ar X iv : h ep - p h / 97 10 29 8 v 1 9 O ct 1 99 7 Decay constants in the heavy quark limit in models

In quark modelsà la Bakamjian and Thomas, that yield covariance and Isgur-Wise scaling of form factors in the heavy quark limit, we compute the decay constants f (n) and f (n) 1/2 of S-wave and P-wave mesons composed of heavy and light quarks. Heavy quark limit scaling √ M f = Cst. is obtained, and it is shown that this class of models satisfies the sum rules involving decay constants and Isgur-Wise functions recently formulated by us in the heavy quark limit of QCD. Moreover, the model also satisfies the selection rules of the type f (n) 3/2 = 0 that must hold in this limit. We discuss different Ansätze for the dynamics of the mass operator at rest. For non-relativistic kinetic energies p 2 2m the decay constants are finite even if the potential V (r) has a Coulomb part. For the relativistic form p 2 + m 2 , the S-wave decay constants diverge if there is a Coulomb singularity. Using phenomenological models of the spectrum with relativistic kinetic energy and regularized short distance part (Godfrey-Isgur model or Richardson potential of Colangelo et al.), that yield ρ 2 ∼ = 1 for the elastic Isgur-Wise function, we compute the decay constants in the heavy quark limit, and obtain f B ∼ = 300 MeV, of the same order although slightly smaller than in the static limit of lattice QCD. We find the decay constants of D * * with j = 1 2 of the same order of magnitude. The convergence of the heavy quark limit sum rules is also studied.