Neutrino Mass Matrix a la Mode

Abstract

With the accumulation of many years of solar and atmospheric neutrino oscillation data, the approximate form of the 3 times 3 neutrino mixing matrix is now known. What is not known is the (presumably Majorana) neutrino mass matrix M_{nu} itself. In this chapter, the approximate form of M_{nu} 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 U_{e3} not equal 0 with maximal CP violation is also discussed. A specific automatic realization of this M_{nu} from radiative corrections of an underlying non-Abelian discrete A_4 symmetry in the context of softly broken supersymmetry is presented.