Chiral and $U(1)_A$ restoration: Ward Identities and effective theories

Abstract: We discuss our recent results regarding chiral and $U(1)_A$ restoration, both from the formal point of view of QCD Ward Identities (WI) and from an Effective Theory analysis provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature. Our results lead to relevant conclusions regarding the behavior of chiral partners (in terms of susceptibilities) in the limit of exact restoration and provide useful results for lattice analysis. In addition, it helps to understand the temperature dependence of lattice screening masses in terms of quark condensate combinations. The U(3) ChPT calculation supports the conclusions obtained within the WI analysis. Finally, the role of the thermal $f_0(500)$ state in chiral symmetry restoration, regarding the scalar susceptibility, is also discussed.