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

Abstract

We investigate the possibility of explaining the enhancement in semileptonic decays of $\bar B \to D^{(*)} τ\bar ν$, the anomalies induced by $b\to sμ^+μ^-$ in $\bar B\to (K, K^*, ϕ)μ^+μ^-$ and violation of lepton universality in $R_K = Br(\bar B\to K μ^+μ^-)/Br(\bar B\to K e^+e^-)$ 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 $\bar B \to D^{(*)} τ\bar ν$ by tree level interactions and $b\to s μ^+μ^-$ 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 $R(D^{(*)})$ anomaly, we show that with the severe constraint from $\bar B \to K ν\bar ν$, it is impossible to solve the anomalies in $b\to s μ^+μ^-$ process simultaneously.