Epsilon expansion for infrared Yang-Mills theory in Landau gauge

TL;DR

This paper uses an epsilon expansion approach to analyze infrared solutions of Landau gauge Yang-Mills theory, reproducing known behaviors and identifying the physically relevant decoupling solution as an infrared-stable fixed point.

Contribution

It introduces an epsilon expansion method to study infrared solutions of Yang-Mills theory, connecting Dyson-Schwinger solutions with renormalization group analysis.

Findings

Both scaling and decoupling solutions are reproduced by the epsilon expansion.

The decoupling solution is identified as an infrared-stable fixed point.

Results align with recent lattice calculations.

Abstract

The study of the Dyson-Schwinger equations of Landau gauge Yang-Mills theory has revealed two types of solutions for the gluon and ghost propagators, with a scaling and a massive (decoupling) behavior in the extreme infrared, respectively. We show that both types of solutions are quantitatively reproduced by applying renormalization group equations of Callan-Symanzik type in an epsilon expansion to the infrared limit of Landau gauge Yang-Mills theory when a mass term for the gluons is added to the action. Only the decoupling solution corresponds to an infrared-stable fixed point in three and four space-time dimensions and is hence expected to be physically realized, in agreement with the results of recent lattice calculations.