Neutrino masses, mixing and hierarchy

Abstract

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for Δsol and Δatm, 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 Λ2=m2/m3=Δsol/Δatm≈0.16, 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.