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

Abstract

We investigate the possibility of explaining the enhancement in semileptonic decays of $\bar{B}\to D^{(\ast )}\tau \bar{\nu }$, the anomalies induced by $b\to s{\mu }^{+}{\mu }^{-}$ in $\bar{B}\to (K,K^{\ast },\varphi ){\mu }^{+}{\mu }^{-}$ and violation of lepton universality 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 type right-handed squark coupled to quarks and leptons yield interactions which are similar to leptoquark induced interactions that have been proposed to explain the $\bar{B}\to D^{(\ast )}\tau \bar{\nu }$ 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 rare processes in $B$ and $D$ decays. Although this interaction can provide a viable solution to $R(D^{(\ast )})$ 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.

Comments: RevTex, 13 pages, three figures. In our earlier version, we had neglected a contribution to C^{NP}_9 and obtained erroneous conclusions which we have corrected them in this version