What fraction of boron-8 solar neutrinos arrive at the Earth as aν2mass eigenstate?

Abstract

We calculate the fraction of $^{8}\mathrm{B}$ solar neutrinos that arrive at the Earth as a ${\ensuremath{\nu}}_{2}$ mass eigenstate as a function of the neutrino energy. Weighting this fraction with the $^{8}\mathrm{B}$ neutrino energy spectrum and the energy dependence of the cross section for the charged current interaction on deuteron with a threshold on the kinetic energy of the recoil electrons of 5.5 MeV, we find the integrated weighted fraction of ${\ensuremath{\nu}}_{2}$'s to be $(91\ifmmode\pm\else\textpm\fi{}2)%$ at the 95% CL. This energy weighting procedure corresponds to the charged current response of the Sudbury Neutrino Observatory (SNO). We have used SNO's current best fit values for the solar mass squared difference and the mixing angle, obtained by combining the data from all solar neutrino experiments and the reactor data from KamLAND. The uncertainty on the ${\ensuremath{\nu}}_{2}$ fraction comes primarily from the uncertainty on the solar $\ensuremath{\delta}{m}^{2}$ rather than from the uncertainty on the solar mixing angle or the standard solar model. Similar results for the Super-Kamiokande experiment are also given. We extend this analysis to three neutrinos and discuss how to extract the modulus of the Maki-Nakagawa-Sakata mixing matrix element ${\mathrm{U}}_{e2}$ as well as place a lower bound on the electron number density in the production region for $^{8}\mathrm{B}$ solar neutrinos.