Do Two Flavour Oscillations Explain both KamLAND Data and the Solar Neutrino Spectrum?

Abstract

The recent measurement of Delta_{sol} by the KamLAND experiment with very small errors, makes definitive predictions for the energy dependence of the solar neutrino survival probability P_{ee}. We fix Delta_{sol} to be the KamLAND best fit value of 8*10^{-5} eV^2 and study the energy dependence of P_{ee} for solar neutrinos in the framework of two flavour oscillations and also of three flavour oscillations. For the case of two flavour oscillations, P_{ee} has a measurable slope in the 5-8 MeV range but the solar spectrum measurements in this range find P_{ee} to be flat. The predicted values of P_{ee}, even for the best fit value of theta_{sol}, differ by 2 to 3 sigma from the Super-K measured values in each of the three energy bins of the 5-8 MeV range. If future measurements of solar neutrinos by Super-K and SNO find a flat spectrum with reduced error bars (by a factor of 2), it will imply that two flavour oscillations can no longer explain both KamLAND data and the solar spectrum. However a flat solar neutrino spectrum and the Delta_{sol} measured by KamLAND can be reconciled in a three flavour oscillation framework with a moderate value of theta_{13} approx 13 degrees.