Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

TL;DR

This paper investigates the chiral symmetry properties and scaling behavior of overlap fermions on quenched lattices, demonstrating precise relations, scale independence of quark mass, and small discretization errors.

Contribution

It provides numerical evidence for the validity of the Gell-Mann-Oakes-Renner relation and analyzes the scaling and critical slowing down of overlap fermions.

Findings

Gell-Mann-Oakes-Renner relation holds within 1% accuracy

Quark mass from PCAC relation is consistent across scales

Small O(a^2) corrections observed in meson masses

Abstract

The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at $m_0a = 0.006$. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The $\pi$ and $\rho$ masses at a fixed $m_{\pi}/m_{\rho}$ ratio indicate small $O(a^2)$ corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.