Neutrino Mass Matrix and Hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for ∆sol and ∆atm, and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, Mν and a mixing matrix, U , where both Mν and U are given in terms of powers of Λ, the analog of the Cabibbo angle λ in the Wolfenstein representation, and two parameters, ρ and κ, each of order one. The expansion parameter, Λ, is defined by Λ = m2/m3 = √ (∆sol/∆atm) ≈ 0.16, and ρ expresses our ignorance of the lightest neutrino mass m1, (m1 = ρΛ 4m3), while κ scales s13 to the experimental upper limit, s13 = κΛ 2 ≈ 0.16κ. These matrices are similar in structure to those for the quark and lepton families, but with Λ about 1.6 times larger than the λ for the quarks and charged leptons. The upper limit for the effective neutrino mass in double β-decay experiments is 4×10−3eV if s13 = 0 and 6×10−3eV if s13 is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.