Low-energy-threshold analysis of the Phase I and Phase II data sets of the Sudbury Neutrino Observatory

Results are reported from a joint analysis of Phase I and Phase II data from the Sudbury Neutrino Observatory. The effective electron kinetic energy threshold used is ${T}_{\mathrm{eff}}=3.5$ MeV, the lowest analysis threshold yet achieved with water Cherenkov detector data. In units of ${10}^{6}$ cm${}^{\ensuremath{-}2}$ ${\mathrm{s}}^{\ensuremath{-}1}$, the total flux of active-flavor neutrinos from $^{8}\mathrm{B}$ decay in the Sun measured using the neutral current (NC) reaction of neutrinos on deuterons, with no constraint on the $^{8}\mathrm{B}$ neutrino energy spectrum, is found to be ${\ensuremath{\Phi}}_{\mathrm{NC}}=5.{140}_{\ensuremath{-}0.158}^{+0.160}{\text{(stat)}}_{\ensuremath{-}0.117}^{+0.132}\text{(syst)}.$ These uncertainties are more than a factor of 2 smaller than previously published results. Also presented are the spectra of recoil electrons from the charged current reaction of neutrinos on deuterons and the elastic scattering of electrons. A fit to the Sudbury Neutrino Observatory data in which the free parameters directly describe the total $^{8}\mathrm{B}$ neutrino flux and the energy-dependent ${\ensuremath{\nu}}_{e}$ survival probability provides a measure of the total $^{8}\mathrm{B}$ neutrino flux ${\ensuremath{\Phi}}_{{}^{8}\mathrm{B}}=5.{046}_{\ensuremath{-}0.152}^{+0.159}{\text{(stat)}}_{\ensuremath{-}0.123}^{+0.107}\text{(syst)}$. Combining these new results with results of all other solar experiments and the KamLAND reactor experiment yields best-fit values of the mixing parameters of ${\ensuremath{\theta}}_{12}=34.{06}_{\ensuremath{-}0.84}^{+1.16}$ degrees and $\ensuremath{\Delta}{m}_{21}^{2}=7.{59}_{\ensuremath{-}0.21}^{+0.20}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ eV${}^{2}$. The global value of ${\ensuremath{\Phi}}_{{}^{8}\mathrm{B}}$ is extracted to a precision of ${}_{\ensuremath{-}2.95}^{+2.38}%$. In a three-flavor analysis the best fit value of $\mathrm{sin}{}^{2}{\ensuremath{\theta}}_{13}$ is $2.{00}_{\ensuremath{-}1.63}^{+2.09}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. This implies an upper bound of $\mathrm{sin}{}^{2}{\ensuremath{\theta}}_{13}<0.057$ ($95%$ C.L.).