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

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.

Comments: Invited talk given at the international workshop Hot Quarks 2008, Estes Park, Colorado, USA, August 18-23 2008. Accepted as a regular article in Eur.Phys.J.C. 18 pages EPJC style, 23 figures