Oscillations of the mixed pseudo--Dirac neutrinos

Abstract

Oscillations of three pseudo--Dirac flavor neutrinos $\nu_e, \nu_\mu, \nu_\tau$ are considered: $0 < m^{(L)} = m^{(R)} \ll m^{(D)}$ for their Majorana and Dirac masses taken as universal before family mixing. The actual neutrino mass matrix is assumed to be the tensor product $ M^{(\nu)} \otimes {(\begin{array}{cc} \lambda^{(L)} & 1 1 & \lambda^{(R)} \end{array})}$, where $M^{(\nu)}$ is a neutrino family mass matrix ($ M^{(\nu) \dagger} = M^{(\nu)}$) and $\lambda^{(L,R)} = m^{(L,R)}/m^{(D)}$. The $ M^{(\nu)}$ is tried in a form proposed previously for charged leptons $e, \mu, \tau$ for which it gives $m_\tau = 1776.80$ MeV versus $m^{exp}_\tau = 1777.05^{+0.29}_{-0.20}$ MeV (with the experimental values of $m_e$ and $m_\mu$ used as inputs). However, in contrast to the charged -lepton case, in the neutrino case its off-diagonal entries dominate over diagonal. Then, it is shown that three neutrino effects (the deficits of solar $\nu_e$'s and atmospheric $\nu_\mu$'s as well as the possible LSND excess of $\nu_e$'s in accelerator $\nu_\mu$ beam) can be explained by neutrino oscillations though, alternatively, the LSND effect may be eliminated (by a parameter choice). Atmospheric $\nu_\mu$'s oscillate dominantly into $\nu_\tau$'s, while solar $\nu_e$'s -- into (automatically existing) Majorana sterile counterparts of $\nu_e$'s.