We study effects of pion thermal width on the spectral function of the sigma in the O(4) linear sigma model with the resummation technique called Optimized Perturbation Theory. To reckon with the thermal width, we use a complex pole of the pion propagator for the internal mass in the self-energy of the sigma. As a result of this prescription, two broad peaks are found in the spectral function at nonzero temperature and a sharp peak at the two pion threshold, which can be obtained in absence of thermal width of the pion, turned out to be smeared out.
To analyze the behavior of the spectral function, we search the complex energy plane for the poles of the sigma propagator and elucidate the correlation between the pole location and the smeared structure of the spectrum. We find that the thermal width also broadens a sharp peak of the diphoton emission rate from the decay: sigma ® 2 gamma.

Radiation Laboratory, Riken, Japan