Abstract
Working in the framework of three chiral neutrinos with Majorana masses, we investigate a scenario first realized in an explicit model by Zee: that the neutrino mass matrix is strictly off-diagonal in the flavor basis, with all its diagonal entries precisely zero. This CP-conserving ansatz leads to two relations among the three mixing angles ( θ 1, θ 2, θ 3) and two squared mass differences. We impose the constraint | m 3 2− m 2 2|≫| m 2 2− m 1 2| to conform with experiment, which requires the θ i to lie nearby one of four 1-parameter domains in θ-space. We exhibit the implications for solar and atmospheric neutrino oscillations in each of these cases. A unique version of the Zee ansatz survives confrontation with experimental data, one which necessarily involves maximal just-so vacuum oscillations of solar neutrinos.
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