Solar neutrino results and violation of the equivalence principle: An analysis of the existing data and predictions for SNO

Violation of the equivalence principle (VEP) can lead to neutrino oscillation through the nondiagonal coupling of neutrino flavor eigenstates with the gravitational field. The neutrino energy dependence of this oscillation probability is different from that of the usual mass-mixing neutrino oscillations. In this work we explore, in detail, the viability of the VEP hypothesis as a solution to the solar neutrino problem in a two generation scenario with both the active and sterile neutrino alternatives, choosing these states to be massless. To obtain the best-fit values of the oscillation parameters we perform a ${\chi }^2$ analysis for the total rates of solar neutrinos seen at the chlorine (Homestake), gallium (GALLEX and SAGE), Kamiokande, and SuperKamiokande (SK) experiments. We find that the goodness of these fits is never satisfactory. It markedly improves, especially for VEP transformation to sterile neutrinos, if the chlorine result is excluded from the analysis. The 1117-day SK data for recoil electron spectrum are also examined for signals of VEP oscillations. For these fits, we consider variations of the standard solar model by allowing the absolute normalizations of the ${}^8\mathrm{B}$ and hep neutrinos to vary. Here the fits are quite good but the best fit values of the parameters are rather different from those from the total rates fits. A combined fit to the total rates and recoil electron spectrum data is also performed. We present the 90% confidence limit contours for all the three analyses mentioned above. The best-fit parameters obtained from the recoil electron spectrum and the combined analysis of rate and spectrum are used to predict the charge current and scattering electron spectrum at SNO.