Three-neutrino mixing and combined vacuum oscillations and MSW transitions of solar neutrinos

Assuming three-flavor neutrino mixing takes place in vacuum, we investigate the possibility that the solar {nu}{sub e} take part in MSW transitions in the Sun due to {Delta}m{sub 31}{sup 2}{approximately}(10{sup {minus}7}{minus}10{sup {minus}4}) eV{sup 2}, followed by long wavelength vacuum oscillations on the way to the Earth, triggered by {Delta}m{sub 21}{sup 2} (or {Delta}m{sub 32}{sup 2}) {approximately}(10{sup {minus}12}{minus}10{sup {minus}10}) eV{sup 2}, {Delta}m{sub 31}{sup 2} and {Delta}m{sub 21}{sup 2} ({Delta}m{sub 32}{sup 2}) being the corresponding neutrino mass squared differences. The solar {nu}{sub e} survival probability is shown to be described in this case by a simple analytic expression. Depending on whether the vacuum oscillations are due to {Delta}m{sub 21}{sup 2} or {Delta}m{sub 32}{sup 2} there are two very different types of interplay between the MSW transitions and the vacuum oscillations of the solar {nu}{sub e}. 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, {sup 7}Be and {sup 8}B neutrino fluxes are affected by the transitions in the Sun and the oscillations in vacuum. The specific features of the new solutionsmore » are discussed. One of the distinctive predictions of the hybrid MSW + vacuum oscillation solutions found is the existence of strong and very characteristic distortions of the spectrum of {sup 8}B neutrinos. {copyright} {ital 1997} {ital The American Physical Society}« less