The gluon propagator in Coulomb gauge from the lattice

TL;DR

This paper demonstrates that the static transverse gluon propagator in Coulomb gauge on the lattice is multiplicatively renormalizable and matches the Gribov formula, providing a method to compute it at finite temporal spacing.

Contribution

It introduces a procedure to calculate the gluon propagator on the lattice at finite temporal spacing and confirms its agreement with the Gribov formula across all momenta.

Findings

The static transverse propagator satisfies multiplicative renormalizability.

The propagator agrees with the Gribov formula at all momenta.

The mass parameter M is approximately 0.88 GeV.

Abstract

We show that in the lattice Hamiltonian limit the static transverse propagator $D(|\vec{p}|)\propto\int d p_0 D(|\vec{p}|,p_0)$ satisfies multiplicative renormalizability. We give a procedure to calculate $D(|\vec{p}|)$ on available lattices at finite temporal spacing. The result agrees at all momenta with the Gribov formula $D(|\vec{p}|)\propto(|\vec{p}|^2+ M^4 |\vec{p}|^{-2})^{-{1/2}}$, with $M=0.88(1) {\rm GeV} \simeq 2 \sqrt{\sigma}$.