Getting the most from the statistical analysis of solar neutrino oscillations

(Abridged.) 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, we analyze 81 observables, including the Cl rate, the total Ga rate and its winter-summer difference, the 44 spectrum bins from SK and the 34 spectrum bins from SNO. We carefully evaluate and propagate the effects of 31 correlated systematic uncertainties, including 12 SSM input errors, the 8B neutrino energy spectrum uncertainty, as well as 11 and 7 systematics in SK and SNO, respectively. Concerning the output, we express the chi-squared analysis results in terms of ``pulls,'' embedding the single contributions to the total chi-squared. 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 results confirm the current best-fit solution (LMA), but also allow, with acceptable statistical significance, other solutions in the low-mass (LOW) or in the quasi-vacuum oscillation (QVO) regime, while the small mixing angle (SMA) solution could be recovered only by ad hoc ``recalibrations'' of several SSM and experimental systematics.