On the Landau gauge matter-gluon vertex in scalar QCD in a functional approach

TL;DR

This paper investigates the Landau gauge matter-gluon vertex in scalar QCD using a functional approach, revealing a dynamic suppression of the Abelian diagram that is largely independent of the scalar's color representation.

Contribution

It introduces a numerical analysis of the matter-gluon vertex in scalar QCD, extending previous quark-based studies to scalars in different color representations, and demonstrates the dynamic suppression of the Abelian diagram.

Findings

Suppression of the Abelian diagram is observed in scalar QCD.

The suppression occurs dynamically and is largely independent of the scalar's color representation.

Numerical techniques are developed that can be applied to fermionic cases.

Abstract

Recently the quark-gluon vertex has been investigated in Landau gauge using a combined Dyson-Schwinger and nPI effective action approach. We present here a numerical analysis of a simpler system where the quarks have been replaced by charged scalar fields. We solve the coupled system of Dyson-Schwinger equations for the scalar propagator, the scalar-gluon vertex and the Yang-Mills propagators in a truncation related to earlier studies. The calculations have been performed for scalars both in the fundamental and the adjoint representation. A clear suppression of the Abelian diagram is found in both cases. Thus, within the used truncation the suppression of the Abelian diagram predominantly happens dynamically and is to a high degree independent of the colour structure. The numerical techniques developed here can directly be applied to the fermionic case.