(g)over-cap-coupling (g(B*B pi), g(D*D pi)): a quark model with Dirac equation

We discuss the strong coupling of heavy mesons to a pion (g) over cap, in t he 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 l ight 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) over cap is stabl e and large: (g) over cap = 0.6(1), where we assume no quark current renorm alization ((g(A))(q) = 1). Such a large result is strongly constrained by r equiring that the model parameters fit the spectrum; we show that this impl ies a large "effective" light mass. It is also supported phenomenologically by a similar situation with heavy baryons, as well as by experience with n ucleon (if one invokes additivity). We also calculate the couplings to heav y meson excitations, and show that the Adler-Weisberger sum rule is well sa turated by a few levels (in contrast to the case of small (g) over cap). We discuss uncertainties of our approach, and rise several questions which re main to be answered. The main mystery is the large, unusual discrepancy wit h QCD sum rules for (g) over cap, whereas a good agreement is found for orb ital excitations.