Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes

Abstract

Triangular mass matrices for neutrinos and their charged partners contain full information on neutrino mixing in a most concise form. Although the scheme is general and model independent, triangular matrices are typical for reducible but indecomposable representations of graded Lie algebras which, in turn, are characteristic for the standard model in noncommutative geometry. The mixing matrix responsible for neutrino oscillations is worked out analytically for two and three lepton families. The example of two families fixes the mixing angle to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance oscillation of solar neutrinos. In the case of three families we classify all physically plausible choices for the neutrino mass matrix and derive interesting bounds on some of the moduli of the mixing matrix.