Maximally-Mixed Three Generations of Neutrinos and the Solar and Atmospheric Neutrino Problems

Abstract

Motivated by the indication that both the Solar and the atmospheric neutrino puzzles may simultaneously be solved by (vacuum as well as matter-induced resonant) oscillations of two generations of neutrinos with large mixing, we have analyzed the data on the Solar and atmospheric neutrinos assuming that all {\it three} neutrinos are maximally mixed. It is shown that the results of two-generation analyses are still valid even in the three-generation scheme, {\it i.e.}, the two puzzles can be solved simultaneously if $\Delta m_{21}^2 = m_2^2-m_1^2\simeq 10^{-10}\mbox{eV}^2$ and $\Delta m_{31}^2 = 10^{-3}\sim 10^{-1}\mbox{eV}^2$. We have also demonstrated explicitly that with the use of the see-saw mechanism it is possible to have large or maximal mixings for neutrinos even though their masses are highly non-degenerate.