Chiral Symmetry Restoration and Scalar-Pseudoscalar partners in QCD

TL;DR

This paper investigates the degeneration of scalar and pseudoscalar susceptibilities at the QCD chiral transition, using model-independent Chiral Perturbation Theory and lattice data to confirm the restoration pattern and the role of the sigma resonance.

Contribution

It demonstrates the compatibility of chiral-restoring behavior of susceptibilities with lattice results and models the scalar susceptibility using the sigma resonance within unitarized ChPT.

Findings

Scalar-pseudoscalar susceptibilities degenerate at the transition.

Lattice data confirms the degeneration pattern.

Sigma resonance describes the scalar susceptibility peak.

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.