Probing the R-parity violating supersymmetric effects in $B_c\to J/ψ\ell^-\barν_{\ell},η_c\ell^-\barν_{\ell}$ and $Λ_b\toΛ_c\ell^-\barν_{\ell}$ decays
Motivated by recent $R_D$, $R_{D^*}$ and $R_{J/ψ}$ anomalies in $B\to D\ell^- \barν_{\ell}$, $B\to D^*\ell^- \barν_{\ell}$ and $B_c\to J/ψ\ell^- \barν_{\ell}$ decays, respectively, we study possible R-parity violating supersymmetric effects in $B_c\to J/ψ\ell^- \barν_{\ell},η_c\ell^- \barν_{\ell}$ and $Λ_b \to Λ_c \ell^- \barν_{\ell}$ decays, which are also induced by $b\to c \ell^- \barν_{\ell}$ at quark level. We find that (I) the constrained slepton exchange couplings $λ_{i33}\tildeλ'^*_{i23}$ involving in $b\to c τ^- \barν_τ$ transition from relevant latest experimental data still have quite large effects on all (differential) branching ratios and the normalized forward-backward asymmetries of the exclusive semileptonic $b\to c τ^- \barν_τ$ decays as well as the ratios of the (differential) branching ratios; (II) after satisfying the data of $R_D$ and $R_{D^*}$, the upper limit of $R_{J/ψ}$, $R_{η_c}$ and $R_{Λ_c}$ could be increased by 10%, 112% and 24%, respectively, from their upper limits of the Standard Model predictions by the $λ_{i33}\tildeλ'^*_{i23}$ couplings. The results in this work could be used to probe R-parity violating effects and will correlate with searches for direct supersymmetric signals at the running LHCb and the forthcoming Belle-II.