Matter-enhanced neutrino oscillations in the standard solar model

The effects of matter-enhanced neutrino oscillations on solar-neutrino experiments can be calculated accurately only if uncertainties in the standard solar model are treated properly. As the oscillation probability depends on the neutrino energy, while modifications in the parameters of the standard solar model produce correlated changes in the various solar-neutrino sources, Monte Carlo calculations appear to offer the only means for addressing this problem. We consider the effects of matter-enhanced neutrino oscillations for 1000 standard solar models that were constructed by varying the solar input parameters according to their estimated probability distributions. From these Monte Carlo calculations [carried out for a neutrino parameter grid of ${10}^4$ cases corresponding to 3×${10}^8$ separate Mikheyev-Smirnov-Wolfenstein (MSW) calculations] we derive 95%-C.L. limits on the neutrino mass difference $\delta m^2$ and mixing angle ${sin}^{2}2\theta$ for possible outcomes for the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, and Kamioka II experiments and the assumption of two-flavor oscillations. We find that ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ counting rates as large as 128 solar-neutrino units (SNU) or as small as 4 SNU are not ruled out by present 95%-C.L. results from the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ and Kamioka II experiments, given possible solar and nuclear cross-section uncertainties. Considering all three of the experiments, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ (existing results), Kamioka II (existing results), and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ (hypothesized results), we find the allowed neutrino parameters form two distinct "islands" in the $\delta m^2-{sin}^{2}2\theta$ plane for ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ results between 20 and 100 SNU, even with our restrictive assumption of oscillations between only two flavors. Thus additional experiments may be required to distinguish between solutions that are each consistent with the results from the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, and Kamioka II experiments. We explore the implications of future Kamioka II results of improved accuracy. To permit analyses of new experiments that focus on individual fluxes, we also present separate predictions of the MSW effect for ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+$p$ (hep) neutrinos.