Bulk viscosity of strongly interacting matter in the relaxation time approximation

TL;DR

This study investigates the bulk viscosity of strongly interacting matter using the relaxation time approximation, incorporating thermal mean field effects and comparing Boltzmann and Bose-Einstein gases.

Contribution

It introduces a thermodynamically consistent method to include temperature-dependent masses in bulk viscosity calculations within the relaxation time approximation.

Findings

Both methods agree in the small mass limit for the viscosity ratio.

Temperature-dependent masses introduce a $eta_ ext{lambda}$-function in the viscosity ratio.

The relaxation time approximation may be insufficient for Bose-Einstein gases due to infrared effects.

Abstract

This paper presents how thermal mean field effects are incorporated consistently in the hydrodynamical modelling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity over its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the $\beta_\lambda$-function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cut-off. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of $\zeta/\tau_R$ for gases obeying Bose-Einstein statistics.