Ghost-gluon and ghost-quark bound states and their role in BRST quartets

TL;DR

This paper develops a non-perturbative framework for understanding ghost-gluon and ghost-quark bound states in infrared Landau gauge QCD, revealing their role in BRST quartets and using truncated Bethe-Salpeter equations.

Contribution

It introduces a non-perturbative BRST quartet mechanism for gluons and quarks, employing truncated Bethe-Salpeter equations with dressed vertices to identify bound states.

Findings

Derived non-perturbative BRST quartets for gluons and quarks.

Formulated Bethe-Salpeter equations for ghost-gluon and ghost-quark bound states.

Highlighted the importance of dressing the quark-gluon vertex for consistent truncation.

Abstract

A non-perturbative version of the BRST quartet mechanism in infrared Landau gauge QCD is proposed for transverse gluons and quarks. Based on the positivity violation for transverse gluons the content of the respective non-perturbative BRST quartet is derived. To identify the gluon's BRST-daughter and second parent state, a truncated Bethe-Salpeter equation for the gluon-(anti-)ghost bound state is investigated. We comment shortly on several equivalent forms of this equation. Repeating the same construction for quarks leads to a truncated Bethe-Salpeter equation for a fundamentally charged quark-(anti-)ghost bound state. It turns out that a cardinal input to this equation is given by the fully dressed quark-gluon vertex, and that it is indispensable to dress the quark-gluon vertex in this equation in order to obtain a consistent truncation.