Towards the Continuum Limit of the Overlap Quark Propagator in Landau Gauge

TL;DR

This study investigates the continuum limit of the Landau gauge quark propagator using overlap fermions in quenched lattice QCD, focusing on the nonperturbative functions $Z(p)$ and $M(p)$ across different lattice spacings.

Contribution

It provides a comparative analysis of the quark propagator functions at different lattice spacings, demonstrating their consistency in the continuum limit.

Findings

Good agreement of $Z(p)$ and $M(p)$ in the chiral limit across lattices

Nonperturbative functions calculated for various quark masses

Extrapolation to the chiral limit shows consistent behavior

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 were done on two lattices with different lattice spacing $a$ and similar physical volumes to explore the quark propagator in the continuum limit. We have calculated the nonperturbative wavefunction renormalization function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of bare quark masses and perform a simple linear extrapolation to the chiral limit. We find the behaviour of $Z(p)$ and $M(p)$ in the chiral limit are in good agreement between the two lattices.