Effect of pion thermal width on the sigma spectrum

Abstract

We study the effect of thermal width of $\pi$ on the spectral function of $\sigma$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to $\mathcal{O}(4)$ linear sigma model. In order to take into account finite thermal width of $\pi$, we replace the internal pion mass in the self-energy of $\sigma$ 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 $\sigma \to \pi \pi$ 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 $\sigma$ propagator and analyze the behavior of the spectral function with these poles.

5 pages, 6 figures

References in corpus (3)

• Theoretical approaches to hadrons in nuclear matter
• Momentum dependence of the spectral functions in the O(4) linear sigma model at finite temperature
• On the thermal sunset diagram for scalar field theories

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