The lattice gluon propagator in renormalizable $\xi$ gauges

TL;DR

This paper investigates the SU(3) gluon propagator in various renormalizable gauges on a lattice, revealing infrared saturation and effective gluon mass generation consistent with continuum studies.

Contribution

It provides lattice results for the gluon propagator in $R_\xi$ gauges up to $\xi=0.5$, extending understanding beyond Landau gauge and comparing with continuum analyses.

Findings

Longitudinal gluon dressing function remains constant at $\xi$

Transverse gluon propagator saturates in the infrared

Evidence for a dynamically generated effective gluon mass

Abstract

We study the SU(3) gluon propagator in renormalizable $R_\xi$ gauges implemented on a symmetric lattice with a total volume of (3.25 fm)$^4$ for values of the guage fixing parameter up to $\xi=0.5$. As expected, the longitudinal gluon dressing function stays constant at its tree-level value $\xi$. Similar to the Landau gauge, the transverse $R_\xi$ gauge gluon propagator saturates 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.