Treating solar model uncertainties: A consistent statistical analysis of solar neutrino models and data

We describe how to consistently incorporate solar model uncertainties, along with experimental errors and correlations, when analyzing solar neutrino data to derive confidence limits on parameter space for proposed solutions of the solar neutrino problem. Our work resolves ambiguities and inconsistencies in the previous literature. As an application of our methods we calculate the masses and mixing angles allowed by the current data for the proposed MSW solution using both Bayesian and frequentist methods, allowing purely for solar model flux variations, to compare with previous work. We also show that solutions which simply suppress the ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ solar neutrino flux are strongly disfavored and have a likelihood ratio of at most ${10}^{\mathrm{-}8}$ compared to the best MSW solution. Finally, we consider the effects of including metal diffusion in the solar models and also discuss implications for future experiments.