The ghost-gluon vertex in the presence of the Gribov horizon

TL;DR

This paper investigates the ghost-gluon vertex in Landau gauge Yang-Mills theories within the refined Gribov-Zwanziger framework, demonstrating infrared behavior consistent with lattice simulations and other nonperturbative approaches.

Contribution

It provides analytical results for the ghost-gluon interaction vertex at one-loop level in the RGZ framework, confirming compatibility with lattice data and Schwinger-Dyson solutions.

Findings

Infrared behavior of the ghost-gluon vertex matches lattice results.

Analytical expressions derived in the zero gluon momentum limit.

Results are consistent across SU(2), SU(3), and other nonperturbative methods.

Abstract

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.