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

Understand

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.