The four-gluon vertex and the running coupling in Landau gauge Yang-Mills theory

TL;DR

This paper investigates the behavior of the running coupling in Landau gauge SU(N_c) Yang-Mills theory through the four-gluon vertex, revealing a nontrivial infrared fixed point significantly smaller than that of the ghost-gluon vertex.

Contribution

It provides a numerical analysis of the four-gluon vertex and its impact on the running coupling, highlighting differences in infrared fixed points within Yang-Mills theory.

Findings

Infrared fixed point is three orders of magnitude smaller than ghost-gluon coupling.

Numerical solutions obtained from Dyson-Schwinger equations.

Nontrivial infrared behavior of the four-gluon vertex.

Abstract

We summarise results for the running coupling from the four-gluon vertex in Landau gauge, SU($N_c$) Yang-Mills theory as given by a combination of dressing functions of the vertex and the gluon propagator. These functions have been determined numerically from the corresponding set of Dyson-Schwinger equations. In the infrared we obtain a nontrivial infrared fixed point which is three orders of magnitude smaller than the corresponding one in the coupling of the ghost-gluon vertex.