Tripartite neutrino mass matrix

The 3x3 Majorana neutrino mass matrix is written as a sum of 3 terms, i.e., Mν=MA+MB+MC, where MA is proportional to the identity matrix and MB,C are invariant under different Z3 transformations. This Mν is very suitable for understanding atmospheric and solar neutrino oscillations, with sin22θatm and tan2θsol fixed at 1 and 0.5 respectively, in excellent agreement with present data. It has in fact been proposed before, but only as an ansatz. This Letter uncovers its underlying symmetry, thus allowing a complete theory of leptons and quarks to be constructed