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Published November 1, 2012 | Submitted
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Statistical Evaluation of Experimental Determinations of Neutrino Mass Hierarchy


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 Δm^2_(32). These intervals are deduced from the parent distribution of the estimation of Δm^2_(32) based on experimental data. Due to existing experimental constraints on |Δm^2_(32)|, the estimation of Δm^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 |Δm^2_(32)|.

Additional Information

Submitted on 12 Oct 2012 (v1); last revised 21 Oct 2012 (this version, v2). We would like to thank Petr Vogel, Haiyan Gao, Jianguo Liu, Alan Gelfand, and Laurence Littenberg for fruitful discussions and careful reading. This work was supported in part by Caltech, the National Science Foundation, and the Department of Energy under contracts DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, operates the Thomas Jefferson National Accelerator Facility, and DE-AC02-98CH10886.

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