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 8x10(-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 2-3 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) approximate to 13 degrees.