Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

Understand

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.