An Infrared Safe perturbative approach to Yang-Mills correlators

TL;DR

This paper introduces a massive extension of the Faddeev-Popov action to study Yang-Mills correlators, demonstrating finite running coupling and good agreement with lattice data in 3 and 4 dimensions, with implications for infrared safety.

Contribution

It proposes a phenomenological massive extension approach that ensures infrared safety and matches lattice results, providing a new perturbative framework for Yang-Mills correlators.

Findings

The running coupling remains finite at all scales for d>2.

Perturbation theory is reliable at all energies due to small coupling.

Excellent agreement with lattice simulations in 3 and 4 dimensions.

Abstract

We investigate the 2-point correlation functions of Yang-Mills theory in the Landau gauge by means of a massive extension of the Faddeev-Popov action. This model is based on some phenomenological arguments and constraints on the ultraviolet behavior of the theory. We show that the running coupling constant remains finite at all energy scales (no Landau pole) for $d>2$ and argue that the relevant parameter of perturbation theory is significantly smaller than 1 at all energies. Perturbative results at low orders are therefore expected to be satisfactory and we indeed find a very good agreement between 1-loop correlation functions and the lattice simulations, in 3 and 4 dimensions. Dimension 2 is shown to play the role of an upper critical dimension, which explains why the lattice predictions are qualitatively different from those in higher dimensions.