Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

TL;DR

This paper derives a non-Abelian extension of the quark-gluon vertex form factors using Slavnov-Taylor identities, providing detailed momentum-dependent expressions that improve understanding of strong interaction kernels in QCD.

Contribution

It introduces a novel non-Abelian quark-gluon vertex form factor calculation based on Slavnov-Taylor identities, including the quark-ghost scattering kernel, for arbitrary Euclidean momenta.

Findings

Vertex form factors exhibit features beyond the Abelian approximation.

Results impact the modeling of quark gap and Bethe-Salpeter equations.

Provides momentum-dependent expressions for the non-Abelian vertex.

Abstract

We determine the non-Abelian version of the four longitudinal form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. The potential phenomenological impact of these results is evaluated through the study of special renormalization-point-independent combinations, which quantify the strength of the interaction kernels appearing in the standard quark gap and Bethe-Salpeter equations.