Oscillations of the mixed pseudo--Dirac neutrinos

Abstract

Oscillations of three pseudo--Dirac flavor neutrinos $ν_e, ν_μ, ν_τ$ 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^{(ν)} \otimes {(\begin{array}{cc} λ^{(L)} & 1 1 & λ^{(R)} \end{array})}$, where $M^{(ν)}$ is a neutrino family mass matrix ($ M^{(ν) \dagger} = M^{(ν)}$) and $λ^{(L,R)} = m^{(L,R)}/m^{(D)}$. The $ M^{(ν)}$ is tried in a form proposed previously for charged leptons $e, μ, τ$ for which it gives $m_τ= 1776.80$ MeV versus $m^{exp}_τ= 1777.05^{+0.29}_{-0.20}$ MeV (with the experimental values of $m_e$ and $m_μ$ 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 $ν_e$'s and atmospheric $ν_μ$'s as well as the possible LSND excess of $ν_e$'s in accelerator $ν_μ$ beam) can be explained by neutrino oscillations though, alternatively, the LSND effect may be eliminated (by a parameter choice). Atmospheric $ν_μ$'s oscillate dominantly into $ν_τ$'s, while solar $ν_e$'s -- into (automatically existing) Majorana sterile counterparts of $ν_e$'s.