Extracting Mass Hierarchy Information from Simple Analysis of Neutrino Mass Splitting

Abstract

Based on the independent measurements on neutrino mass splitting $|\Delta m_{\mu \mu }^2|$, $|\Delta m_{ee}^2|$, $\Delta m_{21}^2$, and recent measurements by the T2K Collaboration, we carry out a simple fitting analysis on $\Delta m_{32}^2$ and $\Delta m_{31}^2$ in normal hierarchy and inverse hierarchy respectively, suggesting $Δm^2_{32}=(2.46\pm0.07)\times10^{-3}~\mbox{eV}^2$ and $Δm^2_{31}=(2.53\pm0.07)\times10^{-3}~\mbox{eV}^2$ in normal hierarchy, or $\Delta m_{32}^2$=$-(2.51\pm0.07)\times10^{-3}~\mbox{eV}^2$ and $\Delta m_{31}^2$=$-(2.44\pm0.07)\times10^{-3}~\mbox{eV}^2$ 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.

5 latex pages, 5 figures. Final version as published

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