A study about the F-estimator for the neutrino mass hierarchy in the JUNO experiment

TL;DR

This paper evaluates the F-estimator's effectiveness in determining neutrino mass hierarchy in JUNO, demonstrating its ability to distinguish between normal and inverted hierarchies by analyzing its dependence on atmospheric mass-squared differences.

Contribution

It extends previous work by analyzing the F-estimator's dependence on elta m^2_{atm} and shows its potential to reliably differentiate hierarchies in JUNO data.

Findings

F-estimator's minimum counts are well separated for true and wrong hierarchies.

The analysis confirms the estimator's robustness against elta m^2_{atm} degeneracy.

The method can achieve 5c measurements within six years of JUNO data collection.

Abstract

At present, it is still unknown whether the correct mass ordering of the neutrino mass eigenstates is either $m_1$, $m_2$, $m_3$ (Normal Hierarchy, NH), or $m_3$, $m_1$, $m_2$ (Inverted Hierarchy, IH). The new analysis method proposed by Stanco et al. (arXiv:1707.07651v3) should fix some issues of the currently most used estimator, $\Delta \chi^2$, and make it possible to reach $5\,\sigma$ measurements in less than six years of data taking with JUNO (Jiangmen Underground Neutrino Observatory) if a degeneracy in the atmospheric mass, $\Delta m^2_{atm}$, is accepted. In this note, the analysis introduced in the paper above was extended to more detailed studies on the dependence of the new F estimator to $\Delta m^2_{atm}$. A fit to the values of the new estimator as a function of $\Delta m^2_{atm}$, calculated for both the true hierarchy and the wrong hierarchy, was performed. The study of the fitting function showed that the average minimum counts, corresponding to the best value for $\Delta m^2_{atm}$, either for the true hierarchy or for the wrong hierarchy, are well separated, and allow to distinguish easily between NH and IH.