Target Neutrino Mass Precision for Determining the Neutrino Hierarchy

Recent works combining neutrino oscillation and cosmological data to determine the neutrino hierarchy found a range of odds in favor of the normal hierarchy. These results arise from differing approaches to incorporating prior knowledge about neutrinos. We develop a hierarchy-agnostic prior and show that the hierarchy cannot be conclusively determined with current data. The determination of the hierarchy is limited by the neutrino mass scale Sigma(nu) measurement. We obtain a target precision of sigma(Sigma(nu)) = 0.014 eV, necessary for conclusively establishing the normal hierarchy with future data.