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We investigate the possibility of explaining the enhancement in semileptonicdecays of $\bar B \to D^{(*)} \tau \bar \nu$, the anomalies induced by $b\tos\mu^+\mu^-$ in $\bar B\to (K, K^*, \phi)\mu^+\mu^-$ and violation of leptonuniversality in $R_K = Br(\bar B\to K \mu^+\mu^-)/Br(\bar B\to K e^+e^-)$within the framework of R-parity violating (RPV) MSSM. Exchange of down typeright-handed squark coupled to quarks and leptons yield interactions which aresimilar to leptoquark induced interactions that have been proposed to explainthe $\bar B \to D^{(*)} \tau \bar \nu$ by tree level interactions and $b\to s\mu^+\mu^-$ anomalies by loop induced interactions, simultaneously. However,the Yukawa couplings in such theories have severe constraints from other rareprocesses in $B$ and $D$ decays. Although this interaction can provide a viablesolution to $R(D^{(*)})$ anomaly, we show that with the severe constraint from$\bar B \to K \nu \bar \nu$, it is impossible to solve the anomalies in $b\to s\mu^+\mu^-$ process simultaneously.

Consequences of R-Parity violating interactions for anomalies in $\bar B\to D^{(*)} \tau \bar \nu$ and $b\to s \mu^+\mu^-$