Lepton generation-weighting factors and neutrino mass formula

Abstract

A candidate for the simple empirical neutrino mass formula is found, predicting the mass proportion m_1:m_2:m_3 = 0:4:24 and so, the mass ratio Delta m^2_{32}/Delta m^2_{21} = 35 not inconsistent with its experimental estimate. It involves only one free parameter and three generation-weighting factors suggested by the successful mass formula found previously for charged leptons (the simplest neutrino mass formula would predict m_1:m_2:m_3 = 1:4:24 and thus, Delta m^2_{32}/Delta m^2_{21} \simeq 37). A more involved variation of this equation follows from a special seesaw neutrino model with specifically "conspiring" Dirac and Majorana neutrino mass matrices. In this variation m_1:m_2:m_3 \simeq \epsilon^{(\nu)}:4:24, where O(\epsilon^{(\nu)}) = 10^{-3}.