Three-flavor oscillation solutions for the solar neutrino problem

The good agreement of standard solar models with helioseismology and the combined analysis of the solar neutrino experiments suggest that the solution of the solar neutrino problem is located in particle physics rather than in astrophysics. The most promising solution is neutrino oscillations, which usually are analyzed within the reduced two-flavor scheme, because the solutions found therein reasonably well reproduce the recent data of Super-Kamiokande about the recoil-electron energy spectrum, zenith-angle and seasonal variations, and the event rate data of all the neutrino detectors. In this work, however, a survey of the complete parameter space of three-flavor oscillations is performed. Basically 8 three-flavor solutions could be identified, where the best one with $\Delta m_{12}^2=2.7\mathrm{}\times {10}^{-10}\hspace{0.5em}{\mathrm{eV}}^2,$ $\Delta m_{13}^2=1.0\mathrm{}\times {10}^{-5}\hspace{0.5em}{\mathrm{eV}}^2,$ ${\Theta }_{12}=23\mathrm{}°,$ and ${\Theta }_{13}=1.3\mathrm{}°$ (denoted SVO) is slightly more probable than any two-flavor solution. However, as the greatest value for $\Delta m_{23}^2$ of these three-flavor solutions is about $2.5\times {10}^{-4}\hspace{0.5em}{\mathrm{eV}}^2,$ none of these solutions is consistent with the results of the atmospheric neutrino problem where $\Delta m_{23}^2\gtrsim {10}^{-3}\hspace{0.5em}{\mathrm{eV}}^2.$ The relatively weak improvement of the fit using three-flavor instead of two-flavor oscillations, which appears to be due to an inconsistency of the different kinds of data, indicates that there are possibly still systematic errors in at least one data set or that the statistics is not yet sufficient. In addition, the abilities of SNO and Borexino to discriminate the various two- and three-flavor solutions are investigated. Only with very good statistics in these experiments can the correct solution to the solar neutrino problem be identified unambiguously.