Vertex functions of Coulomb gauge Yang--Mills theory

TL;DR

This paper numerically solves Dyson--Schwinger equations for three-gluon and ghost-gluon vertices in Coulomb gauge Yang--Mills theory, revealing infrared behaviors and including previously neglected diagrams.

Contribution

It introduces a comprehensive truncation of Dyson--Schwinger equations that accounts for back-coupling and neglected diagrams, improving the understanding of vertex functions.

Findings

Ghost-gluon vertex is infrared finite

Three-gluon vertex diverges in the infrared

Comparison shows differences from bare-vertex approximations

Abstract

The canonical recursive Dyson--Schwinger equations for the three-gluon and ghost-gluon vertices are solved numerically. The employed truncation includes several previously neglected diagrams and includes back-coupling effects. We find an infrared finite ghost-gluon vertex and an infrared diverging three-gluon vertex. We also compare our results with those obtained in previous calculations, where bare vertices were used in the loop diagrams.