Probing the R-parity violating supersymmetric effects in $B_c\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell },{\eta }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ and ${\Lambda }_b\to {\Lambda }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ decays

Abstract

Motivated by recent $R_D$, $R_{D^{\ast }}$ and $R_{J/\psi }$ anomalies in $B\to D{\ell }^{-}{\bar{\nu }}_{\ell }$, $B\to D^{\ast }{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell }$ decays, respectively, we study possible R-parity violating supersymmetric effects in $B_c\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell },{\eta }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ and ${\Lambda }_b\to {\Lambda }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ decays, which are also induced by $b\to c{\ell }^{-}{\bar{\nu }}_{\ell }$ at quark level. We find that (I) the constrained slepton exchange couplings ${\lambda }_{i33}{\tilde{\lambda }}_{i23}^{\prime \ast }$ involving in $b\to c{\tau }^{-}{\bar{\nu }}_{\tau }$ 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 $b\to c{\tau }^{-}{\bar{\nu }}_{\tau }$ decays as well as the ratios of the (differential) branching ratios; (II) after satisfying the data of $R_D$ and $R_{D^{\ast }}$, the upper limit of $R_{J/\psi }$, $R_{{\eta }_c}$ and $R_{{\Lambda }_c}$ could be increased by 10%, 112% and 24%, respectively, from their upper limits of the Standard Model predictions by the ${\lambda }_{i33}{\tilde{\lambda }}_{i23}^{\prime \ast }$ 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.

21 pages, 5 figures

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