Three-flavor MSW solutions of the solar neutrino problem

We perform an updated phenomenological analysis of the Mikheyev-Smirnov-Wolfenstein (MSW) solutions of the solar neutrino problem, assuming oscillations between two and three neutrino families. The analysis includes the total rates of the Homestake, SAGE, GALLEX, Kamiokande and Super-Kamiokande experiments, as well as the day-night asymmetry and the 18-bin energy spectrum of Super-Kamiokande. Solutions are found at several values of the ${\theta }_{13}$ mixing angle. Among the most interesting features, we find that solar neutrino data alone put the constraint ${\theta }_{13}\lesssim 55°–59°$ at 95% C.L., and that a fraction of the MSW solutions extends at and beyond maximal $({\nu }_1,{\nu }_2)$ mixing $({\theta }_{12}>~\pi /4),$ especially if the neutrino square mass splitting is in its lower range ${(m}_2^2-m_1^2\sim {10}^{-7}\hspace{0.5em}{\mathrm{eV}}^2)$ and if ${\theta }_{13}$ is nonzero. In particular, bimaximal (or nearly bimaximal) mixing is possible for atmospheric and MSW solar neutrino oscillations within the stringent reactor bounds on ${\theta }_{13}.$