Effect of the pion thermal width on the sigma spectrum

We study the effect of the thermal width of π on the spectral function of σ applying a resummation technique called the optimized perturbation theory at finite temperature (T) to the O(4) linear sigma model. In order to take into account a finite thermal width of π, we replace the internal pion mass in the self-energy of σ with that of the complex pole found in a previous paper. The obtained spectral function for T > or approx. 100 MeV turns out to possess two broad peaks. Although a sharp peak at σ→ππ threshold was observed in the one-loop calculation without the pion thermal width, the peak is shown to be smeared out. We also search for the poles of the σ propagator and analyze the behavior of the spectral function with these poles