  Deviations from the standard model prediction have been observed in several
leptonic and semileptonic $B$ meson decays to $\tau\nu$ final states mediated
via $b \to u$ and $b \to c$ charged current interactions. The measured value of
ratio of branching ratios $R_{\pi}^l$ of $B^- \to \tau^-\,\nu_{\tau}$ to $B^0
\to \pi^+\,\l^-\,\nu$ decays, where $l = (e,\,\mu)$, is larger than the
standard model prediction by more than a factor of two. Similarly, a combined
excess of $3.9\sigma$ from the standard model expectation has been reported by
HFAG for the values of $R_D$ and $R_{D^{\ast}}$, where $R_{D,\,D^{\ast}}$
represents the ratio of branching ratios of $B \to (D,\,D^{\ast})\,\tau\nu$ to
corresponding $B \to (D,\,D^{\ast})\,l\nu$ decays, respectively. Very recently,
hint of lepton flavor violation has been observed in the ratio of branching
fractions of $B \to K\,e^+\,e^-$ to $B \to K\,\mu^+\,\mu^-$ decays as well. In
this context, we employ an effective Lagrangian approach to study the decay
branching fractions and the ratio of branching fractions of $\Lambda_b \to
\Lambda_c\,l\,\nu$ and $\Lambda_b \to p\,l\,\nu$ decays within the standard
model and beyond. We constrain the new physics parameter space using the
existing experimental data on $R_D$, $R_{D^{\ast}}$, and $R_{\pi}^l$. We give
predictions for various observables in the context of various new physics
scenarios.
