Confidence in a neutrino mass hierarchy determination

Emilio Ciuffoli,Jarah Evslin,Xinmin Zhang

doi:10.1007/jhep01(2014)095

Emilio Ciuffoli, Jarah Evslin + Show 1 more

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https://doi.org/10.1007/jhep01(2014)095

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Abstract

Abstract In the next decade, a number of experiments will attempt to determine the neutrino mass hierarchy. Feasibility studies for such experiments generally determine the statistic $ \overline{{\varDelta {\chi^2}}} $ . As the hierarchy is a discrete choice, Δχ2 does not obey a one degree of freedom χ2 distribution and so the number of σ’s of sensitivity to the hierarchy is not the square root of $ \overline{{\varDelta {\chi^2}}} $ . We present a simple Bayesian formula for the sensitivity to the hierarchy determination that can be expected from the median experiment as a function of $ \overline{{\varDelta {\chi^2}}} $ .

Highlights

In the two decades a number of reactor, accelerator and atmospheric neutrino experiments will attempt to determine the neutrino mass hierarchy, which is the sign of the mass difference ∆M321 = M32 − M12 where Mi is the ith eigenvalue of the neutrino mass matrix
We present a simple Bayesian formula for the sensitivity to the hierarchy determination that can be expected from the median experiment as a function of ∆χ2
The critical question is given ∆χ2, what is the sensitivity of a typical experiment to the hierarchy? In ref. [1] the authors showed that the most naive answer, the p value that would be obtained if ∆χ2 satisfied a one degree of freedom χ2 distribution, gives the incorrect answer

Summary

Introduction

We present a simple Bayesian formula for the sensitivity to the hierarchy determination that can be expected from the median experiment as a function of ∆χ2. Where χ2N (χ2I ) is the χ2 statistic equal to a weighted sum of the squares of the differences between the data and predictions given the normal (inverted) hierarchy, choosing all of the nuisance parameters so as to minimize χ2N (χ2I ). We will define the best fit hierarchy to be that which yields the lowest value of χ2, and so the hierarchy determined by the experiment corresponds to the sign of ∆χ2.

Results

Conclusion