  Correlation functions are important probes for the behavior of quantum field
theories. Already at tree-level, the Refined Gribov Zwanziger (RGZ) effective
action for Yang-Mills theories provides a good approximation for the gluon
propagator, as compared to that calculated by nonperturbative methods such as
Lattice Field Theory and Dyson-Schwinger Equations. However, the study of
higher correlation functions of the RGZ theory is still at its beginning. In
this work we evaluate the ghost-antighost-gluon vertex function in Landau gauge
at one-loop level, in $d=4$ space-time dimensions for the gauge groups SU(2)
and SU(3). More precisely, we extend the analysis conducted in [1] for the
soft-gluon limit to an arbitrary kinematic configuration. We introduce
renormalization group effects by means of a toy model for the running coupling
and investigate the impact of such a model in the ultraviolet tails of our
results. We find that RGZ results match fairly closely those from lattice
simulations, Schwinger-Dyson equations and the Curci-Ferrari model for three
different kinematic configurations. This is compatible with RGZ being a
feasible theory for the strong interaction in the infrared regime.
