Infrared singularities in Landau gauge Yang-Mills theory

TL;DR

This paper explores the infrared behavior of Landau gauge Yang-Mills theory, revealing two distinct fixed points: a scaling solution with dominant ghost dynamics and a decoupling scenario with massive gluons, using a novel analysis framework.

Contribution

It introduces a new framework for infrared power counting that accounts for finite scales, identifying two qualitatively different infrared fixed points in the Dyson-Schwinger equations.

Findings

Identification of two infrared fixed points: scaling and decoupling.

Scaling solution features strong divergences in vertex functions.

Decoupling solution shows massive gluons with no vertex enhancement.

Abstract

We present a more detailed picture of the infrared regime of Landau gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau gauge gluon dressing function cannot be infrared divergent.