Approximate Symmetries in the Two-Neutrino Theory

Abstract

It is shown that if there are two neutrinos, the Lagrangian of the electromagnetic interactions and the leptonic weak interactions which preserve strangeness are invariant under three-dimensional rotations in an internal "leptonic spin" space. These rotations transform ${\ensuremath{\nu}}_{1}$ into ${\ensuremath{\nu}}_{2}$ and $e$ into $\ensuremath{\mu}$. Only the $\ensuremath{\mu}\ensuremath{-}e$ mass difference does not satisfy this invariance. Some consequences of the symmetry for lepton scattering experiments are discussed. Extensions of the symmetry to other leptonic interactions are considered. In the "conventional" two-neutrino theory, all weak interactions obey the symmetry, and the baryons and mesons are scalars under the rotations. Alternative possibilities in which the baryons form multiplets in leptonic spin space are also presented and their relation to the suggestion of "neutrino flip" interactions is discussed.