Toward a Neutrino Mass Matrix

left-handed (two-component) neutrinos νe, νμ, and ντ with the left-handed fields se, sμ, and sτ that are the charge conjugates of the right-handed neutrino fields νre, νrμ, νrτ , i.e., se = −iσ2 ν∗ re = (ν† re2,−ν re1), etc. The six left-handed neutrino fields form a six-vector, N = (νe, νμ, ντ , se, sμ, sτ ). The only mass term available for two left-handed neutrino fields Ni and Nj isMij (Ni1Nj2−Ni2Nj1) + h.c. Because the fields Ni anticommute, the six-by-six complex mass matrix