Effect of pion thermal width on the sigma spectrum

Details Effect of pion thermal width on the sigma spectrum Effect of pion thermal width on the sigma spectrum

2003-04-22

arxiv.org/abs/hep-ph/0304204v2

Phys.Rev. D68 (2003) 111901

Physics

High Energy Physics

High Energy Physics - Phenomenology

5 pages, 6 figures

Scientific paper

10.1103/PhysRevD.68.111901

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 ${\cal O}(4)$ 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.

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