The non-perturbative BRST quartet mechanism in Landau gauge QCD: Ghost-gluon and ghost-quark bound states

TL;DR

This paper investigates the non-perturbative BRST quartet mechanism in Landau gauge QCD, demonstrating positivity violation for gluons and deriving Bethe-Salpeter equations for gluon-ghost and quark-ghost bound states, with numerical solutions in two dimensions.

Contribution

It introduces a non-perturbative BRST quartet framework in Landau gauge QCD and derives truncated Bethe-Salpeter equations for gluon-ghost and quark-ghost bound states.

Findings

Positivity violation identified for transverse gluons.

Derived truncated Bethe-Salpeter equations for bound states.

Numerical solution obtained for the gluon-ghost bound state in 2D.

Abstract

The non-perturbative BRST quartet mechanism in infrared Landau gauge QCD is presented. It is demonstrated that positivity violation for transverse gluons allows to identify the gluon's non-perturbative BRST quartet. To describe the respective BRST-daughter state a truncated Bethe-Salpeter equation for the gluon-ghost bound state is investigated. An analogous construction for quarks yields a truncated Bethe-Salpeter equation for the quark-ghost bound state. The gluon-ghost bound state equation in two space-time dimensions has been numerically solved.