Matter-enhanced three-flavor oscillations and the solar neutrino problem

We present a systematic analysis of the three-flavor Mikheyev-Smirnov-Wolfenstein (MSW) oscillation solutions to the solar neutrino problem, in the hypothesis that the two independent neutrino square mass differences, $\delta m^2$ and $m^2$, are well separated: $\delta m^2\ll m^2$. At zeroth order in $\frac{\delta m^2}{m^2}$, the relevant variables for solar neutrinos are $\delta m^2$ and two mixing angles $\omega$ and $\phi$. We introduce new graphical representations of the parameter space ($\delta m^2$, $\omega$, $\phi$) that prove useful both to analyze the properties of the electron-neutrino survival probability and to present the results of the analysis of solar neutrino data. We make a detailed comparison between the theoretical predictions of the Bahcall-Pinsonneault standard solar model and the current experimental results on solar neutrino rates, and discuss thoroughly the MSW solutions found by spanning the whole three-flavor space ($\delta m^2$, $\omega$, $\phi$). The allowed regions can be radically different from the usual "small mixing" and "large mixing" solutions, characteristic of the usual two-generation MSW approach. We also discuss the link between these results and the independent information on neutrino masses and mixings coming from accelerator and reactor oscillation searches.