Neutrino mass from R-parity violation in split supersymmetry

We investigate how the observed neutrino data can be accommodated by R-parity violation in Split Supersymmetry. The atmospheric neutrino mass and mixing are explained by the bilinear parameters &xi_i, inducing the neutrino-neutralino mixing as in the usual low-energy supersymmetry. Among various one-loop corrections, only the quark-squark exchanging diagrams involving the order-one trilinear couplings λ′_i23,i32 can generate the solar neutrino mass and mixing if the scalar mass m_s is not larger than 10⁹ GeV. This scheme requires an unpleasant hierarchical structure of the couplings, e.g. λ_i23,i32 ∼ 1, λ′_i33 ≲ 10⁴ and ξ_i ≲ 10^-6. On the other hand, the model has a distinct collider signature of the lightest neutralino which can decay only to the final states, l₂,W(*) and v/Z(*), arising from the bilinear mixing. Thus, the measurement of the ratio; Γ(eW(*)) : Γ(μW(* )): Γ(τW(*)) would provide a clean probe of the small reactor and large atmospheric neutrino mixing angles as far as the neutralino mass is larger than 62 GeV.