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

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_pi^2/4pi^2f_pi^2 and to zeroth order in the parameter (m_pi/m_sigma)^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.

11.10.Wx
11.30.Rd
11.55.Fv
25.75.-q
sigma model: linear
finite temperature
pi: dispersion relation
vertex function
propagator
Ward identity: chiral

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