On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

TL;DR

This paper investigates how three-point functions, specifically the ghost-gluon and three-gluon vertices, influence the propagators in Landau gauge Yang-Mills theory by solving Dyson-Schwinger equations with new models and lattice data comparisons.

Contribution

It introduces a dynamic treatment of the ghost-gluon vertex and a new three-gluon vertex model, revealing their significant impact on propagator solutions and lattice agreement.

Findings

Vertices significantly affect mid-momentum propagator behavior

Three-gluon vertex dressing becomes negative at low momenta

Enhanced agreement between Dyson-Schwinger and lattice results

Abstract

We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.