Yang-Mills propagators in linear covariant gauges from Nielsen identities

TL;DR

This paper computes gluon and ghost propagators in Yang-Mills theory across various linear covariant gauges using Nielsen identities, revealing significant gauge dependence and providing insights into the behavior of these propagators.

Contribution

The study extends the calculation of Yang-Mills propagators to a range of linear covariant gauges using Nielsen identities, offering quantitative results and analysis of gauge dependence.

Findings

Ghost propagator varies significantly with gauge parameter

Gluon propagator shows qualitative behavior consistent with expectations at large gauge parameter

Ghost-gluon coupling remains stable across gauges

Abstract

We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter $0<\xi \le 5$. Extrapolating the propagators to $\xi \to \infty $ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values $\xi\lesssim 1/2$ of the gauge fixing parameter. It is shown that the correlation functions, and in particular the ghost propagator, change significantly with increasing gauge parameter. In turn, the ghost-gluon running coupling as well as the position of the zero crossing of the Schwinger function of the gluon propagator remain within the uncertainties of our calculation unchanged.