Statistical significances and projections for proton decay experiments

TL;DR

This paper analyzes statistical methods for proton decay experiments, advocates for Bayesian approaches, and provides current limits and future projections for proton lifetime detection at major neutrino detectors.

Contribution

It highlights flaws in traditional significance measures and applies Bayesian methods to set limits and project future sensitivities in proton decay searches.

Findings

Bayesian measures are more conservative and reliable.

Current lower limits on proton lifetime are established from Super-Kamiokande data.

Future experiments could significantly improve detection sensitivity.

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 multi-channel counting experiments are discussed in a general context and illustrated with examples. We argue in favor of conservative Bayesian-motivated statistical 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\% CL published limits. Finally, we present projections for exclusion and discovery reaches for proton partial lifetimes in $p \rightarrow \overline \nu K^+$ and $p \rightarrow e^+ \pi^0$ decay channels at Hyper-Kamiokande, DUNE, JUNO, and THEIA.