U_A(1) breaking at finite temperature from the Dirac spectrum with the dynamical HISQ action

TL;DR

This study examines the fate of the $U_A(1)$ symmetry at high temperatures in QCD by analyzing the Dirac spectrum with dynamical HISQ fermions, providing insights into symmetry restoration above the critical temperature.

Contribution

It presents a detailed lattice QCD analysis of $U_A(1)$ symmetry breaking above $T_c$ using the HISQ action and multiple quark masses, focusing on the Dirac eigenvalue spectrum.

Findings

No clear gap in Dirac eigenvalues above $T_c$

Dirac eigenvalue density shows linear quark mass dependence

Results suggest partial $U_A(1)$ symmetry restoration above $T_c$

Abstract

We investigate $U_A(1)$ breaking above $T_c$ in terms of the Dirac spectrum on configurations with (2+1)-flavors, using the HISQ action. The strange quark mass is at its physical value. We use several light quark masses corresponding to the Goldstone pion masses in the range of about 115 -- 230 MeV on lattices of size 32$^3 \times$8 and 48$^3 \times$8. We calculate the 100 lowest-lying Dirac eigenvalues at temperatures below and above $T_c$. We investigate the volume dependence of the Dirac eigenvalue density to determine whether there is a gap around zero, which can appear if $U_A(1)$ symmetry is restored in the chiral symmetric phase. We also investigate the quark mass dependence of the Dirac eigenvalue density at zero and check whether there is a linear behavior that would signal the $U_A(1)$ breaking above $T_c$.