Effect of pion thermal width on the sigma spectrum

Abstract

We study the effect of thermal width of $π$ on the spectral function of $σ$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to take into account finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without pion thermal width, the peak is proved 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.