Constructing the off-Diagonal Part of Active-Neutrino Mass Matrix From Annihilation and Creation Matrices in Neutrino-Generation Space

The off-diagonal part of the active-neutrino mass matrix is constructed from two 3 x 3 matrices playing the role of annihilation and creation matrices acting in the neutrino-generation space of ν1, ν2, ν3. The construction leads to a new relation, Mμτ = 4√3Meμ , which predicts in the case of tribimaximal neutrino mixing that m3 - m1 η(m2 - m1) with η = 5.28547. Then, the maximal possible value of Δm232/= Δm221 is equal to η2 - 1 = 26.9362 and gives m1 = 0. With the experimental estimate Δm221 ∼ 8.0 x 10-5 eV2, this maximal value, if realized, predicts Δm232 ∼ 2.2 x 10-3 eV2, near to the popular experimental estimation Δm232 ∼ 2.4 x 10-3 eV2. (author)