Neutrino Mass from R-parity Violation in Split Supersymmetry

Abstract

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 $ξ_i$ 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 $10^9$ GeV. This scheme requires an unpleasant hierarchical structure of the couplings, e.g., $λ_{i23,i32}\sim 1$, $λ'_{i33} \lesssim 10^{-4}$ and $ξ_i \lesssim 10^{-6}$. On the other hand, the model has a distinct collider signature of the lightest neutralino which can decay only to the final states, $l_i W^{(*)}$ and $νZ^{(*)}$, arising from the bilinear mixing. Thus, the measurement of the ratio; $Γ(e W^{(*)}) : Γ(μW^{(*)}) : Γ(τW^{(*)})$ 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.