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

TL;DR

The paper demonstrates that the QCD scalar susceptibility $\chi_S(T)$ near the chiral transition can be accurately described by saturating it with the thermal $f_0(500)$ pole within Unitarized Chiral Perturbation Theory. By fitting finite-temperature lattice data across different pion masses and connecting to $T=0$ resonance phenomenology, the authors extract consistent low-energy constants and reproduce the critical behavior of $\chi_S$ without resorting to purely hadron-resonance gas models. The approach yields a thermal evolution of the $f_0(500)$ pole and compatible $\rho(770)$ properties, validating the role of thermal resonances in chiral restoration and providing a cohesive bridge between lattice QCD results and effective hadronic theories. Overall, the saturated resonance framework offers a robust, QCD-grounded description of the crossover region in the QCD phase diagram.

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.

Figures (2)

• Figure 1: From Ding:2024sux: Temperature dependence of the dimensionless subtracted quark condensate $M$ (left) and the chiral susceptibility $\chi_M$ (right) obtained on lattice for different ratios of $H=m_l/m_s$ and with temporal extent $N_\tau = 8$.
• Figure 2: Left: fit 1, 2, and 3 of the $f_0(500)$ saturated scalar susceptibility. Right: difference between the dimensionless order parameter $M$ evaluated at two different pion masses using the constants obtained from fit 4. A characteristic uncertainty of $10\%$ has been assigned to the lattice data corresponding to the $M$ differences. The uncertainty bands correspond to the uncertainties in the fit parameters.