# Target Neutrino Mass Precision for Determining the Neutrino Hierarchy

## TL;DR

This paper investigates the potential to determine the neutrino mass hierarchy using current and future data, emphasizing the importance of precise measurements of the neutrino mass scale and developing a hierarchy-agnostic prior.

## Contribution

It introduces a hierarchy-agnostic prior and identifies the required measurement precision of the neutrino mass scale to conclusively determine the hierarchy.

## Key findings

- Current data cannot conclusively determine the hierarchy.
- A target precision of 0.014 eV in neutrino mass sum is needed.
- Prior choice significantly affects hierarchy determination.

## 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.