The role of the thermal $f_0(500)$ or sigma in chiral symmetry restoration

Abstract

We analyze the $f_0(500)$ state generated as a pole of $\pi \pi$ scattering within unitarized low-energy effective theories at finite temperature. First, we report on the $\sigma$ self-energy in the LSM, which is used as a benchmark in order to test the hypotheses carried out. The relation of that thermal pole with the scalar susceptibility is studied within a scalar saturation approach, which yields results complying with lattice data. The robustness and predictability of this method are studied in terms of the low-energy constants involved and the unitarization method. Our analysis highlights the importance of this thermal state to describe the main qualitative features of the scalar susceptibility around the chiral transition.

Comments: Proceedings of XIII Quark Confinement and the Hadron Spectrum. 7 pages, 3 figures