On non-primitively divergent vertices of Yang-Mills theory

TL;DR

This paper calculates non-primitively divergent vertices in Yang-Mills theory, showing their minimal impact on lower correlation functions and clarifying their tensor structures and hierarchy.

Contribution

It provides the first detailed calculation of the two-ghost-two-gluon and four-ghost vertices, including full tensor structures and their influence on lower vertices.

Findings

Two-ghost-two-gluon vertex has negligible impact on the three-gluon vertex.

Four-ghost vertex is extremely small and has minimal effect on propagators.

Hierarchy reduces relevant dressing functions based on color structure.

Abstract

Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations - including two-loop terms - is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below $2\%$ is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions.