We describe scalar-pseudoscalar partner degeneration at the QCD chiral transition in terms of the dominant low-energy physical states for the light quark sector. First, we obtain within model-independent one-loop chiral perturbation theory that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low $T$. Next, we show that this chiral-restoring behavior for ${\chi }_P$ is compatible with recent lattice results for screening masses and gives rise to degeneration between the scalar and pseudoscalar susceptibilities $({\chi }_S,{\chi }_P)$ around the transition point, consistently with an $O(4)$-like current restoration pattern. This scenario is clearly confirmed by lattice data when we compare ${\chi }_S(T)$ with the quark condensate, expected to scale as ${\chi }_P(T)$. Finally, we show that saturating ${\chi }_S$ with the $\sigma /f_0(500)$ broad resonance observed in pion scattering and including its finite temperature dependence, allows us to describe the peak structure of ${\chi }_S(T)$ in lattice data and the associated critical temperature. This is carried out within a unitarized chiral perturbation theory scheme which generates the resonant state dynamically and is also consistent with partner degeneration.

• Received 18 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.076007