Probe the effects of split SUSY in rare B decays

We study the decays of $B\to K^{(*)} \ell^{+} \ell^{-}$ 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 $B\to K\ell^+\ell^-$ ($\ell=e$ and $\mu$) and the $K^*$ 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 $B\to K^* \tau^{+} \tau^{-}$.