Sensitivity to the Neutrino Mass Hierarchy

TL;DR

This paper introduces a simple formula to estimate the sensitivity of neutrino mass hierarchy experiments, accounting for the discrete nature of the hierarchy and the non-standard distribution of the test statistic.

Contribution

It provides a novel, straightforward method to evaluate the expected confidence level of hierarchy determination based on median experiment results.

Findings

Derived a formula linking Delta chi^2 to confidence levels

Clarified the non-Gaussian distribution of the test statistic

Facilitated more accurate sensitivity estimates for future experiments

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 expected value of Delta chi^2. As the hierarchy is a discrete choice, Delta chi^2 does not obey a one degree of freedom chi^2 distribution and so the number of sigmas of confidence of the hierarchy determination is not the square root of the expected Delta chi^2. We present a simple formula for the sensitivity to the hierarchy that can be expected from the median experiment as a function of the expected Delta chi^2.