Scaling behavior of the overlap quark propagator in Landau gauge

TL;DR

This study investigates the momentum-dependent properties of the quark propagator in Landau gauge using overlap fermions in quenched lattice QCD, analyzing lattice spacing effects and continuum approach.

Contribution

It provides a nonperturbative analysis of the wave function renormalization and mass functions across different lattice spacings, highlighting the approach toward the continuum limit.

Findings

Z(p) and M(p) agree between finer lattices in the chiral limit

Data indicates the need for even finer lattices for better accuracy

Large momentum behavior used to estimate the quark condensate

Abstract

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations are done on three lattices with different lattice spacings and similar physical volumes to explore the approach of the quark propagator toward the continuum limit. We have calculated the nonperturbative momentum-dependent wave function renormalization function Z(p) and the nonperturbative mass function M(p) for a variety of bare quark masses and perform an extrapolation to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable agreement between the two finer lattices in the chiral limit, however the data suggest that an even finer lattice is desirable. The large momentum behavior is examined to determine the quark condensate.