On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

TL;DR

This paper investigates the infrared behavior of QCD Green functions in the Maximally Abelian gauge using Dyson-Schwinger equations, revealing Abelian infrared dominance and relating different solution types.

Contribution

It provides the first results on infrared properties in the Maximally Abelian gauge and demonstrates the relation between decoupling and scaling solutions.

Findings

Abelian part of the gauge field propagator is enhanced at low momenta.

Infrared dominant diagrams are sunset diagrams.

Relation between decoupling and scaling solutions is established.

Abstract

Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.