$\overrightarrow{B}{X}_s{l}_i^{+}{l}_j^{-}$ decays with $R$-parity violation

We consider $\overrightarrow{B}{X}_s{l}_i^{+}{l}_j^{-}$ decays in the minimal supersymmetric standard model with explicit $R$-parity violation. From the present upper limits on the branching ratios for these processes, we obtain the constraints on the product combinations of the $R$-parity-violating couplings which are in many cases more severe than the previous ones. Taking into account the invariant dilepton mass spectrum and the forward-backward asymmetry of the emitted leptons, we show that the spectra and asymmetries obtained from $R$-parity-violating interactions are different from the SM ones. Therefore, they may be used in the future to disentangle $R$-parity-violating effects from the SM in these processes. We also show that it is possible to discriminate two types of $R$-parity-violating effects from each other. The general expectation of the enhancement of the forward-backward asymmetry of the emitted leptons in the minimal supersymmetric standard model with $R$ parity may be corrupted by $R$-parity violation.