A Dyson-Schwinger study of the four-gluon vertex

TL;DR

This paper presents a self-consistent Dyson-Schwinger equation calculation of the four-gluon vertex in Landau gauge Yang--Mills theory, revealing its momentum dependence and tensor structure, with implications for understanding non-perturbative QCD interactions.

Contribution

It introduces a truncated Dyson-Schwinger approach to compute the four-gluon vertex self-consistently, using lower Green functions as input, and explores its momentum and tensor structure.

Findings

Full momentum dependence of the vertex resolved

Tree-level tensor structure dominates with suppressed other structures

Qualitative fit for the vertex and running coupling obtained

Abstract

We present a self-consistent calculation of the four-gluon vertex of Landau gauge Yang--Mills theory from a truncated Dyson--Schwinger equation. The equation contains the leading diagrams in the ultraviolet and is solved using as the only input results for lower Green functions from previous Dyson--Schwinger calculations that are in good agreement with lattice data. All quantities are therefore fixed and no higher Green functions enter within this truncation. Our self-consistent solution resolves the full momentum dependence of the vertex but is limited to the tree-level tensor structure at the moment. Calculations of selected dressing functions for other tensor structures from this solution are used to exemplify that they are suppressed compared to the tree-level structure except for possible logarithmic enhancements in the deep infrared. Our results furthermore allow one to extract a qualitative fit for the vertex and a running coupling.