How well do we (and will we) know solar neutrino fluxes and oscillation parameters?

Individual neutrino fluxes are not well determined by the four operating solar neutrino experiments. Assuming neutrino oscillations occur, the pp electron neutrino flux is uncertain by a factor of 2, the $^{8}\mathrm{B}$ flux by a factor of 5, and the $^{7}\mathrm{Be}$ flux by a factor of 45. For matter-enhanced oscillation (MSW) solutions, the range of allowed differences of squared neutrino masses, \ensuremath{\Delta}${\mathit{m}}^{2}$, varies between 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{eV}}^{2}$ and 1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{eV}}^{2}$, while 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\le}${\mathrm{sin}}^{2}$2\ensuremath{\theta}\ensuremath{\le}1.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ or 0.5\ensuremath{\le}${\mathrm{sin}}^{2}$2\ensuremath{\theta}\ensuremath{\le}0.9. For vacuum oscillations, \ensuremath{\Delta}${\mathit{m}}^{2}$ varies between 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ ${\mathrm{eV}}^{2}$ and 1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{eV}}^{2}$, while 0.7\ensuremath{\le}${\mathrm{sin}}^{2}$2\ensuremath{\theta}\ensuremath{\le}1.0. The inferred ranges of neutrino parameters depend only weakly on which standard solar model is used. Calculations of the expected results of future solar neutrino experiments (SuperKamiokande, SNO, BOREXINO, ICARUS, HELLAZ, and HERON) are used to illustrate the extent to which these experiments will restrict the range of the allowed neutrino mixing parameters. For example, the double ratio (observed ratio divided by standard model ratio) of neutral current to charged current event rates to be measured in the SNO experiment varies, at 95% confidence limit, over the range 1.0 (no oscillations into active neutrinos), 3.${1}_{\mathrm{\ensuremath{-}}1.3}^{+1.8}$ (small mixing angle MSW), 4.${4}_{\mathrm{\ensuremath{-}}1.4}^{+2.0}$ (large mixing angle MSW), and 5.${2}_{\mathrm{\ensuremath{-}}2.9}^{+5.6}$ (vacuum oscillations). We present an improved formulation of the ``luminosity constraint'' and show that at 95% confidence limit, this constraint establishes the best available limits on the rate of creation of pp neutrinos in the solar interior and provides the best upper limit to the $^{7}\mathrm{Be}$ neutrino flux. The actual rate of creation of solar neutrinos in the solar interior to the rate predicted by the standard solar model can vary (while holding the CNO neutrino flux constant) between 0.55 and 1.08 for pp neutrinos and between 0.0 and 6.35 for $^{7}\mathrm{Be}$ neutrinos. \textcopyright{} 1996 The American Physical Society.