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Experimental data on $ R(D^{(*)}) $, $ R(K^{(*)}) $ and $ R(J/\psi) $,provided by different collaborations, show sizable deviations from the SMpredictions. To describe these anomalies many new physics scenarios have beenproposed. One of them is leptoquark model with introducing the vector andscalar leptoquarks coupling simultaneously to the quarks and leptons. To lookfor similar possible anomalies in baryonic sector, we investigate the effectsof a vector leptoquark $U_3 (3,3, \frac{2}{3})$ on various physical quantitiesrelated to the tree-level $ \Lambda_b \rightarrow \Lambda_c \ell ~\overline{\nu}_\ell$ decays ($ \ell=\mu, ~\tau $), which proceed via $ b\rightarrow c~\ell ~ \overline{\nu}_\ell$ transitions at quark level. Wecalculate the differential branching ratio, forward-backward asymmetry andlongitudinal polarizations of lepton and $\Lambda_{c}$ baryon at $ \mu $ and $\tau $ lepton channels in leptoquark model and compare their behavior withrespect to $ q^2 $ with the predictions of the standard model (SM). In thecalculations we use the form factors calculated in full QCD as the main inputsand take into account all the errors coming from the form factors and modelparameters. It is observed that

Effects of vector leptoquarks on $ \Lambda_b \rightarrow \Lambda_c~\ell ~ \overline{\nu}_\ell$ decay