Modeling early stages of relativistic heavy ion collisions: Coupling relativistic transport theory to decaying color-electric flux tubes

Abstract

In this study we model early-time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism, coupling the dynamical evolution of the initial color field to the dynamics of the many particles system produced by the decay. The latter is described by relativistic kinetic theory in which we fix the ratio $\ensuremath{\eta}/s$ rather than insisting on specific microscopic processes, and the backreaction on the color field is taken into account by solving self-consistently the kinetic and the field equations. We study isotropization and thermalization of the system produced by the field decay for a static box and for a $1+1\mathrm{D}$ expanding geometry. We find that regardless of the viscosity of the produced plasma, the initial color-electric field decays within 1 fm/$c$; however, in the case where $\ensuremath{\eta}/s$ is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late-time evolution of the ratio between longitudinal and transverse pressure. In the case of small $\ensuremath{\eta}/s$ ($\ensuremath{\eta}/s\ensuremath{\lesssim}0.3$) we find ${\ensuremath{\tau}}_{\text{isotropization}}\ensuremath{\approx}0.8$ fm/$c$ and ${\ensuremath{\tau}}_{\text{thermalization}}\ensuremath{\approx}1$ fm/$c$, in agreement with the common lore of hydrodynamics. Moreover, we have investigated the effect of turning from the relaxation time approximation to the Chapman-Enskog one: We find that this improvement affects mainly the early-time evolution of the physical quantities, the effect being milder in the late-time evolution.