Lepton mass hierarchy and neutrino mixing

Abstract

We speculate that the mass spectrum of three neutrinos might have a normal hierarchy as that of three charged leptons or that of three up-type (or down-type) quarks. In this spirit, we propose a novel parametrization of the 3×3 lepton flavor mixing matrix. Its mixing angles θl and θν can be related to the mass ratios me/mμ and m1/m2 in a specific texture of lepton mass matrices with vanishing (1,1) elements: tanθl=me/mμ and tanθν=m1/m2 . The latter relation, together with solar and atmospheric neutrino oscillation data, predicts 0.0030 eV≲m1≲0.0073 eV, 0.009 eV≲m2≲0.012 eV and 0.042 eV≲m3≲0.058 eV. The smallest neutrino mixing angle is found to be θ13≈θl/2≈3°, which is experimentally accessible in the near future.