A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories

TL;DR

This paper investigates the impact of Gribov copies on the infrared behavior of gluon propagators in Euclidean Yang-Mills theories within linear covariant gauges, highlighting suppression and enhancement phenomena and comparing with other methods.

Contribution

It provides a detailed analysis of Gribov copies effects in linear covariant gauges and explores the role of the gluon condensate in modifying propagator behavior.

Findings

Transverse gluon propagator is suppressed for small gauge parameter.

Longitudinal gluon component remains unchanged or becomes suppressed.

Green function G_{tr} shows infrared enhancement and reduces to ghost propagator in Landau gauge.

Abstract

The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate <A^2> is also considered. In this case, the transverse component of the gluon propagator and the Green function G_{tr} remain suppressed and enhanced, respectively. Moreover, the longitudinal part of the gluon propagator becomes suppressed. A comparison with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations is provided.