Quasi Goldstone fermion as a sterile neutrino.

The existence of sterile neutrinos is hinted by the simultaneous presence of diverse neutrino anomalies. We suggest that the quasi Goldstone fermions (QGF{close_quote}s) arising in supersymmetric theory as a result of spontaneous breaking of global symmetry such as the Peccei-Quinn symmetry or the lepton number symmetry can play the role of the sterile neutrino. The smallness of the mass of QGF{close_quote}s ({ital m}{sub {ital S}}{approximately}10{sup {minus}3}{endash}10 eV) can be related to the specific choice of superpotential or K{umlt a}hler potential (e.g., no-scale kinetic terms for certain superfields). Mixing of QGF{close_quote}s with neutrinos implies {ital R}-parity violation. It can proceed via the coupling of QGF{close_quote}s with Higgs supermultiplets or directly with a lepton doublet. A model which accounts for the solar and atmospheric anomalies and dark matter is presented. {copyright} {ital 1996 The American Physical Society.}