The Gribov horizon and the one-loop color-Coulomb potential

TL;DR

This paper recalculates the one-loop color-Coulomb potential considering the Gribov horizon's effect, which modifies the gluon propagator and enhances the infrared behavior, resulting in a potential that rises linearly with a logarithmic correction.

Contribution

It introduces a method to incorporate the Gribov horizon effect into the one-loop Coulomb potential calculation using a gluon mass term, revealing a linearly rising potential with a logarithmic modification.

Findings

The Gribov horizon makes the transverse gluon propagator less singular.

The Coulomb potential becomes more singular in the infrared.

The resulting potential rises linearly with a logarithmic correction.

Abstract

We recalculate the color-Coulomb potential to one-loop order, under the assumption that the effect of the Gribov horizon is to make i) the transverse gluon propagator less singular; and ii) the color-Coulomb potential more singular, than their perturbative behavior in the low-momentum limit. As a first guess, the effect of the Gribov horizon is mimicked by introducing a transverse momentum-dependent gluon mass term, leading to a propagator of the Gribov form, with the prescription that the mass parameter should be adjusted to the unique value where the infrared behavior of the Coulomb potential is enhanced. We find that this procedure leads to a Coulomb potential rising asymptotically as a linear term modified by a logarithm.