Flavor anomalies at the LHC and the R-parity violating supersymmetric model extended with vectorlike particles

In this paper, we consider a solution to explain the three discrepancies with the standard model (SM) predictions in flavor observables, i.e. anomalies in $B\rightarrow K^\ast\mu^+\mu^-$ and $R_K=\mathcal{B}(B\rightarrow K\mu^+\mu^-)/\mathcal{B}(B\rightarrow K e^+e^-)$ at the LHCb and an excess in $h\rightarrow \mu\tau$ at the CMS in the context of R-parity violating (RPV) supersymmetry. We demonstrate that these anomalies can be explained within a unified framework: the minimal supersymmetry model (MSSM) extended with $5+\overline{5}$ vectorlike (VL) particles. The new trilinear RPV couplings involving VL particles in our model can solve the $b\rightarrow s$ anomalies , and the mixing between the SM-like Higgs boson and the VL sneutrino can yield the extra $h \rightarrow \mu \tau$ decay mode.