Statistical significances and projections for proton decay experiments

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 -nu over bar K+ and p -e+ pi 0 decay channels at Hyper-Kamiokande, DUNE, JUNO, and THEIA.

Automated summary

In this study, we examine the statistical significances for the exclusion and discovery of proton decay at current and future neutrino detectors. We discuss various counterintuitive flaws associated with frequentist and modified frequentist statistical measures of significance in the context of multichannel counting experiments, and provide examples to illustrate these flaws. We argue in favor of conservative Bayesian-motivated statistical measures, and use them to obtain current lower limits on proton partial lifetime at different confidence levels based on Super-Kamiokande's data, extending the 90% C.L. published limits. Finally, we present projections for exclusion and discovery reaches for proton partial lifetimes in the p -nu over bar K+ and p -e+ pi 0 decay channels at Hyper-Kamiokande, DUNE, JUNO, and THEIA.