Three-Neutrino Mixing and Combined Vacuum Oscillations and MSW Transitions of Solar Neutrinos

Assuming three flavour neutrino mixing takes place in vacuum, we investigate the possibility that the solar νe take part in MSW transitions in the Sun due to ∆m31 ∼ (10 −7 − 10−4) eV 2, followed by long wave length vacuum oscillations on the way to the Earth, triggered by ∆m21 (or ∆m 2 32) ∼ (10−12 − 10−10) eV 2, ∆m31 and ∆m 2 21 (∆m 2 32) being the corresponding neutrino mass squared differences. The solar νe survival probability is shown to be described in this case by a simple analytic expression. Depending on whether the vacuum oscillations are due to ∆m21 or ∆m 2 32 there are two very different types of interplay between the MSW transitions and the vacuum oscillations of the solar νe. Performing an analysis of the most recently published solar neutrino data we have found several qualitatively new solutions of the solar neutrino problem of the hybrid MSW transitions + vacuum oscillations type. The solutions differ in the way the pp, 7Be and 8B neutrino fluxes are affected by the transitions in the Sun and the oscillations in vacuum. The specific features of the new solutions are discussed. ∗Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, BG–1784 Sofia, Bulgaria.