Scaling Behavior of the Landau Gauge Overlap Quark Propagator

TL;DR

This study investigates the scaling behavior of the Landau gauge overlap quark propagator in quenched lattice QCD, analyzing how it approaches the continuum limit across different lattice spacings.

Contribution

It provides a detailed nonperturbative analysis of the momentum-dependent quark propagator functions and their scaling behavior in the continuum limit.

Findings

Good agreement of $Z(p^2)$ and $M(p^2)$ on finer lattices in the chiral limit

Calculated the nonperturbative wavefunction renormalization and mass functions

Determined the quark condensate value

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 towards the continuum limit. We have calculated the nonperturbative momentum-dependent wavefunction renormalization function $Z(p^2)$ and the nonperturbative mass function $M(p^2)$ for a variety of bare quark masses and extrapolate to the chiral limit. We find the behavior of $Z(p^2)$ and $M(p^2)$ are in good agreement for the two finer lattices in the chiral limit. The quark condensate is also calculated.