The gluon propagator in linear covariant $R_\xi$ gauges

TL;DR

This paper derives explicit analytical expressions for the gluon propagator in linear covariant gauges using a screened massive expansion, showing IR finiteness and good lattice agreement across gauges.

Contribution

It provides the first analytical derivation of the gluon propagator in generic linear covariant gauges with no free parameters, extending previous Landau gauge results.

Findings

Gluon propagator is finite in the IR for all $\xi$ values.

The gluon dressing function is uniquely determined at one-loop without free parameters.

Excellent agreement with lattice data for $0<\xi<0.5$.

Abstract

Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant $R_\xi$ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any $\xi$, with a slight decrease of its limit value when going from the Landau gauge ($\xi=0$) towards the Feynman gauge ($\xi=1$). An excellent agreement is found with the lattice in the range $0<\xi<0.5$ where the data are available.