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, Δχ^2, and make it possible to reach 5 σ measurements in less than six years of data taking with JUNO (Jiangmen Underground Neutrino Observatory) if a degeneracy in the atmospheric mass, Δ 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 Δ m^2_atm. A fit to the values of the new estimator as a function of Δ 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 Δ 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.