Correlations of solar neutrino observables for SNO

Neutrino oscillation scenarios predict correlations, and zones of avoidance, among measurable quantities such as spectral energy distortions, total fluxes, time dependences, and flavor content. The comparison of observed and predicted correlations will enhance the diagnostic power of solar neutrino experiments. A general test of all presently allowed $\left(2\mathrm{}\nu \right)$ oscillation solutions is that future measurements must yield values outside the predicted zones of avoidance. To illustrate the discriminatory power of the simultaneous analysis of multiple observables, we map currently allowed regions of $\Delta m^2-{\sin }^{2}2\theta$ onto planes of quantities measurable with the Sudbury Neutrino Observatory (SNO). We calculate the correlations that are predicted by vacuum and MSW (active and sterile) neutrino oscillation solutions that are globally consistent with all available neutrino data. We derive approximate analytic expressions for the dependence of individual observables and specific correlations upon neutrino oscillations parameters. We also discuss the prospects for identifying the correct oscillation solution using multiple SNO observables.