Statistical significances and projections for proton decay experiments

Abstract

We study the statistical significances for exclusion and discovery of proton decay at current and future neutrino detectors. Various counterintuitive flaws associated with frequentist and modified frequentist statistical measures of significance for multichannel counting experiments are discussed in a general context and illustrated with examples. We argue in favor of conservative Bayesian-motivated statistical \ae{}measures, and as an application we employ these measures to obtain the current lower limits on proton partial lifetime at various confidence levels, based on Super-Kamiokande's data, generalizing the 90% C.L. published limits. Finally, we present projections for exclusion and discovery reaches for proton partial lifetimes in $p\ensuremath{\rightarrow}\overline{\ensuremath{\nu}}{K}^{+}$ and $p\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\pi}}^{0}$ decay channels at Hyper-Kamiokande, DUNE, JUNO, and THEIA.