Study of the day-night effect for the Super-Kamiokande detector. I. Time-averaged solar neutrino survival probability

This is the first of two articles aimed at providing comprehensive predictions for the day-night (D-N) effect for the Super-Kamiokande detector in the case of the Mikheyev-Smirnov-Wolfenstein (MSW) νₑ→ν_μ(τ) transition solution of the solar neutrino problem. The one-year-averaged probability of survival of the solar νₑ crossing the Earth's mantle, the core, the inner 2/3 of the core, and the (core+mantle) is calculated with high precision (better than 1%) using the elliptical orbit approximation to describe the Earth's motion around the Sun. Results for the survival probability in the indicated cases are obtained for a large set of values of the MSW transition parameters Δm² and sin²2θV from the ``conservative'' regions of the MSW solution, derived by taking into account possible relatively large uncertainties in the values of the ⁸B and ⁷Be neutrino fluxes. Our results show that the one-year-averaged D-N asymmetry in the νₑ survival probability for neutrinos crossing the Earth's core can be, in the case of sin²2θV<~0.013, larger than the asymmetry in the probability for (only mantle crossing+core crossing) neutrinos by a factor of up to 6. The enhancement is larger in the case of neutrinos crossing the inner 2/3 of the core. This indicates that the Super-Kamiokande experiment might be able to test the sin²2θV<~0.01 region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.