Study of the axial U(1) anomaly at high temperature with lattice chiral fermions

Abstract

We investigate the axial $U(1)$ anomaly of two-flavor QCD at temperatures 190--330 MeV. In order to preserve precise chiral symmetry on the lattice, we employ the M\"obius domain-wall fermion action as well as overlap fermion action implemented with a stochastic reweighting technique. Compared to our previous studies, we reduce the lattice spacing to 0.07 fm, simulate larger multiple volumes to estimate finite size effect, and take more than four quark mass points, including one below physical point to investigate the chiral limit. We measure the topological susceptibility, axial $U(1)$ susceptibility, and examine the degeneracy of $U(1)$ partners in meson/baryon correlators. All the data above the critical temperature indicate that the axial $U(1)$ violation is consistent with zero within statistical errors. The quark mass dependence suggests disappearance of the $U(1)$ anomaly at a rate comparable to that of the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry breaking.