Quenched chiral logarithms in lattice QCD with exact chiral symmetry

TL;DR

This study confirms the presence of quenched chiral logarithms in lattice QCD with overlap Dirac quarks and accurately measures their coefficient, supporting predictions from quenched chiral perturbation theory.

Contribution

First precise determination of quenched chiral logarithm coefficient using overlap fermions and topological susceptibility in lattice QCD.

Findings

Confirmed quenched chiral logarithm in pion mass with coefficient δ=0.203

Measured topological susceptibility and derived η' mass consistent with theoretical predictions

Found good agreement between different methods of determining δ in quenched QCD

Abstract

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $ \beta = 5.8 $ on the $ 8^3 \times 24 $ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $ \delta = 0.203 \pm 0.014 $, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $ \eta' $ mass in quenched chiral perturbation theory, $ m_{\eta'} = (901 \pm 64) $ Mev, and an estimate of $ \delta = 0.197 \pm 0.027 $, which is in good agreement with that determined from the pion mass.