A connection between inclusive semileptonic decays of bound and free heavy quarks

A relativistic constituent quark model, formulated on the light-front, is used to derive a new parton approximation for the inclusive semileptonic decay width of the B-meson. A simple connection between the decay rate of a free heavy-quark and the one of a heavy-quark bound in a meson or in a baryon is established. The main features of the new approach are the treatment of the b-quark as an on-mass-shell particle and the inclusion of the effects arising from the b-quark transverse motion in the B-meson. In a way conceptually similar to the deep-inelastic scattering case, the B-meson inclusive width is expressed as the integral of the free b-quark partial width multiplied by a bound-state factor related to the b-quark distribution function in the B-meson. The non-perturbative meson structure is described through various quark-model wave functions, constructed via the Hamiltonian light-front formalism using as input both relativized and non-relativistic potential models. A link between spectroscopic quark models and the B-meson decay physics is obtained in this way. Our predictions for the B -> X_c l nu_l and B -> X_u l nu_l decays are used to extract the CKM parameters |V_cb| and |V_ub| from available inclusive data. After averaging over the various quark models adopted and including leading-order perturbative QCD corrections, we obtain |V_cb| = (43.0 +/- 0.7_exp +/- 1.8_th) 10^-3 and |V_ub| = (3.83 +/- 0.48_exp +/- 0.14_th) 10^-3, implying |V_ub / V_cb| = 0.089 +/- 0.011_exp +/- 0.005_th, in nice agreement with existing predictions.