Yang-Mills two-point functions in linear covariant gauges

TL;DR

This paper investigates how the ghost propagator in SU(3) Yang-Mills theory varies with the gauge-fixing parameter in linear covariant gauges, revealing that it vanishes in the infrared for positive gauge parameters, contrasting with the Landau gauge.

Contribution

It introduces a combined approach using Schwinger-Dyson equations and Nielsen identities to analyze gauge dependence of ghost and gluon propagators in Yang-Mills theory.

Findings

Ghost dressing function approaches zero in the infrared for $\xi>0$

Gluon masses exhibit logarithmic divergence in the infrared

Results contrast with the finite value in Landau gauge

Abstract

In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $\xi$ in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $\xi>0$ are infrared finite, as is the case in the Landau gauge $(\xi=0)$. Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to $\xi$ in terms of certain auxiliary Green's functions, which are subsequently computed under the same assumptions as before. Within both formalisms we find that for $\xi>0$ the ghost dressing function approaches zero in the deep infrared, in sharp contrast to what happens in the Landau gauge, where it known to saturate at a finite (non-vanishing) value. The Nielsen identities are then extended to the case of the gluon propagator, and the $\xi$-dependence of the corresponding gluon masses is derived using as input the results obtained in the previous steps. The result turns out to be logarithmically divergent in the deep infrared; the compatibility of this behavior with the basic assumption of a finite gluon propagator is discussed, and a specific Ansatz is put forth, which readily reconciles both features.