Role of the thermal f_0(500) in chiral symmetry restoration

Abstract

We show that the sigma/f_0(500) state with finite-temperature T corrections to its spectral properties included plays an essential role for the description of the scalar susceptibility chi_S, signaling chiral symmetry restoration. First, we use the O_4 linear sigma model as a test bed to derive the connection between chi_S and the sigma propagator and to check the validity and reliability of the approach where chi_S is saturated by the sigma/f_0(500) inverse self-energy, which we calculate at finite T to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal f_0(500) state generated in unitarized chiral perturbation theory (UChPT). Such an approach allows us to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the hadron resonance gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed and confirm the validity of the thermal f(0)(500) saturated approach and hence the importance of that thermal state for chiral symmetry restoration.