Scrutinizing $R$-parity violating interactions in light of $R_{K^{(\ast)}}$ data

The LHCb has measured the ratios of $B\to K^\ast\mu^+\mu^-$ to $B\to K^\ast e^+ e^-$ 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 $B\to K^\ast\ell^+\ell^-$ and $B\to K\ell^+\ell^-$ is feasible for a parameter space of the Yukawa couplings that is consistent with the bounds coming from $B\to K^{(\ast)}\nu\bar{\nu}$ and $D^0\to \mu^+\mu^-$ decays and $B_s-\bar{B}_s$ mixing.