A new method for computing the quark-gluon vertex

TL;DR

This paper introduces a novel nonperturbative method to compute the quark-gluon vertex using background field relations, gauge techniques, and Ward identities, providing form factors across various momenta.

Contribution

It presents a new approach combining the background field method and Ward identities to determine all form factors of the quark-gluon vertex nonperturbatively.

Findings

Form factors computed for specific kinematic configurations.

Results show good agreement with lattice data.

Method enables analysis of the vertex at arbitrary momenta.

Abstract

In this talk we present a new method for determining the nonperturbative quark-gluon vertex, which constitutes a crucial ingredient for a variety of theoretical and phenomenological studies. This new method relies heavily on the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. The longitudinal part of this latter quantity is fixed using the standard gauge technique, whereas the transverse is estimated with the help of the so-called transverse Ward identities. This method allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. Numerical results are presented for the form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum), and compared with the corresponding lattice data.