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.
Highlights
The two-flavor QCD Lagrangian in the massless limit has a global SUð2ÞL × SUð2ÞR × Uð1ÞV × Uð1ÞA symmetry
Since the anomaly refers to symmetry breaking at the cutoff scale where the theory is defined, and the anomalous Ward-Takahashi identity holds at any temperature [1], it is natural to assume that the anomaly survives the chiral phase transition and the physics of the early universe is not Uð1ÞA symmetric
As we found in our previous study that the lattice artifact from mixed action is large even though the overlap and Möbius domain-wall fermion actions are very similar to each other, we reweight the gauge configurations of the Möbius domain-wall fermion determinant by that of the overlap fermion
Summary
The two-flavor QCD Lagrangian in the massless limit has a global SUð2ÞL × SUð2ÞR × Uð1ÞV × Uð1ÞA symmetry. Since the effective potential can have more complicated structure as the degrees of freedom increase, it was argued that the chiral phase transition likely becomes first order when Uð1ÞA symmetry is recovered (we refer the readers to [10] for a different aspect of the firstorder scenario from ’t Hooft anomaly matching), though other scenarios are theoretically possible [11,12,13,14,15,16]. After removing the lattice artifact due to the violation of the Ginsparg-Wilson relation at high temperature, we observed that chiral limit of the Uð1ÞA susceptibility is consistent with zero [30].
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