Chiral properties of domain-wall quarks in quenched QCD

TL;DR

This study examines the chiral properties of quenched domain-wall QCD at different lattice spacings, finding that chiral symmetry is not realized with the plaquette action but is achieved with the RG-improved gauge action at finer lattice spacings.

Contribution

The paper demonstrates that the realization of chiral symmetry in quenched domain-wall QCD depends on the gauge action and lattice spacing, showing improved chiral properties with RG-improved actions at higher energies.

Findings

Chiral symmetry not realized with plaquette action at $a^{-1} \,\simeq\, 2$ GeV.

Chiral symmetry is realized with RG-improved gauge action at $a^{-1} \,\simeq\, 2$ GeV.

Quark mass vanishes exponentially in the chiral limit with RG-improved action at finer lattice spacing.

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.