Study of the day-night effect for the Super-Kamiokande detector. II. Electron spectrum deformations and day-night asymmetries

Using the results of a high precision calculation of the solar neutrino survival probability for Earth crossing neutrinos in the case of the MSW ${\nu }_e\to {\nu }_{\mu \left(\tau \right)}$ transition solution of the solar neutrino problem, performed in an earlier study, we derive predictions for the one-year-averaged day-night (D-N) asymmetry in the deformations of the $e^{-}$ spectrum to be measured with the Super-Kamiokande detector, and for the D-N asymmetry in the energy-integrated one-year signal in this detector. The asymmetries are calculated for the solar ${\nu }_e$ crossing the Earth mantle only, the core, and the (mantle+core) for a large representative set of values of the MSW transition parameters $\Delta m^2$ and ${\sin }^{2}2{\theta }_V$ from the “conservative” MSW solution region obtained by taking into account possible uncertainties in the values of the ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}$ neutrino fluxes. The effect of the uncertainties in the value of the bulk matter density and in the chemical composition of the core on the D-N asymmetry predictions is studied. It is shown, in particular, that for ${\sin }^{2}2{\theta }_V<~0.013$ the one-year average D-N asymmetry for neutrinos crossing the Earth core can be larger than the asymmetry for (only mantle $\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}+\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}$ crossing) neutrinos by a factor of up to six. Iso-(D-N) asymmetry contours in the $\Delta m^2-{\sin }^{2}2{\theta }_V$ plane for the Super-Kamiokande detector are derived in the region ${\sin }^{2}2{\theta }_V\gtrsim {10}^{-4}$ for only mantle crossing, core crossing, and (only mantle crossing+core crossing) neutrinos. The dependence of the D-N asymmetry in the three data samples on the recoil-$e^{-}$ energy threshold is also investigated. Our results indicate that the Super-Kamiokande experiment might be able to test the ${\sin }^{2}2{\theta }_V<~0.01$ region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.