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

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, $\mathrm{\Delta }{\chi }^2$, 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, $\mathrm{\Delta }{m}_{atm}^2$, 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 $\mathrm{\Delta }{m}_{atm}^2$. A fit to the values of the new estimator as a function of $\mathrm{\Delta }{m}_{atm}^2$, 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.