Neutrino masses, mixing and hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for Δ_sol and Δ_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, M_ν and a mixing matrix, U, where both M_ν 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

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, and ρ expresses our ignorance of the lightest neutrino mass m₁, (m₁=ρΛ⁴m₃), while κ scales s₁₃ to the experimental upper limit, s₁₃=κΛ²≈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^?3 eV if s₁₃=0 and 6×10^?3 eV 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.