Transport coefficients and resonances for a meson gas in Chiral Perturbation Theory

TL;DR

This paper introduces a systematic method within Chiral Perturbation Theory to calculate transport coefficients of a meson gas, accounting for particle collisions and unitarity, with implications for understanding heavy-ion collisions.

Contribution

It develops a modified ChPT approach incorporating particle widths and unitarity to accurately compute transport properties of a meson gas at low temperatures.

Findings

Bulk viscosity is negligible compared to shear viscosity except near the phase transition.

Transport coefficients follow expected asymptotic limits and large-N_c scaling.

Results are consistent with kinetic theory analyses across temperature regimes.

Abstract

We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high energy description of scattering amplitudes, generating dynamically the $\rho (770)$ and $f_0(600)$ mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-$T$ regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain that bulk viscosity is negligible against shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Different asymptotic limits for transport coefficients, large-$N_c$ scaling and some applications to heavy-ion collisions are studied.