Neutrino Mass Matrix and Hierarchy

Abstract

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 k, each of order one. The expansion parameter, Λ, is defined by Λ^2 = m_2/m_3 = √(Δ_sol/Δ_atm) ≈ 0.16, and ρ expresses our ignorance of the lightest neutrino mass m_l, (m_1 = ρ(Λ^4)m_3), while k scales s_13 to the experimental upper limit, s_13 = k(Λ^2)≈ 0.16k. 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 s_13 = 0 and 6 × 10^(–3)eV if s_13 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.