Departure from Equilibrium of the Quasi-Particle Distribution Functions in High Energy Nuclear Collisions

TL;DR

This paper rigorously derives how shear and bulk viscous effects distort particle distribution functions in high energy nuclear collisions, impacting photon and dilepton emission calculations.

Contribution

It provides a systematic method to incorporate viscous distortions into quasi-particle distributions in high energy collision simulations.

Findings

Distortions can be derived rigorously within the quasi-particle approximation.

The linear sigma model at finite temperature illustrates the method.

Implications for photon and dilepton emission calculations.

Abstract

In simulations of high energy heavy ion collisions that employ viscous hydrodynamics, single particle distributions are distorted from their thermal equilibrium form due to gradients in the flow velocity. These are closely related to the formulas for the shear and bulk viscosities in the quasi-particle approximation. Distorted single particle distributions are now commonly used to calculate the emission of photons and dilepton pairs, and in the late stage to calculate the conversion of a continuous fluid to individual particles. We show how distortions of the single particle distribution functions due to both shear and bulk viscous effects can be done rigorously in the quasi-particle approximation and illustrate it with the linear $\sigma$ model at finite temperature.