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 ${\xi }_i$ 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 ${\lambda }_{i23,i32}^{\prime }$ 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., ${\lambda }_{i23,i32}\sim 1$, ${\lambda }_{i33}^{\prime }\lesssim 10^{-4}$ and ${\xi }_i\lesssim 10^{-6}$. On the other hand, the model has a distinct collider signature of the lightest neutralino which can decay only to the final states, $l_i{W}^{(\ast )}$ and $\nu Z^{(\ast )}$, arising from the bilinear mixing. Thus, the measurement of the ratio; $\Gamma (e{W}^{(\ast )}):\Gamma (\mu W^{(\ast )}):\Gamma (\tau W^{(\ast )})$ 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.

10 pages, 3 figures, version submitted to JHEP

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