What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement

TL;DR

This paper investigates the infrared behavior of QCD vertex functions in Landau gauge, revealing insights into gluon confinement and the origin of a linear potential between heavy quarks through Dyson-Schwinger equations.

Contribution

It provides a detailed analysis of QCD vertex functions in the infrared, demonstrating gluon confinement and linking chiral symmetry breaking to the linear quark potential.

Findings

Gluon confinement evidenced by positivity violation of the gluon propagator.

Infrared singularities in the quark-gluon vertex generate a linear potential.

Chiral symmetry breaking is necessary for scalar amplitudes in the vertex.

Abstract

The infrared behaviour of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.