Natural constraints on the gluon-quark vertex

TL;DR

This paper investigates the gluon-quark vertex in QCD by testing a vast array of vertex models against physical criteria, revealing that only a tiny fraction are consistent with observed phenomena, thus constraining theoretical models.

Contribution

It introduces a comprehensive analysis of the gluon-quark vertex by testing 1,660,000 ansätze against physical constraints, significantly narrowing down realistic models.

Findings

Only 0.55% of vertex ansätze are compatible with physical criteria.

Tight bounds are established on the domain of realistic gluon-quark vertices.

The study aids in constraining models for QCD and hadronic physics.

Abstract

In principle, the strong-interaction sector of the Standard Model is characterised by a unique renormalisation-group-invariant (RGI) running interaction and a unique form for the dressed--gluon-quark vertex, $\Gamma_\mu$; but, whilst much has been learnt about the former, the latter is still obscure. In order to improve this situation, we use a RGI running-interaction that reconciles both top-down and bottom-up analyses of the gauge sector in quantum chromodynamics (QCD) to compute dressed-quark gap equation solutions with 1,660,000 distinct Ansaetze for $\Gamma_\mu$. Each one of the solutions is then tested for compatibility with three physical criteria and, remarkably, we find that merely 0.55% of the solutions survive the test. Plainly, therefore, even a small selection of observables places extremely tight bounds on the domain of realistic vertex Ansaetze. This analysis and its results should prove useful in constraining insightful contemporary studies of QCD and hadronic phenomena.