  We consider Yang-Mills theories quantized in the Landau gauge in the presence
of the Gribov horizon via the refined Gribov Zwanziger (RGZ) framework. As the
restriction of the gauge path integral to the Gribov region is taken into
account, the resulting gauge field propagators display a nontrivial infrared
behavior, being very close to the ones observed in lattice gauge field theory
simulations. In this work, we explore a higher correlation function in the
Refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at
one-loop level. We show explicit compatibility with kinematical constraints, as
required by the Ward identities of the theory, and obtain analytical
expressions in the limit of vanishing gluon momentum. We find that the RGZ
results are nontrivial in the infrared regime, being compatible with lattice YM
simulations in both SU(2) and SU(3), as well as with solutions from
Schwinger-Dyson equations in different truncation schemes, Functional
Renormalization Group analysis, and the RG-improved Curci-Ferrari model.
