Chiral and $U(1)_A$ restoration for the scalar/pseudoscalar meson nonets

TL;DR

This paper investigates how chiral and $U(1)_A$ symmetries are restored in scalar and pseudoscalar mesons at finite temperature using QCD Ward Identities and Chiral Perturbation Theory, connecting theoretical predictions with lattice results.

Contribution

It provides a comprehensive analysis of symmetry restoration patterns in meson nonets combining Ward Identities and ChPT, highlighting conditions for $U(1)_A$ partner degeneracy.

Findings

$U(1)_A$ partner restoration occurs when chiral partners degenerate.

ChPT confirms $U(1)_A$ restoration in the light chiral limit.

Temperature scaling of meson masses aligns with Ward Identity predictions.

Abstract

We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.