The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region $\Omega$ in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region $\Omega$ acquires a gauge independent meaning in the class of the physical correlators.