Target Neutrino Mass Precision for Determining the Neutrino Hierarchy

Abstract

Recent works combining neutrino oscillation and cosmological data to determine the neutrino hierarchy found a range of odds in favour 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.

Comments: v3: Version accepted in Phys Rev D. Minor clarifications and added robustness tests, conclusions unchanged