Modelling Early Stages of Relativistic Heavy Ion Collisions: Coupling Relativistic Transport Theory to Decaying Color-electric Flux Tubes

TL;DR

This paper models the early dynamics of relativistic heavy ion collisions by coupling a decaying color electric field with relativistic kinetic theory, analyzing isotropization and thermalization times across different viscosities.

Contribution

It introduces a coupled model of color field decay and particle system evolution, exploring effects of viscosity and approximation methods on system isotropization and thermalization.

Findings

Color electric field decays within 1 fm/c regardless of viscosity.

Oscillations in the field persist for high viscosity, affecting pressure ratios.

Low viscosity cases show isotropization at ~0.8 fm/c and thermalization at ~1 fm/c.

Abstract

In this study we model early times dynamics of the system produced in 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 $\eta/s$ rather than insisting on specific microscopic processes. We study isotropization and thermalization of the system produced by the field decay for a static box and for a $1+1$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 $\eta/s$ is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late times evolution of the ratio between longitudinal and transverse pressure. In case of small $\eta/s$ ($\eta/s\lesssim0.3$) we find $\tau_{isotropization}\approx 0.8$ fm/c and $\tau_{thermalization}\approx 1$ 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 times evolution of the physical quantities, the effect being milder in the late times evolution.