Statistical evaluation of experimental determinations of neutrino mass hierarchy

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, the 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 Δm322. These intervals are deduced from the parent distribution of the estimation of Δm322 based on experimental data. Because of existing experimental constraints on |Δm322|, the estimation of Δm322 is better approximated by a Bernoulli distribution (a binomial distribution with one 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 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 by using a simple example with a confined parameter space, which approximates the MH determination problem with experimental constraints on the |Δm322|. © 2012 American Physical Society.