ITP South Building 6420

The preference of the normal neutrino mass hierarchy from the recent cosmological constraints and the global fits of neutrino oscillation experiments does not seem like a wise choice at first glance since it obscures the neutrinoless double beta decay and hence the Majorana nature of neutrinos. Contrary to this naive expectation, we point out that the actual situation is the opposite. Choosing the normal mass hierarchy opens up the possibility of determining the solar octant and simultaneously measuring the two Majorana CP phases. If the neutrino mass hierarchy is normal, the funnel region would completely disappear if the solar mixing angle lives in the higher octant. With a typical O(meV) sensitivity on the effective mass |mee|, the neutrinoless double beta decay experiment can tell if the funnel region really exists and hence if the solar octant takes the higher octant. With the sensitivity further improved to sub-meV, the two Majorana CP phases can be simultaneously determined. We need the normal neutrino mass hierarchy with very good reasons.