Probing the infrared behavior of the ghost-gluon vertex in Quantum Chromodynamics

Full text: The present work concerns the ghost-gluon vertex of quantum chromodynamics, which, according to the Taylor identity, has no perturbative corrections to any order, in the Landau gauge and for a specific momentum configuration. We study this vertex for a momentum configuration for which there is no proof of such a result, which is the one with a zero gluon momentum. The framework we adopt for it is the 'Dynamical Perturbation Theory' approach, which consists of inserting some nonperturbative character of the theory into its perturbative expansion. It is a phenomenological attempt only, intended to probe infrared properties of the theory by means of loop calculations. We have made use of two nonperturbative properties: first, a finite gluon mass, since there are even more indications that the gluon presents a mass, though it is a dynamical one - it intrinsically changes from finite in the infrared, to zero in the ultraviolet. Second, a recent result on the effective charge of quantum chromodynamics, which itself considers a dynamical gluon mass. We calculate the 1-loop correction to the ghost-gluon vertex, aiming at verifying how close to 1 the ghost-gluon vertex renormalization function is. The result obtained was positive in this direction: indeed, it does not differ much from unity. Moreover, our result fits better the lattice data when we consider the mentioned effective charge, than when we set the coupling constant as a fit parameter. Therefore, our somewhat phenomenological approach based on a dynamical gluon mass is, at least, consistent, and supports the approximation, usually performed in the study of the Schwinger-Dyson equations of quantum chromodynamics, of the ghost-gluon vertex renormalization function to be identically equal to 1. (author)