Chiral Symmetry Restoration and Scalar-Pseudoscalar partners in QCD

Abstract

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 (ChPT) that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low $T$. Next, we show that this chiral-restoring behaviour 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 to describe the peak structure of ${\chi }_S(T)$ in lattice data and the associated critical temperature. This is carried out within a unitarized ChPT scheme which generates the resonant state dynamically and is also consistent with partner degeneration.

Comments: 9 pages, 4 figures. Enlarged version to appear in Phys.Rev.D