Electrical conductivity of a pion gas

Abstract

The electrical conductivity of a pion gas at low temperatures is studied in the framework of linear response and chiral perturbation theory. The standard ChPT power counting has to be modified to include pion propagator lines with a nonzero thermal width in order to properly account for collision effects typical of kinetic theory. With this modification, we discuss the relevant chiral power counting to be used in the calculation of transport coefficients. The leading order contribution is found and we show that the dominant higher order ladder diagrams can be treated as perturbative corrections at low temperatures. We find that the DC conductivity $\ensuremath{\sigma}(T)$ is a decreasing function of $T$, behaving for very low $T$ as $\ensuremath{\sigma}(T)\ensuremath{\sim}{e}^{2}{m}_{\ensuremath{\pi}}\sqrt{{m}_{\ensuremath{\pi}}/T}$, consistently with nonrelativistic kinetic theory. When unitarization effects are included, $\ensuremath{\sigma}(T)$ increases slowly as $T$ approaches the chiral phase transition. We compare with related works and discuss some physical consequences, especially in the context of the low-energy hadronic photon spectrum in relativistic heavy ion collisions.