Weak-interaction-induced neutrino oscillations

Neutrino oscillation is a natural theoretical possibility in gauge theories if we do not a priori exclude the right-hand components of neutrino fields. The quantitative aspects of the oscillation phenomenon (oscillation length, etc.) are controlled by the neutrino mass matrix. We explore the possibility that neutrinos are massless in the lowest order of weak interactions and higher-order radiative corrections bring about small, but calculable, masses. We have made a systematic search of models which would have such a feature. We find that in one class of models, the neutrino-mass matrix elements would generally be less than ${10}^{\ensuremath{-}2}$ eV. But such theories would contain flavor-changing neutral currents involving charged lepton fields. Another class of models, which can easily be compatible with all known weak-interaction phenomenology, would necessarily involve large gauge groups (e.g., direct products of at least three non-Abelian factors) and a large number of unknown parameters (making it impossible to meaningfully estimate the neutrino masses).