New constraints on R-parity violation from K and B systems

We have derived new upper limits on several products (two at a time) of lepton number violating ${\lambda }^{\mathrm{\prime }}$-type couplings from the consideration of $\mathrm{\Delta }S=2$ and $\mathrm{\Delta }B=2$ box graphs. Each box contains one scalar lepton and one W-boson or one charged-Higgs-boson as internal lines. Most of these bounds are more stringent than previously obtained. Some of these product couplings drive $K_L$ (and some other $B_d$) decays to two charged leptons at enhanced rates. Some of them can explain the rare $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ event recently observed at BNL.