Viscous coefficients of a hot pion gas

TL;DR

This paper calculates the shear and bulk viscosities of a hot pion gas using both real-time correlation functions and the Chapman-Enskog method, incorporating in-medium effects on the pion interactions.

Contribution

It provides a comprehensive evaluation of pion gas viscosities by applying real-time formalism and solving the relativistic transport equation with in-medium modifications.

Findings

Viscosity coefficients are computed for a hot pion gas.

In-medium spectral modifications significantly affect the viscosities.

Results are relevant for understanding transport properties in heavy-ion collisions.

Abstract

The steps essentially involved in the evaluation of transport coefficients in linear response theory using Kubo formulas are to relate the defining {\em retarded} correlation function to the corresponding {\em time-ordered} one and to evaluate the latter in the conventional perturbation expansion. Here we evaluate the viscosities of a pion gas carrying out both the steps in the {\em real time} formulation. We also obtain the viscous coefficients by solving the relativistic transport equation in the Chapman-Enskog approximation to leading order. An in-medium $\pi\pi$ cross-section in used in which spectral modifications are introduced in the propagator of the exchanged $\rho$.