Dynamical description of relativistic heavy-ion collisions out-of equilibrium

The aim of this dissertation is to study and shed light on the nonequilibrium nature of the medium as created in the beginning of heavy-ion collisions, including the initial production of particles through string fragmentation and the Quark-Gluon Plasma state by studying its kinetic and chemical equilibration as a function of time as well as its description and characterization at finite chemical potential. We will first introduce the Quantum-ChromoDynamics (QCD) and explain how this theory has been developed throughout the years to become an important part of the Standard Model of Particle Physics. We will present how the theory of QCD is defined and what are its basic properties and symmetries, and also how it can be solved by using lattice techniques. The only way to experimentally investigate the properties of QCD is by means of heavy-ion collisions and in particular we will detail which probes confirm that a Quark-Gluon Plasma has been produced in heavy-ion collisions. We will present the remaining challenges in our understanding of QCD which are focused around the QCD phase diagram. In the second chapter, we study the nonequilibrium field theory and the associated techniques such as the Keldysh contour where the Green's functions are the essential degrees-of-freedom. From the evolution equation for the Green's functions, i.e. the Kadanoff-Baym equations, we apply a gradient expansion in order to obtain generalized transport equations. In the quasiparticle approximation we recover the Boltzmann equation where one can relate the damping rate of the particle to its interaction rate and to the equilibration time of the system. In the next chapter we introduce the Parton-Hadron-String Dynamics (PHSD) which applies the generalized transport equation to the description of relativistic heavy-ion collisions. We present the main ingredients which are used to describe a heavy-ion collision from the collision of the initial nuclei up to the final particle spectra. We close this chapter by presenting a few results from the PHSD in comparison with experimental data to briefly illustrate the mechanisms of particle production and baryon stopping. We start our investigations in chapter 4 about the nonequilibrium properties of the QGP as produced in relativistic heavy-ion collisions. For that purpose, we compare the evolution from the PHSD to a hydrodynamical model where local equilibrium is assumed and assess the differences between these two descriptions. In chapter 5 we focus on the very early pre-equilibrium stage of ultra-relativistic heavy-ion collisions and especially on the content of the QGP phase at this stage. We study the implications of a QGP being initially populated by exclusively gluons or quarks and antiquarks on final experimental observables such as rapidity spectra of bulk particles or photon and dilepton spectra. The next chapter will also discuss the production of particles in the early stage of heavy-ion collisions but at lower collisional energies where a microscopic explanation of the strangeness enhancement, i.e. the "horn", will be addressed. In particular we will study the modification of the string fragmentation process in a high-density environment due to the partial restoration of chiral symmetry. In chapter 7 we will present the Dynamical QuasiParticle model in detail and will investigate the properties of strongly interacting matter at finite temperature and chemical potential by evaluating the QCD equation of state, the partonic interaction rates and the associated transport coefficients, in comparison with the available lattice QCD data. Secondly, we will incorporate the ingredients from the DQPM such as the parton masses and the interaction cross sections into the PHSD transport approach in order to study the QGP phase at finite baryon chemical potential as produced in heavy-ion collisions. After illustrating the different regions of the QCD phase diagram which are probed in heavy-ion collisions, we will compare our results for bulk observables such as rapidity and p${}_T$ spectra with experimental data and conclude on the effect of the finite μ${}_B$ dynamics of the QGP.