Landau gauge Yang-Mills correlation functions

TL;DR

This paper uses a functional renormalisation group approach to compute non-perturbative Landau gauge Yang-Mills correlation functions, including the gluon mass gap and vertices, showing agreement with lattice results.

Contribution

It introduces a systematic vertex expansion scheme for the effective action in Landau gauge Yang-Mills theory, providing self-consistent calculations of propagators and vertices.

Findings

Gluon mass gap is dynamically generated.

Calculated propagators and vertices agree with lattice data.

Convergence of the expansion scheme is demonstrated.

Abstract

We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.