Quark propagator from an improved staggered action in Laplacian and Landau gauges

TL;DR

This paper compares the quark propagator in Landau and Laplacian gauges using improved staggered actions, demonstrating reduced errors and similar results across gauges, with implications for understanding gauge-dependent quantities.

Contribution

It provides the first detailed comparison of quark propagators in Landau and Laplacian gauges using improved staggered actions and applies tree-level corrections for more accurate results.

Findings

Improved 'Asqtad' action reduces errors compared to standard action.

Landau and Laplacian gauges yield similar quark propagator results.

Infrared quark mass in the chiral limit is approximately 260 MeV.

Abstract

Studies of gauge dependent quantities are afflicted with Gribov copies, but Laplacian gauge fixing provides one possible solution to this problem. We present results for the lattice quark propagator in both Landau and Laplacian gauges using standard and improved staggered quark actions. The standard Kogut-Susskind action has errors of \oa{2} while the improved ``Asqtad'' action has \oa{4}, \oag{2}{2} errors and this improvement is seen in the quark propagator. We demonstrate the application of tree-level corrections to these actions and see that Landau and Laplacian gauges produce very similar results. In addition, we test an ansatz for the quark mass function, with promising results. In the chiral limit, the infrared quark mass, $M(q^2 = 0)$ is found to be $260\pm 20$ MeV.