Going beyond the propagators of Landau gauge Yang-Mills theory

TL;DR

This paper advances the understanding of Landau gauge Yang-Mills theory by simultaneously solving Dyson-Schwinger equations for propagators and vertices, introducing a new model for the three-gluon vertex, and comparing results with lattice data.

Contribution

It presents a novel simultaneous solution of Dyson-Schwinger equations for propagators and the ghost-gluon vertex, along with a new lattice-motivated three-gluon vertex model.

Findings

Reproduces lattice data accurately

Confirms zero crossing of the three-gluon vertex

Identifies differences between decoupling and scaling solutions

Abstract

We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.