Strong Couplings of Charmed Mesons and Quarkonia

TL;DR

This paper calculates the strong coupling constants of charmed mesons and quarkonia using a relativistic dispersion approach, revealing discrepancies with QCD sum rule predictions and analyzing SU(3) flavor symmetry violations.

Contribution

It introduces a relativistic dispersion method to extract strong couplings of mesons with charm quarks, highlighting differences from QCD sum rule results and flavor symmetry effects.

Findings

Strong couplings are larger than QCD sum rule estimates.

Replacing light quarks with strange quarks reduces coupling magnitudes.

SU(3) flavor symmetry violation impacts coupling constants.

Abstract

We extract the strong coupling constants of three mesons, each of which is composed of either two charm quarks or one charm quark and one light (i.e., $u$, $d$, or $s$) quark, from the matrix elements for the transitions of two of these mesons induced by appropriate quark currents within the framework of a relativistic dispersion approach to the constituent-quark picture of mesons. Among others, we also analyse the impact of the violation of the SU(3) flavour symmetry by the quark masses. In the case of mesons containing one light quark, we observe, in two respects, discrepancies between our findings and the predictions of QCD sum rules: our strong couplings exceed considerably the ones emerging from QCD sum rules, and, in our approach, the replacement of a light quark by a strange quark entails, in contrast to QCD sum rules, a reduction of the magnitudes of the strong couplings.