Recent advances on chiral partners and patterns

TL;DR

This paper reviews recent findings on chiral symmetry restoration in QCD, emphasizing the role of Ward Identities and susceptibilities in understanding partner degenerations and the influence of the thermal $f_0(500)$ state.

Contribution

It provides a comprehensive analysis of $O(4)$ and $U(1)_A$ symmetry restoration patterns using Ward Identities and compares results with lattice QCD data.

Findings

$U(1)_A$ partners degenerate in the $O(4)$ restoration limit.

Susceptibilities reveal symmetry restoration patterns.

Thermal $f_0(500)$ state impacts chiral transition observables.

Abstract

We review recent results on chiral $SU(2)_L\times SU(2)_R\approx O(4)$ and $U(1)_A$ symmetry restoration in QCD. In particular, we discuss how Ward Identities allow one to derive general results on partner degeneration, which shed light on the distinction between the $O(4)$ and $O(4)\times U(1)_A$ patterns of the chiral transition. For that purpose, susceptibilities associated with the $O(4)$ and $U(1)_A$ symmetries are studied. From this analysis we conclude that in the ideal regime of exact $O(4)$ restoration (formally achieved in the limit of two massless flavours), $U(1)_A$ partners degenerate as well. We also discuss the role of the thermal $f_0(500)$ state to describe thermodynamic observables sensitive to chiral restoration, such as the scalar susceptibility. We pay special attention to the consistency of our results with recent lattice analysis.