Probe the effects of split SUSY in rare B decays

We study the decays of $B\to K^{(\ast )}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ in split supersymmetry with R-parity violation. We find that the decay branching ratio of $B\to K{\tau }^{+}{\tau }^{-}$ in the new physics model due to the scalar interactions can be $1.8\times {10}^{-6}$ which is about one order of magnitude larger that in the standard model, whereas those of $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ ($\mathrm{\ell }=e$ and $\mu$) and the $K^{\ast }$ modes are insensitive to the new physics. On the other hand, the forward-backward asymmetries of $B\to K{\tau }^{+}{\tau }^{-}$ and $K{\mu }^{+}{\mu }^{-}$, vanishing in the standard model, can be over 10 and 1%, respectively. In addition, we show that the new interactions will significantly change the forward-backward asymmetry in $B\to K^{\ast }{\tau }^{+}{\tau }^{-}$.