Influence of Gribov ambiguities in a class of nonlinear covariant gauges

TL;DR

This paper investigates the impact of Gribov ambiguities in nonlinear covariant gauges for Yang-Mills theories, providing new insights into infrared behavior and renormalization group trajectories, with implications for nonperturbative studies.

Contribution

It introduces a class of nonlinear covariant gauges that handle Gribov ambiguities and analyzes their effects on gluon and ghost propagators at one-loop order.

Findings

Gluon and ghost behave as massive fields at low energy

Infrared-safe renormalization-group trajectories exist without Landau poles

Gluon propagator remains transverse away from Landau gauge

Abstract

We consider Yang-Mills theories in a recently proposed family of nonlinear covariant gauges that consistently deals with the issue of Gribov ambiguities. Such gauges provide a generalization of the Curci-Ferrari-Delbourgo-Jarvis gauges which can be formulated as an extremization procedure and might be implemented in numerical calculations. This would allow for nonperturbative studies of Yang-Mills correlators in a broad class of covariant gauges continuously connected to the well-studied Landau gauge. We compute the ghost and gluon propagators in the continuum formulation at one-loop order in perturbation theory and we study their momentum dependence down to the deep infrared regime, with and without renormalization group improvement. In particular, we show that the theory admits infrared-safe renormalization-group trajectories with no Landau pole. Both the gluon and the ghost behave as massive fields at low energy, and the gluon propagator is transverse even away from the Landau gauge limit. We compare our results to those obtained in the usual Curci-Ferrari model, which allows us to pinpoint the specific effects arising from our treatment of Gribov copies.