Temperature of approximate axial $U(1)_A$ restoration

Determine the temperature at which the axial \(U(1)_A\) symmetry of QCD is approximately restored, particularly relative to the chiral crossover temperature \(T_\chi\).

Background

The paper discusses lattice determinations of the restoration of axial $U(1)_A$ using differences between correlators in the $\pi^a$ and $a_0^a$ channels. Existing studies do not agree on the relevant temperature.

Most studies cited in the paper place approximate restoration near 200 MeV, while another result places it near 300 MeV. Results for two massless flavors suggesting restoration at the chiral transition support the paper’s proposed connection between fractional topological structures and axial-symmetry breaking, but the general temperature scale remains unresolved.