Dilepton decays and oscillation of $B_{s}$ in split supersymmetry with R-parity violation

Abstract

We study $B$ physics phenomenology in the scenario of split supersymmetry without R-parity. By assuming the constraints of bilinear (trilinear) R-parity violating couplings, which are introduced to solve the problem of the atmospheric (solar) neutrino mass, we show that the decay branching ratios of $B_{s}\to \ell^{+} \ell^{-}$ and the mixing of $B_s-\bar{B}_s$ can be large. Explicitly, we find that $B(B_s\to\mu^+\mu^-)=O(10^{-7})$ and $\Delta m_{B_s}=O(10^{-9}) GeV$, which should be observed at future hadron colliders.