  Recently, several hints of lepton non-universality have been observed in the
semileptonic B meson decays in terms of both in the neutral current ($b\to s l
\bar{l}$) and charged current ($b\to c l \bar{\nu_{l}}$) transitions. Motivated
by these inspiring results, we perform the analysis of the baryon decays
${\Sigma_b}\to \Sigma_c l \bar{\nu_{l}}$ and $\Omega_b\to \Omega_c l
\bar{\nu_{l}} (l=e,\mu,\tau)$ which are mediated by $ b \to c l \bar{\nu_{l}}$
transitions at the quark level, to scrutinize the nature of new physics (NP) in
the model independent method. We first use the experimental measurements of
$\mathcal{B}( B\to D^{(*)} l\bar{\nu_{l}})$, ${\rm R}_{D^{(*)}}$ and ${\rm
R}_{J/\psi}$ to constrain the NP coupling parameters in a variety of scenarios.
Using the constrained NP coupling parameters, we report numerical results on
various observables related to the processes ${\Sigma_b}\to \Sigma_c l
\bar{\nu_{l}}$ and $\Omega_b\to \Omega_c l \bar{\nu_{l}}$, such as the
branching ratios, the ratio of branching fractions, the lepton side
forward-backward asymmetries, the hadron and lepton longitudinal polarization
asymmetries and the convexity parameter. We also provide the $q^2$ dependency
of these observables and we hope that the corresponding numerical results in
this work will be testified by future experiments.
