Probing the gluon self-interaction in light mesons

TL;DR

This paper explores how gluon self-interactions affect light meson properties by solving advanced Dyson--Schwinger and Bethe--Salpeter equations, revealing nonperturbative effects on meson masses.

Contribution

It introduces a comprehensive approach that includes gluon self-interactions and complex momentum dependencies, surpassing the rainbow-ladder approximation.

Findings

Indications of nonperturbative cancellation of gluon self-interaction effects in rho-meson mass.

Enhanced understanding of gluon self-interaction influence on light meson properties.

Methodology that fully incorporates momentum dependencies in meson calculations.

Abstract

We investigate masses and decay constants of light mesons from a coupled system of Dyson--Schwinger and Bethe--Salpeter equations. We explicitly take into account dominant non-Abelian contributions to the dressed quark-gluon vertex stemming from the gluon self-interaction. We construct the corresponding Bethe-Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the influence of the gluon self-interaction on the properties of mesons. As a first result we find indications of a nonperturbative cancellation of the gluon self-interaction contributions and pion cloud effects in the mass of the rho-meson.