Probing the Quark-Gluon Plasma properties through Heavy Quarks' dynamics: transport coefficients and elliptic flow

Quantum Chromodynamics (QCD) is the non-abelian gauge field theory that within the Standard Model describes the strong interaction between quarks and gluons. QCD exhibits two main properties:confinement and asymptotic freedom. The former implies that in ordinary matter quarks and gluons are bounded within colorless hadrons. The latter is related to the decrease of the QCD strength coupling with increasing characteristic energy of the process. Asymptotic freedom implies that under extreme conditions of high temperature and density the interaction affecting quarks and gluons is so weakly that they are released from the bounding state to form a deconfined phase of matter known as the Quark-Gluon Plasma (QGP). Numerical solutions of QCD equations on lattice (lQCD) predict that such transition is properly a crossover at almost zero baryon density and with a critical temperature Tc=155 MeV. The study of nuclear matter under extreme conditions is the main program of the experiments at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) where ultrarelativistic Heavy-Ion Collisions (HICs) are conducted to create an almost baryon free QGP with initial T = 3Tc. In this scenario Heavy Quarks (HQs), mainly charm and bottom, play a unique role. Due to their large masses HQs are created at the initial stage of HICs by hard perturbative QCD scattering processes. Moreover, their thermalization time is comparable with the QGP lifetime. Hence HQs can probe the entire evolution of the fireball carrying more information about their initial properties. The most important observables in the HQ sector are the nuclear modification factor RAA and the elliptic flow v2. The challenge of each theoretical framework is to provide a simultaneous description of these two observables that have been measured both at RHIC and LHC energies. In this thesis we study the HQ dynamics within the QGP by means of a relativistic Boltzmann transport approach. In this framework we treat non-perturbative QCD effects by prescription of a Quasi-Particle Model (QPM) in which light quarks and gluons of the bulk are dressed with effective masses and the T dependence of the strength coupling is fitted to lQCD thermodynamics. In the first part of this thesis we discuss HQ transport coefficients by performing simulations in static QCD medium. We compare our extracted drag and diffusion coefficients with results obtained through a Montecarlo integration. Afterwards, we investigate charm suppression and compare the results among various theoretical models. In the second part, we focus on the dynamical evolution of HQs within the QGP by carrying out simulations of realistic HICs. We observe that within our QPM interaction, which implies a T-dependent drag coefficient almost constant near Tc, we are able to describe simultaneously the RAA and v2 of D mesons both at RHIC and LHC energies. In order to compare with the experimental measurements we couple the final HQ spectra to a hybrid coalescence plus fragmentation hadronization model which is suitable to describe the large magnitude of the observed charmed baryon-to-meson ratio. In the same framework, we provide our predictions for B meson RAA and v2 and compare our results with the available experimental data. A goal of this work is to include the effect of enhanced baryon production in HICs on the nuclear modification factor. Finally, we present our estimate of the HQ spatial diffusion coefficient Ds(T) within our Boltzmann approach. We show that our phenomenological predictions of Ds for charm quark are in agreement with lQCD expectations, meaning that through the study of HQ thermalization we can probe the QCD interaction within the present uncertainties of lQCD. We point out also that the possibility to calculate transport coefficients at the bottom mass scale allows to reduce uncertainties coming from the adopted transport model and to bring the estimate of Ds closer to the quenched lQCD.