Neutrino Mass Matrix a la Mode

With the accumulation of many years of solar and atmospheric neutrino oscillation data, the approximate form of the 3× 3 neutrino mixing matrix is now known. What is not known is the (presumably Majorana) neutrino mass matrix Mν itself. In this chapter, the approximate form of Mν is derived, leading to seven possible neutrino mass patterns: three have the normal hierarchy, two have the inverse hierarchy, and two have three nearly degenerate masses. The generalization of this to allow Ue3 6= 0 with maximal CP violation is also discussed. A specific automatic realization of this Mν from radiative corrections of an underlying non-Abelian discrete A4 symmetry in the context of softly broken supersymmetry is presented. —————— Contribution to a special issue of the Proceedings of the Indian National Science Academy With the recent addition of the SNO (Sudbury Neutrino Observatory) neutral-current data [1], the overall picture of solar neutrino oscillations [2] is becoming quite clear. Together with the well-established atmospheric neutrino data [3], the 3× 3 neutrino mixing matrix is now determined to a very good first approximation by