Statistical Evaluation of Experimental Determinations of Neutrino Mass Hierarchy

TL;DR

This paper discusses statistical methods for reporting and evaluating the ability of experiments to determine the neutrino mass hierarchy, emphasizing Bayesian approaches and proper confidence interval construction.

Contribution

It introduces a Bayesian framework for interpreting experimental data on neutrino mass hierarchy and highlights the need for Feldman-Cousins intervals due to parameter constraints.

Findings

Bayesian approach effectively quantifies evidence for hypotheses.

Feldman-Cousins method is necessary for confidence intervals under constraints.

Metrics for future experiment sensitivity are developed.

Abstract

Statistical methods of presenting experimental results in constraining the neutrino mass hierarchy (MH) are discussed. Two problems are considered and are related to each other: how to report the findings for observed experimental data, and how to evaluate the ability of a future experiment to determine the neutrino mass hierarchy, namely, sensitivity of the experiment. For the first problem where experimental data have already been observed, the classical statistical analysis involves constructing confidence intervals for the parameter {\Delta}m^2_{32}. These intervals are deduced from the parent distribution of the estimation of {\Delta}m^2_{32} based on experimental data. Due to existing experimental constraints on |{\Delta}m^2_{32}|, the estimation of {\Delta}m^2_{32} is better approximated by a Bernoulli distribution (a Binomial distribution with 1 trial) rather than a Gaussian distribution. Therefore, the Feldman-Cousins approach needs to be used instead of the Gaussian approximation in constructing confidence intervals. Furthermore, as a result of the definition of confidence intervals, even if it is correctly constructed, its confidence level does not directly reflect how much one hypothesis of the MH is supported by the data rather than the other hypothesis. We thus describe a Bayesian approach that quantifies the evidence provided by the observed experimental data through the (posterior) probability that either one hypothesis of MH is true. This Bayesian presentation of observed experimental results is then used to develop several metrics to assess the sensitivity of future experiments. Illustrations are made using a simple example with a confined parameter space, which approximates the MH determination problem with experimental constraints on the |{\Delta}m^2_{32}|.