Confinement and Green functions in Landau-gauge QCD

TL;DR

This paper investigates the infrared behavior of Landau gauge Green functions in QCD, demonstrating gluon confinement, analyzing the gluon propagator's structure, and deriving a linearly rising quark potential consistent with confinement.

Contribution

It provides a detailed functional analysis of Landau gauge Green functions, revealing confinement mechanisms and deriving a consistent infrared finite coupling and linearly rising potential.

Findings

Gluons violate positivity, indicating confinement.

Infrared finite coupling in Yang-Mills sector.

Linearly rising quark potential with mass-independent string tension.

Abstract

In a functional approach to QCD the infrared behaviour of Landau gauge Green functions is investigated. Positivity violation for, and thus confinement of, gluons is demonstrated, and the analytic structure of the gluon propagator is studied. Quark confinement is related to an infrared divergence of the quark-gluon vertex. In the latter various components are dynamically induced due to the spontaneous breaking of chiral symmetry. As a result an infrared finite running coupling in the Yang-Mills sector is derived whereas the running coupling related to the quark-gluon vertex is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation, which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equations are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry.