Chiral properties of domain-wall quarks in quenched QCD

Abstract

We investigate the chiral properties of quenched domain-wall QCD (DWQCD) at the lattice spacings ${a}^{\ensuremath{-}1}\ensuremath{\simeq}1$ and 2 GeV for both plaquette and renormalization-group (RG) improved gauge actions. In the case of the plaquette action we find that the quark mass defined through the axial Ward-Takahashi identity remains non-vanishing in the DWQCD chiral limit that the bare quark mass ${m}_{f}\ensuremath{\rightarrow}0$ and the length of the fifth dimension ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty},$ indicating that chiral symmetry is not realized with quenched DWQCD up to ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2$ GeV. The behavior is much improved for the RG-improved gauge action: while a nonvanishing quark mass remains in the chiral limit at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}1$ GeV, the result at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2$ GeV is consistent with an exponentially vanishing quark mass in the DWQCD chiral limit, indicating the realization of exact chiral symmetry. An interpretation and implications are briefly discussed.