Pion dispersion relation at finite temperature in the linear sigma model from chiral Ward identities

Abstract

We develop one-loop effective vertices and propagators in the linear sigma model at finite temperature satisfying the chiral Ward identities. We use these in turn to compute the pion dispersion relation in a pion medium for small momentum and temperatures on the order of the pion mass at next to leading order in the parameter m π 2/4 π 2 f π 2 and to zeroth order in the parameter ( m π / m σ ) 2. We show that this expansion reproduces the result obtained from chiral perturbation theory at leading order. The main effect is a perturbative, temperature-dependent increase of the pion mass. We find no qualitative changes in the pion dispersion curve with respect to the leading order behavior in this kinematical regime.