Decoupling of solar and atmospheric neutrino oscillations

The scheme of mixing of three neutrinos with a mass hierarchy is considered for the explanation of the solar and atmospheric neutrino problems through neutrino oscillations. It is shown that the recent results of the CHOOZ experiment imply that the element Ue3 of the neutrino mixing matrix is small, that the oscillations of solar neutrinos are described by the two-generation formalism and that the oscillations of solar and atmospheric neutrinos decouple. Furthermore, if |Ue3| ≪ 1 the oscillations of atmospheric neutrinos do not depend on matter effects and are described by the two-generation formalism. In this case, with an appropriate identification of the mixing parameters, the two-generation analyses of solar and atmospheric neutrino data provide direct information on the mixing parameters of three neutrinos. It is also shown that the smallness of |Ue3| will be checked by the long-baseline neutrino oscillation experiments under preparation. PACS numbers: 14.60.Pq, 26.65.+t, 95.85.Ry Typeset using REVTEX