Neutrino bimaximal mixing and unitary deformation of fermion universality

Abstract

An effective texture is presented for six Majorana neutrinos, three active and three (conventional) sterile, based on a 6x6 mass matrix whose 3x3 Dirac component (i.e., active--sterile component) is conjectured to get a hierarchical fermion universal form, similar to the previously constructed 3x3 mass matrices for charged leptons as well as for up and down quarks. However, for neutrinos this form becomes unitarily deformed by the action of bimaximal mixing, specific in their case. The 3x3 lefthanded and righthanded components (i.e., active-active and sterile-sterile components) of the 6x6 mass matrix are diagonal with degenerate entries of opposite sign. They dominate over the 3x3 Dirac component. In such a texture the neutrino masses are $ m_1 = -m_4 \simeq m_2 = -m_5 \simeq m_3 = -m_6 $ with the mass-squared differences $\Delta m^2_{21} \ll \Delta m^2_{32} \simeq \Delta m^2_{31}$ and $\Delta m^2_{41} = \Delta m^2_{52} = \Delta m^2_{63} = 0$. The last equality implies in our texture the absence of oscillations for three (conventional) sterile neutrinos. Thus, these neutrinos are here effectively decoupled, what is realized evidently in another way than through the popular seesaw mechanism. There remain the oscillations of three active neutrinos, getting the form as for bimaximal mixing, but with the mass spectrum following from our texture.