First look at heavy-light mesons with a dressed quark-gluon vertex

TL;DR

This paper explores the effects of a dressed quark-gluon vertex on heavy-light mesons, extending the Dyson-Schwinger-Bethe-Salpeter framework to unequal quark masses and analyzing corrections to the rainbow-ladder approximation.

Contribution

It introduces a simplified interaction kernel to study corrections beyond rainbow-ladder in heavy-light mesons with unequal quark masses.

Findings

Quantified corrections to rainbow-ladder truncation.

Extended analysis to heavy-light pseudoscalar mesons.

Opened phenomenological predictions for heavy quark symmetry.

Abstract

Following up on earlier work, we investigate possible effects of a dressed quark-gluon vertex in heavy-light mesons. In particular, we study corrections to the popular rainbow-ladder truncation of the Dyson-Schwinger-Bethe-Salpeter equation system. We adopt a simple interaction kernel which reduces the resulting set of coupled integral equations to a set of coupled algebraic equations, which are solved numerically. In this way, we extend previous studies to quark-antiquark systems with unequal current-quark masses, at first for the pseudoscalar case, and investigate the resulting set of problems and solutions. We attempt to find patterns in - as well as to quantify corrections to - the rainbow-ladder truncation. In addition, we open this approach to phenomenological predictions of the heavy quark symmetry.