ar X iv : h ep - p h / 99 03 49 9 v 1 2 6 M ar 1 99 9 NEARLY DEGENERATE NEUTRINO MASSES AND NEARLY DECOUPLED NEUTRINO OSCILLATIONS

We introduce a simple flavor symmetry breaking scheme, in which charged lepton masses have a strong hierarchy and neutrino masses are almost degenerate. It is possible to obtain a natural suppression of lepton flavor mixing between the 1st and 3rd families as well as the approximate decoupling of atmospheric and solar neutrino oscillations with nearly bi-maximal mixing factors. The similarity and difference between lepton and quark flavor mixing schemes are briefly discussed. In the standard model neutrinos are assumed to be the massless Weyl particles. But most extentions of the standard model (such as the grand unified theories of quarks and leptons) allow the existence of massive neutrinos, although the masses of three active neutrinos ν e , ν µ and ν τ could be much smaller than those of their charged counterparts. Whether the smallness of the masses of three neutrinos are attributed to the neutrality of their electric charges or to the Majorana feature of their fields, remains an open question. The recent observation of the atmospheric and solar neutrino anomalies, particularly that in the Super-Kamiokande experiment, has provided strong evidence that neutrinos are massive and lepton flavors are mixed 1. Analyses of the atmospheric neutrino deficit in the framework of two-flavor neutrino oscillations yield the following mass-squared difference and mixing factor: ∆m 2 atm ∼ 10 −3 eV 2 , sin 2 2θ atm > 0.8. (1) In addition, the hypothesis that solar ν e neutrinos change to another active species through long-wavelength vacuum oscillations with the parameters ∆m 2 sun ∼ 10 −10 eV 2 , sin 2 2θ sun ≈ 1 , (2) can provide a consistent explanantion of all existing solar neutrino data 2. In the framework of three-flavor neutrino oscillations, the significant hierarchy between ∆m 2 atm and ∆m 2 sun together with the no observation of ¯ ν e → ¯ ν e oscillation in the CHOOZ experiment implies that the ν 3-component in ν e is rather small (even negligible) and the atmospheric and solar neutrino oscillations approximately decouple 3. If this picture is true, then the solar and atmospheric a Talk given by one of us (H.