Infrared behavior of QCD from the Dyson-Schwinger formalism

TL;DR

This paper examines the infrared properties of Landau gauge Yang-Mills theory using Dyson-Schwinger equations, highlighting the significance of the scaling solution and its implications for confinement, chiral symmetry breaking, and the $U_A$(1) problem.

Contribution

It identifies the scaling solution as the relevant infrared behavior and clarifies the status of previous DSE results, linking confinement and chiral symmetry breaking.

Findings

Confirmation of the scaling solution as the infrared behavior

Relation between confinement and chiral symmetry breaking

Infrared singularity in the quark-gluon vertex enabling $U_A$(1) solution

Abstract

We discuss the properties of two different types of infrared solutions of Landau gauge Yang-Mills theory and argue for one of these (the 'scaling solution'). We furthermore clarify the status of previously obtained results from DSEs on a four-torus. Including quarks we discuss a relation between confinement and dynamical chiral symmetry breaking based on the scaling solution of Yang-Mills theory. An infrared singularity in the quark-gluon vertex allows for a solution of the $U_A$(1) problem along the lines of a mechanism suggested by Kogut and Susskind long ago.