Abstract
We take as a starting point the Gelmini -- Roncadelli model enlarged by a term with explicit lepton number violation in the Higgs potential and add a neutrino singlet field coupled via a scalar doublet to the usual leptons. This scenario allows us to take into account all three present indications in favour of neutrino oscillations provided by the solar, atmospheric and LSND neutrino oscillation experiments. Furthermore, it suggests a model which reproduces naturally one of the two 4-neutrino mass spectra favoured by the data. In this model the solar neutrino problem is solved by large mixing MSW ν_e\toν_τtransitions and the atmospheric neutrino problem by transitions of ν_μinto a sterile neutrino.
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