Constructing the off-diagonal part of active-neutrino mass matrix from annihilation and creation matrices in neutrino-generation space

Abstract

The off-diagonal part of the active-neutrino mass matrix is constructed from two $3\times 3$ matrices playing the role of annihilation and creation matrices acting in the neutrino-generation space of ${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$. The construction leads to a new relation, $M_{\mu \tau }=4\sqrt{3}{M}_{e\mu }$, which predicts in the case of tribimaximal neutrino mixing that $m_3-m_1=\eta (m_2-m_1)$ with $\eta =5.28547$. Then, the maximal possible value of $\Delta m_{32}^2/\Delta m_{21}^2$ is equal to ${\eta }^2-1=26.9362$ and gives $m_1=0$. With the experimental estimate $\Delta m_{21}^2\sim 8.0\times 10^{-5}{\mathrm{eV}}^2$, this maximal value, if realized, predicts $\Delta m_{32}^2\sim 2.2\times 10^{-3}{\mathrm{eV}}^2$, near to the popular experimental estimation $\Delta m_{32}^2\sim 2.4\times 10^{-3}{\mathrm{eV}}^2$.

Comments: 9 pages