Shear Viscosity of a Hot Pion Gas

TL;DR

This paper calculates the shear viscosity of a hot pion gas using the Kubo formalism and skeleton expansion, providing new analytical results for the mean free path and viscosity, and analyzing their temperature and mass dependence.

Contribution

It applies the skeleton expansion to pions in chiral perturbation theory to derive analytical expressions for shear viscosity and mean free path in a hot pion gas.

Findings

The shear viscosity to entropy ratio exceeds the AdS/CFT bound.

Derived a new analytical expression for the pion mean free path.

Analyzed temperature and mass dependence of shear viscosity.

Abstract

The shear viscosity of an interacting pion gas is studied using the Kubo formalism as a microscopic description of thermal systems close to global equilibrium. We implement the skeleton expansion in order to approximate the retarded correlator of the viscous part of the energy-momentum tensor. After exploring this in $g\phi^4$ theory we show how the skeleton expansion can be consistently applied to pions in chiral perturbation theory. The shear viscosity $\eta$ is determined by the spectral width, or equivalently, the mean free path of pions in the heat bath. We derive a new analytical result for the mean free path which is well-conditioned for numerical evaluation and discuss the temperature and pion-mass dependence of the mean free path and the shear viscosity. The ratio $\eta/s$ of the interacting pion gas exceeds the lower bound $1/4\pi$ from AdS/CFT correspondence.