MSWνe→νstransition solution of the solar neutrino problem

We study the stability of the two-neutrino MSW solution of the solar neutrino problem, corresponding to solar ${\nu }_e$ transitions into a sterile neutrino, ${\nu }_e\to {\nu }_s$, with respect to changes of the total fluxes of ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrinos, ${\Phi }_{\mathrm{B}}$ and ${\Phi }_{\mathrm{Be}}$. For any value of ${\Phi }_{\mathrm{Be}}$ from the interval $0.7{\Phi }_{\mathrm{Be}}^{\mathrm{BP}}<~{\Phi }_{\mathrm{Be}}<~1.3{\Phi }_{\mathrm{Be}}^{\mathrm{BP}}$ the ${\nu }_e\to {\nu }_s$ MSW transitions provide at 95% C.L. a description of the existing solar neutrino data for $0.40{\Phi }_{\mathrm{B}}^{\mathrm{BP}}\lesssim {\Phi }_{\mathrm{B}}\lesssim 36{\Phi }_{\mathrm{B}}^{\mathrm{BP}}$ ${\Phi }_{\mathrm{B}}^{\mathrm{BP}}$ and ${\Phi }_{\mathrm{Be}}^{\mathrm{BP}}$ being the fluxes in the solar model of Bahcall and Pinsonneault [Rev. Mod. Phys. 69, 85 (1992)]. The corresponding allowed regions of values of the parameters $\Delta m^2$ and ${sin}^{2}2\theta$, characterizing the solar neutrino transitions, are derived. The physical implications of the found MSW ${\nu }_e\to {\nu }_s$ solutions for the future solar neutrino experiments are considered as well.