\begin{document}$ b \to c \tau \bar\nu $\end{document} and \begin{document}$ b \to s \ell^+ \ell^- $\end{document} data. More recently, the Belle Collaboration has reported the first measurement of the \begin{document}$ D^* $\end{document} longitudinal polarization fraction in the \begin{document}$ B \to D^* \tau \bar\nu $\end{document} decay. Motivated by this intriguing result, along with the recent measurements of \begin{document}$ R_{J/\psi} $\end{document} and \begin{document}$ \tau $\end{document} polarization, we present the study of \begin{document}$ b \to c \tau \bar\nu $\end{document} decays in supersymmetry (SUSY) with \begin{document}$ R $\end{document}-parity violation (RPV). We consider \begin{document}$ B \to D^{(*)} \tau \bar\nu $\end{document}, \begin{document}$ B_c \to \eta_c \tau \bar\nu $\end{document}, \begin{document}$ B_c \to J/\psi \tau \bar\nu $\end{document} and \begin{document}$ \Lambda_b \to \Lambda_c \tau \bar\nu $\end{document} modes and focus on the branching ratios, LFU ratios, forward-backward asymmetries, polarizations of daughter hadrons, and the \begin{document}$ \tau $\end{document} lepton. The RPV SUSY was capable of explaining the \begin{document}$ R_{D^{(*)}} $\end{document} anomalies at the \begin{document}$ 2\sigma $\end{document} level, after taking into account various flavor constraints. In the allowed parameter space, the differential branching fractions and LFU ratios are largely enhanced by the SUSY effects, especially in the large dilepton invariant mass region. Moreover, a lower bound \begin{document}$ {\mathcal B}(B^+ \to K^+ \nu \bar\nu) > 7.37 \times $\end{document} 10−6 is obtained. These observables could provide testable signatures at the high-luminosity LHC and SuperKEKB, and correlate with direct searches for SUSY."> <inline-formula><tex-math id="M1">\begin{document}${ {b\rightarrow c\tau\bar{\nu}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/9e83524a-0afd-4df7-998b-5f7a74295605/CPC-2019-0121_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/9e83524a-0afd-4df7-998b-5f7a74295605/CPC-2019-0121_M1.png"/></alternatives></inline-formula> decay in supersymmetry with <i>R</i>-parity violation -
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