The effect of an infrared divergent quark-antiquark interaction kernel on other Green functions

TL;DR

This paper investigates how an infrared divergent quark-antiquark interaction kernel affects Green functions in Landau gauge QCD, revealing implications for confinement and the structure of higher n-point functions.

Contribution

It demonstrates that linear confinement can be modeled with an infrared divergent kernel within a Dyson-Schwinger framework, affecting the structure of Green functions and circumventing the decoupling theorem.

Findings

Infrared divergence leads to Casimir scaling in four-point functions.

Higher n-point functions inherit the infrared singularity in certain color channels.

Linear confinement is compatible with Green's function methods despite infrared singularities.

Abstract

The n-point Green functions of Landau gauge QCD are systematically investigated in a Dyson-Schwinger approach assuming a static linearly rising potential between fundamental color charges. Besides quarks also scalar matter in the fundamental representation is considered. Starting from the hypothesis of an 1/k^4 infrared divergent matter-antimatter vertex restrictions on the general color tensor structure of this divergence are derived. Consequences for the other four-point functions of QCD, resp., scalar QCD, are presented. Hereby Casimir scaling is found. It is shown that possible singular contributions to the three-point functions vanish due to cancellations within the color algebra. On the other hand, higher n-point functions inherit the infrared singularity of the matter-antimatter vertex in certain color channels. The presented results show that linear confinement is consistently possible in a Greens function approach, however, at the expense that the decoupling theorem is circumvented by infrared singularities.