Unitarity Constraints on Neutrino Mass and Mixings

Recent observations of atmospheric neutrinos and especially their zenithangle dependence , strongly suggest that muon neutrinos maximally mix with the tau neutrinos. Motivated by this observation and recent theoretical work on neutrino mass models , we explored 3 the implications of imposing the constraint that two neutrino flavors (which for definiteness we take to be νμ and ντ ) are similarly coupled to the mass basis in addition to the unitarity constraints. Although the invisible width of the Z particle constraints the number of active neutrino flavors to be three, it is nevertheless worthwhile to consider the possibility of the existence of sterile neutrino states for a number of reasons: i) The possibility of oscillation of atmospheric muon neutrinos into sterile states is not completely ruled out. ii) If the LSND results 4 are confirmed, since the analysis of LSND, atmospheric 1 and solar 5 neutrinos point out to different mass scales, one needs to introduce sterile neutrinos. iii) Serious problems such as the abundance of alpha particles that arise when core-collapse supernovae with neutrino-driven wind are considered as sites of r-process nucleosynthesis can be avoided by the oscillations of active neutrinos into sterile ones . Even though cosmological and astrophysical bounds rule out heavier sterile states , the effect of the lighter sterile neutrinos on big-bang nucleosynthesis is controversial . Hence we consider three active flavors and an arbitrary number (which could be taken to be zero) of sterile neutrinos. The N × N neutrino mixing