Can the Zee ansatz for neutrino masses be correct?

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 $({\theta }_1,{\theta }_2,{\theta }_3)$ and two squared mass differences. We impose the constraint $|m_3^2-m_2^2|\gg |m_2^2-m_1^2|$ to conform with experiment, which requires the ${\theta }_i$ to lie nearby one of four 1-parameter domains in $\theta$-space. We exhibit the implications for solar and atmospheric neutrino oscillations in each of these cases. A unique version of the Zee {\it ansatz} survives confrontation with experimental data, one which necessarily involves maximal just-so vacuum oscillations of solar neutrinos.

Comments: 7 pages, harvmac, typo corrected, ref. added, text modified