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 nonperturbative meson structure is described through various quark-model wave functions, constructed via the Hamiltonian light front formalism, using as input both relativistic and nonrelativistic potential models. A link between spectroscopic quark models and B-meson decay physics is obtained in this way. Our predictions for the $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{c}l{\ensuremath{\nu}}_{l}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}l{\ensuremath{\nu}}_{l}$ decays are used to extract the CKM parameters $|{V}_{\mathrm{cb}}|$ and $|{V}_{\mathrm{ub}}|$ from available inclusive data. After averaging over the various quark models adopted and including leading-order perturbative QCD corrections, we obtain $|{V}_{\mathrm{cb}}|=(43.0\ifmmode\pm\else\textpm\fi{}{0.7}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{1.8}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $|{V}_{\mathrm{ub}}|=(3.83\ifmmode\pm\else\textpm\fi{}{0.48}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.14}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3},$ implying $|{V}_{\mathrm{ub}}{/V}_{\mathrm{cb}}|=0.089\ifmmode\pm\else\textpm\fi{}{0.011}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.005}_{\mathrm{th}},$ in nice agreement with existing predictions.