Infrared massive gluon propagator from a BRST-invariant Gribov horizon in a family of covariant gauges

A distinctive feature observed in lattice simulations of confining non-Abelian gauge theories, such as quantum chromodynamics, is the presence of a dynamical mass for the gauge field in the low-energy regime of the theory. In the Gribov-Zwanziger framework in the Landau gauge, such mass is a consequence of the generation of the dimension-two condensates $⟨A_{\mu }^a{A}_{\mu }^a⟩$ and $⟨{\overline{\phi }}_{\mu }^{ab}{\phi }_{\mu }^{ab}-{\overline{\omega }}_{\mu }^{ab}{\omega }_{\mu }^{ab}⟩$, where $A$ is the gluon field and the fields $\overline{\phi }$, $\phi$, $\overline{\omega }$, and $\omega$ are Zwanziger’s auxiliary fields. In this work, we show that, in the recently developed BRST-invariant version of the refined Gribov-Zwanziger theory, these condensates can be introduced in a BRST-invariant way for a family of $R_{\xi }$ gauges. Their values are explicitly computed to first order and turn out to be independent of the gauge parameters contained in the gauge-fixing condition, as expected from the BRST invariance of the formulation. This fact supports the possibility of a gauge-parameter independent nonzero infrared gluon mass, whose value is the same as the one in the Landau gauge.