Exact analysis of the combined data of SNO and Super-Kamiokande

Comparison of solar-neutrino signals in SNO and Super-Kamiokande (SK) detectors results in discovery of $\nu_e \to \nu_{\mu,\tau}$ oscillations at level $3.1 - 3.3 \sigma$ \cite{SNO}. This comparison involves the assumption of neutrino spectrum and a choice for the thresholds of detection in both experiments. In this Letter we obtain an exact formula for the comparison of the signals which is valid for arbitrary spectra and thresholds. We find that the no-oscillation hypothesis is excluded at 3.3$\sigma$. If the energy-dependent component of the survival probability for electron neutrinos is small as compared with the average value, i.e. in the case of small distortion of the observed spectrum, the oscillation hypothesis can also be tested to similar accuracy. The oscillation to sterile neutrino only, is excluded at $3.3 \sigma$ level, and oscillation to active neutrinos is confirmed at the same level, though with some reservations.