On non-primitively divergent vertices of Yang-Mills theory

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.

11 pages, 10 figures

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• The strong running coupling from the gauge sector of Domain Wall lattice QCD with physical quark masses
• Gauge Sector Dynamics in QCD
• On mass generation in Landau-gauge Yang-Mills theory
• Ghost dynamics in the soft gluon limit
• Exploring smoking-gun signals of the Schwinger mechanism in QCD
• Schwinger mechanism for gluons from lattice QCD
• Gluon dynamics from an ordinary differential equation
• Gluon mass scale through the Schwinger mechanism
• Schwinger-Dyson truncations in the all-soft limit: a case study
• Glueballs from bound state equations
• Ghost dynamics from Schwinger-Dyson equations