Semileptonic decays of $B^{(*)}$, $D^{(*)}$ into ${\nu} l$ and pseudoscalar or vector mesons

We perform a study of the $B^{(*)}$, $D^{(*)}$ semileptonic decays, using a different method than in conventional approaches, where the matrix elements of the weak operators are evaluated and a detailed spin-angular momentum algebra is performed to obtain very simple expressions at the end for the different decay modes. Using only one experimental decay rate in the $B$ or $D$ sectors, the rates for the rest of decay modes are predicted and they are in good agreement with experiment. Some discrepancies are observed in the $\tau$ decay mode for which we find an explanation. We perform evaluations for $B^*$ and $D^*$ decay rates that can be used in future measurements, now possible in the LHCb collaboration.