g-coupling (g_B*Bpi,g_D*Dpi); A quark model with Dirac equation

TL;DR

This paper introduces a Dirac equation-based quark model to analyze the strong coupling g of heavy mesons to pions, resulting in a stable, large value of g that differs from QCD sum rule estimates, and explores related phenomenological implications.

Contribution

The paper presents a refined Dirac equation-based quark model that predicts a large, stable value of the coupling g, contrasting with previous models and QCD sum rule results.

Findings

The model predicts g ≈ 0.6, a large and stable coupling value.

The model's predictions are consistent with heavy baryon phenomenology.

The Adler-Weisberger sum rule is well saturated by a few levels in this model.

Abstract

We discuss the strong coupling of heavy mesons to a pion g, in the heavy quark limit. This quantity is quite remarkable since its values as estimated by different methods (various quark models and the QCD sum rules), are surprisingly different. The present quark models are mostly based on free spinors and their predictions depend crucially on the choice of the light quark mass. We propose a quark model based on the Dirac equation in a central potential, which gives a more refined description of Dirac spinors. We show that within such a Dirac model, the value of g is stable and large: g = 0.6(1), where we assume no quark current renormalization ((g_A)q = 1). Such a large result is strongly constrained by requiring that the model parameters fit the spectrum; we show that this implies a large ``effective'' light mass. It is also supported phenomenologically by a similar situation with heavy baryons, as well as by experience with nucleon (if one invokes additivity). We also calculate the couplings to heavy meson excitations, and show that the Adler-Weisberger sum rule is well saturated by a few levels (in contrast to the case of small g). We discuss uncertainties of our approach, and rise several questions which remain to be answered. The main mystery is the large, unusual discrepancy with QCD sum rules for g, whereas a good agreement is found for orbital excitations.