Toward background field independence within the Gribov horizon

We introduce a background gauge akin to the Landau-DeWitt but deformed by presence of parameter for quantization Euclidean Yang-Mills theories. In limit where field vanishes, standard linear covariant gauges are recovered. This allows an explicit investigation effects infinitesimal Gribov copies and their impact dependence physical correlators. Similarly gauges, introduction gauge-invariant dressed fields is essential restore Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Hence, we construct BRST symmetric action in which eliminates regular analogy recently introduced invariant (refined) Gribov-Zwanziger action. The issue its relation discussed light nonperturbative driven elimination copies.