Can the Zee ansatz for neutrino masses be correct?

TL;DR

This paper examines the Zee ansatz for neutrino masses, analyzing its compatibility with experimental data and its implications for neutrino oscillations, highlighting a unique viable scenario involving maximal solar neutrino oscillations.

Contribution

It provides a detailed analysis of the Zee ansatz's viability, identifying a specific version consistent with experimental constraints and describing its implications for neutrino oscillation phenomena.

Findings

A unique Zee ansatz scenario aligns with experimental data.

The viable scenario involves maximal vacuum oscillations of solar neutrinos.

The analysis constrains neutrino mixing angles and mass differences.

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.