Statistical Issues on the Neutrino Mass Hierarchy with Δχ2

Abstract

The neutrino mass hierarchy determination (ν MHD) is one of the main goals of the major current and future neutrino experiments. The statistical analysis usually proceeds from a standard method, a single-dimensional estimator 1D−Δχ2 that shows some drawbacks and concerns, together with a debatable strategy. The drawbacks and considerations of the standard method will be explained through the following three main issues. The first issue corresponds to the limited power of the standard method. The Δχ2 estimator provides us with different results when different simulation procedures were used. Regarding the second issue, when χminNH2 and χminIH2 are drawn in a 2D map, their strong positive correlation manifests χ2 as a bidimensional variable, instead of a single-dimensional estimator. The overlapping between the χ2 distributions of the two hypotheses leads to an experiment sensitivity reduction. The third issue corresponds to the robustness of the standard method. When the JUNO sensitivity is obtained using different procedures, either with Δχ2 as one-dimensional or χ2 as two-dimensional estimator, the experimental sensitivity varies with the different values of the atmospheric mass, the input parameter. We computed the oscillation of Δχ2¯ with the input parameter values, Δm2input. The MH significance using the standard method, Δχ2, strongly depends on the values of the parameter Δm2input. Consequently, the experiment sensitivity depends on the precision of the atmospheric mass. This evaluation of the standard method confirms the drawbacks.