Coulomb gauge ghost propagator and the Coulomb potential

TL;DR

This paper investigates the ghost propagator and Coulomb potential in Coulomb gauge on the lattice, demonstrating their insensitivity to Gribov issues and showing no scaling violations within numerical accuracy, thus clarifying their behavior in non-Abelian gauge theories.

Contribution

The study provides the first lattice evaluation showing the ghost propagator and Coulomb potential are unaffected by Gribov ambiguities and scaling violations, using an improved gauge fixing scheme.

Findings

Ghost propagator and Coulomb potential are insensitive to Gribov problem.

No scaling violations observed in the quantities within numerical accuracy.

Coulomb potential from A0-propagator agrees qualitatively with Coulomb kernel evaluation.

Abstract

The ghost propagator and the Coulomb potential are evaluated in Coulomb gauge on the lattice, using an improved gauge fixing scheme which includes the residual symmetry. This setting has been shown to be essential in order to explain the scaling violations in the instantaneous gluon propagator. We find that both the ghost propagator and the Coulomb potential are insensitive to the Gribov problem or the details of the residual gauge fixing, even if the Coulomb potential is evaluated from the A0--propagator instead of the Coulomb kernel. In particular, no signs of scaling violations could be found in either quantity, at least to well below the numerical accuracy where these violations were visible for the gluon propagator. The Coulomb potential from the A0-propagator is shown to be in qualitative agreement with the (formally equivalent) expression evaluated from the Coulomb kernel.