Pion propagation in the linear sigma model at finite temperature - art. no. 056007

We construct effective one-loop vertices and propagators in the linear sigm a model at finite temperature, satisfying the chiral Ward identities and th us respecting chiral symmetry, treating the pion momentum, pion mass and te mperature as small compared to the sigma mass. We use these objects to comp ute the two-loop pion self-energy. We find that the perturbative behavior o f physical quantities, such as the temperature dependence of the pion mass, is well defined in this kinematical regime in terms of the parameter m(pi) (2)/4 pi(2)f(pi)(2) and show that an expansion in terms of this reproduces the dispersion curve obtained by means of chiral perturbation theory at lea ding order. The temperature dependence of the pion mass is such that the fi rst and second order corrections in the above parameter have the same sign. We also study pion damping both in the elastic and inelastic channels to t his order and compute the mean free path and mean collision time for a pion traveling in the medium before forming a sigma resonance and find very goo d agreement with the result from chiral perturbation theory when using a va lue for the sigma mass of 600 MeV.