Bayesian Analysis of a Future Beta Decay Experiment's Sensitivity to Neutrino Mass Scale and Ordering

Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiment's sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $\beta$-decay spectrum, we assess a high-precision $\beta$-decay experiment's sensitivity to the neutrino mass scale and ordering, for one assumed design scenario. We find that such an experiment could measure the electron-weighted neutrino mass within $\sim40\,$meV after 1 year (90$\%$ credibility). Neutrino masses $>500\,$meV could be measured within $\approx5\,$meV. Using only $\beta$-decay and external reactor neutrino data, we find that next-generation $\beta$-decay experiments could potentially constrain the mass ordering using a two-neutrino spectral model analysis. By calibrating mass ordering results, we identify reporting criteria that can be tuned to suppress false ordering claims. In some cases, a two-neutrino analysis can reveal that the mass ordering is inverted, an unobtainable result for the traditional one-neutrino analysis approach.