Bulk viscosity of low-temperature strongly interacting matter

TL;DR

This paper investigates the bulk viscosity of a pion gas at low to moderate temperatures using unitarized Chiral Perturbation Theory, extending the theory to include a pion chemical potential and analyzing the temperature dependence of viscosity.

Contribution

It introduces a method to include pion chemical potential in bulk viscosity calculations and controls zero modes in the Boltzmann equation for a pion gas.

Findings

Bulk viscosity depends on temperature similarly to previous studies.

Numerical values of viscosity are closer to Davesne's results.

Viscosity vanishes at zero temperature, consistent with non-relativistic gases.

Abstract

We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation Theory at low and moderate temperatures, below any phase transition to a quark-gluon plasma phase. We argue that inelastic processes are irrelevant and exponentially suppressed at low temperatures. Since the system falls out of chemical equilibrium upon expansion,a pion chemical potential must be introduced, so we extend the existing theory to include it. We control the zero modes of the collision operator and Landau's conditions of fit when solving the Boltzmann equation with the elastic collision kernel. The dependence of the bulk viscosity with temperature is reminiscent of the findings of Fernandez-Fraile and Gomez Nicola, while the numerical value is closer to that of Davesne. In the zero-temperature limit we correctly recover the vanishing viscosity associated to a non-relativistic monoatomic gas.