A new method for determining the quark-gluon vertex

TL;DR

This paper introduces a nonperturbative method to calculate the quark-gluon vertex form factors using a novel relation with the background field method, validated against lattice data in Landau gauge.

Contribution

It develops an all-order relation connecting the quark-gluon vertex with the background field vertex, enabling nonperturbative form factor calculations in covariant gauges.

Findings

Good agreement with lattice data for form factors

Proposes a mechanism for the divergence of a form factor

Calculates form factors in key kinematic configurations

Abstract

We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex, in a general covariant gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the calculation of certain (fully-dressed) auxiliary three-point functions, using lattice data as input for the gluon propagators appearing in their diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding rather good agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.