collision describing the origin of elliptic flow. This phenomenon is a consequence of the initial spatial anisotropy, as the overlap region of colliding nuclei has an almond shape due to the geometric configuration of the collision. When the energy density is large enough (e.g. QGP), particles created in the overlap region reinteract. This implies that a strong pressure gradient will be generated on the particle located along the short axis,

x-axis in Fig. 1.5, and a weaker pressure gradient on the particles located along the long-axis, y-axis in Fig. 1.5. This angular anisotropy of pressure will generate angular anisotropy of momentum, leading to asymmetries in the final state particle distributions [START_REF] Pasechnik | Phenomenological Review on Quark-Gluon Plasma: Concepts vs. Observations[END_REF]. The angular distribution of the final state particles can be written as:

d N d φ ∝ 1 + 2 ∞ n=1 ν n cos n φ -ψ n (1.2)
where φ is the azimuthal angle, ψ n is the reaction plane angle, n is the order of harmonic, and ν is the flow coefficient. The ν 2 is the second order coefficient, named elliptic flow, that points to the anisotropic geometry of the collision. Non-zero ν 2 coefficient probes the spatial anisotropy of the final state particles.

Unexpected observations in small systems

As discussed in Sec.1.2.1, the production of strange hadrons is enhanced in AA collisions as a signature of the formation of the QGP. This is also true for the elliptic flow of charged particles, which points to the collective behavior of the particles formed in a deconfined state.

Surprisingly, these and other behaviors have been observed in small systems, i.e., pp and pA collisions, particularly in high multiplicity events. In such systems, the energy-density and the temperature are not supposed to be large enough to create a QGP.

Strangeness enhancement in small systems: as discussed in Sec.1.2.1, the production of strange hadrons in AA collisions is enhanced relative to pp collisions. This effect was further investigated as a function of charged-particle multiplicity in smaller systems. and square shapes, respectively [START_REF] Adam | Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions[END_REF][START_REF] Abelev | Multiplicity Dependence of Pion, Kaon, Proton and Lambda Production in p-Pb Collisions at s N N = 5.02 TeV[END_REF][START_REF] Abelev | Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at s N N = 2.76 TeV[END_REF]. The plot shows the ratios of the yields of four strange hadrons (K 0 s , Λ, Ξ, Ω) to the pion one as a function of charged-particle multiplicity measured at midrapidity. A clear smooth transition from pp to p-Pb, and to Pb-Pb collisions is observed for all the ratios. In addition, the ratios at high multiplicity events in pp collisions reach values comparable to those measured at low multiplicity of Pb-Pb collisions. The comparison to the calculations from MC models is also presented in the figure [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF][START_REF] Pierog | EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider[END_REF][START_REF] Bierlich | Effects of color reconnection on hadron flavor observables[END_REF]. PYTHIA 8.2 and EPOS LHC event generator calculations describe the production of K 0 s , while they underestimate the results of the other particles.

Elliptic flow of charged particles in small systems: since it is hard to define the reaction plane in small systems, the two-particle angular correlation is the technique used to study the collective behavior of pp and pA collisions. The two-particle ∆Φ-∆η correlation of charged particles in pp and pA collisions is dominated by the near-side jet peak structure at (∆Φ, ∆η ) = (0,0), and by the away-side structure along the ∆η-axis at ∆Φ = π. The distribution of the two-particle angular correlation of charged particles as a function of ∆Φ and ∆η [START_REF] Adam | Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions[END_REF][START_REF] Abelev | Multiplicity Dependence of Pion, Kaon, Proton and Lambda Production in p-Pb Collisions at s N N = 5.02 TeV[END_REF][START_REF] Abelev | Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at s N N = 2.76 TeV[END_REF]. The results are compared to the calculations from PYTHIA8, DIPSY, and EPOS LHC [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF][START_REF] Pierog | EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider[END_REF][START_REF] Bierlich | Effects of color reconnection on hadron flavor observables[END_REF].

Unexpected observations in small systems

|< 0.5 η | 〉 η /d ch N d 〈

Introduction

is presented in Fig. 1.7. The analysis is performed by CMS collaboration in p-Pb collisions at s NN = 5.02 TeV [START_REF] Chatrchyan | Observation of Long-Range Near-Side Angular Correlations in Proton-Lead Collisions at the LHC[END_REF]. In the left panel of Fig. 1.7, corresponding to the low multiplicity events (less than 35 tracks/event), both the near-side and the away-side structures are observed. However, the right panel, representing the high multiplicity of events (more than 110 tracks/event), reveals an additional long-range near-side structure in the two-particle correlation distribution. Such structure was expected to be only observed in AA collisions as it is interpreted as a signature of QGP creation. The origin of this behavior in small systems is yet to be fully understood. similar measurements for the two-particle angular correlation performed at the LHC for pp and p-Pb collisions can be found in the following references [START_REF] Abelev | Long-range angular correlations on the near and away side in p-Pb collisions at s N N = 5.02 TeV[END_REF][START_REF] Khachatryan | Observation of Long-Range Near-Side Angular Correlations in Proton-Proton Collisions at the LHC[END_REF][START_REF] Aaij | Measurements of long-range near-side angular correlations in s NN = 5TeV proton-lead collisions in the forward region[END_REF]. How to explain QGP-like behaviors in small systems: the origin of the QGP-like behaviors observed in small systems remains unclear. Such observables are typically interpreted as QGP signatures in AA collisions. Several interpretations have been proposed to understand these findings, such as the formation of QGP droplets or the influence of Multi-Parton Interactions (MPI). The QGP droplets refer to events with local high-density regions created in the high multiplicity events of pp or pA collisions. On the other hand, MPI are defined as several parton-parton interactions that take place in a single hadron-hadron collision. Due

Charmonium production in small systems

to the composite nature of hadrons, it is possible to have multiple parton hard scatterings in a single pp collision at the LHC.

Charmonium production in small systems

Quarkonia are bound states of heavy quark and anti-quark pairs (Q Q). Mesons made up of charm and anti-charm quarks are called charmonia (cc), while those made up of bottom and anti-bottom quarks are called bottomonia (b b). Quarkonia are excellent tools to study the QGP. Due to their heavy masses, they are produced in the initial stages of the collision, during the hard processes, and experience the full evolution of the created medium. In addition, their production is sensitive to both soft and hard QCD scales. In this thesis, we study J/ψ and ψ(2S) production, which are the first and the second excited states of spin-1 charmonia, respectively.

Charmonia production mechanisms in pp collisions

Color Evaporation Model (CEM): CEM assumes that a heavy quark pair will hadronize into a quarkonium state if its invariant mass is below a threshold required to create the lightest open-heavy flavor pair. The model assumes that the color state of the pair at its hadronization is independent of that at its production. The production cross-section is expressed as:

σ C E M ψ = F ψ 2M D 2M c d σ c c d m c c d m c c , (1.3)
where F ψ is a phenomenological factor related to probability of the heavy quark pair hadronizing into a quarkonium state. One of the main limitations of this model is that it cannot describe the polarization observables for the charmonia production and some discrepancies in the transverse momentum spectra [START_REF] Lansberg | New Observables in Inclusive Production of Quarkonia[END_REF].

Color Singlet Model (CSM):

CSM is based on the factorization approach to describe charmonium production [START_REF] Lansberg | New Observables in Inclusive Production of Quarkonia[END_REF]. The model separates the cross-section into perturbative parts related to the production of the heavy quark pair, and non-perturbative parts associated to the hadronization of the charmonium state. Hadronization is then described by a quarkonium wave function that is process and flavor independent. The cross-section is written as follows:

d σ C SM ψ+X = i , j d x i d x j f i (x i , µ F ) f j (x j , µ F ) × d σi+j→(Q Q)+X (µ R , µ F ) × 〈|ψ(0)| 2 〉 (1.4)
where f i (x i , µ F ) and f j (x j , µ F ) are the parton densities of the colliding hadrons, and d σi+j→(Q Q)+X is equivalent to the partonic cross section of a pair of heavy quarks with zero heavy-quark relative velocity (ν = 0). |ψ(0)| 2 is the universal wave function. Unlike the CEM, CSM assumes that the final charmonium state is produced with the same quantum numbers as the heavy quark pair.

Color Octet Mechanism (COM) and Non-Relativistic QCD (NRQCD): COM+NRQCD includes aspects of both CEM and CSM [START_REF] Bodwin | Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production[END_REF]. This model is based on the factorization approach to describe the cross-section of the charmonium production as in the CSM. In addition, COM+NRQCD assumes that the quantum numbers (n) change between the production of the heavy quark pair and the hadronization process. In this model, the hadronization is described by the universal Long-Distance Matrix Elements (LDME) O n Q . The cross-section is written as follows:

d σ N RQC D ψ+X = i , j d x i d x j f i (x i , µ F ) f j (x j , µ F ) × d σi+j→(Q Q) n +X (µ R , µ F , µ Λ ) × 〈O n Q 〉 (1.5)
The LDMEs can be obtained by fitting experimental distributions, e.g., p T spectra at different energies. The model allows the transition from color octet states to final physical mesons.

Cold nuclear matter effects

From a theoretical point of view, charmonium production in pA collisions is expected to be affected by several nuclear effects, the so-called Cold Nuclear Matter (CNM) effects.

Gluon (anti)shadowing: the parton distribution function represents the probability of finding a parton that carries a fraction x of the nucleon momentum at an energy scale Q 2 . It is known that the parton distribution functions are modified in the nucleus compared to the proton. Early deep inelastic experiments revealed such an effect, suggesting that the measured nuclear effects are due to the modification of the parton distribution functions.

The nuclear Parton Distribution Functions (nPDF) have a dependence on both x and Q 2 .

The modification of PDFs for a parton type i in a nucleus A can be expressed via the factor 20

Charmonium production in small systems

R A i as:

R A i (x,Q 2 ) = f A i (x,Q 2 ) f i (x,Q 2 ) , (1.6)
where f A i ( f i ) is the parton distribution function of a parton type i in the nucleus (proton). Fig. 1.8 presents the R A i factor as a function of x in the EPPS16 parametrization. The plot shows four distinct regions as a function of x:

• Shadowing which corresponds to the region x ≲ 10 -2 . This effect is described as a depletion in the nucleus compared to the proton. Shadowing can be explained by the recombination of low-x gluons in nuclei due to the high phase-space density, reducing the effective probability to find low-x gluons, and increasing the probability to find higher-x gluons (low-x gluons recombine into a higher-x one).

• Anti-shadowing points to the enhancement observed in the region 10 -2 ≲ x ≲ 10 -1 . This enhancement is interpreted as a result of the increase of the gluon density due to the recombination of lower x gluons.

• European Muon Collaboration (EMC) effect, which dominates the region 10

-1 ≲ x < 1.
The origin of this effect is still unclear [START_REF] Aubert | The ratio of the nucleon structure functions F 2 n for iron and deuterium[END_REF].

• Fermi motion, corresponds to an excess observed in the region of x → 1. This effect is due to the non-stationary nucleons in the nucleus.

It is worth noting that the values of the transition points between the different regions are only rough estimates.

Gluon saturation: at low-x values, the gluon PDF shows an increase of the gluon density.

The larger the energy, the larger the density is. When the gluon occupation reaches a maximum of ∼ 1/α s , the density becomes very large, leading to a saturation of the partonic distribution [START_REF] Iancu | The Color glass condensate and high-energy scattering in QCD[END_REF][START_REF] Ma | Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions[END_REF]. The framework where the saturation approach is employed is called Color Glass Condensate (CGC).

Fully coherent energy loss: the model assumes that the heavy quark pair is produced in a color octet state and remains in a color octet for much longer than the hard process time.

During this time, and at any x F (where x F is defined as the longitudinal fraction momentum between the J/ψ and the projectile proton in pA collisions), the gluon radiation from the quarks is assumed to be soft. At sufficiently high energy, the quarkonium hard production process looks like a small angle scattering of color charges [START_REF] Arleo | J/ψ suppression in p-A collisions from parton energy loss in cold QCD matter[END_REF]. As discussed in Ref. [START_REF] Arleo | Heavy-quarkonium suppression in p-A collisions from parton energy loss in cold QCD matter[END_REF],

EPPS16

x

R A i (x, Q 2 0 )
Figure 1.8: The x-dependence of the factor R in the EPPS16 parameterization [START_REF] Eskola | EPPS16: Nuclear parton distributions with LHC data[END_REF].

quarkonia are expected to be suppressed at large x F , or large rapidity, due to gluon radiation and the associated energy loss.

Comover: the comover framework considers the possibility for quarkonia to dissociate due to the interaction with the produced soft particles (the comovers) that travel along with the heavy-quark pair. In this model, the dissociation is stronger for quarkonium states with a larger size due to their weaker binding. Additionally, suppression is stronger where the comover density is larger. It is important to note that, besides the comover interaction, the model includes the shadowing effect in the calculation to describe the nuclear modification of the parton distribution functions in the nucleus [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF].

Nuclear absorption: when a cc passes through a nuclear medium, it may undergo breakup of the heavy-quark pair due to the interaction with the primordial nucleus, the so-called nuclear absorption. This approach suggests that the time spent by the cc to pass through the nucleus is larger than charmonium formation time. As ψ(2S) meson has a larger formation time than the J/ψ, it will be more suppressed due to the stronger break-up effect [START_REF] Lourenco | Energy dependence of J/psi absorption in proton-nucleus collisions[END_REF]. This effect is negligible at the LHC energies, as the charmonium formation time is expected to be larger than the nuclei crossing time.

Experimental results of charmonium production in pA collisions

In this section, we present selected experimental results on J/ψ and ψ(2S) production in p-Pb collisions performed by ALICE. We focus on the nuclear modification factor measurements (R pPb ) in p-Pb collisions. The nuclear modification factor is an observable used to quantify the nuclear effects by evaluating the ratio of the production of a particle in pA collisions relative to its production in pp collisions properly normalized. R pA can be evaluated as:

R pP b (y cms , p T ) = d 2 σ J/ψ pP b /d y cms d p T A P b • d 2 σ J/ψ pp /d y cms d p T (1.7)
where the p-Pb production cross section is divided by the corresponding quantity for pp collisions, normalized by times the atomic mass number of the Pb nucleus (A Pb = 208).

Figure 1.9 presents the R pA for the J/ψ yields measured in p-Pb collisions at s NN = 8.16 TeV [START_REF] Acharya | Inclusive J/ψ production at forward and backward rapidity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The R pA in the backward rapidity region, -4.46 < y cms < -2.96, is compatible with unity (y = 1) within uncertainties. At forward rapidity, 2.03 < y cms < 3.53, the R pA varies from 0.8 to 0.6, showing a clear suppression of J/ψ production in p-Pb collisions with respect to pp collisions. ALICE results are compatible, within uncertainties, with a similar measurement performed by the LHCb collaboration (depicted in blue in the same figure) [START_REF] Aaij | Prompt and nonprompt J/ψ production and nuclear modification in pPb collisions at s NN = 8.16 TeV[END_REF]. Theoretical models based on shadowing fairly describe the results when nCTEQ15 [START_REF] Kovarik | nCTEQ15 -Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework[END_REF] or EPPS16 [START_REF] Eskola | EPPS16: Nuclear parton distributions with LHC data[END_REF] parametrization sets of nPDFs are adopted. EPS09NLO nPDF parametrization, which is also based on shadowing, shows a slightly worse agreement with the data at forward rapidity [START_REF] Eskola | Nuclear PDFs at NLO -status report and review of the EPS09 results[END_REF]. Moreover, models which include Color Glass Condensate (CGC) approach show a good agreement in their domain of validity [START_REF] Ma | ψ(2S) versus J /ψ suppression in proton-nucleus collisions from factorization violating soft color exchanges[END_REF][START_REF] Ducloué | Forward J /ψ production at high energy: centrality dependence and mean transverse momentum[END_REF]. The parton coherent energy loss model describes quantitatively the results at both rapidity regions [START_REF] Arleo | Quarkonium suppression in heavy-ion collisions from coherent energy loss in cold nuclear matter[END_REF]. Finally, the calculations of the transport and the comover model, which include contributions from the interaction of the final state heavy-quark pair with the parton/hadron system, describe the results as well in the probed region [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Chen | Cold and Hot Nuclear Matter Effects on Charmonium Production in p+Pb Collisions at LHC Energy[END_REF].

In Fig. 1.10, the J/ψ and ψ(2S) nuclear modification factor in p-Pb collisions at s NN = 8.16 TeV are compared. Both particles are reconstructed from their decay channel into dimuon in the muon spectrometer. A stronger suppression is observed for the ψ(2S) yields relative to the J/ψ in the backward rapidity region. At forward rapidity, both particles exhibit a similar suppression. The results are compared to the theoretical calculations from CGC+ICEM [START_REF] Ducloué | Forward J /ψ production at high energy: centrality dependence and mean transverse momentum[END_REF] and comover models [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF]. The CGC+ICEM model describes fairly the observed suppression for both particles. Note that the CGC+ICEM calculations are only available at forward rapidity, corresponding to the low Bjorken-x values in the Pb nucleus. The comover model Figure 1.9: Comparison of the ALICE and LHCb [START_REF] Acharya | Inclusive J/ψ production at forward and backward rapidity in p-Pb collisions at s NN = 8.16 TeV[END_REF][START_REF] Aaij | Prompt and nonprompt J/ψ production and nuclear modification in pPb collisions at s NN = 8.16 TeV[END_REF] results on the y cms -dependence of the J/ψ nuclear modification factor in p-Pb collisions at s NN = 8.16 TeV. The horizontal bars correspond to the bin size. For ALICE, the vertical error bars represent the statistical uncertainties, the boxes around the points the uncorrelated systematic uncertainties, and the filled box around unity the correlated uncertainties. For LHCb, the vertical error bars represent the combination of statistical and systematic uncertainties. The results are also compared to several model calculations [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Lansberg | Towards an automated tool to evaluate the impact of the nuclear modification of the gluon density on quarkonium, D and B meson production in proton-nucleus collisions[END_REF][START_REF] Albacete | Predictions for Cold Nuclear Matter Effects in p+Pb Collisions at s N N = 8.16 TeV[END_REF][START_REF] Ma | ψ(2S) versus J /ψ suppression in proton-nucleus collisions from factorization violating soft color exchanges[END_REF][START_REF] Ducloué | Forward J /ψ production at high energy: centrality dependence and mean transverse momentum[END_REF][START_REF] Arleo | Quarkonium suppression in heavy-ion collisions from coherent energy loss in cold nuclear matter[END_REF][START_REF] Chen | Cold and Hot Nuclear Matter Effects on Charmonium Production in p+Pb Collisions at LHC Energy[END_REF].

1.5 Quarkonium studies as a function of charged-particle multiplicity predicts a stronger suppression for the states with a larger size, i.e., a weaker binding. In the case of charmonia, it suggests a stronger suppression of ψ(2S) relative to the J/ψ. Comover model calculations describe fairly the results of both J/ψ and ψ(2S) at forward and backward rapidity.

ALI-PUB-483666

Figure 1.10: The nuclear modification factor of the ψ(2S) and J/ψ production in p-Pb collisions at forward and backward rapidity regions [START_REF] Acharya | Measurement of nuclear effects on ψ(2S) production in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The results are compared to the theoretical calculations from CGC+ICEM and comover models [START_REF] Ma | ψ(2S) versus J /ψ suppression in proton-nucleus collisions from factorization violating soft color exchanges[END_REF][START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF] In conclusion, the results of the nuclear modification factor of charmonium production in pA collisions were discussed. The observed behavior of R pA is reproduced by several models considering different CNM effects. However, none of these models is favored by the data.

More differential analyses are needed to understand which of the CNM effects plays a major role in charmonium production.

Quarkonium studies as a function of charged-particle multiplicity

The scrutiny of quarkonium yields as a function of the impact parameter of the collision, or the collision centrality, is a common and long standing practice in heavy-ion physics. The extension of these studies to small systems, i.e. pp and p-A, is limited due to the difficulty to determine the collision centrality in such cases, where the unknowns on the shape and fluctuations of the initial geometry of the collision are important. The study of particle yields as a function of charged-particle multiplicity have emerged as an alternative to cope with such difficulties and to allow us to compare the results in all collision systems (from the small to the large ones). This section summarises the quarkonium studies as a function of charged-particle multiplicity at the LHC.

Figure 1.11 presents the results of the inclusive production of J/ψ yields as a function of charged-particle multiplicity, both measured at midrapidity (|y| < 0.9), in pp collisions at s = 13 TeV [START_REF] Acharya | Multiplicity dependence of J/ψ production at midrapidity in pp collisions at s = 13 TeV[END_REF]. In this study, the J/ψ yields and the charged-particle multiplicity are normalized to their average values obtained from the integrated multiplicity interval. The yields show a faster than a linear increase with increasing charged-particle multiplicity. This result is compared to several models attributing the observed behavior to different initial and/or final state effects. In particular, the trend of the data is described quantitatively by the coherent particle production model (CPP) [START_REF] Kopeliovich | J/ψ in high-multiplicity pp collisions: Lessons from pA collisions[END_REF], the color glass condensate model (CGC) [START_REF] Ma | Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions[END_REF], and the 3-Pomeron CGC model [START_REF] Levin | Multiplicity dependence of quarkonia production in the CGC approach[END_REF]. The percolation model describes the data trend up to at least four-to-five times the average multiplicity [START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF], while EPOS3 [START_REF] Drescher | Parton based Gribov-Regge theory[END_REF] and PYTHIA 8.2 [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF] event generators describe a faster than linear increase but not as strong as observed in the data. Figure 1.11: J/ψ self-normalized yields as a function of charged-particle multiplicity in pp collisions at s = 13 TeV, both measured at midrapidity [START_REF] Acharya | Multiplicity dependence of J/ψ production at midrapidity in pp collisions at s = 13 TeV[END_REF]. The results are compared with several theoretical models.

Quarkonium studies as a function of charged-particle multiplicity

The comparison between forward and midrapidity J/ψ yields as a function of midrapidity charged-particle multiplicity in pp collisions at s = 13 TeV is reported in Ref. [START_REF] Acharya | Forward rapidity J/ψ production as a function of charged-particle multiplicity in pp collisions at s = 5.02 and 13 TeV[END_REF] (see also Fig. 4.8 in Sec. 4.2). The J/ψ self-normalized yields at forward rapidity also increase with charged-particle multiplicity, the increase is compatible with a linear trend within uncertainties. This increase is less rapid than that of the J/ψ measurement at midrapidity shown in Fig. 1.11. The trend at forward rapidity is also described qualitatively by the theoretical computations of CPP, 3-pomeron CGC, percolation, and CGC+ICEM models, as well as EPOS3 and PYTHIA 8.2 event generators. One observes that most of model calculations expect such variation when studying J/ψ yields in different rapidity intervals.

The CMS collaboration has investigated the multiplicity dependence of the production of a heavier quarkonium state, namely bottomonia, in pp and p-Pb collisions at different collision energies [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF][START_REF] Sirunyan | Investigation into the event-activity dependence of Υ(nS) relative production in proton-proton collisions at s = 7 TeV[END_REF]. Figure 1.12 presents the ratio of the excited to the ground state The ratios of the Υ(2S)-over-Υ(1S) and Υ(3S)-over-Υ(1S), with p T > 0 GeV, as a function of the number of tracks (N track ) in various collision systems. The lines are fits to the data with an exponential function. The vertical error bars represent the combined statistical and systematic uncertainties on the bottomonia ratio, while the horizontal error bars represent the uncertainty on N track [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF][START_REF] Sirunyan | Investigation into the event-activity dependence of Υ(nS) relative production in proton-proton collisions at s = 7 TeV[END_REF]. bottomonium yields as a function of the number of tracks (N track ). The Υ(2S)-over-Υ(1S) ratio shows a decrease as we move from the lowest to the highest multiplicity interval. A similar trend is observed for the results in pp collisions at s = 7 TeV and s = 2.76 TeV, as well as Introduction for p-Pb results at s NN = 5.02 TeV. The same behavior is observed for the Υ(3S)-over-Υ(1S) as a function of N tracks . It is worth mentioning that the CMS measurement cannot be directly compared to the charmonium measurements carried out by the ALICE collaboration, as the multiplicity estimator is different in the two measurements. Additionally, in the CMS results, the bottomonium yields and the number of tracks are not normalized to their average value, as is done in charmonia results from the ALICE collaboration. Despite the caveats, the ALICE and CMS results are consistent within the limited measurement precision.

Several nuclear effects may affect the production of hadrons in pA collisions compared to pp collisions, as discussed in Sec. 1.4.2. To understand the influence of the nuclear environment on quarkonium production, ALICE measured the J/ψ normalized yields as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The J/ψ yields show an increasing trend with increasing multiplicity at both forward and backward rapidity as presented in Fig. 1.13. For the yields reconstructed at backward rapidity, this increase is faster than a linear with increasing multiplicity. While the yields reconstructed at forward rapidity exhibit a slower than a linear increase with increasing multiplicity. In this study, the measurement is sensitive to multiple parton interactions and multiple nucleon-nucleon interactions, in addition to the cold nuclear matter effects which are expected to play a role in p-Pb collisions due to the presence of the heavy nuclei. The results are described by EPOS3 [START_REF] Drescher | Parton based Gribov-Regge theory[END_REF] calculation. However, it remains unclear which is the dominant effect at the origin of the differences observed when studying quarkonium production at various rapidity intervals.

Motivation of this thesis

This thesis focuses on the production of the excited charmonium state ψ(2S) as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV. The ψ(2S) production yields are studied and compared to those of the ground state J/ψ. As mentioned in Sec. 1.5, these studies represent an alternative to look at particle production as a function of the collision impact parameter or the collision centrality, and to compare the results in all collision systems (from pp up to A-A collisions). The results are sensitive to multiple parton interactions, multiple nucleon interactions, and the influence of cold nuclear matter effects.

In particular, the measurements reported in this thesis bring additional information on the role of final state effects at play in p-Pb collisions, as the role of initial state effects is expected to be similar for ground and excited quarkonium states. Therefore, in the ratio of the excited-to-ground state quarkonium yields initial state effects are expected to cancel. 1.13: Self-normalised J/ψ yields as a function of midrapidity charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The results at forward (backward) rapidity are represented by blue (red) points in the figure. The vertical lines represent statistical uncertainties, while the boxes depict the systematic uncertainties. The dashed line represents the one-to-one correlation to guide the eye.

Motivation of this thesis

0 2 4 6 |<1 η | NSD  〉 η / d ch N d 〈 η / d ch N
The experimental setup is introduced in chapter 2, the analysis details are described in chapter 3, whereas the results are presented and discussed in chapter 4.

Part II ALICE Run 2 2 A Large Ion Collider Experiment (ALICE)

In this chapter, we present an overview of the ALICE experiment at the LHC. In Sec.2.1, we introduce the Large Hadron Collider (LHC) and discuss the particle acceleration process. In Sec.2.2, we present the sub-detectors used to perform the analysis.

The Large Hadron Collider

The Large Hadron Collider (LHC) is the largest and the most powerful particle collider ever built [START_REF] Bruning | LHC Design Report Vol.1: The LHC Main Ring[END_REF]. The LHC is operated by the European Council for Nuclear Research (CERN) 1 , and is located at the Swiss-French border. The LHC accelerates hadrons, such as protons and lead ions, to nearly the speed of light, making them collide at a center-of-mass energy of up to s = 13 TeV in pp collisions. The full acceleration process involves a series of interconnected linear and circular accelerators. Each accelerator boosts the particles up to the highest energy they should achieve before injecting them into the next accelerator in the sequence. The CERN accelerator complex is schematically depicted in Fig. 2.1, which includes the LINAC3 and the LINAC4 as sources of the beams, as well as the Booster and the Proton Synchrotron (PS). The LINAC4 accelerates negative hydrogen ions up to 160 MeV, and prepares them to be injected into the PS Booster. Before being injected into the PS Booster, the ions are stripped of their two electrons. The PS Booster, which consists of four superimposed synchrotron rings, accelerates the protons up to 2 GeV and injects them into the PS, where they receive further acceleration to reach energies of up to 26 GeV. Protons are then injected into the Super Proton Synchrotron (SPS), where they are accelerated up to 450 GeV, and transferred to the two beam pipes of the LHC. In the case of lead ions, the acceleration process starts at the LINAC3. The LINAC3 uses radiofrequency cavities to charge cylindrical conductors where the lead ions pass. As the ions move through these conductors, which are alternately charged with positive and negative charges, they are accelerated. The resulting accelerated ions are then injected into the Low Energy Ion Ring (LEIR), where they are gathered into dense bunches and further accelerated for injection into the PS. The PS accelerates both the protons injected from the PS Booster or lead ions injected from the LEIR. The ions are then injected into the SPS, which operates up to 450 GeV. The SPS accelerates the bunches and injects them as trains of bunches into the LHC ring. In the LHC ring, the beams travel in opposite directions in two separated beam pipes and are made to collide at four interaction points around the LHC ring. These four points correspond to the location of the four main experiments at the LHC: ALICE, ATLAS, LHCb, and CMS. A Large Ion Collider Experiment (ALICE) [START_REF] Aamodt | The ALICE experiment at the CERN LHC[END_REF][START_REF] Abelev | Performance of the ALICE Experiment at the CERN LHC[END_REF] is a heavy-ion dedicated experiment at the LHC. It is designed to study the physics of strongly interacting matter at extreme energy densities. ALICE is described in detail in Sec.2.2. A Toroidal LHC Apparatus (ATLAS) [START_REF] Aad | The ATLAS Experiment at the CERN Large Hadron Collider[END_REF] and the Compact Muon Spectrometer (CMS) [START_REF] Chatrchyan | The CMS Experiment at the CERN LHC[END_REF] are multipurpose detectors that scrutinize the largest range of physics possible at the LHC. The Large Hadron Collider beauty experiment (LHCb) [START_REF] Alves | The LHCb Detector at the LHC[END_REF] studies the difference between matter and anti-matter by studying b-quark physics.

ALICE experiment

ALICE consists of 19 sub-detectors, which allow for studying a broad range of observables.

These sub-detectors can be classified into three main categories. First, the forward detectors measure general quantities such as particle multiplicity, luminosity, and collision's central-

Central detectors Inner Tracking System (ITS)

The ITS consists of six cylindrical layers of silicon detectors [START_REF] Dellacasa | ALICE technical design report of the inner tracking system (ITS)[END_REF]. The layers are located at radii ranges between 4 and 43 cm, covering a pseudorapidity range of |η|< 0.9. To achieve the required resolution and cope with the high particle density expected in heavy-ion collisions, different technologies are used to design the different ITS layers. Specifically, the two innermost layers use silicon pixel detectors (SPD), the following two layers use silicon drift detectors (SDD), and the outer two layers are equipped with double-sided microstrip detectors (SSD) as they face a low particle density. The SDD and SSD layers are equipped with analog readout so that they can be used to measure the energy loss for low-p T reconstructed particles. The inner tracking system contributes to the majority of the physics topics addressed by the ALICE experiment as discussed in the physics performance report [START_REF] Fabjan | ALICE: Physics Performance Report[END_REF].

The main tasks of the ITS are to reconstruct the primary vertex with a resolution of at least 100 µm, to localize the secondary vertices for the decay of D and B hadrons, to track charged particles with p T < 200 MeV/c, and to improve the momentum and resolution of particles reconstructed by the Time Projection Chamber. In this thesis, we are exploiting the SPD detector to reconstruct the primary vertex and measure the charged-particle multiplicity.

Time Projection Chamber (TPC)

The TPC is a large cylindrical field cage with an inner radius of 85 cm and an outer radius of 250 cm [START_REF] Dellacasa | ALICE: Technical design report of the time projection chamber[END_REF]. The detector has an active volume of 90 m 3 filled with Ne/CO 2 /N 2 . The volume of the TPC is separated by an electrode in the middle. The TPC is the main tracking system of the central barrel. It is used for particle identification and to track and measure charged-particle momentum.

Forward detectors Zero Degree Calorimeter (ZDC)

The ZDC consists of two sets of hadronic calorimeters, ZP and ZN, optimized to measure the spectator protons and neutrons, respectively [START_REF] Dellacasa | ALICE technical design report of the zero degree calorimeter (ZDC)[END_REF]. The spectator protons are separated from the interaction beam by means of the dipole magnet, while the spectator neutrons are moving at zero degrees. Therefore, the ZN is located at zero degrees with respect to the beam pipe, and the ZP is located externally to the outgoing beam pipe on the side where positive protons are deflected. The hadronic calorimeters are quartz-fiber calorimeters with silica optical fibers as active material embedded in a dense absorber and located along the beam pipe at a z = ±116 m from the interaction point. The hadronic calorimeters are completed by two Zero Electromagnetic calorimeters (ZEM) located at z = ±7 m. The ZP and ZN measure the energy deposited by the spectator neutrons and protons, which provide information about the collision geometry. The smaller number of spectators, the more central the collision is. On the other hand, the ZEM mainly measures the energy deposit of photons emitted at forward rapidity. In this thesis, the information from the ZDC is used to reject background events from beam-gas interactions.

V0 detector

The V0 detector comprises two arrays of plastic scintillators, V0-A, and V0-C, placed at either side of the interaction point at z = 329 cm and -86 cm, respectively [START_REF] Cortese | ALICE technical design report on forward detectors: FMD, T0 and V0[END_REF]. Each V0 ring is segmented into four rings in the radial direction, and each ring is divided into eight sections in the azimuthal direction. The V0 detectors cover the pseudorapidity regions of 2.8 < η < 5.1 and -3.7 < η < -1.7. The V0 has different functionalities. It serves as a minimum bias trigger.

In addition, the V0 detector serves as centrality estimator by measuring the multiplicity of the particles, as well as to measure the charged-particle multiplicity, to determine the collision event plane, and to reject background events from beam-gas interactions. In the analysis of this thesis, the V0 detector serves as a MB trigger and to reject beam-gas events.

Muon Spectrometer

The Muon Spectrometer is designed to reconstruct quarkonia, i.e., J/ψ, ψ(2S) and Υ(nS), as well as φ, and heavy-flavor decays, in their decay channel into dimuon with the highest possible accuracy and down to zero p T [START_REF] Dellacasa | ALICE technical design report of the dimuon forward spectrometer[END_REF]. The spectrometer triggers and reconstructs the trajectory of muons in the pseudorapidity window -4 < η < -2.5. Fig. 2.3 presents the main parts of the spectrometer. It consists of the following sub-detectors: a front absorber needed to reduce the flux of hadrons and photons at large rapidity, ten planes of muon tracking chambers, a muon filter required to reduce the fake muon tracks, followed by four planes of trigger chambers. In this thesis, the information from the Muon Spectrometer is exploited to reconstruct the charmonium yields.

Absorbers

The front passive absorber is the closest part of the muon spectrometer to the interaction point and is located inside the solenoid magnet. The absorber is made of carbon and concrete, which helps to limit multiple scattering and energy loss experienced by traversing muons. Moreover, the absorber protects the other ALICE detectors from the secondary interactions that occur within the absorbing material. The spectrometer is shielded throughout its length by an inner beam shield, which is made of tungsten, lead, and stainless steel. This shield is required to minimize the background from primary particles produced in the collisions and their decay products produced in the beam pipe and the shield itself. In order to have additional protection for the trigger chambers, a 1.2 m iron wall, the muon filter, is placed in front of the first station of the trigger chambers. The front absorber and the filter wall combined stop muons with total momentum of less than 4 GeV/c.

Tracking system

The muon tracking (MCH) system is located after the front absorber. It comprises five stations, with two detection planes each, consisting of 4. The MWPCs operate on the principle of gas ionization and electron amplification. The detector comprises a set of parallel and equally spaced anode wires placed between two cathode planes. The anode wires have a high voltage ∼ 1650 V, while the cathode planes are connected to the ground. This develops an electric field with the maximum being at the wire surface. The volume between the two cathodes is filled with Ar+CO 2 gas. Fig. 2.5 presents a schematic cross-section of the MWPC structure. When a charged particle crosses the detector, it ionizes the gas. The electric field drifts the freed electrons toward the anode wires, generating a cascade of secondary electrons. This induces a charge distribution on the cathode pads near the avalanche. These inputs can also be combined logically to compose like-sign or unlike-sign dimuon triggers, which are of prime importance in the following analysis.

Multiplicity determination and charmonium production analysis

In this chapter, we present the step-by-step procedure to extract and evaluate the selfnormalized charmonium yields as a function of the self-normalized charged-particle multiplicity. In Sec.3.1, we define the observables studied in this chapter. In Sec.3.2, we present the analyzed data sample and the event and track selections. In Sec.3.3, we discuss the methodology used to evaluate the charged-particle multiplicity and its associated uncertainty. In Sec.3.4, we explain the fit procedure followed to extract the raw charmonium yields and relative yields, as well as the ratio of the excited-to-ground state yields ratio. In Sec.3.5, we discuss the corrections applied to the raw yields to obtain the self-normalized charmonium yields. Finally, in Sec.3.6, we report the different sources of systematic uncertainties on the self-normalized charmonium yields.

Observable definition

The analysis is performed in the non-single diffractive event class (NSD). The non-single diffractive class is defined as the sum of non-diffractive, diffractive, and double diffractive events in the collision. In a single-diffractive collision, only one of the beam particles breaks up and produces particles at large rapidity on one side of the detector. Two observables are discussed in this chapter to obtain the final physics results. The first one is the self-normalized charged-particle multiplicity. In this analysis, the number of tracklets, or track segments (N tr ), reconstructed by joining pairs of hits in the SPD layers in the rapidity range |y l ab | < 1, serves as charged-particle multiplicity estimator. We assume that the number of tracklets is proportional to the number of charged particles (dN ch /dη) as follows:

d N ch d η ∝ N tr ∆η , (3.1)
we obtain the proportionality factor from Monte Carlo (MC) simulations. Then, the selfnormalized charged-particle multiplicity can be calculated as follows:

d N ch /d η < d N ch /d η > i ∝ 1 ∆η < N i tr > < d N ch /d η > , ( 3.2)
where < d N ch /d η > is the average number of the charged particles in the NSD event class, and the superscript i denotes the charged-particle multiplicity interval.

The second observable discussed in this chapter is the self-normalized charmonium yields.

The yields of the charmonium ground state (J/ψ) and its radial excited state (ψ(2S)) are extracted from the fit to the dimuon invariant mass spectrum. The measurement is performed for both the integrated sample, and for multiple intervals of charged-particle multiplicity. The raw yields are then corrected to obtain the self-normalized charmonium yields as follows: dN /dy 〈dN /dy〉

i = N i N N eq MB N i ,eq MB (Aϵ) (Aϵ) i ϵ i MB ϵ MB , (3.3)
where N is the raw yield of the charmonia (either J/ψ or ψ(2S)), N eq MB is the number of equivalent minimum bias (MB) events corresponding to the analyzed data sample, Aϵ is the detector acceptance times efficiency, and ϵ MB is the efficiency of the minimum bias trigger to select the event class of the analyzed data sample. Whenever the quantity is marked with the index i , it refers to the value in each charged-particle multiplicity interval i ; otherwise, it refers to the multiplicity integrated quantity.

Data sample and event and track selection

The analysis of the multiplicity dependence of charmonium production is performed in p-Pb collisions, at center-of-mass energy per nucleon pair of s NN = 8.16 TeV. Data was collected during November and December 2016 by the ALICE experiment at the CERN LHC.

The asymmetry of the p-Pb collisions leads to a shift in the center-of-mass rapidity (y cms )

Data sample and event and track selection

with respect to the laboratory frame (y lab ). This shift (∆y) depends on the charges (Z 1 , Z 2 ) and the atomic numbers (A 1 , A 2 ) of the colliding particles, and can be computed as follows:

∆y = 1 2 ln Z 1 A 2 Z 2 A 1 , (3.4)
which results in ∆y = ±0.465 for p-Pb collisions. Two beam configurations are defined due to the rapidity shift for p-Pb collisions:

• the forward rapidity region refers to the scenario in which the proton beam is directed from the interaction point (IP) towards the muon spectrometer. In this configuration, the center-of-mass rapidity range covered by the muon spectrometer is 2.03 < y cms < 3.53.

• the backward rapidity region refers to the situation in which the lead beam is directed from the IP towards the muon spectrometer. In this configuration, the center-of-mass rapidity range covered by the muon spectrometer is -4.46 < y cms < -2.96.

A scheme of the two configurations for p-Pb collisions is depicted in Fig. Two data sets are used in this analysis, one per collision configuration, to extract the charmonium raw yields. The data collected from the forward and the backward configurations were named in the ALICE internal scheme as LHC16r and LHC16s, respectively. Each data sample is subdivided in different runs, corresponding to a limited period of time. The full list of the run numbers analyzed for each data set can be found in Appendix A.

Event selection

The charmonium yields are measured using the dimuon triggered data sample, while the charged-particle multiplicity is evaluated using the MB triggered data sample. The following trigger classes are utilized to perform the measurement:

• CINT7-B-NOPF-MUFAST (CINT7-MUFAST) is a MB trigger that requires a signal coincidence in the V0A and V0C detectors. We use this trigger class to evaluate the charged-particle multiplicity.

• CINT7-B-NOPF-CENT (CINT7-CENT) is also a MB trigger that requires a signal coincidence in the V0A and V0C detectors. This trigger class is used to evaluate the normalization factor correction for the charmonium yield measurement. The ALICE physics offline selection removes background contamination from beam-gas or beam-collider interaction events. Additionally, this selection allows the application of a set of predefined cuts that removes the pile-up events from the data sample. However, the pile-up rejection criteria are customized for MB events rather than the dimuon-triggered events. Since the muon tracks reconstructed in the muon spectrometer originate from the initial hard scattering events, these events usually produce more charged particles than the MB events. As a result, the rejection criteria may remove many good events in the dimuon-triggered sample. Consequently, the offline physics selections are modified to avoid removing good high multiplicity events in the p-Pb multiplicity-dependent analysis.

SPD pile-up selection criteria

The ALICE pile-up selection algorithm is based on identifying the main vertex in the SPD detector for a single event and then looping over all the other vertices corresponding to the same event. The algorithm criteria defines a threshold distance between the two vertices (d ),

and a minimum number of contributing tracklets per vertex (N contributors ) to find the vertices.

In the default case, if two vertices are found within a distance d > 0.8 cm and have at least

N contributors > 3
, the event is identified as a pile-up event and rejected from the analysis. In the p-Pb multiplicity dependent analysis, the rejection depends on the number of tracklets produced in the event. For the events with fewer tracklets than 50, the events with two vertices found within a distance d > 0.6 cm and N contributors > 3 are rejected. For the events with a number of tracklets larger than 50, the rejection is done if two vertices are found within a distance d > 0.8 cm and N contributors > 5.

Correlation between the number of clusters and number of tracklets

A customized cut is applied to the correlation between the number of clusters (N cl ) and the number of tracklets (N tr ), as discussed in Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF]. The cut is defined as in the following: if (N tr < 165):

N cl = 65 + 5.5 • N tr -0.009 • N 2 tr ,
and if (N tr > 165):

N cl = 65 + 4 • N 2 tr .

Muon track selection

The following cuts are applied to the muon tracks to remove fake tracks. For the single muon track selections:

• The geometrical acceptance: the muon spectrometer acceptance is -4 < η lab < -2.5.

Any muon track reconstructed outside of this interval is rejected.

• MID-MCH matched tracks: the muon track candidate is considered a true track if the tracks reconstructed in the muon chambers matched a track segment in the trigger chambers.

• Polar angle of the muon tracks: this cut considers the polar angle of the muon track at the end of the front absorber (θ abs ). This requires that θ abs must fall in the range 2 • < θ abs < 10 • . This cut ensures the selected muon track did not experience significant multiple scattering, by rejecting the tracks that traverse the front absorber through the high Z -material part.

• The track total momentum and distance of closest approach (pDCA): the DCA is defined as the distance between the primary vertex and the straight line extrapolation of the track exiting the front absorber. The product of the track momentum (p) and its DCA (pDCA) must be within 6σ, which helps to reject the beam-induced interaction and particles produced in the front absorber.

In the case of the dimuon selections, the criteria also requires that the muon pair is within the acceptance of the muon spectrometer, i.e., 2.5 < y lab < 4.

Multiplicity determination

Multiplicity estimator

We use the number of tracklets (N tr ), as multiplicity estimator for the charged-particle multiplicity (dN ch dη ). The tracklets are formed by combining hits in both SPD layers that point towards a primary vertex. The SPD detector also determines the position of the primary vertex. average number of tracklets per event to remain constant regardless of where in the detector the collision occurs. The observed z-dependence of the < N tr > is due to inefficiencies of the SPD. For the p-Pb multiplicity dependent analysis, the method mentioned in Refs. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF][START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF] is used to equalize the average number of the 〈N tr 〉, and evaluate the average number of corrected tracklets < N corr >. For each event, the number of missing or excessive tracklets ∆N with respect to a reference value (N tr (v 0 z )) is evaluated as:

∆N = N tr (v z ) N tr (v 0 z ) -N tr (v z ) < N tr (v z ) > (3.5)
Then, the number of raw tracklets N tr per event is randomized by Poisson smearing the excess ∆N to obtain the number of corrected tracklets; i.e. N cor r

N corr = N tr ± gRandom → Poisson(∆N ) . (3.6)
This correction corresponds to a data-driven event-by-event procedure to take into account the detector inefficiencies. Figure 3.3 presents the resultant values of the average number corrected tracklets per event, represented with red markers. The corrected distribution is independent of the z-vertex location of the interaction, as expected.

From corrected tracklets to charged-particle multiplicity

To obtain the number of charged particles (N ch ) from the number of corrected tracklets (N corr ), one needs to evaluate the correlation factor between the two quantities. DPMJET event generator [START_REF] Roesler | The Monte Carlo event generator DPMJET-III[END_REF] is used to evaluate the correlation distribution as it cannot be obtained from the data. In this analysis, two methods are used to extract and cross-check the N ch value corresponding to a given N corr interval:

1. Fit the 2D N corr -N ch distribution over the integrated interval, and in bins of N corr .

Then, N ch is computed for each N corr bin as follows:

< N ch > i = f (< N corr >),
where (i ) is the N corr bin and f is the fitting function. The uncertainty of each value is taken from the uncertainty of the fit. For each bin of N corr , a linear fit to the 2D N corr -N ch distribution is used to extract the correlation factor and evaluate the corresponding N ch . In the case of the integrated 2D

N corr -N ch distribution, the following fit functions are used:

1. Linear fit to the 2D distribution, fixing the origin of the function at zero

f (N corr ; α) = α(N corr ) ,
where N ch is evaluated as:

N ch = f (N corr ; α) → Eval N corr .
× α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0]
× α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] pol2 corr N × α ) ∈ + corr (N α pol3 pol4 bin[0]*x[0] (b) Backward rapidity
f (N corr ; α, ϵ) = α(N corr + ϵ) , N ch = f (N corr ; α, ϵ) → Eval N corr .

A second-order polynomial fit function with free fitting parameters

N ch = pol2 → Eval N corr .
4. A third-order polynomial fit function with free fitting parameters

N ch = pol3 → Eval N corr .

A fourth-order polynomial fit function with free fitting parameters

N ch = pol4 → Eval N corr .
The fit functions are shown in Fig. 3.4. The fits to the distribution are similar at the intermediate N corr range and start to diverge at large N corr . To assess the possible dispersion of these fits, N ch is evaluated in each N corr bin for each fit function. Then, the results are compared to the corresponding value extracted from the fit of the projection on the N ch axis. Fig. 3.5

shows the result of the N ch values obtained from the different fit functions in each N corr bin for both forward and backward rapidity regions. Figure 3.6 presents the ratio of the N ch extracted from the different fits to the value extracted from the projection on the N ch axis for each N corr bin. In this result, we conclude that the N ch values evaluated from the linear bin-by-bin fit and the second-order polynomial are the closest to the ones extracted from the projections onto the N ch axis. In the J/ψ multiplicity-dependent analysis, which was performed using the same data set, the second-order polynomial was used to evaluate the N ch , as the bin-by-bin linear fit was not stable due to the low statistics in the MC for the highest multiplicity intervals [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. To be consistent with the J/ψ analysis, the second-order polynomial fit is also used to compute the charged-particle multiplicity in this analysis. The uncertainty of this measurement is obtained by comparing the values extracted from the second-order polynomial and the maximum spread of the values extracted from the other fit functions, as depicted in Fig. 3

Systematic uncertainties on the multiplicity measurements

In this section, we discuss the sources of systematic uncertainties considered for the chargedparticle multiplicity measurements.

Charged-particle multiplicity evaluation

Several fit functions were used to evaluate the correlation factor between N corr and N ch from MC. Either from fits over the full range of N corr , or from the distributions obtained in bins of N corr . In summary, the systematic uncertainty is extracted from the maximum spread of the N ch using all the fit functions with respect to the values extracted from the second-order polynomial (the central value). More details in Sec. 3.3.3.

MC input

This uncertainty is assessed using two different MC event generators to extract the correlation factor between the number of corrected tracklets and the charged-particle multiplicity.

In Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF], EPOS and DPMJET event generators were used to extract the correlations and evaluate the N ch values. The uncertainty was determined by comparing the result evaluated from each generator for each data set. The uncertainty from this source amounts to 2% in both rapidity regions.

z-vertex equalization

This is due to the non-flat distribution of the average number of reconstructed tracklets as a function of the z-coordinate of the primary vertex. As explained in Sec. 3.3.1, an eventby-event correction is applied to the number of tracklets to correct for this effect. The uncertainty on the correction procedure is determined by comparing the results varying the reference value (from the maximum to the minimum of the average number of tracklets), as well as varying the randomization procedure (using a binomial distribution instead of a poissonian one). Details can be found in Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF]. The systematic uncertainty due to the z-vertex equalization amounts to 3%.

Total systematic uncertainty

The uncertainty sources on the charged-particle multiplicity are presented in Tab. Values marked with an asterisk are correlated in multiplicity.

Self-normalized charged particle multiplicity

The final values obtained for the charged-particle multiplicity and its corresponding selfnormalized charged-particle multiplicity are summarized in Tab.

Charmonium signal extraction

The charmonium yields are extracted exploiting the low-p T dimuon triggered data sample (CMUL7) 1 . For each selected pair of opposite-charge muon tracks (the selection criteria are discussed in Sec.3.2.2), the dimuon invariant mass (M µµ ) is computed as follows:

M µµ = 2m 2 µ + 2E µ 1 E µ 2 (1 -cos θ 12 ), (3.7)
where m µ is the mass of the muon, E µ is the energy of the muon, and θ 12 is the angle between the two muon tracks. The number of J/ψ and ψ(2S) particles are evaluated by fitting the invariant mass distribution in the mass range of the J/ψ and ψ(2S). The following sections describe the fit procedure to extract charmonium raw and relative yields, as well as their corresponding uncertainties.

Fit procedure

The charmonium signal is fitted using either a double crystal ball (CB2) or a pseudo-Gaussian function with power-law tails (as implemented first by the NA60 Collaboration) [START_REF]Quarkonium signal extraction in ALICE[END_REF]. Both particle data group (PDG) [START_REF] Zyla | Review of Particle Physics[END_REF], such as:

m ψ(2S) = m J/ψ + (m P DG ψ(2S) -m P DG J/ψ ) . (3.8)
The width correlation between the two particles is evaluated from MC simulations by PYTHIA for pp collisions at s = 13 TeV, which amounts to 5%. This ratio could also be calculated by exploiting the large data set from pp collisions at a s = 13 TeV. The high statistics of this data sample allowed for the J/ψ and ψ(2S) widths to be left as free parameters during the fit process. This results in a ratio of 1.01 ± 0.05 [START_REF] Acharya | Energy dependence of forward-rapidity J/ψ and ψ(2S) production in pp collisions at the LHC[END_REF]. To account for the possible variation in the width of the ψ(2S) peak, both ratios, 1.05 and 1.01, are used to evaluate the ψ(2S) raw yields and the corresponding systematic uncertainty.

The background shape is delineated using two functions: a sum of two exponential functions (SumExp) or a fourth-order polynomial convoluted with an exponential function (expo*pol4). Finally, two mass ranges are used in the fit to extract charmonium raw yields: signal shapes as red and yellow shaded areas, respectively. The background is depicted with a grey dashed line. Finally, the total mass fit is displayed as a continuous blue line.

The raw yields extracted as a function of fit configuration are presented in Fig. 3.10 and Fig. 3.11, for the J/ψ and ψ(2S), respectively. The most significant influence on yield extraction originates from the sets of tail parameters used in the fit (be it data or MC). As we do not use the same number of tails from data and MC, to account for this influence, the yields obtained from each fit configuration are weighted when averaging over all configurations to obtain the resultant yield and its corresponding uncertainty. The weighting is done to backward rapidity, integrated in multiplicity [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. Superimposed is a typical fit function, shown as a solid blue line (see text for details). The J/ψ and ψ(2S) contributions are shown as red and yellow shaded areas, respectively. The background is depicted as a dashed grey line. The inset shows the region of the ψ(2S) mass. balance the number of tests using tails from data and MC. The yields and the statistical uncertainties are evaluated from the weighted average. The systematic uncertainty is obtained using the root-mean-square (RMS) of the values.

)1.00_1.7_4.8 )1.00_1.7_4.8

ψ ( σ CB_expo*pol4_pp13_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pp13_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pp13_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pp13_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pp13_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pp13_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pp13_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pp13_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_pPbJC_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pPbJC_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pPbJC_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pPbJC_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pPbJC_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pPbJC_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pPbJC_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pPbJC_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_pPbRA_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pPbRA_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pPbRA_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pPbRA_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pPbRA_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pPbRA_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pPbRA_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pPbRA_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_MCpp13_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_MCpp13_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_MCpp13_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_MCpp13_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_MCpp13_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_MCpp13_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_MCpp13_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_MCpp13_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_MCpPbJC_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_MCpPbJC_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_MCpPbJC_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_MCpPbJC_ )1.00_1.7_4.8 ψ ( σ NA60_expo*pol4_MCpPb_ )1.00_2.0_5.0 ψ ( σ NA60_expo*pol4_MCpPb_ )1.05_1.7_4.8 ψ ( σ NA60_expo*pol4_MCpPb_ )1.05_2.0_5.0 ψ ( σ NA60_expo*pol4_MCpPb_ )1.00_1.7_4.8 ψ ( σ NA60_SumEx_MCpPb_ )1.00_2.0_5.0 ψ ( σ NA60_SumEx_MCpPb_ )1.05_1.7_4.8 ψ ( σ
ψ ( σ CB_expo*pol4_pp13_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pp13_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pp13_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pp13_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pp13_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pp13_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pp13_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pp13_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_pPbJC_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pPbJC_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pPbJC_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pPbJC_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pPbJC_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pPbJC_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pPbJC_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pPbJC_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_pPbRA_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_pPbRA_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_pPbRA_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_pPbRA_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_pPbRA_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_pPbRA_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_pPbRA_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_pPbRA_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_MCpp13_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_MCpp13_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_MCpp13_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_MCpp13_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_MCpp13_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_MCpp13_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_MCpp13_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_MCpp13_ )1.00_1.7_4.8 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.00_2.0_5.0 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.05_1.7_4.8 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.05_2.0_5.0 ψ ( σ CB_expo*pol4_MCpPbJC_ )1.00_1.7_4.8 ψ ( σ CB_SumEx_MCpPbJC_ )1.00_2.0_5.0 ψ ( σ CB_SumEx_MCpPbJC_ )1.05_1.7_4.8 ψ ( σ CB_SumEx_MCpPbJC_ )1.05_2.0_5.0 ψ ( σ CB_SumEx_MCpPbJC_ )1.00_1.7_4.8 ψ ( σ NA60_expo*pol4_MCpPb_ )1.00_2.0_5.0 ψ ( σ NA60_expo*pol4_MCpPb_ )1.05_1.7_4.8 ψ ( σ NA60_expo*pol4_MCpPb_ )1.05_2.0_5.0 ψ ( σ NA60_expo*pol4_MCpPb_ )1.00_1.7_4.8 ψ ( σ NA60_SumEx_MCpPb_ )1.00_2.0_5.0 ψ ( σ NA60_SumEx_MCpPb_ )1.05_1.7_4.8 ψ ( σ

Raw yield extraction

Integrated multiplicity, p T and y raw charmonium yields

This section presents the results of J/ψ and ψ(2S) raw yields integrated in multiplicity, p T , and y. The raw yields as a function of fit configuration are shown in Fig. 3.10 and Fig. 3.11 for J/ψ and ψ(2S), respectively. The plots show the raw yields extracted for the forward rapidity data set in the top panels, and the backward rapidity data set in the bottom panels. The yields are grouped by the tail parameters used in the fit (notice the vertical dashed lines in the figures). The horizontal red dashed line presents the weighted average over all the fit trials, whereas the dotted line presents the standard deviation, which is used to evaluate the systematic uncertainty. The J/ψ and ψ(2S) raw yield results are summarized in table 3.5.

N J/ψ

N ψ(2S) Forward 133720 ± 626 (stat.) ± 4868 (syst.) 2301 ± 212 (stat.) ± 272 (syst.) Backward 194020 ± 759 (stat.) ± 7087 (syst.) 2721 ± 247 (stat.) ± 347 (syst.) Table 3.5: J/ψ and ψ(2S) raw yields integrated over multiplicity, p T and y for both forward and backward rapidity.

Multiplicity differential raw yield extraction

The charmonium raw yields are also extracted in multiplicity intervals, where the binning was determined by the available statistics and the stability of the fits. The choice of the multiplicity intervals is driven by the statistics of the ψ(2S) yields. The results of the raw yields extracted for each fit configuration, and for each multiplicity interval can be found in App.C and App.D, for J/ψ and ψ(2S), respectively. Tab. 3.6 and Tab. 3.7 summarize the results obtained for J/ψ and ψ(2S) raw yields for the forward and backward rapidity regions. The bottom row of each table shows the difference between the yields extracted in the integrated multiplicity interval and the total summation of the yields extracted in the multiplicity intervals. The difference is found to be negligible in both rapidity regions (with respect to the statistical uncertainty).

Relative raw yield evaluation

The relative raw yield in a multiplicity interval i , is defined as the ratio of the raw yield extracted in the multiplicity interval (i ) to the raw yield extracted in the integrated multiplicity

N i R = N i raw N tot . (3.9)
The relative raw yield is computed by assuming that the signal part (the signal shape function, the tail parameters, and the width) is correlated in the numerator and the denominator of equation 3.9. On the other hand, the combinatorial background component is assumed to be uncorrelated as a function of multiplicity, which was verified by comparing the invariant mass distributions in different multiplicity intervals, i.e., different background shapes are observed at low multiplicity compared to high multiplicity interval. Having all the different combinations of the fitting model in the integrated and differential multiplicity, we obtained 192 variations to evaluate the charmonium relative raw yields, with 162 variations for CB2 and 32 for NA60 signal shapes. The mean over all these combinations gives the central value for each multiplicity interval, and its corresponding statistical uncertainty is evaluated as the mean over all the statistical uncertainties of the combinations. The systematic uncertainty is evaluated as the standard deviation. The relative raw yields in the differential multiplicity intervals and their corresponding uncertainties are summarized in Tab. 3.8 and Tab. 3.9, for J/ψ and ψ(2S), respectively. While the J/ψ statistical uncertainties are of the order of 1%, the uncertainty of the ψ(2S) yields ranges between 20%-30%, apart from the last interval at backward rapidity where the uncertainty increases to 38%.

ψ(2S)-over-J/ψ relative ratio

We are also interested in studying the difference in the behavior of the J/ψ and ψ(2S) as a function of charged-particle multiplicity. To do so, one needs to evaluate the ψ(2S)over -J/ψ relative ratio. The ratio is computed considering the correlation on the signal part of the fit function, as described in the previous section for the relative yield. The values extracted for each multiplicity interval are summarized in Tab.3.10 for both the forward and backward rapidity regions.

Charmonium yield corrections

The charmonium corrected yields are computed as expressed in Eq. 3.3 (see Sec. 3.1).

Forward rapidity

Backward rapidity 3.10: Relative ψ(2S)-over-J/ψ yield ratio per multiplicity interval at forward and backward rapidity.

N cor r N R J/ψ ± stat ± syst N cor r N R J/ψ ± stat

Normalization factor

The data sample used to extract charmonium yields includes only MB events with two opposite charge muons, i.e., CMUL7 events. We correct the number of CMUL7 events in each multiplicity interval i , N i CMUL7 , by a normalization factor to evaluate the equivalent number of MB events where no specific selections are applied. The equivalent number of MB events N eq MB , which corresponds to the number of dimuon analyzed events N CMUL7 , is obtained as:

N eq,i MB = F i norm × N i CMUL7 , (3.10)
where:

• N eq,i MB is the number of MB events in the multiplicity interval i .

• F i norm is the normalization factor in the multiplicity interval i .

• N i CMUL7 is the number of CMUL7 events in the multiplicity interval i .

To obtain the F i norm , two different "offline" methods are used in this analysis. Both methods compare the physics-selected MB event sample to those containing dimuon trigger (MUL) input. The first offline method can be obtained as in the following equation:

F off1,i norm = N i MB N i MB&0MUL , (3.11)
in which the normalization factor is evaluated directly from the ratio of the MB events to a sub-sample of the MB events, which requires an opposite-charge dimuon trigger (0MUL) to be fired. This method suffers from the low statistics in the MB&0MUL events sample.

To improve the statistical precision of the method, an indirect normalization approach is followed:

F off2,i norm = N i MB N i MB&0MSL × N i CMSL7 N i CMSL7&0MUL , (3.12)
where the MSL trigger is used as an intermediate trigger to evaluate the normalization factor.

The MSL trigger requires at least one single muon to be detected in coincidence with a MB trigger. This trigger has higher statistics than the 0MUL trigger.

The normalization factor as a function of the run number evaluated by the indirect method is presented in Fig. 3.12 for the forward and backward rapidity regions. The central F norm value is evaluated as the weighted average over all the run numbers in a data-taking period, for the forward and backward rapidity data set, as in the following equation:

F norm = n i =1 F i norm × N i CMUL7 n i =1 N CMUL7 , (3.13)
where n is the number of runs analyzed. In Fig. 3.12, we observe that the F norm values at forward rapidity are about twice those at backward rapidity. This is due to the fact that the muon spectrometer in the backward rapidity region measures the muons in the Pb fragmentation side, which increases the probability of detecting a muon or a dimuon in a MB event.

The values of the normalization factor over integrated multiplicity as well as in multiplicity intervals are reported in Tab.3.11 and Tab.3.12 for the forward and backward rapidity region data sets, respectively. In this analysis, we consider the F off2 norm for the charmonium corrected yields determination. As a consequence, the procedure has been repeated for the integrated-multiplicity sample, to benefit from the higher statistics in the integrated case.

Forward rapidity region

The results of the multiplicity integrated exercise, performed in fine p T and y intervals, showed no influence on the simulated distributions, as expected for measurements in fine bins. The iterative procedure was also done using the same number of p T and y bins that can be used in the multiplicity intervals measurement to observe possible discrepancies.

Five bins of p T and four bins of y were considered to extract and correct J/ψ raw yields.

The considered variation of the simulated distributions per iteration in the multiplicityintegrated exercise is shown in Fig. 3.15. The influence of these variations on the p T and y averaged efficiency is presented in Fig. 3

Trigger efficiency evaluation

The multiplicity measurement is performed in the non-single diffractive (NSD) event class.

The measurement needs to be corrected by the efficiency of the MB trigger to select NSD events with a reconstructed SPD vertex that passes the QA criteria.

Trigger efficiency evaluation in the integrated multiplicity interval

The trigger efficiency evaluation for the integrated multiplicity interval was carried out in an independent analysis [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF]. The trigger efficiency was assessed from two MC samples, using one run for each of the forward and backward data sets of p-Pb collisions. One of the MC samples was generated with the HIJING event generator, and the other one with the DPMJET event generator. The ESD1 data was used to perform the estimation. HIJING 1.36 [START_REF] Wang | hijing: A monte carlo model for multiple jet production in pp, pA, and AA collisions[END_REF] is based on combining the perturbative QCD process with the soft interactions. DPMJET [START_REF] Roesler | The Monte Carlo event generator DPMJET-III[END_REF] is based on the Gribov-Glauber approach and treats both soft and hard scatterings similarly.

The particles generated with the previous event generators are then transported through the detector using GEANT 3 software package [START_REF] Acharya | Charged-particle pseudorapidity density at mid-rapidity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The trigger efficiency for the NSD events with vertex reconstructed that passed the selections is ϵ MB = 97.4 ± 1% [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF].

In this analysis, we adopt the same procedure to evaluate the trigger efficiency in multiplicity intervals as in Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF]. The trigger efficiency in the integrated multiplicity interval was evaluated using the ESD data, while we are using AOD2 data for the data analysis. To understand the potential impact of evaluating the efficiency using AOD instead of ESD on the result, we compute the trigger efficiency in the integrated multiplicity interval for one run from AOD data, and compare it to the corresponding value estimated using ESD data.

The MB trigger efficiency to select the NSD events is defined as:

ϵ M B = 1 + f N SD noV t x -f d at a noV t x /ρ MC , (3.14)
where,

• f N SD noV t x is the fraction of NSD-generated events in which no vertex is reconstructed or selected.

• f d at a noV t x is the fraction of reconstructed events in data with no vertex selected.

• ρ MC is the MC efficiency for events with no vertex.

The value of f N SD noV t x is evaluated as:

f N SD noV t x = N MC N SD -N MC sel ect edV t x N MC M B , ( 3.15)
where N MC N SD is the number of NSD generated events, N MC sel ect edV t x is the number of reconstructed events with selected vertex, and N MC M B is the number of generated MC events that pass the MB trigger. To compute ρ MC , one needs to define the fraction of reconstructed events in MC with no selected vertex, which can be evaluated as:

f M B -MC noV t x = N MC M B -N MC sel ect edV t x N MC M B , ( 3.16)
where N MC sel ect edV t x is the number of reconstructed MC events with selected vertex. Then, ρ MC can be evaluated as

ρ MC = f M B -MC noV t x f N SD noV t x . ( 3.17)
Finally, we obtain

f d at a noV t x = N d at a M B -N d at a sel ect edV t x N d at a M B , (3.18)
where N d at a M B is the number of reconstructed MB events, N d at a sel ect edV t x is the number of reconstructed MB events with selected vertex.

Using AOD sample for run 266318: f N SD noV t x = 0.0125 and f M B -MC noV t x = 0.0042. Using Eq.3.17, ρ MC = 33.88%. From data, N d at a M B = 0.0177. The ϵ M B estimated from our DPMJET AODs was ϵ M B = 0.9779, which is consistent with the value evaluated in Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF].

Trigger efficiency evaluation in multiplicity intervals

We used the equations in the previous section to evaluate the MB trigger efficiency to select NSD events per multiplicity interval in each period. First, the trigger efficiency is evaluated for each run number and for each multiplicity interval. Then the central value is computed as the weighted average over all the run numbers. We used the number of CINT7 events in each run as a weight. The values obtained for the integrated multiplicity interval and multiplicity intervals for each period are reported in Tab.3.14. A decrease of the trigger efficiency is found for the two lowest multiplicity intervals. This points to the fact that the vertex finding algorithm encounters difficulties in finding track candidates to reconstruct the vertex at low multiplicity.

Sources of systematic uncertainties

Several sources of systematic uncertainties contribute to charmonium yield extraction.

These are: (i) signal extraction, (ii) normalization factor, (iii) the effect of the resolution and pile-up on the multiplicity classification, (iv) vertex equalization, (v) the acceptance times efficiency correction and (vi) the MB trigger efficiency. The following sections discuss these sources of systematic uncertainties.

Signal extraction

The uncertainty on the signal extraction was discussed in Sec.3.4.2. To summarize, several signal and background configuration combinations are used to extract the charmonium yields in two mass fit ranges. The largest impact on the number of candidates originates from the different tail parametrizations used (data vs. MC). The average yield and the uncertainties extracted over all the trials are weighted to balance the number of tests using tails from MC and data. In the integrated multiplicity, the uncertainty amounts to about 3.6% (3.7%) and 12.0% (12.8%) in the forward (backward) rapidity range for the raw yields of J/ψ and ψ(2S), respectively. In multiplicity intervals, the systematic uncertainty ranges between (3.5 -3.9)% and (9.6 -16.0)% for the raw yields of J/ψ and ψ(2S), respectively.

In the case of the relative raw yields, we assumed that the uncertainty is partially correlated with multiplicity. The systematic uncertainty ranges between (0.6-1.4)% and (3.8-12.8)% for the relative yields of J/ψ and ψ(2S), respectively. In the case of the ψ(2S)-over-J/ψ relative

Sources of systematic uncertainties

yields, we found that the systematic uncertainty varies between (3.8-11.8)%.

Normalization factor

Two methods are used to compute the normalization factor from which the systematic uncertainty is estimated. We studied the bin-by-bin spread of the normalization factor evaluated from each method. In both periods, all the values are found to be within 2.5% of the central values. We assign the 2.5% as the systematic uncertainty from the normalization factor for the relative J/ψ and ψ(2S) relative yield measurement. In the case of ψ(2S)-over-J/ψ, the uncertainty resulting from the normalization factor cancels out.

The multiplicity axis resolution and pile-up

Similar to the J/ψ analysis [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF], the uncertainty on the multiplicity axis resolution and the pile-up is evaluated as a single contribution. Two effects are considered to evaluate the uncertainty due to the multiplicity resolution: the bin flow due to randomization seed and the bin flow due to edge effect. The uncertainty coming from pile-up and multiplicity resolution is estimated by extracting the charmonium yields with a different randomization seed for the event-by-event correction, or introducing a small shift to the N corr intervals (bin offset = ±0.1), or by changing the pile-up rejection criteria. The maximum spread of the yields extracted from these variations from the central values in both forward and backward rapidity regions is within 2%, which is assigned as a systematic uncertainty. The major contribution to this uncertainty comes from the pile-up rejection criteria, meaning the same influence is expected for J/ψ and ψ(2S). The limited statistics of the ψ(2S) analysis do not allow for a more precise determination of this uncertainty. Therefore, a 2% uncertainty is also assigned to the raw yields of ψ(2S). In the case of the relative yields, the systematic uncertainty is considered to be negligible.

Vertex equalization

The uncertainty from vertex equalization is estimated by comparing the values of the charmonium yields extracted when considering a variation on the equalization procedure to correct the data. In particular, in one case the Poissonian vertex equalization with respect to the maximum of N tr (v z ) was used, while in the other the binomial vertex equalization with respect to the minimum of the N tr (v z ) was considered. The systematic uncertainty from the vertex equalization is taken from Ref. [START_REF] Crkovská | Study of the J/ψ production in pp collisions at s = 5.02 TeV and of the J/ ψ production multiplicity dependence in p-Pb collisions at s N N = 8.16 TeV with ALICE at the LHC[END_REF] and amounts to 2%.

Acceptance times efficiency

We described the A × ε measurement in Sec.3.5.2. In summary, the iterative procedure is performed considering a realistic p T and y distribution for J/ψ, resulting in a small increase of the average value by a similar amount in all measurement multiplicity intervals. Table 3.13 summarizes the iterative procedure results for J/ψ. The values of the A × ϵ for the last iteration step fluctuate by at most 1% (4%) in the measurement multiplicity intervals for the forward (backward) rapidity range. The results presented in this thesis have been published in Ref. [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. The results are reported for the charmonium yields extracted at forward (2.03 < y cms ≤ 3.53) and backward (-4.46 < y cms < -2.96) rapidity. The statistical and systematic uncertainties are depicted with vertical lines and boxes, respectively. In both rapidity regions, the measurement shows an increase of the self-normalized yields with increasing multiplicity, compatible with a linear (y = x) increase depicted with a dashed line in the plot.

Summary of systematic uncertainties

0 1 2 3 4 5 |<1 η | NSD  〉 η / d ch N d 〈 η / d ch N d 0 2 4 6 8 NSD  〉 y / d (2S) Ψ N d 〈 y / d (2S) Ψ N d = 8.
In Fig. 4.2, the ψ(2S) self-normalized yields are compared to the theoretical calculation from the percolation + comover + EPS09 model [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF][START_REF] Eskola | EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions[END_REF][START_REF] Paukkunen | Nuclear PDFs Today[END_REF]. The percolation model is based on parton saturation or string interactions. The main assumption of this model is that in high-energy heavy ion collisions, a high-density partonic medium is formed with characteristic properties such as shear viscosity and high opacity. Each parton-parton collision contains the formation of the fundamental source of particle production, called flux tubes (strings), as considered by the model. In this framework, the number of partonparton interactions is reflected by the number of produced strings. These strings have a certain transverse size and different space-time rapidity, and they can interact (overlap) with each other reducing their total effective number. In the case of quarkonium production, particularly of charmonia, the number of initially produced charmonia is proportional to the number of collisions in analogy to any hard process; in this model, it is then proportional to the number of produced strings. On the other hand, the charged-particle multiplicity distribution, mainly soft particles, is proportional to the number of participant strings [START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF]. In the theoretical calculation presented in Fig. 4.2, the percolation model is coupled to the calculation from the comover model and the parameterization from EPS09 nuclear parton distribution functions. The comover model describes the dissociation of charmonia due to their interaction with the produced soft particles that travel along with them. There are two common features of the comover model. First, the comover dissociation affects the ψ(2S) more than the J/ψ, due to the larger size of the first, i.e., a weaker binding between the two quarks of the charmonia state. Second, the comover suppression is stronger when the comover densities are larger [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF], i.e., at larger multiplicity. EPS09 is a parameterization at LO and NLO, of the nuclear parton distribution functions (nPDF). EPS09 uses the data from deep-inelastic lepton-nucleus scattering measurements, the Drell-Yan dilepton production data from fixed target proton-nucleus collisions, and the neutral-pion production data measured in d+A and pp collisions at RHIC. The uncertainty of the model originates from the uncertainty on data and is evaluated using the Hessian method [START_REF] Eskola | EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions[END_REF][START_REF] Paukkunen | Nuclear PDFs Today[END_REF]. As shown in

J/ψ results

The self-normalized yields of J/ψ as a function of the self-normalized charged-particle multiplicity have been measured by ALICE in p-Pb collisions at s NN = 8.16 TeV [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. The J/ψ yields are measured at forward (2.03 < y cms < 3.53) and backward (-4.46 < y cms < -2.96) rapidity from their decay channel into dimuon. The charged-particle multiplicity is measured at midrapidity (| y lab | < 1). The J/ψ results are presented as a function of charged-particle multiplicity in Fig. 4.3 [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. Thanks to the larger abundance of J/ψ, with respect to ψ(2S), a finer multiplicity binning and a higher multiplicity reach (∼ 6 times the average multiplicity) could be achieved. At both rapidity regions, and up to ∼ 1.5 times the average multiplicity, the yields increase with increasing multiplicity, with a trend compatible with a linear approach (y = x), depicted with a dashed line in the figure. At higher multiplicities, the yields seem to deviate from the linear behavior, and exhibit a faster than linear trend for the yields extracted at backward rapidity, and slower than a linear trend for the yields extracted at forward rapidity. The underlying mechanism behind this difference in the be-

0 2 4 6 |<1 η | NSD  〉 η / d ch N d 〈 η / d ch N d 0 2 4 6 8 NSD  〉 y / d N d 〈 y / d N d = 8.16 TeV NN s Pb, - ALICE, p - µ + µ → ψ J/ < 3.

ψ(2S)-over-J/ψ results

In this section, we discuss the ψ(2S)-over-J/ψ self-normalized yields as a function of the self-normalized charged-particle multiplicity The measurement is performed by evaluating the self-normalized ratio of the ψ(2S) and J/ψ yields in the same multiplicity interval. The measurement of the multiplicity dependence of J/ψ performed by ALICE at the same energy [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF], see Sec.4.1.2, was performed considering different multiplicity intervals than those used for the ψ(2S) analysis. Hence, we had to re-evaluate the multiplicity dependence of the J/ψ yields with the multiplicity intervals of our ψ(2S) analysis, see Sec.3.4 for the details of the analysis. Fig. 4.5 presents the results of this thesis, compared to those of Ref. [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]. We obtain a good agreement for the J/ψ yields, regardless of the different multiplicity intervals considered in both analyses. Comparison between the results for the J/ψ normalized yields obtained for this thesis multiplicity intervals and Ref. [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF].

The double ratio (ψ(2S)-over-J/ψ) measurement allows one to disentangle any possible difference in the multiplicity dependence between the charmonium excited and ground states. The results are shown in Fig. 4.6. The ψ(2S)-over-J/ψ is compatible with a flat distribution, within uncertainties, at both forward and backward rapidity in p-Pb collisions at s NN = 8.16 TeV. In Fig. 4.6, the multiplicity dependence of ψ(2S)-over-J/ψ is compared to the comover model calculations [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF]. The comover model suggests a stronger suppression for ψ(2S) with respect to the J/ψ, due to the weaker binding of the ψ(2S). The effect is stronger for high multiplicity events. A stronger suppression is expected at backward rapidity compared to forward rapidity due to the larger density of soft particles, which increases the probability of interaction with charmonia and, therefore, the dissociation probability. The comover model calculation is compatible with our results within uncertainties.

0 2 4 6 NSD |<1 η |  〉 η / d ch N d 〈 η / d ch N d 0 0.5 1 1.5 2 NSD  〉 ) ψ (J/ N 〈 ) ψ (J/ N / 〉 (2S)) ψ ( N 〈 (2S)) ψ ( N = 8.16 TeV NN s Pb - ALICE, p < 3.53 cms y 2.03 < - µ + µ → (2S) ψ , ψ J/ Data Comover ALI-PUB-525632
(a) Forward rapidity The self-normalized ψ(2S)-over-J/ψ yields as a function of self-normalized charged-particle multiplicity from p-Pb collisions at s NN = 8.16 TeV, for the forward rapidity region in the top panel and backward rapidity region in the bottom panel [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. The results are compared to the comover model calculations [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF].

0 2 4 6 NSD |<1 η |  〉 η / d ch N d 〈 η / d ch N d 0 0.5 1 1.5 2 NSD  〉 ) ψ (J/ N 〈 ) ψ (J/ N / 〉 (2S)) ψ ( N 〈 (2S)) ψ ( N = 8.16 TeV NN s Pb - ALICE, p < -2.96 cms y -4.46 < - µ + µ → (2S) ψ , ψ J/ Data

J/ψ results

The forward and midrapidity self-normalized J/ψ yields as a function of the chargedparticle multiplicity in pp collisions are presented in Fig. 4.8 [START_REF] Acharya | Multiplicity dependence of J/ψ production at midrapidity in pp collisions at s = 13 TeV[END_REF][START_REF] Acharya | Forward rapidity J/ψ production as a function of charged-particle multiplicity in pp collisions at s = 5.02 and 13 TeV[END_REF]. At forward rapidity (2.5 < y cms < 4.0), J/ψ particles are measured via their decay channel into dimuon. At midrapidity (|y y cms | < 0.9), J/ψ particles are measured via their decay channel into dielectron. On the central and right panels of Fig. 4.8, we find the measurements performed in

ALI-PUB-530595

Figure 4.8: Self-normalized yield of J/ψ as a function of midrapidity self-normalized chargedparticle multiplicity. The yields are measured in their decay channel into dimuon at forward rapidity in pp collisions at s = 5.02 and 13 TeV, respectively, in the left and the central panel. The result in the right panel shows the yields measured at midrapidity from pp collisions at s = 13 TeV [START_REF] Acharya | Multiplicity dependence of J/ψ production at midrapidity in pp collisions at s = 13 TeV[END_REF][START_REF] Acharya | Forward rapidity J/ψ production as a function of charged-particle multiplicity in pp collisions at s = 5.02 and 13 TeV[END_REF]. The measurements are compared to the theoretical calculations from PYTHIA 8.2 [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF], EPOS3 [START_REF] Drescher | Parton based Gribov-Regge theory[END_REF], Percolation [START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF], 3-Pomeron CGC [START_REF] Levin | Multiplicity dependence of quarkonia production in the CGC approach[END_REF], CGC+ICM [START_REF] Ma | Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions[END_REF], and CPP [START_REF] Kopeliovich | J/ψ in high-multiplicity pp collisions: Lessons from pA collisions[END_REF]. pp collisions at s =13 TeV. The forward J/ψ trend is compatible with a linear increase (y = x) with increasing multiplicity within uncertainties. At midrapidity, the increase is stronger than linear. On the left and central panels of Fig. 4.8, we can compare the forward rapidity measurement at s = 5.02 TeV and 13 TeV. No energy dependence is observed for the J/ψ self-normalized yields. The measurements are compared to the 3-pomeron color glass condensate (3-pomeron CGC) [START_REF] Levin | Multiplicity dependence of quarkonia production in the CGC approach[END_REF], CGC with improved color evaporation model (CGC+ICEM) [START_REF] Ma | Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions[END_REF], percolation [START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF], coherent particle production (CPP) [START_REF] Kopeliovich | J/ψ in high-multiplicity pp collisions: Lessons from pA collisions[END_REF], EPOS3 [START_REF] Drescher | Parton based Gribov-Regge theory[END_REF], and PYTHIA 8.2 [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF] calculations. The percolation model, EPOS3, and PYTHIA 8.2 event generators have already been introduced in Sec.4.1.1, 4.1.2, and 4.2.1, respectively.

The CPP model treats pp, pA, and AA collisions with similar bases. The model assumes a linear dependence between the mean multiplicity of light and heavy particle production and the number of nucleon-nucleon collisions. In the CGC+ICEM model, the charmonia are produced via the color evaporation model. The model describes the hadronization by employing non-relativistic QCD. In this model, the production of the heavy flavor particles is sensitive to the configuration of the gluons in pp and pA collisions. The model uses a saturation scale to control the dynamics of these gluons. In the computation of the CGC, the probability of producing charmonia increases via a sizable contribution of the multi-pomeron mechanism, particularly the 3-pomeron. The measurements are compatible qualitatively with the theoretical computations from 3-pomeron CGC, percolation, and CPP models within uncertainties, while EPOS3 and PYTHIA 8.2 event generators underestimate the trends at high multiplicity.

ψ(2S)-over-J/ψ results

The forward ψ(2S)-over-J/ψ self-normalized yield ratio as a function of the midrapidity charged-particle multiplicity is presented in Fig. 4.9. The double ratio measurement allows

0 2 4 6 |<1 η | INEL>0  〉 η / d ch N d 〈 η / d ch N d 0 0.5 1 1.5 2 INEL>0  〉 ) ψ (J/ N 〈 ) ψ (J/ N / 〉 (2S)) ψ ( N 〈 (2S)) ψ ( N = 13 TeV s ALICE, pp, < 4.0 cms y , 2.5 < - µ + µ → (2S) ψ , ψ J/ Data y = x PYTHIA 8.2 PYTHIA 8.

(no CR) Comover

ALI-PUB-525624

Figure 4.9: ψ(2S)-over-J/ψ self-normalized yield ratio, measured at forward rapidity, as a function of the midrapidity charged-particle multiplicity [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. The result is compared to PYTHIA 8.2 and comover model calculations [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF][START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF].

one to disentangle any possible differences in the multiplicity dependence between the charmonium excited and ground states. The resulting trend is compatible with a flat behavior within uncertainties. The result is compared to PYTHIA 8.2 event generator calculations which predict a similar behavior for both particles within uncertainties. PYTHIA 8.2 calculations with and without CR reproduce the results up to the highest probed multiplicity. The result is also compared to the comover model calculation [START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF]. The comover model predicts a stronger suppression for the ψ(2S) with respect to J/ψ, as the former has a larger size than the J/ψ. The comover model calculation describes the measurement, within uncertainties, in the model calculation domain. The precision of the measurement and of the model calculations does not allow us to conclude on whether final state effects might play a significant role in pp collisions at high multiplicity. (see caption for details) [START_REF] Abelev | J /ψ Production as a Function of Charged Particle Multiplicity in pp Collisions at s = 7 TeV[END_REF][START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF][START_REF] Acharya | Studies of J/ψ production at forward rapidity in Pb-Pb collisions at s NN = 5.02 TeV[END_REF][START_REF] Adam | Measurement of an excess in the yield of J /ψ at very low p T in Pb-Pb collisions at s NN = 2.76 TeV[END_REF]. It is important to mention that the average chargedparticle multiplicity for pp collisions is ∼ 6 [START_REF] Abelev | J /ψ Production as a Function of Charged Particle Multiplicity in pp Collisions at s = 7 TeV[END_REF], whereas the correspondent value for 0-90% Pb-Pb collisions is ∼ 545 [START_REF] Adam | Centrality Dependence of the Charged-Particle Multiplicity Density at Midrapidity in Pb-Pb Collisions at s NN = 5.02 TeV[END_REF]. Despite this difference, the self-normalized yields exhibit a striking similar behavior in both colliding systems. The trend also presents similarities with the p-Pb results at backward rapidity (Pb-going). Note that the overall increase of multiple parton interactions (from pp to Pb-Pb) is expected to cancel in the self-normalized ratios, that are only sensitive to the relative evolution with charged-particle multiplicity in a given colliding system. Model calculations are required to interpret these similarities.

Comparison of charmonium results across system size

Analogously, in Fig. 4.11(a) are displayed the self-normalized yields of ψ(2S) in pp and p-Pb collisions as a function of charged-particle multiplicity. The results are compatible, within the uncertainties. As argued earlier in this chapter, the ψ(2S)-over-J/ψ ratio is evaluated to pin down possible differences between the multiplicity dependence of excited and ground states. The ratios, shown in Fig. 4.11(b), are compatible with unity for both colliding systems. A larger data sample would be needed to conclude on the possible differences among ground and excited states, and to clarify the role of initial and final state effects.

Bottomonium results

The self-normalized yields of Υ(1S), Υ(2S), and Υ(3S) are presented as a function of chargedparticle multiplicity in Fig. 4.12(a) [START_REF]Multiplicity dependence of Υ production at forward rapidity in pp collisions at s = 13 TeV[END_REF]. The measurement is performed in pp collisions at s = 13 TeV, where the bottomonium yields are measured at forward rapidity, 2.5 < y cms < 4.0, [START_REF] Abelev | J /ψ Production as a Function of Charged Particle Multiplicity in pp Collisions at s = 7 TeV[END_REF], whereas p-Pb ones refer to the NSD event class [START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]; all for p T > 0. The Pb-Pb data points include J/ψ with 0.3 < p T < 12 GeV/c to reduce the low-p T contribution from photoproduction, which is significant only in more peripheral collisions [START_REF] Acharya | Studies of J/ψ production at forward rapidity in Pb-Pb collisions at s NN = 5.02 TeV[END_REF][START_REF] Adam | Measurement of an excess in the yield of J /ψ at very low p T in Pb-Pb collisions at s NN = 2.76 TeV[END_REF][START_REF] Acharya | Coherent J/ψ photoproduction at forward rapidity in ultra-peripheral Pb-Pb collisions at s NN = 5.02 TeV[END_REF]. The vertical bars represent the statistical uncertainties, and the boxes are the systematic ones. The dashed line indicates the one-to-one correlation, to guide the eye. from their decay channel into a dimuon, and the charged-particle multiplicity is measured at midrapidity, |y cms | < 1. The yields show an increase with charged-particle multiplicity. This behavior is compatible with a linear increase (y = x) depicted with a dashed line in the figure. The bottom panel of Fig. 4.12(a) shows the ratio of the bottomonium yields to the charged-particle multiplicity, i.e., the ratio of the y-axis to the x-axis. The nearly linear trends of the Υ yields in the top panel of Fig. 4.12(a) result in a flat distribution of the ratios in the bottom panel, suggesting a similar behavior of the Υ states with multiplicity. The selfnormalized Υ(2S)-over-Υ(1S) ratio as a function of charged-particle multiplicity is displayed in Fig. 4.12(b). The Υ(2S)-over-Υ(1S) ratio is compatible with unity, within uncertainties, in the probed multiplicity region. The measurement is compared to several theoretical calculations. No relevant difference is observed between PYTHIA 8.2 event generator calculations with and without color reconnection, which describe the observed behavior of the ratio. The 3-pomeron CGC and CPP calculations are compatible with the flat distribution of the self-normalized Υ(2S)-over-Υ(1S) ratio within uncertainties. The measurement is also compared to the comover model calculation, which predicts a stronger suppression, 20% to 40%, of the Υ(2S) compared to the Υ(1S). The self-normalized Υ(3S)-over-Υ(1S) ratio is also reported in Ref. [START_REF]Multiplicity dependence of Υ production at forward rapidity in pp collisions at s = 13 TeV[END_REF] as a function of charged particle multiplicity in pp collisions

0 2 4 6 |<1 η |  〉 η / d ch N d 〈 η / d ch N d 0 2 4 6 8 〉 y / d N d 〈 y / d N d ALICE - µ + µ → ψ J/ = 8.
0 2 4 6 |<1 η |  〉 η / d ch N d 〈 η / d ch N d 0 2 4 6 8 10 〉 y / d N d 〈 y / d N d = 8.
(a) ψ(2S) self-normalized yields 0 2 4 6 |<1 η |  〉 η / d ch N d 〈 η / d ch N d 0 0.5 1 1.5 2 〉 ) ψ (J/ N 〈 ) ψ (J/ N / 〉 (2S)) ψ ( N 〈 (2S)) ψ ( N ALICE - µ + µ → (2S) ψ , ψ J/ = 13
0 1 2 3 4 5 6 |<1 η | INEL>0  〉 η / d ch N d 〈 η / d ch N d 0 2 4 6 8 10 12 INEL>0  〉 y / d ϒ N d 〈 y / d ϒ N d = 13 TeV s ALICE pp < 4 y , 2.5 < - µ + µ → (nS) ϒ y = x (1S) ϒ (2S) ϒ (3S) ϒ 0 1 2 3 4 5 6 |<1 η | INEL>0  〉 η / d ch N d 〈 η / d ch N d 0.5 1 1.5 2 2.5 〉 η / d ch N d 〈 η / d ch N d / 〉 y / d ϒ N d 〈 y / d ϒ N d (a) Υ self-normalized yields 0 1 2 3 4 5 6 |<1 η | INEL>0  〉 η / d ch N d 〈 η / d ch N d 0 0.5 1 1.5 2 2.5 3 INEL>0  〉 (1S) ϒ N 〈 / (1S) ϒ N 〉 (2S) ϒ N 〈 / (2S) ϒ N = 13 TeV s ALICE pp < 4 y , 2.5 < - µ + µ → (2S) ϒ (1S), ϒ Data PYTHIA 8.2 comovers PYTHIA 8.2 (no CR) CPP 3-pomeron CGC (b) Υ(2S)-over-Υ(1S)
Figure 4.12: The multiplicity dependence of (a) self-normalized bottomonium yields, (b)Υ(2S)-over-Υ(1S) [START_REF]Multiplicity dependence of Υ production at forward rapidity in pp collisions at s = 13 TeV[END_REF]. The vertical error bars represent the statistical uncertainty on the yields, while the height and the width of the box represent the systematic uncertainty on the yields and the charged-particle multiplicity, respectively. The measurement in (b) is compared to the 3-pomeron CGC [START_REF] Levin | Multiplicity dependence of quarkonia production in the CGC approach[END_REF], PYTHIA 8.2 [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF], and CPP [START_REF] Kopeliovich | J/ψ in high-multiplicity pp collisions: Lessons from pA collisions[END_REF] calculations. at s = 13 TeV. The multiplicity dependence of the Υ(3S)-over-Υ(1S) ratio shows a trend compatible with a flat distribution. However, a firm conclusion on the behavior of the ratio requires further investigation using a larger data sample.

CMS collaboration also reported some measurements of the bottomonium states. In particular, the ratio of the excited-over-ground state yields, Υ(nS)/Υ(1S), as a function of the number of tracks (N track ), where both quantities are measured at midrapidity (|y cms | < 1. [START_REF] Adam | Centrality Dependence of the Charged-Particle Multiplicity Density at Midrapidity in Pb-Pb Collisions at s NN = 5.02 TeV[END_REF] in pp collisions at s = 2.76 TeV [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF] and 7 TeV [START_REF] Sirunyan | Investigation into the event-activity dependence of Υ(nS) relative production in proton-proton collisions at s = 7 TeV[END_REF] (see Fig. 4.13). A clear decreasing trend is visible for both excited-over-ground state ratios, from low to high N track intervals. The excited-over-ground bottomonium ratio in pp collisions is also compatible with the measurement performed in p-Pb collisions at s NN = 5.02 TeV, which is depicted with blue markers in Fig. 4.13 [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF]. Two hypotheses are suggested to explain the difference in the behavior between the Υ(2S)-over-Υ(1S) and Υ(3S)-over-Υ(1S) in Ref. [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF]. First, the Υ(1S) might be systematically produced with much more soft particles than the excited states, creating an artificial dependence when studying the production at small multiplicities. Second, the interaction with the final state comoving particles might result in a stronger suppression for the excited bottomonium states relative to the ground state, due to their weaker binding.

In both cases, the ratio is expected to decrease as a function of multiplicity in pp and p-Pb collisions [START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF].

The measurement from CMS collaboration displays a non-normalized measurement contrary to the measurements from ALICE. In order to compare the two results, the selfnormalized Υ(2S)-over-Υ(1S) as a function of N tracks / < N tracks > are evaluated for the CMS data in Ref. [START_REF] Chowdhury | Study of Υ production as a function of charged-particle multiplicity in proton-proton collisions at s = 13 TeV with ALICE at the LHC[END_REF], and presented in Fig. 4.14. The results show a ∼ 40% decrease of the yields with increasing N tracks / < N tracks >, which might deviate from the flat distribution observed in the measurement performed by ALICE. Note that the CMS measurement is performed at s = 2.76 TeV with no rapidity gap between the yields and the multiplicity. On the other hand, ALICE results are for s = 13 TeV and with a rapidity gap between the two measured quantities. The bottomonium results from ALICE and CMS are compatible within the current precision. p T intervals. This increase becomes stronger with increasing p T . On the right panel, the multiplicity dependence of the self-normalized D-meson, J/ψ, and heavy-flavor decay electrons are represented together. The comparison is made for the prompt D-meson yields with 2.0 < p T < 4.0 GeV/c, heavy-flavor decay electrons with 3.0 < p T < 6.0 GeV/c and J/ψ with p T < 4 GeV/c to ensure that particles have similar kinematics. Prompt D mesons are originated from charm-quark decays, inclusive J/ψ are also predominantly from charmquark decays (contribution from b-decays is of the order of 10%), while heavy-flavour decay electrons stem from a mixture of charm and beauty quark decays. Fig. 4.15(b) shows that J/ψ, prompt D-mesons, and heavy-flavor decay electron yields exhibit similar behavior as a function of charged-particle multiplicity. This suggests that hadronization does not play a significant role on the evolution with charged-particle multiplicity (similar results are observed for prompt D and inclusive J/ψ), and that there are no striking differences on charm and beauty quark decays evolution with charged-particle multiplicity (similar results for prompt D and heavy-flavor decay electrons).

Open heavy-flavor results

ALICE Run 3 and 4 upgrades

This chapter outlines the main ALICE Run 3 and 4 upgrades relevant to this thesis. These upgrades were carried out during the Long Shutdown 2 (LS2) from 2019 to 2022. In Sec.5.1, we discuss the main motivations for the upgrades. In Sec.5.2 and 5.3, we present the central and forward detector upgrades, respectively. Finally, we discuss the new ALICE online-offline computing system.

Motivations for Run 3 and 4 upgrades

As explained in the upgrade Letter Of Intent [START_REF] Abelev | Upgrade of the ALICE Experiment: Letter Of Intent[END_REF], the ALICE upgrades after the LS2 aim at exploiting the full potential of the LHC, focusing on heavy-ion collisions for the higher precision study of the quark-gluon plasma. In this regard, the Run 3 and 4 ALICE upgrade is based on reading out all Pb-Pb (pp) collisions at an interaction rate of 50 (400) kHz.

Therefore, major upgrades have taken place during LS2 for the detectors at the central barrel and the forward arm, in addition to the upgrade of the online-offline system. Fig. 5.1 presents a schematic of the ALICE detector after the LS2. A last note about the ALICE upgrade program, two new detectors should be installed or upgraded during LS3 (2026-2028): the Forward Calorimeter (FoCal) [START_REF]A Forward Calorimeter (FoCal) in the ALICE experiment[END_REF] and the upgraded ITS (ITS3) [START_REF]Expression of Interest for an ALICE ITS Upgrade in LS3[END_REF]. They will not be discussed in the following, as they can be considered as Run 4 only upgrades.

Central barrel detectors upgrades

The Inner Tracking System (ITS)

The description of the ITS detector during Run 2 is discussed in Sec.2.2.1. One of the main limitations of the Run 2 ITS detector is the readout capabilities. As mentioned in Ref. [START_REF] Abelev | Upgrade of the ALICE Experiment: Letter Of Intent[END_REF], the ITS readout electronics can reach a maximum of about 1 kHz regardless of its occupancy. This implies that Run 2 ITS will not be adequate for the readout capabilities for Run 3 physics objectives. The layout of the upgraded ITS detector is shown in Fig. 5.2.

The upgraded ITS detector consists of seven cylindrical layers of silicon detectors compared to six layers during Run 2. As the upgrade of ALICE included the reduction of the beam pipe radius, the innermost layer of the ITS is located at a closer distance to the interaction point (2.2 cm compared to 3.4 cm during Run 2). In addition to moving the detector closer to the interaction point, the ITS upgrade will involve reducing the material budget and pixel size. These enhancements are expected to significantly improve the tracking efficiency and impact parameter resolution of the detector. The ITS silicon pixels are based on Monolithic Active Pixel Sensor (MAPS), which reduces the silicon material budget per layer seven times compared to the ITS Run 2. Significant improvements in the spatial resolution, especially at low-p T [START_REF] Reidt | Upgrade of the ALICE ITS detector[END_REF][START_REF] Abelev | Technical Design Report for the Upgrade of the ALICE Inner Tracking System[END_REF], are expected.

Central barrel detectors upgrades

The Time Projection Chamber (TPC)

The Time Projection Chamber (TPC) is the main charged particle tracker and particle identifier detector of ALICE. During Run 2, the TPC consisted of a cylindrical drift field cage and two readout planes on the end caps (see Sec.2.2.1 for the details). The design of the readout was based on the Multi Wire Proportional Chambers (MWPC) technology with cathode pad readout. The readout chambers use a scheme of wire grids consisting of a plane of anode wires, cathode wires, and a gating grid. As the event rate is increased during Run 3, and with the requirements of a continuous readout. The TPC MWPCs read-out chambers have been replaced with Gas Electron Multipliers (GEM), allowing the TPC to be continuously read out. The front end of the TPC has also been upgraded to cope with the increased data-taking rate [START_REF] Antonioli | Upgrade of the ALICE Readout & Trigger System[END_REF].

The Fast Interaction Trigger

The Fast Interaction Trigger (FIT) detector is the Run 3 replacement of the V0, T0, and FMD detectors. The FIT consists of three sub-detectors: the FT-zero (FT0), FV-zero (FV0), and the Forward Diffractive Detector (FDD). FT0, FV0, and the FDD serve as the leading fast trigger for ALICE during Run 3 and 4. In addition, FIT provides information for measuring the event multiplicity, initial indication for vertex location, beam-gas rejection, collision time, and event-plane position. All the aforementioned requirements are expected to be fulfilled with the FIT with high precision compared to the V0, T0, and FMD detectors during Run 2 [START_REF] Antonioli | Upgrade of the ALICE Readout & Trigger System[END_REF].

The new Muon Spectrometer

The Muon Tracking Chambers (MCH)

MCH detector is based on multi-wire proportional chambers with cathode pads read-out.

The Muon Identifier (MID)

The MID detector relies on Resistive Plate Chamber (RPC), the same detector as in Run 2. In the continuous readout scheme, the task to provide p T -dependent muon-triggered signals was replaced by the need to readout all RPCs at much higher rate. Thus, the readout architecture was upgraded similarly to the MCH one. The front-end readout electronics situated on the RPC detectors was also upgraded to mitigate the aging process of the RPCs

Online-Offline computing system

and increase the readout rate capabilities. The RPCs now operate in a genuine avalanche mode which leads to a reduced charge generated within the gas, thereby limiting the aging effects. The counterpart is the need to amplify the analog signals from the RPCs and a new front-end electronics circuit was designed for this purpose [START_REF] Antonioli | Upgrade of the ALICE Readout & Trigger System[END_REF].

The Muon Forward Tracker (MFT)

The MFT is an all-silicon detector added to the muon spectrometer in the region between the ITS and the front absorber. The presence of the MFT in this region during Run 3 will allow to reduce the uncertainty in the matching between the muon tracks and the primary vertex. The MFT pixel detector is based on CMOS monolithic pixel sensor technology, the same technology employed by the upgraded ITS detector [START_REF]Technical Design Report for the Muon Forward Tracker[END_REF]. In addition, the MFT will allow distinguishing between the muon tracks from the primary vertex and those originating from the decay of B-hadrons. The MFT consists of two half cones, each consisting of five silicon discs, placed along the beam axis at a distance of z = -460, -493, -531, -687, -768 mm from the interaction point, and covers the pseudorapidity range of 2.5 < η lab < 3.6.

Online-Offline computing system

The general workflow of the new ALICE Online-Offline (O2) computing system is presented in Fig. 5.4. It includes data processing starting from the raw data to the Analysis Object Data (AO2D), which are used for the physics analysis. The upgraded ALICE computing system supports both continuous and triggered raw data processing.

First, the collected data are transferred from the detector readouts into the common readout units using detector data links or gigabit transceivers. At this point, data are divided into Sub-Time Frames (STF) corresponding to the first level processing granularity and covering a period of about 11.4 ms (128 LHC orbits in 2022). In the second step, all the STFs of a given period converge to an event processing node, where the STFs are merged into complete Time Frames (TF). At this step, further calibration and data compression are performed. Then, the compressed TF is stored in a disk buffer for temporary storage. The final processing step is an asynchronous operation where the data are stored on the grid, and reconstruction and calibration are performed. Finally, the analysis is performed using the AODs within the O2 framework.

Systematic uncertainty of tracking efficiency of the Muon Tracking Chambers

In this chapter, we present the methodology used to compute the systematic uncertainty of the tracking efficiency of the muon tracking chambers. The results discussed in this chapter are obtained using Run 3 data from pp collisions at s = 13.6 TeV. In Sec.6.1, we introduce the track reconstruction algorithm used in Run 3, and highlight the main differences with respect to the algorithm used in Run 2. In Sec.6.2, we present the equations used to estimate the tracking efficiency of the muon chambers. In Sec.6.3, we show the main results obtained for the muon tracking efficiency, both per muon tracking (MCH) chamber, and per station.

Results are presented in intervals of p T , η, or φ, as well as an integrated quantity. Finally, in Sec.6.4, we conclude with the comparison between the tracking efficiency computed from simulations and from data, in order to assess the systematic uncertainty on the tracking efficiency.

Muon track reconstruction

Muon track reconstruction: Run 2 algorithm

The reconstruction process starts in stations 4 and 5, where the particle multiplicity is lower compared to the other stations. The steps discussed in this section are explained in Ref. [START_REF] Blanco | Study of J /ψ production dependence with the charged particle multiplicity in p-Pb collisions at s NN = 5.02 TeV and pp collisions at s = 8 TeV with the ALICE experiment at the LHC[END_REF].

1. The reconstruction process starts in station 5 of the MCH by combining the information of the clusters from both chambers and by connecting them to build track segments. These segments are then extrapolated to a primary vertex, reconstructed by the SPD detector, through the magnetic field. For each reconstructed track segment, the local position, the direction, the impact parameter to the primary vertex, and their associated uncertainties are computed.

2. The track candidates that are out of the spectrometer acceptance and those which does not pass the initial momentum cut are rejected. If several compatible clusters are found in the same chamber, the track is duplicated to consider all the possibilities. 5. The tracks sharing the same clusters are removed, also those with an impact parameter and/or momentum out of given limits. [START_REF]The physics of the quark-gluon plasma[END_REF]. The remaining candidates are propagated to stations 3, 2, and 1, sequentially. The algorithm searches for at least one compatible cluster in each station. The track parameters are recalculated at each step, and only candidates that pass the impact parameter and momentum cuts are kept. In addition, when several compatible clusters are found in the same chamber, the track is duplicated to consider all the possibilities. 7. The candidates that share one or more clusters in stations 1, 2, or 3 are removed. The candidates with the largest number of clusters are kept. In case of a similar number of clusters, the track with a lower χ 2 , i.e., better quality, is kept. By this step, the reconstructed tracks are called MCH standalone tracks.

8. The MCH tracks are matched with a track segment reconstructed from the same collision in the Muon Trigger Chambers to identify the muon tracks. The reconstructed tracks after this step are called MCH-MTR tracks. 9. Finally, the reconstructed tracks are extrapolated to the primary vertex. The track parameters are recalculated and corrected for the energy loss and multiple scattering in the front absorber.

Muon track reconstruction

Muon track reconstruction: Run 3 algorithm

As mentioned in Sec.5.3.2, the Muon Identifier (MID) is used to identify the muon tracks.

Thanks to its excellent timing, the MID is able to separate tracks that belong to adjacent bunch crossings. Steps 1-7 are the same in Run 2 and Run 3. 11. For all track types, the track parameters are recalculated and corrected for the energy loss and multiple scattering in the front absorber.

A scheme of the different types of tracks that can be reconstructed in the upgraded Muon spectrometer (MFT+MCH+MID) is shown in Fig. 6.1. They are defined as follows:

• Global muon track is a matched track in the MFT, MCH, and MID detectors.

• Global forward track is a matched track in the MFT and MCH detectors.

• Muon standalone track is a matched track in the MCH and MID detectors.

• MCH standalone track is a track in the MCH only.

• MFT standalone track is a track in the MFT only.

Tracking efficiency estimation from reconstructed tracks

We present here a method to evaluate the tracking efficiency of the muon chambers based on the reconstructed MCH standalone tracks. This method is exploiting the redundancy of the chambers, considering that the efficiency of one chamber is independent of that of the other chambers. This method can be applied on both data and simulations, and the comparison of results provides an indicator on how well the simulation reproduces the data.

The difference between the tracking efficiency computed from data and from simulation can then be used to assess the systematic uncertainty on the tracking efficiency. However, since this method is based on reconstructed MCH standalone tracks, there is an intrinsic bias due to the tracking reconstruction algorithm, which requires at least three clusters in stations 4 and 5 and at least one cluster per station in stations 1, 2, and 3 as explained in the previous section. Thus this method cannot be used to compute the MCH tracking efficiency needed for corrections (which is extracted from dedicated MC simulations as described in 3.5.2).

The total number of tracks (N Tot ) crossing a station can be expressed as:

N Tot = N i -j + N i -0 + N 0-j + N 0-0 , (6.1)
where N i -j is the number of tracks having a cluster in both chambers of the station, N i -0

(N 0-j ) is the number of tracks having only one cluster in the first (second) chamber of the station and N 0-0 is the number of tracks having no cluster at all. In this last case, the track is simply not reconstructed as it does not fulfill the conditions of the tracking algorithm. An illustration of the four cases is given in Fig. 6.2 for station 1.

Considering that the efficiency of chamber i (ϵ i ) is independent from the efficiency of chamber j (ϵ j ), one can write the number of tracks with a cluster in chamber i and j as:

N i -j = ϵ i × ϵ j × N Tot . ( 6.2)
In the same way, the number of tracks with a cluster in the chamber i or j can be written as:

N i -0 = ϵ i × (1 -ϵ j ) × N Tot , (6.3
)

N 0-j = (1 -ϵ i ) × ϵ j × N Tot . ( 6.4)
Using Eq.6.3 and Eq.6.4, the efficiency of the chambers i and j can be expressed as:

ϵ i = N i -j N i -j + N 0-j , (6.5)
ϵ j = N i -j N i -j + N i -0 . ( 6.6)
The efficiency of the first three stations can be written as a function of their chambers efficiency:

ϵ St (1)(2)(3) = 1 -(1 -ϵ i ) × (1 -ϵ j ), (6.7)
where (i , j ) denote the chambers in the first, the second, or the third station, and can take the values (1,2), [START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF][START_REF] Chatrchyan | Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC[END_REF], or [START_REF] Zyla | Review of Particle Physics[END_REF][START_REF]The physics of the quark-gluon plasma[END_REF], respectively. The efficiency of stations 4 and 5 is evaluated as a whole due to the tracking algorithm requirements, and is given by:

ϵ St (45) = i =10 i =7 ϵ i + i =10 i =7 (1 -ϵ i ) j =10 j =7, j ̸ =i ϵ j . ( 6.8)
Then the muon chamber tracking efficiency is given by the product of the station's efficiency: [START_REF] Kovarik | nCTEQ15 -Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework[END_REF] . (6.9)

ϵ t r acki ng = ϵ St (1) × ϵ St (2) × ϵ St (3) × ϵ St

Tracking efficiency studies in pp collisions at s = 13.6 TeV

We apply the method explained in the previous section to estimate the MCH tracking efficiency from pp collisions at s = 13.6 TeV. Only a very small sample of the collected data has been analyzed, in particular run number 523306, from the LHC22m period. The run 523306 corresponds to data taken on 14/08/2022, starting at 00:09:56 and up to 00:24:24.

The pp interaction rate was about 500 kHz, with low pile-up (< 2%).

Integrated MCH tracking efficiency

The tracking efficiency integrated over p T , η, and φ is presented in Fig. 6.3 as a function of the chamber ID. The tracking efficiency is higher than 90% for all of the MCH tracking chambers, apart from chamber 3, which shows a value of 83%. We expect a chamber efficiency above 95% so the chambers with a value below that threshold, i.e. chambers 3, 5 and 8, will be investigated further in the following.

The tracking efficiency of the MCH stations is evaluated using Eq.6.7 and Eq.6.8, and is shown in Fig. 6.4. The computed tracking efficiency for each station is higher than 99%, thanks to the chambers redundancy. In the same figure, the tracking efficiency for the full MCH detector, computed with Eq.6.9, is shown and reaches a value of 98.5%.

Tracking efficiency as a function of p T , η, and φ

Here we present the efficiency of the MCH chambers as a function of the track kinematic variables p T , η, and φ. and stations, respectively. The MCH chambers show efficiency values higher than 90% for all η intervals, except for chamber 3, which has an efficiency ranging between 80 -85%. The issue with chamber 3 low efficiency is going to be discussed in more detail in 6.3.3. The MCH efficiency per station is presented in Fig. 6.8, showing a high efficiency for all the stations, as well as for the full MCH detector in all η intervals. No trend is observed for the efficiency as a function of η.

We have also studied the efficiency of the MCH detector as a function of the azimuthal angle φ. Figure 6.9 presents the efficiency of the MCH chambers for four intervals of φ.

Chamber 3 shows a very low efficiency ∼ 60% in the range 0 < η < 1.57. This particular φ angle corresponds to a specific location in station 2 and gives a first indication about where the problem may come from. A relatively low efficiency ∼ 85% is observed for different φ intervals in chambers 5 and 8, as already spotted in the p T and η dependent studies. The efficiency of the MCH stations and the overall efficiency of the MCH detector is higher than 98% in all the φ intervals.

< -1.57 Φ -3.14 < < 0.00 Φ -1.57 < < 1.57 Φ 0.00 < < 3.14 Φ 1.57 < < -1.57 Φ -3.14 < < 0.00 Φ -1.57 < < 1.57 Φ 0.00 < < 3.14 Φ 1.57 < < -1.57 Φ -3.14 < < 0.00 Φ -1.57 < < 1.57 Φ 0.00 < < 3.14 Φ 1.57 < < -1.57 Φ -3.14 < < 0.00 Φ -1.57 < < 1.57 Φ 0.00 < < 3.14 Φ 1.57 <

2D tracking efficiency studies per MCH chamber

In order to understand the low tracking efficiency observed for chambers 3, 5 and 8 and identify any potential dead areas in the MCH chambers, we have represented the tracking efficiency of the MCH chambers in 2D, exploiting η and φ variables. Figure 6.11 displays the computed tracking efficiency as a function of η and φ for the 10 MCH chambers. A very low tracking efficiency, depicted by a blue color, is clearly visible in some areas of chambers 2, 3, 5, and 8. These are the areas likely to have hardware or detector issues that will require to be fixed. We also need to understand these issues so they can be implemented in simulations to reproduce as well as possible the real status of the detector.

The 2D η and φ representation from Fig. 6.11 cannot be translated directly to chamber coordinates. To investigate the low tracking efficiency spots, we will also use the 2D representation of the fired pads (see Fig. 6.12) from the Quality Control (QC) of this particular run. The QC embraces several processes to ensure, online and offline, that we are taking good-quality data.

In chamber 2, the low tracking efficiency in the range (φ ∼ 2.9) -(η ∼ 2.6) translates into a reduced tracking efficiency along the edges of the top left quadrant of chamber 2.

Vertically, one could retrieve a problem on the high voltage of this sector, which implies that the particle detection is disabled. Horizontally, this corresponds to a SOLAR board (readout board which interfaces up to 40 FEE boards to the DAQ) that lost its configuration.

In chamber 3, the low tracking efficiency (blue band) is visible in the azimuth range [0,1] and spans over almost the full η range. This region corresponds to the top right quadrant of chamber 3 (third column of top part of (φ ∼ 2.9) -(η ∼ -2.6)) where a vertical blue line is visible. This observation aligns with the quality control plot depicted in figure 6.12, which indicates a low occupancy region (blue line) in the first quadrant. The low efficiency is due to a fault on a wire inside the chamber that required to disconnect a group of wires from the high-voltage distribution circuit. This quadrant was opened and repaired during the 2022 winter shutdown.

In chamber 5, the low tracking efficiency is centered at (φ ∼ 0) and extends over the full η range. This problem is also visible in the bottom part of Fig. 6.12 in the middle of the right side of chamber 5. However, this issue seems to be transient and only appeared in a few runs. Its origin, low voltage power supply issue, or SOLAR board loss of configuration was not clearly established.

In chamber 8, the low tracking efficiency is strongest at (φ ∼ -1.4) and large η and extends up to (φ ∼ -0.8) and (η ∼ 3.5). This can be correlated to a fully missing slat in the bottom right part of chamber 8. This fault is due to a faulty channel in the low-voltage power supply, thus the FEE is not powered.

We have successfully correlated the low tracking efficiency areas from pp data with the issues detected by the Quality Control for a dedicated run. This demonstrates that our tracking efficiency calculation method can effectively reproduce the inactive parts of the MCH detector.

Tracking efficiency studies in pp collisions at

s = 13.6 TeV - 3.8 - 3.6 - 3.4 - 3.2 - 3 - 2.8 - 2.6 - η - - - Φ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) chamber 1 4 - 3.8 - 3.6 - 3.4 - 3.2 - 3 - 2.8 - 2.6 - η 3 - 2 - 1 - 0 1 2 3 Φ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (b) chamber 2 - 3.8 - 3.6 - 3.4 - 3.2 - 3 - 2.8 - 2.6 - η - - - Φ 0

Tracking efficiency studies in Monte Carlo

In this section, we present the estimated MCH tracking efficiency based on MC simulations for pp collisions at s = 13.6 TeV. We used an ideal MC simulations (named LHC21i3g2 in the ALICE jargon) that considers a perfect detector to calculate the results since the software to retrieve and to include realistic data taking conditions has not been released at the time of this thesis. The same procedure as the one described in Sec.6.2 was followed to estimate the MCH tracking efficiency.

Integrated MCH tracking efficiency

The tracking efficiency integrated over p T , y, and φ is presented in Fig. 6.13 as a function of the chamber ID. The computed tracking efficiency is higher than 99.2% for all the MCH chambers.

Tracking efficiency as a function of p T , η, and φ

In this section, we present the MCH tracking efficiency extracted from MC as a function of the track kinematic variables p T , η, and φ. The p T -differential chamber efficiency is presented in Fig. 6.15. The tracking efficiency exceeds 99% for all MCH chambers and across all p T intervals.

In Fig. 6.16, we present the η-differential of the MCH chamber efficiency. The MCH chambers show an efficiency higher than 99% in all η intervals. No trend is observed for the efficiency as a function of η.

Finally, we have also studied the azimuthal angle φ dependence of the MCH tracking efficiency, which is presented in Fig. 6.17. The tracking efficiency is higher than 99% for all the chambers in all φ intervals.

In conclusion, the MCH chamber efficiency has been studied as a function of p T , η, and φ.

We obtained an efficiency exceeding 99% in all the results, which is compatible with the expectations from ideal MC simulations.

2D tracking efficiency studies per MCH chamber

In this section, we show the results for the MCH tracking efficiency as a function of η and φ obtained from ideal MC simulations. A similar study has been carried out using data presented in Sec.6.3.3. Such analysis helps identify potential dead areas in the MCH chambers that might not be visible in the 1D efficiency studies. As an example, Fig. 6.18 displays the φ-η dependence of the MCH tracking efficiency for chamber 1 and chamber 10.

The result shows ∼ 100% tracking efficiency in all the MCH chambers, similar to the efficiency obtained for chambers 1 and 10 shown in the example. It is worth noting that using the ideal MC we are not expecting to see any dead areas effect in the 2D MCH tracking efficiency, as there are no detector conditions implemented in such simulations.

Systematic uncertainty determination

To estimate the uncertainty of the MCH tracking efficiency, we compare the efficiency computed from data and that obtained from MC simulations. The results of these comparisons are presented in Fig. 6.19 for the tracking efficiency per chamber ID and in Fig. 6.20 for the efficiency per station ID. Significant differences are observed between the values obtained from data and MC, for both chamber and station tracking efficiencies. These discrepancies arise from two sources.

Systematic uncertainty determination

The first and dominant source is the missing description of realistic and time-dependent detector conditions in the MC simulations, which are, for now, only ideal. The work is ongoing to include in the MC simulations a realistic detector status so MC simulations can be anchored to data.

The second source is related to the kinematic distributions of the muon tracks in MC simulation. It is crucial to tune these distributions to data to ensure that they describe the kinematics of the true distributions. A data-driven procedure is performed to tune the MC p T , φ, and η distributions on data. The same procedure has been followed when computing the A × ε for the ψ(2S) multiplicity-dependent analysis. Fig. 3.13, presents the flow chart of the iterative procedure that we followed to tune the MC distributions in data.

Part IV

Conclusion 7 Conclusion

In ultra-relativistic heavy-ion collisions, a deconfined state of quarks and gluons called Quark Gluon plasma (QGP) is formed. Several soft and hard observables are used to probe the QGP, such as charmonia. Charmonia are bound states of charm and anti-charm quarks. Given the heavy mass of the charm quarks, they are produced in the initial stages of the collision, before the QGP formation, and experience the full evolution of the system. Besides the QGP effects, these observables might be influenced by the presence of the nuclei, referred to as cold nuclear matter effects. Proton-nucleus collisions are used as a control system to disentangle the QGP effects from the cold nuclear matter effects, since the energy density of the system is not sufficient to create a QGP. Recently, several intriguing QGP-like behaviors have been observed at high multiplicity in small systems, i.e., proton-proton and protonnucleus collisions. For example, the non-zero elliptic flow of charged particles, and the strange hadron production enhancement. These findings are surprising, as they are usually interpreted as QGP signatures in heavy-ion collisions. Multiparton interactions (MPI) are one of the scenarios proposed to interpret these behaviors. Charmonium production as a function of charged-particle multiplicity is a tool to probe the MPIs.

In this thesis, we measured the self-normalized charmonium yields as a function of the self-normalized charged-particle multiplicity. The analysis is performed using the data set of p-Pb collisions at s NN = 8.16 TeV collected by the ALICE experiment. The charged-particle multiplicity is measured at midrapidity, |y| < 1, exploiting the information of the inner tracking system, where the number of track segments was used as a multiplicity estimator.

The correlation between the number of tracklets and the charged-particle multiplicity is evaluated using MC simulations. The information from the muon spectrometer is used to reconstruct the charmonium yields from their decay channel into dimuon at forward, 2.03 < y cms < 3.53, and backward, -4.46 < y cms < -2.96, rapidity. The charmonium yields are extracted by fitting the invariant mass distribution of unlike-sign muon pairs. A significant effort was dedicated to achieve a stable fit procedure because of the limited statistics of ψ(2S).

The normalized ψ(2S) yields show an increase with increasing normalized multiplicity at both forward and backward rapidity. The yield increase is compatible with a linear trend with a slope close to unity. Moreover, the measurements are compared to the calculation from the percolation + comover + EPS09 model. The model describes the data trend within uncertainties in both rapidity regions. To disentangle any possible final state effect at play in p-Pb collisions, we measured the self-normalized ψ(2S)-over-J/ψ yields as a function of the self-normalized charged-particle multiplicity. The ratio presents a flat behavior; i.e. a similar behavior is observed for the J/ψ and ψ(2S) as a function of multiplicity. The results are compared to the calculation from the comover model, which suggests a stronger suppression for the ψ(2S) relative to J/ψ as a function of multiplicity. The comover model calculations are compatible with the data within uncertainties. The limited statistics prevents us from ruling out or drawing conclusions about possible final state effects.

The LHC Run 3 data-taking will provide higher luminosity to the experiments. This will allow us to perform measurements with higher precision. ALICE has been upgraded to cope with the increase of the collision rate. One of the main upgrades is the replacement of the electronics of the sub-detectors to enable ALICE to read out all Pb-Pb collisions at a high interaction rate. The main contribution of this thesis to the Run 3 data-taking is the development of the tools required to study the systematic uncertainty related to the tracking efficiency of the muon tracking chambers. We present the tracking efficiency of the muon tracking detector, both in bins of p T , η, and φ, and integrated. The comparison between the tracking efficiency computed from ideal simulations and data from Run 3 is also presented. Such comparison is needed to assess the systematic uncertainty on the tracking efficiency when the anchored simulations will be available. ALICE aims at collecting 50 nb -1 of p-Pb collisions as well as 200 pb -1 of pp collisions during Run 3 and 4 [107]. This luminosity increase will enhance the precision of measurements, particularly in the case of pp collisions, where the statistical uncertainty is expected to be reduced ∼ 3 times compared to Run 2 for the multiplicity-dependent charmonium production. In addition, the larger luminosity will allow us to reach higher multiplicity events, where MPIs are expected to play a more prominent role. Furthermore, with the new muon forward tracker, we are able to separate the charmonia produced at the primary vertex and those originating from B-hadron decays. For multiplicitydependent analysis, this will provide deeper insights into the behavior of charmonia and beauty-flavored hadrons as a function of multiplicity relative to currently available measurements.

B Fit description and tail parameters

The functions used to delineate the signal lineshape are the so called extended Crystal-Ball and extended NA60 functions.

B.1 Extended Crystal-Ball

The extended Crystal-Ball (CB) has seven parameters: normalisation factor N , two Gaussian core parameters (mean x and width σ), and four tail parameters (α, n, α′ and n′). The function is defined as:

f (x) = N •          exp -(x-x) 2 2σ 2 for α′ > (x-x) σ > -α A • B -(x-x) σ -n for (x-x) σ ≤ -α C • D + (x-x) σ -n ′ for (x-x) σ ≥ α ′ (B.

D ψ(2S) raw yields in multiplicity intervals

Introduction 1 . 1

 11 The Standard Model of particle physics and Quantum Chromodynamics The Standard Model (SM) is the cornerstone of our understanding of the fundamental constituents of Nature. It provides a comprehensive framework for describing elementary particles and their interactions. Fig.1.1 presents an overview of the particles in the SM. The SM classifies elementary particles into four types: two families of spin-1 /2 fermions (leptons and quarks), one family of spin-1 bosons known as gauge bosons (which serve as force carriers), and a spin-0 particle called the Higgs boson. The quarks consist of three generations: the first (and lighter) is made up of up (u) and down (d) quarks, the second of charm (c) and strange (s) quarks, the third of top (t) and bottom (b)

Figure 1 . 1 :

 11 Figure 1.1: The standard model of elementary particles [1].

1. 1 Figure 1 . 2 :

 112 Figure 1.2: Summary of measurements of the QCD coupling constant α s as a function of the energy scale Q [5].

Figure 1 . 3 :

 13 Figure 1.3: Conceptual drawing for the QCD phase diagram [8].

1. 2 Figure 1 . 4 :

 214 Figure 1.4: Schematic representation of the time evolution of a heavy-ion collision. Taken from [8].

Figure 1 . 5 :

 15 Figure 1.5: Conceptual drawing of a heavy-ion collision which describes the origin of the collective flow. Taken from Ref.[23].

Fig. 1

 1 .6 presents the ratio of strange hadrons yield to pions as a function of charged-particle multiplicity. The plot compares the results obtained by the ALICE collaboration from pp at s = 7 TeV, p-Pb at s NN = 5.02 TeV, and Pb-Pb at s NN = 2.76 TeV depicted in closed circles, diamond,

Figure 1 . 6 :

 16 Figure 1.6: Ratios of strange to pion yields (π + π -) as a function of charged-particle multiplicity measured at midrapidity |y| < 0.5. The presented results are shown for pp, p-Pb, and Pb-Pb systems at s = 7 TeV, s NN = 5.02 TeV and s NN = 2.76 TeV, respectively[START_REF] Adam | Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions[END_REF][START_REF] Abelev | Multiplicity Dependence of Pion, Kaon, Proton and Lambda Production in p-Pb Collisions at s N N = 5.02 TeV[END_REF][START_REF] Abelev | Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at s N N = 2.76 TeV[END_REF]. The results are compared to the calculations from PYTHIA8, DIPSY, and EPOS LHC[START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF][START_REF] Pierog | EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider[END_REF][START_REF] Bierlich | Effects of color reconnection on hadron flavor observables[END_REF].

Figure 1 . 7 :

 17 Figure 1.7: 2D particle correlation in p-Pb collisions s NN = 5.02 TeV for pairs of chargedparticles with 1 < p T < 3 GeV/c for particles with multiplicity (a) N t r k < 35, (b) N t r k ≥ 110 [29].

Figure 1 .

 1 Figure1.12: The ratios of the Υ(2S)-over-Υ(1S) and Υ(3S)-over-Υ(1S), with p T > 0 GeV, as a function of the number of tracks (N track ) in various collision systems. The lines are fits to the data with an exponential function. The vertical error bars represent the combined statistical and systematic uncertainties on the bottomonia ratio, while the horizontal error bars represent the uncertainty on N track[START_REF] Chatrchyan | Event Activity Dependence of Y(nS) Production in s N N =5.02 TeV pPb and s=2.76 TeV pp Collisions[END_REF][START_REF] Sirunyan | Investigation into the event-activity dependence of Υ(nS) relative production in proton-proton collisions at s = 7 TeV[END_REF].

Figure 2 . 1 :

 21 Figure 2.1: The CERN accelerator complex.

  ity. Second, central barrel detectors at mid-rapidity are important for reconstructing and identifying the trajectories of charged hadrons, photons, and electrons. Third, the muon spectrometer, at forward rapidity, reconstructs and identifies muons. The muon spectrometer aims to measure the production of heavy quark resonances, open heavy flavor decays, and Z-bosons down to zero transverse momentum (p T ). Fig.2.2 presents the sub-detectors of ALICE during the Run 2 data-taking period. Only the main sub-detectors are outlined in the following subsections.

Figure 2 . 2 :

 22 Figure 2.2: ALICE detector schematic during Run 2, superimposed a zoom-in of the region close to the interaction point.

Figure 2 . 3 :

 23 Figure 2.3: The ALICE muon spectrometer. The figure shows the absorbers, the tracking, and the trigger systems. The red lines depicted in the figure define the muon spectrometer acceptance [76].

Figure 2 . 4 :

 24 Figure 2.4: A schematic view of the quadrant and slat structures.

Figure 2 . 5 :

 25 Figure 2.5: Schematic cross section of a MWPC.

Figure 2 . 6 :

 26 Figure 2.6: Working principle of the muon trigger system algorithm to estimate the tracks p T (figure from Ref.[77]).

Figure 3 . 1 :

 31 Figure 3.1: Schemes of the two configurations for p-Pb collisions. On the left is the forward rapidity configuration, where the proton beam is directed towards the muon spectrometer. On the right panel, the backward rapidity configuration, in which the lead beam is directed towards the muon spectrometer.

•

  CMSL7-B-NOPF-MUFAST (CMSL7) is a single muon low p T trigger. It requires the detection of at least one muon having an online p µ T ≳ 0.5 GeV/c in coincidence with a signal in the V0A and V0C detectors. This trigger is used to evaluate the normalization factor correction for the charmonium yields. • CMUL7-B-NOPF-MUFAST (CMUL7) is a dimuon low p T trigger cut. It requires the detection of two muons of opposite charge having both an online p µ T ≳ 0.5 GeV/c in coincidence with a signal in the V0A and V0C detectors. This trigger is used to extract the charmonium raw yields.

Figure 3 .Figure 3 . 2 :

 332 Figure 3.2 presents the distributions of the correlation between N cl and N tr in the forward

Figure 3 .

 3 Figure 3.3 presents the average number of tracklets < N tr > as a function of the z-coordinate of the primary vertex in the SPD. The blue points in the figure show a dependence of the raw number of tracklets on the z-coordinate of the vertex. However, we would expect the

2 .

 2 figure represent the profile of the N ch on the 2D distribution, while the lines represent the functions used to fit the distribution.

Figure 3 . 4 :

 34 Figure 3.4: 2D correlation of charged-particle multiplicity and corrected number of tracklets simulated by DPMJET for forward (backward) rapidity region in the top (bottom) panel.

2 .

 2 Linear fit to the 2D distribution with free parameters at the origin

. 7 .

 7 The values of the systematic uncertainties in each bin for both forward and backward rapidity regions are tabulated in Tab.3.1.

  (a) Forward rapidity (b) Backward rapidity

Figure 3 . 5 :

 35 Figure 3.5: Extracted N ch values in each N corr bin for each fit function, for the forward rapidity in the top panel and the backward rapidity in the bottom panel.

  (a) Forward rapidity (b) Backward rapidity

Figure 3 . 6 :

 36 Figure 3.6: Ratio of N ch extracted from the different fits to the corresponding value extracted from the projection of N corr on the N ch axis in each N corr bin.

Figure 3 . 7 :

 37 Figure 3.7: Ratio of N ch extracted from the different fits to the corresponding value extracted from second-order polynomial in each multiplicity interval, for both (a) forward rapidity and (b) backward rapidity. The maximum spread of N ch from unity is considered as the systematic uncertainty.

Figure 3 . 8 :

 38 Figure 3.8: The set of tails used when fitting the signal shape with (a) CB2 on the top panel or with (b) NA60 function on the bottom panel.

[ 1 . 7 , 4 . 8 ]

 1748 GeV/c 2 and [2.0-5.0] GeV/c 2 . Taking into account all the aforementioned fit configurations, the number of tests performed in a given multiplicity interval with the CB2 signal shape is: 5 tails × 2 widths × 2 backgrounds × 2 invariant mass ranges = 40, and with the NA60 signal shape: 2 tails × 2 widths × 2 backgrounds × 2 invariant mass ranges = 8. A total of 40 + 8 = 48 different fit configurations are used to extract charmonium raw yields and their uncertainties. An example of the dimuon invariant mass fit is displayed in Fig.3.9 for the integrated multiplicity interval in p-Pb collisions at s NN = 8.16 TeV at the forward (backward) rapidity region in the top (bottom) panel. The figure shows the J/ψ and ψ(2S)

Figure 3 . 9 :

 39 Figure 3.9: Invariant-mass distribution of opposite-sign muon pairs in (a) forward and (b)backward rapidity, integrated in multiplicity[START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. Superimposed is a typical fit function, shown as a solid blue line (see text for details). The J/ψ and ψ(2S) contributions are shown as red and yellow shaded areas, respectively. The background is depicted as a dashed grey line. The inset shows the region of the ψ(2S) mass.

Figure 3 .

 3 Figure 3.10: J/ψ raw yields as a function of the fit configuration for forward rapidity in the top panel, and for backward rapidity in the bottom panel. The yields are extracted over integrated multiplicity, p T , and y.

Figure 3 .

 3 Figure 3.11: ψ(2S) raw yields as a function of fit configuration for forward (backward) rapidity in the top (bottom) panel. The yields are extracted over integrated multiplicity, p T , and y.

Figure 3 . 12 :

 312 Figure3.12: Dimuon trigger normalization factor at forward and backward rapidity as a function of the run number. The normalization factor in this plot is evaluated using the indirect offline (F off2,i norm ) method over the integrated multiplicity.

Figure 3 . 14 :Figure 3 . 15 :Figure 3 . 16 :

 314315316 Figure 3.14: Result of the iterative procedure for the J/ψ A × ε for each multiplicity interval at forward (a) and backward (b) rapidity.

4 4 . 1

 41 Results and discussion on multiplicity dependence of charmonium productionIn this chapter, we present the measurement of the self-normalized charmonium (J/ψ and ψ(2S)) yields as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV, using the ALICE detector at the LHC (CERN). The charmonium yields are measured at forward (2.03 < y cms < 3.53) and backward (-4.46 < y cms < -2.96) rapidity regions in their decay channel into dimuon, while the charged-particle multiplicity is measured at midrapidity (|y lab | < 1). The multiplicity dependent measurement of the charmonium yields and the excited-over-ground state ratio in p-Pb collisions are discussed in the first section. The comparison to the available model calculations is displayed for each measurement. In the second section, the measurements of the multiplicity dependence of the charmonium and bottomonium yields in pp collisions are reported. The third section discusses the open-heavy flavor multiplicity dependent measurements in pp collisions. Charmonium multiplicity dependence in p-Pb collisions at s NN = 8.16 TeV4.1.1 ψ(2S) resultsThe measured ψ(2S) self-normalized yields, in p-Pb collisions at s NN = 8.16 TeV, are presented in Fig.4.1 as a function of midrapidity (|y lab | < 1) charged-particle multiplicity.

Figure 4 . 1 :

 41 Figure 4.1: ψ(2S) self-normalized yields as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV. The yields are measured at the forward (backward) rapidity region depicted with the blue (red) marker. The vertical error bars represent the statistical uncertainties of the yields, whereas the width and the height of the box give the systematic uncertainty of the multiplicity and the yields, respectively. The dashed line is the one-to-one correlation between the x-and y-axis to guide the eye.

Fig. 4 . 2 ,

 42 Fig.4.2, the percolation + comover + EPS09 model describes the multiplicity dependence of the self-normalized ψ(2S) production within uncertainties at both forward and backward rapidity.

Figure 4 . 2 :

 42 Figure 4.2: Self-normalized ψ(2S) yields as a function of self-normalized charged-particle multiplicity from p-Pb collisions at s NN = 8.16 TeV [83], for ψ(2S) measured at (a) forward rapidity, and (b) backward rapidity in the top and bottom panel, respectively. The results are compared to the percolation + comover + EPS09 model calculation[START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Ferreiro | High multiplicity pp events and J /ψ production at LHC[END_REF][START_REF] Armesto | Percolation approach to quark -gluon plasma and J / psi suppression[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF][START_REF] Eskola | EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions[END_REF][START_REF] Paukkunen | Nuclear PDFs Today[END_REF].

Figure 4 . 3 :

 43 Figure 4.3: Self-normalised J/ψ yields as a function of midrapidity charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV [63], for the measurement performed at forward (backward) rapidity presented in blue (red) points in the figure. The vertical lines present statistical uncertainty, while the box is systematic. The dashed line represents the one-toone correlation to guide the eye.

Figure 4 . 4 :

 44 Figure 4.4: Self-normalized J/ψ yields as a function of self-normalized charged-particle multiplicity, measured at midrapidity, in p-Pb collisions at s NN = 8.16 TeV compared to the EPOS 3 event generator calculation[START_REF] Drescher | Parton based Gribov-Regge theory[END_REF][START_REF] Werner | Analysing radial flow features in p-Pb and p-p collisions at several TeV by studying identified particle production in EPOS3[END_REF]. The measurement in a (b) presents the J/ψ yields extracted at forward (backward) rapidity.

Figure 4 . 5 :

 45 Figure 4.5: Comparison between the results for the J/ψ normalized yields obtained for this thesis multiplicity intervals and Ref.[START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF].

Comover

Figure 4 . 6 :

 46 Figure 4.6:The self-normalized ψ(2S)-over-J/ψ yields as a function of self-normalized charged-particle multiplicity from p-Pb collisions at s NN = 8.16 TeV, for the forward rapidity region in the top panel and backward rapidity region in the bottom panel[START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. The results are compared to the comover model calculations[START_REF] Ferreiro | Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers[END_REF][START_REF] Esposito | The nature of X(3872) from high-multiplicity pp collisions[END_REF].

Figure 4 .

 4 Figure 4.10 presents the comparison of J/ψ self-normalized yields as a function of chargedparticle multiplicity in pp, p-Pb and Pb-Pb collisions at various center-of-mass energies

Figure 4 . 10 :

 410 Figure 4.10: Normalized yield of inclusive J/ψ as a function of the normalized chargedparticle pseudorapidity density, measured at midrapidity, in various collision systems. The pp results are normalized to INEL collisions[START_REF] Abelev | J /ψ Production as a Function of Charged Particle Multiplicity in pp Collisions at s = 7 TeV[END_REF], whereas p-Pb ones refer to the NSD event class[START_REF] Acharya | J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at s NN = 8.16 TeV[END_REF]; all for p T > 0. The Pb-Pb data points include J/ψ with 0.3 < p T < 12 GeV/c to reduce the low-p T contribution from photoproduction, which is significant only in more peripheral collisions[START_REF] Acharya | Studies of J/ψ production at forward rapidity in Pb-Pb collisions at s NN = 5.02 TeV[END_REF][START_REF] Adam | Measurement of an excess in the yield of J /ψ at very low p T in Pb-Pb collisions at s NN = 2.76 TeV[END_REF][START_REF] Acharya | Coherent J/ψ photoproduction at forward rapidity in ultra-peripheral Pb-Pb collisions at s NN = 5.02 TeV[END_REF]. The vertical bars represent the statistical uncertainties, and the boxes are the systematic ones. The dashed line indicates the one-to-one correlation, to guide the eye.

  ψ(2S)-over-J/ψ

Figure 4 .

 4 Figure 4.11: (a) The normalized ψ(2S) yield as a function of the normalized chargedparticle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV [83]. Quoted is the correlated event-class normalization uncertainty. (b) Ratio of normalized ψ(2S)-over-J/ψ yield as a function of the normalized chargedparticle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV [83]. The pp results are normalized to the INEL>0 event class, whereas the p-Pb ones refer to the NSD one.

Fig. 4 . 100 4Figure 4 . 13 :

 4100413 Fig.4.15(a) presents the self-normalized average yields of prompt D 0 , D + and D * as a function of charged-particle multiplicity, measured at |η| <1, in pp collisions at s = 13 TeV. On the left panel, the D-meson yields are displayed in different p T intervals. The measurement shows a yield increase as a function of charged-particle multiplicity in all the

Figure 4 . 14 :

 414 Figure 4.14: The normalized Υ(2S)-over-Υ(1S) yields as a function of N tracks / < N tracks > measured at midrapidity in pp collisions at s = 2.76 TeV. The figure is taken from Ref.[96].

Figure 4 . 15 :

 415 Figure 4.15: Self-normalized D 0 , D + and D * yields as a function of charged-particle multiplicity in pp collisions at s = 13 TeV at midrapidity. (a) The yields are shown in different intervals of p T , (b) The multiplicity dependence of D 0 , D + and D * self-normalized yields, for the p T interval 2 < p T < 4 GeV/c, compared to the self-normalized J/ψ yields with p T < 4 GeV/c, and compared to the heavy flavor decay electrons yields with 3 < p T < 6 GeV/c.

Figure 5 . 1 :

 51 Figure 5.1: ALICE detector schematic after the LS2. Superimposed a zoom-in of the region close to the interaction point.

Figure 5 . 2 :

 52 Figure 5.2: The layout of the ITS detector during Run 3.

  The system consists of 5 stations, each composed of two chambers. The first two stations are based on a quadrant structure, while the last three are based on a slat structure. Significant modifications have been implemented in the electronics of the MCH to accommodate the continuous readout scheme for Run 3. However, the overall detector implementation and the physical location and layout of its electronics have remained unchanged. The diagram shown in Fig.5.3 depicts the muon tracking system's electronics. The signal originating from the Front-End Electronics (FEE) is transmitted to the GigaBite Transceiver (GBT) readout card, which multiplexes 40 FEE signal outputs into a single gigabit serial stream. This stream is then directed to the Common Readout Unit (CRU). The CRUs are interconnected with the online computing system (O2) through the DDL3 interfaces, enabling the transmission of detector data to the O2 and receiving DCS (Detector Control System) information from it[START_REF] Antonioli | Upgrade of the ALICE Readout & Trigger System[END_REF].

Figure 5 . 3 :

 53 Figure 5.3: Schematic of the ALICE muon tracking chambers electronics during Run 3 [102].

3 .

 3 Steps 1 and 2 are repeated with the clusters in station 4.4. The track candidates of station 4 (5) are extrapolated to station 5 (4). The algorithm looks for at least one compatible cluster in the other station to validate the candidate.

8 .

 8 The MCH tracks are matched to the track segments reconstructed in the MID detector.The MID track segment must belong to the same time period as the MCH track within some uncertainty related to the MCH tracks cluster time dispersion (around ±4 bunch crossings). The MCH-MID track is extrapolated to the primary vertex reconstructed by the ITS detector. The tracks that are out of the spectrometer acceptance or do not pass the momentum cuts are rejected. At this step in Run 3, the reconstructed track is called a muon standalone track. 9. The muon tracks are matched to the track segments reconstructed in the Muon Forward Tracker, i.e., MFT standalone tracks. Only the tracks that pass the impact parameter and the momentum cuts, and those within the MFT acceptance are kept. In cases where no MFT track can be matched, the track is labeled as an MCH-MID track, and the track parameters are updated. 10. Finally, the remaining tracks are extrapolated to the primary vertex reconstructed by the ITS detector. The final tracks are called global muon tracks.

Figure 6 . 1 :

 61 Figure 6.1: Scheme of the track types reconstructed in the muon spectrometer in Run 3. The sketch is taken from Ref.[106].

Figure 6 . 2 :

 62 Figure 6.2: Conceptual drawing showing the possible responses of the MCH chambers to a track. The sketch is taken from Ref.[105].

Figure 6 .Figure 6 . 3 :

 663 Figure 6.3: The tracking efficiency of the MCH chambers vs. chamber ID extracted from a sample of pp collisions at s = 13.6 TeV.

Figure 6 . 4 :

 64 Figure 6.4: The tracking efficiency of the MCH stations vs. station ID and of full MCH extracted from a sample of pp collisions at s = 13.6 TeV.

Figure 6 . 5 :

 65 Figure 6.5: The tracking efficiency of the MCH tracking chambers vs. chamber ID. The efficiency for each chamber is shown in six intervals of p T .

Figure 6 . 6 :

 66 Figure 6.6: The tracking efficiency of the MCH tracking stations vs. station ID. The efficiency for each station is shown in six intervals of p T . The last bin of the figure shows the MCH detector efficiency.

Figure 6 . 7 :

 67 Figure 6.7: The tracking efficiency of the MCH tracking chambers vs. chamber ID. The efficiency for each chamber is shown in four intervals of η.

Figure 6 . 8 :

 68 Figure 6.8: The tracking efficiency of the MCH tracking stations vs. station ID. The efficiency for each station is shown in four intervals of η. The last bin of the figure shows the MCH detector efficiency.

Figure 6 . 9 :

 69 Figure 6.9: The tracking efficiency of the MCH tracking chambers vs. chamber ID. The efficiency for each chamber is shown in four intervals of azimuthal angle φ.

Figure 6 . 10 :

 610 Figure 6.10: The tracking efficiency of the MCH tracking stations vs. station ID. The efficiency for each station is shown in four intervals of azimuthal angle φ. The last bin of the figure shows the MCH detector efficiency.

Figure 6 . 11 :

 611 Figure 6.11: MCH chambers tracking efficiency as a function of η and φ.

Figure 6 . 12 :

 612 Figure 6.12: Plots from Quality Control for run 523306 showing the 2D x-y distribution of fired pads. The top part (a) shows chambers 1, 2, 3 and 4 bending planes on the first line and non-bending planes on the second line. The top part (b) shows chambers 5, 6, 7, 8, 9 and 10 bending planes on the first line and non-bending planes on the second line.

Figure 6 . 13 :Fig. 6 .

 6136 Figure 6.13: The tracking efficiency of the MCH chambers vs. chamber ID extracted from an ideal MC simulation for pp collisions at s = 13.6 TeV.

Figure 6 . 14 :

 614 Figure 6.14: The tracking efficiency of the MCH chambers vs. station ID extracted from an ideal MC simulation for pp collisions at s = 13.6 TeV. The last bin of the figure presents the MCH detector efficiency.

  c h a m b e r 1 c h a m b e r 2 c h a m b e r 3 c h a m b e r 4 c h a m b e r 5 c h a m b e r 6 c h a m b e r 7 c h a m b e r 8 c h a m b e r 9 c h a m b e r 1

Figure 6 . 15 :

 615 Figure 6.15: The tracking efficiency of the MCH tracking chambers vs. chamber ID. The efficiency for each chamber is shown in four intervals of p T . The results are obtained with an ideal MC for pp collisions at s = 13.6 TeV.

Figure 6 . 16 :Figure 6 . 17 :

 616617 Figure 6.16: The tracking efficiency of the MCH tracking chambers vs. chamber ID. The efficiency for each chamber is shown in four intervals of η. The results are performed with an ideal MC for pp collisions at s = 13.6 TeV.

Figure 6 . 18 :

 618 Figure 6.18: MCH chambers tracking efficiency as a function of η and φ from ideal MC simulation for pp collisions at s = 13.6 TeV. The presented plots are for chambers 1 and 10.

c h a m b e r 1 c h a m b e r 2 c h a m b e r 3 c h a m b e r 4 c h a m b e r 5 c h a m b e r 6 c h a m b e r 7 c h a m b e r 8 c h a m b e r 9 c h a m b e r 1 Figure 6 . 19 :

 1619 Figure 6.19: Comparison between MCH chamber efficiency extracted from ideal MC (in red) and the one extracted from data (in blue) for pp collisions at s = 13.6 TeV.

Figure 6 . 20 :

 620 Figure 6.20: Comparison between MCH station efficiency extracted from ideal MC (in red) and the one extracted from data (in blue) for pp collisions at s = 13.6 TeV.

Figure C. 3 :

 3 Figure C.3: Number of J/ψ for the forward rapidity in multiplicity intervals.

Fig. D. 1 ,

 1 Fig. D.1, D.2, D.4, D.5 and D.6 report the fit results for ψ(2S) in all multiplicity intervals for both periods.

Figure D. 1 :

 1 Figure D.1: Number of ψ(2S) for the forward rapidity in multiplicity intervals.

Figure D. 2 :

 2 Figure D.2: Number of ψ(2S) for the forward rapidity in multiplicity intervals.

Figure D. 3 :

 3 Figure D.3: Number of ψ(2S) for the forward rapidity in multiplicity intervals.

  Figure D.4: Number of ψ(2S) for the backward rapidity in multiplicity intervals.

Figure D. 6 :

 6 Figure D.6: Number of ψ(2S) for the backward rapidity in multiplicity intervals.

Table of contents

 of 6.4 Tracking efficiency studies in Monte Carlo . . . . . . . . . . . . . . . . . . . . . 126 6.4.1 Integrated MCH tracking efficiency . . . . . . . . . . . . . . . . . . . . . 126 6.4.2 Tracking efficiency as a function of p T , η, and φ . . . . . . . . . . . . . . 127 6.4.3 2D tracking efficiency studies per MCH chamber . . . . . . . . . . . . . 127 6.5 Systematic uncertainty determination . . . . . . . . . . . . . . . . . . . . . . . . 130

IV Conclusion 7 Conclusion A Data set run numbers B Fit description and tail parameters

B.1 Extended Crystal-Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 B.2 Extended NA60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 C J/ψ raw yields in multiplicity intervals D ψ(2S) raw yields in multiplicity intervals Bibliography xii

Table 3 .

 3 1: Systematic uncertainty on the N ch -N corr correlation for the forward and backward rapidity regions. The uncertainty is obtained by comparing the values extracted from the second-order polynomial and those extracted from the other fit functions. The maximum spread of the values is assigned as systematic uncertainty.

	Forward rapidity region Backward rapidity region
	N corr bin	syst.(%)	N corr bin	syst.(%)
	1-20	3.66	1-18	3.99
	21-32	1.01	19-27	1.4
	33-40	0.43	28-41	0.53
	41-48	0.30	42-50	0.27
	49-64	0.59	51-59	0.55
	65-300	1.61	60-73	1.05
			74-102	1.84
			103-350	3.11

3.3.3 Average charged-particle multiplicity (<dN ch dη>) in the integrated

N corr bin

The < dN ch dη > is measured in an independent analysis performed in p-Pb collisions at s NN = 8.16 TeV (see Ref.

[START_REF] Zaccolo | Charged-Particle Multiplicity Distributions over Wide Pseudorapidity Range in Proton-Proton and Proton-Lead Collisions with ALICE[END_REF]

). In this analysis, the average charged-particle multiplicity is extracted from p-Pb collisions at s NN = 8.16 TeV in the rapidity range |η lab | < 1. The obtained values and their systematic uncertainties are presented in Tab.3.2.

Table 3 .

 3

2: 〈dN ch /dη〉 at midrapidity in |η lab | < 1.

Table 3 .

 3 3: Systematic uncertainty sources on the charged particle multiplicity measurement.

	3.3.

Table 3 . 4

 34 3.4.

		Forward rapidity region	Backward rapidity region
	N corr 〈N corr 〉 〈N ch 〉	dN ch /dη 〈dN ch /dη〉	N corr	〈N corr 〉 〈N ch 〉	dN ch /dη 〈dN ch /dη〉
	1-20	10.4	13.47	0.33	1-18	9.50	12.40	0.31
	21-32	26.85	33.76	0.83	19-27	23.42	29.78	0.73
	33-40	36.90	46.07	1.13	28-41	34.73	43.76	1.08
	41-48	44.88	55.78	1.37	42-50	46.33	58.00	1.43
	49-64	56.35	69.66	1.72	51-59	55.29	68.91	1.70
	65-300 83.95 102.64	2.53	60-73	66.38	82.32	2.03
					74-102	85.26 104.93	2.58
					103-350 118.24 143.65	3.53

: Mean number of corrected tracklets (〈N corr 〉), average charged particle multiplicity (〈N ch 〉), and corresponding relative charged particle multiplicity dN ch /dη 〈dN ch /dη〉 in p-Pb collisions.

Table 3 .

 3

		Forward rapidity region			Backward rapidity region
	N cor r bin	N J/ψ ± stat ± syst	N cor r bin	N J/ψ ± stat ± syst
	0-300	133720 ± 626 ± 4868		0-350	194020± 759±7087
	1-20	16082 ± 203(1.26%) ± 568 (3.53%)	1-18	14037± 187(1.33%) ± 489(3.48%)
	21-32	19915 ± 232 (1.17%) ± 709 (3.56%)	19-27	16306± 204(1.25%) ± 578(3.54%)
	33-40	15800 ± 212 (1.34%) ± 580(3.67%)	28-41	34020± 304(0.89%) ± 1216(3.57%)
	41-48	15594 ± 213 (1.36%) ± 572(3.67%)	42-50	25093± 265(1.06%) ± 909(3.62%)
	49-64	27525± 285(1.03%) ± 1028(3.73%)	51-59	23736± 266(1.12%) ± 853(3.59%)
	65-300	38754 ± 352(0.91%) ± 1430(3.69%)	60-73	31013± 312(1.01%) ± 1129(3.64%)
			74-102	36449± 346(0.95%) ± 1361(3.73%)
			103-350	13182± 218(1.65%) ± 518(3.93%)
	Σ in bins	133670	Σ in bins	193836
	∆	50		∆	184
		Forward rapidity region		Backward rapidity region
	N cor r bin	N ψ(2S) ± stat ± syst	N cor r bin	N ψ(2S) ± stat ± syst
	0-300	2301 ± 212 ± 277	0-350	2721 ± 247 ± 347
	1-20	290 ± 61(21%) ± 34 (11.8%)	1-18	206± 51(24.7%) ± 29(14.2%)
	21-32	325 ± 76 (23.3%) ± 43 (13.3%)	19-27	224± 59(26.5%) ± 32(14.3%)
	33-40	371 ± 75 (20.3%) ± 36 (9.6%)	28-41	393± 92(23.4%) ± 63 (16.0%)
	41-48	311 ± 80 (25.7%) ± 38 (12.3%)	42-50	385± 84(21.7%) ± 49 (12.6%)
	49-64	456 ± 111 (24.4%) ± 58 (12.6%)	51-59	298 ± 91 (30.7%) ± 39 (13.0%)
	65-300	555 ± 131 (23.6%) ± 85 (15.3%)	60-73	417 ± 108 (25.9%) ± 54 (13.0%)
			74-102	542 ± 125 (23.07%) ± 78 (14.3%)
			103-350	235 ± 86 (36.4%) ± 36 (15.1%)
	Σ in bins	2308	Σ in bins	2700
	∆	7	∆		21

6: J/ψ raw yield integrated p T and y, in multiplicity intervals. Σ is the sum over all multiplicity intervals and ∆ is the difference between Σ and integrated result.

Table 3 .

 3 7: ψ(2S) raw yield integrated p T and y, in multiplicity intervals. Σ is the sum over all multiplicity intervals and ∆ is the difference between Σ and integrated result.

interval

(N tot

):

Table 3 .

 3 8: Relative J/ψ yield per multiplicity interval at forward and backward rapidity.

			65-300 0.2898 ± 0.0030 (1.02%) ± 0.0020 (0.69%)	49-64 0.2058 ± 0.0023 (1.14%) ± 0.0016 (0.80%)	41-48 0.1166 ± 0.0017 (1.44%) ± 0.0008 (0.67%)	33-40 0.1182 ± 0.0017 (1.42%) ± 0.0008 (0.66%)	21-32 0.1489 ± 0.0019 (1.26%) ± 0.0009 (0.56%)	1-20 0.1203 ± 0.0016 (1.34%) ± 0.0008 (0.63%)
	103-350 0.0680 ± 0.0012 (1.7%) ± 0.0010 (1.41%)	74-102 0.1878 ± (1.03%) 0.0019 ± 0.0016 (0.73%)	60-73 0.1598 ± 0.0017 (1.08%) ± 0.0010 (0.65%)	51-59 0.1223 ± 0.0015 (1.19%) ± 0.0008 (0.66%)	42-50 0.1293 ± 0.0015 (1.13%) ± 0.0009 (0.73%)	28-41 0.1754 ± 0.0017 (0.97%) ± 0.0011 (0.61%)	19-27 0.0840 ± 0.0011 (1.31%) ± 0.0006 (0.74%)	1-18 0.0724 ± 0.0010 (1.39% ± 0.0004 (0.6%)	± syst

Table 3 .

 3 11: Normalization factor measurement in the forward rapidity region.

	N corr	F off1 norm	F off2 norm	F off1 norm /F off2 norm
	0-300	680.67 ± 5.76	680.03 ± 1.53	1.001 ± 0.008
	1-20	2418.37 ± 45.06 2397.46 ± 14.33 1.009 ± 0.019
	21-32	892.28 ± 21.38	879.15 ± 5.23	1.015 ± 0.024
	33-40	649.83 ± 19.51	625.91 ± 4.18	1.038 ± 0.031
	41-48	494.66 ± 8.76	510.52 ± 3.26	0.969 ± 0.017
	49-64	410.93 ± 7.77	407.98 ± 2.47	1.007 ± 0.013
	65-300	281.24 ± 7.63	276.52 ± 1.13	1.017 ± 0.028
		Backward rapidity region
	N corr	F off1 norm	F off2 norm	F off1 norm /F off2 norm
	0-350	372.89 ± 1.14	372.59 ± 0.42	1.001 ± 0.003
	1-18	2517.31 ± 40.74 2484.21 ± 11.27 1.013 ± 0.016
	19-27	867.88 ± 10.96	843.36 ± 3.57	1.029 ± 0.013
	28-41	462.83 ± 3.63	463.17 ± 1.30	0.999 ± 0.008
	42-50	299.41 ± 2.68	296.95 ± 0.97	1.008 ± 0.009
	51-59	223.41 ± 1.96	222.95 ± 0.73	1.002 ± 0.009
	60-73	166.86 ± 1.23	165.95 ± 0.47	1.005 ± 0.007
	74-102	109.99 ± 0.72	110.31 ± 0.29	0.997 ± 0.007
	103-350	66.01 ± 0.80	65.45 ± 0.28	1.009 ± 0.012

Table 3 .

 3 [START_REF] Aamodt | Two-pion Bose-Einstein correlations in central Pb-Pb collisions at s N N = 2.76 TeV[END_REF]: Normalization factor measurements in the backward rapidity region.

	Run

Table 3 .

 3

		Forward rapidity		Backward rapidity
	N corr	A × ϵ	A×ϵ A×ϵ(integrated) .	N corr	A × ϵ	A×ϵ A×ϵ(integrated) .
	int.	0.2733	1.0	int.	0.2446	1.0
	1-20	0.2708	0.9908	1-27	0.2358	0.9638
	21-32 0.2727	0.9978	28-41 0.2478	1.0129
	33-40 0.2765	1.0117	42-50 0.2455	1.0035
	41-48 0.2702	0.9886	51-59 0.2474	1.0112
	49-64 0.2748	1.0054	60-88 0.2384	0.9744
	65-300 0.2737	1.0015	89-350 0.2455	1.0035

.

[START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF]

, and amounts to 3% and 6% for forward and backward rapidity ranges. These values are consistent with those obtained in multiplicity intervals. These results are summarized in Tab. 3.13. 13: Multiplicity dependence of J/ψ A × ϵ in the last iteration step. The ratio to the integrated value is also quoted.

Table 3 .

 3 14: NSD trigger efficiency in the measurement multiplicity intervals (in percentage).

	MB ∈	1.1
		1 1.05		0.989321	1		1	1	1		1
		0.95
		0.9
		0.85
		0.8	0.77529
		0.75
		0.7
		0.65
		0.6	0-0	1-20	21-32	33-40	41-48	49-64		65-300
											corr N	bin
						(a) Forward rapidity
	MB ∈	1.1
		1 1.05		0.988626	1	1	1	1	1	1	1
		0.95
		0.9
		0.85
		0.8	0.776543
		0.75
		0.7
		0.65
		0.6	0-0	1-18	19-27	28-41	42-50	51-59	60-73	74-102	103-350
											corr N	bin
						(b) Backward rapidity
				Figure 3.17: MB trigger efficiency in multiplicity intervals.

Table 3 .

 3

	Tab.3.15 summarizes the systematic uncertainties for ψ(2S) raw and relative yields. Similarly,
	Tab.3.16 summarizes the systematic uncertainties of the J/ψ-over-ψ(2S) raw and relative
	yields.
	sources		Forward rapidity region	Backward rapidity region
			raw yields	rel. yields	raw yields	rel. yields
	signal extraction	10-13% (11.8%) ⋄	4-8% ⋄	13-16% (12.8%) ⋄	5-13% ⋄
	F nor m		2.5%	-	2.5%	-
	bin-flow and pile-up		2.0%	2.0%	2.0%	2.0%
	vertex equalisation		2.1%	2.1%	2.1%	2.1%
	A × ϵ		1.0%	-	4.0%	-
	event class norm.		1.0%*	1.0%*	1.0%*	1.0%*
	sources		Forward rapidity region	Backward rapidity region
			raw yields	rel. yields	raw yields	rel. yields
	signal extraction		7-13% (9%) ⋄	4-8% ⋄	11-13% (10%) ⋄	5-12% ⋄
	F nor m		negl.	negl.	negl.	negl.
	bin-flow and pile-up	negl.	negl.	negl.	negl.
	vertex equalisation		negl.	negl.	negl.	negl.
	A × ϵ		1.0%	-	4.0%	-
	event class norm.		1.0%*	1.0%*	1.0%*	1.0%*
	Table 3.16: Summary of the systematic uncertainties for ψ(2S)-over-J/ψ. The * (⋄) marker
	points to the values that are (partially) correlated with multiplicity.

15: Summary of the systematic uncertainties for ψ(2S). The * (⋄) marker points to the values that are (partially) correlated with multiplicity.

Table B .

 B 1 summarises the parameters used for the Crystal-Ball tail description. In the table the tails extracted from data or MC are specified. The tails tagged as RA refer to those

	ψ J/ N raw
	:	38754	±			352 (0.91% , stat)	±	1430 (3.69% ,syst)
										1)
	where
			A =	n |α|	n	• exp -	|α| 2 2	,	B =	n |α|	-|α| ,
	C =	n′ |α′|		n	′ • exp -	|α′| 2 2	,	D =	n′ |α′|	-|α′| .

The acronym CERN was defined for the French appellation for Conseil Européen pour la Recherche Nucléaire.

See Sec.3.2.1 for the details about the trigger classes.

ESD stands for Event Summary Data.

AOD stands for Analysis Object Data, and is a filtered and reduced version of ESD.

Acknowledgement

I would like to express my deepest gratitude to all those who have contributed to the completion of this thesis. This journey would not have been possible without the support, guidance, and encouragement of many individuals.

First and foremost, I extend my heartfelt thanks to my supervisors Zaida Conesa del Valle and Christophe Suire. Thank you for the guidance, help, and support during these three years. Thank you both for your availability to discuss and to answer my questions and for your patience, especially when correcting my typos! I am also grateful to all the members of the ALICE group at IJCLab. Thank you Cynthia,

defense and for all the comments and suggestions you gave me.

I came for the first time to France via a collaboration between AN-Najah National

Data set run numbers

Two data sets periods are used in this analysis to extract the charmonia raw yields: the LHC16r is the data set for p-Pb at forward rapidity, while the LHC16s is the p-Pb at backward rapidity. The analysed data sample consists of the following run numbers:

• p-Pb period (LHC16r): 266318, 266316, 266312, 266305, 266304, 266300, 266299,

Dimuon acceptance times efficiency

This section investigates the possible variations of the A × ε as a function of charged-particle multiplicity. No A × ε variation is expected in p-Pb collisions in terms of detector occupancy. However, the p T , y distributions of the charmonium yields may change as a function of multiplicity which may lead to such effect [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. A data-driven iterative procedure is performed in order to tune the MC p T and y distributions to the ones extracted from the data. The A × ε is evaluated for the integrated multiplicity interval and for each multiplicity interval.

Due to the limited statistics of ψ(2S), it was not possible to extract p T and y distributions from data in all multiplicity intervals, and do the iterative procedure. As a consequence, the exercise was performed for J/ψ, and we assumed that the evolution of the A × ε as a function of charged-particle multiplicity is the same for both charmonium states. The flow chart of Fig. 3.13 illustrates the data-driven iterative procedure. First, the p T and y distributions are extracted from MC. Then, the initial value of the A × ε is evaluated as the ratio of the MC reconstructed to generated distributions. In order to tune the MC distributions on data, for each multiplicity interval, the J/ψ raw yields are extracted in five p T

Quarkonium multiplicity dependence in pp collisions

ψ(2S) results

The multiplicity dependence of the ψ(2S) self-normalized yields in pp collisions at s = 13 TeV is reported in Ref. [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. ψ(2S) mesons were reconstructed from their decay channel into dimuons in the rapidity interval 2.5 < y cms < 4.0, while the charged-particle multiplicity was measured at midrapidity |η cms | < 1. As shown in Fig. 4.7, the ψ(2S) self-normalized

(no CR)

ALI-PUB-525620 Figure 4.7: Self-normalized ψ(2S) yields, measured at forward rapidity, as a function of the midrapidity charged-particle multiplicity, in pp collisions at s = 13 TeV [START_REF] Acharya | Measurement of ψ(2S) production as a function of charged-particle pseudorapidity density in pp collisions at s = 13 TeV and p-Pb collisions at s NN = 8.16 TeV with ALICE at the LHC[END_REF]. The results are compared to PYTHIA 8.2 calculations with and without color reconnection [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF]. yields increase with charged-particle multiplicity. The resulting trend is compatible, within uncertainties, with a linear increase depicted with a dashed line in the figure. The result is compared to PYTHIA 8.2 calculations [START_REF] Sjostrand | An introduction to PYTHIA 8.2[END_REF], with and without color reconnection (CR). PYTHIA 8.2 event generator describes the charm quark production during the initial hard processes and with multiparton interactions (MPI). The number of charged particles produced is proportional to the number of events containing MPI. The color reconnection scenario represents the fusion of the final state partons. In Fig. 4

B.2 Extended NA60

The function has the following eleven parameters: normalisation factor N, two Gaussian core parameters (mean x and width σ), and eight tail parameters (α

. The function is defined as:

and