We study the effect of the thermal width of $π$ on the spectral function of $σ$. 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 $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without 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.

Contribution to the International Workshop on QCD: QCD@Work 2003 - Conversano (Italy) 14-18 June 2003 (eConf C030614)