Quark propagator in Landau and Laplacian gauges with overlap fermions

TL;DR

This study compares the quark propagator's properties in Landau and Laplacian gauges using overlap fermions in quenched lattice QCD, revealing gauge-dependent differences in wave-function renormalization and similar mass functions.

Contribution

It provides a detailed comparison of the quark propagator in two gauges and analyzes the effects of lattice spacing on these properties in quenched lattice QCD.

Findings

Mass functions are similar across gauges.

Wave-function renormalization is more suppressed in Laplacian gauge.

Finite lattice spacing effects are significant on coarser lattices.

Abstract

The properties of the momentum space quark propagator in Landau gauge and Gribov copy free Laplacian gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are done on two lattices with different lattice spacing $a$ and the same physical volume. We have calculated the nonperturbative wave function renormalization function $Z(q)$ 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 focus on the comparison of the behavior of $Z(q)$ and $M(p)$ in the chiral limit in the two gauge fixing schemes as well as the behavior on two lattices with different lattice spacing $a$. We find that the mass functions $M(p)$ are very similar for the two gauges while the wave-function renormalization function $Z(q)$ is more strongly infrared suppressed in the Laplacian gauge than in the Landau gauge on the finer lattice. For Laplacian gauge, it seems that the finite $a$ error is large on the coarse lattice which has a lattice spacing $a$ of about 0.124 fm.