  We use a recent formalism of the weak hadronic reactions that maps the
transition matrix elements at the quark level into hadronic matrix elements,
evaluated with an elaborate angular momentum algebra that allows finally to
write the weak matrix elements in terms of easy analytical formulas. In
particular they appear explicitly for the different spin third components of
the vector mesons involved. We extend the formalism to a general case, with the
operator $\gamma^\mu -\alpha\gamma^\mu \gamma_5$, that can accommodate
different models beyond the standard model and study in detail the $B \to D^{*}
\bar{\nu} l$ reaction for the different helicities of the $D^*$. The results
are shown for each amplitude in terms of the $\alpha$ parameter that is
different for each model. We show that $\frac{d \Gamma}{d M_{\rm inv}^{(\nu
l)}}$ is very different for the different components $M=\pm 1, 0$ and in
particular the magnitude $\frac{d \Gamma}{d M_{\rm inv}^{(\nu l)}}|_{M=-1}
-\frac{d \Gamma}{d M_{\rm inv}^{(\nu l)}}|_{M=+1} $ is very sensitive to the
$\alpha$ parameter, which suggest to use this magnitude to test different
models beyond the standard model. We also compare our results with the standard
model and find very similar results, and practically identical at the end point
of $M_{\rm inv}^{(\nu l)}= m_B- m_{D^*}$.
