Exclusive semileptonic decays of heavy mesons in quark model

Semileptonic decays $D\to K,K^*,\pi,\rho$, $D_s\to \eta,\eta',\phi$, and $B\to D,D^*,\pi,\rho$ are analyzed within the dispersion formulation of the quark model. The form factors at timelike $q$ are derived by the analytical continuation from spacelike $q$ in the form factors of the relativistic light--cone quark model. The resulting double spectral representations allow a direct calculation of the form factors in the timelike region. The results of the model are shown to be in good agreement with all available experimental data. From the analysis of the $B\to D,D^*$ decays we find $|V_{cb}|=0.037\pm 0.004$, and the $B\to\pi,\rho$ decays give $|V_{ub}|=0.004\pm 0.001$.