  We study the exclusive $b \to u \ell^- \bar{\nu}_{\ell} (\ell=\tau,\mu,e)$
decays in the MSSM with and without R-parity violation. From the experimental
measurements of branching ratios $\mathcal{B}(B^-_u \to \tau^-
\bar{\nu}_{\tau})$, $\mathcal{B}(B^-_u \to M'^0 \ell'^- \bar{\nu}_{\ell'})$ and
$\mathcal{B}(\bar{B}^0_d \to M'^+ \ell'^- \bar{\nu}_{\ell'})$ $(\ell'=\mu,e,
M'=\pi,\rho)$, we derive new upper bounds on the relevant new physics
parameters within the decays. Using the constrained new physics parameter
spaces, we predict the charged Higgs effects and the R-parity violating effects
on the branching ratios, the normalized forward-backward asymmetries of charged
leptons, and the ratios of longitudinal to transverse polarization of the
vector mesons, which have not been measured or have not been well measured yet.
We find that the charged Higgs effects and the R-parity violating effects could
be large and measurable in some cases. Our results could be used to probe new
physics effects in the leptonic decays as well as the semileptonic decays, and
will correlate with searches for direct supersymmetric signals in future
experiments.
