Option of three pseudo--Dirac neutrinos

Abstract

As an alternative for popular see-saw mechanism, the option of three pseudo% -Dirac neutrinos is discussed, where ${1/2}(m^{(L)} + m^{(R)}) \ll m^{(D)}$ for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product $ M^{(\nu)} \otimes {(\{array} {cc} \lambda^{(L)} & 1 1 & \lambda^{(R)} \{array})}$, where $ M^{(\nu)}$ is a neutrino family mass matrix ($ M^{(\nu) \dagger} = M^{(\nu)}$) and $\lambda^{(L,R)} \equiv m^{(L,R)}/m^{(D)}$ with $ m^{(L)}$, $ m^{(R)}$ and $ m^{(D)} $ being taken as universal for three neutrino families. It is shown that three neutrino effects (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 nicely described by the corresponding neutrino oscillations, though the LSND effect may, alternatively, be eliminated (by a parameter choice). Atmospheric $\nu_\mu $'s oscillate dominantly into $\nu_\tau $'s, while solar $\nu_e $'s - into (existing here automatically) Majorana sterile counterparts of $\nu_e $'s. A phenomenological texture for neutrinos, compatible with the proposed description, is briefly presented.