Gauge fixing and the gluon propagator in renormalizable xi gauges

TL;DR

This paper develops and tests convergence techniques for covariant R_xi gauge fixing on large lattice volumes, enabling the study of the gluon propagator's infrared behavior and its dependence on the gauge parameter.

Contribution

It introduces effective methods for gauge fixing in large lattice volumes with various xi parameters, facilitating detailed infrared gluon propagator analysis.

Findings

Longitudinal gluon dressing functions remain constant at xi.

Transverse gluon propagators saturate in the infrared, indicating a dynamical gluon mass.

Gauge fixing techniques enable studies at larger volumes and xi values.

Abstract

Covariant $R_\xi$ gauge fixing is notoriously difficult for large lattice volumes, large $\xi$ and small $N_c$. We thoroughly test different convergence techniques, which allows the gauge fixing of lattice configurations with a total volume of (3.25 fm)$^4$, up to $\xi=0.5$. We are able to study the gluon propagator in the infrared region and its dependence on the gauge fixing parameter $\xi$. As expected, the longitudinal gluon dressing functions stay constant at their tree-level value $\xi$. Similar to the Landau gauge, the transverse $R_\xi$ gauge gluon propagators saturate at a non-vanishing value in the deep infrared for all values of $\xi$ studied. We compare with very recent continuum studies and perform a simple analysis of the found saturation with a dynamically generated effective gluon mass.