Day-night effect predictions for the SNO detector

Detailed predictions for the day-night (D-N) asymmetry in the energy-integrated one year signals in the Sudbury Neutrino Observatory (SNO) detector in the case of the Mikheyev-Smirnov-Wolfenstein (MSW) νₑ→ν_μ(τ) and/or νₑ→νₛ transition solutions of the solar neutrino problem are presented. The asymmetries in the charged current (CC) and ν-e^- elastic-scattering (ES) event rates are calculated for both MSW solutions; in the case of the νₑ→νₛ transition solution the D-N asymmetry in the neutral current (NC) event rate are derived as well. The asymmetries are calculated for three night samples of events which are produced by the solar neutrinos crossing (i) the Earth's mantle only (Mantle), (ii) the Earth's core (Core) and (iii) the Earth's core and/or the mantle (Night). The effects of the uncertainties (i) in the values of the cross sections of the CC and NC neutrino-induced reactions on deuterium, and (ii) in the value of the bulk matter density and/or the chemical composition of the Earth's core, on the corresponding D-N asymmetry predictions are analyzed. It is shown, in particular, that due to the strong enhancement of the transitions of the solar neutrinos crossing the Earth's core, at sin²2θV<~0.01, the corresponding one year average D-N asymmetry in the Core sample of CC events in the case of the νₑ→ν_μ(τ) solution can be larger by a factor of up to ~8 than the asymmetry in the Night sample. In certain subregions of the MSW solution regions at small sin²2θV, the predicted magnitude of the Core D-N asymmetry in the CC sample is very sensitive to the value of the electron fraction number in the Earth's core. Iso-(D-N) asymmetry contours in the Δm²-sin²2θV plane for the SNO detector are derived in the region sin²2θV10^-4 for the Core and Night samples of the CC, ES, and NC events. The dependence of the D-N asymmetries considered on the final-state e^- threshold energy in the CC and ES reactions is also investigated. Our results show, in particular, that the SNO experiment will be able to probe a substantial part of the small mixing angle and most of the large mixing angle MSW νₑ→ν_μ(τ) solution regions by performing Night and Core D-N asymmetry measurements.