coupling (gB*Bπ,gD*Dπ); A quark model with Dirac equation

We discuss the strong coupling of heavy mesons to a pion g, in the heavyquark limit. This quantity is quite remarkable since its values as estimated bydifferent methods (various quark models and the QCD sum rules), aresurprisingly different. The present quark models are mostly based on freespinors and their predictions depend crucially on the choice of the light quarkmass. We propose a quark model based on the Dirac equation in a centralpotential, which gives a more refined description of Dirac spinors. We showthat 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 largeresult is strongly constrained by requiring that the model parameters fit thespectrum; we show that this implies a large ``effective'' light mass. It isalso supported phenomenologically by a similar situation with heavy baryons, aswell as by experience with nucleon (if one invokes additivity). We alsocalculate the couplings to heavy meson excitations, and show that theAdler-Weisberger sum rule is well saturated by a few levels (in contrast to thecase of small g). We discuss uncertainties of our approach, and rise severalquestions which remain to be answered. The main mystery is the large, unusualdiscrepancy with QCD sum rules for g, whereas a good agreement is found fororbital excitations.Comment: 20 pages, LaTeX file, uses JHEP.cls, (2 references added