A connection between inclusive semileptonic decays of bound and free heavy quarks
Abstract
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 -> Xc l nul and B -> Xu l nul decays are used to extract the CKM parameters |Vcb| and |Vub| from available inclusive data. After averaging over the various quark models adopted and including leading-order perturbative QCD corrections, we obtain |Vcb| = (43.0 +/- 0.7exp +/- 1.8th) 10-3 and |Vub| = (3.83 +/- 0.48exp +/- 0.14th) 10-3, implying |Vub / Vcb| = 0.089 +/- 0.011exp +/- 0.005th, in nice agreement with existing predictions.
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