The QCD scalar susceptibility and thermal scalar resonances in chiral symmetry restoration

Abstract: Building upon recent results on the role of thermal resonances in chiral symmetry restoration, we show that a description of the QCD scalar susceptibility at finite temperature $T$ saturated by the thermal properties of the lightest scalar resonance, the $f_0(500)$, is compatible both with lattice QCD data at nonzero $T$ and with the $T=0$ light resonance properties coming from experimental data. The thermal $f_0(500)$ is generated within the framework of Unitarized Chiral Perturbation Theory. This method allows us to achieve a good description of lattice QCD results with a reliable pion mass dependence. In particular, we perform direct fits to the chiral susceptibility measured in lattice data at different pion masses and temperatures, obtaining a remarkable agreement for the susceptibility and for mass differences of the light quark condensate. In addition, the fitted low-energy constants are compatible with $T=0$ phenomenology. Our results confirm the role of unitarized approaches and thermal resonances in the dynamics of the QCD transition.