Gauge fixing and the gluon propagator in renormalizable xi gauges

Covariant $R_ξ$ gauge fixing is notoriously difficult for large lattice volumes, large $ξ$ 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 $ξ=0.5$. We are able to study the gluon propagator in the infrared region and its dependence on the gauge fixing parameter $ξ$. As expected, the longitudinal gluon dressing functions stay constant at their tree-level value $ξ$. Similar to the Landau gauge, the transverse $R_ξ$ gauge gluon propagators saturate at a non-vanishing value in the deep infrared for all values of $ξ$ studied. We compare with very recent continuum studies and perform a simple analysis of the found saturation with a dynamically generated effective gluon mass.

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