Quasi Goldstone fermion as a sterile neutrino

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Abstract
The existence of sterile neutrino is hinted by simultaneous explanation of diverse neutrino anomalies. We suggest that the quasi Goldstone fermions (QGF) arising in supersymmetric theory as a result of spontaneous breaking of global symmetry like the Peccei-Quinn symmetry or the lepton number symmetry can play a role of the sterile neutrino. The smallness of mass of QGF ($m_S \sim 10^{-3}-10$ eV) can be related to the specific choice of superpotential or K\"ahler potential (e.g., no-scale kinetic terms for certain superfields). Mixing of QGF with neutrinos implies the $R$-parity violation. It can proceed via the coupling of QGF with the Higgs supermultiplets or directly with the lepton doublet. A model which accounts for the solar and atmospheric anomalies and the dark matter is presented.Comment: 16 pages plus 3 figures include
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