Statistical Issues on the Neutrino Mass Hierarchy with $\Delta {\chi }^2$

Abstract

The Neutrino Mass Hierarchy Determination ($\nu$ 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 $(1D-\Delta {\chi }^2)$ that shows some draw-backs and concerns, together with a debatable strategy. The draw-backs and considerations of the standard method will be explianed through the following three main issues. First issue is the limited power of the standard method. The $\Delta {\chi }^2$ estimator provides us with different results when different simulation procedures were used. Second issue, when ${\chi }_{min(NH)}^2$ and ${\chi }_{min(IH)}^2$ are drawn in a $2D$ map, their strong positive correlation manifests ${\chi }^2$ as a bi-dimensional instead of single dimensional estimator. The overlapping between the ${\chi }^2$ distributions of the two hypotheses leads to the experiment sensitivity reduction. Third issue is the robustness of the standard method. When the JUNO sensitivity is obtained using different procedures, $\Delta {\chi }^2$ as one dimensional and ${\chi }^2$ as two dimensional estimator, the experimental sensitivity varies with the different values of the atmospheric mass, the input parameter. We computed the oscillation of $|\overline{\Delta {\chi }^2}|$ with the input parameter values, $|\Delta m^2{|}_{input}$. The MH significance using the standard method, $\Delta {\chi }^2$, strongly depends on the values of the parameter $|\Delta m^2{|}_{input}$. Consequently, the experiment sensitivity depends on the precision of the atmospheric mass. This evaluation of the standard method confirms the draw-backs.

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