NLO Next to Leading Order. NN Neural Network. NRQCD Non-Relativistic QCD. PCA Point of Closest Approach. PDF Parton Distribution Function. pQCD Perturbative QCD. PSU Power Supply Unit. QFT Quantum Field Theory. QGP Quark-Gluon Plasma. RP Reaction Plane

Keywords: AOD Analysis Object Data, CEM Colour Evaporation Model, CNM Cold Nuclear Matter Slow Control Adapter, GUI Graphical User Interface, IP Interaction Point, LHC Large Hadron Collider, lQCD Lattice QCD, MCH Muon CHambers

I would like to take a moment to express my deepest appreciation to all of my friends who have been there, always, whether it was in person or virtually. You all have been a great source of motivation and optimism throughout this journey! I am deeply thankful to all of my family, in Lebanon and in France

everyone who has been a part of my journey over the past three years. I apologize as I may forget or not be able to recall each and every name. These years have been a time of immense learning, and I have been fortunate to encounter so many people who have inspired and guided me along the way.

To begin with, I would like to thank my thesis supervisors, Ginés, Guillaume, and Maxime. It was a great pleasure to have the opportunity to work with you! I am very grateful to Ginés for his constant support throughout this journey. He has always been ready to o er various ideas and advice, and he always managed to find time for our discussions, even with his demanding role as Subatech director. Thank you for your helpfulness and generosity in sharing your insights and knowledge! I would like to express my sincerest gratitude to Guillaume, who has supported me throughout these years, always equipped with the right advice to give! Guillaume's dedication and availability (even on evenings and weekends), has been invaluable to me. Our exchanges have been incredibly enriching and have allowed me to broaden my knowledge and understanding of our field. Thank you so much for this, for your continuous good mood and for your kindness! Last but not least, Maxime, I am very thankful for all the very long exchanges we had, and for always addressing all my questions and uncertainties. Indeed, very often my "do you have 5 minutes" exchanges would last for entire afternoons! These were essential in helping me navigate some of the challenging aspects of my research. Thank you for all the time and e ort you have devoted, for all the doubts you helped me clarify, and for all the laughs we shared, I am deeply appreciative! I want to thank immensely my thesis jury and reviewers for taking the time to read my manuscript and for all the insightful questions and constructive feedback. I am honored to have had the opportunity to present my work to such a distinguished panel of experts in our field. I am very grateful for the whole PLASMA team, with whom I was always able to discuss, and would always have advice to share with me! Their collaboration, expertise, and enthusiasm were iii critical to me! Thank you, Marie, Philippe, Diego, Rafael, Barbara, Emine, Laurent, Gilles and Alexandre for all the rich discussions we have shared, and for all the help you never hesitated to provide me with, I feel very lucky to have been a part of this team! I would also like to thank all of my colleagues in the ALICE collaboration, for always providing me with a stimulating and supportive work environment! Stefano, I want to express my gratitude for all the various ideas you always brought to my work. Your insight and creativity challenged me to always think from di erent angles, thank you! I would also like to thank Sarah for always following my work and for all the valuable advice she gave me! For all the people that I met at CERN and had so many interesting conversations with, Andry, and our passion for python, Charlotte, for your continuous encouragement whether at point 2 or on Duolingo. Thanks to everyone I have interacted and collaborated with in ALICE, and especially within the MFT team, it was a true pleasure! Of course, I want to extend my appreciation to my o ce colleague, Ophélie, who has always been there whether to share joy or to hear me complain, and with whom I always had rich and very passionate discussions. Thank you for making the o ce a warm space! I would also like to thank my fellow doctoral students/post-docs, Nicolas, Victor, Momo and Kunal, for the great atmosphere we have shared within the group! Bon courage for your journey! I want to also share my appreciation to all the colleagues with whom I interacted, worked, and discussed at Subatech, and with whom the CERN missions were always fun! Especially, thank you Stéphane, Stéphane, Christophe, Patrick, Patrice, Didier, Amanda, Farah, Meriadeg, Sophie, Véronique, Sara, and to everyone I came in contact with within these years in the Subatech halls! I want to give a special shoutout to all my fellow Subatech doctoral students and postdocs who have been my companions on this journey. Thank you, Stéphane, for the engaging conversations we've had over the years. It all began during my M1 internship at Grenoble, and I am very grateful for the opportunities we've had to discuss a wide, very wide, range of topics! Thank you, Quentin, for your constant optimism which was always uplifting, and for not giving up on encouraging me to do sports! Many thanks to Vincent, Grégoire, Arthur, Claudia, Johannes, Léonard, Johan, Mahbobeh, Maxime, Victor, Nadège, Tobie, Alexander, Eamonn, Etienne, Michael, Keerthana, and Yajing! We've shared countless conversations, co ee breaks, and laughs that have added enjoyment to the hours spent in the lab! I am very grateful for the friendships that we've formed and the support that we've given each other.

Résumé en français 167

Bibliography

List of Figures 1.5 (left) Lattice QCD discrete space sketch [START_REF] Bi | Lattice QCD GPU Inverters on ROCm Platform[END_REF]. (right) Normalized pressure, energy and entropy density as a function of temperature, with the calculated prediction with a hadronic thermodynamical model HRG (Hadron Resonance Gas). The black horizontal line represents the energy density limit for an ideal gas, and the yellow band corresponds to the crossover region. [START_REF] Bazavov | Equation of state in (2+1)-flavor QCD[END_REF]. . . . . . . . . . . . . . . . (right) The interaction potential between q q as a function of their distance for di erent temperatures [START_REF] La | Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity[END_REF]. . . . . .

(left)

The nuclear modification factor of J/Â in Pb-Pb collisions [START_REF] Acharya | Studies of J/Â production at forward rapidity in Pb-Pb collisions at Ô sNN = 5.02 TeV[END_REF]. (right)

The elliptic flow v 2 of J/Â in Pb-Pb collisions [START_REF] Acharya | J/Â elliptic and triangular flow in Pb-Pb collisions at Ô sNN = 5.02 TeV[END_REF]. . . . . . . . . . . . . . . . .

(left)

The nuclear modification factor of Υ in Pb-Pb collisions [START_REF] Acharya | Υ production and nuclear modification at forward rapidity in Pb-Pb collisions at sNN=5.02TeV[END_REF]. (right) The elliptic flow v 2 of Υ in Pb-Pb collisions [START_REF] Acharya | Measurement of "(1S) Elliptic Flow at Forward Rapidity in Pb-Pb Collisions at sNN =5.02 TeV[END_REF]. . . . . . . . . . . . . . . . . . . . .

(left)

The nuclear modification factor of J/Â in p-Pb collisions [START_REF] Acharya | Inclusive J/Â production at forward and backward rapidity in p-Pb collisions at Ô sNN=8.16 TeV[END_REF]. (right) The nuclear modification factor of Υ in p-Pb collisions [START_REF] Acharya | Υ production in p-Pb collisions at sNN=8.16 TeV[END_REF]. . . . . . . . . . . . . .

2.10

The J/Âv 2 , in p-Pb at forward and backward rapidities and Pb-Pb at forward rapidity [START_REF] Acharya | Search for collectivity with azimuthal J/Â-hadron correlations in high multiplicity p-Pb collisions at sNN=5.02 and 8.16 TeV[END_REF]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.11

The inclusive (left) J/Â and (right) Â(2S) cross-section measurements as a function of the transverse momentum p T at forward rapidity pp collisions at Ô s = 5.02, 7, 8, and 13 TeV at the top, and the ratio of the 5.02, 7, and 8 TeV to [START_REF] Aoki | The QCD transition temperature: Results with physical masses in the continuum limit II[END_REF] TeV measurements at the bottom. Both figures are extracted from [START_REF]Inclusive quarkonium production in pp collisions at Ô[END_REF]. . . . . . 3.11 A full scheme of the online-o ine computing system [START_REF] Buncic | Technical Design Report for the Upgrade of the Online-Offline Computing System[END_REF]. . . . . . . . . . . . .

3.12

The di erent aspects of the online-o ine computing system [START_REF] Alkin | ALICE Run 3 Analysis Framework[END_REF]. . . . . . . . .

Introduction

Subatomic physics aims at describing matter and its behaviour at infinitesimal scales. The Standard Model defines the theoretical framework that describes the elementary particles and three out of the four fundamental forces. Elementary particles are divided into fermions, the constituents of matter, and bosons, the carriers of interactions. The fermions are divided into quarks and leptons. Quantum chromodynamics is the quantum field theory that describes the strong interaction, responsible for the strong nuclear force that is at the basis of nuclear structure. Gluons are the carriers of the strong interaction and quarks are the elementary particles forming all nuclear matter. In normal conditions, quarks and gluons are confined into nuclear matter; they cannot propagate freely like electrons or photons. Nevertheless, at high temperature and high energy density, there is a crossover to a new state of nuclear matter: the Quark-Gluon Plasma (QGP). This is a dense medium composed of strongly interacting matter within which quarks and gluons are free to move. Properties of the QGP can be studied with ultra-relativistic heavy-ion collisions by reproducing the necessary conditions in particle colliders such as the Large Hadron Collider (LHC).

The ALICE detector is located around one of the LHC collision points and specifically designed to study heavy-ion collisions. The measurement of inclusive quarkonium, an important probe of the QGP, is possible with ALICE down to p T = 0 GeV/c in two rapidity regions: midrapidity, through their dielectron decay channel using central detectors, and forward rapidity, through their dimuon decay channel with the muon spectrometer. The front absorber of the muon spectrometer has been designed to filter particles and let only muons pass through. The counterpart is that the multiple scattering within it prevents to have a good spatial resolution at the level of the interaction point. Hence, only inclusive measurements were possible during the first two data taking periods of LHC (Run 1 and Run 2). In order to overcome this limitation and to extend the ALICE physics program at forward rapidities, a new high-resolution tracking detector, the Muon Forward Tracker (MFT), has been designed starting in 2011 and was installed late 2020.

The MFT constitutes the context of this thesis during which the LHC was in a period xxiii known as the second long shutdown. During this period, the LHC was upgraded to increase its luminosity. A drastic change of the general readout system and online/o ine software of ALICE had to be made to cope with this increase. The work of this thesis is divided into two parts. The first one is hardware oriented. It concerns the validation of the board controlling and monitoring the powering of the MFT and the creation of software tools to communicate with it. The second part concerned the preparation of data analysis. First, new methods based on Machine Learning for the matching between tracks from the MFT and the muon spectrometer have been developed. Once the track matching is done, the pairing of muon tracks to extract J/Â has been improved. And finally the separation between prompt and non-prompt J/Â could be studied.

This document is divided into two parts, the first consists of an introductory part (from chapter 1 to 4), and the second is devoted to the work of this thesis and the obtained results (from chapter 5 to 8). Chapter 1 tackles a brief theoretical background, consisting of tools that allow the understanding of heavy-ion collisions. The J/Â probe is then introduced in chapter 2, notably the mechanisms responsible for its production are discussed, and its expected evolution in di erent collision systems. The ALICE apparatus for Run 3 is presented in detail in chapter 3, followed by a description of the MFT detector in chapter 4, both hardware-and software-wise. The power control of the MFT is presented in chapter 5, focusing on the software developments specific to the MFT commissioning and its adaptation to the framework of the MFT Detector Control System, which is the o cial Run 3 software that handles the full detector control. In chapter 6, machine learning techniques are applied to the track matching between the muon spectrometer and the MFT tracks. The purpose of this work is to improve the performances of the track matching. Muon tracks are then extracted after matching application. Information on the point of closest approach between the muon tracks is required for the separation of prompt and non-prompt J/Â contributions. Thus, chapter 7 describes the vertex reconstruction algorithm and its first assessments. Finally, quality evaluations with o cial Run 3 simulations are presented in chapter 8, with the goal of preparing the upcoming data taking and analysis. New measurements, which are now accessible with the MFT and as a result of developments introduced in previous chapters, are also presented.

Chapter 1

Physics of heavy-ion collisions Ultra-relativistic heavy-ion collisions constitute an essential tool for studying the properties of nuclear matter. The first chapter focuses on the physics of these collisions, where essential theoretical notions are addressed. The Standard Model (SM), the model that governs all physics and, in particular, in the microscopic and macroscopic worlds (the two infinities), is introduced first. It helps to understand our environment in-depth by describing how elementary particles and three forces are related to each other, omitting gravity 1 . Then Quantum ChromoDynamics (QCD) is introduced, which is the quantum field theory describing the strong interaction, one of the three forces of the SM responsible for the nuclear structure. At very high temperature or pressure, QCD predicts that the nuclear medium becomes a Quark-Gluon Plasma (QGP). The thermodynamic conditions of the Universe until 1 µs after the Big Bang correspond to those allowing the existence of a QGP. After this section, the most important aspects of collisions are presented, starting with the di erent collision systems, their space-time evolution, and their geometry. Finally, di erent experimental signatures of the QGP are discussed.

The Standard Model

The SM of particle physics describes the electromagnetic, weak, and strong interactions along with the particles that make up matter [START_REF] Workman | Review of particle physics[END_REF][START_REF] Halzen | Quarks and Leptons: An Introductory Course in Modern Particle Physics[END_REF]. According to this model, elementary particles are divided into three groups (Figure 1.1):

Fermions: particles with a spin of 1/2 from which matter is built. They are divided into two categories: quarks and leptons, each of which consists of six particles and their respective six anti-particles, and are classified based on how they interact, as the interactions are exerted between charges (electric, weak, and colour charges for the electromagnetic, weak and strong interactions respectively). The lightest and most stable particles form the first generation, while second and third generation particles decay rapidly due to the weak interaction. The three generations of quarks are the (up,down) quarks as the first generation, the (charm,strange) as the second generation, and the third generation is formed by the (top,bottom) quarks. Quarks have an electric charge of (+2/3 e) for (u, c, t), and of (-1/3 e) for (d, s, b); as for the anti-quarks, they possess the opposite electric charge. Quarks are the only fermions with a colour charge and thus are sensitive to the strong interaction. Additionally, they mix into colourless composite particles, known as hadrons, divided into baryons (composed of three quarks) and mesons (composed of a quark and an anti-quark). As for the three generations of leptons, the first is composed of the (e ≠ , ‹ e ), followed by (µ ≠ , ‹ µ ), and lastly the (• ≠ , ‹ τ ). e ≠ , µ ≠ and • ≠ leptons have negative electric charge, while anti-leptons have a positive electric charge. As for the ‹ e , ‹ µ and ‹ τ neutrinos (and their corresponding anti-neutrinos), they have a null electric charge.

Gauge bosons: particles with spin of 1. They are the carriers of interactions and are composed of the following elementary particles: ¶ Photons, carriers of electromagnetic interactions, can be exchanged between fundamental particles that have an electric charge. There is no direct interaction taking place between photons, since they are electrically neutral.

with Newton's gravitational constant G =6.70861 ◊ 10 ≠39 ~c (GeV/c 2 ) ≠2 and with the finestructure constant -= 1 4fiÁ 0 ◊ q 2 ~c = 1 137 [START_REF] Zyla | Review of particle physics[END_REF]. As one can observe, the intensity of the electromagnetic force is 43 orders of magnitude stronger than that of gravitation, making the gravitational e ects completely negligible at the subatomic scale.

The SM is constructed with Quantum Field Theory (QFT) [START_REF] Dasgupta | An introduction to quantum field theory[END_REF], based on symmetry principles, such as gauge invariance [START_REF] Yang | Conservation of isotopic spin and isotopic gauge invariance[END_REF], Lorentz invariance, and wave equations (Dirac, Maxwell, Yang-Mills, Klein-Gordon) [START_REF] Halzen | Quarks and Leptons: An Introductory Course in Modern Particle Physics[END_REF]. Gauge symmetries describe the interactions mentioned above. The gauge group of the SM is composed of SU(3) c ◊ SU(2) L ◊ U (1) Y , and can be classified as follows: ¶ SU(3) c , a unitary group at the basis of the quantum field theory of strong interactions known as the QCD [START_REF] Han | Three-triplet model with double SU(3) symmetry[END_REF], which will be described in the next section. ¶ SU(2) L ◊ U (1) Y , describes the electro-weak interaction, the unification of both electromagnetism and weak interaction. The Higgs mechanism was introduced to explain the unification between these two interactions [START_REF] Weinberg | Conceptual foundations of the unified theory of weak and electromagnetic interactions[END_REF] and the masses of the W and Z bosons (not yet measured at that time).

Quantum ChromoDynamics

The strong interaction taking place between partons, elementary particles carrying a colour charge, is described with quantum chromodynamics [8]. It is a non-abelian (non-commuting) quantum field theory, invariant under SU(3) Lie's group. The colour charge, forming the fundamental representation of a SU(3) symmetry group, are referenced after the three primary colours: red, green, and blue (R, G, B), and their respective anticolours: cyan, magenta, and yellow ( R, Ḡ, B). This quantum variable is deemed necessary after the formation of the quark model in order to respect Pauli's exclusion principle, which would have been violated while implementing the quark scheme for the ∆ ++ baryon (J=3/2): ∆ ++ = uuu, with each u quark having the same spin of J=1/2. Thus the colour charge allows to re-write its wavefunction as u R u G u B , preventing the violation of Pauli's exclusion principle. The interaction between colour charges is mediated by eight bicoloured gluons [START_REF] Halzen | Quarks and Leptons: An Introductory Course in Modern Particle Physics[END_REF], forming a SU(3) octet, as follows:

R Ḡ, R B, G R, G B, B R, B Ḡ, 1 Ô 2 (R R ≠ G Ḡ), 1 Ô 6 (R R + G Ḡ ≠ 2B B) (1.2)
Gluons, being coloured, can interact with each other. The R R+G Ḡ+B B state, being colourless (or white), has no interaction and thus has no existence. In the following, the Lagrangian of the QCD will be presented. It describes mathematically the strong interaction taking place between quarks and gluons.

1.2. Quantum ChromoDynamics

Lagrangian QCD

Feynman diagrams (Figure 1.2) are tools that describe the mathematical expressions characterizing the subatomic particles behaviour. The diagrams are drawn according to the Feynman rules. They depend on the Lagrangian of the interaction and can be derived from the QCD action, which is renormalizable and invariant under Poincaré and local gauge transformations. The quark field dynamics are described by the QCD lagrangian density, with the action principle:

"S =0 for all "q (1.3)
where the action S is given by:

S = i ⁄ d 4 xL q (1.4)
with the Lagrangian of a single flavour non-interacting quark given by:

L q = ÿ f qf (i" µ ˆµ ≠ m q f )q f (1.5)
where q f are quark-field spinors with the index f running over di erent flavours of quarks (f = u,d,s,c,b,t) with mass m q f and " µ represents Dirac "≠matrices.

Chapter 1. Physics of heavy-ion collisions

The free Lagrangian is invariant under SU(3) c transformations as follows:

q α f ae (q α f ) Õ = U α β q β f (1.6)
where UU † = U † U =1 , det(U)=1with U = e ≠igsT a θa , and g2 s =4 fis the QCD coupling constant. ◊ a is an arbitrary parameter and T a = ⁄ a /2 constitute traceless Hermitian generators, where ⁄ a (a oe [ [1; 8]]) are the Gell-Mann matrices. The Lie algebra is defined by the commutation relations: [T a ,T b ]=if abc T c , where f abc are the structure constants. The gluonic part is described by the lagrangian L G , where gluon fields are denoted by G a µ (x) (a going from 1 to 8), it is given by the following equation:

L G = ≠ 1 4 G a µν G µν a (1.7)
with the non-Abelian field strength tensor

G µν a = ˆµG ν a ≠ ˆνG µ a ≠ g s f abc G µ b G ν c
, where the last term represents the interaction between gluons. The interaction lagrangian, L interaction , is described with the following term:

L interaction = ≠ ÿ f g s (q f " µ T a q f )G a µ (1.8)
Thus, we can re-write the complete QCD lagrangian as follows:

L QCD = L q + L G + L interaction (1.9) = ÿ f qf (i" µ ˆµ ≠ m q f )q f ≠ 1 4 G µν G µν ≠ ÿ f g s (q f " µ T a q f )G a µ (1.10) = ÿ f qf (i" µ D µ ≠ m q f )q f ≠ 1 4 G µν G µν (1.11) with the SU(3) c covariant derivative D µ = ˆµ + ig s G a µ T a .

Renormalization and the running coupling constant

-s (Q 2 )
The scattering cross-section ‡ of a process can be calculated based on Richard Feynman's diagrams (Figure 1.2), following the Feynman rules. Nevertheless, vacuum fluctuations introduce fermions-antifermions and gluonic loop processes, leading to a divergence into the calculations. Thus, in QCD, the interactions must be renormalized by these fluctuations, giving rise to a running coupling constants (Q 2 ), which describes the strength of the strong interaction depending on the energy scale given by Q 2 2 . The evolution of this running constant is given 1.3. Quark-Gluon Plasma

Lattice QCD

As mentioned previously, lQCD is used to estimate the critical temperature required for the transition to the QGP state. Lattice QCD [START_REF] Kenneth | Confinement of quarks[END_REF] is a non-perturbative implementation of QFT based on a discrete space-time (see Figure 1.5 -left), in which rotational and translational Lorentz symmetries are broken, and gauge symmetry is preserved. The space consists of sites corresponding to quark fields Â(x), and links corresponding to gluonic field G µ a parallel transporter U(x) ≥ e i

s x i x j G µ a (y)dxµ .
The canonical partition function in the Euclidean space-time describes a system of particles in spatial volume V, in thermal contact with a heat bath at a temperature T, as it is the sum of all the possible states achievable by the system. Associated with the particles is a set of conserved charges N i . It is defined as follows:

Z = ⁄ DG µ a DÂ(x)D Â(x)e ≠S = Tr[e ≠(H≠µ i N i )/T ] (1.14)
where S is the action and H is the hamiltonian. Therefore, essential thermodynamical quantities can be obtained from the partition function as pressure p,e n t r o p yS, free energy density f , entropy density s and energy density ':

f = ≠T V ln(Z) (1.15) p = ≠f = ˆ(TlnZ) ˆV (1.16) S = ˆ(TlnZ) ˆT (1.17) ' = E V = T 2 V ˆlnZ ˆT (1.18) s = S V = ' + p T (1.19) ' ≠ 3p T 4 = T T p(T ) T 4 (1.20)
These variables are the essential constituents for the lQCD analyses. Figure 1.5 -right, shows the pressure, energy and entropy densities as a function of temperature computed by lattice QCD with 2 light (u,d) and 1 heavier (s) quark flavours [START_REF] Bazavov | Equation of state in (2+1)-flavor QCD[END_REF]. A clear increase of the thermodynamical variables is observed around T c =1 5 4± 9 MeV, at µ B =0.

One can also observe that the energy density limit for an ideal gas is not reached. Thus, even in a deconfined states, the interactions between partons are still prevalent. To attain this state of matter, impossible to observe in nature, ultra-relativistic heavy-ions collisions are used to reproduce the necessary conditions, as will be detailed in the next section.

N coll . The impact parameter is the distance between the centers of the two colliding nuclei.

Central collisions, at small b, yield large interaction regions with large numbers of participants N part , while peripheral collisions, characterized by large values of b, yield smaller interaction regions with large numbers of spectator nucleons N spect . Experimental data is used to allow the estimation of these quantities by theoretical methods, such as the Glauber model [START_REF] Michael | Glauber modeling in high-energy nuclear collisions[END_REF]. This model considers the independent distribution of nucleons inside a nucleus A, with the probability density distribution fl A (x, y, z). In this model, a heavy-ion collision between target nucleus A and projectile B, with an impact parameter ≠ ae b , collide on the incident beam direction z≠axis. The calculations will focus around two flux tubes (Figure 1.9), located at a distance ≠ ae s with respect to the center of the target nucleus A. The probability of a nucleon to be located in this flux tube per unit of transverse area for the target particle A is:

' T A ( ≠ ae s )= ⁄ fl A ( ≠ ae s,z)dz (1.25)
With a similar expression for the projectile nucleus B. One can define the probability of nucleons to overlap within the flux tubes for an impact parameter ≠ ae b with the integrated product of the probabilities, such as:

' T AB ( ≠ ae b )= ⁄ ' T A ( ≠ ae s ) ' T B ( ≠ ae s ≠ ≠ ae b )d 2≠ ae s (1.26)
This formula can be interpreted as an e ective overlap area, for which a nucleon in A and in B can interact together. The probability of interaction is then given by ' T AB ( ≠ ae b ) ‡ NN inel , with ‡ NN inel is the inelastic cross section. Thus, the probability of having n interactions between nucleus A and B (with respectively A A and A B nucleons), supposing that one nucleon in A can only interact with one nucleon in B,a sfl B ‡ NN inel dz π 1, is given with the following binomial distribution:

P (n, ≠ ae b )= Q a A A A B n R b Ë ' T AB ( ≠ ae b ) ‡ NN inel È n Ë 1 ≠ ' T AB ( ≠ ae b ) ‡ NN inel È A A A B ≠n (1.27)
with the first term representing the combinations possible for n collisions for a total number of possible interactions A A A B , followed by the probability term of having n collisions, and the last term represents the probability of having A A A B ≠ n misses. Thus, the number of nucleon-nucleon collisions possible between A and B is:

N coll ( ≠ ae b )= A A A B ÿ n=1 nP (n, ≠ ae b )=A A A B ' T AB ( ≠ ae b ) ‡ NN inel (1.28)
QCD factorization theorem [START_REF] John C Collins | Factorization of hard processes in QCD[END_REF], the cross-section is given as:

d ‡ A+B≠ ae h+X = f a (x 1 ,Q 2 ) ¢ f b (x 2 ,Q 2 ) ¢ d ‡ ab≠ ae c+X (x 1 ,x 2 ) ¢ D c≠ ae h (z, Q 2 ) (1.33)
The term d ‡ ab≠ ae c+X (x 1 ,x 2 ) is the cross section for the production of parton c from the scattering of partons a and b which is calculated using pQCD at a given order ins . The other terms are non-perturbative:

• The Parton Distribution Function (PDF) f a (x 1 ,Q 2 ) represents the probability of finding a parton of flavour a inside the hadron A with a momentum fraction x 1 = p a /p p . The PDF appears twice in the equation: for parton a coming from hadron A and for parton b coming from hadron B. The final cross section must be summed over all possible combinations of a, b and c.

• The Fragmentation Function (FF) D c≠ ae h (z, Q 2 ) describes the probability that the parton c fragments into a final state hadron h with a momentum fraction z = p h /p c .

PDF and FF rely on experimental measurements: PDFs are determined in Deep Inelastic Scattering (DIS) of electrons o protons or nuclei, while FFs come from jet measurements in high-energy e + e ≠ collisions and electron-hadron collisions, where the clean environment allows for the determination of the state of the quark before hadronization.

Quarkonium suppression

One of the first probes proposed to study the QGP properties consists of measurements of quarkonium production (bound states of charmonium cc and bottomonium b b). Their constituents, are produced at the early stages of collisions, thus experimenting the full system evolution. At LHC energies, their main production process is through gluon fusion. Matsui and Satz proposed in 1986 that the suppression of quarkonium production implies the presence of QGP [START_REF] Matsui | J/Â suppression by quark-gluon plasma formation[END_REF]. In order to illustrate the suppression, one should look at the non-relativistic potential of interaction in a vacuum, between a quark and its anti-quark as a function of their distance r, known as the Cornell potential [START_REF] Eichten | Charmonium: The model[END_REF]:

V (r)=≠ - r + ‡r (1.34)
with the constants ‡ describing the confinement string tension, anda coe cient determined by lQCD. The first term represents the Coulombian-like contribution of the interaction potential due to gluon exchange between the quark and its anti-quark, and the second term describes the confinement behaviour, prevailing at significant distances. At high energy densities, or high temperatures (Equation 1.18), the density of coloured partons increases. As the partons are

Conclusion

The Standard Model, describing visible matter and its fundamental interactions, is presented in this chapter. The strong interaction is described using the QCD formalism. In particular, the QCD phase diagram was presented, which predicts two essential behaviours of matter. First, the confined matter which exists at the low-temperature phase with a unitary baryon density. Then, at very high temperatures, there is a crossover to the QGP, made of strongly interacting partons floating in a deconfined free state. This state is hardly observable in nature. Therefore, to reach these temperature scales, ultra-relativistic heavy-ion collisions take place in particle accelerators. Following these collisions, several stages of matter are described by the Bjorken model. If the medium is dense enough and the energies reached are su cient, the QGP is produced in one of these stages. In order to investigate the QGP state and its properties, it is necessary to study various probes at di erent energies. Thus, the probes are categorized into soft and hard probes. One of the studied hard probes is the charmonium, which is created at the beginning of the collision. More precisely, the suppression of the latter is observed when a QGP is created. The next chapter will focus on the production of one of the most stable states studied of charmonium, the J/Â particle.

Chapter 2

The J/Â properties and production As discussed in the first chapter, ultra-relativistic heavy-ion collisions are the only experimental tool allowing the study of the QGP state by bringing finite volumes into high energy densities, thus bringing the nuclear matter to asymptotic freedom regime. The J/Â, belonging to the charmonium family, is an essential QGP hard probe since the presence of a deconfined phase influences its production rate. The J/Â particle was first detected in 1974 by two independent groups at Brookhaven National Laboratory and the Standford Linear Accelerator Center, confirming the quark model proposed by Gell-Man [START_REF] Gell-Mann | A schematic model of baryons and mesons[END_REF] and Zweig [START_REF] Zweig | An SU(3) model for strong interaction symmetry and its breaking[END_REF]. The resonance discovered was around the mass of 3.1 GeV/c 2 , in p-Be [START_REF] Aubert | Experimental observation of a heavy particle J[END_REF] and e ≠ e + [START_REF] Augustin | Discovery of a narrow resonance in e+e-annihilation[END_REF] collisions. This chapter will focus mainly on the J/Â, starting with an introduction of the charmonium state, followed by the production mechanisms of the J/Â and its production in ultra-relativistic heavy-ion collisions.

Finally, important experimental results will be discussed.

Chapter 2. The J/Â properties and production cc pair should be produced in a specific colour-singlet state. This model is based on the factorization for the cross-section calculation of the charmonium production, which separates the perturbative (cross-section for the cc production) and the non-perturbative contributions (the probability that the cc pair generates a J/Â particle), suggesting that the perturbative and non-perturbative processes are correlated. The production cross-section of a charmonium state following the interaction between 2 partons, p 1 and p 2 , is factorized as:

d ‡ charmonium+X = ÿ p 1 ,p 2 f p 1 ,p 2 ¢ d ‡ p 1 +p 2 aeQ Q+X ¢|Ψ charmonium (0)| 2 (2.1)
with the parton distribution functions f , and |Ψ charmonium (0)| 2 the probability amplitude of hadronization into a charmonium state. The production cross-section of a charmonium state can be obtained experimentally or with lQCD. This model faces limitations reproducing the charmonium behaviour as it provides good estimation for data only at low energies [START_REF] Abe | J /Â and Â(2S ) Production in pp Collisions at Ô s =1 .8TeV[END_REF][START_REF] Abe | Production of J /Â Mesons from ‰ c Meson Decays in pp Collisions at Ô s =1 .8TeV[END_REF].

The Colour Evaporation Model

The CEM [START_REF] Fritzsch | Producing heavy quark flavors in hadronic collisions-' A test of quantum chromodynamics[END_REF][START_REF] Einhorn | Hadronic production of the new resonances: Probing gluon distributions[END_REF][START_REF] Amundson | Quantitative tests of color evaporation: Charmonium production[END_REF] was proposed by Fritzsch, describing quarkonium production following a statistical approach. The probability of a charmonium state formation is independent of the colour of the cc pair; thus, the main di erence with the previous model is the non-fixed quantum state during its evolution. In this model, the perturbative and the non-perturbative processes are considered uncorrelated. The exchange of soft-gluons with the colour field destroys all previous information containing the quantum state of the cc pair, creating a probability for it to evolve to any given charmonium state. The production cross-section of a charmonium state is given by the following equation:

‡ charmonium = F charmonium ⁄ 2m H 2m Q dm Q Q d ‡ Q Q dm Q Q (2.2)
with the quarks mass m Q and the open heavy flavour hadrons mass m H (composed of one heavy quark). F charmonium is the hadronization probability to a charmonium state, obtained experimentally. A conclusion drawn from the CEM model is the independence of the ratio of two charmonium states to the kinematics. However, experimental data shows some dependencies [START_REF]Measurement of Â(2S) production as a function of charged-particle pseudorapidity density in pp collisions at Ô s = 13 TeV and p-Pb collisions at Ô s NN = 8.16 TeV with ALICE at the LHC[END_REF]. Thus, while this model describes quarkonium production well, it still has its limitations.

Non-Relativistic QCD and the Colour Octet Model

The COM [START_REF] Rey | Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium[END_REF] mainly di ers from the latter in that it additionally takes into account the contributions from the colour-octet states. The Non-Relativistic QCD (NRQCD) formalism is used, with the transitions into the colour-singlet state treated non-perturbatively. The production

J/Â production in heavy-ion collisions

Another essential reason that makes the J/Â a very interesting QGP probe is that its production rate is a ected by the medium. In this section, the di erent processes and e ects on the production of the J/Â in ultra-relativistic heavy-ion collisions are discussed, and illustrated by experimental results. They are divided into two categories: hot nuclear e ects induced by the QGP phase and cold nuclear e ects induced by hadronic phase.

Hot nuclear effects Sequential suppression

As discussed in chapter 1 (Equation 1.35), the increase of colour density induces a decrease in the range of the strong interaction (Debye screening e ect). If this range, called Debye radius, is smaller than the radius of a bound state, the latter cannot be produced [START_REF] Matsui | J/Â suppression by quark-gluon plasma formation[END_REF]. The reduction of the interaction potential between c and c quarks in the QGP can lead to the sequential suppression. In particular, this reduction can prevent the formation of bound states and leads to their suppression, depending on the temperature of the medium. This results in a dissociation temperature T D , characterizing each bound state, above which it melts completely. Thus, a precise determination of di erent dissociation temperatures are required in order to estimate the QGP temperature. Various approaches can be used, such as lQCD temperature calculations and di erent potential models [START_REF] Karsch | Signatures of charmonium modification in spatial correlation functions[END_REF][START_REF] Ding | Charmonium properties in hot quenched lattice QCD[END_REF]. The di erent values of the ratio of the dissociation to critical temperatures for di erent main charmonium resonances are presented in Table 2.2, obtained with a potential model [START_REF] Satz | Colour deconfinement and quarkonium binding[END_REF]. The T D is observed to increase with the increase of the binding energy.

Charmonium state J/Â ‰ c Â(2S)

T D /T c 2.10 1.16 1.12 Table 2.2: T D /T c for the main charmonium states [START_REF] Satz | Colour deconfinement and quarkonium binding[END_REF].

Recombination

The production cross-section of the c and c quarks is proportional to the center of mass-energy; thus, the higher the energy, the higher the production of charm quarks. This can lead to a phenomenon known as recombination [START_REF] Thews | Enhanced J/Â production in deconfined quark matter[END_REF][START_REF] Thews | Quarkonium Production via Recombination[END_REF], which was first described in 1980, before Matzui and Satz article. This process occurs at high energy, where charm quarks density is so important that it allows the recombination of these quarks into a charmonium state. At higher energies,

J/Â production in heavy-ion collisions

the recombination mechanism is stronger and can thus counterbalance the suppression. This process can occur during the evolution of the medium or during the hadronization phase [START_REF] Andronic | Decoding the phase structure of QCD via particle production at high energy[END_REF].

Interaction with comovers

The comovers particles are final state constituents that can interact with charmonium states. This results in the suppression of charmonium due to these interactions, in particular through inelastic collisions. After such interactions, open charm can be created with the following process: cc + h ae D + D + X, where h refers to the comoving hadron. As can be observed in Figure 2.4, with the increasing energy density, the number of comovers particles increases and thus the suppression due to the comovers becomes significant.

The interplay between the explained mechanisms on the J/Â production probability is sketched in Figure 2

Cold Nuclear Matter effects

Shadowing and anti-shadowing effects

As heavy-quark production occurs at the earliest moments of collision, the initial state has great influence on the production of quarkonium, in particular PDFs. PDFs are described in the chapter 1, with their contribution to the cross-section calculation presented in Equation 1.33. Their determination relies on experimental measurements. However, there is a di erence between the PDF in a free nucleon from the one inside a nucleus (nPDF). It was first discovered in 1983 by the European Muon Collaboration (EMC) by looking at the parton momentum distribution in Iron and in Deuterium, where a di erence was observed [START_REF] Aubert | The ratio of the nucleon structure functions F2N for iron and deuterium[END_REF]. The nPDF of a parton flavour i

Cronin effect

During the initial stages of the collision, partons undergo elastic scattering multiple times on colliding nuclei, acquiring transverse momentum at each collision. Therefore, the partons acquire a transverse momentum, shifted toward higher momenta value. This e ect, known as the Cronin e ect [START_REF] Cronin | Production of hadrons at large transverse momentum at 200, 300, and 400 GeV[END_REF][START_REF] Kharzeev | Cronin e ect and high-[Formula Presented] suppression in pA collisions[END_REF], was first observed in pA collisions. Thus, this e ect leads to the hardening of the transverse momentum distribution for the J/Â production in AA and pA collisions with respect to pp collisions.

Nuclear absorption

The nuclear absorption corresponds to the dissociation of the charmonium states, caused by successive scatterings with spectator nucleons. The survival probability, S abs , of a bound state can be determined with:

S abs = e ≠ρ A σ abs L (2.6)
where fl A is the nuclear density, L is the mean propagation length, and ‡ abs is the e ective cross-section for quarkonium breaking. With the Glauber model, explained in the chapter 1, the cross-section is extracted from pA collisions data and extrapolated to the AA collisions.

Experimental results

As discussed in the first chapter, the properties of the QGP can be studied with heavy-ion collisions (AA) at relativistic energies, compared along with di erent collision systems (pp and pA). Lead nuclei are accelerated, to speeds close to the speed of light, enough to create, while colliding, a QGP droplet that can be studied with particle detectors. In this section, a review of experimental results will be presented, along with discussions on their physical implications.

Quarkonium: regeneration vs suppression

The hot nuclear matter e ects can be investigated through measurements of the elliptic flow v 2 (presented in Equation 1.32) and the nuclear modification factor R AA . The R AA factor is a scaled ratio that compares the yields of particles in AA collisions with respect to pp collisions. It can be expressed by the following equation:

R AA = 1 ÈN coll Í • dN AA /dp T dN pp /dp T (2.7)
where ÈN coll Í is the average number of nucleon-nucleon collisions, N AA,pp correspond to the particle invariant yields in AA and pp collisions respectively.

Experimental results

Unlike the J/Â particle, there is no observable e ect of regeneration. It is compared with two transport models, with and without the regeneration mechanism. The model predicts data well, and the regeneration e ect is negligible within the measurement precision. This is in agreement with the expectations, as the b quark, being heavier than the c quark, has a lower production rate, thus the regeneration mechanism is supposed to be less important or even non-existent for the Υ mesons.

In

Cold Nuclear Matter effects

In order to fully understand Pb-Pb collisions, as previously discussed, hot nuclear matter e ects need to be disentangled from the CNM e ects. Thus, measurements in p-Pb collision systems are presented in the following, where CNM mechanisms can be disentangled.

In Figure 2.9 -left, the nuclear modification factor of the J/Â is presented at Ô s NN =5.02

TeV at forward rapidity. In Figure 2.9 -right, the Υ(1S) is presented at

Ô s NN =8.16.F o rb o t h
particles, the trend is similar, as suppression increases with the decreasing p T . The di erent theoretical models, within their bandwidth, are in accordance with the data. Models with only suppression due to a shadowing contribution present a flat trend, which is not reflected by data. The nCTEQ15 model [START_REF] Kova Ík | nCTEQ15 -Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework[END_REF], describing well data, includes the interactions with comoving particles, in addition to the shadowing e ects. Models based on the Colour Glass Condensate (CGC) [START_REF] Iancu | THE COLOR GLASS CONDENSATE AND HIGH ENERGY SCATTERING IN QCD[END_REF] also reproduce well data. CGC is based on a non-linear evolution equation, and takes into account parton saturation for low-x partons.

Finally, in Figure 2.10 is presented the elliptic flow in p-Pb collisions, for the J/Â particle,

Charmonium production in pp collisions

In order to constrain the theoretical models discussed in this chapter, charmonium measurements in pp collision system are required, which are also considered as a reference for the measurements done in Pb-Pb and p-Pb systems. First, inclusive J/Â (Figure 2.11 -left) and Â(2S) (Figure 2.11 -right) cross-section measurements are presented at forward rapidity region (2.5 <y<4) in di erent collision energies Ô s = 5.02, 7, 8, and 13 TeV, via the muonic decay down to p T = 0 GeV/c. In addition, the ratio between cross-sections at di erent collision energies is done to reduce the energy-related uncertainties. An increase of the cross-section is observed with the increasing energy. A strong hardening of the J/Â cross-section spectra at 13 TeV is noticed with respect to other energy scales. It can be explained by a predicted increase of prompt J/Â mean p T with energy, and an increase of the non-prompt contribution at high p T (by FONLL). For both charmonium states, the NRQCD model describes the prompt contribution, and FONLL describes the non-prompt contributions. The models are in good agreement with the cross-section data. The same is also observed for the di erent ratios for both charmonium states within uncertainties, except for the 7-to-13 TeV J/Â ratio. As can be seen, the latter is slightly overestimated by the models, as it's expected to be closer to the 8-to-13 TeV ratio.

In order to separate the di erent contributions, measurements for J/Â prompt and nonprompt are presented at midrapidity region (|y| < 0.9)a t Ô s = 13 TeV (Figure 2.12) and 5.02 TeV (Figure 2.13). For both prompt J/Â measurements in the di erent collision energies, there is an agreement observed between the data and the Improved CEM model (ICEM) [START_REF] Cheung | Production and polarization of prompt J/Â in the improved color evaporation model using the k T -factorization approach[END_REF] and NRQCD based models, except for the NRQCD Lipatov calculations [START_REF] Sp Baranov | Are there any challenges in the charmonia production and polarization at the LHC?[END_REF]. A slight overestimation of the data at low p T is observed for the latter. The Lipatov factorization approach is based on p T dependent gluon distribution functions, and takes into account the J/Â contributions from the excited charmonium states. As for the non-prompt J/Â, an agreement is observed between the FONLL model and the data. An indication of the decrease of the nonprompt fraction at lower collision energy is observed, as the fraction of non-prompt production is extracted for each energy scale, with the following results: Chapter 2. The J/Â properties and production

f visible, Ô s=13 TeV B (p T > 1GeV/c, |y| < 0.9) =

Conclusion

The J/Â particle, consisting of an important QGP probe, is described in this chapter. It is a charmonium state that can be categorised into two groups. The prompt J/Â, produced directly as a result of hard processes or following the feed-down of excited states. The nonprompt J/Â, which are produced as a result of the weak-decays of B hadrons. Their production mechanisms are described by several theoretical models. The J/Â production is very sensitive to the medium, making it a valuable probe. In particular, the di erent e ects on the production of the J/Â in hot nuclear matter following heavy-ion collisions essentially involve an interplay between charmonium suppression and recombination mechanisms. CNM e ects are also studied in order to disentangle the e ects of QGP from the nuclear e ects induced by the presence of heavy nuclei. Thus, to visualise the mentioned hot nuclear matter e ects and CNM e ects, the J/Â and Υ is studied in Pb-Pb and p-Pb collisions respectively. An indication of the regeneration and thermalization mechanisms of cc pairs is observed, which is not the case for the b b pairs. Finally, to constrain the theoretical models, the production of J/Â is studied in pp collisions. The measurements presented in this chapter are performed in ALICE, a detector at the LHC accelerator, where only inclusive quarkonium measurements can be performed at forward rapidities, due to design limitations. The methods envisaged and implemented to overcome these limitations will be the subject of the following chapters.

Chapter 3

The Large Hadron Collider and ALICE As discussed in the first chapter, heavy-ion collisions at ultra-relativistic energies are the only experimental tool allowing the study of the Quark-Gluon Plasma. Within this chapter, the colossal machinery behind these tools is detailed. Starting with the presentation of the Large Hadron Collider (LHC), the world's most powerful particle accelerator, permitting the creation of conditions that are similar to those of the very early Universe. Inside the accelerator, two high-energy particle beams guided by a strong magnetic field travel in opposite directions close to the speed of light before colliding. Around one of the collision points is located A Large Ion Collider Experiment (ALICE), designed for the study of heavy-ion collisions. A description of the ALICE detector will be also provided in this chapter.

Chapter 3. The Large Hadron Collider and ALICE

The Large Hadron Collider

A brief history of the Large Hadron Collider

After the end of World War II, European researchers were faced with several di culties, including the threat of destruction of culture, migration of researchers, and insu cient means devoted to research in each country, as scientific research was becoming increasingly expensive. Thus, a solution was proposed with the creation of a European atomic physics laboratory, allowing the share of the financial costs between the di erent member countries of this organization.

At the European conference of culture in 1949, Louis de Broglie made a first o cial proposal for the creation of the latter [START_REF]Bureau d'études pour un Centre européen de la culture[END_REF]. Afterwards, at the UNESCO meeting in Paris in 1951, the European Council for Nuclear Research, with the acronym CERN, was born. The first CERN accelerator, the Synchrocyclotron (SC), was built in 1957. The SC was capable of accelerating protons up to 600 MeV. It was followed by the Proton Synchrotron (PS) [START_REF] Tksmt Inoue | High accuracy control of a proton synchrotron magnet power supply[END_REF] and the Super Proton Synchrotron (SPS) [START_REF] Agakichiev | Enhanced production of low-mass electron pairs in 200 GeV/nucleon S-Au collisions at the CERN super proton synchrotron[END_REF] accelerators. The story of the LHC [81]

Structure

The LHC is located in a tunnel with a circumference of 27 km, between 50 and 175 m beneath the France-Switzerland borders. Inside the accelerator, two beams of particles are guided in where proton beams can reach a maximum energy of 6.8 TeV.

Lead beams A pure Pb source is heated to around 800 o C, resulting in a partial extraction of Pb atoms. The Pb atoms are then passed to the Electron Cyclotron Resonance [START_REF] Geller | ECRIS: The Electron Cyclotron Resonance Ion Sources[END_REF], where electrons are stripped from Pb atoms. Following this, Pb 27+ ions are then accelerated with Linac3 up to 4.2 MeV per nucleon, losing more electrons in the process. Then, accelerated up to 72 MeV per nucleon and separated into bunches in the Low Energy Ion Ring (LEIR) [START_REF] Chanel | LEIR: the low energy ion ring at CERN[END_REF]. Following this step, the chain is the same as for the protons. First, the Pb ions are accelerated in the PS up to 5.9 GeV per nucleon, where all the remaining electrons are stripped (Pb 82+ ). Then, they are injected into the SPS, where they reach an energy of 177 GeV per nucleon. Finally, they are separated into 2 opposite directions into the LHC accelerator, where the maximum energy reached per nucleon is of 2.51 TeV in Run 2.

Luminosity

In order to characterize a collision between two bunches, luminosity measurements, an essential parameter, is required. The instantaneous luminosity L indicates the rate of inelastic collisions that can be produced, in units of cm ≠2 s ≠1 . It can be calculated theoretically with the following equation:

L = 1 ‡ p ◊ dR dt (3.1)
where ‡ p is the production cross-section of a determined processes and dR dt is the number of such processes per unit of time. In the case of the LHC, a circular accelerator, the luminosity can be calculated with:

L = ÿ i,j N i N j f rev I overlap (3.2)
with f rev is the revolution frequency, equal to the collisions frequency, N i/j the number of colliding particles, with i, j the index of bunches per beam, and I overlap is the integral of the overlap area between the two bunches. The integrated luminosity L int is obtained by the integration of L over time.

The four giants

The four largest experiments surrounding the collision points of the LHC accelerator as displayed in Figure 3.1 are the following:

A Toroidal LHC ApparatuS (ATLAS) [START_REF] Aad | The ATLAS experiment at the CERN large hadron collider[END_REF]: ATLAS is a general-purpose detector designed to study the standard model of physics and beyond with Higgs boson, supersymmetric particles, and other physics beyond SM, as well as contributing to the QGP study. It is located 100 m under ground, weights 7,000 tonnes, with the dimensions of a cylinder, measuring 46 m long and 25 m in diameter, making it the largest detector of the LHC. It comprises six subsystems around the interaction point, necessary for the measurements of trajectory, momentum, and energy. For precise momentum measurements, a large magnet system bends the path of the charged particles passing through, with a magnetic field of 2 T. The acceptance pseudorapidity of this detector is |÷| < 2.5, with p T acceptance for muon measurements down to 3 GeV/c. The ATLAS detector is displayed on Figure 3.2.

Figure 3.2:

The ATLAS detector structure [START_REF] Pequenao | Computer generated image of the whole ATLAS detector[END_REF].

Compact Muon Solenoid (CMS) [89]:

The CMS, as the ATLAS detector, is also a general-purpose detector with the same physics objectives. It is the heaviest detector of the LHC, weighing 14,000 tonnes, with dimensions of 21 m long and 15 m in diameter. The detector is constructed around a large solenoid magnet, taking the form of a cylindrical coil of superconducting cable, creating a magnetic field of 4 T, around 100,000 times stronger than that of the earth. The pseudorapidity region of this detector is |÷| < 2.5, with the minimum transverse momentum for muon measurements going from 1.2 to 3.5 GeV/c. The CMS detector structure is displayed in Figure 3.

A Large Ion Collider Experiment

As discussed previously, ALICE is the only LHC experiment dedicated to the QGP study with heavy-ion collisions, particularly with unique low p T measurements. The several independent detectors, operated synchronously, can be grouped within the following three categories. First, the global detectors, located around the interaction point (IP). They provide general quantities measurements, such as the collision centrality, collision time, and particle multiplicity. Then, the central barrel detectors are necessary for the identification and tractography of charged particles and photons. Lastly, the muon spectrometer, placed in the forward rapidity region ≠4.0 <÷<≠2.5, intended for the measurement of muons. The axis parallel to the beam pipe of the ALICE detector, z≠axis, is oriented to the IP of ATLAS, known as A-side. The C-side concerns the opposite direction, pointing toward the CMS detector. The x≠axis is oriented toward the center of the LHC, and the y≠axis points upwards. First, a description of the ALICE apparatus after LS2 upgrades is presented (Figure 3.5), with a detailed description provided for two detectors relevant for this thesis: the Inner Tracking System (ITS) and the muon spectrometer. The ALICE objective for Run 3 is to study rare events at low p T , such as open heavy-flavours for which the definition of a trigger is a challenge. For this goal, the detector electronics is improved [START_REF]Upgrade of the ALICE Readout & Trigger System[END_REF] in order to allow for continuous readout. This results in no dead time for the data acquisition, leading to an increase of statistics and performance of the rare events. In addition, an increase of the data rate is expected, up to 50 kHz for Pb-Pb collisions (few kHz in Run 2). The final increase of statistics is expected to be around 100 times more data than Run 1 (depending on the physics channel). In addition, the track reconstruction resolution and measurements at low p T for certain detectors are improved.

Global detectors

The Zero Degree Calorimeter (ZDC): The ZDC [START_REF] Gallio | ALICE Zero-Degree Calorimeter[END_REF] detector comprises two hadronic calorimeters and two electromagnetic calorimeters placed around the IP. The hadronic calorimeters, farthest detectors located on opposite sides of the IP with z = ± 112.5 m, measure the energy deposited by the spectator particles. As for the electromagnetic calorimeters, placed in the forward region of the detector at 7 m from the IP, they detect the energy deposited by photons at forward rapidity. The ZDCs, based on the Cherenkov light detection, are composed of quartz fibers, read out by photomultiplier tubes (PMTs).

The Cherenkov light, produced by the charged particles passing through the quartz material at a speed higher than the speed of light within this material, is collected and transformed into an amplified signal with the PMTs. Thus, properties such as the centrality of collisions and their reaction plane can be estimated by these calorimeters.

consists of an electromagnetic calorimeter. PHOS is made of dense scintillating crystals, and its detection channels are based on lead-tungstate crystals. Additionally, in front of the calorimeter is located a Multi-Wire Proportional Chamber (MWPC), used as a Charged Particle Veto (CPV). PHOS measures photons and neutral mesons via their photonic decay channel, allowing the study of jet quenching for measurements at high p T .

The High Momentum Particle Identification Detector (HMPID):

The HMPID [START_REF] Volpe | The High Momentum Particle IDentification (HMPID) detector PID performance and its contribution to the ALICE physics program[END_REF], located at 4.9 m from the IP with an azimuthal coverage of ∆" =5 8 o within the pseudorapidity rapidity region |÷|AE0.6, is based on the Ring Imaging CHerenkov (RICH) technology. It is composed of 7 modules for the measurement of the cone angle of the Cherenkov radiation, allowing for particle identification. The HMPID extends other central barrel detectors (such as the ITS, TPC, and TOF) information, allowing for kaons and pions separation up to 3 GeV/c, and kaons and protons separation up to 5 GeV/c.

The Time Of Flight detector (TOF):

The TOF detector [START_REF] Akindinov | Performance of the ALICE Time-Of-Flight detector at the LHC[END_REF], located radially at 3.7 m from the IP, is composed of a cylindrical array with an active area of 141 m 2 , arranged in 18 sectors based on Multigap Resistive Plate Chambers (MRPC), covering the full azimuthal angle in the central pseudorapidity region of |÷|AE0.9. TOF measures the time at which the partcile crossed the detector with a resolution better than 50 ps. The di erence of this time and the collision time, provided by FT0, allows to determine the particle velocity. The detector identifies protons with p T < 4 GeV/c, pions and kaons with p T < 2.5 GeV/c.

The Transition Radiation Detector (TRD):

The TRD [START_REF] Acharya | The ALICE transition radiation detector: Construction, operation, and performance[END_REF] consists of a cylinder with a diameter of 7 m and 7 m long; it covers the full azimuthal angle and is located in the pseudorapidity region of |÷|AE0.84, radially situated from 2.9 m to 3.68 cm from the IP, around the TPC. Each TRD readout chamber consists of MWPC with an amplification and a drift region, filled with XeCO 2 gas mixture, and a radiator, where energetic electrons passing through produce transition radiation. Thus, this detector distinguishes between electron-pion particles with p T Ø 1 GeV/c, and provides tracking information to complete other central barrel detectors.

The Time Projection Chamber (TPC):

The TPC [START_REF] Gera | Upgrade of the ALICE time projection chamber for the LHC Run3[END_REF], a 90 m 3 cylinder filled with Ne≠ CO 2 ≠ N 2 gas, covers the full azimuthal angle, with the middle pseudorapidity region coverage of |÷|AE0.9. Charged particles passing through will ionize the gas, thus producing electron-ion pairs. With the electric field, the liberated electrons will drift towards the TPC endplates, based on Gas Electron Multipliers (GEM), thus collecting track information for particle identification task, tracking and momentum measurements for charged particles.

Frames (STFs), with each STF around 11.4 ms long. Following this step, data arrives from the FLPs to the Event Processing Nodes (EPNs), where the Sub-Time Frames are merged within complete TFs, and where calibration and further data compression is done for a total factor of compression of around 35. The compressed TFs are then stored on a 60 PB disk bu er. These synchronous operations will be followed by the asynchronous process, where data reconstruction and final calibrations from the Condition and Calibration Data Base (CCDB) are done on EPNs and on the Worldwide LHC Computing Grid-like environments, to be finally stored permanently under Compressed Time Frames (CTFs) and AODs. Following this, analysis of the AODs can be performed within the O 2 analysis framework, discussed in the following, for physics measurements and analysis purposes.

Online-Offline analysis framework

The results of the asynchronous operations are the AOD files, which are stored in ROOT trees, allowing bulk reading and writing. With the continuous data flow expected for Run 3, collision vertices are associated to tracks with an index, and collisions and tracks related parameters are presented in separate tables, mapping a data format based on structure-ofarrays, which is proven e cient in leveraging modern hardware capabilities. Thus, the data model for Run 3 is a collection of flat tables, arranged in a database-like relational database structure, based on the index connections. A scheme of the workflow is displayed in Figure 3.12. Many operations between the separate tables are available, similar to database operations, such as join, group, filter, and combine the di erent flat tables. Data analysis within O 2 is structured around analysis workflows, consisting of modular and flexible collections of interconnected Data Processing Layers (DPLs) data processors, known as tasks. For each user, specific tasks, in C++ language, are created with specific data tables as inputs. The outputs vary depending on user needs, from data tables intended for further processing to the ones intended for storage.

With the sequential manner of input data processing through pipelines, common tasks can be shared among di erent analyses, such as table reader, writer, calibrations, and quality filtering tasks.

Conclusion

The LHC, the most powerful particle collider in the world, is presented in this chapter. The LHC was in a long shutdown period during which detectors were upgraded in order to prepare for the next data taking period, Run 3, which o cially started on the 5 th of July 2022. The ALICE detector is then detailed after the LS2 upgrades. With the upgrades carried out for Run 3, the physics program of ALICE is extended. In particular, due to the higher interaction rate expected and to the improved electronics, increased statistics can be achieved. Also, an improved spatial resolution at midrapidity will be accomplished with the upgraded ITS. Finally, at forward rapidity, a better signal extraction is expected and a separation of the prompt and non-prompt J/Â contributions will be attainable with a new detector, the MFT, added to the muon spectrometer. The MFT, constituting the subject of this thesis, will be fully described in the next chapter.

Chapter 4

The Muon Forward Tracker As discussed in chapter 3, the muon spectrometer has been designed to study essentially open heavy-flavours, quarkonia states, and the low mass vector mesons, via their muonic decay channel at forward pseudorapidities. Nevertheless, the front absorber, located between the spectrometer and the interaction point, is limiting the physics program. In order to overcome these limitations, a new detector, the Muon Forward Tracker (MFT), has been installed between the interaction point and the front absorber during the LS2, covering the pseudorapidity region of ≠3.6 <÷<≠2. [START_REF] Amundson | Quantitative tests of color evaporation: Charmonium production[END_REF]. In this chapter, the MFT detector will be described, hardware and software-wise.

Physics motivation

The muon spectrometer allows to access a whole range of physics via the measurement of muons at forward rapidity. First, the study of the open heavy-flavours is performed [START_REF] Dainese | Heavy-flavour production in Pb-Pb collisions at the LHC, measured with the ALICE detector[END_REF], shedding light notably on the normalization of the quarkonium yield, in-medium heavy quarks energy loss, and other e ects as shadowing. Additionally, on the quarkonium side [START_REF] Martinez | Quarkonium production measurements with the ALICE detector at the LHC[END_REF], the evaluation of q q production, dissociation, and recombination to the production of charmonium and bottomonium states is performed, as discussed in chapter 2. Finally, for the measurements of low mass vector mesons [START_REF] Abelev | Light vector meson production in pp collisions at s=7 TeV[END_REF], studies concerning the modification of their spectral function and the dilepton thermal radiation due to the cooling of the QGP have been performed. However, due to the multiple scattering in the front absorber, the origin of muons is impossible to determine with su cient precision. Therefore, muons produced from heavy quarks decays cannot be distinguished from those produced by pion and kaon decays, thus introducing a high background. In addition, only inclusive measurements are possible, due to the missing information on secondary vertices. Thus, prompt and non-prompt J/Â measurements as well as the muons produced from charm and beauty decays can not be disentangled. Furthermore, the multiple scatterings lead to a reduced angular resolution, thus the resonances have a limited mass resolution (Equation 4.1), in particular at the low masses (Ê and " mesons). To address these limitations, the MFT upgrade [START_REF]Technical Design Report for the Muon Forward Tracker[END_REF]122] has been proposed. The MFT is located 40 cm from the interaction point and in front of the front absorber. The first goal of this detector is to improve the muon pointing resolution. A precise determination of the muon production vertices can be provided with the extrapolation of muon tracks to the IP. By overcoming the limitations due to the design of the muon spectrometer, the MFT extends

MUON only MUON + MFT

Layout of the MFT

The MFT detector is composed of 5 double-sided disks coaxial around the LHC beam pipe (Figure 4.2), on which are positioned silicon pixel sensors. A high-resolution tracker in a radioactive and high-multiplicity environment is subject to several requirements and constraints, as detailed in the following section. Then, a complete description of MFT apparatus is presented.

Requirements and constraints

For high multiplicity environments, the sensors must have a very small spatial resolution (about 5 µm) to ensure track separation. Therefore, the MFT must have a high granularity. Then, to prevent multiple scattering and resolution degradation, the material budget must be as low as possible. A radiation-tolerant material is also essential for the radioactive environment in which the MFT is located (designed to withstand 400 kRad and 5.10 12 1MeV n eq /cm 2 with a ten-fold security factor). In addition, the readout of the MFT must be able to withstand Run 3 collisions rate of 50 kHz in Pb-Pb and 500 kHz in pp collisions. The integration of all services (power, readout, cooling) is challenging given the limited volume: 35 cm for the diameter of the first disk, 46 cm for the last disk, with 36 cm of total length. In addition, one of the beam pipe supports is crossing the volume allocated to the MFT. The power consumption of sensors have to be as low as possible to limit cooling power (the higher, the more material it would require). Furthermore, because of the frontal absorber, the MFT can only be extracted through the A-side, implying the removal of ITS and TPC first. As these complex operations require a lot of time (disconnection, extraction, repositioning, reconnection), they cannot be done during a winter shutdown. Hence, the MFT cannot be accessed during a whole LHC Run (3-4 years), but only during long shutdowns. Thus, the MFT must have high reliability.

Global structure

For insertion reasons, the structure of the MFT is divided into two halves, labeled H0 (bottom half) and H1 (top half). A total of 936 ALPIDE sensors [START_REF] Aglieri Rinella | The ALPIDE pixel sensor chip for the upgrade of the ALICE Inner Tracking System[END_REF], representing an area of 0.5 m 2 , are distributed over 280 ladders, which consist of Flexible Printed Circuits (FPCs) connected to between 2 and 5 sensors. Each face of half-disk contains between 24 and 34 ladders, and is divided into four zones (composed of 3 to 5 ladders). The number of zones per disk is a trade-o between high segmentation and the number of control lines and components. The disks are labeled from 0 to 4 (Table 4.2) with a diameter increasing with the distance from the IP to the front absorber. In order to power the ALPIDE sensors, three di erent voltage supplies are requested: digital, analog and back-bias (see section 4.2.3). The low voltage power supply modules (CAEN LV) are located 40 meters away from the MFT, outside the ALICE

The ALPIDE chip

In order to fulfill a part of the mentioned requirements, mainly in terms of readout rate, spacial and momentum resolutions, the ALice PIxel DEtector (ALPIDE) chip [START_REF] Aglieri Rinella | The ALPIDE pixel sensor chip for the upgrade of the ALICE Inner Tracking System[END_REF] was designed to equip both the ITS and the MFT. It consists of a 0.18 µm Complementary Metal Oxide Semiconductor (CMOS) Imaging Sensor process of TowerJazz [START_REF] Senyukov | Charged particle detection performances of CMOS pixel sensors produced in a 0.18 µm process with a high resistivity epitaxial layer[END_REF], based on Monolithic Active Pixel Sensors (MAPS) technology [START_REF] Alexander | Monolithic Active Pixel Sensors (MAPS) in a quadruple well technology for nearly 100% fill factor and full CMOS pixels[END_REF]. Each chip measures 15 mm x 30 mm, composed of a 512 rows x 1024 columns pixels matrix, and 50 µm thick. The detection principle of the ALPIDE chip is presented in Figure 4.4. When a charged particle crosses the p-type epitaxial silicon layer, it will create electron-hole pairs in the material. The electrons, confined by the potential barriers, will drift thermally, reaching the depletion volume (corresponding to the white zone on Figure 4.4), then focused on the diode and generating a signal at the input of the pixel front-end electronics, where signal amplification and digitization is performed. A reverse backbias voltage is applied on the substrate to increase the depletion volume, thus compensating the e ciency decrease due to irradiation. To ensure proper conditions, a separate analog and digital power supply are provided to the ALPIDE chips, at 1.8 V each with a 10% tolerance, as well as a back-bias negative voltage, ranging from 0 to -3 V. The digital voltage is intended for the readout, as the analog is intended for the pixel circuitry. The power consumption of the chips is estimated to be around 24 mW for the analog power supply, and 187 mW for the digital power supply. As for the back-bias consumption, it is estimated to be very low, around 9 mW. b Integration time of 4µs,a n di n t e r a c t i o nr a t eo f100kHz.

Half-

c Non-Ionizing Energy Loss. Including a safety factor 10.

d Total Ionizing Dose. Including a safety factor 10.

Table 4.3:

The maximum hit densities and radiation levels obtained for 5.5 TeV Pb-Pb collisions simulations with PYTHIA generator and with FLUKA and GEANT transport models [START_REF]Technical Design Report for the Muon Forward Tracker[END_REF].

area is defined using the covariance matrix elements for the MCH track after extrapolation as follows:

Ò (x MFT ≠ x MCH ) 2 +(y MFT ≠ y MCH ) 2 < 3 ◊ Ò ‡ 2 XX,MCH + ‡ 2 YY,MCH (4.3
)

" MFT ≠ " MCH < 3 ◊ ‡ φφ,M CH (4.4) tan⁄ MFT ≠ tan⁄ MCH < 3 ◊ ‡ tanλtanλ,M CH (4.5)
A ‰ 2 score is then calculated between the MCH and the MFT candidate tracks. The MCH-MFT pair with the minimum ‰ 2 score is selected as a match. The ‰ 2 is presented with the following equation:

‰ 2 = P T ◊ C ≠1 ◊ P (4.6)
with the residuals of parameters P given with the 5 ◊ 1 vector as:

P = Q c c c c c c c c c c c a x MFT ≠ x MCH y MFT ≠ y MCH " MFT ≠ " MCH tan⁄ MFT ≠ tan⁄ MCH A q p T B MFT ≠ A q p T B MCH R d d d d d d d d d d d b
and the covariance residuals C described by a diagonal 5 ◊ 5 matrix with the diagonal elements ∆ ‡ 2 between the MFT and MCH diagonal covariance elements of the 5 coordinates (Equation 4.2).

Nonetheless, in high multiplicity environments, the ‰ 2 method encounters some limitations, a ecting the performance of the matching. Matching with machine learning is presented in chapter 6.

Conclusion

In order to extend the ALICE physics program at forward rapidity, the MFT detector was designed, built and installed. The MFT project took 9 years from design to installation. This chapter was dedicated to the MFT description, a detector based on silicon pixel sensors (with high spatial resolution and resistance to radiation). It is composed of 5 double-sided disks segmented into 4 zones for the readout and power management. The powering and monitoring of the MFT with the PSU will be the subject of the next chapter, which consists of the first part of work for this thesis. Finally, the algorithms for track reconstruction and matching are presented. The introduced track parameters consist of input data that will be used for matching with machine learning, that will be detailed in chapter 6.

Chapter 5

Power control of the MFT This chapter describes the first part of the work carried out in this thesis, consisting of software developments with the goal of fully powering and controlling the MFT detector. First, the PSU is presented, which is responsible for the hardware powering and safety of the detector. Then, the first software designed to control the entire detector is detailed. It allowed detector commissioning, firmware developments and detector calibrations, as the o cial ALICE framework was still under development. A full description is also provided for the latter in the following. It consists of the o cial software for Run 3 developed for the MFT, thus running 24h/24h in the ALICE site, allowing complete control and monitoring of the MFT detector.

The Power Supply Unit

As discussed in chapter 4, three voltage supplies are required for the proper functioning of the sensors: the analog voltage to power pixel circuits, the digital voltage to power the readout and the slow control, and the back-bias voltage to increase the depletion zone. In order to decrease the voltage drop between the low voltage power supply and the sensors, the PSU is installed between the 4 th and the 5 th disks (Disk03 and Disk04), as illustrated in Figure 5.1. The power management in the MFT detector is divided as the detector is composed of a total of 80 zones. It is divided first by half-MFT (bottom or top), then by face (front or back), by half-disk (0 to 4), and finally by zone (0 to 3). Some constraints were imposed on the PSU design, as it can not overlap with the acceptance of the detector, and it must be equipped with radiation-tolerant components (up to 75 krad). In addition, considerations such as tradeo between the granularity and the number of control lines constrained by available volume are taken into account to optimize the reliability of the MFT power supply system. Hence, the MFT is composed of four main PSU boards controlled through a dedicated CRU. More precisely, on each PSU main board, composed of around 3300 components, is attached a PSU mezzanine, composed of around 600 components (Figure 5.1), on which 5 Giga-Bit Transceiver -Slow Control Adapters (GBT-SCAs) [START_REF] Caratelli | The GBT-SCA, a radiation tolerant ASIC for detector control and monitoring applications in HEP experiments[END_REF] are located. The GBT-SCA is a radiation tolerant ASIC for detector control, with the purpose of managing slow control information (as will be detailed in section 5.2.1). In particular, each GBT-SCA is intended to establish communication with a corresponding face of half-disk (Figure 5.2, Figure 5.4). The cruciality of this aspect will be displayed in the following, on which the simultaneous communication with the detector is based. On the other side, the PSU is connected via long SamTech cables to the PSU interface board, equipped with a GBTx and a GBT-SCA. They are located in the same racks as the RUs, on the sides of the end of the front absorber. They are used to convert the optical signal coming from the CRU to an electrical signal, sent to the PSU mezzanine in the detector, and the other way around. Thus, each PSU interface is responsible for the communication with five half-disk faces, along with the transfer of information of the corresponding face of the half-PSU. Therefore, in order to control the complete detector, composed of twenty half-disk faces, the total number of PSU interface boards required is four. Figure 5.1 shows the full PSU mapping within the MFT detectors. The PSUs are supplied with low voltage by two types of low voltage power supply units. The A3009 CAEN modules, with outputs of 8 V, powering the analog and digital parts of the sensors. The A3006 CAEN modules, with an input of ±8 V, powering the back-bias part of the sensors and the amplifiers of the PSU. The main features of the PSU can be summarized as follows: ¶ Voltage conversion, from the input received from CAEN modules at 8V, to the di erent

Detector commissioning

The GBTx ASIC is a 3.2-4.48 Gb/s transceiver that manages the communication between the counting room and the front-end modules. The GBTx-SCA communication is transparent to the slow control protocol, as the GBTx encodes slow control packets and sends them as SCA packets to the requested GBT-SCA. Thus, the operation of sending commands and receiving answers from the GBT-SCA by the detector is managed by a GBTx. The two e-ports allowing the GBTx and GBT-SCA communication correspond to primary and auxiliary port. They consist of two functionally identical e-ports, ensuring redundancy in case of failures on optical links. Essentially, the main user interface ports composing the GBT-SCA consist of the following: I2C channels, implements 7-bit and 10-bit addressing transactions with a configurable transfer rate.

JTAG channel, allows programming, configuring and serial communication with devices by performing bus transactions of up to 128-bit length.

SPI channel, implements a synchronous serial bus master with a transaction length up to 128 bits and a configurable transfer rate.

GPIO channel, provides 32 configurable input-output lines latched with external clock signal or internal clock.

DAC channel, implements 4 independent digital-to-analog converter outputs with 8-bit resolution, generating voltage between 0 V to 1 V.

ADC channel, implements a 12-bit resolution analog-to-digital converter, with 32 multiplexed analog inputs, with automatic o set calibrations and gain error corrections. One of the 32 analog inputs is connected to the temperature sensor. Additionally, the inputs have a switchable 100 µA current source compatible for the use of resistance temperature sensors.

Clock and reset logic allows activating or deactivating a core in the SCA chip.

In total, the MFT detector consists of 8 GBTx (including both primary and auxiliary access, for redundancy purpose), present on the 4 PSU interface boards. They are connected to a total of 24 GBT-SCAs: 20 SCAs are present on the 4 PSU mezzanine boards, each connected to a specific face of a half-disk. The remaining 8 SCAs are present on the 4 PSU interface cards for the slow control of this board. The GBTX and GBT-SCA allows the implementation of the main features of the PSU mentioned in section 5.1. In particular, the features consist of switching on and o each zone independently, monitoring the voltages, currents, temperatures, and humidity, controlling the back-bias voltage, setting the latch-up current thresholds, monitoring the 80 whether the GBT-SCA is connected to a disk or to a PSU interface. For all the SCAs connected to the disks, the configuration sequence consists of enabling all GPIOs, ADC, DAC and disabling I2C, SPI and JTAG. Concerning the configuration for the SCAs connected on the PSU interface, the configuration is more or less the same, with a di erence of DAC disabling and an additional command to enable current on a specific ADC pin out, consisting of the PT100 and PT1000 temperature sensors.

The monitoring sequence: Six types of monitoring sequences are sent, each depending on the object that is being monitored and controlled. This is necessary because each face of a half-disk has a specific architecture (an example of Disk04 architecture is displayed in Figure 5.4). The ADC, DAC, and GPIOs addresses change from one half-disk face to the other. The condition of continuity of the monitoring sequences sent in parallel to 24 GBT-SCAs in a loop is mandatory for the detector operation. Each monitoring sequence has a duration of approximately • = 100 ms, which can be modified but should nonetheless respect the condition of • < 6 s. If this condition is not respected or if the communication to the detector is lost, the fail-safe feature is triggered. Thus, if the monitoring sequence stops running for more than 6 seconds, the detector is switched o in response. This duration can not be modified, as the PSU was constructed with components1 that definitely set this duration. A temporization was introduced to the list of commands sent in the monitoring sequence, allowing a custom temporization of each sequence. The GBT-SCA monitoring sequence per face of a half-disk is responsible essentially for the following:

• ADC: The measurements of voltages and currents (analog, digital, and back-bias), temperature sensors, humidity sensors, and the latch-up information.

• DAC: Setting the back-bias voltage and latch-up thresholds for each of the four zones.

• GPIO: Control of the multiplexer to set back-bias voltage and latch-up thresholds on specific zones, enabling or disabling the DC-DC converters, and resetting zones after a latch-up state is triggered.

For the PSU interface, the monitoring consists of ADC and GPIO control, allowing to monitor the temperature sensors on the board, and to reset communication between the GBTx and GBT-SCA in case of failure.

Requirements

For the functioning of the software, the following specific python packages are required:

with one GBT-SCA, thus is responsible for the control of one face of a half-disk. A total of 20 processes is required for the MFT disks control, as well as 4 processes for the PSU interface boards control. Each process is composed of a configuration sequence, sent once per GBT-SCA at the beginning, followed by the monitoring sequences sent in loop with a period of 4s, each consisting of 4 sub-cycles. Each sub-cycle is delimited by the GPIO multiplexer actions, which are defined by a binary command to enable or to disable a specific GPIO address. Thus, the sub-cycle will start with setting the back-bias voltage, or setting a specific analog, digital, or back-bias threshold, on 4 corresponding DACs, each corresponding to one zone, then enabling the specific GPIO address for 25 ms, during which ADC commands are sent to read di erent registers. The sub-cycle ends by disabling the corresponding GPIO. In addition to these SCA operations, enabling and disabling the DC-DC converters for 2 specific zones by the face of half-disk, as well as resetting a specific zone after a latch-up notification or a specific warning flag, is possible by adding the address registers on the GPIO actions throughout the cycles. The chronology of the sub-cycles is displayed in Figure 5.4, where the monitoring sequence is displayed for one zone. This process is a hexadecimal command-response exchange on the lowest GBT-SCA level, which is then treated by a central process. The central process retrieves the data sets containing configuration/monitoring sequences specific for each GBT-SCA. Then, it launches the GUI interface process, followed by the creation of di erent shared memory containers by GBT-SCA in order to link the information received on the GUI (user operation), allowing to modify the SCA commands accordingly. The shared memory contains essentially the commands to send to the GBT-SCA, data retrieved from the GBT-SCA, and configuration settings (start/stop communication with each GBT-SCA, activation/deactivation of DC-DC converters, latch-up reset, ...). Numerous multi-processes are created per GBT-SCA, allowing a parallelism of the communication with the whole MFT detector. Calibrations are then required, as will be discussed in the next section. This software allowed CRU firmware commissioning and developments, as the goal is to provide a correct routing to the register addresses of the di erent GBT-SCAs, so that the information reaches the corresponding disks with both primary and auxiliary ports (Figure 5.6).

Calibrations

The measured quantities (currents, voltages, temperatures, humidity) and those to be set (U BB , thresholds) are digitized via ADCs and DACs respectively. Di erent factors, such as conversion factor, gain and o set, can vary from one component to another. Therefore, calibration is required to convert physical quantities into digitized values and vice versa. In particular, few subtleties have to be considered, as the di erence in resolution between DACs (8-bit resolution) and ADCs (12-bit resolution). Thus, with each cycle, the responses are converted, analyzed (in order to check the good functioning and potentially create warnings or errors), and stored. This

Conclusion

The powering of the MFT is managed by the PSU, located between the two farthest disks from the IP. The control is ensured by GBT-SCAs components. The first part of this thesis work is described in this chapter, with the goal of fully piloting the MFT detector. At the start, when the o cial framework was under development, the MFT control was required to perform onsurface commissioning. Thus, a commissioning software was fully developed allowing the control of the MFT detector through a user interface. It was approved by the MFT Collaboration and used during the whole commissioning period. It allowed detector commissioning, firmware developments and tests, detector calibrations and set the way for the o cial framework creation.

For the o cial software in the DCS framework, the developments of the dedicated software (FRED Server), the building of the database (ConfDB) for storing detector's data, and the creation of the scripts for datapoints links with the panels (WinCC OA) are explained in this chapter. It allows the full control of the MFT during Run 3 operations. This framework is running 24h/24h in the ALICE cavern, allowing the entire detector's powering, monitoring, and control. Once the detector is operational, the aim is then to be able to derive physics performance and prepare the Run 3 analysis.

Chapter 6

Matching with Machine Learning As discussed in chapter 4, the MFT will allow access to a broad physics program by overcoming limitations imposed by the front absorber. In particular, access to the vertex of global muon tracks will be possible, allowing the separation of prompt and non-prompt J/Â contributions at forward rapidity. For this purpose, e cient matching between MCH and MFT tracks from pp to Pb-Pb collisions down to low p T is crucial to correctly identify global muon tracks.

In particular, high multiplicity is expected in the MFT in Pb-Pb collisions, resulting in a significant background and thus leading to a considerable amount of fake matches. Therefore, powerful tool is requested in order to overcome and manage this background to maintain high performance. In this chapter, developments based on machine learning methods are presented for the matching to face these challenges.

A linear summation function is then defined as follows:

y j = n ÿ i=1 w ij x i + b (6.2)
where b is a constant bias neuron. It can be added to a layer to enhance the model flexibility.

An activation function is then applied on the summation function, with its output constituting the value of neuron j of the next hidden layer. Di erent activation functions can be deployed for the propagation, such as the sigmoid function with output values ranging from 0 to 1, the hyperbolic tangent function (tanh), with values ranging from -1 to 1, and the rectified linear activation function (reLU), outputs 0 when the input AE 0, or outputs the input value if it's positive. For the matching purpose, as a result of the tests that were conducted, the sigmoid function is selected. Thus, the neuron j of the hidden layer is given by:

z j = 1 1+e ≠y j (6.
3)

The propagation between all the neurons for all the layers in the neural network follows the same logic. It is known as the forward propagation. The final value computed by the model, z, corresponds to a probability score, thus z oe [0, 1] (the output layer in Figure 6.

-right).

A threshold value C is then selected for the classification purpose. As a result, the output predicts 1 if z>C. The threshold can be tuned to obtain the best performance.

To quantify the performance of a NN model, the loss function is introduced. It represents the di erence between the true result and the NN calculated prediction. Thus, the smaller the outputs of the loss function the better the performance. For the classification process, the loss function is a negative log-likelihood, given by:

L = ≠z MC ◊ log(z) ≠ (1 ≠ z MC ) ◊ log(1 ≠ z) (6.4)
where z MC is the matching truth (1 or 0), provided by MC for each MCH-MFT tracks associated in the input of the network. For the classification task, the negative log-likelihood is used in order to strongly penalize the learning algorithm, if the prediction and truth are not in accordance. As if the z MC =1and z ƒ 0 (or vice versa), L aeOE , while if z MC ƒ z, then L ae 0.

In order to reduce the error on the predicted output, the weight parameters are adjusted to minimise the loss function outputs. This is known as the backward propagation process in a NN, and is introduced with specific optimizers. The knowledge is updated and propagated through the NN, changing thus the weights of neurons accordingly and minimising the loss 6.1. Machine Learning function after each iteration. For this purpose, the weights are updated as following:

w (t+1) ij = w (t) ij ≠ - ˆL ˆwij (6.5)
where t indicates the iteration step andis a learning rate. The learning rate defines the size of each step updating the weights at each iteration. Ifis too high, there is a high probability that the learning will diverge, and thus no minimization is possible for the loss function. In the opposite, ifis too small, the number of iterations needed to reach the minimum and thus to train the NN model is higher and might be time-consuming. The di erent scenarios are presented in Figure 6.3. As for the term ˆL ˆwij , it is calculated with the chain rule as follows:

ˆL ˆwij = ˆL ˆz ˆz ˆyj ˆyj ˆwij =(z ≠ z MC )x i (6.6)
This iterative optimization with the goal of finding the global minimum of the Loss function is known as the gradient descent. As will be discussed latter, the optimizer choice might introduce other internal parameters to tune the weights. Additionally, a dynamic learning rate can be used, thus the user can define an initial value of -, which will be tuned and adapted with the iterations.

Each iteration consists of one forward and one backward propagation for a selected number of training samples. This number is defined as the batch size, the higher it is the more memoryconsuming the process is. Finally, an epoch is defined as one forward and one backward propagation for all the training data samples.

The dataset is thus divided into the training and testing samples. The training sample is used to fit and build the model. The testing sample is used to evaluate the performance of the model, allowing an error estimation on a new set of data on which the model was not trained. A split ratio is thus applied on the main dataset, dividing it into these two sub-categories.

In order to favor the equitable distribution of information within each link, a drop-out rate could be added. It indicates a proportion of links that will be removed between the selected layers. This is not used in the context of matching, as the selected model structures are relatively small. Therefore, in order to improve the learning process, a search and selection of the mentioned parameters must be done in order to find the best performing model. This procedure is referred to as the hyperparameter tuning.

Data production and structure

The generators used throughout this chapter are PiParam and MuBoxGun. PiParam generates a number of pions, representing the background on the MFT side. MuBoxGun generates the muons that hit the MFT disks and pass through the absorber to the MCH. The detector e ects and propagation are taken into account with GEANT3 [START_REF] Brun | GEANT 3: user's guide Geant 3.10[END_REF]. As the generated MFT tracks are numerous, one should expect unbalanced datasets due to the high expected pion background. Thus, pre-processing is required to optimize the learning process with NNs, as will be discussed in section 6.4.2.

For the matching task, the input layer consists of a vector composed of the MCH and MFT track coordinates, expressed in the MFT coordinate system (as discussed in chapter 4, with Equation 4.2). The selected input layer corresponds to the following vector:

X = I x MCH ,y MCH ," MCH , tan⁄ MCH , A q p T B MCH ,x MFT ,y MFT ," MFT , tan⁄ MFT , A q p T B MFT ,‰ 2 J
All of the values are evaluated at the 5 th disk matching plane, thus for z =77.5 cm. For each MCH track, a subset of MFT tracks are selected based on a search area, which corresponds to the same 3 ‡ cut around the MCH track as in Equation 4.5. The output layer consists of one dimension, providing a matching probability score calculated by the NN. It is then transformed to a binary output of 0 or 1, through a threshold value. It indicates a mismatch or a correct match respectively between the associated tracks. The threshold defines the minimum probability accepted for correct track matching identification. If 1 is predicted, the MCH-MFT track is considered as a forward muon track. The output thus classifies each MCH-MFT track as a match (signal) or not (background). Two di erent NN approaches were tested in order to find the most convenient one for this challenge.

Performance evaluation criteria

An assessment workflow is used to evaluate the training process of the NN. Various steps of this workflow and useful definitions are presented in this section. It allows the determination of the training quality, as well as the matching performance.

Training evaluation

The loss function (Equation 6.4) is crucial for evaluating the training process, as it is applied on both training and testing datasets and can reflect if the NN model is able to learn patterns, or if there is an issue of overfitting or underfitting. Overfitting occurs when the model memorizes the training data pattern with the statistical fluctuations, thus performs poorly on testing data.

Performance evaluation criteria

Underfitting occurs when the model is unable to identify any pattern, thus predicts poorly on both training and testing datasets.

Another useful metric is the accuracy. It is a percentage calculating the correct predictions done by the model for both training and testing data, with the following formula: accuracy = correct predictions all predictions (6.7)

Thus, the higher the accuracy the better the model is learning.

In order to reflect the e ciency and the purity of the training, the F score is essential. In order to understand this metric, the extraction of the matrix following Table 6.1 will be required. True Negative (TN) occurs when the MC truth and the ML model does not predict a match, with MC = ML = 0. The Fake Positive (FP) indicates when the ML predicts an incorrect match, the Fake Negative (FN) is when the ML mis-predicts a true match, and the True Positive (TP) means there is a correct match and both MC = ML = 1. Thus, in order to calculate the purity of the predictions, the proportion of positive identifications that are actually correct, the precision variable is needed:

ML = 0 ML = 1 MC = 0 TN FP MC = 1 FN TP
Precision = TP TP + FP (6.8)
As for the e ciency of the predictions, the recall is calculated. It represents the proportion of positive results on real tracks:

Recall = TP TP + FN (6.9)
The combination of both precision and recall will result in the F β measurement, which reflects the network's accuracy by combining both the purity and the e ciency of the predictions:

F β =(1+-2 ) ◊ precision ◊ recall -2 ◊ precision + recall =(1+-2 ) TP (1 + -2 )TP + -2 FN + FP (6.10)
For the matching, the weight is equally partitioned on both aspects (-=1). Thus, in this study, the F score is defined as F 1 :

F score =2◊ precision ◊ recall precision + recall = TP TP +0.5 ◊ (FP + FN) (6.11)
Finally, once the training is satisfactory and the models are selected, an evaluation is done to matched MCH-MFT tracks correspond to the one with the highest probability score. Tools to evaluate the matching performance are then required to perform a comparison between the di erent methods and models in order to assess the optimal one. First, for this purpose, the pairing purity is calculated in order to visualize the correct sample in the predicted signal:

P GM pairing = N GM true N GM Rec (6.12)
where N GM true is the number of Global Muon (GM) tracks with correct MCH-MFT matching, and N GM Rec is the total number of all reconstructed global muon tracks (including the correct and the fake matches). Additional to the sample purity, the pairing e ciency should be accounted for in order to visualize how much of the signal is conserved for the pairing e ciency:

' GM pairing = ' GM true + ' GM fake = N GM Rec N GM Pairable (6.13)
where the N GM Pairable is the number of pairable global muon tracks, which are the tracks that have been correctly reconstructed by both MFT and MCH and comes from the same generated particle. The pairing e ciency is thus the sum of both true and fake e ciencies, which are presented as below:

' GM true = N GM true N GM Pairable (6.14) ' GM fake = N GM fake N GM Pairable (6.15)
with N GM fake the number of fake matched Global Muon (GM) tracks. All concepts and key quantities to optimize and to assess the performances of model have been introduced. The next section is dedicated to their applications on MCH-MFT track matching.

Model selection

The first designed machine learning tool was developed with the MultiLayer Perceptron (MLP), which is a Neural Network toolkit available in the ROOT framework. A preliminary study was concluded with MLP, which is presented below. Due to optimizations for time-consumption reduction, another ML algorithm has been also developed, consisting of the NN method with TensorFlow (TF) python package, reducing the time-consumption considerably. Thus, the algorithmic development and the full analysis will be presented with the TF package in the following. The datasets used for both ML methods consist of the following: for the training purpose, a dataset composed of 1000 events, each consisting of 800 fi and 80 µ has been produced. As for the testing and evaluation purposes, a dataset of 500 events, each composed of 800 fi and 10 µ is used.

Preliminary study

The MLP consists of a feed-forward neural network with a configurable structure, as described in section 6.1.1. The input vector is normalized, and the information is propagated between the layers with sigmoid activation functions. As for the used optimization method, it is known as the Robbins-Monro stochastic approximation [START_REF] Robbins | A stochastic approximation method[END_REF], where the values of the weights are updated after each iteration in order to minimize the total errors. The evolution of the weights for a t +1 iteration is described with the following: (6.17) where the ÷ is the learning rate, " and ' are parameters. They are initialized and then adjusted after each step, in order to minimize the error referred to as e p between the output predictions (z p ) and the MC response (z MC,p ): e p =z p ≠ z MC,p .

w (t+1) ij = w (t) ij +∆w (t) ij (6.16) ∆w (t) ij = ≠÷(de p /dw ij + ")+'∆w (t≠1) ij
A series of tests have been done on the network structure in order to choose the optimal model. First, the choice of input parameters is studied, in order to assess and choose for the best performing structure. Thus, Table 6.2 presents these tests, with the corresponding training F score as an evaluation method of comparison between the di erent structures. The column of 11 parameters consists of the vector described in section 6.2. tests. The score is extracted after 100 epochs for each selected structure. Tests on the network structure were also done, with additional input neurons containing di erent combinations of the main parameters, but the training process did not benefit from this additional combined

Official framework

After the MultiLayer Perceptron preliminary tests, TensorFlow python package has been deployed for the matching classification task. First, the developed algorithm will be detailed in the following, describing the workflow of the matching with ML within the various phases. For this goal, the algorithm structure is detailed in Figure 6.10. It is composed of the following workflow:

Pre-processing: The datasets are highly unbalanced, as will be further described in the following, making the learning process complicated since the signal is very small compared to the background. A data sampling method is proposed as a solution for this unbalance, where its importance and results are discussed in this section. This method consists of applying cuts mainly on the search area for MCH-MFT tracks scan, with the goal to reduce the background (fake associations) and keep the signal as intact as possible. Additionally, to further reduce the time-consumption, a dimensional reduction is proposed in order to project the data in a new reduced dimension while conserving its variance (described in section 6.6). Once these steps are done, the data is split into training and testing sub-datasets for the processing step.

Processing: The model architecture is set in YAML files. Di erent options are proposed to allow building model structures. After the model structure selection and hyperparameter tuning (detailed in section 6.1.1), the training is then performed on a dedicated training dataset. Next, a first evaluation based on the criteria explained in section 6.3.1 is done to assess the models. Then, depending on the output, an option to retrain the model is proposed. If the model has a good performance, it is extracted and saved for matching purposes. Following this, a selection of models, based on their performance, are loaded in order to be compared. Once the optimal models are identified, they are selected for the next stage, the post-processing.

Post-processing:

A new dataset is used for this stage, along with the selected NN models. For each MCH-MFT pair, a matching probability score is calculated by each NN model. The highest probability score between the MCH track and the corresponding MFT candidate is extracted and considered as a match. Some additional cuts can be considered on the selection of the matches, thus after the extraction of all MCH-MFT tracks with the highest probability score. Then, to further improve the purity of the set, an additional threshold is applied on the probability, discarding all the MCH-MFT matches with a probability below the selected threshold. This threshold selection can a ect both the purity and the e ciency. Following these steps, the matching performance is assessed by evaluating the di erent variables discussed in section 6.3.2, where the di erent models and methods are compared, in order to finally select the best model for the matching.

For the classification task, the loss function L was calculated as described previously with the equation 6.4. The weights are updated with the AdamsOptimiser [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF], which consists of an adaptive learning rate method, with the following equations:

m (t) = -1 m (t≠1) +(1≠ -1 )Ò w L (t) (6.18) v (t) = -2 v (t≠1) +(1≠ -2 )(Ò w L (t) ) 2 (6.19) m(t) = m (t) 1 ≠ -t 1 (6.20) v(t) = v (t) 1 ≠ -t 2 (6.21) w (t+1) = w (t) ≠ ÷ m(t) Ô v(t) + ' (6.22)
where ÷ is the learning rate, t the iteration, -the exponential decay rates, and ' is a small number preventing any division by 0. Di erent structures were tested for the assessment, with both the F score on training and testing calculated to check if there's an overfitting issue. For the testing purpose, a learning rate of ÷ =5◊ 10 ≠4 is set, with the sigmoid activation function. The first test was concluded on the di erent network structures. As for the choice of the activation function, the sigmoid is selected following tests done with di erent functions, notably the tanh and the reLU functions. The tanh tests had poor performance, with F score decreasing to around 0.6 when the function is integrated for both

Machine Learning integration in O 2

In order to include the matching with ML learning methods into O 2 environment, a specific pipeline should be integrated. The goal of this section is to provide the ability to exploit these methods fully for Run 3 data. This requires adjustments, allowing to benefit from the advantages of the di erent environments.

In order to integrate the ML on python to the O 2 C++ environment, ONNXRuntime [139] is used in order to convert a ML model from python format to ONNX format, thus allowing its deployment in a C++ environment. The full workflow architecture is described in the Figure 6.21, where the previous algorithm (Figure 6.10) is adapted and made more general, to allow other ML methods applications. It consists of the following 3 main categories:

Training data production: the production is done in O 2 , where simulations are tuned depending on the matching requirements. Once the simulations are done, the MCH-MFT tracks combinations within a search area on a matching plane are extracted, for the next step process.

Training and model selection: in the python environment, the parameters are extracted, where preliminary checks are done in order to judge the necessity of data pre-processing, such as dimensional reduction and data sampling. Then, the ML training takes place, where di erent methods are proposed, leading to a model which is saved in a ONNX format, in order to be able to use it within O 2 . Following this, still on python, first model evaluations take place, which were discussed previously.

Matching on runtime simulations: on the O 2 environment side, realistic MC production is launched. Then, when the matching is taking place to find the global muon tracks, the selected method is used to calculate the MCH-MFT track matching probability, thus, producing the global muon tracks. After this step, the final performance evaluations are done in order to assess the used methods and calculate the expected signal extraction, purity, e ciency, and di erent variables as discussed previously.

Conclusion

High performance of the matching between MCH and MFT tracks is essential for Run 3 analysis, as it impacts the quality of global muon tracks that will be used. The standard algorithm deployed to find the global tracks is based on a ‰ 2 criteria between MCH and MFT tracks. In high multiplicity environments, a more refined tool is required for a high performance matching. Therefore, this chapter consists of the second part of this thesis, addressing the matching task with machine learning. A full workflow was then designed with TensorFlow, allowing to train, test and assess the matching performance. As a result, promising performance for matching with ML was observed. It allows to recover high matching e ciency and purity, in comparison to the standard ‰ 2 method, especially at low p T , thus required for low-mass dimuons physics. Finally, to further improve the performances of the learning process, a Principal Component Analysis method was developed to reduce ressource consumption while keeping the same matching performances. This work will improve the results of physics analysis and especially the study of prompt and non-prompt J/Â.

Chapter 7

Vertex reconstruction As mentioned in chapter 4, prompt and non-prompt charmonia disentanglement was not possible before Run 3 at forward rapidities. As a matter of fact, the main reason is that the muon multiple scattering and energy loss in the front absorber lead to a worsening of the muon spectrometer resolution. One of the main goal of the MFT detector is to work around this issue. Indeed, as discussed in chapter 5, high quality global muon track are required, which means high matching performance between the reconstructed muon spectrometer and MFT tracks. For the separation of prompt and non-prompt contributions, in addition to the matching, vertexing is also required. It will be thoroughly discussed in this chapter, where the development of the algebra, algorithm and first preliminary tests are presented.

The inverse matrix is calculated to introduce the " factors, as they are convenient for the following calculations.

A crucial di erence between the mid and forward rapidity equations concerns the transformation from the local to the laboratory frame. At midrapidity, it consists of a rotation with the following transformation matrix:

M i = Q c c c a cos-i ≠sin-i 0 sin-i cos-i 0 00 1 R d d d b (7.6)
withi the rotation angle between the local track frame and the laboratory frame. As for the forward rapidity region, no transformation from local to laboratory frame is needed, as it consists of the same frame, -=0, thus the transformation matrix is unitary:

M i = I = Q c c c a 100 010 001 R d d d b (7.7)
The vertex of a set of muon tracks (illustrated in Figure 7.3), with corresponding local points { Pi }, consists of a linear combination of Pi such as:

V = ÿ i T i • Pi ,
where V = {V x ,V y ,V z } is in the laboratory frame (7.8) With ∆i presenting the local residuals, defined as following:

∆i = Pi ≠ M T i V = Pi ≠ V (7.9)
Thus, V is considered as the barycenter between the P i , with their respective weights, calculated as:

V = ÿ j (E j ) ≠1 ÿ i E i • Pi = ÿ i T i • Pi (7.10)
Finally, T i can be presented by:

T i = ÿ j (E j ) ≠1 E i (7.11)

‰ 2 minimization by Newton-Raphson

As mentioned above, the PCA corresponds to the point with the minimum ‰ 2 score. The ‰ 2 is given with the following equation:

‰ 2 = 1 2 ÿ i ∆T i • E i • ∆i (7.
12)

The iterative Newton-Raphson method for the ‰ 2 minimization is used in both mid and forward rapidity regions. At each iteration, tracks are propagated in the direction that minimizes the ‰ 2 . Thus, to reach the point where its first derivative is zero, and its second derivative is positive. The iterations of the tracks propagation function is based on a Taylor expansion, with the following correction dχ 2 ∂z ( d 2 χ 2 ∂z 2 ) ≠1 applied between each iteration. According to the Newton-Raphson minimization, the track point evolution follows:

Q c c c a x 2 y 2 z 2 R d d d b = Q c c c c c c c a x 1 ≠ ∂x 1 ∂z 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 ≠ 1 2 ∂ 2 x 1 ∂z 2 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 2 y 1 ≠ ∂y 1 ∂z 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 ≠ 1 2 ∂ 2 y 1 ∂z 2 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 2 z 1 ≠ ∂z 1 ∂z 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 ≠ 1 2 ∂ 2 z 1 ∂z 2 3 dχ 2 ∂z 1 d 2 χ 2 ∂z 2 2 ≠1 4 2 R d d d d d d d b (7.13)
More precisely, each iteration consists of the following calculations:

• the updated (x, y, z) coordinates for each track,

• the new coordinates of the PCA V ,

• the tracks residuals ∆i ,

• the updated ‰ 2 following these new coordinates with Newton-Raphson.

These iterations take place until the convergence of the ‰ 2 . The vertex for the tracks is found and extracted, as well as the ‰ 2 score. This score will consist also as an assessment metric for the PCA. As mentioned, the smaller the ‰ 2 value, the higher the probability of the presence of a crossing point between given tracks. Thus, cuts on this ‰ 2 score might be applied to consider or discard the PCA as a secondary vertex. This will be further detailed in the next chapter, where data quality assessment is done with cuts applied on ‰ 2 PCA on o cial simulations. As observed in the presented equations (Equation 7.13), the track derivatives are required for the iterative minimization. Their first and second order derivatives are the following:

ˆ(x, y, z) ˆz = A cos" tan⁄ , sin" tan⁄ , 1 B (7.14) ˆ2(x, y, z) ˆz2 = A fl.sin" tan 2 ⁄ , ≠ fl.cos" tan 2 ⁄ , 0 B (7.15)
with the track curvature2 fl = 1 r = 0.3qBz p T , with B z the magnetic field on the z-axis, q is the charge of the particle (in the unit of the elementary charge, e), and r is the radius (in meter).

In addition, the first and the second order z derivatives of ‰ 2 are also required for the minimization. Thus, the corresponding equations are the following:

ˆ‰2 ˆz = ÿ i ∆T i • E i • ˆ∆ i ˆz (7.16) ˆ2‰ 2 ˆz2 = ÿ i Q a ˆ∆ T i ˆz • E i • ˆ∆ i ˆz + ∆T i • E i • ˆ2 ∆i ˆz2 R b (7.17) with ˆ∆ i ˆz = ÿ k (" ik ≠ T k ) • ˆP k ˆz and ˆ2 ∆i ˆz2 = ÿ k (" ik ≠ T k ) • ˆ2 Pk ˆz2 (7.18)
where k refers to the total number of input tracks.

Particular case of PCA calculation

If no weights are taken into consideration for the tracks, the covariance matrix corresponds to a unitary matrix. In the following, the presented equations necessary for the PCA finding are adapted for this particular case, which is currently used in O 2 at both mid and forward rapidities. The V and the local residuals become:

V = ÿ i T i • Pi = 1 N ÿ i Pi with T i = 1 N I ∆i = ÿ k (" ik ≠ R ik ) Pk , with R ik = I T i I k N = 1 N I (7.19)
Then, for the minimization of the ‰ 2 , the following equations can be obtained:

ˆ‰2 ˆz = ÿ i ∆T i ˆ∆ i ˆz ˆ‰2 ˆz2 = ÿ i Q a ˆ∆ T i ˆz ˆ∆ i ˆz + ∆T i ˆ2 ∆i ˆz2 R b (7.20)

Seed finder methods

Where the derivatives of the residuals are expressed as follow:

ˆ∆ i ˆz = ÿ k (" ik ≠ R ik ) ˆP k ˆz ˆ2 ∆i ˆz2 = ÿ k (" ik ≠ R ik ) ˆ2 Pk ˆz2 (7.21)
Finally, for k = j with R ij = 1 N I, the residual derivatives can be calculated with the following terms:

R ij • ˆPj ˆz = 1 N Q c c c a ∂x j ∂z ∂y j ∂z 1 R d d d b (7.22) R ij • ˆ2P j ˆz2 = 1 N Q c c c a ∂ 2 x j ∂z 2 ∂ 2 y j ∂z 2 0 R d d d b (7.23)
The 3D minimization method presented is the only method used at midrapidity for the PCA finding, where track types are described by helix models due to the magnetic field. However, muon tracks at forward rapidities are not as a ected by the magnetic field as at midrapidity. Thus, the quadratic and linear track models allow an accurate description of their trajectories. If the Newton-Raphson method is applied to the tracks at a point far from the PCA, di culties may be encountered that limit the performance of the method. In particular, depending on the nature of the tracks (helix vs linear), the minimization algorithm may face di culties to convergence because of either a large number of iterations required to reach the PCA, or null first order derivatives of the tracks. This will be demonstrated in the next section. At forward rapidities, seed finder methods have been developed to constrain this decrease of performance by providing a starting seed close to the PCA during the 3D minimization. The way the seed is calculated is detailed in the following section.

Seed finder methods

The seed finder is essential for the PCA finding and for the reduction of time and computing resource consumption. It provides an initial seed close to the PCA for the iterative Newton-Raphson minimization process. Several methods are developed for this seed initialization.

Then, the z≠coordinate is calculated from the equations with y(T 0 )=y(T 1 ) and z(T 0 )=z(T 1 ) conditions. Thus this leads to the following equation: Z= b 0 ≠b 1 a 0 ≠a 1 . The same steps are also done on the (x,z) plane. Finally, the average of these 2 calculated z≠coordinates corresponds to the extracted seed z.

Analytical approach:

In order to be more accurate, the curvature of the tracks are taken into account with the following developed analytical method. The principle of this method consists of solving the track propagation equations analytically for each track in order to find the Z seed at the PCA (z T 0 ¥ z T 1 ). With the p T at the order of 1 GeV/c and the magnetic field of 0.5 T, the curvature radius is at the order of 6 m. In the case of the MFT, ∆z r π 1. Hence, the track equation can be approximated by the following quadratic formula:

Q c c c a x y z R d d d b = Q c c c a x 0 +∆z cos(φ 0 ) tan λ 0 + (q/p T 0 )Hz∆z 2 k sin(φ 0 ) 2tan 2 λ 0 y 0 +∆z sin(φ 0 ) tan λ 0 + (q/p T 0 )Hz∆z 2 k cos(φ 0 ) 2tan 2 λ 0 ∆z + z 0 R d d d b (7.24) with k = 0.3|B z | and H z = B z |B z |
. In order to establish the equations at the crossing point, an estimation of x and y is provided by the FwdTrackHelper tool at the PCA. The goal is to find the z≠coordinate at the PCA in the equation. For the initial points, the track is propagated to z 0 =0, and the corresponding x 0 and y 0 are extracted. Additionally, the required values can be extracted, determining the variables as follows:

A x = q/p T 0 ◊ H z ◊ k ◊ sin(" 0 ) 2 ◊ tan 2 ⁄ 0 (7.25) B x = cos" 0 tan⁄ 0 (7.26) C x = x ≠ x 0 (7.27)
The same is done for A y , B y , and C y . In order to find the z≠coordinate, the following second degree equations are established:

A x ∆z 2 + B x ∆z + C x =0 (7.28) A y ∆z 2 + B y ∆z + C y =0 (7.29)
Where the corresponding ∆z = z ≠ z 0 are calculated. This leads to finding the z≠coordinate at PCA for the track, which is the average of the solutions for both Equation 7. Finally, the relative error is calculated for all track models as follows:

∆xyz = Ò ∆2 x + ∆2 y + ∆2 z =0.00084cm (7.33)
A high precision can be deduced for the first validation test, where the vertex reconstruction algorithm ensures a high accuracy between the reconstructed and generated PCA. Additionally, a better precision can be deduced for the linear muon tracks.

The resolution validation tests are presented on the right panels of Figure 7.10, Figure 7.11 and Figure 7.12. The resulting values of ∆x , ∆y and ∆z are shown in Table 7 The relative error is also calculated, with the following result:

∆xyz = Ò ∆2 x + ∆2 y + ∆2 z =0.11cm (7.34)
As opposed to the validation loops, no important di erence can be observed between the linear and helix associated track models. As for the di erent errors contributions in Figure 7.12, the same trend can be noticed for x≠ and y≠coordinates. As for the errors on the z≠coordinate, the trend is wider and therefore reflecting the errors calculated in the table Table 7.2. The calculated resolutions are within the expected and predicted interval, reflecting the errors implemented on the coordinates for the resolution validation. Following these preliminary tests, the vertex reconstruction tool at forward rapidities has been o cially integrated to O 2 .

Conclusion

One of the main objectives of the MFT is to allow the separation of the prompt and non-prompt J/Â contributions. This consists of the goal of the third part of this thesis, with an algorithmic approach developed and deployed in O 2 for finding the vertex of global muon tracks at forward rapidity. This algorithm aims at finding the point of closest approach variable for n tracks, and calculate a ‰ 2 score for the distance between the vertex and each of the tracks at a specific plane. The higher the probability of these n tracks to cross is, the lower the ‰ 2 is. The algorithm can be summarized as follows: first, a seed finder method is executed, in order to minimize approximately the distance between two tracks on (x,y) plane (dichotomy method is selected). After which, an iterative method takes place, the Newton-Raphson minimization, which is used to converge to a spatial point at a ‰ 2 minima, with high precision, thus following a 3D minimization. Following these developments, validation tests were carried out, ensuring that the algorithm works as intended and e ectively. As a result to this algorithm, new measurements as the longitudinal decay length, the longitudinal and transverse pseudo-proper time can now be calculated at forward rapidities, as performed in the MFT TDR. Therefore, a separation between prompt and non-prompt J/Â can be achieved. In the next chapter, o cial simulations are evaluated using the vertexing reconstruction algorithm. Background function: the ratio of two polynomials is used to describe the background shape.

The numerator consists of a polynomial of the second order and the denominator one of the third order. Thus, this function is composed of 7 parameters in total.

The result is shown in Figure 8.1. The number of J/Â extracted for this dataset consists of N J/ψ =62398± 500, with a mass of µ J/ψ =3.112 ± 0.001 GeV/c 2 and a mass resolution around 86 MeV/c 2 .

Vertexing resolution

Firstly, the ability of the vertexing algorithm to reconstruct the vertices at the correct positions is tested in this simulation by looking at the di erence between the reconstructed (V Rec z ) and generated (V MC z ) z-coordinates of the vertices. The distribution is extracted for opposite-charge dimuons, with a p T > 0.5 GeV/c cut on the selected muons. Track type 4, equivalent to Run 2 muon tracks, is used for this study and thus, tracks are extrapolated to the primary vertex reconstructed by the ITS. Therefore, if the vertexing algorithm runs properly, the resolution width of the ∆V z = V Rec z ≠ V MC z distribution has to be compatible with the resolution of the ITS on the vertex reconstruction. This distribution is presented in Figure 8.2. The ∆V z mean and width are -0.0078 cm and 0.0057 cm respectively. As expected, the latter is compatible with the ITS primary vertex resolutions.

Secondly, a similar test is conducted using track type 0 (global muon tracks) to get an estimation of the Run 3 resolutions. This study aims at understanding the resolution e ects on the pseudo-proper time distribution. The di erence between the Z position of the primary vertex Z IP and a secondary vertex Z SV is firstly studied. As this MC production contains only prompt decays, the charmonium decay vertices (denoted as secondary vertex: SV) are

The pseudo-proper time t z is presented in Figure 8.19 -right. An additional cut on the invariant mass of 2.5 GeV/c 2 <m µµ < 3.5 GeV/c 2 is applied to minimize the background. In in the range [-0.002,0.002] ns, the total extracted number of J/Â is N J/ψ =4 4 7 5± 54 with a signal-to-background of S B =2.25.

Non-prompt J/Â signal characterization

After examining the prompt J/Â production, this section will focus on the non-prompt production with the goal of assessing its essential characteristics. First, the same strategy as in the previous section is followed with the study of ∆ z = IP z ≠ SV z for the true reconstructed global muon tracks as presented in Figure 8.20 -left, and the fake reconstructed tracks as shown in Figure 8.20 -right. In this section, the J/Â is produced from the b-hadron decays. The mean of true reconstructed muons coming from J/Â mother particles is displaced around 0.56 cm, with a resolution of 1.18 cm. As for the trend of the fake reconstructed muons, with a noticeable peak around zero. Di erent set of cuts are applied on the ∆ z distribution in Figure 8.21, to find the best one, in order to extract the signal with the less possible background-like distribution, as performed previously for prompt J/Â. The number of reconstructed J/Â without cuts is N J/ψ =3172± 33 (in black), while the number of reconstructed true J/Â is N J/ψ =1 9 6 8± 30. Therefore, the fraction to be re-integrated to the signal distribution for cross-section calculations is of 0.38. When a ‰ 2 MCH≠MFT < 20 cut is applied, the extracted number of J/Â is N J/ψ =2 4 1 2± 31, with a fake tracks contamination of 0.18. Finally, the set of cuts with the lowest contamination consists of an additional ‰ 2 PCA < 1.5 ◊ 10 ≠3 cut, resulting in a N J/ψ =2 0 1 7± 30, with a contamination of a fraction of 0.02.

In

Conclusion

The O 2 environment is in development for the framework preparation for Run 3 data analysis. On this topic, work is on-going to produce and assess the quality of simulations, constituting the last part of this thesis. The simulations will allow the understanding of the impact on our physics observables coming from the various e ciency and fake rate of the detector, as fake matching and resolution e ects. First, assessment of the developed tool for the vertexing is done, where detector resolution e ects are studied. Then, the first o cial simulations of pp collisions at Ô s = 13 TeV with embedded signal of prompt and non-prompt J/Â are studied, with di erent kinematics resolutions presented where the fake matching e ect was visualized. Then, the decay length was extracted for the non-prompt J/Â. Finally, the distribution for the longitudinal pseudo-proper time with all the di erent prompt and non-prompt contributions was presented.

Conclusion

The work of this thesis was mainly devoted to the commissioning of the MFT and to the preparation of the Run 3 analyses, as it took place during the second long shutdown of the LHC. It is the period when all the detectors and upgrades were in preparation for the next data taking period, which o cially started on the 5 th July 2022.

The first part of this thesis was dedicated to the on-surface commissioning of the detector, and the preparation of the o cial framework enabling detector operations during Run 3. In particular, this work consisted of the creation of a specific software, from front-end to back-end, which allows communication, monitoring and the control of the MFT. It was approved by the collaboration, and extensively used for the whole period of the on-surface commissioning of the MFT and as a reference to validate the o cial control software. This work required the understanding of the functioning of complex electronics and its communication protocol, in order to integrate this into a more general and user-friendly framework, allowing complete operations of the MFT. This work consists of the control of 24 GBT-SCA in parallel, allowing a fluid control of the whole detector. In addition, the entire development of a graphical interface was necessary to achieve this. In parallel, the middleware software (FRED) was developed for the MFT within the DCS framework. This was successfully completed and is currently running 24 hours a day on the experiment during the last period of the on-site commissioning and the Run 3 operations. This work consisted of an essential brick for the MFT detector. The development of the MFT-FRED software was essential to allow constant communication with the detector through messages. This part is mainly in charge of sending periodically commands to the detector and decoding the detector's responses. It receives also commands from the operator to change some settings (calibration) or to execute some actions (reset, enabling/disabling some components, etc.). Thus, this middleware establishes the communication between the operator and the MFT. Database development was also necessary to store the di erent configurations. Finally, additional developments were required to collect and distribute the information to the panels of the graphical interface. Specifically, creating and structuring data points on WinCC OA allowed their display in a proper way on the panels available to the operator.

The second part of the work in this thesis focused on the track matching between the muon spectrometer and the MFT. Tools based on ML have been designed and implemented in order to exploit neural networks to extract global tracks. This study proved the usefulness of ML for the matching task at high multiplicity environments, as the purity and e ciency results based on ML were significantly better than those based on a standard ‰ 2 method. The development of a full framework for data pre-processing, ML training, and performance evaluation has been developed in this thesis. With machine learning applied to small signal over background environments ( S B =0 .22), muon tracks could be unravelled with S B =3 2 , compared to the ‰ 2 methods, where S B =1 0 . In particular, with ML, the pairing purity increases (from 0.91 to 0.97) and the e ciency of the fake tracks is reduced considerably (from 0.1 to 0.03) compared to the ‰ 2 method. It is also important to note the dependence of these results on the training datasets. In the future, the training of these tools on data that describe collisions will be exploited. More specifically, o cial simulations based on PYTHIA8 will be studied, in order to prepare the NN for the Run 3 data. Another prospect for this work should focus on the evaluation of uncertainties due to the matching with ML.

The third part of this thesis focused on finding the vertices of muon tracks. The construction of the algorithm responsible for this task is an essential building block for Run 3. It will allow the separation of the di erent contributions of the production of J/Â. The prompt (from collision point) and non-prompt (from B-decay) J/Â could be extracted for the first time in ALICE at forward rapidities. For this task, the algorithm consists of two essential cores. The first is composed of a seed finder method, consisting of a 2D minimization of the distance between the tracks. It is then followed by a 3D minimization, with Newton-Raphson method for finding the vertex of the muon tracks. Initial evaluations have shown the e ciency of this algorithm, with a capacity of vertex reconstruction with an uncertainty of 8.4 ◊ 10 ≠4 cm. This vertexing algorithm was o cially implemented in the O 2 environment.

The last part of this thesis consisted of first evaluations of pp collisions with o cial Run 3 MC simulations, using the new vertexing algorithm. As the preparation unfolds for Run 3, the O 2 environment is in continuous developement for the analysis framework preparation. In this part, the resolution of vertexing was studied, and the importance of matching was highlighted. Notably, for the reduction of fake tracks, the importance of cuts application arises. Moreover, the fraction of signal that can be lost due to the cuts to reduce the fake matching was investigated. Finally, the first pseudo-proper time measurement with the di erent contributions of prompt and non-prompt J/Â was presented.

When the data will arrive, many analyses prospects can be investigated for Run 3. Firstly, the cross section of the B-hadron can be measured, adding a complementary measurement to the one done by LHCb extended towards more central collisions. Additionally, the extraction of the beauty contributions can be performed with ML tools. A study should therefore be carried out to see whether beauty extraction with ML is more e cient than with standard methods. The separation of charm and beauty contributions can also be achieved down to low p T .

Résumé en français

La ChromoDynamique Quantique (QCD) est la théorie quantique des champs qui décrit l'interaction forte, responsable de la force nucléaire forte qui est à la base de la structure nucléaire (proton, neutrons et plus généralement hadrons). Dans des conditions normales, les quarks et les gluons sont confinés dans la matière nucléaire. Néanmoins, à haute température et haute densité d'énergie, un nouvel état de la matière nucléaire existe connu sous le nom de Plasma de Quarks et de Gluons (PQG). Il s'agit d'un milieu dense composé de matière en forte interaction au sein duquel les quarks et les gluons sont déconfinés. Les propriétés du PQG peuvent être étudiées en reproduisant les conditions nécessaires par des collisions ultra-relativistes d'ions lourds dans des collisionneurs de particules tels que le Large Hadron Collider (LHC, CERN). Le détecteur ALICE, situé autour de l'un des points de collisions du LHC, est conçu pour étudier le PQG à travers les collisions d'ions lourds (majoritairement entre noyaux de Pb).

L'une des sondes historiques proposées pour étudier les propriétés du PQG est la mesure de la production de quarkonia, particules composées d'un quark lourd et de son anti-quark, plus précisément la suppression de l'une d'entre elles, le charmonium J/Â. Cependant, un autre mécanisme a ectant la production de ce dernier a également été observé : la recombinaison. Celle-ci se produit à très haute densité dénergie, quand le nombre de quarks charmés est si important qu'il permet la recombinaison de ces quarks dans un état de charmonium J/Â. La mesure inclusive de quarkonia peut être e ectuée dans ALICE jusqu'à une impulsion transverse p T de 0 GeV/c dans deux régions de rapidité di érentes. À mi-rapidité (|y| < 0.9), les mesures de quarkonia sont e ectuées via leur canal de désintégration diélectronique et la séparation des contributions prompte et non-prompte est possible. À rapidité vers l'avant (2.5 < y<4), seule la mesure inclusive de quarkonia peut être faite par leur canal de désintégration muonique dans le spectromètre à muons.

Le spectromètre à muons est composé de stations de trajectographie (Muon CHambers, MCH) et de déclenchement (Muon TRigger, MTR) et d'un absorbeur frontal situé après le point d'interaction (IP). Il a été conçu pour étudier d'importants sujets de physique lié à la mesure des saveurs lourdes ouvertes, de la production de quarkonia et de mésons vecteurs légers.

Cependant, en raison de la di usion multiple qui se produit dans l'absorbeur frontal entraînent un manque de précision sur l'origine des muons, certaines des performances du spectromètre sont limitées. Les muons produits par les désintégrations de hadrons de saveurs lourdes ne peuvent pas être distingués de ceux produits par la désintégration de pions et de kaons, ce qui introduit un bruit de fond élevé. En outre, seules des mesures inclusives de JÂ sont possibles en raison de l'absence d'information sur les vertex secondaires. Pour remédier à ces diverses limitations, le Muon Forward Tracker (MFT) a été proposé, construit et installé. ment de logiciels, du plus bas niveau (communication directe avec les registres des GBT-SCA) au plus haut niveau (interface graphique pour les opérateurs). La PSU est responsable de l'alimentation et de la surveillance de tous les capteurs du détecteur. Le détecteur comprend quatres cartes PSU principales et un total de 28 GBT-SCAs, assurant le transfert simultané des informations de contrôle et de surveillance du détecteur. Pour cette partie de ma thèse, j'ai développé le logiciel de commissioning pour le détecteur, connu sous le nom de PSU Control, responsable du contrôle complet du détecteur. Il a été approuvé et utilisé par la collaboration MFT pendant toute la période de commissioning, et a servi de référence pour le logiciel o ciel de l'expérience ALICE pour le Run 3. J'ai ensuite développé ce dernier, le Detector Control System (DCS) du MFT, également détaillé dans le chapitre 4.

La deuxième partie de mon travail, presenté dans le chapitre 6, concerne un aspect très important de l'upgrade du MFT : l'association de traces entre le MCH et le MFT afin d'extraire les traces de muons à rapidité à l'avant. La méthode utilisée pour l'association consiste à extrapoler les traces MCH à un plan spécifique du MFT, et de sélectionner la trace MFT sur la base d'un critère de score chi 2 . Cependant, en raison de la di usion multiple à l'intérieur de l'absorbeur entre le MFT et le MCH, une incertitude sur l'extrapolation des traces est introduite. Ainsi, la méthode peut perdre en e cacité et en pureté d'association lors du processus d'extraction des muons, notamment dans des environnements à forte multiplicité et pour des particules à faible p T . Par conséquent, des outils plus ra nés sont nécessaires pour la tâche d'associations de traces. Pour cela, j'ai conçu et étudié des méthodes de machine learning afin de calculer la probabilité d'association entre les traces MFT et MCH. J'ai développé une procédure logicielle complète pour cela, du pré-traitement des données à l'évaluation des performances en passant par la phase d'apprentissage, afin de trouver la meilleure méthode d'association pour une extraction optimale des traces de muons. L'extraction de traces de muons en a été ainsi améliorée, avec le rapport signal (vraies traces de muons extraites) sur bruit (fausses traces extraites) passant de 10 à 32 avec le machine learning. Le chapitre 7 est dédié à la troisième partie de mon travail, consacrée aux développements algorethmiques nécessaires à la séparation des J/Â prompts et non-prompts. Plus précisément, cela porte sur le développement de l'algorithme de reconstruction des vertex des traces de muons à rapidité à l'avant. L'algorithme est composé de deux principales parties : tout d'abord, une minimisation 2D est e ectuée sur la distance séparant les traces de muons afin d'obtenir une première estimation de la position du vertex, suivie ensuite d'une minimisation 3D avec la méthode de Newton-Raphson pour obtenir précisément la position du vertex des muons. J'ai également e ectué des évaluations et des tests pour valider cet algorithme, qui promet une précision importante, avec une capacité de reconstruction avec une incertitude de 8,4 × 10 ≠4 cm.

La dernière partie de cette thèse, présentée dans le chapitre 8, a consisté en la première évaluation des simulations Run 3 o cielles des collisions proton-proton (pp) afin de préparer l'environment et des outils d'analyse. Les travaux portent sur un large éventail de sujets, allant de l'évaluation de la qualité de ces simulations, à la compréhension de l'impact provenant de l'e cacité et de la pureté de l'association de traces sur les observables physiques, à la préparation de codes d'analyse pour mesurer di érentes observables. Plus précisément, des simulations o cielles de collisions pp à 13 TeV ont été produites en utilisant l'algorithme de reconstruction des vertex décrit dans le chapitre 7. Di érentes résolutions ont été étudiées, notamment l'e et d'association incorrecte de traces a été souligné. Enfin, pour la première fois dans la région de la rapidité à l'avant, des mesures de temps propre ont été e ectuées permettant des premières separation entre les contributions de J/Â prompts et non-prompts.

1. 1

 1 Standard Model elementary particles, values extracted from the PDG [1]. . . . . 1.2 All Feynman diagram vertices of the Standard Model [9]. . . . . . . . . . . . . . 1.3 The coupling constant as a function of the momentum transfer [3]. . . . . . . . . 1.4 The phase diagram for nuclear matter, in terms of temperature and of the net baryon density. Figure adapted from [15]. . . . . . . . . . . . . . . . . . . . . . .

1. 6

 6 Sketch of three collision systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Sketch of the space-time evolution of heavy-ion collisions at LHC energies. . . . 1.8 Coordinate system describing a collision between A and B nuclei. . . . . . . . . 1.9 Sketch of Glauber model geometry, (a) longitudinal and (b) transversal view [19]. 1.10 (left) First order QCD diagrams for ss production [21]. (right) Strange hadrons to pions production ratio as a function of charged particle multiplicity at midrapidity for pp collisions at Ô s =7TeV, Ô s =1 3TeV, p-Pb and Pb-Pb at Ô s NN =5.02 TeV, and Xe-Xe at Ô s NN =5.44 TeV [22]. . . . . . . . . . . . . . 1.11 (left) Panel (a) presents schematically the collision zone between two incoming nuclei for non central collisions. Panel (b) illustrates initial-state anisotropy in the collision zone converting into final-state elliptic flow, and panel (c) measured as anisotropy in particle momentum [24]. (right) The integrated elliptic flow v 2 of the charged particles as a function of center-of-mass energies [23]. . . . . . . . xi 1.12 (left) Comparison of direct photons from model NLO pQCD predictions in pp scaled to Pb-Pb collisions with data in Pb-Pb collisions at 2.76 TeV. (right) Comparison of models with pQCD photons with QGP formation with data in Pb-Pb collisions at 2.76 TeV. Both figures are extracted from [25]. . . . . . . . . 1.13 (left) A sketch illustrating the jet quenching [26]. (right) Azimuthal distribution in di erent collision systems with STAR [27]. . . . . . . . . . . . . . . . . . . . . 1.14 (left) Charmonia state in vacuum vs in QGP, where Debye screening takes place preventing the formation of bound state.

2. 12

 12 The (left) prompt and (right) non-prompt J/Â cross-section measurements as a function of the transverse momentum p T in midrapidity pp collisions at Ô s = 13 TeV. Both figures are extracted from [77]. . . . . . . . . . . . . . . . . . . . . 2.13 The (left) prompt and (right) non-prompt J/Â cross-section measurements as a function of the transverse momentum p T in midrapidity pp collisions at Ô s = 5.02 TeV compared between ALICE, CMS, and ATLAS measurements. Both figures are extracted from [77]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The CERN detailed accelerator structure [82]. . . . . . . . . . . . . . . . . . . . 3.2 The ATLAS detector structure [88]. . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The CMS detector structure [90]. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The LHCb detector structure [93]. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 The Run 3 ALICE detector structure [95]. . . . . . . . . . . . . . . . . . . . . . 3.6 The ITS2 scheme [108]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 A schematic view of the ALICE muon spectrometer in the (z,y) plane [112]. . . 3.8 A schematic view of the front absorber with its composition [50]. . . . . . . . . . 3.9 A schematic view of the ALICE muon chambers. . . . . . . . . . . . . . . . . . . 3.10 A schematic view of the RPC structure in the muon identification chambers [94].

4. 1

 1 Dimuon mass distribution for Pb-Pb collisions simulated with HIJING at 0-10 % centrality at Ô s NN = 5.5 TeV without the MFT (left) and with the MFT (right) [111]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 (up) A Schematic view of the location of the MFT inside the ALICE central barrel [111]. (bottom) The MFT fully installed in its final position around the beam pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 (left) A Schematic view of the full MFT detector [111]. (right) An assembled half-cone view of the MFT detector. . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Schematic view of the cross-section of a CMOS pixel [108]. . . . . . . . . . . . . 4.5 (left) A detailed view of a half disk's face components. (right) A schematic view of the half-disk 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 (left) A detailed view of the patch-panel, the FT0+C and readout cables. (right) A view of the barrel and the readout cables (bottom of the picture and on the right, folded for transport), with power cables, water pipes and air ducts. . . . . 4.7 (left) A mapping of the ÷ and " for the MFT tracks. (right) The position x and y for the MFT clusters in the last disk. . . . . . . . . . . . . . . . . . . . . . . . 4.8 A sketch describing the functioning of the track finding with Cellular Automaton in the MFT [111]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 (left) Map for obtaining global muon tracks. (right) Example of the matching [111]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 The di erent track types present in the muon spectrometer for Run 3. . . . . . . 4.11 Display of the matching plane during the task of MCH-MFT track matching. . . 4.12 The coordinate system used in the muon spectrometer. . . . . . . . . . . . . . . 5.1 MFT map with the di erent elements of the PSUs and the connections linking them. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Power Supply Unit features scheme for one disk. . . . . . . . . . . . . . . . 5.3 (left) A detailed view of the first test-bench. (right) A photo of the full test-bench view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 (up) A detailed view of the GBT-SCA registers for the face of half-disk 4. (bottom) A schematic representation of the monitoring sequence sent to the PSU interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 A schematic algorithmic map of the commissioning software. . . . . . . . . . . . 5.6 A schematic overview for the o cial firmware used for the MFT. . . . . . . . . . 5.7 The commissioning software, display of one of the last o cial GUI panel for 5 face of disks. 4 of these panels are required for the full MFT control. . . . . . . 5.8 The ALFRED scheme, with the display of relational links between the di erent levels, done with DIM protocol (adapted from [132]). . . . . . . . . . . . . . . . 5.9 The PSU relational database diagram. . . . . . . . . . . . . . . . . . . . . . . . 5.10 The full DCS structure for the MFT control: ALF on the lowest module, FRED middle module detailed within the di erent processes, and WinCC OA the supervisory process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 An example of the display for ALFRED communication on low level, before publishing the response to winCC. . . . . . . . . . . . . . . . . . . . . . . . . . 5.12 The organization of datapoints, responsible for the information displayed on the panels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13 Expert view of the status of the MFT. . . . . . . . . . . . . . . . . . . . . . . . 5.14 Expert view of a face of a half-disk. . . . . . . . . . . . . . . . . . . . . . . . . . 5.15 Control of a face of a half-disk (cooling,PSU,Readout Unit). . . . . . . . . . . . 5.16 Control of the PSU of a half-cone. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.17 History preview, monitoring of di erent measures trends. . . . . . . . . . . . . . 5.18 General overview of the full MFT status. . . . . . . . . . . . . . . . . . . . . . . 6.1 An example of supervised vs unsupervised learning. . . . . . . . . . . . . . . . . 6.2 (left) A scheme of a neuron [136]. (right) A neural network structure. . . . . . . 6.3 The loss function minimization (2D visualization) with di erent learning rates scenario. (a) Consists of a large -, resulting in deviation, (b) of very small -, slow convergence to the minima, and (c) consists of a coherent rate behaviour. . 6.4 (left) Correct matches as a function of the chi2 rank. (right) the ‰ 2 score for signal and background with a cut applied on the maximum admitted score. . . . 6.5 (left) The distribution of the x MFT as a function of " MCH for true and fake matched tracks. (right) Zoomed-in figure on the x MFT as a function of " MCH ..

Figure 1 . 2 :

 12 Figure 1.2: All Feynman diagram vertices of the Standard Model [9].

  .4. The suppression steps trend indicate first the dissociation of the J/Â coming from Â(2S), followed by the dissociation of the contribution from ‰ c .

Figure 2 . 4 :

 24 Figure 2.4: The J/Â production probability vs the energy density (Equation 1.18)[ 50].

Figure 2 . 8 :

 28 Figure 2.8: (left) The nuclear modification factor of Υ in Pb-Pb collisions [67]. (right) The elliptic flow v 2 of Υ in Pb-Pb collisions [68].

Figure 2 . 11 :Figure 2 . 13 :

 211213 Figure 2.11: The inclusive (left) J/Â and (right) Â(2S) cross-section measurements as a function of the transverse momentum p T at forward rapidity pp collisions at Ô s = 5.02, 7, 8, and 13 TeV at the top, and the ratio of the 5.02, 7, and 8 TeV to 13 TeV measurements at the bottom. Both figures are extracted from [74].

3 .Figure 3 . 4 :

 334 Figure 3.4: The LHCb detector structure [93].

  ALICE Cosmic Rays Detector 2 AD | ALICE Diffractive Detector 3 DCal | Di-jet Calorimeter 4 EMCal | Electromagnetic Calorimeter 5 HMPID | High Momentum Particle Identification Detector 6 ITS-IB | Inner Tracking System -Inner Barrel 7 ITS-OB | Inner Tracking System -Outer Barrel 8 MCH | Muon Tracking Chambers 9 MFT | Muon Forward Tracker MID | Muon Identifier PHOS / CPV | Photon Spectrometer TOF | Time Of Flight T0+A | Tzero + A T0+C | Tzero + C TPC | Time Projection Chamber TRD | Transition Radiation Detector V0+ | Vzero + Detector ZDC | Zero Degree Calorimeter

Figure 3 . 5 :

 35 Figure 3.5: The Run 3 ALICE detector structure [95].

Figure 4 . 3 :

 43 Figure 4.3: (left) A Schematic view of the full MFT detector [111]. (right) An assembled half-cone view of the MFT detector.

6. 1 97 6. 2 102 6. 3 104 6. 4 110 6. 5 6 . 6

 197210231044110566 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.1.1 Artificial neural network . . . . . . . . . . . . . . . . . . . . . . Matching application . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2.2 Data production and structure . . . . . . . . . . . . . . . . . . . Performance evaluation criteria . . . . . . . . . . . . . . . . . . . 6.3.1 Training evaluation . . . . . . . . . . . . . . . . . . . . . . . . 102 6.3.2 Matching performance . . . . . . . . . . . . . . . . . . . . . . . Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Preliminary study. . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.2 O cial framework . . . . . . . . . . . . . . . . . . . . . . . . Results and performance . . . . . . . . . . . . . . . . . . . . . . Principal component analysis . . . . . . . . . . . . . . . . . . . . 6.7 Machine Learning integration in O 2 . . . . . . . . . . . . . . . . . 6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 χ 2

 2 minimization by Newton-Raphson . . . . . . . . . . . . . . . . 7.4 Seed finder methods . . . . . . . . . . . . . . . . . . . . . . . . 7.5 First assessments and results . . . . . . . . . . . . . . . . . . . . 7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 8 . 1 :

 81 Figure 8.1: The invariant mass distribution of dimuons with the signal and background contributions.

Figure 8 . 19 :

 819 Figure 8.19: (left) The invariant mass and (right) the t z distribution of dimuons.

Figure 8 . 8 . 3 .Figure 8 . 23 :

 883823 Figure 8.23: The pseudo-proper time t z distributions for the dimuons with the di erent J/Â prompt and non-prompt contributions.

  2.1 Level scheme of charmonium resonances [36]. . . . . . . . . . . . . . . . . . . . .

2.2 The production processes of cc with Feynman diagrams. . . . . . . . . . . . . . 2.3 Feynman diagram of the weak-decay of B-hadron to J/Â with leading order contribution [50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The J/Â production probability vs the energy density (Equation 1.18) [50]. . . . 2.5 Illustration of R A i (x, Q 2 ) as a function of x [59]. . . . . . . . . . . . . . . . . . . 2.6 The J/Â nuclear modification calculated with EPS09 nPDFs as a function of rapidities and p T in Pb-Pb collisions [60]. . . . . . . . . . . . . . . . . . . . . .

  6.6 A range of di erent performance scenarios (left) with their corresponding ROC curves (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 The Neural Network structure for the best performing model. . . . . . . . . . . 6.8 The learning process visualization as a function of di erent epochs, where the predictions (z) are displayed for both MC and ML (left) 10 epochs (right) 1600 epochs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9 The MC distribution of true tracks in the (x MFT ," MCH ) plane (up). The ML distribution of the predicted global muon tracks (bottom) for ML poorly performing model (left) and for the ML best performing model (right). . . . . . . . . . . . . 6.10 The matching with ML algorithm structure. . . . . . . . . . . . . . . . . . . . . .21 The workflow for matching with di erent methods in O 2 ..............122 7.1 A schematic presentation for the prompt and non-prompt J/Â production. . . . 7.2 The t z distribution for Pb-Pb collisions at 5.5 TeV with di erent prompt and non-prompt J/Â distributions [111]. . . . . . . . . . . . . . . . . . . . . . . . . . Algorithmic overview for the PCA finder in forward rapidities. . . . . . . . . . . The ∆ z for PYTHIA8 simulation with embedded prompt J/Â signal, with and without an initial seed provided by the seed finder (with dichotomy method). . . 7.8 A schematic demonstration of the linear approximation method with (left) linear and (right) quadratic tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 The distance XY of two tracks as a function of Z, where the generated minimum is presented in red and the reconstructed minimum in green. . . . . . . . . . . . 7.10 The calculated ∆ z for loop validation (left) and realistic (right) -with error propagation datasets as a function of track type. . . . . . . . . . . . . . . . . . . 7.11 The ∆ XY Z for loop validation (left) and realistic -(right) with error propagation datasets as a function of track type. . . . . . . . . . . . . . . . . . . . . . . . . . PCA distributions for the dimuons with di erent signal and background contributions with cuts on V z , matching and PCA ‰ 2 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8 (left) The pseudo-proper time t z and (right) ‰ 2 PCA distributions for the dimuons with cuts on V z , matching+PCA ‰ 2 and a treated background (signal contribution removed). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9 The pairing purity and true e ciency presented as a function of di erent ‰ 2 cut. 8.10 The ∆÷ = ÷ Rec ≠ ÷ MC distribution for (left) true global muon tracks and (right) all track types without any applied cuts. . . . . . . . . . . . . . . . . . . . . . . .13 The ∆p T = p Rec T ≠ p MC T distribution for (left) separated track types and (right) global muon tracks with matching ‰ 2 cut application. . . . . . . . . . . . . . . . 154 8.14 The ∆p z = p Rec MC z distribution for (left) true global muon tracks and (right) all track types without any applied cuts. . . . . . . . . . . . . . . . . . . . . . . 155 8.15 The ∆p z = p Rec with matching ‰ 2 cut application. . . . . . . . . . . . . . . . 155 8.16 The distribution for (left) true and (right) fake global muons signal, J/Â ae µµ of the distance between the collision vertex and the secondary vertex, expected to be around 0 cm for prompt quarkonia, with di erent cuts applied. . . . . . . 156 8.17 (left) A sketch for the di erent contributions composing the distribution of ∆ z for the dimuons coming from J/Â particles. (right) The ∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Purity and di erent e ciencies for the selected matching methods assessments. . 7.1 The loop validation results for vertexing reconstruction with calculated ∆x , ∆y and ∆z for di erent track models geometry helix and linear. . . . . . . . . . . . 7.2 The resolution validation results for vertexing reconstruction with calculated ∆x , ∆y and ∆z for di erent track models geometry helix and linear. . . . . . . . . .

	7.3 A schematic presentation of the point of closest approach between muon tracks. 7.4 z z distribution for (left) separated track types and (right) ≠ p MC global muon tracks 6.5 The S ratio comparison for selected matching methods with and without S + B additional applied cuts

6.11 The distribution of the y MFT as a function of tan ⁄ MCH for true and fake matched tracks for non-treated (left) and treated datasets (right) . . . . . . . . . . . . . . 6.12 Early fusion vs late fusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13 The loss trend following the reLU activation function. . . . . . . . . . . . . . . . 6.14 (left) Loss and (right) accuracy as a function of number of epochs. . . . . . . . . 6.15 (left) True positive as a function of false positive percentage and (right) true and false estimations for the di erent selected models. . . . . . . . . . . . . . . . . . 6.16 Di erent distributions for non-treated MC dataset (left) and extracted global muon tracks after ML application (model 20 ◊ 20 ◊ 20 ◊ 20) (right). . . . . . . . 6.17 The extracted muon tracks with di erent methods as a function of p T (up) and as a function of ‰ 2 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.18 The performance assessment of di erent methods with pairing purity, pairing e ciency, true and fake e ciencies as a function of p T ...............118 6.19 The distribution of predicted global muon tracks as a function of ‰ 2 (left) and best ML model method application (right). . . . . . . . . . . . . . . . . . . . . . 6.20 The trend for accuracy and loss as a function of iteration number for (left) x oe R 21◊m and (right) z oe R 17◊m .. . . . . . . . . . . . . . . . . . . . . . . . . 67.5 A 3D scheme of two crossing muon tracks. . . . . . . . . . . . . . . . . . . . . . 7.6 A schematic representation of the di erent consecutive steps of the dichotomy method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 7.12 The calculated ∆ per axis for loop validation (left) and realistic (right) -with error propagation datasets as a function of axis. . . . . . . . . . . . . . . . . . . 8.1 The invariant mass distribution of dimuons with the signal and background contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The ∆V z = V Rec z ≠ V MC z distribution for MCH standalone tracks. . . . . . . . . 8.3 The ∆V z = Z IP ≠ Z SV distribution for global muon tracks with di erent cuts. . 8.4 The MC IP vertex vs the reconstructed SV for J/Â ae µµ signal for global muon tracks (up) without any cut (bottom left) with ‰ 2 PCA < 10 ≠3 and (bottom right) with additional matching ‰ 2 < 15 cut. . . . . . . . . . . . . . . . . . . . . . . . 8.5 The distribution for true MC signal (J/Â ae µµ) of the distance between the collision vertex and the secondary vertex, expected to be around 0 cm for prompt quarkonia, with di erent cuts applied. . . . . . . . . . . . . . . . . . . . . . . . 8.6 The pseudo-proper time t z distribution for the dimuons with opposite-charge, without any cut applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 (left) The pseudo-proper time t z and (right) ‰ 2 8.11 The ∆÷ = ÷ Rec ≠ ÷ MC distribution for (left) separated track types and (right) global muon tracks with matching ‰ 2 cut application. . . . . . . . . . . . . . . . 8.12 The ∆p T = p Rec T ≠ p MC T distribution for (left) true global muon tracks and (right) all track types without any applied cuts. . . . . . . . . . . . . . . . . . . . . . . 8z ≠ p z distribution for all the muon tracks coming from J/Â in black, and for only the true muon tracks from J/Â........................................157 8.18 The distribution for the global muons signal, J/Â ae µµ from prompt J/Â,o f the distance between the reconstructed IP and the SV, with di erent cuts applied.157 8.19 (left) The invariant mass and (right) the t z distribution of dimuons. . . . . . . . 158 8.20 The distribution for (left) true and (right) fake global muons signal, J/Â ae µµ coming from displaced J/Â decay of the distance between the reconstructed IP and the SV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.21 The distribution for the global muons signal, J/Â ae µµ from the displaced J/Â, of the distance between the reconstructed IP and the SV, with di erent cuts applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.22 The pseudo-proper time (left) t z and (right) t xyz distributions for the dimuons coming from the non-prompt J/Â decays. . . . . . . . . . . . . . . . . . . . . . . 160 8.23 The pseudo-proper time t z distributions for the dimuons with the di erent J/Â prompt and non-prompt contributions. . . . . . . . . . . . . . . . . . . . . . . . 161 List of Tables 2.1 Table of the mass and binding energy for di erent charmonium states [37]. . . . 2.2 T D /T c for the main charmonium states [37]. . . . . . . . . . . . . . . . . . . . . 4.1 Table describing the extended physics program with the MFT [111]. . . . . . . . 4.2 Detailed description table for the disks structure geometry [111]. . . . . . . . . 4.3 The maximum hit densities and radiation levels obtained for 5.5 TeV Pb-Pb collisions simulations with PYTHIA generator and with FLUKA and GEANT transport models [111]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Table describing the variables TN, FN, TP and TN. . . . . . . . . . . . . . . . . 6.2 The F score for di erent structures of hidden layers with di erent input layer vectors.106 6.3 The resulting F score for training with di erent number of epochs. . . . . . . . . . 6.4 The training and testing F score for di erent structures of hidden layers. First two lines consist of EF, and last line of LF. . . . . . . . . . . . . . . . . . . . . . . .

1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Quantum ChromoDynamics . . . . . . . . . . . . . . . . . . . . . 4 1

  .2.1 Lagrangian QCD . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Renormalization and the running coupling constants (Q 2 ) . . . . . . . 6

1.3 Quark-Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . . . 8 1

  .3.1 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 Lattice QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Different aspects of collisions . . . . . . . . . . . . . . . . . . . . 10

	1.4.1 Collisions systems. . . . . . . . . . . . . . . . . . . . . . . . . 10
	1.4.2 Space-time evolution . . . . . . . . . . . . . . . . . . . . . . . 11
	1.4.3 Key variables used in heavy-ion collisions. . . . . . . . . . . . . . . 12
	1

.5 QGP experimental evidence . . . . . . . . . . . . . . . . . . . . . 15

	1.5.1 Strangeness enhancement . . . . . . . . . . . . . . . . . . . . . 15
	1.5.2 Elliptic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
	1.5.3 Direct photons and thermal dileptons production . . . . . . . . . . . 18
	1.5.4 Jet quenching . . . . . . . . . . . . . . . . . . . . . . . . . . 19
	1.5.5 Heavy-flavour production . . . . . . . . . . . . . . . . . . . . . 19
	1.5.6 Quarkonium suppression . . . . . . . . . . . . . . . . . . . . . . 20
	1

.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

  starts around 1977, with the former directors of CERN, John Adams and Leon van Hove. They pioneered the project of the largest hadron accelerator, with the prospect of achieving collisions at center-ofmass energies in the TeV scale. Around 1997, it was o cially approved, then put in operation around 2008. The first collisions took place around November 23 rd 2009, marking the o cial start of the first LHC data taking period, also known as Run 1. At the 30 th of November, a world record was set with a beam energy reaching 1.18 TeV. A second world record was set just after, around the 16 th of December, with collisions at center-of-mass energy of 2.36 TeV. During the first Run, di erent collision systems were used: pp collisions with a center-of-mass energy peak at 8 TeV, p-Pb collisions reaching 5.02 TeV, and Pb-Pb collisions with a peak at 2.76 TeV. This Run lasted until February 2013, after which the first long shutdown (LS1) took place for two years, allowing detector upgrades to take place to prepare for the next Run, with increased collision energy scale. The second operational Run took place from 2015 to 2018. During this period, a top collision energy of 13 TeV, 8.16 TeV and 5.02 TeV was reached in pp, p-Pb and Pb-Pb collisions, respectively. In addition, a new Xe-Xe collision system at 5.44 TeV was delivered. After Run 2, and during the timeline of this thesis, the LHC was in the second long shutdown (LS2) period. Preparations were ongoing for the next data taking period, with increased luminosity and a wider physics program resulting from detectors upgrades. Run 3 has o cially started with pp collisions on the 5 th of July 2022.

Table 4 . 1 :

 41 Table describing the extended physics program with the MFT [111].

	Observable	p min T (GeV/c)	uncertainty	p min T (GeV/c)	uncertainty
	Inclusive J/Â R AA Â Õ R AA Prompt J/Â R AA J/Â from b-hadrons	05 % at 1 GeV/c 03 0 % at 1 GeV/c not accessible not accessible	05 % at 1 GeV/c 05 % at 1 GeV/c 01 0 % at 1 GeV/c 01 0 % at 1 GeV/c
	Open charm in single µ			17 % at 1 GeV/c
	Open beauty in single µ			21 0 % at 2 GeV/c
	Open HF in single µ	43 0 % at 4 GeV/c
	no c/b separation
	Low mass spectral func. and QGP radiation		not accessible	1 ≠ 22 0 % at 1GeV/c

Table 4 . 2 :

 42 Detailed description table for the disks structure geometry[START_REF]Technical Design Report for the Muon Forward Tracker[END_REF].

	Disk	Radius (mm)	Particles a (c m ≠2 )	QED electrons b (c m ≠2 )	NIEL c (1MeVn eq /cm 2 )	TID d (krad)
	25.01 2 .78 .95 .7 ◊ 10 12 09 2 .61 .96 .9 ◊ 10 ≠2 1.1 ◊ 10 12 25.01 2 .98 .65 .9 ◊ 10 12 19 8 .01 .76 .0 ◊ 10 ≠2 1.1 ◊ 10 12 25.01 2 .68 .65 .7 ◊ 10 12 21 0 4 .31 .64 .8 ◊ 10 ≠2 1.1 ◊ 10 12 38.21 1 .93 .43 .5 ◊ 10 12 31 3 0 .11 .12 .7 ◊ 10 ≠2 1.1 ◊ 10 12 39.21 2 .93 .13 .8 ◊ 10 12 41 4 3 .50 .92 .2 ◊ 10 ≠2 1.3 ◊ 10 12

a Ave r a g e h i t d e n s i t i e s i n c e nt r a l Pb ≠ Pb collisions at Ô s NN =5.5TeV (including secondaries produced in material).

5.1 The Power Supply Unit . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 Detector commissioning

. . . . . . . . . . . . . . . . . . . . . . . 76 5.2.1 The Giga-Bit Transceiver . . . . . . . . . . . . . . . . . . . . . 76 5.2.2 Test-bench. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2.3 The commissioning software . . . . . . . . . . . . . . . . . . . . 78 5.3 Detector Control System . . . . . . . . . . . . . . . . . . . . . . 84 5.3.1 DCS database . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3.2 The FRont-End Device software . . . . . . . . . . . . . . . . . . 86 5.3.3 Supervisory control process. . . . . . . . . . . . . . . . . . . . . 88 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Table 6 . 1 :

 61 Table describing the variables TN, FN, TP and TN.

Table 6 . 2 :

 62 2, at the matching plane. The column of 21 input parameters contains additionally the diagonal covariance elements for each track. The F score presented consists of an average score calculated following a given number of The F score for di erent structures of hidden layers with di erent input layer vectors.

	Hidden layers	21 input parameters 11 input parameters
	20 ◊ 20 ◊ 20 30 ◊ 30 ◊ 30 20 ◊ 20 ◊ 20 ◊ 20 30 ◊ 30 ◊ 30 ◊ 30 20 ◊ 20 ◊ 20 ◊ 20 ◊ 20 30 ◊ 30 ◊ 30 ◊ 30 ◊ 30	0.54 0.5 0.66 0.71 0.51 0.4	0.67 0.62 0.76 0.74 0.55 0.46

Table 6 .

 6 [START_REF] Dasgupta | An introduction to quantum field theory[END_REF] presents the F score on training and testing datasets (not treated, like the MLP for comparison purpose), for the selected networks, after 100 epochs with the 11 dimension inputs (as section 6.4.1).

	Hidden layers	F training score	F testing score
	30 ◊ 60 ◊ 30 20 ◊ 20 ◊ 20 ◊ 20 15_2 ◊ 60 ◊ 40	0.82 0.82 0.92	0.81 0.82 0.9

Table 6 . 4 :

 64 The training and testing F score for di erent structures of hidden layers. First two lines consist of EF, and last line of LF.The first 2 selected network structures consist of early fusion. The first is composed of 3 hidden layers, consisting of 30-60-30 neurons each. The second is composed of 4 hidden layers with 20 neurons each. The last structure is a late fusion network, where the input vector is separated into 2 sub-models, each composed of a hidden layer of 15 neurons, then combined in the same model composed of 2 hidden layers of 60 and 40 neurons. Every structure starts with an additional normalization layer, normalizing the input MCH-MFT coordinates vectors, to simplify the learning process.

  Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.2.2 Vertex definition . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.

	7.1 Physics case review . . . . . . . . . . . . . . . . . . . . . . . . .
	7.2 Vertex reconstruction algorithm . . . . . . . . . . . . . . . . . . .
	7.2.1

Table 7 . 1 :

 71 [START_REF] John C Collins | Factorization of hard processes in QCD[END_REF] and Equation 7.29. This analytical method is done for both tracks, with the final Z seed corresponding The loop validation results for vertexing reconstruction with calculated ∆x , ∆y and ∆z for di erent track models geometry helix and linear.

		∆x (cm) ∆y (cm) ∆z (cm)
	helix-helix 1.26e-04 9.54e-05 1.78e-03
	helix-line	5.09e-05 3.90e-05 6.86e-04
	line-line	1.45e-06 1.27e-06 2.13e-05
	all	5.95e-05 4.53e-05 8.29e-04

Table 7 . 2 :

 72 .2. The resolution validation results for vertexing reconstruction with calculated ∆x , ∆y and ∆z for di erent track models geometry helix and linear.

		∆x (cm) ∆y (cm) ∆z (cm)
	helix-helix	0.0072	0.0074	0.09
	helix-line	0.0079	0.0082	0.11
	line-line	0.0079	0.0088	0.12
	all	0.0077	0.0081	0.11

Quantum gravitation is still not known to this day, and thus not included in the SM.

Q 2 = ≠q 2 with q the transferred energy-momentum 4-vector between two particles (Q 2 being defined positive).

The components consist of RC filters.

In the curvature formula, p T is expressed in GeV/c.

Pendant la période de ma thèse, le LHC était en période d'arrêt prolongé, au cours de laquelle des améliorations de détecteurs ont été e ectuées afin de préparer la prochaine période de prise de données (Run 3).Le MFT est situé à 40 cm du point d'interaction, devant l'absorbeur frontal. Le premier objectif de ce détecteur est d'améliorer la résolution de pointage des traces de muons. Cela peut être réalisé par l'extrapolation des traces de muons reconstruites par le spectromètre à muons et leurs association avec celles du MFT.En surmontant les limites imposées par la conception du spectromètre à muons, le MFT étend le programme de physique dans la région de rapidité vers l'avant. Notamment, sur les saveurs lourdes, un meilleur accès au charme ouvert sera possible. Ainsi, les mesures à faible p T seront possibles grâce à la réduction du bruit de fond. De plus, la séparation entre les J/Â

Acknowledgements

I am both very happy and saddened to finally be able to write this part of my thesis! Firstly, I want to express how rich and beautiful this period has been for me. I would like to thank prompts et non-prompts sera possible, et une meilleure extraction du signal Â(2S) est attendue. En ce qui concerne les dimuons de faible masse, une meilleure résolution en masse est attendue.

Le MFT repose sur la technologie de capteurs monolithiques à pixels actifs (MAPS), permettant une reconstruction de trace avec une excellente résolution dans un environnement à haute multiplicité. Les capteurs sont assemblés dans des circuits intégrés hybrides qui équipent un système de 5 disques à double faces autour du faisceau du LHC. L'alimentation et le contrôle des disques du détecteur sont gérés par une carte spécifique, la Power Supply Unit (PSU), située entre les quatrième et cinquième disques. La communication avec le détecteur est assurée par la technologie GBT-SCAs (Giga-Bit Transceiver -Slow Control Adapter). Le détecteur exige une grande fiabilité car il n'est pas accessible pendant toute la durée de prise de données. En outre, les capteurs doivent être maintenus à une température inférieure à 30 ¶ C. Enfin, tous les services doivent être intégrés dans un volume limité : 35 cm pour le diamètre du premier disque, 46 cm pour le dernier disque, avec 36 cm de distance totale entre ces 2 disques. Ces défis ont été relevés avec succès. Le MFT a achevé la phase de mise en service et a été l'un des premiers détecteurs à être installés dans ALICE en décembre 2020. Une autre étape essentielle a été franchie lorsque les premières données ont été enregistrées avec le faisceau pilote du LHC (collisions proton-proton à 900 GeV) en octobre 2021.

Pour la première partie de mon travail de thèse, j'ai travaillé sur le développement du système de contrôle du détecteur, comme détaillé dans le chapitre 5. Cela implique le développe-

Acronyms

The Fast Interaction Trigger detector (FIT): Fit [START_REF] Bysiak | The Fast Interaction Trigger Upgrade for ALICE[END_REF] is composed of the following three detectors, ranging from -19.5 m to 17 m from the IP:

The FT-zero (FT0) detector: The FT0 consists of two detectors, FT0+A and FT0+C, located on opposite sides of the IP, each composed of 12 Cherenkov counters. These counters are made of quartz fibers, connected to PMTs, with the same detection method using Cherenkov light, as explained for the ZDC. This detector provides a precise collision time with 25 ps resolution, and determines a vertex position for the collisions.

The FV-zero+ (FV0+) detector: The FV0+ is composed of two scintillator counter arrays placed on opposite sides of the IP. Both of these arrays are divided into 32 counters, as each is segmented into four rings in the radial direction, with each of these rings divided into eight sections in the azimuthal direction. When a particle hits a counter, the light produced is transmitted to PMTs through optical fibers. This detector discriminates the beam-beam interaction from the beam-gas background interactions, thus providing a minimum bias trigger. Additionally, it provides the beam luminosity, charged particles multiplicity, and azimuthal distributions.

The Forward Diffractive Detector (FDD):

The FDD is composed of two subdetectors placed on opposite sides of the IP. Each array consists of eight rectangular scintillator pads. When a particle hits a counter, as the V0+, it emits light that is carried by optical fibers to the PMTs. This detector provides measurements of di ractive cross-sections and centrality, selections of ultra-peripheral collisions, and monitoring of the beam quality.

Central barrel detectors

The ALICE Cosmic Ray Detector (ACORDE): The ACORDE [START_REF] Fernández | ACORDE a cosmic ray detector for ALICE[END_REF] detector is placed on the upper surface of the L3 magnet. It is composed of scintillator modules, providing the detection of cosmic rays. In addition, this detector is a cosmic ray trigger for ALICE, used for calibration and detection of atmospheric muon events.

The ElectroMagnetic Calorimeter -Di-jet Calorimeter (EMCal -DCal): EMCal [START_REF] Cortese | ALICE electromagnetic calorimeter technical design report[END_REF] is located at 4.28 m from the IP, with the azimuthal coverage of ∆" =110 o and the pseudorapidity region |÷| < 0.7. It is a layered Pb-scintillator sampling calorimeter. The DCal [START_REF] Allen | ALICE DCal: An Addendum to the EMCal Technical Design Report Di-Jet and Hadron-Jet correlation measurements in ALICE[END_REF] was installed to widen the physics reach of EMCal, allowing the study of back-to-back correlations, covering the azimuthal angle of ∆" =70 o , with the same pseudorapidity region. These electromagnetic calorimeters allow the identification of particles as photons and neutral mesons via their photonic decay channel.

The PHOton Spectrometer (PHOS): PHOS [START_REF]of the Photon Spectrometer (PHOS)[END_REF], located at 4.6 m from the interaction point with an azimuthal coverage of ∆" =7 0 o , in the pseudorapidity region |÷| < 0.12,

Chapter 8

Separation of prompt and non-prompt J/Â contributions The MFT was designed for the separation of the prompt and non-prompt J/Â contributions at forward rapidity in Runs 3 and 4. It provides access to the required information for the muon tracks before the absorber, allowing a precise determination of their production vertices. In particular, after the extraction of global muon tracks, they are gathered in pairs and processed with the vertexing algorithm (as detailed in chapter 7). In order to further prepare for Run 3 analyses, this chapter will focus on investigating the separate prompt and non-prompt J/Â contributions using first o cial MC productions of pp collisions. This consists of a very preliminary study, with the goal to further develop and prepare the analysis framework. In the following, the matching is based on the ‰ 2 method. Indeed, the ‰ 2 matching performance should be su cient in pp collisions, as the e ects discussed in section 6.2.1 are only significant in Pb-Pb collisions for J/Â analyses. Moreover, the access to the ML libraries was not fully available in O 2 at the time of this work.

J/Â pseudo-proper time distribution 8.1.1 Data production and structure

The data used in this section comes from an o cial MC production composed of pp collisions at 900 GeV, with signal embedded of prompt charmonia. More precisely, each event contains 4 J/Â and 2 Â(2S), in order to enhance statistics. This embedded signal is produced using dedicated particle generators. The pp background is based on PYTHIA8 simulations. The propagation of particles through detectors is done with GEANT4. Through this chapter, muon tracks are categorized as the following:

• Track typ e 0: global muon tracks, MFT-MCH-MID matched tracks.

• Track typ e 2: forward tracks, MCH-MFT matched tracks.

• Track typ e 4: MCH standalone tracks.

Track type 1 consists of MFT tracks and 3 of MCH-MID tracks. However, these track types won't be used in the following.

Signal J/Â ae µ + µ ≠ extraction

In order to have an indication on the J/Â mass resolution, the signal will be extracted with the evaluation of the invariant mass distribution:

with m µ + /µ -, E µ + /µ -and p µ + /µ -being respectively the mass, energy, and momentum of muons, and ◊ µ + µ -the opening angle between them. In addition, a cut of p T > 0.5 GeV/c is applied on the selected muons. This cut removes part of the background coming from pion decays. Di erent methods can be used to perform signal extraction. In this study, the oppositecharge dimuon distribution is fitted using empirical function. This fit contains both contributions from the signal (J/Â) and background (mainly coming from pions and combinatorial background) to the mass spectrum. As this chapter is dedicated to the separation of the prompt and non-prompt J/Â contributions, muons produced by Â(2S) are discarded.

Di erent functions were tested for the fitting procedure. The selected fit functions will be those that give the smallest ‰ 2 fitting score. The final selected functions are:

Signal function: an extended Crystal-Ball function is used. It consists of a gaussian function with additional tails on both sides to take into account the response of the detectors (energy loss and resolution).