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 ${ \Delta m^2_{ 32}}/{ \Delta m^2_{ 21}}$ is equal to $\eta^2 -1 = 26.9362$ and gives $m_1 = 0$. With the experimental estimate ${ \Delta m^2_{ 21}}\sim 8.0\times 10^{ -5} { \rm eV}^2$, this maximal value, if realized, predicts $\Delta m^2_{ 32} \sim 2.2\times 10^{ -3} { \rm eV}^2$, near to the popular experimental estimation $\Delta m^2_{ 32} \sim 2.4\times 10^{ -3} { \rm eV}^2$.
Categories: hep-ph