The axial U(1) symmetry at finite temperature

On behalf of the JLQCD collaboration I will present our study the axial U(1) symmetry at finite temperature in two-flavor lattice QCD. The restoration of this symmetry is a subject of ample debate in the community in the last years. The final result, besides the theoretical interest, could be relevant for the heavy ion physics experiments. We employ the Mobius domain-wall fermions with different lattice sizes L = 2-4 fm. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. This is a crucial aspect of this measurement. Above the phase transition, a strong suppression of the low-lying modes is observed in both of overlap and domain-wall Dirac spectra. We, however, find a sizable violation of the Ginsparg-Wilson relation in the Mobius domain-wall Dirac eigenmodes, which dominates the signals of the axial U(1) symmetry breaking near the chiral limit. We also find that the use of overlap fermion only in the valence sector is dangerous since it suffers from the artifacts due to partial quenching. Reweighting the Mobius domain-wall fermion determinant to that of the overlap fermion, we observe the axial U(1) breaking to vanish in the chiral limit, which is stable against the changes of the lattice volume and lattice spacing.