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 $a^{-1}\simeq 1$ 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 $m_f\to 0$ and the length of the fifth dimension $N_s\to \infty$, indicating that chiral symmetry is not realized with quenched DWQCD up to $a^{-1}\simeq 2$ GeV. The behavior is much improved for the RG-improved gauge action: while a non-vanishing quark mass remains in the chiral limit at $a^{-1}\simeq 1$ GeV, the result at $a^{-1}\simeq 2$ 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.

36 pages, 18 eps figures