The LHCb has measured the ratios of $B\to K^{*}{\mu }^{+}{\mu }^{-}$ to $B\to K^{*}{e}^{+}{e}^{-}$ branching fractions in two dilepton invariant mass squared bins, which deviate from the standard model predictions by approximately $2.5\sigma$. These new measurements strengthen the hint of lepton flavor universality breaking which was observed earlier in $B\to K{\ell }^{+}{\ell }^{-}$ decays. In this work we explore the possibility of explaining these anomalies within the framework of $R$-parity violating interactions. In this framework, $b\to s{\ell }^{+}{\ell }^{-}$ transitions are generated through tree and one loop diagrams involving exchange of down-type right-handed squarks, up-type left-handed squarks and left-handed sneutrinos. We find that the tree level contributions are not enough to explain the anomalies, but at one loop, simultaneous explanation of the deviations in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ and $B\to K{\ell }^{+}{\ell }^{-}$ is feasible for a parameter space of the Yukawa couplings that is consistent with the bounds coming from $B\to K^{(*)}\nu \overline{\nu }$ and $D^0\to {\mu }^{+}{\mu }^{-}$ decays and $B_s-{\overline{B}}_s$ mixing.

• Received 9 August 2017

DOI:https://doi.org/10.1103/PhysRevD.96.095033