Getting the most from the statistical analysis of solar neutrino oscillations

We present a thorough analysis of the current solar neutrino data, in the context of two-flavor active neutrino oscillations. We aim at performing an accurate and exhaustive statistical treatment of both the input and the output information. Concerning the input information, we analyze 81 observables, including the total event rate from the chlorine experiment, the total gallium event rate and its winter-summer difference, the 44 bins of the Super-Kamiokande (SK) energy-nadir electron spectrum, and the 34 day-night energy spectrum bins from the Sudbury Neutrino Observatory (SNO) experiment. We carefully evaluate and propagate the effects of 31 sources of correlated systematic uncertainties, including 12 standard solar model (SSM) input errors, the ${}^{8}\mathrm{B}$ neutrino energy spectrum uncertainty, as well as 11 and 7 systematics in SK and SNO, respectively. Concerning the output information, we express the ${\ensuremath{\chi}}^{2}$ analysis results in terms of ``pulls,'' embedding the single contributions to the total ${\ensuremath{\chi}}^{2}$ coming from both the observables and the systematics. It is shown that the pull method, as compared to the (numerically equivalent) covariance matrix approach, is not only simpler and more advantageous, but also includes useful indications about the preferred variations of the neutrino fluxes with respect to their SSM predictions. Our final results confirm the current best-fit solution at large mixing angle (LMA), but also allow, with acceptable statistical significance, other solutions in the low-mass (LOW) or in the quasivacuum oscillation (QVO) regime. Concerning the LMA solution, our analysis provides conservative bounds on the oscillation parameters, and shows that the contribution of correlated systematics to the total ${\ensuremath{\chi}}^{2}$ is rather modest. In addition, within the LMA solution, the allowed variations from SSM neutrino fluxes are presented in detail. Concerning the LOW and QVO solutions, the analysis of the pull distributions clearly shows that they are still statistically acceptable, while the small mixing angle (SMA) solution could be recovered only by ad hoc ``recalibrations'' of several SSM and experimental systematics. A series of Appendixes elucidate various topics related to the ${\ensuremath{\chi}}^{2}$ statistics, the winter-summer difference in GALLEX-GNO, the treatment of the SK and SNO spectra, and a quasi-model-independent comparison of the SK and SNO total rates.