Gauge fixing and the gluon propagator in renormalizable xi gauges

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.

Comments: 7 pages, 5 figures, contribution to the 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe, Japan