Extracting Mass Hierarchy Information from Simple Analysis of Neutrino Mass Splitting

Abstract: Based on the independent measurements on neutrino mass splitting $|\Delta m^2_{\mu\mu}|$, $|\Delta m^2_{ee}|$, $\Delta m^2_{21}$, and recent measurements by the T2K Collaboration, we carry out a simple fitting analysis on $\Delta m^2_{32}$ and $\Delta m^2_{31}$ in normal hierarchy and inverse hierarchy respectively, suggesting $\Delta m^2_{32}=(2.46\pm0.07)\times10^{-3}~\mbox{eV}^2$ and $\Delta m^2_{31}=(2.53\pm0.07)\times10^{-3}~\mbox{eV}^2$ in normal hierarchy, or $\Delta m^2_{32}$=$-(2.51\pm0.07)\times10^{-3}~\mbox{eV}^2$ and $\Delta m^2_{31}$=$-(2.44\pm0.07)\times10^{-3}~\mbox{eV}^2$ in invert hierarchy. The simple analysis indicate that both normal and inverted hierarchy are consistent with current experimental measurements on mass splitting. The p-value for normal hierarchy and that for inverted hierarchy are 62% and 55%, respectively. This reveals a slight favor for the normal hierarchy. It is suggested that further measurements on the mass splitting with higher accuracy are necessary to determine the neutrino mass hierarchy.