Matter-enhanced Three-flavor Oscillations and the Solar Neutrino Problem

Abstract

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, $δm^2$ and $m^2$, are well separated: $δm^2 \ll m^2$. At zeroth order in $δm^2/m^2$, the relevant variables for solar neutrinos are $δm^2$ and two mixing angles, $ω$ and $ϕ$. We introduce new graphical representations of the parameter space $(δm^2,\,ω,\,ϕ)$, 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 $(δm^2,\,ω,\,ϕ)$. 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.