Ghost-gluon Vertex in the Presence of the Gribov Horizon: General Kinematics

Correlation functions are important probes for the behavior of quantum field theories. Already at treelevel, 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 -gluon vertex function in Landau gauge at one -loop level, in d 1 / 4 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 CurciFerrari model for three different kinematic configurations. This is compatible with RGZ being a feasible theory for the strong interaction in the infrared regime.