On the effective restoration of $U(1)_A$ symmetry at finite temperature

TL;DR

This study uses anisotropic lattice QCD to identify the temperature at which the $U(1)_A$ symmetry effectively restores, finding it occurs significantly above the chiral crossover temperature.

Contribution

It provides the first precise lattice QCD determination of the $U(1)_A$ symmetry restoration temperature using fine temporal resolution ensembles.

Findings

$U(1)_A$ symmetry effectively restores at $319(22)$ MeV.

Degeneracy of pseudoscalar and scalar susceptibilities observed.

Restoration occurs above the chiral crossover temperature.

Abstract

The $U(1)_A$ symmetry of the massless QCD Lagrangian is explicitly broken by the axial anomaly, but it may be effectively restored at finite temperature. Determining the temperature at which this occurs is important for understanding the chiral transition and the structure of the QCD phase diagram. A commonly used probe of effective $U(1)_A$ restoration is the degeneracy of flavour non-singlet pseudoscalar and scalar susceptibilities. Using anisotropic lattice QCD ensembles with Wilson-clover fermions generated by the \textsc{Fastsum} collaboration, we study this degeneracy through hadronic correlation functions over a wide range of temperatures. The fine temporal resolution of our Generation 3 ensembles allows us to determine the temperature at which the pseudoscalar and scalar channels become degenerate. We find evidence for the effective restoration of $U(1)_A$ symmetry at $T_{U(1)_A}=319(22)$ MeV, well above the chiral crossover temperature.