  In this paper, we discuss the gluon propagator in the linear covariant gauges
in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into
account via the so-called Refined Gribov-Zwanziger framework. We point out
that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon
propagator displays a massive (decoupling) behaviour, while for $D=2$, a
scaling one emerges. All results are discussed in a setup that respects the
Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced
non-perturbative BRST transformation. We also propose a minimizing functional
that could be used to construct a lattice version of our non-perturbative
definition of the linear covariant gauge.
