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

摘要

The off-diagonal part of the active-neutrino mass matrix is constructed from two 3 × 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, M_μτ = 4√3M _eμ, 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 Δm₃₂²∕Δm₂₁² is equal to η² ? 1 = 26.9362 and gives m₁ = 0. With the experimental estimate Δm₂₁² ～ 8.0 × 10^?5eV², this maximal value, if realized, predicts Δm₃₂² ～ 2.2 × 10^?3eV², near to the popular experimental estimation Δm₃₂² ～ 2.4 × 10^?3eV².