Reexamination of neutrino oscillation solutions to the solar-neutrino problem

Abstract

A deficit of solar neutrinos compared to the standard solar model prediction has been measured in both the Homestake and Kamiokande-II experiments, with quite different detectors. We analyze the parameter space for oscillations of two neutrinos to find regions that can explain both experiments. Long-wavelength vacuum oscillation solutions are found with $\delta m^2\simeq 0.5-2.5\times {10}^{-10\mathrm{}}$ e${\mathrm{V}}^2$ and ${sin}^{2}2\theta \gtrsim 0.7$. Matter-enhanced oscillation solutions are found for (i) nonadiabatic transitions having $\delta m^2{\theta }^2\approx {10}^{-8\mathrm{}}$ e${\mathrm{V}}^2$ and $\delta m^2\approx 3\times {10}^{-8\mathrm{}}-2\mathrm{}\times {10}^{-5\mathrm{}}$ e${\mathrm{V}}^2$, and (ii) adiabatic transitions having $\delta m^2\approx {10}^{-7\mathrm{}}-{10}^{-4\mathrm{}}$ e${\mathrm{V}}^2$ with ${sin}^{2}2\theta \gtrsim 0.5$. The two-neutrino long-wavelength and matter-enhanced solutions predict ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ measurements in the ranges 50-80 and 5-115 solar-neutrino units (SNU), respectively, compared to 130 SNU without oscillations. We emphasize the distinctive features of each solution, including their predictions for future $\nu -e$ scattering experiments and detectable seasonal variations in the long-wavelength solutions. We also find the range of three-neutrino vacuum oscillation solutions.