$U(1)_A$ symmetry restoration at finite temperature with mesonic correlators

The $U(1)_A$ symmetry of the massless QCD Lagrangian is explicitly broken in the quantised theory by the anomaly. It may be effectively restored at some finite temperature, which would have important consequences for the order of the chiral transition and the QCD phase diagram. It has been argued in the literature that one way to probe the effective restoration of $U(1)_A$ is to check for the degeneracy of pseudoscalar and flavour non-singlet scalar correlators. In this work, we consider a new method of examining this degeneracy based upon hadron correlation functions on the anisotropic FASTSUM ensembles. The anisotropic nature and our newest Generation 3 ensembles aid in a determination of the effective restoration of the $U(1)_A$ symmetry which we find to be $T_{U(1)_A} \sim 320$ MeV, well above the chiral transition temperature, which is $T_{\rm pc} \sim 180$ MeV for our choice of Wilson-Clover fermions.