Study of the day-night effect for the Super-Kamiokande detector. III. The case of transitions into sterile neutrino

Abstract

Using the results of a high precision calculation of the solar neutrino survival probability for Earth crossing neutrinos in the case of the Mikheyev-Smirnov-Wolfenstein (MSW) ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ transition solution of the solar neutrino problem, we derive predictions for the one-year averaged day-night $(D\ensuremath{-}N)$ asymmetries in the deformed recoil-${e}^{\ensuremath{-}}$ spectrum and in the energy-integrated event rate due to the solar neutrinos, to be measured with the Super-Kamiokande detector. The asymmetries are calculated for three event samples, produced by the solar ${\ensuremath{\nu}}_{e}$ crossing the Earth mantle only, the core, and the mantle only + the core (the full night sample), for a large set of representative values of the MSW transition parameters $\ensuremath{\Delta}{m}^{2}$ and ${\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}$ from the ``conservative'' ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ solution regions, obtained by taking into account the possible uncertainties in the predictions for the ${}^{8}\mathrm{B}$ and ${}^{7}\mathrm{Be}$ neutrino fluxes. The effects of the uncertainties in the value of the bulk matter density and in the chemical composition of the Earth core on the predictions for the $D\ensuremath{-}N$ asymmetries are investigated. The dependence of the $D\ensuremath{-}N$ effect related observables on the threshold recoil-${e}^{\ensuremath{-}}$ kinetic energy, ${T}_{e,th},$ is studied. It is shown, in particular, that for ${\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}<~0.030,$ the one year average $D\ensuremath{-}N$ asymmetry in the sample of events due to the core-crossing neutrinos is larger than the asymmetry in the full night sample by a factor which, depending on the solution value of $\ensuremath{\Delta}{m}^{2},$ can be \ensuremath{\sim}(3--4) $(\ensuremath{\Delta}{m}^{2}<5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{eV}}^{2})$ or \ensuremath{\sim}(1.5--2.5) $(5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{eV}}^{2}\ensuremath{\lesssim}\ensuremath{\Delta}{m}^{2}\ensuremath{\lesssim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{eV}}^{2}).$ We find, however, that at small mixing angles ${\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}\ensuremath{\lesssim}0.014,$ the $D\ensuremath{-}N$ asymmetry in the case of solar ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ transitions is considerably smaller than if the transitions were into an active neutrino, ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}(\ensuremath{\tau})}.$ In particular, a precision better than 1% in the measurement of any of the three one year averaged $D\ensuremath{-}N$ asymmetries considered by us would be required to test the small mixing angle nonadiabatic ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ solution at ${\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}\ensuremath{\lesssim}0.01.$ For $0.0075\ensuremath{\lesssim}{\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}<~0.03,$ the magnitude of the $D\ensuremath{-}N$ asymmetry in the sample of events due to the core-crossing neutrinos is very sensitive to the value of the electron number fraction in the Earth's core, ${Y}_{e}(\mathrm{core}):$ a change of ${Y}_{e}(\mathrm{core})$ from the standard value of 0.467 to the conservative upper limit of 0.50 can lead to an increase of the indicated asymmetry by a factor of \ensuremath{\sim}(3--4). Iso-$(D\ensuremath{-}N)$ asymmetry contours in the $\ensuremath{\Delta}{m}^{2}\ensuremath{-}{\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}$ plane for the Super-Kamiokande detector are derived in the region ${\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{V}>~{10}^{\ensuremath{-}4}$ for the three event samples studied for ${T}_{e,th}=5\mathrm{MeV}$ and 7.5 MeV, and in the case of the samples due to the core crossing and (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---for ${Y}_{e}(\mathrm{core})=0.467$ and 0.50. The possibility to discriminate between the ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ and ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}(\ensuremath{\tau})}$ solutions of the solar neutrino problem by performing high precision $D\ensuremath{-}N$ asymmetry measurements is also discussed.