No planar degeneracy for the Landau gauge quark-gluon vertex

TL;DR

This paper computes the transverse part of the quark-gluon vertex in quenched QCD using Dyson-Schwinger equations, revealing weak angular dependence but emphasizing its importance for precise physical predictions.

Contribution

It introduces a basis system for the vertex's tensor structures, analyzes the angular dependence, and confirms the significance of tensor couplings in chiral symmetry breaking within Dyson-Schwinger frameworks.

Findings

Weak angular dependence of vertex form factors.

Dynamically generated tensor coupling is key to chiral symmetry breaking.

Quark propagator shows poles only on the real time-like axis.

Abstract

Based on a suitable basis system for the quark-gluon vertex' transverse tensor structures and on carefully chosen kinematical variables, the transverse part of the quark-gluon vertex in quenched QCD in the Landau gauge is obtained from a system of Dyson-Schwinger equations. We demonstrate by analysing this solution that the angular dependence of these transverse quark-gluon vertex form factors is seemingly weak. We nevertheless argue that this does not imply a planar degeneracy for this vertex because even this mild dependence cannot be neglected when aiming for reasonably precise results for derived quantities. Last but not least, for a self-consistently coupled systems of 3PI Dyson-Schwinger equations for the quark propagator and the quark-gluon vertex we confirm that the core ingredient to dynamical chiral symmetry breaking is the dynamically generated tensor coupling of glue to quarks which itself is only possible because of chiral symmetry breaking. Furthermore, we find (i) a relation in between the calculated chirality violating vertex form factors; (ii) that the quark propagator is identical within numerical errors when obtained either from a decoupling solution or the scaling solution for the Yang-Mills propagators and vertex functions; and (iii) that the resulting quark propagator is consistent with possessing poles only on the real time-like half-axis. Furthermore, we provide high-precision fits for the form factors based on sometimes astonishingly simple model functions.