Earth regeneration of solar neutrinos at SNO and Super-Kamiokande

We analyze the 1258-day Super-Kamiokande day and night solar neutrino energy spectra with various ${\chi }^2$ definitions. The best-fit lies in the large mixing angle (LMA) region at $(\Delta m^2,{\tan }^2\theta )=(5.01\mathrm{}\times {10}^{-5}{\mathrm{eV}}^2,0.60),$ independently of whether systematic errors are included in the ${\chi }^2$ definition. We compare the exclusion and allowed regions from the different definitions and choose the most suitable definition to predict the regions from SNO at the end of three years of data accumulation. We first work under the assumption that Super-Kamiokande “sees” a flux-suppressed flat energy spectrum. Then, we consider the possibility of each one of the three Mikheyer-Smirnov-Wolfenstein regions being the solution to the solar neutrino problem. We find that the exclusion and allowed regions for the flat spectrum hypothesis and the LMA and low probability, low mass solutions are alike. In three years, we expect SNO to find very similar regions to that obtained by Super-Kamiokande. We evaluate whether the zenith angle distribution at SNO with optimum binning will add anything to the analysis of the day and night spectra; for comparison, we show the results of our analysis of the 1258-day zenith angle distribution from Super-Kamiokande, for which the best-fit parameters are $(\Delta m^2,{\tan }^2\theta )=(5.01\mathrm{}\times {10}^{-5}{\mathrm{eV}}^2,0.56).\mathrm{}$