Impact of the pre-equilibrium stage of ultra-relativistic heavy ion collisions: isotropization, photon production and elliptic flows

Abstract

The currently accepted theory that governs the dynamics of quarks and gluons, within the Standard Model of fundamental interactions, is the Quantum Chromodynamics (QCD). Its non-abelian nature provides two important features: while at high energies the interaction becomes small and quarks and gluons interact weakly (asymptotic freedom), at low energies the interaction becomes strong and quarks are confined inside hadrons (color confinement). The asymptotic freedom of QCD implies the existence of a super-dense and ultra-hot form of matter in which the color charged particles are deconfined, the quark-gluon plasma (QGP). Many phenomenological approaches and numerical simulations of the QCD clearly indicate the existence of a transition from the hadronic matter to the quark-gluon plasma at large energy density, $\epsilon>0.5-1 GeV/fm^3$. Creating and studying the quark-gluon plasma in laboratory is one of the main challenges of experiments at the Large Hadron Collider (LHC) and at the Relativistic Heavy Ion Collider (RHIC). Through ultra-relativistic heavy ion collisions, which generate energies of $0.9-5.5 TeV$ per nucleon at LHC and $20-200 GeV$ per nucleon at RHIC, one try to get detailed information on the high temperature and low baryon density region of the phase diagram of QCD. In this thesis we present our study, within the framework of relativistic transport kinetic theory, of the formation and the dynamical evolution of the quark gluon plasma in ultra-relativistic heavy ion collisions. In particular we investigate the time scales and the mechanisms responsible of the isotropization of the fluid produced in the initial out-of-equilibrium stage of the collision, aiming at spotting the impact of this pre-equilibrium phase on collective flows of the bulk matter and on photon observables. In the first part of this thesis we present our model of the early times dynamics of relativistic heavy ion collisions, in which an initial color-electric field decays to a particle plasma by the Schwinger effect. One of the main novelties of our work consists in the coupling of field evolution to plasma dynamics by solving consistently the classical field equations and the relativistic Boltzmann equation; the self-consistent solution of the problem allows to take into account the back-reaction of the color currents on the classical field. We find that the color-electric field experiences a rapid decay for small $\eta/s$, in both 1+1D and 3+1D space-time configurations; looking at the ratio of longitudinal over transverse pressure we find that the system acquires a substantial degree of isotropy in less than 1 fm/c for $\eta/s=1/4\pi$, in agreement with the common lore of hydrodynamic approaches. In the second part of this thesis, we extend our approach up to the implementation of a realistic initial condition in which the color-electric field is smoothly distributed in the transverse plane. This configuration, relevant to heavy ion collisions at RHIC and LHC energies, allows to investigate the effect of the pre-equilibrium dynamics on observables, such as spectrum and elliptic flow of photons emitted from the quark-gluon plasma. To this end we compare the photon production starting from classical color field as discussed above with the standard initial condition of a plasma in thermal equilibrium. We find that the pre-equilibrium stage produces abundantly photons, comparable in number with those produced by the equilibrated quark-gluon plasma during the whole fireball lifetime. This early contribution enhances the spectrum mainly in a transverse momentum range ($p_T>2-3 GeV$) where thermal emission becomes less important. The pre-equilibrium phase has an impact also on the photon elliptic flow, since photons coming from the early times evolution of the fireball suppress the contribution to the momentum anisotropy brought by QGP thermal photons.