The bound state corrections to the leptonic decays of the $B$-meson. The light-front approach versus ACM model

A generalization of the parton-like formula is used for the first time to find the differential distributions in the inclusive semileptonic weak decays of the $B$-meson. The main features of this 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. Using the $b$-quark light-front (LF) distribution function related to the equal time momentum wave function taken from the ACM model we compute the electron energy spectra and the total semileptonic widths of the $B$-meson. We find an impressive agreement between the electron energy spectra calculated in the LF approach and the ones obtained in the ACM model, provided the $b$-quark mass is identified with the average of the floating $b$-quark mass in the ACM model. In spite of the simplicity of the model we obtain a fair good description of the CLEO data for $|V_{cb}|=0.042$.